Transport characterisation of group III-nitride materials with dominating surface effects

Transcription

1 Transport characterisation of group III-nitride materials with dominating surface effects Tamara Brooke Fehlberg BE (Hons), BSc This thesis is presented for the degree of Doctor of Philosophy of The University of Western Australia School of Electrical, Electronic and Computer Engineering The University of Western Australia 2009

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3 Declaration of Published Work Appearing in this Thesis This thesis contains published work and/or work prepared for publication, which has been co-authored. The bibliographic information of the published works, where they appear in the thesis and the details of contribution of the multiple authors to each publication are set out following this declaration, pages iii iv. Signature: Tamara B. Fehlberg (Candidate) Signature: Professor Brett D. Nener (Supervisor) Signature: Associate Professor Giacinta Parish (Supervisor) i

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5 Published Work and Statement of Candidate Contribution 1. Characterisation of Multiple Carrier Transport in Indium Nitride Grown by Molecular Beam Epitaxy Tamara B. Fehlberg, Gilberto A. Umana-Membreno, Brett D. Nener, Giacinta Parish, Chad S. Gallinat, Gregor Koblmüller, Siddharth Rajan, Sarah Bernardis and James S. Speck Japanese Journal of Applied Physics Part 2 Volume 45 (Nos ), L1090-L1092, Oct The content of this paper is covered in section 5.2. The contributions to this work by the multiple authors is: Tamara B. Fehlberg Gilberto A. Umana-Membreno Brett D. Nener Giacinta Parish Chad S. Gallinat, Gregor Koblmüller, Siddharth Rajan, Sarah Bernardis and James S. Speck All, except technical discussions Supervisor Supervisor InN material provided by UCSB. 2. Characterisation of Multiple Carrier Transport in Indium Nitride Grown by Molecular Beam Epitaxy Tamara B. Fehlberg, Gilberto A. Umana-Membreno, Brett D. Nener, Giacinta Parish, Chad S. Gallinat, Gregor Koblmüller, Sarah Bernardis and James S. Speck physica status solidi (c) Volume 4, Number 7, Pages , 2007 The content of this paper is covered in section 5.2. The contributions to this work by the multiple authors is: Tamara B. Fehlberg Gilberto A. Umana-Membreno Brett D. Nener Giacinta Parish Chad S. Gallinat, Gregor Koblmüller, Sarah Bernardis and James S. Speck All, except technical discussions Supervisor Supervisor InN material provided by UCSB. iii

6 iv 3. Effect of MBE Growth Conditions on Multiple Electron Transport in Indium Nitride Tamara B. Fehlberg, Chad S. Gallinat, Gilberto A. Umana-Membreno, Gregor Koblmüller, Brett D. Nener, James S. Speck and Giacinta Parish Journal of Electronic Materials Volume 37, Number 5, Pages , May 2008 (Special Issue: III-Nitrides, SiC and ZnO) The content of this paper is covered in section 5.3. The contributions to this work by the multiple authors is: Tamara B. Fehlberg Gilberto A. Umana-Membreno Brett D. Nener Giacinta Parish Chad S. Gallinat, Gregor Koblmüller, and James S. Speck All, except technical discussions Supervisor device processing, Supervisor InN material provided by UCSB. 4. Multiple Carrier Transport in N-face Indium Nitride Tamara B. Fehlberg, Gregor Koblmüller, Gilberto A. Umana-Membreno, Chad S. Gallinat, Brett D. Nener, James S. Speck and Giacinta Parish physica status solidi (b) Volume 245, Issue 5, Pages , May 2008 The content of this paper is covered in section 5.4. The contributions to this work by the multiple authors is: Tamara B. Fehlberg Gilberto A. Umana-Membreno Brett D. Nener Giacinta Parish Gregor Koblmüller, Chad S. Gallinat and James S. Speck All, except technical discussions Supervisor Supervisor InN material provided by UCSB. 5. Characterisation of Electron Transport in MBE Grown Indium Nitride Tamara B. Fehlberg, Gilberto A. Umana-Membreno, Brett D. Nener, Giacinta Parish, Chad S. Gallinat, Gregor Koblmüller, Sarah Bernardis and James S. Speck Proceedings of the Conference on Optical and Microelectronic Materials and Devices 2006 (COMMAD06), Perth, Western Australia, Pages 11-14, 2007 The content of this paper is covered in section The contributions to this work by the multiple authors is: Tamara B. Fehlberg Gilberto A. Umana-Membreno Brett D. Nener Giacinta Parish Chad S. Gallinat, Gregor Koblmüller, Sarah Bernardis and James S. Speck All, except technical discussions Supervisor some device processing, Supervisor InN material provided by UCSB.

7 Abstract Group III-nitride (InN, GaN, AlN) electronics have many important and wide ranging applications, such as high power and high frequency transistors for satellite and mobile communications, solid-state lighting and high efficiency solar power. Performance increases and extension of the device operation regions will be obtained for many III-nitride devices through the incorporation of InN or In-rich InGaN/InAlN to improve transistor speed and move towards longer wavelengths in optical devices, while for high power GaNbased transistor devices, optimising existing passivation materials in transistor designs will enable further performance increases. InN is the least mature of the III-nitride materials. Transport modelling suggests roomtemperature electron mobilities of cm 2 /Vs are possible in low carrier concentration material, however even the highest electron mobilities measured in InN to date are less than a third of that value. The progression towards device quality films requires improvements in growth and understanding of the doping mechanisms, and this requires the accurate characterisation of the transport properties of the carriers in the material. In this work it is shown that for InN, Hall measurements performed over a range of magnetic fields, with a quantitative mobility spectrum analysis (QMSA), are required to distinguish between the multiple conduction paths that exist in all samples due to the presence of multiple carrier species, which include a native electron surface accumulation and a persistent, high, unintentional background (bulk) n-type doping. This technique greatly improves the accuracy of the characterisation of the bulk electron species, as this work shows that the surface electron species has a significant effect on the results obtained through the standard, single magnetic field, Hall characterisation technique. The high unintentional n-type doping is one of the major hurdles in the progression towards commercial InN-based devices. Furthermore, the electrical behaviour of the surface accumulation, and the dependence of such behaviour on surface conditions, is not well understood. In this work, the surface electron transport properties have been measured extensively, over a range of InN samples for a wide range of temperatures. v

8 vi Abstract The Hall bar geometry and magnetic fields up to 12 T were applied, in this work, for the first time in the multiple magnetic field Hall technique transport characterisation of MBE-grown InN, in order to improve the measurement resolution and extraction accuracy of the low mobility surface carrier properties. De-convolution of surface and bulk electronic properties were performed for a range of InN materials, providing correlation between temperature-dependent transport data and other growth parameter metrics and various surface conditions, such as crystal orientation (In- and N-face polarity), surface roughness and distance of the surface from the growth interface (thickness). The capability to confidently extract multiple electron species transport properties has enabled the electron mobility of the bulk species in one sample to be identified as the highest ever reported for MBE-grown InN, with a mobility of 3570 cm 2 /Vs at 300 K. This work also examined, for the first time, the influence of the MBE growth parameters on the transport properties of the distinct bulk and surface electron species in In-face InN, revealing the surface species to be a non-constant and significant influence on the overall transport characteristics. The bulk characteristics, considered independently from the surface electron accumulation, suggest high growth temperature is the most important factor for improving the mobility of the bulk electron species, seconded by an In-rich flux ratio in the growth chamber. More N-rich growth conditions resulted in a broadening of the peaks in the mobility spectrum. The surface electron concentration and mobility varied significantly between growth conditions, with the concentration of the surface electron accumulation correlating strongly with the degree of surface roughness. The N-face polarity of InN was also examined in this work, and for the first time N-face InN was shown via QMSA to also exhibit bulk and surface electron species. N-face InN is capable of withstanding higher temperatures than In-face InN, potentially making it more compatible with GaN and AlN alloys for heterostructure devices. The bulk electron characteristics are comparable to that of In-face InN, yet the surface electron species in N-face InN was revealed to have a much higher mobility than in In-face InN, at over twice the value, with only a slight corresponding reduction in sheet concentration. The surface electron transport properties of N-face InN also showed a much stronger thickness dependence than for In-face InN. In AlGaN/GaN high electron mobility transistors, passivation is used to control the detrimental effects of electrically active surface states and thereby improve device performance, but often only macroscopic device parameters, such as drain current, are measured when qualifying the performance gain. Studying the changes induced in the transport proper-

9 vii ties of the 2DEG will allow a better understanding of the role of the passivant in altering device performance. An investigation of the influence of passivation with silicon nitride on the 2DEG transport in Al x Ga 1 x N/GaN heterostructures, for different stress states in the SiN x passivant and extended over varying Al mole fractions (x), is presented. The stress in the SiN x passivation layer was varied between tensile and compressive ( ± 100 MPa). The passivation of the AlGaN surface resulted in an increase in electron concentration as well as an elimination of photo-induced effects on the 2DEG concentration. The changes in the 2DEG transport properties after passivation were observed to be different for each of the SiN x passivation layers, however the stress in the passivant, within the range studied, was not always the principal factor in the differences. The 2DEG mobility increased after passivation for the sample with the lowest x mole ratio, though the percentage change in the mobility exhibited a strong negative trend with increased AlGaN composition. It was determined that the change in the transport characteristics after passivation, from the unpassivated values, is dependent on the Al mole fraction, and that the optimal passivant stress is also dependent on the Al mole fraction.

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11 Contents Abstract Contents Acknowledgements Symbols, Constants and Abbreviations v ix xv xvii 1 Introduction III-Nitride Semiconductor Materials and Device Applications Indium Nitride AlGaN/GaN High Electron Mobility Transistors Thesis Objectives Thesis Arrangement III-Nitrides Introduction Physical and Chemical Nature Crystal Phases and Orientations Summary Experimental Methods and Analysis Techniques Magnetotransport Measurement of Carrier Transport Properties Experimental Apparatus and Setup Hall Effect Sample Structures Using the van der Pauw Structure Using the Hall Bar Structure Data Processing Multiple Carrier Fitting Quantitative Mobility Spectrum Analysis Techniques QMSA Technique Variants ix

12 x Contents Interpretation of QMSA Technique Outputs Extraction of Transport Properties from Mobility Spectra Single Field Hall Measurement with Multiple Carriers Silicon Nitride for Surface Passivation Introduction Deposition of Silicon Nitride by Plasma Enhanced Chemical Vapour Deposition (PECVD) SiN x Thin Film Material Properties Thin Film Stress Silicon Nitride Film Stress Thin Film Stress Measurement Indium Nitride Introduction Significant Properties of InN Growth of Indium Nitride Early Methods Powders RF-Sputtered Films and Early Epitaxial Methods Single Crystal Growth Growth by MBE Substrate and Buffer Layers MBE Growth Temperatures and Flux Regimes Electrical Properties Band Gap Evolution, Measurement and the Burstein-Moss Effect Surface and Interface Electrons Microscopic Origin of Surface Electrons Measurement of Surface Electrons Evidence of Accumulation at Non-polar and Cubic InN Surfaces Quantization of Electron Accumulation Reduction of Surface Accumulation Electron Accumulation at the Growth Interface Bulk Electrons Unintentional n-type Doping Intentional n-type Doping

13 Contents xi p-type Doping Carrier Transport Properties Theoretical Calculations of Transport Temperature Dependence and Electron Scattering Multiple Carrier Transport Variable Magnetic Field Hall Measurement Alternate Multiple Carrier Techniques Chapter Summary Indium Nitride Characterisation Results Introduction Demonstration of Multiple Carriers in In-face InN Growth Details Magnetotransport Measurement Details Van der Pauw Configuration Hall Bar Configuration Experimental Results and Analysis QMSA Mobility Spectra Extracted Carrier Transport Results Comparison of Variable- and Single-Field Results Further Investigations Repeat Growth of In-face InN Investigation of Process Contamination or Damage Effect of MBE Growth Parameters on Multiple Electron Transport in Inface InN Growth Details Sample Processing Details Measurement Details Surface Morphology Magnetotransport Measurement Details Experimental Results and Analysis Mobility Spectra Extracted Carrier Transport Results Comparison of Variable- and Single-Field Results Multiple Electron Transport in N-Face InN Growth Details

14 xii Contents Sample Processing Details Magnetotransport Measurement Details Experimental Results and Analysis Mobility Spectra Extracted Carrier Transport Results: Bulk Electron Species Extracted Carrier Transport Results: Surface Electron Species Multiple Electron Species in Indium Nitride Comparison of InN Samples Surface and Interface Accumulations InN Experimental Work Summary Aluminum Gallium Nitride/Gallium Nitride High Electron Mobility Transistors Introduction Surface States DEG Carrier Concentration DEG Mobility Current Collapse Surface Passivation Deposition and Plasma Effects on the Surface Effect of Surface Passivation on Carrier Concentration Effect of Surface Passivation on Mobility Effect of Surface Passivation on Other Device Parameters Passivation-Stress-Related Research Surface Passivation with Silicon Nitride AlGaN/GaN HEMT Transport Characterisation Results Introduction Fabrication of Passivated AlGaN/GaN Heterostructure Hall Bar Devices AlGaN/GaN Heterostructure Details Deposition Conditions for SiN x Passivation Layers Measurement Details Thin Film Stress Measurement and Results Magnetotransport Measurement Magnetotransport Results and Analysis Unpassivated AlGaN/GaN Heterostructures Silicon Nitride Passivated AlGaN/GaN Heterostructures

15 Contents xiii Changes in Conductivity After Passivation Changes in the Electron Sheet Concentration After Passivation Changes in Mobility After Passivation AlGaN/GaN HEMT Experimental Work Summary Conclusions Thesis Objectives Thesis Outcomes Future Work Bibliography 205 A Published Papers 225 B Sample Processing and Device Fabrication Procedures 227 B.1 III-Nitrides B.1.1 Solvent Cleaning B.1.2 Etch Mask B.1.3 Thermal Grease/PR Removal B.1.4 Ohmic Contact Mask B.2 Indium Nitride B.2.1 Mesa Etching B ICP RIE Dry Etch (original recipe) B ICP RIE Dry Etch (new recipe) B Straight (Parallel-Plate, Non-ICP) RIE Etch B.2.2 Ohmic Contacts for InN B.2.3 InN Device Fabrication Procedures B In-Polar Hall Bars: InN-HB B In-polar Hall Bars: InN-HB2, i440, n470, n B N-face InN Hall Bars: n500i, n1000i, N 2 000ii, n1000n B.3 AlGaN/GaN Heterostructures B.3.1 Fabrication of AlGaN/GaN Hall Bars

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17 Acknowledgements I would like to firstly thank my supervisors, Assoc. Prof. Gia Parish and Prof. Brett Nener for the opportunities, support, guidance, input, feedback and help they have provided to me through the process of undertaking this project. Their hard work, leadership and commitment has enabled this research to be conducted and I cannot thank them enough. They have also demonstrated to me the most important lesson that research and collaboration is an enjoyable and exciting experience, and I thank them for introducing me to so many people and for helping make conference trips so much fun. I wholeheartedly thank my biggest mentor Dr. Gilberto Umana-Membreno for his guidance, support and help during this research. It defies description. The many, many discussions we have held over the years (on a variety of topics) have been outstanding, while his expertise in pretty much everything equipment, theories, data analysis, programming, processing and coffee beans has been invaluable and his willingness to share such expertise is simply remarkable. I am extremely thankful for being a part of the Microelectronics Research Group. The group is undoubtedly full of brilliant minds and performs on a highly competitive international level, but it is the supportive and approachable nature of MRG that ultimately leads to great things. I thank Prof. Laurie Faraone for heading such a great group, as well as the rest of the academic and research staff for providing the direction, advice, know-how, fun, experience and knowledge to me when I needed it. Special thanks of course also go to Sabine Betts for keeping everyone in line. Special thanks to Dr. Kevin Winchester for getting me started (and keeping me going) in the cleanroom, though I also thank everyone else who I sought help from along the way (which is basically everyone). I am so so lucky to have been a postgrad in MRG at this time and give a huge thanks to everyone in MRG, but most especially the core lunch crew, Tim, Gordon, Ryan, Byron, Jason, Richie, Hatchie, Justin, who made the whole process unbelievably awesome. The magnet crew, Gordon, Ben and Gilberto, also deserve special mention, for helping do LHe fills at odd hours and understanding what I-haven t-been-to-bed-yet the next day really xv

18 xvi Acknowledgements means. I could also have never completed this work without the two hard working MRG coffee machines. Beyond the EE school, of course, this project would simply not have been possible without the assistance and support of those in the School of Physics, especially Dr. Rob Woodward, who gave us so much time and invaluable help with the magnet and cryostat, who put up with us invading his lab and running extremely noisy pumps almost constantly. A huge thanks to Dave McPhee for his never-ending help in keeping us topped up in our neverending demand for liquid gases, and to Gary Light and the rest of the physics workshop for all their help and assistance as well. I also thank everyone at UCSB, especially Dr. Chad Gallinat, Dr. Gregor Koblmüller and Prof. Jim Speck for providing the fantastic quality InN samples, insights, lab tours and to Chad and Gregor for introducing me to burritos in IV. To Prof. Umesh Mishra and Dr. Stacia Keller for providing the excellent HEMT samples and their time for various discussions. Further thanks go to all the visiting researchers from around the world who I have been lucky enough to meet, for their encouragement and interest in my work. I d also like to thank the Robert and Maude Gledden foundation for their scholarship support, which greatly improved the quality of my time performing this work. Lastly, of course to my friends and family for their encouragement, laughter, distractions, support, patience and, ultimately, disinterest. It helps keeps things in perspective.

19 Symbols, Constants and Abbreviations Table 0.1: List of symbols, constants and abbreviations used throughout this document. Symbol Meaning Units q, e charge C F force Nm v velocity ms 1 E electric field Vm 1 J current density Am 2 V H Hall voltage V R H Hall coefficient m 3 C 1 n carrier concentration cm 3 N sheet carrier concentration cm 2 µ mobility cm 2 /Vs σ xx longitudinal conductivity tensor component Ω 1 cm 1 σ xy transverse conductivity tensor component Ω 1 cm 1 σ xx longitudinal conductivity tensor component basis function - σ xy transverse conductivity tensor component basis function - σ f stress in thin film MPa M s biaxial modulus of substrate MPa d s thickness of substrate nm d f thickness of thin film nm R radius of curvature of thin film on substrate m RT HEMT 2DEG UID room temperature high electron mobility transistor two-dimensional electron gas unintentionally doped xvii

20 xviii Symbols, Constants and Abbreviations SI PECVD ICP RIE MBE PA-MBE MOCVD MOVPE MEE MOMBE YSZ QMSA i-qmsa HR.MSA C-V CBED AFM TEM HRXRD XRD AHC MFTA XPS HREELS IRR VBM CBM ADM FWHM TD ROC semi-insulating plasma-enhanced chemical vapour deposition inductively coupled plasma reactive ion etching molecular beam epitaxy plasma-assisted molecular beam epitaxy metal-organic chemical vapour deposition metal-organic vapour phase epitaxy migration-enhanced epitaxy metal-organic molecular beam epitaxy yttrium-stabilised zirconia quantitative mobility spectrum analysis software implementing improved version of quantitative mobility spectrum analysis algorithm software implementing high resolution mobility spectrum analysis algorithm developed in-house at UWA capacitance-voltage convergent beam electron diffraction atomic force microscopy transmission electron microscopy high resolution x-ray diffraction x-ray diffraction atomic hydrogen cleaning modified ThomasFermi approximation x-ray photoemission spectroscopy high-resolution electron-energy-loss spectroscopy infrared reflectance valence band maximum conduction band minimum amphoteric defect model full-width half-maximum threading dislocation radius of curvature

21 Chapter 1 Introduction 1.1 III-Nitride Semiconductor Materials and Device Applications The group III-nitride semiconductors (the III-nitrides) have emerged as a semiconductor system of serious commercial interest. Such interest, and therefore investment, is driving the intense research being undertaken in both academic and industrial research communities. The development of the blue light emitting diode (LED) from gallium nitride-based materials was the stepping stone for a new range of shorter-wavelength light emitting devices and applications in consumer and commercial products using GaN, AlN, InN and their alloys. Further to the development of optical devices, the III-nitrides have proven to be well suited to applications in electronics, especially high power, high frequency transistors. Bright blue and green LEDs and lasers diodes (LDs) are only made possible through the use of III-nitride semiconductors, as opposed to the previous generation of yellowish-green LEDs which were made from group III-phosphide semiconductors. The band gap range of the III-nitride material system covers far more than just blue and green wavelengths, however, spanning across and beyond the visible spectrum, from near IR to deep UV, as shown in Fig GaN-based solid state lighting has enabled full colour large-format LED displays, white solid state consumer lighting, LED backlights for LCD displays and mobile phones, car headlights and dashboard lighting, green traffic lights, low power safety lighting, lasers for high density DVDs (Blu-Ray), and UV LEDs for water purification, to name only a few, with more applications emerging every day. Development of quality GaN crystal growth in the late 80s and early 90s, especially the work of Nakamura [1 7] and Akasaki [8 12], opened the door for GaN electronics and 1

22 2 Chapter 1: Introduction 7 6 AlN T = 300 K (bowing parameters neglected) Bandgap energy E g (ev) SiC GaN ZnO InN Lattice constant a 0 (Å) Figure 1.1: Lattice constant versus bandgap for III-N and other common semiconductors. optoelectronics. Early development was pushed mainly by lighting applications, as GaN and InGaN enabled the development of bright blue LEDs [4, 13]. Remarkably, GaN-based materials proved to be highly efficient, high intensity emitters of blue light even while a very high number of dislocations remained in the material (from 10 8 cm 2 yet often much higher [5, 14]). The wide bandgaps of GaN and AlN also led to high power capabilities and work was eventually begun on GaN-based transistor technology. Asif Khan was fundamental in the development of the aluminum gallium nitride/gallium nitride (AlGaN/GaN) heterostructure transistor device [15 20]. High power and high speed transistors made from AlGaN and GaN, the AlGaN/GaN high electron mobility transistor (HEMT), are now available commercially as power and microwave transistors from a number of companies. GaN-based transistors are capable of tolerating high voltages and generating high current densities, and so are particularly suitable for high power applications. GaN-based transistors can also perform at high frequencies, thereby extending both power and frequency limits for high power devices simultaneously. In all devices power and frequency are forced to trade-off against one another, but in GaN-based devices this trade-off occurs at much higher frequencies than other in other materials systems such as silicon carbide (high power at low frequencies) or gallium arsenide (high frequencies at low power). The AlGaN/GaN HEMT is therefore suited to finally replace older vacuum tube technology for both military and industrial high power, high frequency applications such as satellite communications and RADAR. Solid state devices should enable greater reliability and provide greater functionality in these situations due to their inherently robust and compact nature (in contrast with the bulky nature of tube-based amplifiers).

23 1.1: III-Nitride Semiconductor Materials and Device Applications 3 increasing gallium increasing indium Figure 1.2: The range of absorption of the visible solar spectrum possible by varying the x ratio of the In x Ga 1 x N alloy. Shown is the amount of light from the sun by region of the solar spectrum, and the band gap in ev for changing proportions of indium gallium nitride [21]. GaN-based HEMTs are also being investigated for chemical and biological sensing applications, as the channel of the device can be strongly influenced by the conditions at the surface. Further, modifications to the AlGaN/GaN HEMT device designs, such as the integration of InN into the channel region of the device, as well as continued improvement of crystal and dielectric qualities, and manipulation of surface treatments, may in turn enable even faster operation, higher output power and increased sensitivity for novel sensing applications than is currently possible. Ongoing investigation and characterisation of all aspects of the devices are required to continue to advance the technology. An additional emerging application for which the III-nitrides are well suited is the formation of multi-junction high efficiency solar cells [21 23]. The use of the III-nitride system is highly advantageous as the bandgap energies of InN, GaN and AlN span beyond the spectrum of visible light in both directions (the band gap energies of the III-nitrides extending beyond the visible spectrum are shown in Fig. 1.1). The bandgap of In x Ga 1 x N is almost linearly dependent on the x ratio across the visible spectrum (see Fig. 1.2) which opens up new possibilities for bandgap engineered applications. Graded junctions of IIInitrides would increase the spectral absorption range of a solar cell, therefore enabling the absorption of a superior portion of the incident solar energy, and producing more power per panel than conventional technologies. The ability to keep the multiple wavelength absorption regions in the same material system could potentially provide unique device designs, forgoing the requirement of multiple junctions made from different semiconductor materials. Additionally, in space, solar energy is a necessity for satellite operation, but

24 4 Chapter 1: Introduction the harsh radiation-rich environment is problematic for the semiconductor materials from which the electronics are conventionally made. Electronic control circuits in space require lead and other protective shielding, adding weight and thus cost to the satellites, yet solar cells by necessity require full exposure to all impinging light and other radiation in order to produce electrical energy and so cannot be shielded. The radiation hardness of III-N materials is therefore a great advantage over other material systems for space-based solar power. InN is more radiation hard than the current low bandgap materials used in satellite solar cells, such as GaAs and GaInP [22], and would improve the reliability and lifetime of the solar cells in a radiation filled environment such as in orbit. Indium nitride and In-rich InGaN/InAlN alloys are the least mature of the III-nitride materials, yet they will be essential for the next generation of III-nitride devices in order to enable longer wavelengths in optical devices and higher speeds in transistor technologies. Current commercial devices such as LEDs, laser diodes and transistors already use low-in (low x) In x Al 1 x N and In x Ga 1 x N alloys, but more work is required to overcome the hurdles of high In-content alloy development. InN incorporation presents new challenges as the properties are different enough from GaN and AlN to require different approaches to growth, processing and characterisation. Therefore improvements in the growth, characterisation and understanding of InN properties must be obtained and advanced before InN and In-rich III-nitride alloys can be successfully integrated into III-nitride devices. The characterisation of electrical transport properties of III-nitride semiconductors (in bulk crystal materials, heterostructures and devices) is therefore very important for their continued development. Accurate characterisation provides feedback for improving growth techniques, for optimising device designs, and verifying theoretical models of electrical behaviour in the material. Transport in III-nitrides is often influenced by the surface condition especially in materials such as InN where transport consists of multiple carrier species including surface carriers for which transport depends, at the very least, on the crystal polarity of the surface, and for AlGaN/GaN heterostructures, for which potential applications such as chemical sensors demonstrate that the surface is obviously sensitive to a variety of conditions. Standard single-magnetic-field galvanomagnetic transport measurement techniques are not necessarily adequate for determining with confidence the behaviour of all carrier species in these materials, and this thesis aims to improve the accuracy of transport characterisation while considering the influence of surface parameters on the electrical transport of all carrier species in select III-nitride materials.

25 1.2: Indium Nitride Indium Nitride The integration of InN and indium-rich III-nitride alloys into III-N devices offers various advantages, such as faster operating speeds due to the superior transport properties of InN over GaN and AlN, but also presents new challenges in growth, processing and characterisation, as In-rich nitrides are the least mature and least understood of the III-nitrides. Understanding the properties and behaviour of InN through accurate characterisation techniques is therefore of critical importance. Most early research in III-nitrides focused on GaN and Ga-rich alloys of In x Ga 1 x N, as only dilute In alloys (In x Ga 1 x N, In x Al 1 x N, x < 0.1) were required for the dominant focus of LEDs and LD devices, as they enabled blue and green wavelengths (the bandgap of GaN is beyond the visible spectrum) [6, 7, 10, 24]. Similarly, the incorporation of small amounts of indium in the active GaN layer in the quantum well was found to increase the luminescence efficiency of the devices [24]. Thin films of InN have been grown epitaxially with varied success since 1972 [25], though the first crystal synthesis was attempted as early as 1938 [26]. The use of radio-frequency (RF) sputtering as the dominant deposition technique, until recently, for InN generally resulted in polycrystalline InN films with high oxygen contamination, high electron concentrations (up to cm 3 ) and low electron mobilities ( cm 2 /Vs) [25, 27 29]. RF-sputtered InN had a measured bandgap of 1.89 ev (corresponding to red light) [30, 31] and a requirement for substantially lower temperature processing than both GaN and AlN, with desorption of nitrogen from InN above the growth temperature ( 500 C) as opposed to the much higher temperatures (>1000 C) at which GaN and AlN are grown and can withstand. With these properties, InN was therefore perceived as a material with limited device prospects. The measured properties of InN were deemed either unremarkable or offered no considerable advantage over other semiconductor materials. However, the development of more suitable growth techniques for indium nitride such as molecular beam epitaxy (MBE) and metal organic vapour phase epitaxy (MOVPE) in the last decade has produced highly crystalline material with fundamental properties radically different to those measured in the previous generation of RF-sputtered films [25, 30, 31]. The most significant discovery was that the actual bandgap is much smaller than previously established, at only 0.65 ev [32 35], which is in the infrared spectral region. High quality films have renewed the interest and investigation into indium nitride, at times with heated debate and even controversy. That a semiconductor could have such a vastly different bandgap to that previously upheld is of itself a significant result. Single crystalline

26 6 Chapter 1: Introduction InN results have since suggested that the material has properties that are in fact highly advantageous to a variety of applications. Key favourable properties of InN include the lowest effective mass for electrons in the III-nitride material system, leading to a higher drift electron mobility, greater peak and saturation velocities and superior transient transport properties than either in GaN or AlN, and for some parameters superior properties even to GaAs [36 39]. InN is therefore of particular interest for enabling speed enhancements in III-N heterostructure devices whereby InN would form the channel material for cm and mm-wave devices such as high electron mobility transistors (HEMTs) or heterojunction field effect transistors (HFETs). The predicted cut-off frequency of InN-based FETs is easily up to 1 THz for 0.1 µm gates [37]. Development of an InN-HEMT requires both improvement in bulk InN crystal quality and a reduction in the residual electron concentration. Transport modelling suggests room temperature electron mobilities of cm 2 /Vs are possible in low concentration InN material [40,41], however the current records for electron mobility in InN are only at a third of that value at 3980 cm 2 /Vs [42] and 3570 cm 2 /Vs [43], with the latter value measured as part of the work of this thesis (see section 5.2). Improvement is also necessary in the growth of the top barrier layer to form a suitable heterojunction with a high quality interface, and layers that do not feature intermixing or strain related degradation. The bandgap of InN (at 0.65 ev, in the infrared), much lower than that of either GaN (3.45 ev) or AlN (6.2 ev, in the UV, see Fig. 1.1), as previously discussed, has the potential to enable III-nitride devices to span the visible spectrum and to enable the development of high-speed III-nitride optoelectronics that are compatible with optical fibre wavelengths [24]. In addition to emission-based devices, InN has a strong future in the development of tandem and multi-junction solar cells as the bandgap of In x Ga 1 x N is able to be tailored by varying the mole fraction x to suit the most energetic parts of the solar spectrum, as shown in Fig Current time-domain terahertz (THz) spectroscopy and imaging, for example in security, medical and scientific applications, has been enabled due to the availability of terahertz sources, including semiconductor sources such as InAs, InSb and GaAs which can emit THz radiation when they are excited by femtosecond laser pulses at near infra-red wavelengths (800 nm 1.6 µm) [44, 45]. However, the applications of these imaging techniques are still limited by the power of the available THz emitters, and so the development of brighter sources is of interest. Optically excited THz emission from InN thin films has been reported [44 47]. The THz emission from InN is strong compared to THz emission from other semiconductors; it is slightly less but on the same order of magnitude as optimised (for

27 1.2: Indium Nitride 7 THz emission) p-type InAs, which is significant as an optimised p-type InAs sample is one of the strongest known semiconductor-based sources of THz emission. Since THz emission is inversely proportional to carrier concentration due to free carrier absorption, much stronger THz emission is expected from InN with further improvements in the reduction of the unintentional n-type doping [46]. The accurate characterisation of the electron density in InN is therefore vital for building brighter THz sources by understanding, and reducing, the unintentional background doping mechanisms, predominantly through improvement of crystal growth. While indium nitride epitaxial films are approaching the (crystal) quality required for use in devices, however, further challenges remain that are inherent to the material, mainly due to the band structure. The band structure of InN is very different to the more typical case for semiconductors. The bottom of the conduction band lies well below the Fermi stabilisation energy, E FS, (also known as the charge neutrality level) [48], instead of E FS residing in the bandgap as it does for nearly all other semiconductors [49 51]. This leads to the preferential formation of donor-like defects in InN which results in high unintentional background n-type doping in all InN films, and the presence of an accumulation of electrons on the surface of the material [48, 49]. The surface accumulation of electrons complicates electrical transport characterisation, as two distinct conduction paths are now present through the InN (the surface accumulation layer and the bulk). Preliminary work into the suppression of the surface conduction has achieved at least partial success through oxidation (using ozone and UV light), but the modification of the surface degraded over time. The high unintentional background n-type doping also makes it difficult to grow p-type InN material, while the surface accumulation of electrons, which persists regardless of doping, further complicates characterisation due to the mixed conduction. This accumulation can significantly alter or even mask the conduction of the bulk layer from standard profiling techniques such as Hall measurement using a single magnetic field. As p-type material is essential for optical devices, characterisation techniques that can distinguish between the hole and electron species are required. To date, there is only one report of p-type InN successfully confirmed through measurement of free hole carriers via multi-carrier analysis of variable magnetic field Hall data [52]. The standard means of determining the electrical transport properties of a semiconductor, the galvanomagnetic Hall effect measurement at a single magnetic field, cannot differentiate between contributions from multiple conduction paths or mixed conduction from multiple carrier species, and this is an issue in the characterisation of InN especially. In InN, the high density of the surface electron accumulation obscures the bulk character-

28 8 Chapter 1: Introduction istics. Furthermore, as the quality of the crystal improves with thickness away from the growth interface, the doping and scattering mechanisms (and thus the carrier transport) in InN will change with thickness, resulting in some spread in the characteristics, especially in the mobility. The standard single-field-hall transport characterisation can give no information about any spread in transport characteristics arising from the non-uniform crystal quality. To improve the film quality and to settle the remaining ambiguous properties of InN, more effort in the growth and characterisation of InN is very important. Therefore, a more insightful transport characterisation technique is required if accurate measurement of the properties of InN films is to be obtained. Magnetic field Hall effect measurements conducted as a function of magnetic field with a suitable multi-carrier analysis have been successfully applied in other material systems with mixed conduction as a means of multiple carrier transport characterisation [53 55], but are under-utilised in the characterisation of InN. Prior to this thesis, there were only two papers (on the same data set) relating to the use of multi-carrier analysis for InN transport characterisation [56, 57]. This thesis uses the multiple magnetic field Hall measurement technique to determine the transport characteristics of multiple electron species in InN, specifically addressing the extraction of the transport properties of the surface electron species by improving measurement accuracy using high magnetic fields, improved device structures and quantitative mobility spectrum analysis techniques. The technique has been applied to a selection of molecular beam epitaxially-grown InN films with different surface conditions, including both polarities of c-plane InN (In- and N- face), and differing MBE growth parameters in order to investigate the influence of such conditions on both the bulk and surface electron transport in InN. The development and use of this technique on InN to separate out distinct carrier species will benefit the development of the technology of the growth of InN, and the understanding of the background doping and carrier transport properties, all leading to a benefit in the development of InN and InN-based devices such as InN-based HFETs, In-rich InGaN LEDs, tandem solar cells and THz sources. Results from this thesis have subsequently been published, referenced and cited [43, 58 61], and the multiple magnetic field/multicarrier analysis technique has been applied and reported by other researchers [52, 62, 63], though has not yet been widely adopted for the analysis of InN largely due to specific equipment and software requirements.

29 1.3: AlGaN/GaN High Electron Mobility Transistors AlGaN/GaN High Electron Mobility Transistors As discussed in section 1.1, gallium nitride-based transistors are being developed to meet the requirements for high power and high frequency (GHz) circuits that current siliconand gallium arsenide-based devices are physically unable to achieve. GaN-based HEMTs are now commercially available, and are being marketed for applications such as satellite communications, RADAR, tactical radios and various telecommunication applications (W- CDMA, LTE and WiMAX). GaN-based HEMTs are also promising for the development of sensing applications due to the sensitivity of the 2DEG to surface conditions. AlGaN/GaN high electron mobility transistors, though, are susceptible to suffering from degraded performance under the desired high frequency (RF) operating conditions. This degraded performance is quantified as a large reduction in the actual output power of the device from the expected output power that is calculated using values from the DC performance of the device. This RF dispersion is most generally referred to as current collapse [16, 64 68]. A number of theories have been proposed to explain current collapse, but surface state occupation by electrons, a build up of negative charge referred to as a virtual gate, is now widely accepted as the dominant cause [56, 69 72]. The free (unpassivated) AlGaN surface contains donor-like surface states, due to factors such as dangling bonds at the surface of the crystal. These states then re-trap electrons which results in a net negative charge on the surface that repels the electrons below, reducing the amount of electrons in the channel and hence the current output of the device. The control of surface trap densities in GaN FET devices continues to be a requirement in device development. The best engineering solutions make use of surface passivation with various dielectrics, and also incorporate field plates to manipulate the electric fields over the device [70,73 75]. While field plating device designs and improved III-nitride and dielectric material quality have helped to control the problem, surface trapping effects have not been entirely eliminated, and given the multitude of device designs and application requirements continued investigation of dielectrics for passivation is warranted. Surface states are seen to be unavoidable in this material system due to the strong polarisation fields that result in fixed charge at the surface, which in turn induce the formation of donor-like surface states that contribute to the population of the 2DEG [69, 72, 76 78]. Surface passivation, the deposition of a thin film over the exposed surface of the device, has been a key development in solving the problem of current collapse. It has been demonstrated experimentally that deposition of a thin ( nm) silicon nitride (SiN x ) film on the surface of an AlGaN/GaN structure often, but not always and to varying

30 10 Chapter 1: Introduction extents, improves the performance of the device by reducing current collapse [69, 70, 79, 80]. The reduction of current collapse by surface passivation with SiN x, and alternate passivation materials, further suggests the significance of the role played by surface states in current collapse. Better understanding of the impact of passivation on all aspects of the device and material structure is vital for the continued development of the transistor technology. Varying surface preparation, deposition conditions and even passivation materials produce mixed results and an optimal passivation technology has not been well established. Most frequently a plasma enhanced chemical vapour deposition (PECVD) film of nm deposited at 300 C is used, though without extensive justification other than these are a well developed set of deposition conditions. Alternate passivation materials and techniques are still frequently reported, with recent novel techniques appearing very promising (such as chemical vapour deposition using catalytic cracking of the nitrogen (Cat-CVD) to deposit SiN x [81]). In addition to mitigating current collapse, SiN x passivation is also often seen to increase the density of electrons in the channel (the 2DEG). The reason for this increase is not well understood. One factor to consider is the inherent stress present in the silicon nitride thin layer, which could cause a strain in the crystal lattice of the topmost AlGaN layer of the HEMT. AlGaN is a highly piezoelectric material, meaning strain in the crystal causes electric fields to form. There already exists strain in the AlGaN layer formed during growth [76], a fact that contributes to formation of the 2DEG. It is possible that additional passivant-induced strain may affect the existing piezoelectric and spontaneous electric fields present across the AlGaN layer sufficiently that changes in the interface conditions at the AlGaN/GaN heterojunction occur. Any changes at the interface will impact transport properties such as carrier density of the two dimensional electron gas, which is closely confined at that interface. Such changes in the electric fields have the potential to either improve or degrade the performance of the device, depending on the complex interaction of all physical and electrical properties affected. Determining the optimal amount of stress in the passivation layer required to improve device performance is therefore of interest, and one of the goals of this thesis. The inherent stress present in the silicon nitride passivation layer is dependent upon deposition conditions such as temperature, pressure and power. As such, passivation layers with different internal stress can be deposited on AlGaN/GaN HEMT samples by varying the deposition parameters. If stress/strain is a factor it will be inherently related to the piezoelectric coefficients of the AlGaN layer. As the piezoelectric coefficients of AlN

31 1.4: Thesis Objectives 11 and GaN are different (AlN is more piezoelectric), the percentage composition of AlN in the AlGaN will also be relevant. Studying the changes in the transport properties such as mobility and carrier concentration caused by varying the stress in the device passivation will allow a better understanding of the role stress plays in altering device performance. Characterising the electron transport properties enables refinement of the passivation that may not be obvious if only looking at averaged, macroscopic device parameters such as drain current. 1.4 Thesis Objectives The objectives of this thesis are to investigate the transport phenomena in two III-nitride materials in which the surface conditions play a strong role. The III-nitrides under study are bulk epitaxial InN films of In- and N-face c-plane orientation, with various surface characteristics, and AlGaN/GaN heterostructures with and without passivation by silicon nitride films of varying stress. This type of characterisation is vital for the development of these III-nitride materials for future device applications. Detailed investigations of multiple carrier transport in InN, and of the influence of surface passivation on the 2DEG transport in AlGaN/GaN HEMTs are both lacking in the literature. These investigations therefore contribute a considerable amount of new data and insight into the properties of each of these material systems. This thesis will: Differentiate and extract the transport properties of multiple independent electron species in InN, in the bulk of the semiconductor and in the electron accumulation layer at the semiconductor surface, Determine the temperature dependence of transport properties of each of the multiple electron species in InN between 20 and 300 K, Determine the influence of MBE growth conditions on the transport properties of each of the multiple electron species in InN, with consideration of the role of surface roughness, Determine the influence of crystal polarity on the transport of surface and bulk electron species in InN,

32 12 Chapter 1: Introduction Determine the influence of device processing and surface treatments on transport in InN, Determine the influence of stress in the SiN x surface passivation on 2DEG transport properties in Al x Ga 1 x N/GaN heterostructures, over a range of temperatures, and Determine the dependence of AlN mole fraction (x) on the change in 2DEG transport properties in Al x Ga 1 x N/GaN heterostructures when combined with passivation of the surface with SiN x Thesis Arrangement This thesis is presented in eight chapters. Following this introductory chapter, Chapter 2 introduces the group III-nitride semiconductors and describes physical qualities common across the material system, such as the crystallography, with specific focus on indium nitride and the AlGaN/GaN HEMT heterojunction. Additional properties of these materials are presented in Chapters 4 and 6, which cover other background material specific to InN and AlGaN/GaN HEMTs, respectively. The experimental methods and analysis techniques are detailed and discussed in Chapter 3. Quantitative mobility spectrum analysis (QMSA) techniques, an integral component of the data analysis, is covered in some depth in Section The basis of this technique supports the thesis investigations into carrier transport properties. Also included in this chapter are details of silicon nitride deposition and stress measurement techniques. Chapter 4 details the development of InN growth technology, with focus given to the most popular and successful growth technique, molecular beam epitaxy, the source of InN material measured in this thesis. In particular, the influence of key growth conditions on the materials properties is discussed. Understanding growth methods and growth issues is essential for the experimental investigations into the influence of growth conditions on the electron transport in InN in this thesis. Further in Chapter 4, an overview of the structural and electrical characteristics of InN is presented, with focus on the most important and relevant properties of the semiconductor, such as the differences in crystal polarities, the propensity for unintentional n-type doping and the presence of an inherent surface electron accumulation. The evidence for, and existence of, multiple carrier species in the InN material is identified, and is an important consideration for the transport analysis undertaken in this work. The source of the n-type doping and the surface electron accumulation are considered in terms of the bulk band

33 1.4: Thesis Objectives 13 structure. The historical development of the understanding of transport characteristics of the multiple electron species in the material is outlined, covering both experimental and theoretical literature. The lack of in-depth studies into the multi-carrier aspects of InN is identified and highlights the importance of this thesis work. Chapter 5 covers all the experimental work conducted into InN as part of this thesis. Three main experiments are included. The first is the establishment of the measurement and detection of multiple electron species in InN. The second experiment considers three samples grown under different conditions, and discusses the electron transport properties of the electron species in InN in terms of growth conditions and surface morphology. The third experiment considers N-face InN, a different crystal orientation to the samples in the first two experiments, with subsequently different surface properties, and investigates both sample thickness and growth regime variations. The final section of the chapter then discusses trends in the results across all InN samples from the three experiments. Chapter 6 introduces the AlGaN/GaN heterostructure used in the fabrication of high electron mobility transistors. The role of the piezoelectric and spontaneous polarisations in the formation of the two dimensional electron gas is given, highlighting the resultant influence of surface states and the issues surrounding the phenomenon of current collapse. Passivation of the surface of HEMT devices and AlGaN/GaN heterostructure material with silicon nitride and other thin film dielectrics, as presented in the literature, is reviewed and discussed. The influence of the passivation on various aspects of the device and the material properties is outlined. The chapter identifies areas in which investigation into the effects of passivation on the AlGaN/GaN heterostructure are lacking, such as how the deposition conditions of the passivation layer may affect the 2DEG transport properties. The chapter places the work of this thesis in context of the ongoing use of SiN x in HEMT devices. The experimental measurement of AlGaN/GaN heterostructure 2DEG transport properties is presented in Chapter 7. Unpassivated AlGaN/GaN heterostructures are measured and compared with silicon nitride passivated samples with three differently stressed silicon nitride films deposited by PECVD. Four different Al x Ga 1 x N compositions (varying the Al mole fraction x) are considered. The changes in the transport properties of the 2DEG after passivation with each of the differently stress passivants are compared. The temperature dependence of the changes in the transport properties of the 2DEG is measured between 25 and 300 K. Finally the outcomes of this work are summarised in Chapter 8.

34 14 Chapter 1: Introduction The list of papers published as a result of this work, referenced throughout this thesis as Fehlberg et al. [43], Fehlberg et al. [58], Fehlberg et al. [59], Fehlberg et al. [60] and Fehlberg et al. [61], is also included at the end of this document in Appendix A and specifies which sections in this thesis relate to which publication. Further details of the sample processing techniques are presented in Appendix B.

35 Chapter 2 III-Nitrides 2.1 Introduction Group III-nitride semiconductors are those formed between group III elements and the group V element nitrogen (N). Boron (B), aluminium (Al), gallium (Ga) and indium (In) are all capable of forming crystalline semiconductors with nitrogen. While boron nitride is a common and important material, its applications vary more widely than the other III-nitrides which make up the focus of this work and will not be covered. The binary semiconductors AlN, GaN and InN (and their ternary and quaternary alloys) exhibit many similar properties that necessitate similar approaches to measurement and processing techniques. These include physical properties related to the lattice structure of the crystal and some chemical properties that are of particular interest in relation to device processing procedures. The investigated semiconductors in this thesis are InN and the heterostructure of AlGaN and GaN, and their properties relevant to this work are detailed in this chapter. Further information relevant to each III-nitride material under study in this thesis is presented before the related experimental work: indium nitride is reviewed in detail in Chapter 4 and the AlGaN/GaN heterostructure in Chapter Physical and Chemical Nature The III-nitrides have similar crystal properties, with each most commonly occurring in the hexagonal wurtzite crystal phase. The materials have a strong covalent bond between the two constituents, are relatively chemically inert and radiation hard. These properties can be advantageous for use in harsh environments, such as at high temperature, in harsh gaseous environments and under radiation. InN is the least chemically or physically 15

36 16 Chapter 2: III-Nitrides Figure 2.1: The unit cell of the wurtzite crystal structure [83]. stable of the III-nitrides, but is more robust in these respects than many other common semiconductors, especially those with low bandgaps. The strong chemical bonding and chemical inertness of the III-nitrides, however, dictates methods of device processing. Wet etching is generally unfeasible as it is either too slow, non-uniform or results in excessively rough surfaces. Dry (plasma) etching is therefore required for mesa formation. GaN and AlN are both etched easily by a chlorine-based plasma [82], while in this work the most successful etch process developed for InN used a methane/hydrogen/argon plasma chemistry (device processing specifics are given in Appendix B). 2.3 Crystal Phases and Orientations The most common crystal phase of the III-nitrides is hexagonal wurtzite, with a c-plane surface as the most common growth front. The wurtzite unit cell is shown in Fig. 2.1 [83]. The c-plane of the wurtzite phase is non-symmetric and has two possible orientations at the surface, being the (0001) and (000 1) crystal orientations, as shown in Fig. 2.2 [84]. The two polarities are referred to as In/Ga/Al-face (or In/Ga/Al-polar) and N-face (or N-polar) respectively. Both crystal polarities can be In/Ga/Al or N terminated at the surface. Using InN as an example, Fig. 2.2 shows both crystal orientations with In termination. InN films are generally measured to exhibit In terminated surfaces, usually with additional In-monolayers present [85], discussed further in section The polarity of as-grown wurtzite c-plane InN is largely dependent on the substrate and buffer layers that are used for growth. For In-face InN, typical substrates are Ga-face GaN, Si-face SiC, (111) yttrium-stabilised zirconia (YSZ) and sapphire. For N-face InN,

37 2.3: Crystal Phases and Orientations 17 Figure 2.2: The wurtzite crystal structure of InN, showing the two crystal orientations (up and down the page), both with indium termination [84]. typical substrates are N-face GaN, C-face SiC, and nitridated sapphire [86]. Many groups also report mixed polarity present in their films. The two c-plane crystal orientations of the III-nitrides can have considerably different properties. For example, N-face InN and GaN are less chemically stable than the In/Gaface, yet N-face InN is more thermally stable with a dissociation temperature around 100 C higher than In-face InN [34]. The electrical transport is also influenced by the crystal orientation, a finding covered in the experimental work of this thesis by measuring the electrical characterisation of the two c-plane orientations of InN, the results of which are presented in Chapter 5. All AlGaN/GaN HEMT studies for this thesis were performed on Al/Ga-face HEMT material, with the results presented in Chapter 7. Published works on HEMTs most commonly have studied Al/Ga-face material, though interest in N-face HEMTs has recently increased, while for InN the In-face orientation is also the most commonly grown and studied. A well established method of determining the film polarity of GaN is through wet chemical etching [87, 88], and Muto et al. [89] applied this method to investigate the wet etching of both InN polarities. In-face InN films etched smoothly in KOH while N-face InN films etched roughly and were clearly distinguishable from the In-face films after the same etch time. The susceptibility of the N-face surface of InN to become damaged after etching in KOH and NaOH [90] (and thus in other alkaline solutions) presents problems in device processing (a problem also for N-face GaN) due to the alkaline nature of many photoresist developers. Processing techniques were used to protect the N-face InN surface in this

38 18 Chapter 2: III-Nitrides work (by the deposition of silicon nitride, see section 5.4.2), and are detailed further in Appendix B. Recently interest has increased also in non-polar and semi-polar orientations of III-nitride materials, that is along the a-, m- and off-axis planes of the wurtzite structure. The interest in non-polar GaN-based devices stems from properties or applications such as a greater intensity of output from multi-quantum-well LEDs or polarisation sensitive photodetectors [91]. Current methods to grow GaN with these orientations require semi-/nonpolar substrates, such as from miscuts and substrates other than sapphire. The interest in non-polar GaN leads naturally to an interest in semi-polar and non-polar InN, as InN growth is undergoing rapid development. The a-plane orientation (11 20) of InN has been successfully grown on r-plane (11 02) sapphire substrates using GaN/AlN buffer layers [92]. There are no reports of m-plane or semi-polar InN growth. Interest in alternate crystal planes for InN is further invigorated by the presence of a surface electron accumulation on all c-plane InN surfaces (both polarities). The investigation of the presence, or absence, of a similar electron accumulation on the non-polar plane surfaces is discussed in more detail in section The variable magnetic field Hall measurement technique used in this thesis is well positioned as a method of investigating surface conduction in non- and semipolar InN films. While no such films were able to be obtained for this thesis, non-polar InN research will no doubt benefit from the work done in this thesis on polar InN. The III-nitrides can also be grown in the cubic zinc-blende phase. The growth of InN in the cubic zinc-blende (ZB) phase has been reported [92, 93], though it requires suitable substrates and growth conditions to obtain. Zinc-blende InN has been measured to have a surface accumulation of electrons [92], and thus the multiple-carrier transport characterisation techniques developed in the work of this thesis will also be of benefit for ZB InN development. Cubic AlGaN/GaN heterostructures are not of interest, as it is the large polarisation fields that form in the wurtzite phase that induce the high density two dimensional electron gases. 2.4 Summary The III-nitride materials of interest in this work exhibit many properties in common, which enables similar approaches to be taken towards their electrical characterisation. The wurtzite crystal structure results in similar properties between III-nitride materials dependent on the surface polarity of the sample, and the strong physical and chemical bonding enables similar processing procedures to be applied to each material.

39 Chapter 3 Experimental Methods and Analysis Techniques 3.1 Magnetotransport Measurement of Carrier Transport Properties The characterisation of electrical carrier transport is the primary focus of the work in this thesis. The accurate characterisation of electrical carrier transport in semiconductor materials is of vital importance for improvement of the material and development of devices. Knowledge of the carrier concentration and the carrier mobility provides feedback for optimising growth techniques, gives insight into the fundamental properties of the semiconductor and determines useful parameters for device development. In the IIInitrides the accurate characterisation of transport properties is required for the continued extension of the operation regions of many GaN-based devices. As discussed in section 1.1, two ways in which such extensions can be achieved are by the incorporation of InN or In-rich III-N alloys, and by optimising existing passivation materials in AlGaN/GaN transistor designs to ensure maximum performance gain. Measurement of the properties and electrical behaviour of carriers in bulk epitaxial InN is therefore of great importance. The accurate characterisation of the electron concentration in InN is made difficult by the presence of multiple conduction paths through the material, particularly the presence of an electron surface accumulation regardless of surface preparation. Knowledge of the electron concentration for each species is required for understanding the unintentional background doping mechanisms so that they may be 19

40 20 Chapter 3: Experimental Methods and Analysis Techniques reduced through improvements in growth techniques. The high unintentional doping is one of the major hurdles in the progression towards InN-based devices. In AlGaN/GaN high electron mobility transistors, passivation is used to improve device performance, but often only macroscopic devices parameters, such as drain current, are measured when quantifying the performance gain. When varying the stress in the surface passivant, studying the changes in the transport properties of the 2DEG will allow a better understanding of the role stress plays in altering device performance. One of the most effective methods of determining carrier transport properties is through galvanomagnetic measurements. Measurement is made of both the resistivity of the sample and the Hall voltage established under the influence of a magnetic field. These two results can be combined to calculate the concentration of carriers present in the semiconductor, the sign of the carrier species (electrons or holes) and the mobility of the carrier species. The standard Hall measurement measures the Hall voltage, V H, at a single magnetic field B, while passing current I, and calculates the Hall coefficient, R H : R H = V H I B (3.1) the Hall coefficient is then used to calculate the carrier concentration, n: n = 1 q R H (3.2) and the sign of the Hall coefficient (negative or positive) indicates the type of carriers present (electrons or holes, respectively). The resistivity, ρ, is also used in order to determine the Hall carrier mobility, µ: µ = R H ρ (3.3) The mobility shown above is known as the Hall mobility, which differs from the drift (conductivity) mobility by a factor r, known as the scattering factor, where µ Hall = rµ drift [94, 95]. The difference arises because at a finite temperature the charge carriers within a species will have a distribution of energies, and because scattering probabilities are generally energy dependent, not all carriers will have the same drift velocity [95]. The value of r is dictated by the carrier scattering processes and is always greater than unity (therefore

41 3.1: Magnetotransport Measurement of Carrier Transport Properties 21 the Hall mobility is always slightly larger than the carrier drift mobility). Generally, however, r does not exceed about 1.2 for n-type conduction [94], is equal to 1 for degenerate electron gases [94], and is therefore usually assumed to be unity. In this work the value of r has not been calculated and all mobilities given throughout the thesis are equal to the Hall mobilities. This simple measurement is extremely powerful in providing insight into the type, quality and properties of the semiconductor material. This section outlines how to perform the Hall measurement, including sample preparation and configuration, measurement of the resistivity and Hall voltages, and analysis of the results. In the semiconductors of interest in this thesis, the existence of multi-layer and multicarrier conduction within a given sample add a level of complexity to the standard Hall measurement. To enable determination of multi-carrier properties, the standard Hall technique is extended to include measurement of both the resistivity and Hall voltage at multiple magnetic fields. The magnetic field dependence of the measured data is then analysed to determine the existence and properties of multiple carriers. If only one carrier is present, fitting over multiple magnetic fields greatly improves confidence in the result. Detail of the techniques required to measure and analyse Hall and resistivity data for multiple carrier conduction are given in this section Experimental Apparatus and Setup In this work, Hall and resistivity measurements were performed as functions of both magnetic field and temperature. Two different electromagnets were used: the first a simple 2 tesla electromagnet, and the second a superconducting 12 T electromagnet, with the majority of measurements performed using the 12 T magnet. For measurement in the 12 T Oxford Instruments superconducting magnet, samples were mounted and bonded to a custom-designed teflon sample holder. This sample holder accommodated both van der Pauw and Hall bar sample configurations. The current was supplied by a Keithley 220 programmable current source, contacts were switched by a Keithley Model 7065 Hall Effect Card and voltages measured by a HP 3478A multimeter. The measurement configuration and controlling software follows that described in the Keithley Model 7065 Hall Effect Card instruction manual [96]. Measurements were taken at approximately 30 magnetic field values between 0 and 12 T, and at the corresponding negative fields (between 0 and -12 T). The magnetic field was

42 22 Chapter 3: Experimental Methods and Analysis Techniques held at the value while the measurements were taken, as the magnetic field was ramped in both directions, starting from 0 up to 12 T, then as it was ramped back down to 0 T, then to -12 T and back to 0 T. The data taken both ramping up and down from the maximum fields was averaged before being used in the data analysis outlined in this chapter. Sample temperatures were controlled by placing the sample in an Oxford Instruments CF 1200 continuous flow cryostat with liquid helium cryogen, controlled by a Lake Shore 332 Temperature Controller with a magnetically insusceptible Cernox sensor and resistive heating. Measurements were taken between 20 and 300 K, with temperatures of 20, 25, 40, 60, 77, 90, 100, 125, 150, 175, 200, 250 and 300 K being used in various experiments, dependent on time, equipment and resolution required. 2 T magnet measurements were performed in a sample-in-vacuum cold finger cryostat with no temperature control beyond liquid nitrogen and room temperature operation. Only samples in the van der Pauw configuration were able to be measured, with similar source and meter equipment used as in the 12 T setup. In both setups, magnetic and electrical instruments were computer controlled so that the entire measurement was automated, apart from manual setting of the temperature controller and inspection of temperature stability. Hall and resistivity voltages were measured at each magnetic field, with switching of current direction and contacts as detailed in the previous section, which are taken from the Keithley manual [96]. Measurements were taken for both polarities of magnetic field. The magnitude of the current was kept constant for the entire measurement Hall Effect Sample Structures The ideal sample shape for measuring the Hall effect is the Hall bar, shown in Fig. 3.1, a rectangular bar with uniform cross-sectional area. Current flow along the bar enables measurement of the resistivity through measurement of the voltage at two contacts along one side of the bar. Application of a magnetic field perpendicular to the plane of the bar causes carriers to be deflected (by the Lorentz force) and accumulate on one side of the bar, establishing a voltage, termed the Hall voltage (V H ), across the width of the bar. Direct measurement of the Hall voltage is performed between two contacts on either side of the bar. An alternative configuration is to take a sample of arbitrary shape (provided it has no interior voids) and place four contacts on the periphery. Through the work of van der

43 3.1: Magnetotransport Measurement of Carrier Transport Properties 23 Pauw [97] it was proven that the resistivity and Hall coefficients could be calculated by measuring a selection of certain voltage and current connection permutations. Such sample structures are referred to as van der Pauw structures. Though any sample shape may be used, samples with geometric symmetry are preferred; a selection are shown in Fig. 3.2 [98]. Both van der Pauw and Hall bar test structures were used for the measurement of transport properties in this thesis. Further consideration of the requirements and limitations of each structure are presented next. ts B F EH i w z y x Figure 3.1: Ideal Hall bar. Figure 3.2: An assortment of van der Pauw sample shapes and contact configurations [98].

44 24 Chapter 3: Experimental Methods and Analysis Techniques Using the van der Pauw Structure The van der Pauw sample structure is usually the simpler of the two sample types to prepare. The most simple case is of an (approximately) square sample with pressed or soldered contacts (generally indium) at the four corners. This simple preparation is used extensively in the literature, as well as in the work of this thesis. Alternatively, photolithographically defined mesa etched shapes can also be used (such as the Greek cross shown in Fig. 3.2). The voltages required to calculate the resistivity of a van der Pauw structure are measured by passing current through two adjacent contacts, and measuring the voltage between the remaining two. This is performed for all such contact combinations, and with reversed current for each combination. This results in 8 permutations, shown in Fig. 3.3a for a simple square sample [96]. The Hall coefficient is calculated from voltages measured between two non-adjacent contacts with current passed through the remaining two. Including measurements where the current direction is reversed, this results in four permutations. These are shown in Fig. 3.3b [96]. For improved accuracy these measurements are performed at both magnetic field polarities. The resistivity and Hall coefficient are then calculated from these voltages at each magnetic field. The formulas and their usage are described in section According to calculations performed by Wieder [99], the maximum error in the measured resistivity for triangular corner contacts of 12.5% of the edge length in size is 0.25%, and up to 0.4% for square contacts. The error introduced by finite electrodes for the Hall component of the measurement is always greater, up to around 10% for the same contact size. Chwang, Smith and Crowell [100] calculated the correction factor in the Hall voltages for triangular contacts of 10% of the edge length to be around 5%, increasing with contact size and around double for square contacts. In order, then, to minimise errors where pressed indium contacts were used in this work (where contacts were bonded by hand) the contacts were made as small as was possible, which was around 0.5 mm or less (which was 10 % of the side length). Discussion is included for results where the size of the contacts is believed to have contributed to error in the measurement. Measurement of all the contact permutations for both resistivity and Hall voltages is vital for the extension of the van der Pauw technique to multiple magnetic fields. All contact permutations are required in order to eliminate the Hall or resistivity components of the voltages on their counterparts through averaging [101]. The resistivity and Hall coefficients

45 3.1: Magnetotransport Measurement of Carrier Transport Properties 25 V1 i 1 2 V2 1 2 i V1 V2 V3 V i V4 V i V5 V5 V6 V i i V7 1 2 V8 i V7 4 3 V8 i (a) i VH1 VH VH VH2 i i VH3 VH VH VH4 i (b) Figure 3.3: Voltage and current contact permutations for (a) the measurement of resistivity and (b) the measurement of the Hall voltage, in the van der Pauw configuration [96].

46 26 Chapter 3: Experimental Methods and Analysis Techniques can then be calculated by the standard equations [96], calculated at each magnetic field (described further in the next section). This gives the magnetic field dependent resistivity, ρ(b), and Hall coefficient, R H (B). Reduction of error in the geometry and finite contact size of the simple van der Pauw sample configuration could be achieved by using photolithographically defined van der Pauw structures, yet the measurement of all contact permutations (12 measurements at each magnetic field) would still be required. Once adding the complexity of photolithography and plasma mesa etching to sample preparation, it was seen as advantageous to also advance to the Hall bar structure for further magnetotransport characterisation. The Hall bar enables more direct measurement of the resistivity and Hall voltages (simplifying raw data analysis), and halves the number of voltages measured at each field, thereby reducing the measurement time. The Hall bar structure was therefore used extensively in this work, with all samples eventually undergoing photolithography and mesa etching for Hall bar definition. Some samples were also first measured unprocessed in the van der Pauw configuration with pressed indium contacts Using the Hall Bar Structure While in earlier years of semiconductor research van der Pauw samples were often preferred to Hall bars (as sample shapes were manually cut out by tools such as a wire saw or ultrasonic cutter), all Hall bars used for measurement in this thesis are photolithographically defined and mesa etched using plasma-based reactive ion etching and therefore the dimensions of the Hall bars are known to a high degree of accuracy. By using photolithographically defined Hall bar structures most of the geometrically sourced errors in the (non-lithographically defined) van der Pauw configuration can be drastically reduced if not essentially eliminated. A to-scale Hall bar geometry used in this work is shown in Fig The only geometrical error sources in the Hall bar arrangement are due to deviations from the ideal of a rectangular solid (of width w and length l) with constant current density and point-like voltage contacts [98], which in real terms covers: the finite size of the contacts, for which errors are reduced by placing the contacts at the end of thin arms (width of arm w/3 [98], this work uses w/8), and the shorting of the Hall voltage which can be eliminated (< 1%) by an aspect ratio of length/width l/w > 3 [98] (in this work the ratio is 7). At each magnetic field, six voltages are measured: four for resistivity and two for the Hall voltage. The voltages measured are demonstrated in Fig. 3.5.

47 3.1: Magnetotransport Measurement of Carrier Transport Properties 27 D w Figure 3.4: Hall bar sample shape used in the work of this thesis, from mesa etch mask layer. V1 V1 + - V2 i i V2 V3 V3 - + i V4 i V4 (a) VH1 i VH1 - + VH2 VH2 + i (b) Figure 3.5: Voltage and current contact permutations for (a) the measurement of resistivity and (b) the measurement of the Hall voltage, in the Hall bar configuration [96].

48 28 Chapter 3: Experimental Methods and Analysis Techniques Data Processing Raw resistivity and Hall voltages are used to calculate the (magnetic field dependent) resistivity, ρ (Ω cm), and Hall coefficient, R H (cm 3 /C). Units for the input data are volts (V), amperes (A), Gauss (G) and centimetres (cm). For the van der Pauw case, Eqn. 3.4 gives the resistivity and Eqn is used to calculate the Hall coefficient. The voltages are described using the same nomenclature as in Figs. 3.3a and 3.3b. The resistivity, ρ(b), is averaged across the sample between two sets of resistivity calculations each using four of the eight measured voltages, so that ρ(b) = ρ A(B) + ρ B (B) 2 (3.4) where ρ A (B) = π t s f A 4 ln 2 I ( V 1(B) + V 2 (B) V 3 (B) + V 4 (B)) (3.5) ρ B (B) = π t s f B 4 ln 2 I ( V 5(B) + V 6 (B) V 7 (B) + V 8 (B)) (3.6) t s is the thickness of the sample, while f A and f B are geometrical factors based on the symmetry of the sample [96] and determined from the resistance ratios Q A and Q B by where Q 1 Q + 1 = f ln 2 ( ) 1 arc cosh 2 e ln 2 f (3.7) Q A = V 2 V 1 V 4 V 3 Q B = V 6 V 5 V 8 V 7 (3.8) (3.9) The Hall coefficient is found from R H = 108 t s 4 B I ( ) VH1±B V H2±B + V H3±B V H4±B 2 (3.10) where the factor 10 8 is required to correct for the units used (given at the start of this section), and where the voltages in Eqn are the Hall voltages at positive field, minus the same Hall voltage at a negative field, i.e. averaged over the two magnetic field polarities, where the notation used is V H1±B = V H1 (B+) V H1 (B ) (3.11) For the Hall bar case, Eqn calculates the resistivity. The terms w and D are the Hall bar dimensions as shown in Fig. 3.4: w is the width of the bar and D the distance between

49 3.1: Magnetotransport Measurement of Carrier Transport Properties 29 two adjacent arm contacts (all adjacent arms being the same distance apart) resulting in the total length of the bar between the two contacts equal to 2D. These dimensions are set by the mask used for photolithographical processing. As before, t s is the thickness of the sample. The Hall coefficient is calculated using Eqn Voltages use the nomenclature given in Fig ρ = w t ( ) s V1 + V 2 V 3 V 4 2 D I 2 (3.12) R H = t s B I ( V H1±B + V H2±B ) (3.13) Assuming isotropic conduction in the x-y plane, the components, σ xx and σ xy, of the magnetic field-dependent conductivity tensor, σ, which represent the conductivity in the direction of the current and in the transverse direction, respectively, are then calculated from the experimentally determined resistivity and Hall coefficient and the magnetic field by the following equations: σ xx (B) = σ xy (B) = ρ ρ 2 + (R H B) 2 (3.14) R H B ρ 2 + (R H B) 2 (3.15) The conductivity tensor components, σ xx and σ xy, are then used in a quantitative mobility spectrum analysis (QMSA) to determine the contributions of distinct carrier species to the total transport properties, as well as the transport properties of each carrier species. This analysis is described in section Multiple Carrier Fitting When presented with a semiconductor material with multi-carrier conduction, we are still able to calculate the transport properties of each carrier if they have different mobilities or are of different type (electrons or holes). To do this the measurement must be conducted over multiple magnetic fields and then multi-carrier analysis techniques are applied. From Eqns. 3.14, 3.15, 3.2 and 3.3 presented in the previous sections, it is possible to express the conductivity tensor components σ xx and σ xy for a single carrier species as σ xx (B) = nqµ 1 + µ 2 B 2 (3.16) σ xy (B) = ±nqµ2 B 1 + µ 2 B 2 (3.17) with σ xy positive for a hole species and negative for an electron species. Note then that σ xy contains information about the charge of the carrier, whereas σ xx does not.

50 30 Chapter 3: Experimental Methods and Analysis Techniques In order to understand the multi-carrier fitting process, we define two basis functions, σ xx and σ xy which are ideal, normalised representations for a single carrier (they are similar to the equations above, normalised with respect to the conductivity nqµ of the carrier). 1 σ xx (µ, B) = 1 + µ 2 B 2 (3.18) µb σ xy (µ, B) = 1 + µ 2 B 2 (3.19) The basis functions show the form of the conductivity tensor components for a single carrier. Given in Figs. 3.6a and 3.6b are the basis functions σ xx and σ xy respectively, versus magnetic field for electrons with mobility 1 m 2 /Vs (10 4 cm 2 /Vs). The peak in σ xy and the maximum slope of σ xx occur at the same magnetic field, which is where the mobility and magnetic field are related by µb = 1 (3.20) with B in tesla and mobility in m 2 /Vs. These are the most identifiable features of the basis functions, and these features enable the identification of the mobility of the basis function. On a log scale for magnetic field, the basis functions for a carrier with a different mobility are simply a translation of the curves given in Fig A higher mobility shifts the curves to the left, a lower mobility carrier has curves that are shifted to the right. Note that for electrons and holes, the transverse conductivity, σ xy, is of opposite sign. For an electron the σ xy curve starts at zero and becomes negative with increasing magnetic field, while for a hole the σ xy would curve up into positive values. This dependence of σ xy on the sign of the carrier enables the Hall measurement to be used to determine the type of carriers in the material (most simply it dictates the sign of the Hall coefficient, for a single carrier, as positive for holes and negative for electrons). Physically, we can consider the mechanisms of the conductivity tensor components magnetic field dependence. As defined previously, σ xx represents the conductivity in the direction of the applied electric field (along the Hall bar for that sample configuration), while σ xy represents the transverse conductivity (across the Hall bar), perpendicular to both the electric and magnetic fields. For a sample with a single carrier species of mobility µ i, at zero magnetic field all carriers drift parallel to the electric field and σ xx is at its zero field (and maximum) value. As the magnetic field is applied and increases towards a value equal to 1 µ i, carriers divert from the path parallel to the electric field, and so σ xx decreases and σ xy increases. At the magnetic field equal to 1 µ i the transverse conductivity

51 3.1: Magnetotransport Measurement of Carrier Transport Properties 31 1!xx Magnetic field (T) 1 (a)!xx!xy (hole) 0!xy (electron) Magnetic field (T) (b) Figure 3.6: The basis functions of the conductivity tensor components for electrons with mobility 1 m 2 /Vs: (a) σ xx, (b) σ xy (σ xy ) is at its maximum. At magnetic fields beyond 1 µ i the carriers contribute less and less to conductivity in any direction, and thus both σ xx and σ xy decrease. Certain observations can therefore be noted for both σ xx and σ xy. Firstly, for σ xx : The conductivity tensor component at zero magnetic field is equal to the total conductivity of all carriers (σ o ). That is, σ xx (B = 0) = σ o (as σ xy (B = 0) = 0) The curve is strictly positive for all B The curve monotonically decreases (no negative magnetoresistance) The maximum slope is = σ 0 ln(10) 2 ( 1.15 σ 0 ) /decade

52 32 Chapter 3: Experimental Methods and Analysis Techniques while for σ xy : The maximum magnitude is = σ 0 /2 The maximum slope is = σ 0 ln(10) 4 ( 0.57σ 0 ) /decade The total conductivity in a multi-carrier sample is the sum of all of the individual carrier conductivities. The conductivity tensor representation allows us to write the total conductivity in a sample with m carriers as a linear combination of m basis functions, each shifted and scaled by the mobility and carrier concentration of each individual carrier species (with S i = 1 for holes and -1 for electrons): σ xx (B) = σ xy (B) = m n i qµ i σ xx (µ i, B) = i=1 m S i n i qµ i σ xy (µ i, B) = i=1 m i=1 m i=1 n i qµ i 1 + µ 2 i B2 (3.21) S i n i qµ 2 i B 1 + µ 2 i B2 (3.22) The conductivity of any individual carrier in a multi-carrier system is σ i = n i qµ i (3.23) The measured conductivity tensor components contain mobility and density information on all the carriers present in the material. For multiple carriers with different mobilities in the one sample, the force exerted by the magnetic field will be different for each carrier species. Higher mobility carriers experience a greater force and are therefore diverted more for a given magnetic field, reducing their contribution to the parallel conductivity and increasing their influence on the transverse. Carrier species with higher carrier concentration will have a greater influence on the conductivity (consider the basis function scaling by the concentration in the sums in Eqns and 3.22). At this point it is useful to note that while the semiconductor samples measured in either the Hall bar or van der Pauw configuration are required to be isotropic in the x-y (lateral) plane for the above analysis, there is no such requirement in the depth (z) direction, and samples may be non-uniform and/or layered in the z-direction. The Hall measurement, as presented above, does not provide any information on the depth resolution of carriers, and the assignment of a location to each carrier species within the depth of the sample requires information external to the Hall measurement. For this reason it is possible, and indeed useful, to consider the conduction in a given sample in terms of a two-dimensional areal

53 3.1: Magnetotransport Measurement of Carrier Transport Properties 33 density of (potentially multiple) carrier species rather than in terms of volume concentrations during the analysis. This does not change the analysis steps, and in fact simplifies the process as the different thicknesses of the areas of conduction of carriers do not need to be considered. In this case, the thickness in equations 3.5, 3.6, 3.10, 3.12 and 3.13 is assigned a value of 1, resulting in the calculated conductivities (σ xx, σ xy and the values of σ in the mobility spectra) being in the form of sheet (2D) conductivities. In mobility spectra where this is the case the symbol σ 2D is used to indicate the two-dimensional value, having the units Ω 1. The volume conductivity in Ω 1 cm 1 is obtained by dividing σ 2D by the thickness, t s, of the sample. Once carriers are identified after the QMSA stage of the analysis, it may then be appropriate, based on external assumptions or information, to divide the calculated sheet carrier densities by the thickness of the sample in order to calculate the carrier concentration throughout the entire sample volume (cm 3 ), such as for a bulk electron species, or to leave the sheet concentration in terms of a 2D density (cm 2 ), as is more applicable to a surface or interface carrier accumulation. Due to the 2D nature of both the 2DEG in the AlGaN/GaN HEMT samples, and the surface/interface electron species in the InN samples under study, the majority of the conductivities presented in this work as a result of multiple carrier analysis of Hall data are given as sheet conductivities. The final values of the carrier concentrations for the bulk electron species are presented as volume densities, while the values of surface and interface species are given in terms of sheet densities. For an example of how multiple individual carrier species combine to produce a magnetic field dependent set of data, let us consider a sample in which there are two electron species, such as in a sample of InN, assuming a bulk and surface electron species. In the following analysis example we consider all carrier concentrations in terms of sheet density and conductivities in terms of sheet conductivity. Let us consider a bulk electron species with sheet carrier concentration cm 2 (i.e cm 3 over a 1 µm thick sample, a typical example for InN) with a mobility of 2000 cm 2 /Vs. Let us also consider a surface electron species with sheet concentration cm 2 and mobility 500 cm 2 /Vs. The generated conductivity tensor components of each electron species (the basis functions, scaled and shifted according to the concentration and mobility of each species) are shown along with the sum total conductivity tensor components: σ xx in Fig. 3.7a and σ xy in Fig 3.7b. In the interest of clarity it is noted that the conductivities in Figs. 3.7a and 3.7b are sheet conductivities (as indicted by the units and the symbol σ 2D ). The sheet conductivity is equal to the conductivity divided by the thickness, t s, of the sample, which

54 34 Chapter 3: Experimental Methods and Analysis Techniques Sheet conductivity σ2d (Ω -1 ) 2E-2 σxx (total) 12 T σxx (bulk e - ) σxx (surface e 0 - ) -1E Magnetic field (T) Sheet conductivity σ2d (Ω -1 ) 2E-2 0 σxy (bulk e - ) σxy (total) -1E Magnetic field (T) (a) σxy (surface e - ) (b) 12 T Figure 3.7: The generated and the sum total conductivity tensor components ((a) σ xx, (b) σ xy ) for a sample with two electron species with transport properties ( cm 2, 2000 cm 2 /Vs) and ( cm 2, 500 cm 2 /Vs). simply scales the y-axis. The shapes of the curves are the same regardless of whether conductivity or sheet conductivity is plotted. The magnetic field of 12 T is also shown, which is the maximum magnetic field used in this work. It can be seen that while the peak response of the low mobility electron species is not reached at 12 T, there is still a changing influence on the total conductivity tensor at much lower field strengths. In the literature, [56] and [57] used magnetic fields up to only 4.5 T. Looking at Fig. 3.7 it can be seen that the change in the low mobility carrier is much smaller and therefore it is less likely to be accurately extracted. We can see that the magnetic field dependence of the total conductivity tensor components (σ xx and σ xy ) of the sample do not share the same shape as seen for a single (electron) carrier species in Fig Multi-carrier fitting, then, tries to solve the reverse problem: from the two (measured) conductivity tensor components, σ xx and σ xy, separate out the

55 3.1: Magnetotransport Measurement of Carrier Transport Properties 35 contributions from different carries, by fitting a sum of multiple scaled and shifted basis functions. The most simple method of fitting, usually referred to simply as multi-carrier fitting or MCF, assumes a number and type of carriers (e.g. two electrons, or one hole and one electron) and then uses the parameters of n and µ to fit the given number of carriers scaled and shifted basis functions to the measured conductivity tensor components. This type of fitting can quickly lead to values for the multiple species, but relies heavily on the correctness of the assumptions in order to obtain a good fit (and to give the true result). Fitting a single curve for each carrier s contribution also gives no indication of any spread that may exist in the mobility of the species. By contrast, a method was developed that enables the fitting of carriers to the measured conductivity tensor components without making any assumptions as to the number or type of carriers. This method was first outlined by Beck and Anderson (1987) [102] and referred to as mobility spectrum analysis (MSA). This analysis technique has since been developed further into a truly quantitative mobility spectrum analysis (QMSA) [53,55,103] and is discussed in the next section Quantitative Mobility Spectrum Analysis Techniques Quantitative mobility spectrum analysis (QMSA) is the method of finding a solution to the measured conductivity tensor components σ xx and σ xy in terms of electron and hole species with their independent carrier concentrations and mobilities. QMSA, in the most general sense, attempts to find the best simultaneous fit to both of the experimentally obtained conductivity tensor components by fitting a sum of appropriately scaled and shifted basis functions. QMSA converts the magnetic field dependent data into a visually meaningful transformed output, showing the conductivity density of electrons and holes in the mobility domain [55]. The algorithm is not required to make any a priori assumptions about the number or type of carriers present. This is advantageous in systems where the type or number of carriers is unknown or uncertain, yet also removes any presumptions that might be made in systems where the multiple carrier species are believed to be known. For single carrier systems QMSA is also useful because it can be used to find the best fit to data measured over a range of magnetic fields, eliminating errors that may arise from taking only one magnetic field measurement. The development of the QMSA technique is reviewed in detail by Antoszewski, Faraone, Vurgaftman, Meyer and Hoffman (2004) [55], covering early work by Beck and Anderson

56 36 Chapter 3: Experimental Methods and Analysis Techniques (1987) [102] on mobility spectrum analysis, to the development of QMSA by Antoszewski et al. (1995) [53] and the improved additions reported on by Vurgaftman et al. (1998) [103], which were adopted into the i-qmsa program eventually released by Lake Shore Cryotronics, Inc QMSA Technique Variants In this thesis the term QMSA is used to refer to the general technique of performing the quantitative mobility spectrum analysis. In the experimental work in this thesis the quantitative mobility spectrum analysis was performed using specific software programs that apply their own specific QMSA algorithm. They are either the i-qmsa software program from Lake Shore, or by an alternate High Resolution Mobility Spectrum Analysis implementation (HR.MSA) developed in-house by Dr. Umana-Membreno. The use of QMSA (the technique) implemented in these software packages has enabled the detection of, and the determination of transport properties of, multiple electron species in InN and of the 2DEG in AlGaN/GaN HEMTs. The term i-qmsa is used to refer to the computer program from Lake Shore that performs QMSA using the i-qmsa algorithm, based on the improved QMSA algorithm outlined by Vurgaftman et al. (1998) [103]. The i-qmsa algorithm first interpolates between the points given for σ xx and σ xy, and calculates the derivatives of the functions, before beginning an iterative fitting process to these four curves. i-qmsa uses a set of 80 mobility values, evenly spaced logarithmically between 100 and cm 2 /Vs in the fitting. The program outputs both the hole and electron mobility spectra and the resultant fits to σ xx and σ xy. It is important to look at the fit between the measured and calculated σ xx and σ xy conductivity tensor components as sometimes the fit can be very poor (often with data that has slight irregularities or odd points, or for incorrectly processed results for input data). In such a case the mobility spectra obtained are therefore meaningless. One restriction on the program is that it will not take input of magnetic fields greater than 10 T. In order to make use of magnetic field dependent measurements up to 12 T (which improves accuracy of low mobility carrier detection), sometimes in this work a scaling factor of 0.8 has been used to scale the magnetic field. Mathematically, this shifts the conductivity tensor component on a log scale (see description of the conductivity tensor component basis functions above), which after running the algorithm simply linearly scales

57 3.1: Magnetotransport Measurement of Carrier Transport Properties 37 the output mobility, as it is a linear transposition. The mobility is then also scaled so that the condition µb = 1 is maintained. The QMSA conducted in the latter part of this study (notably section 5.4) uses a newer algorithm that is slightly different in implementation to i-qmsa. This new version, which will be referred to as HR.MSA, is a further extension of the technique for which the development is well described in the review by Antoszewski et al. [55]. It is an iterative method, substantially different from prior methods. The algorithm is flexible in mobility domain points and in iterations. It should be noted that this current HR.MSA implementation requires far more processing time than the commercial Lake Shore i-qmsa software. The analysis in this thesis uses 201 points over 6 decades ( cm 2 /Vs) and to fitting iterations, dependent on how stable the fit is after a given number of iterations. It is found that in some cases by using this refined HR.MSA algorithm, in place of i-qmsa, it was possible to generate clearer and cleaner mobility spectra that fit with less error to the experimentally measured conductivity tensor components. As this version was not available until late in the work of this thesis, it is only the most recent results that take advantage of this version of QMSA Interpretation of QMSA Technique Outputs Each QMSA algorithm outputs two mobility spectra, one for holes and one for electrons. The mobility spectra show conductivity contributions to the total conductivity at given values of mobility, for both holes and electrons. When plotted, it is the graphical representation of the result of the fit of the scaled and shifted conductivity tensor component basis functions. An electron mobility spectrum generated by i-qmsa for a sample of InN is given in Fig There are two peaks in the mobility spectrum. In this spectrum the discrete values of mobility at which the solution is determined are shown by circles. Lines between the points are to highlight the peaks in the spectrum. Each peak represents a discrete carrier species. The assignment of each peak to a carrier species requires additional information, external to the Hall measurement. In Chapter 4 and Chapter 5, the assignment of peaks in the mobility spectra to bulk, surface or interface electron species is discussed, giving justification as to the assignment (and therefore not expanded upon in this chapter). The broadness of the peak demonstrates a range of mobilities which are required to obtain the optimal fit, which can show if there is a spread in the species throughout the sample. In InN, the crystal quality is not uniform with depth, and the peak for the bulk electron species is often found to be quite broad, as in this example where

58 38 Chapter 3: Experimental Methods and Analysis Techniques the peak ranges between mobilities of cm 2 /Vs. In all mobility spectra in this work the vertical axis plots conductivity (or sheet conductivity). This enables a visual comparison between peaks, where similar height demonstrates comparable contributions to the total conductivity. An alternate presentation, used for some mobility spectra published by other authors, plots the carrier concentration (of each point in the peak) on the vertical axis (using σ = nqµ at each discrete point). Like all measurement and subsequent analysis, results on transport characteristics involving QMSA should never be taken at face value. This is especially true for the QMSA technique, where unusual features in the measurement data and curiosities of the algorithm can easily manifest in unphysical or nonsensical results. One problem often encountered with QMSA is the appearance of ghost peaks in the hole and electron mobility spectra. Ghost peaks are peaks in the spectra that are highly unlikely to be actual carrier species. Ghost peaks most often result from abnormalities (and inaccuracies) in the measurement data that cannot be sensibly fit to, and therefore manifest as spurious peaks in the mobility spectra. One common cause is an increase in the slope of σ xx that is not accounted for in σ xy. Such an increase in slope suggests the influence of a new carrier, but if no extra change is seen in σ xy the only way to fit to this increased slope is by fitting both a hole and an electron at the same mobility. This results in no change in σ xy (consider how the hole and electron σ xy curves are equal and opposite), but presents two peaks in the mobility spectra, one in the electron spectrum and one in the hole spectrum, at the same value of mobility. Ghost peaks tend to occur more often in data obtained from van der Pauw sample structures, which was another reason the Hall bar structure was preferred for this work Extraction of Transport Properties from Mobility Spectra Each QMSA implementation outputs a hole and an electron mobility spectrum for each measurement analysed (as in Fig. 3.8) but the mobility spectrum representation is usually not the most useful for conveying representative values or trends with temperature. In many instances we wish to assign one value of carrier concentration and mobility to a carrier species, in order to compare samples and results, or to plot the temperature dependence of these parameters. While the carrier concentration is easy enough to consider, the mobility of a species as a whole is less obvious. The mobility spectrum may show a spread of mobilities within the peak assigned to a particular carrier (i.e. the broadness of a peak). Remembering that the QMSA programs output a mobility spectrum comprised of

59 3.1: Magnetotransport Measurement of Carrier Transport Properties 39 Sheet Conductivity conductivity (! σ2d -1 ) (Ω -1 ) 1E-2 1E-3 surface bulk 300 K 1E Mobility [cm 2 /(Vs)] Figure 3.8: The electron mobility spectrum generated by i-qmsa for an InN sample. conductivities at discrete mobility points, in order to choose one representative averaged mobility value of the whole peak, µ, we calculate a mobility weighted by the conductivity contribution of each mobility point in the peak. The carrier concentration of each electron or hole species is calculated from the sum of each point s contribution to the total concentration (Eqn. 3.24). To obtain a single value for the mobility of each carrier species (even though we clearly see a distribution is often a more accurate representation) we calculate a weighted average over the entire peak in the mobility spectrum, in order to represent the mobility of the carrier species as a whole (Eqn. 3.25). As explained earlier in this section, the analysis up to this point may be performed in terms of two dimensional parameters, leaving consideration of carrier depth distribution until the end. In such a case, the mobility spectrum is output in terms of sheet conductivity (σ 2D in units of Ω 1 ), such as that in Fig. 3.8, from which the extracted carrier concentrations are in terms of sheet density (N in units of cm 2 ). If thickness is included from the start, the mobility spectrum will give conductivity (σ in units of Ω 1 cm 1 ) on the vertical axis, and extracted carrier concentrations will be volumetric (n in units of cm 3 ). If the mobility spectrum is generated The carrier concentration, n, and mobility, µ, of each species (i.e. each peak) are calculated from the i points in the mobility spectrum peak for that species by the following equations: n = i µ = 1 qn σ i qµ i i σ i (3.24) (3.25)

60 40 Chapter 3: Experimental Methods and Analysis Techniques We can also calculate the percentage contribution to conduction of each carrier species. Using the conductivity of each species (nq µ) and the total conductivity (σ xx at zero magnetic field = σ 0 ) we calculate the percentage contribution of each carrier species as: σ % = nq µ σ (3.26) As the QMSA algorithms work towards a low error fit, the conductivities of the various carrier species as determined by the peaks in the mobility spectrum may not always add to 100 % of the zero field conductivity. However, the carriers extracted from the mobility spectrum do represent the best fit to the experimental data over all magnetic fields (of which the zero field conductivity is only part). Error analysis of measurement results that have employed QMSA is extremely difficult. As mentioned previously, sources of error in the raw data (for example due to contact size, or simply due to fluctuations in current or temperature) can all influence the calculated conductivity tensor components which can then propagate through the QMSA fitting procedure. Errors in both the raw data and the fitting algorithm can result in an uncertainty in mobility values, changes of peak width (broadening or narrowing a carrier mobility distribution) as well as (in more extreme cases) the generation of significant ghost peaks [102]. There exist no models capable of adequately translating errors in measurement and fitting through to the final mobility spectrum representation [104]. It is a complex transform and formal error analysis of QMSA remains in its infancy. As a result, it is not appropriate to attempt to apply error bars to either of the extracted transport parameters, carrier concentration or mobility. The mobility, especially, as an extracted parameter is a weighted average over a peak (often a broad peak) that demonstrates a multitude of actual carrier mobilities in the sample, and an error bar is not applicable when discussing such a mean value. The mobility is extracted and given a single value only for the purposes of comparison between temperature and samples. It would be possible to define either a standard deviation or full-width at half-maximum to describe the width of a mobility peak, but such definitions are not errors, and are not ever used in any standard way in the presentation of QMSA data, so their use would most likely lead to more confusion than clarity. Ultimately the most information remains, and is best represented, in the mobility spectrum: the location and shape of the peaks. This is analogous to the spectra produced as part of deep level transient spectroscopy, now a standard method of defect measurement, where the spectra need to be presented along with the quantitative analysis to be able to compare devices.

61 3.1: Magnetotransport Measurement of Carrier Transport Properties Single Field Hall Measurement with Multiple Carriers A single-field Hall measurement uses the measured Hall coefficient at a single magnetic field, R H, and the zero-field resistivity, ρ, to calculate the carrier concentration, n SF, and mobility, µ SF, by the standard formulas: n SF = 1 q R H (3.27) µ SF = R H ρ (3.28) As the single-field conductivity (σ = qnµ) is simply a sum of the conductivities of the various carrier species, the single-field values for n and µ are the sum of the various carrier species values (call them n j and µ j for j different species), weighted by the other parameter, so that q n SF µ SF = σ SF = σ surface + σ bulk + σ others = j σ j (3.29) gives n SF = j n j µ j µ SF (3.30) and µ SF = j µ j n j n SF (3.31) In the above analysis, all carrier concentrations are given as volumetric quantities throughout the entire sample thickness (cm 3 ). It should always be noted that results presented in the literature from single field Hall measurements give only averages of carrier concentration and mobility when multiple carriers are present. These averages are generally not representative of any one species. In InN, the bulk electron species is not well represented by the single-field Hall measurement, as the influence the surface accumulation has on the single field calculated properties can be significant, and such influence is not constant across samples with different properties (such as thickness or the bulk electron species concentration).

62 42 Chapter 3: Experimental Methods and Analysis Techniques 3.2 Silicon Nitride for Surface Passivation Introduction The passivation of AlGaN/GaN HEMTs is required to mitigate a build up of negative charge at the surface of the device which contributes to a phenomenon known as current collapse. Current collapse is seen as a reduction in the output power and frequency response at high operating frequencies compared to DC output values [65, 66, 105, 106]. Silicon nitride (Si 3 N 4 or SiN x ) has been used frequently as a surface passivation material for AlGaN/GaN HEMTs, and though it is not the only dielectric used as a passivant, it is by far the most common. While the primary goal of early SiN x passivation was to reduce current collapse, other benefits were also seen such as increased 2DEG concentration, improvements in breakdown voltage and improvements in reliability during annealing studies. The requirements for the passivation of AlGaN/GaN HEMTs and results from the literature are discussed in more detail in Chapter 6, and the experimental work of this thesis in AlGaN/GaN heterostructure passivation is presented in Chapter 7. Some early reports on the use of SiN x in the literature include [65, 70, 79, 80, ]. The continuing incorporation of silicon nitride in varied HEMT device designs warrants exploration into how modification of the film properties through deposition conditions can affect the 2DEG transport properties and be optimised for the required applications. The most widely available method of SiN x deposition is PECVD, and yet little work has been done to improve or investigate its properties beyond identifying the damaging effects of low frequency deposition. In this work the deposition parameters of PECVD SiN x are investigated as a means of determining the range of change in transport properties that can be induced, with the goal of optimising PECVD SiN x for use in various AlGaN/GaN HEMT applications. A significant difference in SiN x thin films that can be obtained by changing deposition parameters is the stress in the film. SiN x films can be deposited with stress that can range from highly compressive to highly tensile. The development of silicon nitride thin film technologies at the Microelectronics Research Group (MRG) at The University of Western Australia (UWA) has constituted a major part of the engineering of micro-electrical-mechanical systems, or MEMS, for various applications such as tuneable optical cavities. These applications have required a thorough and detailed investigation of mechanical, optical and electronic properties of the silicon nitride that can be deposited in the available plasma system. Substantial development

63 3.2: Silicon Nitride for Surface Passivation 43 and publication of the silicon nitride technology at The University of Western Australia has been performed by K. J. Winchester [118] and M. Martyniuk [ ]. Continued development of silicon nitride is reported on in the works of B. A. Walmsley [ ], J. S. Milne [126] and R. J. Westerhout [127]. There is therefore a wealth of existing understanding about the MRG silicon nitride which can be leveraged for the investigation of passivating AlGaN/GaN heterostructure materials with SiN x films of varying stress. The three SiN x films used in this work, presented in Chapter 7, were chosen based on this experience and understanding Deposition of Silicon Nitride by Plasma Enhanced Chemical Vapour Deposition (PECVD) The deposition of silicon nitride at UWA is performed by plasma-enhanced chemical vapour deposition (PECVD). Plasma-enhanced chemical vapour deposition works by inducing a plasma of ions in a vacuum chamber by means of a radio-frequency (RF) power source. The parallel-plate chamber consists of a base plate (anode) electrically separated from the walls of the chamber and the top plate (cathode). The reactant gases are fed into the chamber through the top electrode, forming a plasma of reactant ions in the RF field. The reactants reach the substrate of the base plate by means of both diffusion and acceleration by the electrical field generated by the same RF source that generates the plasma. This configuration is shown in Fig At the surface of the substrate on the heated base plate, the reactant species (charged ions and electrons, as well as neutral molecules) obtain enough energy to undergo chemical reactions to initiate the formation of a thin film. The activation energies of the surface reactions are a function of both temperature and ion bombardment energy [119]. In the parallel-plate configuration, the energy of the ion bombardment and the energy controlling the plasma cannot be controlled independently. The ion bombardment of the reactive species also contributes to damage (and desorption) of both the substrate and thin film [119]. Deposition conditions have therefore been optimised to produce the highest quality films. The PECVD deposition system used in this work is an Oxford Instruments PECVD 80. Precursor gases used for the deposition of silicon nitride are silane (SH 4 ), ammonia (NH 3 ) and nitrogen (N 2 ). The deposition temperature (of the base plate) can be controlled between 50 C and 300 C, the pressure of the chamber controlled between 300 and 900 mtorr, and the RF power set from 50 to 200 W with a fixed frequency of MHz.

64 44 Chapter 3: Experimental Methods and Analysis Techniques Matching network RF Power MHz plasma Precursor gas in Sample Throttle Heater Pump Figure 3.9: Schematic diagram of the PECVD chamber used for deposition of SiN x in this work [127]. Films deposited at this frequency have been shown not to cause damage to the AlGaN surface, unlike films deposited at low frequency (100 khz) [128] SiN x Thin Film Material Properties The PECVD deposition process is conformal, meaning the deposited silicon nitride has an equal thickness on all surfaces, including side walls. The silicon nitride deposited via PECVD is amorphous, having no crystalline qualities, and thus the interface between the silicon nitride and the AlGaN is likely to be at best only partially ordered. Though referred to as silicon nitride, the films deposited in a PECVD system contain large amounts of hydrogen and are not stoichiometric silicon nitride (Si 3 N 4 ) films. For this reason PECVD silicon nitride is generally referred to as SiN x, where the x indicates non-stoichiometry and incorporation of impurities such as hydrogen. Martyniuk [119] determined atomic compositions of UWA PECVD SiN x films by heavy-ion elastic recoil detection analysis and found hydrogen incorporation ranged from 38 % for films deposited at 100 C, down to 20 % for films deposited at 300 C. Above 100 C oxygen incorporation was minimal. Hydrogen incorporation in PECVD SiN x films is a direct result of the hydrogen-rich precursor gases (SiH 4 and NH 3 ) that are used. PECVD SiN x is easily wet-etched by buffered oxide etch (BOE), which in this work is a 16 % buffered solution of hydrofluoric acid (HF). Alternate methods of depositing silicon nitride are used in other laboratories. MBE silicon nitride can be accurately referred to as Si 3 N 4 as it is likely to be close to stoichiometric.

65 3.2: Silicon Nitride for Surface Passivation 45 a0 acompressive atensile a0 a0 Figure 3.10: Visualisation of the influence of thin film stress (compressive or tensile) on the curvature of a thin film/substrate bi-layer [119]. Most other deposition methods will give non-stoichiometric silicon nitride, which should be, but is not always, more accurately designated by the abbreviation SiN x Thin Film Stress The stress in thin films can be considered by looking at a bi-layer structure, in which the top layer is the thin film, which has some inherent stress. In a nominally unstressed thin film, during deposition of the film, the constituents adhere to the substrate separated by some equilibrium distance corresponding to the lowest energy. This separation is shown as a 0 in Fig If the constituents of the thin film arrange themselves during deposition at distances greater than a 0, the resultant film will be under tensile stress. Providing the adhesion of the film to the underlying substrate is not compromised, then the relaxation of the stress in the thin film will result in bending of the substrate. For a tensile stress deposition, the particles will tend to draw together in order to relieve the stress and approach the equilibrium distance a 0. This will cause the substrate to bow upwards, in a concave fashion, as shown on the right in Fig Correspondingly for compressive stress deposition, the constituent particles will be deposited closer together than a 0, and the particles will spread apart in order to approach a zero stress scenario. This will cause the substrate to bow downwards, in a convex fashion, as shown on the left in Fig [119].

66 46 Chapter 3: Experimental Methods and Analysis Techniques The total stress of a thin film is the sum of both intrinsic and extrinsic components. Intrinsic stress is due to the internal structure of the film. It is a complex consideration, but for the purpose of this work can be considered using the simple model described in Fig. 3.10, in which the deviation of the particle deposition distance from a 0 causes stress in the film. Extrinsic stress consists of two components: externally applied forces, which in this work is always zero, and the thermal stress arising from changes in temperature. Assuming there is and remains good adhesion between the thin film and the substrate, changes in temperature (such as the cooling of the sample after deposition) will introduce thermal stress due to the difference in the thermal expansion coefficients of the substrate and the thin film. The thermal expansion coefficients of silicon and silicon nitride are very similar (down to 77 K) and thermal stress in that system is very low. The thermal expansion coefficients of sapphire, GaN, AlGaN and SiN x all differ, and therefore the thermal expansion of the sapphire/gan/algan/sin x system is more complex than in the Si/SiN x case, so some thermal stress will be introduced. It is assumed to be small compared to the intrinsic stress Silicon Nitride Film Stress A silicon nitride thin film can be deposited with tensile, compressive or negligible stress, comprised of both intrinsic and extrinsic components. The attributes of the SiN x thin film can be altered by changing the PECVD deposition conditions. The intrinsic stress, due to the internal structure of the film (related to particle separation distance), is the primary stress altered by changing deposition conditions, though extrinsic stress is also introduced due to the difference in thermal expansion coefficients of the thin film and the substrate as the sample cools from the deposition temperature. The work of Martyiuk [119] shows that the primary contribution to the internal stress of the film is the deposition temperature. At high temperatures ( 300 C) films exhibit tensile stress. Lowering the temperature of deposition reduces the tensile stress in the film. Very low stress films can be achieved at 200 C. Lowering the deposition temperature further causes the film stress to change from tensile to compressive, and high quality compressive films can be deposited at 125 C. This deposition temperature has been the focus of considerable investigation at UWA for use in HgCdTe devices which require low temperature processing (< 150 C), leading to quality films being achievable at this unusually low PECVD deposition temperature. In addition to the temperature, the other deposition conditions such as power and pressure can be altered to control the stress of

67 3.2: Silicon Nitride for Surface Passivation 47 the SiN x. In order to achieve suitably stressed SiN x films in this work, multiple deposition conditions were changed between films. Control of the quality and reproducibility of the neutral stress and low temperature SiN x have been accomplished by J. S. Milne [126] and R. J. Westerhout [127] respectively, and this expertise has been used to provide high quality SiN x films of varied stress for the samples studied in this work. The deposition conditions of each film used in this work are given with the experimental work in Chapter Thin Film Stress Measurement In a bi-layer system consisting of a thin film with intrinsic stress on a substrate (assuming good adhesion), the stress of the thin film will cause the substrate to bow, as discussed above. The resultant radius of curvature of the bi-layer, R, is related to the thin film residual stress, σ f, according to the Stoney formula [119, 129] σ f = M s d 2 s 6R d f (3.32) where d f is the thickness of the thin film, d s is the thickness of the substrate and M s the biaxial modulus of the substrate. Note the thin film stress is not dependent on the thin film s biaxial modulus. The Stoney formula is based on several assumptions: The substrate and thin film are (at least in the transverse direction), homogenous, isotropic and linearly elastic The thickness of the film, d f, and the thickness of the substrate, d s, are laterally uniform and both are very small in comparison to the lateral extent of the system d f d s The substrate thin film system is mechanically free and at uniform temperature The internal stress is laterally homogenous and equi-biaxial as well as constant throughout the film thickness The substrate without the film has zero curvature and The deformations are negligibly small,

68 48 Chapter 3: Experimental Methods and Analysis Techniques which are all applicable in this work. By measuring the radius of curvature and the thickness of the thin film it is possible to calculate the magnitude of the stress. The stress of the SiN x thin films was measured as deposited on 100 µm -thick silicon, which had been placed in the deposition chamber at the same time as the AlGaN/GaN samples under study. The use of such thin silicon is to obtain the maximum curvature of the SiN x film on the silicon substrate (see Eqn. 3.32), in order to improve accuracy in the measurement of the radius of curvature of the silicon and thus calculation of the stress of the SiN x film. The sapphire substrate of the AlGaN/GaN samples is much thicker, and has a greater elastic modulus than silicon, so less bending occurs and measurement of the curvature would be far less accurate. As the thickness of the SiN x films is on the order of 200 nm (d f ), the 100 µm (d s ) silicon substrate still fulfils the requirement of d f d s mentioned above. The 100 µm silicon used as a substrate for measurement has been investigated previously and the thickness and biaxial modulus are known [119]. The thermal expansion coefficients of silicon and silicon nitride are identical (down to 77 K), but the thermal expansion coefficients of sapphire, GaN, AlGaN and SiN x all differ, and therefore the thermal expansion of the sapphire/gan/algan/sin x system is more complex than in the Si/SiN x case. This will mean that any extrinsic stress in the HEMT/SiN x system due to thermal change of lattice constants during cooling from the deposition temperature will be different than in the Si/SiN x system. It is expected, though, that the general trend of the final, total, film stress was the same on the AlGaN/GaN heterostructure as on silicon. The type of stress, tensile or compressive, results from the direction of bowing, as shown in Fig The radius of curvature was measured using a Zygo optical profilometer (NewView 6300). It uses an interferometric technique to measure the differences in height across a sample. Using the software provided with the tool, a radius of curvature could be easily fit to the surface profile of the test samples.

69 Chapter 4 Indium Nitride 4.1 Introduction The group III-nitride compound semiconductor material system has a number of highly attractive fundamental properties, such as direct band gaps, radiation hardness, chemical and physical stability as well as efficient operation of electronic devices despite high crystal defect densities [24, 130]. Many of these properties are already well explored in gallium nitride (GaN), aluminium nitride (AlN), the alloy Al x Ga 1 x N and to some degree In x Ga 1 x N and In x Al 1 x N. As previously discussed in section 1.1, these properties are exploited to fabricate a variety of devices, from LEDs, lasers and UV detectors to highpower, high-speed transistors. Such favourable properties are both under-explored and under-exploited in indium nitride (InN). Utilising the favourable properties of InN along with its characteristics, different to GaN and AlN, with the potential for integration into existing III-nitride technologies, will position InN as a semiconductor material of interest for new device applications. As discussed in section 1.2, InN is only recently experiencing a resurgence of interest and intense research. Previously, poor crystal quality (usually polycrystalline) material hampered efforts to fabricate useful devices. Single-crystalline films were only able to be achieved by more advanced growth methods, with the earliest developments in 1989 [131, 132]. Interestingly, these single-crystalline InN films showed some markedly different characteristics to the polycrystalline films, particularly for characteristics that are far more applicable to making devices. The electrical characterisation of InN is thus essential for the development and understanding of the effects of growth techniques in order to improve the material quality for 49

70 50 Chapter 4: InN future devices and applications. In this thesis (Chapter 5) the influence of growth conditions on electron transport is explored experimentally, and so understanding of growth methods and growth issues are essential for this work. The existence of multiple electron species in all samples of InN (a high background electron concentration and an accumulation of electrons at the surface on all samples) complicates electrical characterisation. This chapter explores the origin of these properties and why it is important to be able to measure them more accurately. In particular, areas are highlighted in which InN material characterisation is lacking in the reported literature, some of which will be addressed by the work in this thesis in Chapter Significant Properties of InN Interest in indium nitride begins with favourable material properties and the subsequent device possibilities, the most important of which are listed below. Many of these properties are detailed in more depth later in the chapter. Low band gap ( 0.65 ev) [32 34] Current generation optoelectronics such as light emitting diodes (LEDs) and lasers already incorporate Ga-rich In x Ga 1 x N both for tuning to longer wavelengths and because the incorporation of In into the active GaN layers considerably increases luminescence efficiency [24]. InN and In-rich InGaN will enable the extension of III-nitride based optoelectronics from the current range of UV, blue and green and extend it through to the yellow, red and infrared regions of the spectrum. This has the potential to mean devices from III-nitrides could tune across the entire visible spectrum (and beyond into both the UV and IR), a feat no other material system can match. The low band gap of InN is promising for enabling the development of III-nitride optoelectronics that are compatible with optical fibre wavelengths, an important passband for commercial applications and commercial viability. InN will benefit not only light emitting devices, but would extend the range of device possibilities in multispectral III-N photodetectors. In particular, high efficiency multijunction solar cells incorporating all of the III-nitrides, and thus absorbing energy over most of the solar spectrum, are highly desirable for satellite electrical power. Superior transport properties to GaN, AlN and GaAs Theoretical calculations have shown that InN is expected to have the highest electron mobility of the III-nitrides [36,37,39,133,134], with mobility calculated to reach

71 4.2: Significant Properties of InN 51 as high as cm 2 /Vs at room temperature (RT) if low doped, uncompensated, dislocation-free material can be achieved [40, 41]. This is largely due to the low effective mass of electrons in InN (determined as 0.07 m 0 in intrinsic InN [130,135], but with values as low as 0.04 m 0 used in the literature [40]), lower than the effective electron mass in GaN and AlN. The peak drift velocity at 300 K in InN is calculated to be greater than for GaN or AlN ( cm s 1 vs 2.9 and cm s 1, respectively [134]), and both the peak and saturation drift velocities are much higher even than those of GaAs, a material often used to make very high frequency devices [36,37,134] (InN calculated saturation drift velocity is cm s 1 while for GaAs the calculated value is cm s 1 [37]). Additionally the drift velocity of electrons in InN is calculated to be far less sensitive to variations in temperature and doping concentration than in GaAs [36]. Such transport properties are obviously advantageous for transistor device applications, such as cm- and mm-wave devices, as a higher mobility (µ) enables higher frequency operation. The velocity (v) of the electrons in the channel of a transistor is equal to v = µe (in the linear low field region). The electric field (E) is limited by the applied voltage, which is limited by material and physical factors. A greater velocity can therefore only be achieved for a given electrical field by an increase in the mobility of the electrons. The superior transport properties of InN also extend to In-rich InGaN. It is predicted that the cutoff frequency of InN-based FETs could easily reach up to 1 THz for 0.1 µm gates [37]. No toxic elements InN has further advantages over GaAs and other low band gap III-Vs in that it contains no toxic components (such as arsenic or phosphorus). Depending on the processing recipes used, it could also be fabricated into devices without employing toxic gases for processing (such as phosphine or chlorine). Native surface electron accumulation As discussed later in this chapter, InN exhibits a native accumulation of electrons at the surface due to the nature of the band structure. While often seen as a hindrance to measurement of bulk properties, there is no doubt that the surface accumulation lends InN to many interesting applications, such as low resistance contacts, strong terahertz surface emission and use as a sensor material.

72 52 Chapter 4: InN 4.3 Growth of Indium Nitride Early Methods The ability to grow high quality single-crystal indium nitride contributed to the resurgence of interest in the material. Such growth has only been recently achieved through the development of advanced semiconductor growth technology. Previous lack of interest in InN and the difficulty producing high quality single-crystal material is introduced by considering the evolution of InN production. The evolution of the InN growth process is outlined below. The early work is detailed by Bhuiyan, Hashimoto and Yamamoto [24] in their 2003 review, and reference only to the most significant developments are given here Powders The first attempts at synthesising InN produced powder or small crystals. The first such attempt, obtaining InN from InF 6 (NH 4 ) 3, was performed in 1938 by Juza and Hahn [26], who reported the crystal structure to be wurtzite. Further attempts at InN synthesisation were made between 1956 and 1969 in other works (see [24]). Initial attempts were poor, as direct reaction of N 2 molecules with indium does not take place even at very high temperatures. Instead early methods made use of indium compounds reacting with ammonia, or of the thermal decomposition of complex compounds containing both In and N, obtaining a InN powder or small crystals. Recently, Bai et al. [136] have revisited such chemical methods and used a solvo-thermal method to prepare InN nanocrystals with mixed wurtzite and zinc blende phases by using the reaction of InCl 3 and Li 3 N at 250 C with xylene as the solvent RF-Sputtered Films and Early Epitaxial Methods The work of Hovel and Cuomo [25], published in 1972, resulted in the earliest epitaxial sample of InN with measurable electrical properties. Reactive RF-sputtering of metallic indium in a nitrogen plasma onto sapphire and silicon substrates between 25 and 600 C produced polycrystalline InN films with highly preferred orientation, as shown by x-ray diffraction. Through the late 1970s and 1980s many groups further contributed to the growth of polycrystalline InN epitaxial films through methods such as RF-sputtering, reactive evaporation, electron beam plasma techniques, reactive cathodic sputtering and chemical vapour deposition (using InCl 3 and NH 3 ). Optical and electrical properties of

73 4.3: Growth of Indium Nitride 53 these films were measured to have band gaps around 1.9 ev, n-type concentrations in the to cm 3 range and mobilities < 100 cm 2 /Vs, with the exception of some films grown by Tansley and Foley [30, 31] with much lower carrier concentrations (these results are discussed in more detail later in the chapter) Single Crystal Growth Bhuiyan, Hashimoto and Yamamoto [24] found the first single crystal growth of InN was as early as 1989 by Matsuoka et al. [131] and Wakahara et al. [132] by plasma-assisted metal-organic vapour phase epitaxy (MOVPE). Since then much progress has been made in single crystal growth, by the advanced methods of either MOVPE or by molecular beam epitaxy (MBE). InN grown by these methods has far less oxygen incorporation than sputtered films, and is single rather than polycrystalline, leading to reduced background unintentional n-type doping. The growth of InN by metal-organic vapour phase epitaxy (MOVPE), also known as metalorganic chemical vapour deposition (MOCVD), has developed significantly over the past couple of years. Generally the source used for In is trimethylindium (TMI) while nitrogen is supplied by ammonia (NH 3 ), with nitrogen (N 2 ) as a carrier gas. Some reactors also make use of a plasma source for N 2 (plasma-assisted MOVPE), but currently the best MOVPE InN films reported do not use it. Growth temperatures are similar to MBE material, around C, with the most popular for high quality being C. At this stage the transport properties of MOVPE material (indicative of crystal quality and impurity incorporation) cannot match those of MBE material. MBE material is believed to have less impurity incorporation than MOVPE material [24]. Other techniques to produce single crystalline InN that have been reported on include: a hybrid-mbe with metalorganics instead of solid sources for the group III elements known as MOMBE (metalorganic molecular beam epitaxy, or chemical beam epitaxy) [137, 138]; high-pressure chemical vapour deposition (HPCVD) [139], which also uses metalorganics in a high-pressure carrier gas to grow InN at temperatures up to 1150 K at 15 bar; and migration enhanced epitaxy (MEE) [140]. Current high quality crystal material is grown by MBE and MOVPE, but the most advanced material (best crystalline and electrical properties) is all grown by MBE [24, 130, 141]. All InN studied in this thesis is grown by MBE, and discussion of issues relating to the growth of high quality InN films is restricted to practices outlined in the literature covering MBE growth.

74 54 Chapter 4: InN Growth by MBE InN MBE chambers most commonly use plasma-assisted MBE, in which the active nitrogen is provided by a plasma source. Indium, gallium and dopants such as magnesium are supplied by standard thermal effusion cells Substrate and Buffer Layers Much work has been carried out on finding and developing optimal substrates and buffer layers for InN growth. Currently the most common substrate used is sapphire, due to its affordability, availability and prevalence in the growth of GaN-based materials. The lattice mismatch between InN and sapphire is, however, around 25 % [142], even greater than the 14.8 % mismatch between GaN and sapphire [143]. Also used with some regularity is SiC, again due to its widespread use in the growth of GaN. Growth on alternative lattice matched substrates such as yttrium-stabilised zirconia (YSZ) (2.5 % mismatch) have also been reported [62], though at this stage their use is not widespread. Growth on (111) Si is also of interest due to a small lattice mismatch (8 % [24]) and low cost of substrate, but in general III-nitride growth on Si is not a mature technology. Typical substrate preparation includes either simple nitridation of the substrate in the MBE chamber (which in the case of sapphire produces AlN), or, more commonly, the growth of buffer layers by both MOCVD (ex-situ GaN templates) and/or in-situ by MBE. Buffer layers of GaN [141], AlN [142] and low temperature InN are all reported for sapphire substrates, and GaN buffers for growth on SiC [34, 144], while growth on YSZ substrates occurs directly with no buffer layer. The use of GaN or AlN buffer layers greatly improves the crystal quality of InN, as the lattice and thermal mismatches between InN and GaN/AlN are much smaller than for sapphire (InN/GaN has an 10 % lattice mismatch, InN/AlN is 13 % [145], while InN/sapphire has a 25 % lattice mismatch [142]). Buffer layers provide a high density of nucleation centres and promote the lateral growth of the main epilayer, improving the crystal quality of the InN [24]. Reports of improved crystal quality with buffer layer engineering (without changing other growth conditions) strongly suggest the improvement of InN film quality is more dependent on surface morphology and crystal quality of the buffer layer than it is on growth mechanism [24, 142].

75 4.3: Growth of Indium Nitride MBE Growth Temperatures and Flux Regimes The two possible polarities of c-plane InN (In-face or N-face) were introduced in section 2.3. Optimal MBE InN growth temperature depends on the polarity of the film grown. In-face (0001) InN films are limited to growth below 540 C [146] due to thermal decomposition, and are usually grown between 440 and 500 C. N-face InN (000 1) can withstand temperatures around 100 C higher, with thermal decomposition inhibiting growth beyond 635 C [144]. N-face InN is grown at higher temperatures than In-face, usually between about 530 and 600 C [34]. Growth regimes are also dependent on polarity. In-face films have two distinct growth regimes, as reported by Gallinat et al. [141, 146]. The In-rich In-droplet regime is characterised by step-flow growth (spiral hillock) and relatively flat surfaces. A 2.5 monolayer (ML) In adlayer was observed during In-droplet growth, which suggests that an In wetting layer is necessary for step-flow growth. The N-rich regime is characterised by rough, three-dimensional surfaces. No In adlayer or droplets were observed ex-situ in N-rich samples, which suggested a dry surface free of excess In during growth [146]. The growth regime and growth temperature of In-face InN therefore affects the crystal formation and quality, and by extension the transport properties of the material. The effect of both temperature and growth regime on electron transport in In-face InN was studied as part of this work and is presented in section 5.3. The growth of N-face InN by MBE was investigated by Koblmüller et al. (2006) [34] between 530 and 595 C, in both N-rich (In/N flux ratio = 0.9) and In-droplet (In/N = 1.4) regimes. AFM studies of the surface morphologies revealed that In-droplet growth conditions resulted in lower surface roughness than N-rich growth. The 530 C In-droplet sample had large atomically-flat terraces with clear step-flow growth features (characterised by arrays of curved terraces, as part of spiral growth hillocks), separated by occasional pits and coalescence boundaries. With a higher temperature in the In-droplet growth regime, the InN surface increased in roughness and a higher density of metallic In droplets was observed, due to the greater thermal dissociation of InN at this temperature. The growth in the N-rich regime, by contrast, was much better at the higher growth temperature, with terrace-like surface structures showing step-flow features, suggesting that there was high surface diffusion of In and N atoms even in that N-rich regime. Koblmüller et al. cited the optimal growth conditions for N-face InN to be at 535 C with a In/N ratio of 1.4. Koblmüller et al. (2007) [144] then further investigated the growth diagram for N-face InN and found that in addition to a dry N-rich growth phase, an In adlayer terminated phase

76 56 Chapter 4: InN existed at higher temperatures for similar In/N flux ratios, as well as the In-rich regime of simultaneous In adlayer and In droplets on the surface during growth. The effect of the growth regime used in the growth of N-face InN on the electrical transport properties is covered in section Electrical Properties The electron affinity of InN, 5.8 ev, is larger than that of any other known semiconductor [130]. Coupled with its low band gap, InN is placed in a unique position. The Fermi stabilisation energy (E FS ) lies deep (0.9 ev) within the conduction band of InN, unlike most semiconductors in which it resides within the band gap (see Fig. 4.1). The only other semiconductor in which E FS is located within the conduction band is InAs, however only by 50 mev [147]. This position of E FS has a profound effect on the formation of donors within and at the surface of InN, and is discussed in the following sections. Knowledge of the relationship between the band edges of InN and the Fermi stabilisation energy is important for understanding the origin and behaviour of the bulk and surface electrons in InN, which is of use in interpreting the measured electrical properties in this work. Figure 4.1: Positions of the valence band maxima and conduction band minima for GaN, InN, GaAs and GaInP and the position of the Fermi stabilisation energy (E FS ) relative to E vac (-4.9 ev) [49].

77 4.4: Electrical Properties Band Gap Evolution, Measurement and the Burstein-Moss Effect It is not possible to fully appreciate the current intensity of interest in InN without addressing the band gap debate. The band gap of InN is of great importance for future device possibilities. It was the emergence of evidence for new, revised, material parameters (especially band gap) with the growth of the first high quality single crystalline InN films that stirred controversy and generated a resurgence of interest in InN. Early growth of InN (generally by sputtering) resulted in InN films with measured band gaps of 1.9 ev. One of the earliest reported band gap measurements was by Trainor and Rose (1974) [148] who used reactive evaporation to grow InN on sapphire and reported optical and electrical properties. They determined that InN is a direct band gap semiconductor, with a fundamental band gap of 1.7 ev. Work by Tansley and Foley [31], who published many of the most significant results at the time, measured the band gap at 1.89 ev ± 0.01 ev for polycrystalline material with a reported carrier concentration of cm 3. Early band gap studies were carried out by measuring the optical absorption edge. The square of the absorption coefficient, α, has a linear dependence on photon energy, ω, for direct band gap material (such as InN). The extrapolation to zero of the fit of α 2 to the linear portion of the data gives the band gap. The band gap of a material can also be found from the peak of the photoluminescence (PL) spectra. Photoluminescence in InN was not reported until It was thought at the time that the InN film quality was too poor for photon emission. Figure 4.2 [86] shows the evolution of the measured band gap of InN samples over time. We can see that in the early years, pre-2000, when RF-sputtering was the predominant film deposition technique, the reported band gap for InN remained constant at a value of around 1.9 ev. Post-2000, however, when growth techniques such as MBE and MOVPE were developed for InN, the ability to successfully deposit single-crystalline InN films was obtained and the band gap that was measured and reported dropped dramatically. The accepted value is now beginning to stabilise at around 0.65 ev as material quality improves further. Even prior to improved crystalline growth by MBE, there was early speculation that the band gap of InN was incorrect. The growth by MOCVD of InGaN alloys with increasing indium content unexpectedly showed band gaps rapidly decreasing with increased In content [131], which suggested the band gap of InN should be well below 1.9 ev. It was

78 58 Chapter 4: InN 2.0 Band Gap (ev) RF sputtered InN (poly-crystalline) MBE-grown InN (single-crystalline) Year Figure 4.2: Evolution of measured InN band gaps over time [24,25,31,33,34,141,148,150, 153]. explained by an unconventionally large bowing parameter [131, 149]. It was, however, only with the MBE growth of thick InN with reduced electron concentrations and higher mobilities that the band gap could finally be established at a much lower energy gap with compelling evidence by multiple researchers [32, 35, 138, ]. Even as recently as 2003 in their review paper, Bhuiyan, Hashimoto and Yamamoto [24] were still not convinced by the evidence presented that the band gap of InN was indeed 0.7 ev, as various calculations predicted deep levels that could be responsible [154]. The simultaneous measurement, however, of both PL and absorption edge at essentially the same energy, by such groups as Walukiewicz et al. [155], indicate that this energy position does indeed correspond to the transition across the fundamental band gap of InN [130]. This low energy gap has found support in more recent band structure calculations performed by two different groups [156, 157]. Meanwhile, most recent high crystal quality InN material grown has been measured with the low band gap. There is at least one exception, being InN grown by HPCVD [139], however that case is expanded upon below. The smaller band gap has further been supported by recent ultra-fast differential transmission measurements [158] and theoretical calculation [159]. The larger band gaps of sputtered InN can be at least partially accounted for by the effect of conduction band filling with increasing free electron concentration on the optical absorption edge, an effect known as the Burstein-Moss shift [49,150]. As seen in Fig. 4.3, for carrier concentrations above cm 3 there is a clear upward shift in the absorption edge towards higher energy values. Above the degeneracy limit, the elevation of the

79 4.4: Electrical Properties InN Absorption edge (ev) (1) our work (2) Ref.[3] (3) Ref.[18] (4) Ref.[19] Cal., non-parabolic Cal., parabolic Free electron concentration, n (cm 3-3 ) Figure 4.3: The energy of the optical absorption edge as a function of the free electron concentration. The curves show the calculated optical absorption edge taking into account the Burstein-Moss effect, including or excluding the conduction band non-parabolicity [150]. The data, as labelled (1)-(4), was collated in [150] from : (1) Ref. 150; (2) Ref. 162; (3) Ref. 163; (4) Ref Fermi level above the conduction-band minimum alters the minimum optical transition energy [31], resulting in a higher energy absorption edge as the concentration increases and the Fermi level moves higher into the conduction band [24, 31, 150, 160, 161], shown schematically in Fig The Burstein-Moss shift alone, however, cannot fully account for the high band gaps reported. The Burstein-Moss shift is discussed in papers as early as 1986 by Tansley and Foley [31]. They calculated the effect of the shift on reported band gaps for RF-sputtered films ranging between 1.89 and nearly 2.1 ev for carrier concentrations between and cm 3, reproduced in Fig These low carrier concentration films have not since been possible to reproduce by that growth method. There is no doubt, however, that Tansley and Foley did report a number of InN films with both low carrier concentration and high band gap. While effects such as quantum confinement have been suggested, the difference could possibly be explained more simply by the creation of indium oxynitrides. The band gap of In 2 O 3 is 3.1 ev. Thus it is likely that early polycrystalline sputtered films, even with low carrier concentration, had such high incorporation of oxygen that the film was actually an indium oxynitride alloy. This is consistent with a larger band gap than current, low oxygen, single crystalline InN films. Wu et al. [160] claim, however, that this theory is

80 60 Chapter 4: InN Figure 4.4: Schematic showing the increased optical absorption threshold energy with partially filled conduction band [130]. Figure 4.5: Band gap as a function of carrier concentration for RF sputtered InN films, showing a Burstein-Moss shift in the measured band gap value. [31] ineffective as a band gap of 1.9 ev in an indium oxynitride alloy would require an In 2 O 3 incorporation of 40 % (assuming a linear composition dependence of the direct bad gap of the alloy), which corresponds to an oxygen concentration above cm 3. However, SIMS results by various groups show the concentration of O is always approximately equal to or less than the free electron concentration [160]. Further, Yoshimoto et al. (2003) [165] used a combination of Rutherford backscattering and x-ray photoemission spectroscopy to determine the oxygen concentration of polycrystalline InN with a band gap of 1.9 ev to be 3 %. They saw, though, an increase in band gap from 1.55 to 2.27 ev as the oxygen concentration increased from 1 % to 6 %. Recent growth of high crystal quality (as determined by XRD) HPCVD-grown InN by Alevli et al. [139] resulted in measured band gaps between 0.7 and 1.5 ev, yet all the samples exhibited very similar electron concentrations which would eliminate the Burstein- Moss effect as the cause for the range of band gaps measured. Interestingly also, it was

81 4.4: Electrical Properties 61 the narrowest FWHM single-phase samples (i.e. those of highest crystal quality) that gave the greatest absorption edge, at around 1.5 ev. Alevli et al. suggested effects such as stoichiometry deviations and the associated point defect chemistry must be considered, as the Burstein-Moss shift does not account for their observed absorption edge shift. No information about photoluminescence (PL) measurements is given in their study (or whether or not PL can be observed in these films). Knowledge of the band gap evolution and the reasons for the significant changes in the value of the energy band gap is a vital part of understanding InN. The Burstein-Moss shift demonstrates that carrier concentration in InN is an important parameter to know accurately, because large carrier concentrations can radically alter measurement results and thus calculated properties. Measuring the bulk electron carrier concentration accurately is one of the major outcomes of the work presented in this thesis Surface and Interface Electrons The presence of an accumulation of electrons on the surface of InN films was first reported by Lu et al. [166] in When the measurement of the electron concentration of InN films with decreasing thickness was extrapolated to zero, the sheet carrier density did not go to zero, but instead demonstrated an excess sheet charge. This excess sheet charge therefore had to originate from either the surface of the InN or the growth interface, or a combination of both. Coupled with the observation that all metals formed an ohmic contact to the InN film, it was determined that at least part of the excess sheet charge measured must come from a surface accumulation of electrons. This conclusion was further supported by C-V measurements using an electrolyte to form the rectifying contact, the results of which were presented in the same article. Since then, measurements of surface electrons have been reported using the same technique of extrapolation of Hall measurement results (carrier concentration, mobility) on samples with decreasing thickness [34, 141, 166], as well as by C-V measurement [49, 166, 167], variable field Hall [52, 56, 57], and importantly also from contactless measurements such as high-resolution electron-energy-loss spectroscopy (HREELS) [48,145,168,169] and photoemission spectroscopy [85, 170, 171]. The presence of surface electrons has been found using all these techniques regardless of surface preparation conditions. Native donor defects are therefore the most likely source of the surface electrons [49]. Some of these techniques are unable to differentiate between a surface electron accumulation and any growth interface electron accumulation that may be present. Some groups

82 -point is much lower than the conduction band edge at ure is calculated using denithin the local density ap- computed from the electronic-structure calculations, reveal other points in k-space. Additionally, the optical spectra, ve expansion 62 of the eigenrving pseudopotentials is followed by a plateau. 11 This behavior is indicative of a non- Chapter 4: an absorption InN edge that is characterized by a steep increase nitio Simulation Package. 5,6 as valence electrons dval. structural properties are obcalculated to be c Å ith the experimental values unately, the conduction and he -point in the Brillouin ive fundamental energy gap lap is mainly a consequence epulsion within DFT-LDA. 9 ther type of pseudopotential for self-interaction correcn the underlying atomic callectrons in the core. 10 The the missing pd repulsion ) 0.58 ev. Additional quaken into account Figure in the 4.6: cal- The wurtzite functionalinn theoryband withinstructure the local density calculated approximation by Mahboob incorporat- et al. using density FIG. 1. The wurtzite InN band structure calculated using density ture that is shown functional here. The theorying within self-interaction the local corrections. density approximation The branch-point incorporating energy E B is self-interaction practically compensates corrections the [48]. shown to be located in the conduction band at the -point The American Physical Society have therefore used a combination of techniques, at least one of which only focused on the surface (such as HREELS or photoemission spectroscopy), to separate out evidence of two species, and have thus determined that an accumulation of carriers must also exist at the growth interface [145, 171]. The works of Mahboob et al. [48,168] have established that in InN the surface accumulation occurs as a result of its very low Γ-point conduction band minimum (CBM). The type of surface states present on InN is governed by the position of the branch point energy at the Γ-point. The branch point energy (E B ), also known as the Fermi stabilisation energy (E FS ) or charge neutrality level (CNL), is the energy at which states change from donor-like (below E B ) to acceptor-like (above E B ). The location of the Γ-point CBM in InN is very low in energy compared to the average conduction band edge (CBE) across the Brillouin zone (BZ), as shown in Fig The branch point energy occurs at approximately the average mid gap energy over the entire BZ, and therefore lies well above the Γ-point CBM. The location of E B high above the Γ-point CBM governs the donor-like attribute of the surface states, allowing them to donate their electrons into the conduction band and form a large electron accumulation at the surface. The large accumulation of electrons causes downward band bending at the surface to maintain charge neutrality [48, 49, 84, 85, 92, 168, 172, 173]. The calculation of the band structure, showing the location of E B in the conduction band at the Γ-point, is given in Fig It is important to understand the origin of the surface electrons in InN in order to correctly interpret results from a variety of experiments, as well as to predict and design devices that account for or make use of the surface accumulation. The band structure

83 4.4: Electrical Properties 63 explanation by Mahboob et al. given above both demonstrates and predicts the inherent and persistent nature of the surface electron accumulation on all wurtzite InN surfaces. A surface accumulation of electrons has also been measured on the surface of zinc blende InN [92]. Likewise, it is prudent to consider the possibility that the region at the InN/substrate growth interface may also exhibit an accumulation of carriers. The band offsets between the buffer or substrate layer and the InN, as well as the high density of defects in this region, are calculated to lead to the formation of either an electron or hole accumulation, depending on crystal orientations [145]. The possibility that an interface accumulation contributes to the properties measured and assigned to the surface electron species is considered for each measurement technique discussed further in section The recently reported universality of the surface electron species sheet concentration [171] is also discussed with respect to each measurement technique Microscopic Origin of Surface Electrons While early measurements, such as those just mentioned, sought to study some properties of the surface electron accumulation, no consistent interpretation as to the origin of the accumulation was presented. More recently, the surface accumulation has been explained by the band structure, specifically by the low Γ-point in relation to the branch point energy. This has given a solid bulk band structure theory for the surface accumulation origin [48, 168]. Yet by early 2006, still no microscopic origins of the surface accumulation had been proposed. The first thorough calculations regarding InN surfaces were performed by Segev and Van de Walle (2006) [172], (2007) [173]. They used band structure and total energy methods to study the electronic properties of the stable reconstructions on both polar (c-plane) and non-polar (a- and m-plane) surfaces of GaN and InN. For the polar InN surfaces, they attributed In-In bonds leading to occupied surface states above the conduction band minimum (CBM) as the source of intrinsic electron accumulation. All calculated surface states for polar InN surfaces were located above the CBM. As the number of surface states is much larger than the number of available bulk states in the near-suface accumulation layer, the surface Fermi level position is approximately determined by the position of the upper proportion of the occupied surface state. The Fermi level pinning was calculated for two regions of surface stoichiometry (In/N ratio). For low ratios, the Fermi level was calculated to be 0.6 ev for (0001) and 0.3 ev for (000 1)

84 64 Chapter 4: InN above the CBM. For high In/N ratios, the Fermi level was only slightly higher for the (0001) orientation at 0.7 ev above the CBM; the (000 1) remained at 0.3 ev above the CBM. The calculated surface states are shown in Figs. 4.7a and 4.7b, for moderate and high In/N ratios, respectively. For non-polar InN surfaces, the occupied surface states were calculated to behave quite differently than for the polar surfaces: on the m- and a-planes, these states were associated with dangling bonds on the N atom [173]. For moderate In/N ratios at the surface, the occupied surface states are below the VBM, and the calculations predicted the absence of electron accumulation. The calculated surface states for m-plane InN in the moderate In/N ratio are shown in Fig. 4.7c. In-rich conditions (high In/N ratio), however, led to Fermi level pinning at 0.6 ev above the CBM on both non-polar planes. Segev and Van de Walle speculated that removal of metallic indium from the surface post growth, if possible, may be able to restore an In/N ratio such that an electron accumulation is absent [172]. Photoemission studies by Veal et al. [84] revealed 3.4 and 2.0 monolayers (ML) of In on the In- and N-polarity c-plane InN surfaces, respectively. These results were confirmed by further ion scattering spectroscopy measurements also performed by Veal et al. [85]. In [85] they also found 3 ML of indium on the surface of a-plane InN, by photoemission studies, detailed further below in section The presence of In adlayers on the a-plane surface would, according to Segev and Van de Walle s calculations, indicate a surface accumulation present. The finding of In adlayers on the atomic hydrogen cleaned (AHC) a-plane InN surface may suggest that the surface accumulation on a-plane InN is unavoidable.

85 4.4: Electrical Properties 65 (a) (b) (c) Figure 4.7: Calculations of surface states for InN on c- and m-planes, with different In/N surface ratios: (a) (0001) c-plane moderate In/N ratio; (b) (0001) c-plane high In/N ratio; (c) m-plane moderate In/N ratio [173].

86 66 Chapter 4: InN Table 4.1: The properties of the surface and growth interface electron accumulations as measured by various techniques. Sample / Buffer Polarity Location Sheet Charge Mobility Measurement Technique Reference (surface or Density growth interface) cm 2 cm 2 /Vs atomic hydrogen cleaned InN InN / AlN In-face surface 2.5 ± 0.2 HREELS+Poisson-MTFA (2004) [168] InN / GaN In-face surface 2.4 ± 0.2 HREELS+Poisson-MTFA (2004) [48] InN / GaN In-face surface 2.4 ± 0.2 HREELS+Poisson-MTFA (2004) [169] InN / AlN, GaN In-face surface 2.4 ± 0.2 HREELS+Poisson-MTFA (2005) [145] InN / GaN/AlN In-face surface 1.65 ± 0.1 XPS + Poisson-MTFA (2007) [92] InN / low T InN N-face surface 1.65 ± 0.1 XPS + Poisson-MTFA (2007) [92] InN / GaN/AlN a-plane surface 1.65 ± 0.1 XPS + Poisson-MTFA (2007) [92] InN / ZB-GaN zinc blende surface XPS + Poisson-MTFA (2007) [92] oxidized InN (surface exposed to air) InN / GaN In-face surface 1.57 C-V (2003) [166] InN / GaN, AlN In-face surface 2.2 depth profiling (2005) [174, 175] InN / GaN In-face surface tunnelling spectroscopy+p-mtfa (2007) [176] InN / GaN In-, N-face surface 0.92 ± 0.21 XPS + Poisson-MTFA (2008) [171] InN / GaN/AlN In-face surface a 0.7 optical Hall (2008) [177] InN / GaN/AlN In-face surface a 8.3 optical Hall (2008) [177] InN / AlN In-face surface+interface 4.3 ± Hall, extrapolated by thickness (2003) [166] InN / GaN In-face surface+interface 2.5 ± Hall, extrapolated by thickness (2003) [166] InN / AlN In-face surface+interface 4.3 ± 0.2 < GaN buffer Hall, extrapolated by thickness (2005) [145] InN / GaN In-face surface+interface 2.5 ± 0.2 > AlN buffer Hall, extrapolated by thickness (2005) [145] InN /GaN In-face surface+interface 5.11 Hall, extrapolated by thickness (2006) [141] InN / GaN N-face surface+interface 3 Hall, extrapolated by thickness (2006) [34] InN:Mg / GaN In-face surface+interface variable field Hall + QMSA (2006) [52] InN / GaN In-face surface and/or interface b variable field Hall + QMSA (2007) [63] InN / AlN In-face interface 1.9 ± 0.4 HREELS subtracted from Hall (2005) [145] InN / GaN In-face interface < 0.5 HREELS subtracted from Hall (2005) [145] a : as part of a multi-layer model. interface contributions unknown. b : assigned to interface in paper, but could equally be surface or combined surface/interface.

87 4.4: Electrical Properties Measurement of Surface Electrons From the first report by Lu et al. [166], evidence of surface electron accumulation in InN has been measured by many different groups using a variety of methods. Table 4.1 details the results obtained from a range of measurements of the surface properties, and is an extended version of that provided by Cimalla et al. [174, 178]. Most measurements report on the sheet density of the surface accumulation, yet very little information on the mobility is available. What specific transport data is available for the surface electrons is presented with the review of InN transport properties in section 4.5. Even with the wealth of measurement techniques and experimental results outlined below, the study of the surface properties of InN will undoubtedly continue for some time. Clearly, the surface has a large impact on the application of InN material into devices. One aim of the work in this thesis is to measure transport properties of all carriers in InN samples, including the surface species, so that their behaviour is better understood. Hall measurements on multiple samples with increasing thickness: Lu et al. [166] were the first to use Hall measurements to identify an excess sheet charge density in InN films. InN films with increasing thickness were grown under the same conditions. Single-field Hall measurements were then conducted to determine the (averaged) sheet carrier concentration and mobility. Plotting the sheet carrier density against thickness should have approached zero at zero thickness if only a bulk carrier existed, however for InN this was not the case, as shown in Fig The resultant charge must be due to a surface accumulation and/or a possible interface charge, though from this measurement alone it is not possible to distinguish the two. The measurement should, however, provide an upper bound on the magnitude of electron sheet density at the surface. The use of this technique is also reported elsewhere [34, 141, 145]. Capacitance-voltage measurements: The excess of electrons at the surface of InN means that all metals deposited on the material form good ohmic contacts. In order, then, to form a rectifying contact to perform C-V measurements a different approach must be used. It was found that a weakly rectifying contact can be formed between InN and a KOH- or NaOH-based electrolyte [166, 167] in ethylendiaminetetraacetic acid (EDTA). A platinum electrode is used to charge the electrolyte, and standard C-V profiling can then be conducted. This method has been used extensively in the literature [49,52,166,167,179]. This method interacts with only the near

88 68 Chapter 4: InN surface electrons, and does not measure any contribution from an interface accumulation. The C-V profile obtained by Lu et al. [166] is shown in Fig C-V measurements are able to give an estimation of the depth of the surface electron accumulation, as demonstrated by the concentration versus depth profile in Fig. 4.9 [166]. Results give a depth of about 5 nm [52, 177] to 6 nm [166]. Peak volume concentration of the electron accumulation may reach over cm 3. Calculated surface profiles by King, Veal and McConville [180] using the Poisson-MTFA method (see below and section ) also predict a depth of approximately 5 nm for the majority of the surface electron accumulation. No reports have discussed the likely depth of surface carriers in samples with surface roughness much greater than 5 nm, though it is not unlikely that many InN films exhibit such a degree of surface roughness. High resolution electron-energy-loss spectroscopy: The electron accumulation at clean InN surfaces has been measured by Mahboob et al. [168] using high-resolution electron-energy-loss spectroscopy (HREELS). Colakerol et al. [181] concluded that the HREELS measurement performed by Mahboob et al. revealed a conduction band plasmon with energy that increased as the incident electron energy decreased, which indicated a higher electron density within 80 Å of the surface than in the bulk. The InN surfaces were prepared by atomic hydrogen cleaning (AHC) in the HREELS vacuum chamber and then measured under ultra-high vacuum (thus remaining clean). No contacts, or contact with the surface, were required, which is an advantage to this technique as it eliminates any source of surface contamination, a problem that may Figure 4.8: Sheet carrier density as measured by single-field Hall effect measurements, for InN films grown on AlN and GaN buffers as a function of InN film thickness [166].

89 4.4: Electrical Properties 69 Figure 4.9: The surface charge profile of an InN sample obtained by C-V measurement. The inset shows the corresponding I-V curve before zero potential correction [166]. arise from measurement methods that do require contact. Using a band gap of 0.75 ev the calculated surface sheet concentration was given as (2.5 ± 0.2) cm 2 [168]. Piper et al. [169] also used HREELS to measure the surface electron accumulation on InN, and calculated the surface state sheet density to be independent of temperature at cm 2, using band gaps of and ev at 295 and 565 K respectively in the calculations. They attributed the consistency with temperature to be due mainly to the small change in InN band gap with temperature, compared to the band gap change that occurs in other narrow-gap materials. Veal et al. [145], too, used HREELS and from the spectra determined a surface state sheet density of 2.4 ± cm 2 for In-face InN on both AlN and GaN buffer layers, equating to a band bending of 0.7 ev at the surface. The use of HREELS is advantageous in that only the near-surface space charge region is probed, allowing it to be distinguished from any charge that may be accumulated at the InN/buffer layer interface. The surface state densities calculated are therefore fully independent of any interface charge. High resolution x-ray photoemission spectroscopy: High resolution x-ray photoemission spectroscopy (XPS) measures the binding energy of ejected photoelectrons. The binding energy scale is given with respect to the Fermi edge of a ion-bombarded silver reference sample. XPS is used to calculate the valence band minimum (VBM) to surface Fermi level separation by extrapolating the leading edge of the valence band photoemission to the background level, in order to account for the

90 70 Chapter 4: InN broadening of the photoemission spectra [171]. The VBM to Fermi level separation is then used in a solution of Poisson s equation within a modified Thomas-Fermi approximation (the Poisson-MTFA method) to calculate the band bending and surface state density profile. This calculation also requires a representative bulk carrier concentration which may be measured by a technique such as single or multiple field Hall effect measurement. King et al. [171] reported that their calculations were relatively insensitive to the value of the bulk electron concentration used. The calculations yielded similar surface state densities when using either of two different values for the bulk concentration, based on the measured values from either the single-field Hall measurements on the samples used for the XPS, or from the multi-field Hall measurements performed on the samples in this work in section 5.3 (the growth conditions for the samples in [171] were selected to match those in section 5.3). The XPS technique with Poisson-MTFA calculations was used by King et al. [92,171, 180] and Veal et al. [84,85] to study a variety of InN surfaces, such as both polarities of c-plane, a-plane and also zinc blende InN. King et al. (2007) [92] performed XPS studies on In-face, N-face and a-plane surfaces cleaned by atomic hydrogen (AHC) to remove surface oxides. Details of the AHC process can be found in [92]. The photoemission spectra results for all wurtzite InN films were coincident in energy, which indicated that the same VBM to surface Fermi level separation existed in the three samples. The VBM to surface Fermi level separation reported for each of the InN films was 1.53 ± 0.1 ev, which was deemed by King et al. to be universal i.e. applicable to all wurtzite InN surfaces. They attributed the universal presence of the surface accumulation to the bulk band structure, explaining it in terms of the low Γ-point as detailed in section above, regardless of the microscopic origins of the states for different surfaces. Despite differences in the bulk Fermi level positions, King et al. explained that the pinning of the Fermi level at the surface at the same energy for all three wurtzite InN samples meant that the band bending close to the surface is similar which results in similar near-surface charge profiles. The surface electron species sheet density was then calculated to be (1.65 ± 0.1) cm 2 for all three wurtzite InN surfaces measured. Subsequently, King et al. (2008) [171] examined c-plane samples of both In-face and N- face InN grown under In-rich, stoichiometric and N-rich growth conditions. Their work was motivated by the published version of results in section 5.3 of this work, and as a result the InN samples were not subjected to atomic hydrogen cleaning, in order to better match the conditions of the samples in this work, though the improvement in

91 4.4: Electrical Properties 71 growth techniques in the subsequent time (and the considerable roughness of the samples measured in this work) obscures the comparison somewhat. They measured the valence band photoemission spectra of each sample and found the leading edge of the spectra to be coincident in energy for all samples with the same polarity, regardless of growth regime, indicating that the position of the surface Fermi level relative to the VBM is the same for all. The extrapolation of the leading edge of the valence band photoemission spectra to the background level gave a VBM to surface Fermi level separation of 1.4 ± 0.1 ev for all samples, regardless of growth regime or surface polarity. The surface state sheet density calculated using the Poisson-MTFA method was 9.2 ± cm 2. They attributed the slightly lower value of VBM to surface Fermi level separation than that seen in [92] to be a result of the oxidised (non-ahc) surface. The method employed by King et al. and Veal et al. is used to calculate the sheet density of electrons at the growth interface by subtracting it from other measurement techniques that may measure, yet be unable to differentiate between, both surface and interface accumulations. Details are given in section Variable magnetic field Hall measurements: Distinct carrier species have been identified in InN through the use of variable magnetic field Hall and resistivity measurements along with either multi-carrier fitting (MCF) or quantitative mobility spectrum analysis (QMSA) techniques. In undoped InN, either two [56, 57] or three [63] electron species have been identified, attributed to the bulk and surface electron species, and also (in the case of three electron species) to a growth interface accumulation. In Mg doped InN [52, 62] and in InN grown on yttrium-stabilised zirconia (YSZ) substrates [62], both electron and hole species have been distinguished. In all cases an electron species attributed to the surface electron accumulation was found. The distinct mobilities of the surface and bulk electron species enable their differentiation, as the contribution to the magnetic field-dependent conductivity tensor components is different for each. Though identified, the sheet concentration and mobility of the surface electron species are not always given in reports using this method, but where such properties are reported they are included in Tables 4.1 and 4.3. Due in no small part to the analysis and assumptions made (discussed further in section ), sheet carrier concentrations reported range between and cm 2 and mobilities between 8 and 500 cm 2 /Vs. Disambiguation of the surface electrons and any growth interface electron is dependent on the mobilities of the two species. As this is the technique employed in this work, more detail on the method was presented in section 3.1 and more in-depth analysis of the reported results using this method is presented in section

92 72 Chapter 4: InN Optical Hall measurements: The measurement of the optical Hall effect using magneto-optical generalised ellipsometry (MOGE) at infrared and THz wavelengths is used within a stratified layer model data analysis to determine free carrier properties in InN films by Hofmann et al. (2008) [177] and Darakchieva et al. (2009) [182]. In [177] the analysis appears to have fitted a two layer model, while in [182] the combined MOGE and infrared spectroscopic ellipsometry data were analysed to identify two InN layers with different free electron properties. The modelling in both papers was stated to use the parameters of carrier type, density, mobility and effective mass, but only the type and sheet density of the surface electron accumulation have been reported. In both cases the sheet carrier density of the surface electron species is shown to decrease with increased film thickness (alongside a decrease in the bulk electron concentration), ranging between cm 2 and cm 2. As the fitting to the optical Hall measurement is complex, it is not known if a priori assumptions are required, and therefore if a growth interface accumulation was simply not present, or not considered as part of the model. Other methods: A variety of other methods have been used to determine the existence and properties of the InN surface electron accumulation layer. Photoemission results from Ti deposited on Ar-sputtered InN indicated the existence of an electron accumulation layer [170], though no value for the sheet concentration of the accumulation was obtained. High resolution angle-resolved photoemission spectroscopy (ARPES) was used [181] to observe electrons in the InN surface accumulation layer, and to observe that they resided in quantum well states. Tunnelling spectroscopy experiments [176] were also used to obtain information on quantisation of the electron accumulation. More details of such findings are given in section Evidence of Accumulation at Non-polar and Cubic InN Surfaces Evidence of electron accumulation at non-polar surfaces of InN was first reported by Calarco and Marso [183], and soon after by Calleja et al. [184] through the study of InN nanocolumns. In [184] high quality InN nanocolumns were grown in the (0001) direction by MBE on n-type Si (111) substrates. The nanocolumns were determined to be defectfree single crystalline, and have non-polar (m-plane) side walls that were atomically flat, free of extended defects and were fully relaxed [185]. Nanocolumns of different diameter

93 4.4: Electrical Properties 73 but similar heights were electrically characterised by AFM. In contrast to results on GaN nanocolumns, where the conductivity of the columns was independent of the diameter (indicating conduction through the volume of the column), InN nanocolumns were found to have conductivity that scaled with the reciprocal of the diameter, pointing to the nanocolumn lateral surface as the main conduction path, indicating electron accumulation on the non-polar side walls of the nanocolumns. Further support for the existence of electron accumulation at non-polar InN surfaces, and indeed at all InN surfaces, including zinc-blende, comes from King et al. [92], as detailed above. Using x-ray photoemission spectroscopy (XPS), electron accumulations were measured on the surface of wurtzite (11 20) a-plane and ± c-plane, as well as (001) zinc-blende InN. Veal et al. [85] also found a surface accumulation on a-plane InN by XPS, and calculate that 3 monolayers of indium are required, as part of the microscopic reason for the surface accumulation in accordance with the first principles calculations by Segev and Van de Walle [172] outlined in section above. King et al. found that the Fermi level appears to pin slightly lower above the VBM in the zinc-blende case than in the wurtzite cases, but a surface accumulation of electrons still exists, with the calculated surface state sheet density also slightly lower ( cm 2 ) Quantization of Electron Accumulation Colakerol et al. (2006) [181] used high resolution angle-resolved photoemission spectroscopy (ARPES) to unambiguously observe that electrons in the InN surface accumulation layer were quantised perpendicular to the surface; that is, residing in quantum well states. The two states exhibited quantum well characteristics perpendicular to the surface, but had the characteristics of the conduction band in the plane parallel to the surface. Colakerol et al. then solved Poisson s equation numerically within the modified Thomas-Fermi approximation (the Poisson-MTFA method) and a 1D independent electron Schrödinger equation to predict the existence of two subbands with minima at and ev below E F, with associated electron effective masses of 0.12 m 0 (E2) and m 0 (E1) respectively. These effective mass values agree quite well with those calculated as a function of electron density by Wu et al. [135], assuming the region near the surface has volume electron concentration between and cm 3. Veal et al. (2007) [176] further investigated the dependence of the subband energies in the InN surface accumulation on the doping concentration through the use of electron tunnelling spectroscopy. Tunnelling spectra all exhibited a zero tunnelling plateau of

94 74 Chapter 4: InN 0.6 V corresponding to the band gap of InN, and a separation of 1.3 ev between the features determining the VBM and the pinned Fermi level. Additional features in all three spectra were observed between the CBM and pinned surface Fermi level. They also used Poisson-MTFA and an exponential well approximation to calculate subbands, and found that the features in the tunnelling spectra coincided with the calculated quantised states lying within the surface accumulation potential well. They found that the energetic locations of the subband features vary systematically with the doping level of the InN samples. They demonstrated such behaviour is consistent with the existence of quantised levels within the potential well associated with the surface accumulation layer. As the bulk carrier density is increased, the width of the accumulation layer is reduced and the maximum carrier density (near the surface) increases. They explained the change in well width as being due to the variation of the Thomas-Fermi screening length. King, Veal and McConville (2008) [180] presented an in-depth report on the modelling of the surface electron accumulation which also confirmed the presence of quantised subbands. In the two-dimensional electron gases in AlGaN/GaN HEMTs, multiple magnetic field Hall effect measurements with a quantitative mobility spectrum analysis technique have been used to identify multiple electron species attributed to conduction from electrons in multiple subbands [186]. However, the measurement of electron conduction from separate subbands using this technique is not well established at this time Reduction of Surface Accumulation Cimalla et al. [187] were able to, at least partially, reduce the accumulation of electrons at the surface of InN by oxidisation using ozone and UV light. They oxidised the samples through exposure to UV light for 30 s, followed by flowing a mixture of N 2, O 2 and O 3 over the sample for 60 s and repeating the cycle over a number of hours. They measured the resistance of the sample in-situ and, after an initial decrease, obtained increases in the resistance. Without UV light a similar increase in resistance was achieved, but the oxidation took around four times as long. Single-field Hall measurements revealed improvements in the mobility, and a decrease in carrier concentration for samples greater than 700 nm thick. The reduction in sheet carrier concentration was on the order of the surface accumulation sheet density obtained through other measurements ( cm 2 ) but could not fully account for the change in bulk electron species transport when considered as part of a three-layer conduction model (surface, bulk and interface electron species being consid-

95 4.4: Electrical Properties 75 ered). Cimalla et al. suggested a reduction in band bending at the surface may also have contributed to the change in the measured transport properties. The transport properties degraded over time by around 25 % after a few months. Their study presents a major stepping stone for future work on the passivation or surface modification of InN. Such a study could benefit from employing multi-carrier transport measurement techniques, such as variable field Hall effect measurements, to separate out any residual low mobility carriers from the bulk electron species Electron Accumulation at the Growth Interface Due to the lack of a lattice matched substrate, an area of high dislocation density exists at the growth interface between the InN epilayer and the buffer or substrate. This is especially true for growth on sapphire, AlN or GaN, which have 25, 13, and 11 % lattice mismatches with InN [145], respectively (YSZ substrates are the closet match at only 2.5 % difference [62]). TEM studies of InN films with low bulk defect densities ( 10 9 cm 2 ) have revealed the high defect growth interface region to have a thickness up to nm [182, 188]. Beyond this initial region the defect density is decreased significantly, and decreases further as the epilayers are grown thicker [188]. Veal et al. (2005) [145] and King et al. (2008) [171] each calculated the surface electron sheet density on InN surfaces using Poisson-MTFA charge profile calculations and either HREELS or XPS measurement results, respectively, as described in the previous section. They then used the surface sheet density to calculate values for an accumulation of electrons at the growth interface, by subtracting the HREELS or XPS calculated value from a combined surface-interface measurement: either the extrapolation of Hall results from samples of various thickness [166], or from the sheet concentration obtained for the low mobility peak in a quantitative mobility spectrum analysis of a multiple-field Hall measurement [60], respectively. King et al. [171] claim the sheet concentration of electrons on the surface of all wurtzite InN to be the same, regardless of growth conditions or polarity, as the leading edge of the valence band photoemission spectra of all samples they have measured are coincident in energy. The sheet concentration of electrons is then calculated from a fit to this data via the Poisson-MTFA method. They did, though, find a slight difference between a clean InN surface (obtained by atomic hydrogen cleaning) and an oxidised InN surface (exposed to air), where the two surface state accumulation sheet concentrations, clean and oxidised, calculated from their measurements are cm 2 and cm 2,

96 76 Chapter 4: InN respectively. The value of cm 2 in [171] (2008) is updated from a calculated value of cm 2 used in [145] (2005). Also, the measurement of the oxidised surface was performed after the publication of [145]. In [145] the calculated growth interface electron sheet concentrations, as a difference between extrapolated Hall concentration and HREELS-assisted calculation of surface sheet density, was (1.9 ± 0.4) cm 2 at the InN/AlN interface and < cm 2 at the InN/GaN interface. Updating the results of [145] then gives cm 2 at the InN/AlN interface and cm 2 at the InN/GaN interface. A carrier accumulation at the growth interface could be accounted for from two sources. The first is the high density of dislocation related defects at the interface that, according to the amphoteric defect model, will form donors due to the location of the charge neutrality level above the conduction band minimum (see section above). The second is polarisation charges that form at the junction as a result of differences in the spontaneous polarisation coefficients of the InN and buffer layer, and from any strain-related piezoelectric charge as a result of the lattice mismatch. Any charge carriers, though, are of course not the polarisation charges but free carriers that accumulate locally to compensate the fixed polarisation charges and maintain charge neutrality. Both of these factors are highly influenced by the choice of both substrate and buffer layer for the growth of the InN epilayer. There is no standard buffer layer or substrate used for the growth of InN by all research groups, and as mentioned in section , a variety of substrates and buffer layers are used for InN growth. Substrates used include sapphire, silicon carbide, yttrium-stabilised zirconia and MOCVD GaN templates, while buffer layers may comprise of GaN, AlN or low temperature InN and be deposited by a variety of deposition techniques and under different conditions. The choice of substrate and buffer layer (or layers) can affect the crystal orientation, dislocation density and any potential polarisation charge in the InN layer. Therefore any electron (or hole) accumulation at the growth interface of InN epilayers is likely to vary significantly between samples that employ different substrates or buffer layers. Previous measurements on InAs/GaAs and InAs/GaP heterointerfaces have demonstrated the existence of electron accumulations attributed to donors as a result of misfit dislocations; InAs has a similar (though less extreme) band structure for which the ADM predicts the formation of donor states. In those cases, the lattice mismatches and sheet carrier densities at the interface were: InAs/GaAs 7 % and cm 2 [189]; InAs/GaP

97 4.4: Electrical Properties %, and cm 2 [190]. For the case of InN, there exists not only a greater lattice mismatch between epilayer and buffer layer (for most buffer layers), but also a greater range of energy separation between the charge neutrality level and the Fermi level i.e. more donors will form before the Fermi level rises to the charge neutrality level (Fermi stabilisation energy) at which stage donors and acceptors are created equally. Both of these facts suggest a sheet charge density of greater than cm 2 could exist at the InN/buffer layer interface. According to Veal et al. [145], in the case of In-face InN (In-face towards the surface, N-face towards the buffer, which would be Ga- or Al-face directed towards the InN) the spontaneous polarisation mismatch between the InN and a GaN buffer would result in an electron accumulation of cm 2. Between an InN and AlN buffer a hole gas of cm 2 would be induced, as the spontaneous polarisation coefficient of AlN is larger than that of InN (while that for GaN is smaller). In N-face InN presumably the opposite would occur, and a hole gas may be induced at the growth interface with GaN, and an electron accumulation at the growth interface with an AlN buffer layer. Additionally, Cimalla et al. [191] noted that spontaneous polarisation charge alone cannot account for the interface charge, and proposed that the difference seen in [166] between AlN and GaN buffers in thickness dependent Hall measurements below 100 nm corresponded well to the differences in the strain in the two systems, suggesting that there was also a piezoelectric polarisation charge. As the AlN buffer has a greater lattice mismatch, greater strain is induced and therefore a greater piezoelectric polarisation charge. Any carriers at the interface are most likely sourced from a combination of polarisation charge-induced carriers and donor-type defects. While anecdotal evidence exists for the accumulation of electrons at the growth interface in InN films, no direct measurement of any such accumulation has been confirmed. The analysis of the above studies in light of the results in this work, addressing any implications a growth interface accumulation would have for the measured transport data is discussed further alongside the results of this thesis in section Bulk Electrons Unintentional n-type Doping Currently, all nominally undoped as-grown InN has a high unintentional background concentration of electrons. The electron concentrations range from low cm 3 [34,57,141,

98 78 Chapter 4: InN 182] up to cm 3 [ ]. The origin of this unintentional n-type doping has been considered both theoretically and experimentally [24, 49, 130, 160, 178, 182, 188, ]. Various mechanisms may contribute and consensus for a single explanation does not exist. Note that the background unintentional n-type doping is InN is present even when the effect of the ever-present surface electron accumulation is taken into account in the analysis of Hall measurement data. Candidates for the causes of unintentional n-type doping of InN can be classified into two major groups: donor impurities, and donor-type native defects such as vacancies, dislocations, self-intersititals and antisite defects. The most likely donor impurities are oxygen, hydrogen and silicon [195]. O N and Si In are calculated to have low formation energies [198] and thus be easily incorporated during growth. Interstitial hydrogen is also strongly considered to be a candidate [195]. Hydrogen acts exclusively as a donor in InN (in contrast to GaN and AlN where H is amphoteric and compensates dopants) [86]. Look et al. (2002) [195] used glow discharge mass spectroscopy to eliminate O and Si as primary sources of unintentional n-type doping, but found high levels of H, as much as an order of magnitude higher than the background electron concentration. Candidates for the doping are therefore reduced to H and native defects. In the work of Wu et al. (2004) [160], however, SIMS measurements revealed that neither oxygen nor hydrogen could fully account for the unintentional background doping in their InN samples, which had been grown by MBE. In contrast, Darakchieva et al. [182] measured hydrogen content by elastic recoil detection analysis and determined the hydrogen content to be as large as 9.6 ± cm 3 in the bulk of their InN films, in which the background electron concentration was only cm 3. Hydrogen therefore remains a candidate for a significant part of the background doping. Even though neither oxygen nor silicon are the primary donors in unintentionally doped InN, and hydrogen is only speculated to be, they are all still calculated to form donors [198], and therefore reducing their incorporation can only further improve the properties of the InN grown. It is often assumed in the literature that impurity concentrations are constant throughout even the thickest InN films grown [178,196]. Durbin et al. [200], however, have used nondestructive ion beam analysis techniques (Rutherford backscattering spectrometry and nuclear reaction analysis) to investigate oxygen content in a series of InN films. They found that the surface of the InN is readily oxidised, with around 33 % oxygen in the top 30 nm of the film. They also found that oxygen is readily absorbed from the substrate

99 4.4: Electrical Properties 79 (sapphire or silica glass) to about 60 nm into the film at concentrations around 29 % (their InN films were grown without the use of a buffer layer). They proposed that the highly non-uniform oxygen content may offer an alternative explanation for the role of oxygen as a donor in InN. Nevertheless, in order to reduce unintentional n-type doping due to impurity incorporation, growth methods must be refined. Raising the growth temperature and using an In-rich environment (in which an In adlayer is always present during growth) are both expected to reduce impurity incorporation [201]. Use of buffer layers are also aids to reduce oxygen uptake from sapphire (and other oxygen-rich) substrates. As discussed earlier in this chapter while referring to surface states (section 4.4.2), the type of states (donor- or acceptor-like) formed due to native defects is governed by the relative positions of the Fermi level and Fermi stabilisation energy. This process is described by the amphoteric defect model (ADM). The tendency for n-type conductivity in InN can be explained by the ADM [49, 130]. According to the ADM [49], formation energy of native defects depends on the location of the Fermi energy (E F ) with respect to the Fermi stabilisation energy (E FS ). Equivalently, E FS can be described as the average energy level of native defects (also referred to as the branch point energy or the charge neutrality level). When E F < E FS (or alternatively when E F > E FS ), the formation energy of donor defects is reduced (or increased) and that of acceptor defects is increased (or reduced). This causes the preferential formation of donor (or acceptor) defects, which then pushes E F closer to E FS. When E F reaches E FS, it is pinned there by the creation of donor and acceptor defects at equal rates. In most semiconductors E FS is located in the band gap, and incorporation of native defects produces high resistivity material. In contrast, in InN the location of E FS is extremely high in the conduction band, 0.9 ev above the conduction band edge [49]. The relative positions of E FS and the band edges of some semiconductors have been shown in Fig. 4.1 earlier in this section. For electron concentrations lower than mid cm 3 the Fermi energy in InN is located below E FS and donor-like defects are preferentially formed. The incorporation of native defects can therefore be used to control the electron concentration, as detailed next in section Threading dislocations have been proposed by some researchers to be the main source of native defect donors in high crystal quality material [178, 188, 196, 199]. Edge-type threading dislocations and dislocations of mixed character were found to be dominant in

100 80 Chapter 4: InN wurtzite InN by Lebedev et al. on 800 nm InN with dislocation densities of only cm 2 [188, 199]. Piper et al. [196] and Cimalla et al. [178] found a dependence of electron concentration on growth thickness beyond that accounted for by the surface electron accumulation, and therefore concluded that an imhomogeneous doping mechanism was also present and responsible for additional dependence of electron concentration on film thickness. Both papers postulated the net electron concentration in the films as a function of thickness, d, is then [178] n(d) = N surface d + n b,constant + 1 d d 0 N b,inhomo dz (4.1) where N surface is the surface electron accumulation, n b,constant the bulk background doping from constant concentration sources (such as impurities or point defects) and N b,inhomo, an inhomogeneous bulk doping component that varies with thickness (possibly due to inhomogeneous defects such as threading dislocations). A similar, slightly modified, equation was also presented by Lebedev et al. in [188]. While this does indeed give the total electron concentration in the film (assuming the three electron sources are correct), the problem with this approach is that the concentration calculated from a single-field Hall measurement does not give the actual total electron concentration, n. The measured volume electron concentration, n Hall, determined by a single-field Hall measurement (from which the experimental values plotted in the two papers were obtained) is an averaged value of all electron species in the material weighted by mobility. That is, n Hall = n surface µ surface µ Hall + n bulk µ bulk µ Hall (4.2) where n Hall and µ Hall are calculated in the usual manner from a single-field Hall measurement (n Hall = 1 R H e, µ Hall = R H ρ ). The main outcome of this result is that the surface electron accumulation sheet density cannot simply be subtracted from the total electron density to give the remaining bulk electron density (or added to a calculated bulk density to give a measured total concentration) in order to fit the experimental data, as is performed in all three papers. An amount representative of the surface sheet density is also subtracted from the single-field

101 4.4: Electrical Properties 81 Hall measured sheet concentration in [197] and [141], which is incorrect. The surface electron and bulk electron concentrations must be weighted by their mobilities to obtain an accurate result. We know that the mobility of the surface electrons is much lower than the bulk species [56, 145]. Assuming the electrons from all bulk donors have the same mobility, this error in calculation should only then result in a defect density calculation that is scaled incorrectly by a linear factor (related to the ratio of mobilities of the bulk and surface electron species). Both Piper et al. [196] and Cimalla et al. [178] found that the incorporation into the calculations of positively charged nitrogen vacancies (V + N ) along threading dislocations (TDs) (approximately every 2/1.14 nm along a dislocation), where the dislocation density decreases exponentially away from the InN/buffer layer interface, can give good agreement with single-field Hall results on their films, grown with increasing thickness ( nm [196], nm [178]). TEM studies by Cimalla et al. [178] demonstrated such a reduction in TDs away from the growth interface. The charging of these dislocations as donors can be explained by the ADM. The results from both papers should therefore be interpreted as overestimating the contribution of the surface to the total measured bulk concentration, and therefore the required bulk donor densities to fit the experimental data are likely to be higher than reported. Darakchieva et al. [182] used optical Hall measurements to also extract the densities of the bulk and surface electron species for films between 550 and 1600 nm thick. thickness dependence of their bulk electron concentration did not agree with the results obtained in [196] and [178], both of which had used single-field Hall results. In addition, Darakchieva et al. discussed the disparate nature of results regarding the concentration of threading dislocations in InN. They noted that the magnitude and variation of dislocation densities with thickness are not universal in the literature, but rather are scattered for films of similar thickness, dependent on the growth conditions, substrate and specific nucleation scheme used in each case. For instance, the densities of both screw and edge type dislocations have been shown to decrease with increasing growth temperature [197]. Using TEM, Darakchieva et al. measured a thin 250 nm thick interface highly defective region, above which the dislocation density was estimated to vary only marginally with film thickness (between (1.7 ± 0.2) and (8.8 ± 2.2) 10 9 cm 2 ) a weak variation of dislocation density with film thickness. They also measured similar defect densities in InN films in which the bulk electron concentrations differed by more than an order of magnitude. Similarly, for example, the background electron concentration in InN grown on YSZ [62] is cm 3, which according to the model in [178] would require a dislo- The

102 82 Chapter 4: InN cation density of cm 2 ; yet the InN epilayers on YSZ have an order of magnitude lower dislocation density, of only cm 2. Darakchieva et al. suggest an additionalthickness dependent doping mechanism exists, and once again suggest hydrogen, based on the elimination of O and Si as suitable donors as discussed above. The major source of the unintentional n-type doping in InN is then most likely to be native defects (of which a large part are threading dislocations), which act as donors as described by the amphoteric defect model. Hydrogen incorporation is possibly responsible for a large contribution also, which may be thickness dependent. Oxygen, silicon and other possible impurities likely also act as donors, but their concentration cannot account for the unintentional background electron concentration alone. The inhomogeneous oxygen incorporation seen by Durbin et al. [200] does not extend far enough into the films to be a major thickness-dependent doping contributor. Reducing the unintentional doping, then, requires further improvement in crystal quality (mainly through reduction of threading dislocations) and through the reduction of impurities during growth, both of which are addressed through the manipulation of growth parameters (such as temperature and flux ratios) as well as through substrate and buffer layer choice and optimisation. The accurate measurement of bulk carrier concentration, without contributions from the surface accumulation, would greatly improve understanding of the unintentional doping in InN, as many of the relationships discussed above are inaccurate due to the non-constant contribution of, and inaccurate compensation for, the surface accumulation to the bulk results. Variable magnetic field Hall measurements, with suitable analysis, are well suited for this task, as the bulk electron species properties can be extracted independently of the properties of the surface electron species Intentional n-type Doping While all as-grown InN exhibits strong n-type conductivity (the lowest published values being on the order of cm 3 [34, 43, 57, 61, 141]), intentional and controlled n-type doping is important for device applications. Due to the low Γ-point of the conduction band in InN, below the Fermi stabilisation energy, the amphoteric defect model determines that native defects form donors in InN (see section ). The introduction of native defects could therefore prove to be a way in which to control the electron concentration, alongside standard dopant incorporation during growth. Indeed, in contrast to traditional impurity doping, researchers have shown that highenergy particle irradiation of InN, with H + or 4 He + particles, or electrons, can be used

103 4.4: Electrical Properties 83 to control the n-type conductivity over two orders of magnitude by introducing native donor defects [49, 202]. The free electron concentration was shown to increase approximately linearly with particle fluence before saturating at around cm 3, which corresponds to the point where the Fermi level (E F ) reaches the Fermi stabilisation energy (E FS ) after which point E F is pinned at E FS by the equal creation of donor and acceptor defects, as discussed in the ADM. The n-type doping effect is further supported by a measured blue-shift in the absorption edge with increasing He + ion fluence. This shift is due to the Burstein-Moss effect as a result of filling of the conduction band (by additional electrons provided by the donor defects introduced) [202]. Calculations by Jones et al. [202] suggested that the radiation-induced defects may be triply charged donors. Jones et al. [203] have further studied the effects of controlling electron concentrations with irradiation followed by annealing. The transport results are presented in section 4.5. Jenkins and Dow [204] have theoretically studied the suitable dopants for both n- and p- type InN and found group IV impurities on the In site are not good candidates for donors, while the best candidate is likely to be oxygen or another chalcogen on a N site. The fact that silicon has proven to be a reliable dopant in GaN, however, leads to an obvious investigation of its use in InN. Higashiwaki, Inushima and Matsui [205] and Uedono et al. [206] both doped InN films between and cm 3 using Si. Gallinat et al. reported on successful Si doping between and cm 3 [207] p-type Doping The growth of p-type InN (and by extension p-type In-rich InAlN and InGaN alloys) is essential for the realisation of devices, particularly in optical applications such as solar cells and LEDs. The predominant acceptor dopant attempted so far has been magnesium. Mg is the most common p-type dopant used for both GaN and AlN, though there exist significant issues with its use. Despite this, it has been the primary focus for p-type InN doping. Doping of InN via Mg has been shown (using single-field Hall measurements) to result in films that are compensated, though apparently still n-type, i.e. the results produced a negative Hall coefficient. The problem with measurement of p-type conductivity is that the surface accumulation of electrons persists even when doping extrinsically, and this can easily mask the bulk properties during measurements. This is especially true for single-field Hall measurements. p-type conduction has only been demonstrated conclusively through the use of multiple carrier fitting to multiple magnetic field Hall measurements [52, 62].

104 84 Chapter 4: InN Capacitance-Voltage (C-V ) measurements and analysis have given evidence for acceptor ionization, but C-V cannot determine if free holes are contributing to conduction [167]. Jones et al. (2006) [167] inferred from C-V measurements on their Mg-doped InN samples a doping level of Mg in the low cm 3 range, suggesting between 1 and 10 % of the Mg dopants were acting as acceptors, as SIMS determined a Mg incorporation of to cm 3. Single-field Hall measurements gave sheet concentrations of electrons between and cm 2, and mobilities of cm 2 /Vs. While the sheet carrier concentration is on the order of those reported for the electron accumulation, the mobility is about an order of magnitude too low for conduction to be only from surface electrons (see section 4.5 for further discussion of reported surface electron mobilities). This could indicate that some p-type conduction (with low mobility holes) is contributing to the total conduction as part of a multi-layered multi-carrier conduction path. Conduction contributions from low mobility holes would lead to a decrease in the mobility calculated from a single-field measurement. No PL was seen in Mg-doped samples by Jones et al. [167], attributed in part to a strong electric field caused by the severe band bending in the subsurface region that separates photo-excited holes and electrons. The multiple field Hall measurements by Anderson et al. (2006) [52] revealed clear evidence of holes through the use of quantitative mobility spectrum analysis and multi-carrier fitting (MCF), for Mg doping of cm 3. MCF was used to calculate a hole concentration of cm 2 with mobility of 50 cm 2 /Vs. Curiously, the QMSA spectrum (Fig. 4.10) showed another hole at higher mobilities but with far less conduction contribution, which was not part of their MCF analysis. Only n-type conductivity was observed for a sample with cm 3 Mg doping. Wang et al. (2007) [208] found that as Mg concentration was increased (up to cm 3 ), the single-field Hall electron concentration was reduced, suggesting partial compensation by active Mg acceptors. Further increases in Mg concentration ( cm 3 ), however, caused the electron concentration to increase with increasing Mg incorporation. The increase in electron concentration, coupled with decreasing Hall mobility and larger x- ray rocking curve FWHMs, indicated that Mg overdoping was decreasing the quality of the crystal and introducing new donor levels associated with either new native defects or Mg-related complex defects. Wang et al. [208] were unable to deduce from their available measurement techniques if the reductions in electron concentration seen with initial increase of Mg-doping were due to compensation or due to the incorporation of buried p-type layers. Hole conduction seems unlikely at such low levels of Mg incorporation, based on the variable field Hall results of Anderson et al. described above.

105 derson et al. 4.4: Electrical Properties 85 Appl. Phys. Lett. 89, ic capacitance-voltage measurements on unintentionally N films. Inset: concentration, due primarily to the near ion layer, is cm 2, close to the cm 2 others Ref. 4. FIG. 2. QMSA spectrum of the cm 3 Mg-doped film at 300 K showing light hole, heavy hole, and electron conductions. Figure 4.10: QMSA spectrum of a cm 3 Mg-dopd InN film at 300 K [52]. h a junction on InN without annealing at an hole will be resolvable and can serve as an indication of gh temperature. 10 Etching in 32% HCl redroplets on the surface and a solution of 0.2M a fitting routine which allows for a layer s inhomogeneity, 16 p-type conduction. Quantitative mobility spectrum analysis, EDTA formed a rectifying contact with a as well as standard multiple carrier fitting MCF were used mm used to examine near surface charge to analyze the field dependent data. Resistivity and Hall coefficient were measured, using the van der Pauw geometry, at khz, 50 mv signal was applied to a Pt electhe capacitance measurement. 11 When the ree of the capacitance C 2 Wang increases et al. with(2008) a [209] Thelinearly quantitative extrapolated mobility spectrum the SF Hall-cacluated analysis QMSA concentration of Mg logarithmically spaced fields up to a maximum 12 T. bias, then the mobile charge carriers are negaecrease implies p-type carriers. 12 InN films of spectrum for the cm 3 Mg-doped sample is shown doped in different Fig. 2. This thicknesses sample, measured and used at the 300 gradient K, was clearly to determine p the mobility in the inset of Fig. 1, the surface of holes sheet to elecd the spatial distribution of electrons of the heavy holes along with an electron peak that may represent be type, cm 2 exhibiting /Vs. a spectrum indicative of both light and doped sample as obtained from CV measureell with that observed previously. Fujiwara 4 The density et al. (2008) observed [210] for characterised p type HgCdTe Mgwith doped a n-type N-face conducting InN films layer ( µm thick) the surface conduction. This spectrum is reminiscent of that calculated using the standard equations for also present. 17,18 MCF analysis indicated a heavy hole sheet h, 12 and do not literally reflect by the IR density reflectance, or concentration and calculated of a 4 10 hole 15 concentration cm 2 and mobility of of about cm 3 and optical mobility e accumulation layer, as a depletion layer does of the 50 cm holes 2 /V of s, and an electron cm 2 /Vs with fora Mg sheetdoping carrier concentration of cm 2 and mobility of 200 cm 2 /V s. The in the range to rm until a reverse bias is sufficient to empty ion layer. Nonetheless, the3 total 10amount 19 cm 3 of. close correspondence between the directly measured electron layer can be found from the integral of the sheet concentration and that determined by CV strongly suggests that this is the surface electron. Similar measurements er the applied reverse bias voltage. This is integral of concentration over Growth depth, issues so thesurrounding made on the Mg highest incorporation Mg-doped sample are important. also clearly showed Wang et a al. [208, 211] used entration is indeed a measurement of the acer. Figure 1 compares the CV characteristic of tion. Low mobility carriers are difficult to cleanly separate hole peak that could be associated with light hole conduc- SIMS analysis to determine that the sticking coefficient of Mg on InN is almost unity lm to two Mg-doped films. andthe independent reciprocal ofout. polarity, Yet, theand presence thatofmg the atom light hole diffusion stronglyissuggests negligible. that Polarity inversion ance has a slope which changes sign on the there are p-type regions in this sample as well. The sample sample, indicating that a p-type is alayer known is buried issue inhaving the MBE Mg concentration growth of Mg-doped of GaN, cm 3 was withalso a reversal measured; only n-type conductivity was observed in this case, from Ga- to N- pe layer. agnetic field Hall measurements face polarity can be used occurring similar when to thathe observed Mg adlayer in undoped reaches samples. monolayer coverage during growth influences of different, parallel conducting Only films with Mg content less than cm 3 exhibited [62] any observed detectable a similar PL. Figure effect 3 a in shows their themg-doped PL spectra InN of with the polarity ution is limited by the squared [212]. product Swartz of moimum magnetic field, B 2, which should be et al. switching three such InN films. The spectra of layers with Mg contents unity for unambiguous results. 14 from In-face to N-face with increased Mg flux when growth begins on Ga-face The hole moexpected to be an order ofgan magnitude templates. lower Growth with peakonintensities sapphireindid the range not exhibit of any ev polarity and fullinversion. Wang et of and cm 3 are typical of undoped InN, e electron, corresponding to the difference in width at half maximum FWHM of less than 50 mev. In ffective mass. 15 However, the al. light [211] hole used mass TEM, contrast, convergent the film beam withelectron Mg content diffraction of and cm 3 wet shows etching a to study polarity parable to the electron mass, and the light hole peak PL signal at much lower energy, around 0.58 ev. The ed to be nearly degenerate with inversion the heavy ashole a result dipofobserved Mg doping theand PL spectrum found inversion at 0.56 evdomains is an absorption from In- to N-face when r sufficiently heavy acceptor doping, the light artifact caused by the spectrometer; accounting for this, the Nov 2006 to Redistribution Mg concentration subject to was AIP increased license or copyright, above 1.6 see cm 3.

106 86 Chapter 4: InN Recent attempts by Durbin et al. (2007) [213] to use Zn as a p-type dopant in InN (based on its use in InAs) have shown some promise, but more work must be done to provide conclusive results. The difficulty in confirming the presence of free carrier holes through methods other than variable magnetic field Hall analysis demonstrates that it is an extremely useful measurement technique in the quest for p-type material. Confirmation of actual carriers (not only ionised acceptors) and detail of their transport properties provides invaluable feedback to growers. The use of this technique for n-type material is also important, and experience using the technique for both types of material will be of great benefit to InN development. The work of this thesis provides valuable experience and insight into using this technique which can be applied to the investigation of p-type InN in the future. 4.5 Carrier Transport Properties The lowest electron concentrations and greatest mobilities reported for InN have all been achieved with MBE- or MOCVD-grown material in recent years. The only exception has been the work of Tansley and Foley in the mid-1980s who reported on multiple RFsputtered InN films with electron concentrations below cm 3 [30, 31], with a one-off outstanding result in 1984 where they measured a mobility of 3980 cm 2 /Vs and an electron concentration of mid cm 3 from a single-field measurement ( [42] see reference 6 in [130]). However, no subsequent attempts to obtain InN films by RF-sputtering with such low carrier concentrations have been successful, even in recent years with the original growth equipment used by Tansley and Foley. The majority of transport results reported in the literature are calculated from a Hall measurement using a single magnetic field (which is usually low, around 0.4 T), on a non-photolithographically defined van der Pauw sample with pressed or soldered indium contacts. As described in section , the use of (often large) contacts on the corners can add considerable error to the measurement to begin with. It is noted that Tansley and Foley [30] used photolithographically defined cloverleaf van der Pauw samples for their Hall measurements. Whether or not the use of the cloverleaf/photolithography contributed to their results (by improvement of accuracy, or improvement of material) is unknown (no further processing details were described). The most significant problem, though, with the common single-field Hall measurement, is that InN has at least two electron species that are always present in each sample measured:

107 4.5: Carrier Transport Properties 87 a bulk background n-type concentration and a surface accumulation of electrons, as well as charge carriers (holes or electrons) at the growth interface which may also contribute to conduction. A given sample of InN is therefore a multi-layered structure, in which parallel conduction paths all contribute to conduction, and therefore any measurement of Hall and resistivity voltages (as part of the Hall measurement) will contain (not necessarily equal) contributions from each species. This means the calculated values of carrier concentration and mobility from a single-field Hall measurement are actually a weighted averaged value of the properties of the multiple carrier species. It has been quoted in the literature that films of thickness greater than 1 µm are sufficiently thick for the contribution of the surface electrons to the measured single-field results to be negligible [178]. However, the results presented in the next chapter will conclusively demonstrate that this is not the case. As explained in section 3.1, the values for carrier concentration and mobility calculated from single-field Hall measurement in a multi-carrier system are weighted averages of the properties of each carrier species. Single-field Hall mobilities as a function of thickness have shown that the mobility increases with film thickness [166]. This necessitates that the electron mobility in the bulk must be higher than at the surface and/or interface [145]. The averaged mobility calculated by a single-field Hall measurement is therefore lower than the actual mobility of the bulk electron species, but higher than that of the surface and/or interface species. When the measured single-field mobility is lower than the actual bulk mobility, the reported values for the bulk carrier concentration of InN films are an overestimation (see equation 4.2). The properties of the surface electron species, especially the mobility, can be difficult to measure separately from the bulk. Table 4.2 provides a summary of some significant milestones in the single-field Hall transport results from the literature, showing key results of carrier concentration and mobility for various growth methods and all InN crystal polarities for which transport properties have been reported. Table 4.1, earlier in this chapter, lists surface accumulation properties that have been reported via various techniques. While low cm 3 samples were grown as early as 2000, no recent reports of significantly lower carrier concentrations in In-face InN as measured by single-field Hall have been published, though low ( cm 3 ) concentrations have been reported via other, non-averaging, methods [62, 177, 182, 214] (and in papers from the work of this thesis). While early milestones were achieved using a range of growth techniques, the most recent high quality results are all from MBE-grown material. The reported single-field results for the background electron concentration in N-face InN are not only lower in concentration, but have higher mobility than In-face

108 88 Chapter 4: InN single-field results in the literature. One group has also reported the transport properties of an a-plane InN sample. Regardless of its drawbacks, single-field Hall measurement will remain the dominant form of transport characterisation for InN due to its widespread availability, simplicity and the lack of more specialised equipment and analysis expertise. For the differentiation of carrier species in InN, high magnetic fields are required because of the low mobilities of both the bulk ( cm 2 /Vs) and surface ( cm 2 /Vs) electron species (section 3.1.4). Magnetic fields of 4.5 T have been used with some success for InN [56,57], however much higher fields, at least up to 12 T, enable far more accurate fitting of low mobility carriers Theoretical Calculations of Transport As discussed in Chapter 1, there is great interest in InN for electronics applications due to the theoretically predicted superior transport characteristics to those of GaN or AlN. If InN could be successfully integrated into III-N devices, it is possible the frequency of operation could be increased while still maintaining high power characteristics, a shortfall of other high speed material systems such as GaAs or InP. In much of the early work on InN, the accepted values for parameters such as band gap, electron effective mass and band structure calculations were different enough from currently accepted values that early reports on calculations of transport parameters quote results that are probably fairly inaccurate. The general result, though, is that older calculations have underestimated the transport properties of InN, and indeed more recent modelling with updated parameters gives higher predicted limits for the transport properties of electrons in InN, positioning the material as highly desirable for future devices. The drift velocity of an electron, v d, is related to the electric field across the sample, E, by the parameter known as the drift mobility, µ d, v d = µ d E (4.3) Mobilities quoted from velocity-field simulation results are usually the low-field mobility, taken from the initial linear section of the velocity-field curve. The drift mobility may then vary with changing electric field. The drift velocity peaks when the mobility/electric field product is maximised, and gives the peak transport performance that can be expected from electrons in the material. The calculation of velocity/electric field characteristics of electrons in InN gives theoretical predictions for the maximum mobility in InN. This information is vital in interpreting the results obtained in this work in Chapter 5.

109 4.5: Carrier Transport Properties 89 Table 4.2: Significant results in the bulk electron transport properties of InN, as calculated from single-field Hall measurements. Entries are left blank where details were not reported. Year Reference Temp. Carrier Concentration Mobility Thickness Growth Method K cm 3 cm 2 /Vs µm polycrystalline InN 1972 Hovel and Cuomo [25] (5 8) ± reactive RF sputtering 1984 Tansley and Foley [30] RF sputtering 1984 Tansley and Foley [130] Ref. 6 mid RF sputtering single crystal InN In-face InN 1997 Sato et al. [215] plasma-assisted MOVPE 2000 Lu et al. [140] RT MEE 2002 Yamamoto et al. [216] RT MOVPE 2003 Lu et al. [166] RT MBE 2002 Lu et al. [24] Ref MBE on HVPE GaN 2002 Lu et al. [217] MBE 2006 Gallinat et al. [141] RT MBE on MBE GaN buffer N-face InN 2006 Koblmüller et al. [34] RT MBE non-polar a-plane InN 2007 Veal et al. [85] MBE

110 90 Chapter 4: InN Monte Carlo simulations of electron transport in InN and other III-V semiconductors have been performed by O Leary et al. (1998) [36], Bellotti et al. (1999) [134], Foutz et al. (1999) [37] and O Leary et al. (2005) [38]. O Leary et al. (1998) [36] calculated the velocity-field characteristics of wurtzite InN using a Monte-Carlo approach, using a band gap of 1.89 ev and effective electron mass of 0.11 m e. O Leary et al. (2005) [38] reported updated simulations using a band gap of 0.75 ev and effective mass of m e, and also experimented with changing the nonparabolicity coefficient associated with the lowest energy valley, concluding that the band gap and effective mass play critical roles in influencing the nature of the electron transport. It was determined by simulation that InN theoretically exhibits an extremely high peak drift velocity at room temperature of cm s 1 [38] (up from cm s 1 in [36]) at a doping concentration of cm 3. The theoretical saturation drift velocity is also very high at cm s 1 [38] (down from cm s 1 [36] ), comparable to gallium nitride and larger than that of GaAs, which is around cm s 1. The RT low-field drift mobility maximum was calculated at around cm 2 /Vs [38] (up from cm 2 /Vs in [36] ). The drift velocity characteristics of InN were simulated to be less sensitive to changes in temperature ( K) and doping concentrations (up to cm 3 ) than GaAs, which signifies great potential for InN device applications. There is only a weak temperature dependence of the velocity-field characteristic for InN, in contrast to a strong dependance for GaAs, due to the much larger optical phonon energy and large intervalley energy separation. Foutz et al. (1999) [37] calculated higher saturation and peak electron velocity in InN than in GaAs. In devices with dimensions greater than 0.2 µm, the steady-state electron transport is expected to dominate device performance. For devices with small dimensions, however, the transient average electron velocity can considerably overshoot the corresponding steady-state drift velocity. They calculated InN to have superior transient electron transport characteristics to GaAs. In particular, InN was calculated to have the largest overshoot velocity, and for the distance over which the overshoot occurs, 0.3 µm, to be longer than in either GaN or AlN. When considering the transient response, the calculated velocity of electrons in InN is greater than in GaAs at all distances. The calculations of Foutz et al. [37] were performed using a band gap of 1.89 ev and effective electron mass of 0.11 m e. O Leary et al. (2005) [38] reported updated simulations using a lower band gap and effective mass, reporting that the transient characteristics were also found to be improved with the updated parameters, leading to a larger calculated electron overshoot velocity for InN. and the distance over which the overshoot occurred

111 4.5: Carrier Transport Properties 91 was simulated to exceed 1 µm (up from 0.3 µm in [37] ), which was once more further than that simulated for GaN, AlN or GaAs. Bellotti et al. (1999) [134] used a Monte Carlo approach to study the electron transport in InN, with some small updates in the parameters including an updated band structure. They calculated a peak electron drift velocity of cm s 1, with some reduction in this value along an alternate crystal direction due to band structure curvature variations. The low-field mobility was calculated to be around 3000 cm 2 /Vs. Early work by Chin, Tansley and Osotchan (1994) [133] calculated the theoretical maximum electron mobility in InN as cm 2 /Vs at room temperature. At 77 K, however, the predicted limit was as high as cm 2 /Vs. Updated calculations by Polyakov and Schwierz (2006) [40] predicted that with ionised impurity concentrations around cm 3 (corresponding to low doped, uncompensated, dislocation-free material) the room temperature mobility of electrons in InN could reach cm 2 /Vs, though this was revised to cm 2 /Vs by Polyakov et al. (2009) [41] upon inclusion of piezoelectric scattering and the nonparabolicity effect of the overlap integral G kk. Polyakov and Schwierz have not reported the predicted mobility at 77 K, but given the improvement in mobility the updated parameters demonstrate at room temperature, the 77 K mobility can be reasonably expected to reach, and likely surpass, the limit predicted by Chin, Tansley and Osotchan of cm 2 /Vs, which is as high as the mobility achieved in AlGaN/GaN HEMT 2DEGs, which exhibit the highest measured III-nitride electron mobilities to date (up to cm 2 /Vs at 77 K, measured in this work see section 7.4.2) Temperature Dependence and Electron Scattering Analysis of the temperature dependence of carrier concentration and mobility can provide useful insight into conduction mechanisms and scattering sources within the material. If the carrier concentration rises significantly with temperature it is possible to calculate/extract an activation energy for the carriers. The temperature dependence of the mobility enables estimation of the dominant scattering mechanisms that are limiting the carrier mobility. In InN we expect, as in the other III-nitrides, that scattering by polar optical phonons will dominate at high temperatures, with influence from as low as 150 K. This is due to the high polar optical phonon energy in the III-nitrides. Polar optical phonon scattering is (especially with high energy phonons) highly inelastic, and no closed form for the scattering

112 92 Chapter 4: InN (a) (b) Figure 4.11: Temperature dependent mobility of: (a) low concentration polycrystalline InN films [30]; (b) a low electron concentration InN film ( cm 3 ) [192]. time can be obtained analytically. Various methods (variational method, iterative methods [83]) can be used to find a solution to the scattering time. The high background concentration of InN indicates that there will be a high concentration of ionised donors (mostly native defects, with threading dislocations dominant). Ionised impurity scattering (which can relate to any ionised centres) is therefore likely to be particularly important at low temperatures (< 150 K). There are very few published results on the temperature dependence of electron transport properties in InN. Of those, most reported that the electron concentration of InN was (within experimental error) independent of temperature, an effect of degeneracy due to the high levels of unintentional doping (MBE: cm 3 ) (2006) [188], (MBE: cm 3 ) (2001) [195], (MOVPE: cm 3 ) (2005) [218] and (PSMBE: cm 3 ) (2006) [192]. The measured Hall mobility of each of these films was also largely temperature independent; the mobility in [218], [192] and [188] showed little change up to 200 K, though decreased slightly as the measurement temperature rose to 300 K. Above room temperature in [192] the electron concentration was seen to increase rapidly while the mobility decreased (where measured), assumedly due to the start of intrinsic carrier generation. Of note is that in all these results the electron concentration and mobility were measured by single-field Hall effect measurement, which as previously discussed gives only averaged values for the transport parameters, over all of the carrier species in the material.

113 438 ARTICLE IN PRESS 4.5: Carrier Transport Properties 93 R.E. Jones et al. / Physica B (2006) Electron Mobility (cm 2 /Vs) Acoustic Phonon- Piezoelectric Optical Phonons Ionized Centers Undoped, H + -irradiated InN Undoped, He + -irradiated InN Acoustic Phonon- Deformation Potential Mg-doped, He + -irradiated InN Electron Concentration (cm -3 ) Table 1 Parameters used in InN electron mobili Static dielectric constant, w 0 High-frequency dielectric constant Band gap energy, Eg Effective electron mass at CBE, m 0 * Longitudinal optical phonon energy Deformation potential Acoustic phonon velocity Density Piezoelectric constant electronic structure of the cond energy range. We used a two-b the conduction band structure i interaction between the conduct band [12]. This interaction coup to s-like conduction band st symmetry conduction band stat bolic dispersion relation: Fig. 3. Experimental data of irradiated InN plotted with calculations of Figure 4.12: Experimental electron mobilities data(assuming of irradiated a parabolicinn conduction plotted band) limited with by calculations the of electron " EðkÞ ¼ E g 2 þ E mobilities (assuming dominant a parabolic electron scattering conduction mechanisms. band) Onlylimited data for He by + ion thedoses dominant of electron scattering mechanisms. Only data for He + ion doses of cm 2 and higher are shown 2 2m 0 2 g þ E g_ 2 k cm 2 and higher are shown for the Mg-doped samples. for the Mg-doped samples [202]. where the energy is reference conduction band, and m * 0 is the e One of the most important f resulting energy-dependent ele samples, which had starting mobilities significantly lower than those of undoped InN at similar concentrations Pioneering work by(fig. Tansley 1). At and lower Foley fluences (1984) (o2.2 [30] showed He + temperature /cm 2 ), radia-dependention doping did not determine the electrical properties as in mobility in RF-sputtered InN, undoped giveninn; in Fig. there 4.11a. was little They change determined electron that mobility the mobility was limited or concentration at these doses. After sufficient fluences at low temperatures (2.2by 10 ionised 15 He + /cm impurity 2 and scattering higher), theandmobility at highvalues temperatures by either converged with those of the undoped samples (Fig. 3), polar optical phonons, or possibly by impurities related to the intercrystallite boundary again demonstrating that irradiation can be used to control layers and crystallite theinteriors bulk electrical of the properties. polycrystalline samples. The polycrystalline nature In our theoretical analysis of the electron mobility we of their samples limits considered the usefulness all the main of electron comparison scattering of their mechanisms, mobility data with that of including optical phonon, acoustic piezoelectric, acoustic crystalline MBE grown deformation samples. potential, and ionized center scattering. To roughly estimate the relative contributions of the different Thakur et al. (2006) scattering [192] processes, measuredwe a calculated lower electron the mobilities concentration assuminginn film grownw 2 0by a parabolic conduction band with the band edge electron m i ðkþ ¼ 2pe 3 _Z 2 N i F MBE ( cm effective 3 ) which mass of did0.07m show i 0 [2], strong wheretemperature m 0 is the electron dependence mass of the mobility in vacuum. The other material parameters used in the (but less so the carrier calculations concentration). are listed in Table The mobility 1. As shown peaked in Fig. at3, the 2100 cm 2 /Vs around 175 K. The temperature phonon-limited dependent mobilities mobility are graph significantly is reproduced higher than as Fig. 4.11b. Thakur the experimental mobilities, as well as the ionized-center- the carrier mobilities, concentration over the entire and concentration mobility self-consistently range. This to determine et al. fitted to bothlimited indicates that ionized-center scattering is the dominant the dominant scattering scattering mechanisms. process in the They samples concluded studied, that although in the there low temperature regime may be a contribution from optical phonons at the lowest scattering was dominated free electron by threading concentrations. dislocations, Therefore, while we now above limit 200 our K polar LO phonons and deformation potential considerations were to the scattering dominant by ionized scattering centers. mechanisms. To accurately calculate the electron mobility at high electron concentrations, we had to properly describe the affects the energy dependence o that reduces mobility compared addition, the admixture of the v band wavefunctions reduces th between different conduction increasing mobility with respect incorporate these two effects adopted a theoretical scheme th and other narrow gap semicon Szymanska [13]. The energy-dependent elect ionized defect scattering is given de 2 k, dk where w 0 is the static dielectric co ionized defect centers, and F i is a into account free electron scree reduction of the scattering rates nature of the conduction ban uncompensated material, the c centers (ionized defects) N i ¼ electron concentration. In co singly charged centers, N i ¼ ðnð the compensation ratio. The obtained by averaging the micr with the Fermi Dirac distributio Jones et al. [202] calculated the electron mobilities at RT limited by various dominant electron scattering mechanisms, assuming a parabolic conduction band. These calculations were graphed against experimental data for irradiated InN, reproduced here as Fig They observed that the phonon-limited mobilities calculated were signicantly higher than

114 94 Chapter 4: InN both the experimentally measured mobilities and the ionised-center-limited mobilities, over the entire concentration range. They concluded that ionised-center scattering was the dominant scattering process in the samples studied. They did note, however, that there may have been a contribution from optical phonons at the lowest free electron concentrations Multiple Carrier Transport The measurement of the carrier transport properties of the multiple electron species in InN is not straightforward, as all carriers contribute to conduction and therefore the standard transport measurement technique of single-field Hall calculates only averaged values. Techniques exist, though, to extract the transport properties of multiple species in semiconductors with mixed conduction. One such technique is the combination of multiple magnetic field Hall and resistivity measurements with a multi-carrier analysis, such as multi-carrier fitting (MCF) or quantitative mobility spectrum analysis (QMSA), that utilises the magnetic field dependence of carrier conduction to separate out the conduction contributions of multiple carriers. This technique has been used in the work of this thesis and is described in section Measurement of the optical Hall effect in InN has also been used to extract transport properties of the multiple carrier species in InN, and some attempts have been made to use infrared reflectometry. Table 4.3 lists transport properties of multiple carrier species in InN as collated from the literature. Numerical results for all species were not always published, and a variety of measurement temperatures have been used. Therefore, it is noted in the table where results have had to be estimated from published graphs in order to present a more comprehensive view of published results. Estimation from the graphs made use of graph digitisation software in order to extract values that were as accurate as possible Variable Magnetic Field Hall Measurement Prior to this work, very few publications reported the use of variable magnetic field Hall measurements to determine the individual carrier transport properties of the multiple carrier species in InN, despite it being a well established technique (with suitable analysis) in other material systems in which multiple carrier species co-exist [53 55, 103]. The specialised equipment required, a variable field magnet (preferably high field for InN) with temperature controlled sample cryostat (if temperature dependence is required), and soft-

115 4.5: Carrier Transport Properties 95 Table 4.3: Reported multi-carrier electron transport properties of InN, as determined by various multi-carrier extraction techniques. Reference Method, Sample InN Thickness No. of Carrier Assignment Temperature Carrier Concentration Mobility nm Carriers K bulk (cm 3 ); surf./intf. (cm 2 ) cm 2 /Vs [56] (2004) Variable-field Hall + MCF 60 2 bulk electron (4.5 T) surface electron In-face (assumed) InN / GaN 60 2 bulk electron surface electron x [57] (2004) Variable-field Hall + MCF bulk electron (4.5 T) surface electron 110 data not published In-face InN / GaN bulk electron surface electron 110 data not published [52] (2006) Variable-field Hall + QMSA 500/30 3 surface electron In-face InN:Mg/InN / GaN bulk light hole 300 dnp heavy hole [62] (2007) Variable-field Hall + MCF bulk electron RT dnp In-face InN / YSZ surface electron RT data not published unknown hole RT data not published [63] (2007) Variable-field Hall + QMSA bulk electron (12 T) surface electron <100 interface electron [177] (2008) Optical Hall bulk electron RT 1.91 ± In-face InN / GaN/AlN surface electron RT (cm 3 ) dnp bulk electron RT dnp surface electron RT (cm 3 ) dnp [182] (2009) Optical Hall bulk electron (RT?) dnp dnp InN / GaN or AlN surface electron dnp dnp bulk electron dnp dnp surface electron dnp dnp InN:Si / GaN or AlN bulk electron dnp dnp surface electron dnp dnp : value read off of published graph dnp: data not published

116 An estimation of the range of mobility was made by finding the higher and lower extremes of 96 Chapter 4: InN Fig. 6. A comparison of the single field 0 the bulk electron mobility from a two ca and maximum ranges of the QMSA spe the QMSA spectrum peak at e defined as the mobilities where centration given by the QMSA sp the maximum value. These value function of temperature in Fig. mobility values obtained from and single-field Hall analysis at the presence of the low-mobility still have a significant effect on th Fig. 4. QMSA at 25 K for a 600-nm thick InN layer Figure 4.13: Electron mobility spectrum generated by QMSA for a 600 nm thick grown on a 200-nm thick AlN buffer which clearly shows both mobility InN layer even for this quite thick grown on a 200 nm AlN buffer [56]. bulk and low mobility surface conduction. of variable-field measurements a ware and/or analysis expertise in multiple carrier fitting (MCF) or quantitative mobility spectrum analysis (QMSA), are the two main hurdles to performing these measurements. The first publication using multiple magnetic fields and MCF/QMSA to determine the individual transport parameters of the bulk and surface electrons in InN is by Swartz et al. (2004) [56], with a slightly expanded version of their results appearing soon after (2004) [57]. The only other reports to use this technique (other than those published as a result of the work in this thesis) are Anderson et al. (2006) [52], Pomeroy et al. (2007) [63] and Swartz et al. (2007) [62]. These papers report on finding multiple carriers in InN, though the extracted transport parameters (concentrations, mobilities, conductivity percentage contributions and temperature dependence) are reported only for a select few species and temperatures. The results that are presented in these reports are tabulated in Table 4.3. Swartz et al. [56,57] used a maximum magnetic field of 4.5 T (with single polarity) [219], and the samples had soldered indium contacts in the van der Pauw configuration. They used MCF to fit two electron species to a wide selection of measurement data for MBE grown InN films, between 60 and 7500 nm thick, on both GaN and AlN buffer layers. MCF gave good fits to the experimental data for all samples. As MCF requires some a priori selections, in this instance Swartz et al. chose to fit two electron species, with one at low mobilities ( cm 2 /Vs) and one at high mobilities ( cm 2 /Vs). They also generated QMSA spectra that displayed two electron peaks with distinctly different mobilities. Only one full spectrum was given, reproduced here as Fig

117 4.5: Carrier Transport Properties 97 Swartz et al. [56, 57] assigned the low mobility electron to the surface electron species. Their justification was in two parts, the first being that the sheet charge density of the low mobility electron was seen to be comparable to that reported by Lu et al. [166] for the surface electron sheet concentration measured using C-V. Secondly, the thicknessdependent Hall data reported by Lu et al. [166] demonstrated that the mobility of the surface/interface residual electron accumulation was around 100 to 300 cm 2 /Vs, depending on the buffer layer, which is comparable to the low mobility electron they measured and much lower than the values of the higher mobility electron. Thickness-dependent singlefield Hall data also shows that mobility increases with InN thickness, and therefore the bulk must have a higher mobility than the surface accumulation. Additionally, as the volume concentration at the surface can be as high as cm 3 [49,166], which is higher than the (single-field Hall measured) bulk volume concentration of typical films, one would expect the mobility of the surface electron to be lower than that of the bulk, simply due to (at least) substantial carrier-carrier scattering in the highly populated near surface region. As noted by Swartz et al., if there exist low mobility electrons at the growth interface, or in the buffer, that contribute to conduction, they may be incorporated into the extracted low mobility electron species properties. In two-carrier MCF analysis, multiple low mobility species may be unknowingly combined even if their mobilities are distinct. Using QMSA, the two species will only be combined if they have coincident mobilities and thus appear as part of the same peak in the electron mobility spectrum. If they were distinct, they could be separated out. As Swartz et al. only saw two peaks in their QMSA electron spectra, any interface charge species has either the same mobility as the surface accumulation, or is not contributing to the conduction significantly enough to be resolved. Given that, in these reports, the maximum field used is only 4.5 T, even significant densities of surface and interface species are unlikely to be independently resolved due to their low mobilities (see section for discussion of the magnetic fields required for improved resolution of carriers). Swartz et al. saw little temperature dependence in either the sheet concentration or mobility of the surface electron species, which is consistent with the expectation that the surface species will be degenerate (the Fermi level pinning at the surface is at least 0.6 ev above the CBM [172, 173]). However, Swartz et al. did find that the conductivity of the low mobility species was dependent upon on the film thickness. They suggested that if the majority of the low mobility conduction was from the surface electron accumulation (and not from any growth interface charge) then the improvement in conductivity with increased thickness was most likely related to the improvement in the crystal quality of the

118 98 Chapter 4: InN top region of the InN film for thicker samples. For the conductivity of the low mobility electron species to have increased, either the sheet concentration or the mobility (or a combination of both) must have increased. Recent XPS measurements have shown that the Fermi level pinning, and therefore sheet carrier density, at the surface of InN is fixed for a variety of films measured, regardless of growth conditions [171]. As only the thickness was varied in the samples measured by Swartz et al., it is most likely that the increase in conductivity of the surface electron species was due to increased mobility. Increases in mobility may be expected with an improvement in crystal quality if the dominant scattering mechanism is related to crystal defects. The conductivity percentage contributions from the assigned surface and bulk electron species were given for the thickest sample as an 80 % contribution from the bulk and 20 % from the surface, while for the thinnest sample the contribution of each species was around 50 %. This demonstrates that even for a sample 7.5 µm thick (far thicker than is usual for InN epitaxial films), 20 % of the conduction comes from the surface (and possible growth interface) electron species, which will introduce considerable error into any single-field Hall measurement. The bulk electron species (extracted via MCF) showed improved transport properties (decreasing concentration, increasing mobility) with increasing film thickness. As discussed earlier in this chapter, it has been shown using TEM that the quality of InN improves away from the growth interface [178, 196]. The InN films grown on GaN buffer layers had superior bulk transport properties to those grown on AlN buffer layers. This results demonstrates the way in which the accurate measurement of bulk electron transport properties can be used to examine crystal properties in this case the superior crystal quality of InN films grown on GaN as opposed to AlN buffer layers (a result shown previously by XRD measurements of the crystal quality [220]). Further multiple field investigations, focusing on both Mg-doped InN and the use of yttrium-stabilised zirconia substrates, were reported on by Anderson et al. [52] and Swartz et al. [62] respectively. Accuracy in the characterisation of low mobility carriers was improved in these reports through the use of higher magnetic fields, up to 12 T in [52] and even up to 30 T for select measurements in [62]. Anderson et al. extracted properties for a surface electron species and two independent hole species, attributed to light and heavy holes, in Mg-doped InN. Swartz et al. used multi-carrier fitting to extract a low bulk electron concentration from results of InN grown directly onto (111) YSZ substrates, which have a much smaller lattice mismatch with InN (only 2.5 %). They also found that MCF results required the incorporation of a p-type layer in order to give a good fit to the

119 4.5: Carrier Transport Properties 99 conductivity tensor components. No details of the transport parameters of the fitted hole species were given. It may be possible that a hole accumulation is present at the growth interface, as predicted at the growth interface of N-face InN. Pomeroy et al. [63] used variable magnetic field Hall measurements with QMSA (presumably using i-qmsa but the specific software version is not noted) to supplement the investigation of phonon-plasmon interactions in InN by Raman spectroscopy. They observed three clear electron peaks, one clearly a bulk electron species at mobility contributions of cm 2 /Vs. The other two peaks are at cm 2 /Vs and at/below the 100 cm 2 /Vs limit (of the i-qmsa software). Interestingly, they ascribe the low mobility peak (< 100 cm 2 /Vs) to the surface electron species, and the mid-mobility peak to an interface electron species, with no real justification for the choice. They cite the paper by Swartz et al. [56, 57] for the attribution, yet the mobility of the surface electron species found by Swartz et al. was shown to be between 100 and 300 cm 2 /Vs, and no third peak was seen in those results. As discussed above, however, the low magnetic fields used in [56,57] would likely reduce distinct carrier species extraction ability at these mobilities, and the use of two-carrier MCF explicitly precludes a third carrier being detected. The mobilities of the two higher mobility electron species decreased after annealing to 700 K, with the mid-mobility electron species increasing slightly in concentration. The conductivity of the third (low mobility) peak is reduced by a factor of 1.5. In this analysis, in order to account for their Raman spectrum broadening after annealing, the degradation of the conduction of the low mobility electron (<100 cm 2 /Vs) was required. The presence of a distinct third electron species has not been reported in any other work Alternate Multiple Carrier Techniques Only two other techniques have been used to try and extract both the carrier concentration and mobility of the individual carrier species in InN. The optical Hall technique is used by Hofmann et al. (2008) [177] and Darakchieva et al. (2009) [182] to identify the bulk and surface electron species and decouple their properties. The measurement of the optical Hall effect is performed using magneto-optical generalised Mueller matrix ellipsometry (MOGE) at infrared and THz wavelengths, detailed in [177, 182, 214] and their references. Darakchieva et al. [182] also use infrared spectroscopic ellipsometry (IRSE) data combined with the MOGE data in their analysis. In [177] the analysis is is used within a stratified layer model data analysis, which appears to have

120 100 Chapter 4: InN fitted a two layer model, while in [182] the combined MOGE and IRSE data were analysed to unambiguously identify two InN layers with different free electron properties. In [177] the surface accumulation is reported to be confined to a thin layer, between 3 to 5 nm, with the bulk electron distributed throughout the rest of the InN film. In both papers the surface electron sheet density was extracted and was shown to decrease with decreasing bulk volume concentration. The concentrations of both electron species (surface and bulk) decreased with increasing InN film thickness. Previously bulk concentrations have been seen to decrease with increased film thickness, primarily due to the improved crystal quality as the layer becomes thicker. It may be put forward that the improved crystal quality at the surface of a thicker InN film may also lead to a reduction in the sheet density of the surface electron accumulation. This would require, though, a smaller VBM to Fermi level separation, which Darakchieva et al. were unable to explain, and which is contrary to measurements by King et al. [171] that the VBM to Fermi level separation is equal for all wurtzite InN surfaces. Attempts at using infrared reflectance (IRR) spectrometry to extract multi-layer electrical properties of InN epilayers have had some success in determining the concentration and mobility of bulk electrons or bulk holes (in Mg doped InN) but no extraction of surface or interface electron species have been made with confidence. The modelling to fit to experimental data requires a priori assumptions about the properties of the layers. Kurihara et al. (2008) [221] measured thin ( nm) MOVPE films, but only fit bulk and growth interface electrons to the IRR data, neglecting the surface accumulation. The films, though, were degenerate with very low bulk mobility ( 100 cm 2 /Vs), which precludes the possibility of more insightful results with a different analysis. Ishitani et al. (2008) [222] attempted to fit simulated IRR spectra to determine the properties of the surface electron. Assuming, in an a priori fashion, that the accumulation of surface electrons is cm 3 over a thickness of 1 nm, they try to find a spectra that corresponds to the simulated spectra of a sapphire buffer layer in certain wavelength regions. The reasoning behind this is not explained clearly. They achieved the best fit with a mobility of 10 cm 2 /Vs or less. They later went on to say, though, that surface electron accumulation has negligible effect on the IRR spectra and that the effect of the surface electron has not been detected because of the large plasmon broadening. This makes it difficult to know if IRR is a suitable tool for determining surface electron properties, though it may have use in determining the electrical properties of the bulk electron species with greater accuracy than single-field Hall measurements.

121 4.6: Chapter Summary Chapter Summary The development of high quality single crystal growth has revealed that the inherent properties of indium nitride are indeed favourable for devices, as the bandgap extends the range of III-nitride alloys into the infrared, and the potential maximum drift velocity is far greater than in GaN, AlN or even GaAs. Yet there remain many challenges to realisation of InN and In-rich ternary alloys for devices. The propensity for unintentional n-type doping requires further improvement of growth techniques in order to reduce the background electron concentration, and to realise reliable, high concentration p-type doping. The electrical characterisation of InN is thus essential for the development and understanding of growth techniques in order to improve the material quality for future devices and applications. The existence of an accumulation of electrons on the surface of the material hinders accurate characterisation of the electrical properties, which are vital for the feedback required for the improvement in growth techniques that must be achieved. The galvanomagnetic measurement technique used in this work, with a multi-carrrier analysis technique such as QMSA, enables the accurate characterisation of carrier species in InN, and will be of great use in the development of InN and In-rich III-nitride alloys for device applications.

122

123 Chapter 5 Indium Nitride Characterisation Results 5.1 Introduction This chapter presents and discusses the experimental results of the characterisation of InN that have been performed as part of the work presented in this thesis. The chapter is divided into sections for each of the three experimental blocks, with results for each experiment detailed and discussion presented. In the final section, the results from all the experiments are compared with each other in order to determine more general conclusions. Chapter 4 introduced many of the fundamental properties of InN, including the discovery that not only does it exhibit a strong propensity for unintentional n-type doping (see sections 4.4 and ), but also that the surface of the semiconductor is accumulated with electrons, independent of surface treatment or crystal orientation (see section 4.4.2). There are, then, multiple electron species in any given sample of as-grown InN. This fundamental existence of multiple carrier species in InN complicates the interpretation of the standard single-magnetic-field Hall electrical characterisation technique. Early characterisation of transport and electrical properties did not make allowance for the multiple carriers as the presence of the surface accumulation had not yet been predicted or observed. More importantly though, even the most recent transport results also, for the most part, do not process results beyond the standard single-field Hall calculation, largely due to the lack of variable (high) field magnets, and ambiguity about surface electron properties (Table 4.1), such as a fundamental value (or lack thereof) for the surface density and mobility, which would enable a two layer model to be used. As such, the vast majority of transport 103

124 104 Chapter 5: InN Characterisation Results results published for indium nitride (Table 4.2) are calculated assuming a single electron species, and therefore represent only an averaged value over the multiple electron species present in the material. There are very few results published in the literature describing the distinct transport properties of each individual electron species in indium nitride (Table 4.3). Notable exceptions are Swartz et al. [56, 57, 62], Anderson et al. [52] and Pomeroy et al. [63] who have used techniques similar to this work. Only Swartz et al. [56, 57] were published prior to the majority work of this author (Fehlberg et al. [43, 58 60]). In order to extract contributions of multiple carriers in a mixed conduction material, this work makes use of multiple magnetic fields per measurement and then applies a multiple carrier analysis, as outlined in Sec 3.1.4, to isolate individual carrier species contributions and transport properties. The use of quantitative mobility spectrum analysis techniques (QMSA) means that all multi-carrier analysis in this work is not conducted in an a priori fashion; that is, no assumptions about the number or type of carriers present is required or used before the multi-carrier fitting algorithm is run. For reference, a summary of numerical results from the experimental work detailed in this chapter is presented at the end of the chapter in Table Demonstration of Multiple Carriers in In-face InN Growth Details The first InN measurements in this work were conducted on two In-face InN samples. The samples were grown at UCSB by plasma-assisted molecular beam epitaxy (PA-MBE) on a semi-insulating (Fe-doped) Ga-polar gallium nitride (GaN) template ( 8 mm 8 mm square pieces), with an optimised MBE GaN buffer layer (growth details are reported elsewhere by Gallinat et al. [141, 146]). InN was deposited at a substrate temperature of 450 C under In-droplet conditions. The InN films are 2.7 µm thick, which is thicker than most InN films studied in the literature (generally InN is grown to a thickness of nm, though films of 4, 7.5 and even 10 µm have been reported).

125 5.2: Demonstration of Multiple Carriers in In-face InN Magnetotransport Measurement Details Van der Pauw Configuration The projected mobility of the surface electron accumulation from Hall measurement data on very thin samples was 300 cm 2 /Vs [166], and therefore the surface electron species was unlikely to be resolved using only low magnetic fields. This was confirmed with preliminary measurement of the InN samples in the van der Pauw configuration at magnetic fields up to 2 T. In order to overcome this limitation the samples were then measured in a superconducting magnet at magnetic fields up to 12 T (which is one of the largest magnetic fields generally available in semiconductor research facilities for this type of measurement, though larger field magnets may be found in specialised laboratories). The van der Pauw configuration with pressed indium contacts was again used, though the samples were cleaved to 5 mm square to fit the measurement apparatus. The samples were measured between 77 and 300 K. The i-qmsa software package from Lake Shore Cryotronics, Ltd was used to generate the mobility spectra (the use of quantitative mobility spectrum analysis and the two software algorithms used in this work are described in section 3.1.5). The mobility spectra were unclear, with peaks for electrons and holes occurring at similar mobility values. Both samples gave similar results. All published results demonstrate strong n-type conductivity for InN [34, 85,140,141, 215], and the calculated band structure supports these findings [48, 156, 157, 168]. Mixed conduction in these samples without intentional p-type doping is therefore highly unlikely. In the mobility spectra obtained then, the hole peaks are most likely ghost peaks (the phenomenon of ghost peaks is outlined in section ). The prominent hole peaks and lack of consistent trends of carrier species in the mobility spectra across temperatures resulted in it not being possible to identify which carrier peaks in the spectra were real and which were ghosts peaks, for either electrons or holes. As a result, no transport properties were extracted from the mobility spectra. The presence of ghost peaks can demonstrate a large amount of uncertainty in the data, likely due to errors in contacts (from their size with respect to edge length) and approximations as a result of the simple van der Pauw device configuration. The electron and hole mobility spectra for one of the samples at 300 K is given in Fig. 5.1, showing the multitude of electron and hole peaks.

126 106 Chapter 5: InN Characterisation Results Sheet Conductivity σ 2D (Ω -1 ) 1E-1 1E-2 1E-3 1E-4 1E-5 1E-6 Electrons Holes Mobility [cm 2 /(Vs)] Figure 5.1: Electron (solid line) and hole (dashed line) mobility spectra generated for an In-face InN sample measured in the van der Pauw device configuration at 300 K. 0 Conductivity Tensor Component σ xy(2d) ( Ω -1 ) van der Pauw Hall bar Magnetic Field (T) Figure 5.2: Conductivity tensor component σ xy of the In-face InN sample measured at 300 K in both the van der Pauw and Hall bar device configurations.

127 5.2: Demonstration of Multiple Carriers in In-face InN Hall Bar Configuration In order to extract transport parameters of the electron species in the samples, the mobility spectrum must show clearly defined electron peaks and not ambiguous or ghost peaks (section ). To obtain more accurate resistivity and Hall effect data, and thus clearer mobility spectrum results after applying the QMSA technique via the i-qmsa software, the samples were processed into 8-contact Hall bar devices. The ICP RIE dry etching tool was used for mesa definition. The etching process was developed in-house from InP etch recipes. The etch rate was approximately 0.1 µm/min. Complete details of sample processing steps, tools and recipes are detailed in Appendix B. Unfortunately only one of the two samples was measurable after fabrication into Hall bars. The measured Hall bar device shall be referred to as InN-HB. The Hall bar device was measured at magnetic fields from 0 12 T and temperatures between 77 and 300 K. The results from measurement of the InN-HB Hall bar device showed clear signs of multicarrier contributions to the transport in both Hall coefficient, R H, and the conductivity tensor component, σ xy. Figure 5.2 demonstrates the difference between the conductivity tensor component σ xy for the same InN sample before and after processing into a Hall bar device. Note the distinct flattening of the curve for InN-HB at high magnetic field values, in comparison to the curve of the van der Pauw device, indicating the presence of at least a second carrier with lower mobility (see section for discussion of σ xx and σ xy curve shapes). Later in this chapter, the possibility that the fabrication process is responsible for some of this change (i.e. more significant low mobility carrier conduction) is explored Experimental Results and Analysis QMSA Mobility Spectra The electron mobility spectrum generated by i-qmsa for the Hall bar device InN-HB is given in Fig. 5.3 for the measurement temperature of 300 K. Very similar spectra were obtained for measurements performed at 77, 100, 150, 200, and 250 K. All mobility spectra show clearly two electron peaks (the peaks defined over four orders of magnitude of conductivity). All conductivity values in the mobility spectra (the y-axis) are in terms of sheet conductivity, as there is no initial assumption of any particular details of the depth profile for each carrier.

128 108 Chapter 5: InN Characterisation Results 1E-1 Sheet Conductivity σ 2D (Ω -1 ) 1E-2 1E-3 1E-4 1E-5 1E Mobility [cm 2 /(Vs)] Figure 5.3: Electron mobility spectrum for the Hall bar device InN-HB measured at 300 K. As can be seen in Fig. 5.3, there is a low mobility electron carrier with significant conduction contributions at mobilities ranging from approximately 300 to 1000 cm 2 /Vs, and a high mobility electron carrier distributed between 3000 and 7000 cm 2 /Vs. The exact locations of the peaks along the mobility axis were dependent on the measurement temperature, which can be seen in the extracted results for the mobility (Fig. 5.4). The low mobility carrier was assigned to the surface electron species, as the mobility corresponds to that in the literature obtained via Hall measurements on InN layers of decreasing thickness [166] (in which the projected mobility was around cm 2 /Vs and certainly of much lower mobility than the bulk), while the high mobility electron carrier was assigned to the electron species throughout the bulk of the InN layer. Similar distinction was made by Swartz et al. [56] and their choice was discussed in the previous chapter, section As also discussed in section , if there are any other low mobility electron species that are contributing to conduction through the device, such as at the growth interface, their contributions will form part of the same peak in the mobility spectrum only if their mobilities are the same as for the surface electron accumulation. In this sample, only two electron peaks were seen in all mobility spectra. As there is a wealth of evidence demonstrating the existence of a surface accumulation of electrons, and no direct evidence of a growth interface accumulation, the low mobility peak has been assigned to the surface electron species and will be referred to as such for the remainder of this analysis. Discussion of possible electron accumulation at the growth interface in light of the mobility spectrum data in this thesis is discussed in section

129 5.2: Demonstration of Multiple Carriers in In-face InN 109 The measurement of the conductivity in the Hall bar is performed with no depth resolution, so even after having applied the QMSA technique to the multi-field data, it is not possible to determine if the range of mobility values in the peak are distributed with depth, or simply due to a broad electron mobility distribution throughout the entire layer. Previous studies using methods such as TEM have shown that the quality of the indium nitride crystal does increase with thickness, with marked improvement after around 1 µm [178, 196]. Therefore it is likely that some of the spread in the bulk mobility is due to significant variations of scattering processes over the thickness of the sample due to crystal quality variation Extracted Carrier Transport Results The extracted transport properties for the two electron species are given in Fig The carrier concentration and mobility of each electron species were extracted from the peaks in the mobility spectra. The details of the calculation of the transport properties from the mobility spectrum is described in section The largely temperature independent sheet density of around cm 2 for the higher mobility bulk electron species equates to a bulk density of approximately cm 3 over the 2.7 µm thickness of the InN layer. For comparison, single field Hall results for this device (calculated from measurement data at 1 T) give a bulk concentration of cm 3 at 300 K. Clearly, the low mobility electron species has a significant influence on the results; the electron concentration, when determined from a single magnetic field, is four times the separately extracted bulk electron concentration. It was noted previously, in section 4.5, that literature results often claim that beyond 1 µm film thickness, the surface electron accumulation has little influence on the calculated single-field transport results. This result demonstrates just how inaccurate that assumption can be. The extracted mobility of the bulk electron species is 3570 cm 2 /Vs at 300 K, which is the highest ever reported for indium nitride (this result was published as Fehlberg et al. [43, 58]), other than the one reported value of 3980 cm 2 /Vs by Tansley and Foley in 1984 [130] for RF-sputtered InN. Over the temperature range from 77 to 250 K the mobility of the bulk has a clear temperature dependence, and ranges from 4300 to over 5100 cm 2 /Vs at 150 K, as shown in Fig. 5.4b. For the low mobility carrier attributed to surface accumulation electrons, the sheet charge density of around cm 2 (Fig. 5.4b) is an order of magnitude higher than that reported by Lu et al. from C-V and variable thickness Hall measurements [166] and by other

130 110 Chapter 5: InN Characterisation Results 10 Sheet Concentration (10 14 cm -2 ) Temperature (K) (a) 5000 Mobility [cm 2 /(Vs)] Temperature (K) (b) Figure 5.4: The sheet carrier concentration (a) and mobility (b) for the bulk (open symbols) and surface (closed symbols) electron species in In-face InN device InN-HB, extracted from the mobility spectra obtained by i-qmsa at each measurement temperature.

131 5.2: Demonstration of Multiple Carriers in In-face InN 111 researchers with a variety of techniques (see Table 4.1). Lu et al. estimate the thickness of the surface accumulation to be on the order of 6 nm, with volume concentration as high as cm 3 in the first 2.5 nm. A depth of 6 nm would result in a volume concentration of electrons cm 3 near the surface in this sample. The surface electron species has a largely temperature independent mobility of about 500 cm 2 /Vs, comparable with reported values [56, 166]. While the low mobility peak has been assigned to the surface accumulation region, the peak would also contain any other low mobility carriers with similar mobilities in the material that have a significant contribution to conduction. Theory suggests that a GaN/InN interface charge may exist [145]. If an accumulation of electrons does exist and contributes to conduction at similar mobility values to the surface electron species it is unlikely to be resolved independently of the surface, as the multi-carrier analysis cannot differentiate between similar mobility electron species located in different regions of the material, as they would have an identical magnetic field dependence. The origin of the very high density surface sheet charge observed in this particular sample is unclear. According to King et al. [171] the surface accumulation at oxidised InN surfaces has a universal value of around only cm 2, which would result in cm 2 electrons existing elsewhere than the surface, presumably at the growth interface. Yet the high electrical quality of this material (comparable to that of a 7.5 µm thick layer [56]) suggests that the buffer layer/inn interface must be well ordered and of high quality, and therefore any interface charge as a result of crystal defects is likely to be lower than in other, poorer electrical quality, InN, which has been estimated at less than cm 2 [145]. Possible contamination or alteration from processing, handling and bonding procedures were all investigated on other control samples and the results are discussed in section below, while a comparison of surface and possible interface accumulations across all InN samples studied in this work is discussed in section at the end of this chapter Comparison of Variable- and Single-Field Results As mentioned above, the calculated carrier concentration for this device using data from a single magnetic field (e.g. 1 T) is around four times the separately extracted bulk carrier concentration. The bulk material properties are found to be much better than may be concluded using standard measurement techniques. Fig. 5.5 shows the mobility of device InN-HB over temperature, calculated using single-field (1 T) data (shown as red

132 112 Chapter 5: InN Characterisation Results 5000 Mobility [cm 2 /(Vs)] Temperature (K) Figure 5.5: Mobility of the bulk (open triangles) and surface (closed triangles) electron species, calculated from the mobility spectrum outputs of i-qmsa, and the mobility calculated using single-field data at 1 T (red squares) for device InN-HB. The lines are guides for the eyes. squares), in addition to the extracted mobility values from the multiple carrier analysis. The single-field mobility is only about half that of the bulk mobility, again underestimating the excellent bulk transport properties of the sample because of the degrading effect the surface accumulation has on the measurement of the bulk properties during single field calculations Further Investigations Repeat Growth of In-face InN In order to verify and further explore the measured results in these first InN samples, a repeat 2.7 µm thick In-face InN layer was grown under identical conditions to the sample InN-HB described above. This sample shall be referred to as InN-HB-2. The mesa etching of the Hall bars was performed at UCSB in a parallel-plate straight RIE tool, due to problems with the ICP RIE at UWA. The device InN-HB-2 was also measured between 77 and 300 K at fields of 0 12 T. The i-qmsa-generated electron mobility spectra for the device InN-HB-2 show two electron peaks at all measurement temperatures. The mobility spectrum at 300 K is shown in Fig Immediately it can be seen that the sheet conductivity of the low mobility

133 5.2: Demonstration of Multiple Carriers in In-face InN 113 1E-1 Sheet Conductivity σ 2D (Ω -1 ) 1E-2 1E-3 1E-4 1E-5 1E Mobility [cm 2 /(Vs)] Figure 5.6: Electron mobility spectrum of In-face InN Hall bar device InN-HB-2 at 300 K. electron species is much lower than the bulk, and much lower than in the case of InN-HB where the two species had similar sheet conductivities. The extracted transport results of the surface and bulk electron species for InN-HB-2 are given in Fig Also included are the results from InN-HB for comparison. The InN-HB-2 device has similar bulk characteristics to InN-HB, with a slightly larger volume concentration of around cm 3, and resultant slightly lower mobility of 2860 cm 2 /Vs at 300 K. The small difference in bulk electron transport characteristics is not unexpected given the time lapse between material growths, and the MBE reproducibility is still being improved. The 300 K mobility in these samples matches well with modelling of electron mobility in indium nitride conducted by Polyakov and Schwierz [40]. For indium nitride with ionised impurity concentrations between 1 and cm 3 the theoretical maximum mobility drops from 4000 cm 2 /Vs to around 2400 cm 2 /Vs comparable to the bulk values for InN-HB and InN-HB-2. Of significant interest in these two devices, however, is the large difference between surface electron species characteristics. While the surface electron species in both devices has a temperature independent mobility of around 500 cm 2 /Vs, the surface electron sheet concentration varied over two orders of magnitude between devices, from cm 2 in InN-HB to cm 2 in InN-HB-2. The use of the QMSA technique in this case has enabled these surface sheet concentrations to be extracted from the measured data, and no assumptions regarding the sheet concentrations have been made during the analysis. Likewise, the bulk properties have been

134 114 Chapter 5: InN Characterisation Results Bulk Carrier Concentration (cm -3 ) Sheet Carrier Concentration (cm -2 ) 1E18 InN-HB bulk InN-HB-2 bulk 1E E15 1E14 1E13 Temperature (K) (a) InN-HB surface InN-HB-2 surface 1E Temperature (K) (b) 5000 Mobility (cm 2 /Vs) bulk surface Temperature (K) (c) Figure 5.7: The transport properties (extracted from the mobility spectra) for In-face InN devices InN-HB (triangles) and InN-HB-2 (circles), comparing the volume concentration of the bulk electron species (a), the sheet concentration of the surface electron species (b) and the mobility of both bulk and surface electron species (c).

135 5.3: Effect of MBE Growth Parameters on Multiple Electron Transport in In-face InN 115 determined independently of the properties of the surface electron species. If multiple carrier fitting techniques which require initial estimates had been used, they may have led to different extracted properties based on theoretical assumptions. The measurement of less than the predicted indium nitride native surface accumulation concentration in InN-HB-2 is extremely curious, but was replicated in the measurement of two hall bars from the same wafer, and multiple measurements of a single hall bar after different surface contamination experiments (detailed below). The difference in surface electron species between the two samples suggests that the surface may be susceptible to alteration, given that the samples were grown under identical conditions and the bulk electron species properties in both samples are similar Investigation of Process Contamination or Damage The excessive electron accumulation on InN-HB, beyond that predicted and reported in the literature, was investigated. Multiple Hall bar devices on the repeat sample InN-HB- 2 were used to investigate the possibilities of surface contamination and of oxidation of the surface during processing. Low temperature annealing (<100 C) for more than 24 hours, solvent exposure (heated (60 C) acetone and trichloroethylene) and other possible sources of direct surface contamination during processing and preparing for measurement (e.g. sample bonding) were investigated as causes for the increase in surface accumulation in InN-HB. Such processes, however, did not prove to be responsible for any increase in surface accumulation on InN-HB-2. The only major processing difference between devices on InN-HB and the repeat sample InN-HB-2 was the mesa etching. Devices on InN-HB- 2 were dry-etched in a parallel-plate RIE plasma tool in a different lab to the ICP-RIE plasma tool used for InN-HB. However, further investigations into the difference in etching tools used for Hall bar definition were inconclusive. 5.3 Effect of MBE Growth Parameters on Multiple Electron Transport in In-face InN In this section a quantitative mobility spectrum analysis of multiple magnetic field (0 12 T) Hall-effect data was used to determine the individual transport properties of all electron species in three InN films grown by plasma-assisted molecular beam epitaxy (PA-MBE) under different conditions. The transport properties of both the bulk and surface electron

136 116 Chapter 5: InN Characterisation Results species are correlated with the growth conditions in order to find optimal conditions for the growth of indium nitride with respect to electrical characteristics Growth Details 1 µm thick In-face InN layers were grown on optimised GaN buffer layers on semi-insulating (Fe-doped) Ga-polar GaN templates. Growth of the InN films was performed at UCSB. Details on the growth equipment and buffer layers are detailed elsewhere by Gallinat et al. [141]. Three samples were grown under different conditions. Substrate temperatures and growth regimes were varied. Sample i440 was grown under In-rich conditions (Indroplet growth regime) at a substrate temperature of 440 C. Samples n470 and n450 were grown under N-rich conditions, at temperatures of 470 C and 450 C respectively. While the N-flux was fixed, the In-flux was further reduced for sample n450 compared to that used during the growth of n470. A summary of the growth conditions is given in Table Sample Processing Details 8-contact Hall bar devices were fabricated via hydrogen/methane/argon plasma etching in a standard parallel-plate reactive ion etching tool. These devices were not exposed to an ICP plasma. Metal contacts were e-beam evaporated. Details of sample processing are outlined in Appendix B Measurement Details Surface Morphology The surface morphology of the three InN films were studied under both optical and atomic force microscopes. Table 5.1: InN samples under study; growth conditions and RMS roughness determined via AFM (tapping mode) over multiple 5 µm 5 µm areas. Sample Flux Regime In/N Flux Ratio Growth Temperature RMS Roughness C nm i440 In-droplet > n470 N-rich n450 N-rich <

137 5.3: Effect of MBE Growth Parameters on Multiple Electron Transport in In-face InN 117 (a) (b) (c) Figure 5.8: Surfaces of devices i440 (a), n470 (b) and n450 (c) under an optical microscope. Under an optical microscope the three InN films all have different appearances. The surface of device i440, shown in Fig. 5.8a, appears smooth but with step-like features. The surface of n470, in Fig. 5.8b, has large spots and what appear to be swirl features. Device n450, Fig. 5.8c, has a rough surface and also has large spots as features on the surface. Atomic force microscopy (AFM) imaging of the samples was performed in tapping mode to overcome sticking of the silicon nitride AFM tip to the InN sample surface. AFM imaging was used to calculate RMS roughness values over 5 µm 5 µm areas. The surface roughness of the samples increased with decreasing In-flux during growth. The roughness values are given in Table 5.1, while 2D and 3D images of the AFM scans of each of the samples are given in Fig Note the change in scale in the 2D images from 0 40 µm for samples i440 and n470 to µm, and the cut off peaks in the 3D image, for sample n450, due to its much larger surface roughness Magnetotransport Measurement Details Magnetic field dependent Hall and resistivity voltages were measured from 0 12 T, between 20 and 300 K. A quantitative mobility spectrum analysis with the software package iqmsa from Lake Shore was applied to generate mobility spectra from which the mobility and carrier concentration of both bulk and surface electron species were then extracted.

138 118 Chapter 5: InN Characterisation Results (a) (b) (c) Figure 5.9: 2D and 3D AFM scans for samples i440 (a), n470 (b) and n450 (c). Note the change of height scale in 2D for the roughest sample n450 (c).

139 5.3: Effect of MBE Growth Parameters on Multiple Electron Transport in In-face InN Experimental Results and Analysis Mobility Spectra Variable field Hall and resistivity results demonstrated the presence of multiple electron species in all devices. The electron mobility spectra generated by i-qmsa for each device exhibit two electron peaks; the low mobility peak is assigned to the surface electron accumulation and the high mobility peak to the bulk electron species, as distinguished in the previous work in this chapter (section 5.2) and in the literature [56]. In the following section, the extracted parameters from the low mobility peak are attributed to the surface accumulation electron species and discussed as such. The possibility that conduction from a separate growth interface electron accumulation is contributing to the extracted values is discussed later in the chapter, in section 5.5.2, including response to the considerations of King et al. in [171]. The electron mobility spectra of all three devices at 300 K are given in Fig At all measurement temperatures the electron mobility spectrum of device i440 shows two narrow electron peaks, whereas the two electron peaks for devices n470 and n450 are much broader at all measurement temperatures (the wider peaks of n470 and n450 compared to i440 at 300 K can be seen in Fig. 5.10). Decreasing the In-flux during growth, which resulted in an increase in surface roughness, and therefore surface area, correlates to a broadening of the surface electron peak in the mobility spectrum. An increase in surface roughness is also likely to indicate a less ordered growth interface between the InN and GaN buffer layer. The bulk electron peak is also broader for films grown in the N-rich regime, which may be suggestive of both reduced crystal quality, and/or a change in crystal quality over the thickness of the sample, as suggested by Cimalla et al. [178] and Piper et al. [196]. Note that while the broadening of peaks between samples is indicative of variable crystal quality, other factors such as experimental noise can also contribute to a (very) slight broadening of mobility spectrum peaks generated by QMSA algorithms [55]. The percentage contribution to zero-field conduction of each electron species is easily calculated from the mobility spectrum, and varies between each device. For the In-rich growth sample, i440, the bulk electron species contributes about 80% of the total conduction (that is, the sheet conductivity σ 2D,bulk = N bulk µ bulk product for the bulk species is 80% of the total sheet conductivity of the device at zero magnetic field, σ 2D, with the surface electron contributing the rest). In the N-rich growth samples, n470 and n450, the bulk electron species only accounts for around 70% and 50% of the conductivity respectively. This makes analysis of standard single field data problematic, as the contribution

140 120 Chapter 5: InN Characterisation Results Sheet Conductivity σ 2D (Ω -1 ) 1E-2 1E-3 surface bulk 300 K i440 n470 n450 1E Mobility [cm 2 /(Vs)] Figure 5.10: The electron mobility spectra for In-face InN Hall bar devices i440, n470 and n450, at 300 K. of the surface electron species is clearly not equal between samples and cannot be easily extracted from either the concentration or mobility of a single field measurement. This again highlights the caution that must be used in evaluating single-field results presented in the literature Extracted Carrier Transport Results The volume concentration and mobility of the bulk electron species are graphed in Fig While all films have similar bulk electron densities, at around cm 3 (Fig. 5.11a), i440 and n470 have superior mobilities (2150 cm 2 /Vs and 2430 cm 2 /Vs at 300 K) to n450 (1730 cm 2 /Vs at 300 K). All devices show some temperature dependence of the bulk mobility (Fig. 5.11b). The data in Fig, 5.11b shows that the InN film with the best bulk mobility is that grown at the highest temperature. It can be predicted that the high growth temperature should prevent impurities from incorporating into the material. The data also shows that growing in the In-rich regime, even at the low temperature of 440 C, can also give good mobility results for a similar carrier concentration. In this regime, the excess indium creates an Inadlayer that can also act as a barrier for impurity incorporation. The sample grown under highly N-rich conditions at a lower temperature has a much lower mobility than the other two samples. The fact that N-rich samples have higher roughness and therefore higher surface area creates a greater potential for impurity incorporation during growth. From the

141 5.3: Effect of MBE Growth Parameters on Multiple Electron Transport in In-face InN 121 Carrier Concentration (10 17 cm -3 ) i440 bulk n470 bulk n450 bulk increasing N-flux Temperature (K) (a) Mobility [cm 2 /(Vs)] i440 bulk n470 bulk n450 bulk increasing N-flux Temperature (K) (b) Figure 5.11: The carrier concentration (a) and mobility (b) for the bulk electron species in In-face InN devices i440, n470 and n450, extracted from the mobility spectra at each measurement temperature.

142 122 Chapter 5: InN Characterisation Results Sheet Concentration (10 13 cm -2 ) i440 surface n470 surface n450 surface increasing N-flux Temperature (K) (a) i440 surface n470 surface n450 surface increasing N-flux Mobility [cm 2 /(Vs)] Temperature (K) (b) Figure 5.12: The sheet carrier concentration (a) and mobility (b) for the surface electron species in In-face InN devices i440, n470 and n450, extracted from the mobility spectra at each measurement temperature.

143 5.3: Effect of MBE Growth Parameters on Multiple Electron Transport in In-face InN 123 three devices, however, it is noted that no significant increase in bulk carrier concentration is seen alongside the degradation of the bulk mobility. If impurity incorporation or other crystal defects are a main contributor to the reduction in mobility, it appears as though different mechanisms exist in each device for scattering and unintentional doping, given the concentrations in all three devices are similar but the mobilities are not. Contrary to previously reported results that the surface concentration of indium nitride is fixed at some intrinsic value, measured by various techniques to be between 1.57 and cm 2 [48,166,168,171,174], the low mobility (surface) sheet carrier concentration in these devices increased with surface roughness. The sheet concentration increases from cm 2 for the In-droplet regime device, i440, to cm 2 for the high temperature growth device, n470, with the roughest device, n450, having a surface sheet concentration on the order of cm 2. This result suggests that, especially for poor (rough) samples, assuming a certain surface concentration based on literature reports may not be accurate. The mobility of the surface carriers varies between around 500 cm 2 /Vs for n470 and i440, down to 300 cm 2 /Vs for n450, which also has the largest surface concentration. The surface mobility of n470 is the highest, although the surface is rougher than that of i440. Figure 5.11b shows that n470 also has the highest bulk mobility, suggesting the crystal quality (especially away from the growth interface [178, 196]) is the highest in this device, which will also result in reduced scattering of the surface electron species which reside in the high crystal quality near-surface region. There is no appreciable temperature dependence in the surface electron mobility for any of the devices. It is noted that in Fig for device i440, the extracted parameters, N and µ, of the surface electron species are affected by the relatively low surface contribution to the total sheet conductivity (at only 3 8 %), which has made extraction of the surface-related N and µ imprecise. This can be witnessed in some variations of the sheet concentration and mobility of the i440 surface electron species that fluctuate with temperature. It can generally be seen, though, that when one increases the other decreases i.e. the sheet conductivity (µn product) is remaining consistent over temperature, indicating the variation in the extracted parameters arises from the QMSA fitting. In this case, the extracted transport properties of the surface electron accumulation for device i440 have a more significant error associated with them. For the other two devices, the transport properties are extracted more accurately and with far greater confidence due to their higher surface sheet conductivity contributions to the total sheet conductivity (at %).

144 124 Chapter 5: InN Characterisation Results n450 surface n450 bulk n450 1T single field Hall Mobility [cm 2 /(Vs)] Temperature (K) Figure 5.13: Comparison of single field and multiple-field with quantitative mobility spectrum analysis data (using i-qmsa software) for In-face, N-rich growth regime, device n Comparison of Variable- and Single-Field Results Significant difference exists for each film between the transport characteristics extracted for the multiple electron species and those calculated using only a single magnetic field. In particular, the very N-rich regime device, n450, has average electron mobilities in the bulk over twice that suggested from single field calculations. Figure 5.13 shows the mobility of the bulk and surface electron species for n450 along with the mobility as would be calculated using data from measurements at 1 T. Clearly the bulk characteristics are being significantly obscured by the large, low mobility surface accumulation (which, as mentioned in section , contributes up to 50% of the total conduction in this device). 5.4 Multiple Electron Transport in N-Face InN All InN samples examined in the work in this chapter so far have been In-face ((0001) crystal orientation). However, calculations based on the band structure of InN predict that all surfaces of InN will be accumulated with electrons. N-face InN (000 1) is also predicted by van de Walle and Segev [172, 173] to have a surface electron accumulation calculated from microscopic origins. Experimentally, such an accumulation has been confirmed by XPS measurement [84, 85, 92]. To date, however, multi-carrier transport investigations of N-face InN have not been reported (single-field Hall results are listed in Table 4.2). This section covers the study of multiple electron transport in N-face InN by use of variable magnetic field Hall measurement and quantitative mobility spectrum analysis.

145 5.4: Multiple Electron Transport in N-Face InN 125 Table 5.2: N-face InN samples under study. Sample Flux Regime Thickness Growth Temp. Measured As µm C van der Pauw Hall bar n500i In-rich n1000i In-rich n2000i In-rich n1000n N-rich Growth Details For this study, N-face indium nitride samples were grown to different thicknesses and under different flux conditions via plasma-assisted molecular beam epitaxy (PA-MBE) on c-face SiC substrates using a GaN buffer. The N-face InN samples were grown by G. Koblmüller at UCSB. Investigations into N-face InN growth have been performed and reported on by Koblmüller et al. [34, 144]. Three samples were grown under slightly In-rich conditions at a growth temperature of 540 C. These samples had thicknesses of 500 nm, 1 µm and 2 µm. In the following discussions, these samples are referred to by their thicknesses and In-rich growth condition as n500i, n1000i and n2000i. A fourth sample, denoted n1000n, of approximately 1 µm thickness was grown under N-rich conditions at a substrate temperature of 555 C. Previous studies of x-ray diffraction (XRD) rocking curve widths have shown that for N-face InN the more important off-axis scans (representing twist about the c-axis and pure edge-type threading dislocations (TD)) show no dependence between full-width half-maximum (FWHM) values and the growth conditions which were varied here (i.e. In-rich versus N-rich growth, temperature change), with only a small change in the on-axis FWHM (pure screw and mixed TDs), favouring low temperature In-rich growth [34]. The N-rich growth sample, n1000n, is one of the samples measured to obtain these XRD results by Koblmüller et al. [34]. A summary of the growth conditions of the four samples is given in Table Sample Processing Details This work involved the first attempt at processing of N-face InN into devices at UWA. As is the case for N-face GaN, the N-face surface of InN is more chemically reactive than the In-face polarity, and easily etches in KOH [89]. The N-face surface of InN is therefore also attacked by some photoresist developers (see section 2.3). The In-rich growth N-face samples (n500i, n1000i, n2000i) were therefore initially measured in the van der Pauw configuration, on pieces cleaved to approximately 5 5 mm in size from the growth size

146 126 Chapter 5: InN Characterisation Results (quarter of a 2-inch wafer). The van der Pauw devices were otherwise unprocessed with pressed indium contacts at the corners (of size 0.5 mm). All samples were subsequently processed into 8-contact ( [98]) Hall bar devices, defined using inductively coupled plasma reactive ion etching (ICP RIE) with a methane / hydrogen / argon chemistry in an Oxford Instruments Plasmalab 100 plasma tool. The plasma chemistry and conditions used were not the same as those for device InN-HB discussed in section 5.2 previously (processing conditions are detailed in Appendix B). While some optimisation was conducted, the etch rates remained low (as compared to, say, GaN) at around µm/min. To protect the N-face InN surface during processing a low stress 300 nm silicon nitride (SiN x ) film was deposited by PECVD at 200 C. The SiN x was patterned with standard photoresist techniques and then removed with buffered HF solution. Due to long ICP etch times (and presumably resultant heating, even with grease) some change occurred in the SiN x which resulted in slower etch rates of the SiN x in buffered HF after the plasma etching of the InN. Contact definition masking was performed with the remaining SiN x layer intact, after which buffered HF was used to remove the SiN x from the contact pads prior to contact deposition. Contacts of Cr/Au were thermally evaporated. The remaining SiN x was then fully removed in buffered HF Magnetotransport Measurement Details Both the van der Pauw and Hall bar devices underwent Hall and resistivity measurements at multiple magnetic fields (0 12 T), between 20 and 300 K. The magnetic field dependent data was analysed in a quantitative mobility spectrum analysis using the high resolution HR.MSA algorithm (see section ). The HR.MSA software was developed only after the In-face InN measurements and analysis in sections 5.2 and 5.3 were completed. This newer version of the analysis enables more iterations and fitting refinements. By using the HR.MSA algorithm, in place of i-qmsa, it is possible to generate mobility spectra that are consistent with results from i-qmsa, but that fit with less error to the conductivity tensor components. This has been important in the N-face analysis more-so than in the In-face cases because of the higher mobilities of the surface electron species, approaching the mobilities of the bulk, and therefore requiring better fits to distinguish between the two peaks.

147 5.4: Multiple Electron Transport in N-Face InN Experimental Results and Analysis Mobility Spectra Analysis of van der Pauw Mobility Spectra The mobility spectra of the n500i and n1000i (500 nm and 1 µm thick) van der Pauw devices show two clear electron peaks at all measurements temperatures, as seen in Fig. 5.14a for 100 K. Consistent with the In-face work, the highest mobility electron peaks seen for these samples were assigned to the bulk electron species. The second highest peak was assigned to the surface electron. As the temperature increases, the peaks in the mobility spectra broaden, likely due to increased scattering from sources such as polar optical phonons, widening the distribution of mobilities in each electron species. For the 2 µm thick sample, n2000i, between 100 and 250 K the broadening is such that the high and low mobility peaks in the mobility spectra become indistinguishable; instead of two clear peaks there are contributions from a range of mobility values with no clear peaks. The 100 K mobility spectrum is given in Fig. 5.14c, showing the broad distribution of mobilities contributing to conduction. This broad spectrum represents the best fit to the experimental conductivity tensor components, and as such for these temperatures values cannot be extracted for the transport properties that confidently describe either electron species. Analysis of Hall Bar Mobility Spectra In Fig. 5.14b the mobility spectra for the Hall bar devices on n500i and n1000i at 100 K are given. The mobility spectra for n500i and n1000i for the van der Pauw and Hall bar devices are displayed side-by-side in order to facilitate comparison. Note that the peaks for the Hall bars are much sharper. For the Hall bar device from sample n500i (500 nm) there are two peaks at each temperature that match well with the peaks from the van der Pauw measurements, though the peak representing the surface electron species is at slightly higher mobility values. The peaks are also narrower. The clear peaks in the mobility spectra for the Hall bar devices on n500i and n1000i were assigned to the surface and bulk electron species as in the previous In-face InN analysis. Unlike in the van der Pauw case for n500i, there is a third peak present at a lower mobility, that appears with consistent values across all measurement temperatures. The conductivity contribution of the third peak is around 10 % for all temperatures except 300 K (20,%) which is significant enough to be considered as a real

148 128 Chapter 5: InN Characterisation Results Sheet Conductivity σ 2D (Ω -1 ) 1E-2 1E K surface 1E Mobility [cm 2 /(Vs)] (a) n500i van der Pauw n1000i van der Pauw bulk Sheet Conductivity σ 2D (Ω -1 ) 1E-2 1E K n500i Hall bar n1000i Hall bar surface 1E Mobility [cm 2 /(Vs)] (b) bulk 1E K n2000i van der Pauw 1E K n2000i Hall bar Sheet Conductivity σ 2D (Ω -1 ) 1E-3 1E Mobility [cm 2 /(Vs)] (c) Sheet Conductivity σ 2D (Ω -1 ) 1E-3 1E Mobility [cm 2 /(Vs)] (d) Sheet Conductivity σ 2D (Ω -1 ) 1E-2 1E-3 peak of 2nd subband: peak shifts left (mobility decreases) as temperature rises 200 K 100 K n2000i HB 200 K n2000i HB 100 K n2000i vdp 100 K surface peak bulk peak Sheet Conductivity σ 2D (Ω -1 ) 1E-2 1E K surface bulk n1000n Hall bar 1E Mobility [cm 2 /(Vs)] (e) 1E Mobility [cm 2 /(Vs)] (f) Figure 5.14: Mobility spectra of N-face InN: (a) n500i, n1000i van der Pauw devices at 100 K; (b) n500i, n1000i Hall bar devices at 100 K; (c) n2000i van der Pauw device at 100 K; (d) n2000i Hall bar device at 175 K; (e) comparison of n2000i spectra for Hall bar and van der Pauw devices; (f) example of electron peaks found for sample n1000n at all temperatures, shown here at 100 K.

149 5.4: Multiple Electron Transport in N-Face InN 129 (non-ghost) peak. Interestingly, the two peaks in the van der Pauw measurement of n500i also add to only around only % of the total conduction at zero field, suggesting this third species may be present in those measurements but was not detected from the measurement data due to reduced measurement accuracy as a result of using the van der Pauw configuration. The low mobility of the third electron means the algorithm is fitting to the very end tail of the conductivity tensor components, where noise or geometrical error could easily dominate the influence of such a low mobility carrier. While further work is required to determine the nature of this third peak, one possibility is that it is a second sub-band populated in the two-dimensional well of the surface accumulation. There is evidence presented by Colakerol et al. [181], Veal et al. [176] and King et al. [180] that a second sub-band may be occupied at the surface of InN, with stronger confinement in low-doped material (such as this). For the Hall bar device on sample n1000i (1 µm) there are two clear electron peaks at all measurement temperatures. The peaks are narrower than for the van der Pauw device (as for n500i), and yet account for a greater percentage of the total zero field conductivity than in the van der Pauw measurement ( 92 vs 82 %). That means that the HR.MSA algorithm was able to generate electron species that fit better to the raw Hall bar data than it was able to for the van der Pauw data. There are no indications of a third peak. As this sample is twice the thickness of n500i the bulk electron species has a larger contribution to the total conduction (60 70 % for n1000i vs 55 % for n500i), and thus the contribution of the surface electron species is less. Therefore the influence on the conductivity of a second occupied sub-band in the potential well of the surface accumulation may be sufficiently reduced so as to be beyond detection in this measurement. Unfortunately the electron mobility spectra of sample n2000i (2 µm thick) in the Hall bar configuration do not show the same improvement in definition as the spectra for samples n500i and n1000i. For temperatures K it is possible to distinguish two electron species, but at temperatures 100 K and above the peaks of the two species overlap and no clear distinction is obtainable (as was the case in the van der Pauw measurement). The mobility spectrum for the Hall bar device on n2000i at 175 K is given in Fig. 5.14d showing the lack of distinct electron peaks. If the surface and bulk electron species do not have completely distinct mobility distributions (which appears to be the case) then no improvement in measurement accuracy will enable the identification of these two electron species by this method. If the width and position of the electron peaks in the Hall bar and van der Pauw spectra are compared, good correlation from 40 K up to about 150 K is seen, with the Hall bar device displaying some additional low mobility contributions

150 130 Chapter 5: InN Characterisation Results above 100 K. The electron mobility spectra for n2000i measured in both van der Pauw and Hall bar device configurations is given in Fig. 5.14e showing the spectra covering the same range of mobilities at 100 K, and the additional low mobility contribution from the Hall bar device at 200 K. It is unclear if this additional low mobility contribution is due to increased accuracy from the Hall bar measurement, but the percentage contribution of the electron mobility spectra for the van der Pauw device generally only gave about 85 % of the total zero-field conductivity, while the Hall bar measurement enabled a fit of carriers with contribution of %. If, as for sample n500i, three electron species are considered, it is found that the n2000i mobility spectra can be split into three electron peaks for all temperatures greater than 100 K, except 125, 150 and 175 K. The extracted properties of these three peaks show reasonable trends with temperature (Figs and 5.16), with some noticeable error near the boundaries of detection (100, 200 K). The extracted transport properties of all the electron species are presented in the following sections. The three electron species (bulk, surface and possible second subband) have been plotted when all three could be reasonably extracted (100, K), two only for K and none for K due to the inability to extract individual species from the spectra at those temperatures. At all measurement temperatures, the results for the Hall bar device on the N-rich growth sample, n1000n, showed two clear and narrow peaks in the electron mobility spectrum, as shown for 100 K in Fig. 5.14f. Transport results for both electron species were extracted without complication for this device Extracted Carrier Transport Results: Bulk Electron Species The bulk electron concentrations and mobilities extracted from the mobility spectra are given in Fig for each measurement temperature. The van der Pauw and Hall bar device results are plotted separately, but the graphs are given side-by-side to aid comparison. The lines between measurement points are guides for the eye. Analysis of van der Pauw Results Figure 5.15a shows the values for the volume concentration of the bulk electron species extracted from the mobility spectra for samples measured in the van der Pauw configuration. For all devices the bulk electron density is in the low cm 3 range for the majority of temperatures, which is among the lowest reported for non-compensated unintentionally doped InN, of either In-face or N-face orientation. The bulk electron density is seen to decrease with film thickness, and at low temperatures (60 77 K) is in the high cm 3

151 5.4: Multiple Electron Transport in N-Face InN 131 Concentration (10 17 cm -3 ) n500i n1000i n2000i bulk van der Pauw Temperature (K) Concentration (10 17 cm -3 ) bulk Hall bar n500i n1000i n2000i n1000n n3 hb Temperature (K) (a) (b) n500i n1000i n2000i n03 vdp 300k bulk van der Pauw bulk Hall bar Mobility [cm 2 /(Vs)] Temperature (K) Mobility [cm 2 /(Vs)] n3 hb n500i n1000i n2000i n1000n Temperature (K) (c) (d) Figure 5.15: The extracted transport properties of the bulk electron species in N-face InN. The results for measurements on van der Pauw devices are shown in (a) and (c), the Hall bar device results are shown in (b) and (d).

152 132 Chapter 5: InN Characterisation Results range for the 2 µm thick sample, a remarkable result. The reduction in concentration with increasing thickness is expected due to a decrease in defects such as threading dislocations, which can act as donors [178, 196], away from the growth interface. The apparent temperature dependence of the bulk concentration is discussed with the Hall bar results in the following section. The extracted mobility of the bulk electron species (Fig. 5.15c) increases rapidly with temperature until around 100 K, and peaks around 150 K, before decreasing more slowly. The peak electron mobility for the 2 µm thick sample is over 3000 cm 2 /Vs. The mobility in this material is not as high that seen in In-face material, which peaks at over 5100 cm 2 /Vs for the best sample measured (section 5.2), even though the bulk concentration is lower. The mobility of all devices at 300 K is greater than at 20 K. This is in contrast to In-face InN in which the bulk mobility is generally symmetric around 150 K with mobilities at 20 and 300 K being of a similar value, as seen in all the In-face bulk mobility plots presented previously in this chapter. The extracted mobility of the bulk electron species increases with sample thickness, which, as for the decrease in electron density, is expected to be largely due to an improvement in crystal quality away from the growth interface. Analysis of Hall Bar Results and Comparison The transport properties of the bulk electron species in the Hall bar devices are shown in Figs. 5.15b and 5.15d. The shape of the bulk mobility with respect to temperature for n500i and n1000i Hall bars are the same, but both differ from the shape of the mobility curve for the van der Pauw measurement at temperatures below 150 K. The steep roll-off of mobility with temperature seen in the van der Pauw devices as temperature decreased below 150 K is not seen in the Hall bars. In this way the Hall bar bulk mobilities exhibit similar temperature dependence to the bulk mobility seen in the In-face InN samples. Similarly, the bulk carrier concentration for the n500i and n1000i Hall bars does not show as strong a temperature dependence as the results obtained from the van der Pauw configuration on those same samples. From this result it appears as though the strong roll-off of mobility, and the apparent temperature dependence of the bulk electron concentration seen in the van der Pauw measurements are artefacts of the measurement. Interestingly, the transport properties of the bulk electron in the N-rich growth sample n1000n (Hall bar) show similar trends to the van der Pauw results of n500i and n1000i, i.e. a steeper decrease of mobility at low temperature and apparent decrease of carrier concentration with rising temperature from 20 to 150 K. The bulk concentration in the n500i and n1000i Hall bars is also about

153 5.4: Multiple Electron Transport in N-Face InN 133 twice that of the van der Pauw results. At least part of the increase is due to the improved fit of the conductivity tensor components using the Hall bar devices, for which the electron species now account for % of the conductivity, as opposed to only %, in the van der Pauw measurements. The additional conductivity is mostly incorporated in the increased carrier concentration (as the mobility was similar between both measurements). The reason for ay further increased concentration beyond the additional conductivity is unclear. For temperatures at which the transport properties of the bulk electron species for n2000i could be extracted, the data follows similar trends to that for the samples n500i and n1000i (excepting at 100 and 200 K, which are the limits of extraction of individual species for n2000i). The bulk electron concentration is lower than for the other three samples, reflecting the improvement of InN crystal quality and thus reduction of native dopant defects away from the growth interface. The bulk electron concentration is nonuniform through the depth of the layer (as the crystal quality improves further from the growth interface) and so the values presented here are an average over the depth of the InN layer (an average only, though, of the bulk electrons with similar mobility, and not averaged with the low mobility surface or interface electrons). The marked improvement (i.e. reduction) in the native bulk electron concentration from the 1 µm to 2 µm sample (more so than from 0.5 to 1 µm) shows the crystal quality is greatly improved beyond a 1 µm thickness. The bulk electron concentration for the Hall bar device on the n1000n sample (over the 1 µm thickness) is between 5 (low T) and 3 (high T) cm 3, which is lower than that extracted for either n500i or n1000i (Hall bars). The bulk mobility, however, is also lower than that of n500i or n1000i, at only 1780 cm 2 /Vs at 300 K, peaking at 2060 cm 2 /Vs at 150 K, before dropping to 1440 cm 2 /Vs at 20 K. Samples n500i and n1000i, by comparison, have 300 K mobilities on the order of 2500 cm 2 /Vs. The reduced mobility of InN grown in the N-rich regime was also seen for the In-face InN samples studied in section 5.3.4, where for similar relative bulk concentrations of samples, material grown in the N-rich regime had lower bulk electron mobilities. Growth in the In-rich regime enables the excess indium to create an In-adlayer that can act as a barrier for impurity incorporation, which does not happen in N-rich growth. Koblmüller et al. [34] have also shown that N-rich growth conditions led to a greater surface roughness for N-face InN (seen also in the In-face samples) from which the higher surface area can create a greater potential for impurity incorporation during growth. The incorporation of impurities can act as

154 134 Chapter 5: InN Characterisation Results scattering centers, which could account for the reduced mobility in the N-rich growth sample n1000n compared to the In-rich growth samples in this series Extracted Carrier Transport Results: Surface Electron Species The surface electron sheet concentrations and mobilities extracted from the mobility spectra for both van der Pauw and Hall bar devices are plotted in Fig The results presented here are the transport properties extracted for the low mobility peaks in the mobility spectra produced by the HR.MSA algorithm when fitting to the measured conductivity tensor components. It is again noted that there is evidence that the band bending at the surface of N-face InN is identical to the band bending at the surface of In-face InN regardless of growth regime, as measured by XPS [171]. This leads to a calculation of the surface electron accumulation density that gives a universal density (modified only slightly upon oxidisation by the air) of cm 2 [171], which is smaller than the extracted densities presented in this section. The measurement of band bending, however, can say nothing of the mobility of the electron species at the surface of InN. Consideration of discrepancies between using this technique versus other techniques to measure surface density, and the resultant consideration of a growth interface accumulation, is presented in section Analysis of van der Pauw Results As measured in the van der Pauw configuration, the sheet concentrations of the surface electron species have no clear temperature dependence (Fig. 5.16a), while the mobility appears to follow a similar temperature dependence to the bulk electron species, peaking around 100 K (Fig. 5.16c). Around liquid nitrogen temperatures, a significant percentage of the conduction through the sample comes from the surface accumulation (30 50 % for all three samples). Of note is that there is a clear thickness dependence on both the surface sheet density and the mobility, rather than a fixed concentration for all samples. A change of concentration with sample thickness was also noted by Hofmann et al. using an optical Hall technique [177] on InN films of unspecified polarity, though they saw the concentration of the surface species decrease, rather than increase, with increased thickness. Note also that the surface roughness of these films is comparable and is not expected to be the source of the difference in surface concentration, unlike that seen for the In-face growth series. In the study of In-face InN material detailed previously in this chapter, there is no discernible temperature dependence of the surface electron species, which have lower mobilities ( cm 2 /Vs) compared to the mobilities exhibited by these N-face samples of

155 5.4: Multiple Electron Transport in N-Face InN 135 Sheet Concentration (10 13 cm -2 ) surface van der Pauw n500i n1000i n2000i Temperature (K) Sheet Concentration (10 13 cm -2 ) surface Hall bar n500i n1000i n2000i n1000n Temperature (K) (a) (b) 2000 surface van der Pauw 2000 surface Hall bar Mobility [cm 2 /(Vs)] n500i n1000i n2000i Temperature (K) (c) Mobility [cm 2 /(Vs)] n2000i n500i n1000i n2000i n1000n Temperature (K) (d) Figure 5.16: The extracted transport properties of the surface electron accumulation in N-face InN. The results for measurements on van der Pauw devices are shown in (a) and (c), the Hall bar device results are shown in (b) and (d).

156 136 Chapter 5: InN Characterisation Results cm 2 /Vs for the 500 nm sample and over 1000 cm 2 /Vs for the 1 µm sample. Such an increase in mobility values can only be partially accounted for by a slight reduction in the sheet concentration of the N-face surface electron species, which is between 1 and cm 2, compared to mid cm 2 or higher seen in the In-face InN material. The only measurement in the literature of the mobilities of the surface electron species for different polarities comes from the extrapolation of single-field Hall data to zero thickness. Koblmüller et al. [34] see the mobility for N-face samples extrapolating to around 500 cm 2 /Vs with thickness, while the mobility in In-face GaN buffer layer InN films has been shown to extrapolate to around 300 cm 2 /Vs [166]. The extrapolation of single-field Hall data, however, is only suggestive of the surface mobility as thin samples may have degraded properties due to high levels of defects such as dislocations. Analysis of Hall Bar Results and Comparison For the Hall bar devices, the surface electron sheet concentrations are given in Fig. 5.16b and mobilities in Fig. 5.16d. The sheet carrier concentrations of the surface electron species extracted for Hall bar devices n500i and n1000i are similar to the van der Pauw results, at 3 to cm 2 for n500i and n1000i respectively, which is consistent with the measurement of surface concentrations by other methods (see section 4.4.2). The surface electron sheet concentration for the N-rich grown device n1000n is greater than any of the other N-face devices, at around cm 2, also with a lower mobility, between cm 2 /Vs. The surface electron sheet concentration of N-rich grown In-face InN was also found to be greater than that of In-rich grown In-face InN (see section 5.3.4), which corresponded to a greater surface roughness. The surface roughness of the samples in this study have not been measured by AFM, though the N-rich growth is expected to have a rougher surface based on optical microscopy observations and published results on the surface roughness of N-face InN grown at UCSB under In- and N-rich growth conditions [34]. The surface electron mobility for Hall bar device n1000i agrees well with the van der Pauw measurement, except at low temperatures (< 77 K) where it is greater than measured in the van der Pauw case, a result also seen for the bulk electron species in this sample. The mobility of the surface electron species in device n1000i is around 800 cm 2 /Vs at 300 K and peaks around 1200 cm 2 /Vs. The mobility of the n500i (Hall bar) surface electron species has been measured at a much higher value than in the van der Pauw case (at almost double the value) and is also higher than that of n1000i. This is unexpected, as the quality of the InN at 1 µm from the growth interface (n1000i) should be greater than at

157 5.4: Multiple Electron Transport in N-Face InN 137 Sheet Concentration (10 13 cm -2 ) n2000i n500i n500i 3 rd e - n1000i n2000i n2000i 3 rd e - n1000n surface Hall bar Temperature (K) (a) Mobility [cm 2 /(Vs)] n2000i n500i n500i 3 rd e - n1000i n2000i n2000i 3 rd e - n1000n surface Hall bar Temperature (K) (b) Figure 5.17: The extracted transport properties of the surface electron species for Hall bar devices n500i, n1000i, n2000i and n1000n. The concentration and mobility of the third electron species found in the spectra of n500i and n2000i are also included. 500 nm (n500i). The curious case of the third electron peak for device n500i (Hall bar) is one possible explanation, in that the low mobility of the third electron species was likely previously combined with the second (surface) electron species, which resulted in an overall lower surface electron mobility in the van der Pauw case. The clear distinction between the two in the mobility spectra for the n500i Hall bar device, however, is striking and further investigation would be required to fully identify the origin of those contributions. Unfortunately the results from the thickest (2 µm) sample, n2000i, even using the Hall bar configuration, were not very clear. Results have been extracted for a number of temperatures, but the data becomes unreliable in places, made obvious by the large changes plotted in both the bulk and surface transport graphs. Still, certain trends are clear such as the very low concentration of the bulk electron species, at only cm 3, one of the lowest reported electron concentrations for any InN film. The extracted bulk mobility easily approaches 3000 cm 2 /Vs while the peak in the mobility spectrum reaches around 5000 cm 2 /Vs. The surface electron sheet concentration is greater than any of the other films; indeed there is a strong trend of increasing surface sheet concentration with thickness. This is in contrast to optical Hall results presented by other researchers, outlined above while discussing the van der Pauw results. The transport properties of the third electron species seen in the mobility spectra of both n500i and n2000i Hall bar devices is graphed with the surface electron species results in Fig These third species, which are possibly from occupation of a second subband

158 138 Chapter 5: InN Characterisation Results in the surface potential well, are plotted with smaller, open symbols in the figures. For both devices in which this third peaks is seen, it has a very low mobility ( 200 cm 2 /Vs) and high sheet concentration ( cm 2 ). It is also possible that this third peak is related to some two-dimensional accumulation of electrons at the growth interface, between the InN and the substrate. The lack of consistency of the third peak between samples does not strongly support this theory, though more work would be required. The characteristics of a growth interface in relation to the results in this work are discussed in section below. 5.5 Multiple Electron Species in Indium Nitride In this chapter the measured transport properties of a range of InN samples have been presented. A summary of the samples and results (at 300 K) is given in Table 5.3, and graphed in Fig Both In-face and N-face InN have been measured, as have samples of thicknesses between 500 nm and 2.7 µm, grown in In-rich, stoichiometric and N-rich growth regimes Comparison of InN Samples The InN film with the highest bulk electron species mobility was InN-HB, which was 2.7 µm thick and of In-face orientation. The mobility at 300 K was 3570 cm 2 /Vs, calcu Mobility [cm 2 /(Vs)] bulk electron species In-polar Hall bar N-face van der Pauw N-face Hall bar Electron Sheet Concentration (10 12 cm -2 ) (a) Mobility [cm 2 /(Vs)] surface electron species In-polar Hall bar N-face van der Pauw N-face Hall bar 1x x10 14 Electron Sheet Concentration (10 12 cm -2 ) (b) Figure 5.18: The extracted transport properties of the bulk (a) and surface (b) electron species in the InN samples studied in this work at 300 K.

159 5.5: Multiple Electron Species in Indium Nitride 139 lated as a weighted average over the peak in the mobility spectrum, which had contributions up to 5000 cm 2 /Vs. The bulk electron species concentration was very low, at only cm 3 at 300 K. A low bulk concentration of cm 3 was also measured in N-face InN sample n2000i, though the mobility was much lower than in InN-HB, at 2740 cm 2 /Vs. Interestingly, another N-face sample which had a low bulk concentration, n1000n, of cm 3 had an even lower mobility, only 1780 cm 2 /Vs at 300 K. This result for the N-face samples grown in the In-rich vs N-rich regimes, in which the bulk concentrations were similar yet the mobility of the bulk carrier was much lower in the N-rich growth sample, was also seen for the In-face samples i440, n470 and n450. In that case, all three samples had the same bulk electron species concentration ( cm 3 ) but their mobilities were greatly varied at 2150, 2430 and 1730 cm 2 /Vs, respectively. The properties of the surface electron accumulation, however, do vary between In-face and N-face InN, especially when it comes to the mobility. In both orientations the electron sheet concentrations are largely temperature independent in the range of measurement temperatures employed in this work. This is not surprising as the accumulation is both degenerate and two dimensional. The mobilities of the surface species in the N-face material, however, are much higher than in the In-face InN, as can be seen in Fig. 5.18b showing the mobilities versus the sheet carrier concentration at 300 K. The mobilities in N-face InN ranged from 600 to 1400 cm 2 /Vs, as opposed to only cm 2 /Vs in In-face InN material. The surface electron mobility in N-face InN samples even has a dependence on temperature similar to that of the bulk electron species, while in In-face InN the surface species mobility was largely temperature independent with no clear trends across all samples Surface and Interface Accumulations In this work, multiple magnetic field Hall and resistivity measurements have been conducted to measure the conductivity tensor components σ xx and σ xy as a function of magnetic field between 0 and 12 T. A quantitative mobility spectrum analysis has been applied to these conductivity tensor components to produce electron and hole mobility spectra that provide the best possible fit to σ xx and σ xy. In the electron mobility spectra, in most cases, there have been two discrete and discernible peaks. Each peak is defined by conductivity contributions from consecutive points in the mobility domain, separated by regions of mobility points with conductivity contributions that fall below some discernible minima. For example, the electron spectra at 300 K from InN devices i440 and n1000n are graphed

160 140 Chapter 5: InN Characterisation Results Table 5.3: Summary of multi-electron transport property results from this chapter. The electron concentrations and mobilities shown are at 300 K, although for most samples the concentrations were largely temperature independent. Sample Polarity Growth Thickness Device Type Bulk Electron Species Surface Electron Species Regime Temp. Concentration Mobility Sheet Concentration Mobility C nm cm 3 cm 2 /Vs cm 2 cm 2 /Vs Section 5.2 InN-HB In-face In-rich Hall bar InN-HB-2 In-face In-rich Hall bar Section 5.3 i440 In-face In-rich Hall bar n470 In-face N-rich Hall bar n450 In-face N-rich Hall bar Section 5.4 n500i N-face In-rich v. d. Pauw Hall bar n1000i N-face In-rich v. d. Pauw Hall bar n2000i N-face In-rich v. d. Pauw Hall bar n1000n N-face N-rich Hall bar

161 5.5: Multiple Electron Species in Indium Nitride 141 Sheet Conductivity σ 2D (Ω -1 ) 1E-2 1E-3 low mobility peak high mobility peak 300 K i440 n1000n Sheet Conductivity σ 2D (Ω -1 ) 1E-2 1E-3 low mobility peak high mobility peak 300 K i440 n450 1E Mobility [cm 2 /(Vs)] (a) 1E Mobility [cm 2 /(Vs)] (b) Figure 5.19: Comparing the electron mobility spectra of samples i440 and n1000n at 300 K; i440 and n450 at 300 K. in Fig. 5.19a. It is obvious that there are two peaks in the mobility spectrum for each device. The peaks are separated by a region of mobility for which the QMSA algorithm did not fit any conductivity contributions above the limit of the lower bound of the graph (as the scale is logarithmic, points at even one order of magnitude lower have greatly reduced contribution to the properties of the peak). The widths of the low mobility peaks are comparable only spanning a range about cm 2 /Vs wide (the fineness of the mesh of discrete mobilities at which the conductivities are calculated is governed by the QMSA implementation). Contrast this to the electron mobility spectrum for the device n450, shown with that of i440 in Fig. 5.19b, in which the peaks are much broader. The broadness of the peaks indicate how much spread in mobility the algorithm has had to include in order to fit to the experimental data. Such broadness in the high mobility peak is considered to be related to the variation in film quality throughout the InN epilayer, and the effect that has on the electron scattering (and therefore the electron mobility). The broadness of the low mobility peaks of n450 and n470 (section 5.3) correlated very well with the surface roughness of the InN samples. It is reasonable to expect that the surface roughness will have an influence on the conduction of the surface accumulation electrons, as they are measured to be confined to within 6 nm of the surface [52,166,177], though the surface roughness of samples in this work is as great as 24 nm. In this work (Fig. 5.12b) it has been seen that the roughest surface exhibited the surface electron species with the lowest mobility. Additionally, the rougher the surface, the greater the actual surface area, and therefore a larger area of potential native defects such as dangling bonds that could form donors and contribute to the concentration of the electrons at the surface.

162 142 Chapter 5: InN Characterisation Results As discussed in section , there has been consideration in the literature for an additional accumulation of electrons that resides at the growth interface that is, the region of the InN epilayer that lies just above the interface with the substrate or buffer layer [145, 171, 223]. Certainly, in this region, electrons exist, as they do throughout the rest of the InN film but do they form a localised accumulation with different properties to the nearby bulk region i.e. a 2DEG? If so, they may be expected to contribute to conduction as a discrete electron species with a distinct mobility. If no 2DEG is formed, though, it follows that the conduction from this region would be part of the general bulk conduction throughout the epilayer. As the crystal quality decreases towards the growth interface, the mobility of the bulk electrons in that region may also decrease, but it would be expected that the bulk electron species would present as a continuous peak in the mobility spectrum, with any mobility variation reflected as an increase in the width of the peak. Any accumulation of carriers at the growth interface would be present in the mobility spectrum if it contributed significantly to conduction (which would assumedly occur if it existed in a greater concentration than the electrons throughout the rest of the bulk). It can therefore only be present in the mobility spectrum as part of either the low or the high mobility peak, as there is no evidence of a third electron peak in any of the In-face InN films, and only an irregular third peak seen in some N-face samples, which may possibly be related to the growth interface, given the low mobility, but may also be related to quantisation of the electrons at the surface into discrete subbands. So far, all reports discussing the growth interface make use of subtraction or modelling to determine properties of the theorised electron accumulation. For instance, in [145] Veal et al. subtract the surface state density, as calculated using Poisson-MTFA method from HREELS measurements, from the excess sheet carrier density determined from Hall measurements on samples of decreasing thickness, arising at figures of cm 2 for AlN buffer and < cm 2 for a GaN buffer layer. Unfortunately this method relies on the difference between two measurements with their own potential for error. Firstly, the calculation of the surface state density has been refined multiple times, so while in [145] Veal et al. calculate a figure of cm 2, in their later work [92] they specify a value of cm 2 on atomic hydrogen cleaned InN surfaces. Later again in [171], they calculate a figure of cm 2 on oxidised InN surfaces. While it is likely that this is because their calculations have been refined or corrected over time, these results present a range of values that vary by as much as , which is comparable with the density determined for the assumed growth interface accumulation.

163 5.5: Multiple Electron Species in Indium Nitride 143 Secondly, the Hall measurement from which the excess is determined in [145, 166] is itself subject to error. The extrapolation of data to zero thickness spans multiple films, and although they were grown under the same conditions they are not the same film and therefore will have had an inherent variation. One point could change the gradient of the line, changing the value of the intercept. Taking the difference of two large numbers, both with error bars, is therefore not strong evidence that an interface accumulation (independent of the natural variation of the bulk carrier species) exists. King et al. [171] have also used the published data from the work in this thesis (from section 5.3, published as Fehlberg et al. [60]) to again calculate interface densities. Their methods are similar to those in [145]: they subtracted calculated surface state densities (from XPS measurement of the surface Fermi level pinning) from the electron sheet concentrations for the low mobility surface peak extracted from the multiple magnetic field Hall data in section 5.3 at 300 K. In this instance they also obtained samples from UCSB with similar growth parameters as in this work, being grown in different flux regimes, but without the changes in growth temperature. The samples were therefore different, with the most notable difference being that in this work the surface roughness of the samples is presumably much greater. In [171] the surface roughness is not given, but as there is a few years between the growth runs for the two sample sets, with much work on improving InN growth performed at UCSB during this time, it is likely that the more recent growth technology would enable smoother samples being grown for the King et al. study (particularly because those for this work were overly rough). Also, the XPS measurement was reported to generate approximately 65% of the photoemission signal from within 25 Å of the surface and 95% within 75 Å of the surface, with the majority of the signal originating from photoelectrons generated closest to the surface [171]. In comparison, in the samples studied in this work the surface roughness reached up to 240 Å, with the two rougher samples exhibiting surface roughnesses of at least 90 Å and 140 Å (Table 5.1). How this may affect the surface pinning is unknown but it is highly likely that it is a major contributor to the differences in results. Again, the difference in surface area related to a rougher surface should be noted as a possible source of the discrepancy, especially when considering the difference between the samples studied in this work and those in [171]. The results in this work have generally revealed a low mobility electron species with sheet concentration about two times greater (see Fig. 5.18b) than the cm 2 calculated from non-contact measurements of the surface by King et al. [92, 171]. King et al. [171] assert absolute confidence that the concentration of electrons on the surface

164 144 Chapter 5: InN Characterisation Results of all wurtzite InN is the same, regardless of growth conditions or polarity. The question is then, is such a discrepancy (between non-contact surface profiling and contact-based multi-carrier transport measurement) an indication that an accumulation of electrons is residing at the growth interface? In the case of two carriers in the low mobility peaks in this work, a growth accumulation would be required to have extremely similar properties to the surface accumulation of electrons to fit into the same peak. In the case of narrow, well defined low mobility species peaks in the electron spectra that are consistently narrow over a wide range of measurement temperatures ( K), it seems highly unlikely that such a peak is indicative of two discrete carriers tracking identically with temperature. This is especially true of the N-face samples in which the low mobility electron varied significantly with temperature. However, if poor quality crystal near the growth interface is graded in a continuous manner, then any conduction at the growth interface would form part of the bulk electron peak in the mobility spectra, which is more likely as the bulk peaks are generally broader. In the low mobility peaks that were considerably broad (such as n450) it may be possible (especially given the poor quality of the sample) that there is a highly dislocated growth interface that is contributing with poor mobility electron conduction that is combined into the low mobility peak. Certainly, one limitation of the galvanomagnetic measurements in this work is that there is no inherent depth perception of the conduction. The only evidence, however, for the existence of an electron species localised to the growth interface is through the subtraction of results as described above. Further investigation of depth dependence of electrons in InN is beyond the scope of this work, but is included in the suggestions for future work along with possible means of performing such measurements. 5.6 InN Experimental Work Summary The magneto-transport characterisation of InN was performed on a multitude of InN samples. Variable magnetic field Hall effect and resistivity measurements were combined with a quantitative mobility spectrum analysis to determine the transport properties of the multiple electron species in each sample. Bulk and surface electron species were identified in each sample. In the first experiment, the distinct transport properties of two electron species were identified in MBE-grown In-face InN samples, measured as a function of temperature between 77 and 300 K. The transport properties of both species were extracted from

165 5.6: InN Experimental Work Summary 145 mobility spectra generated using a quantitative mobility spectrum analysis on the magnetic field dependent conductivity tensor components, measured using multiple magnetic field Hall and resistivity measurements. The use of quantitative mobility spectrum analysis enabled the bulk electron species properties to be separated from the raw measurement data, which also contains significant contributions from the large accumulation of electrons at the surface. In one sample the bulk electron species properties were extracted to reveal the very high quality of the sample, with a bulk electron species mobility of 3570 cm 2 /Vs at 300 K, the highest ever reported for MBE InN. The mobility of the bulk electron species was observed to change with temperature and peaked at over 5100 cm 2 /Vs at 150 K. The bulk electron carrier concentration was temperature independent between 77 and 300 K at cm 3. The mobility of the surface electron species was temperature independent at around 500 cm 2 /Vs. Previous to this work, the surface electron species transport properties had only been reported for a 60 nm thick InN film, in which the low mobility conduction is likely to have been significantly poorer than at the surface of the thick (2.7 µm) high quality films in this study. The sheet concentration of the surface electron species was also temperature independent at cm 2, which is greater than that measured through other methods for similar InN material. It was also found that the sheet concentration of the surface electron species varied between InN samples grown under the same conditions, with a repeat sample having surface electron sheet concentration of only cm 2. The large disparity between surface electron sheet concentrations suggested that the surface condition plays an important role, yet the surface accumulation was seen to be unaffected by the use of solvents and low temperature processing procedures. In the second experimental series, the transport properties of distinct electron species in MBE grown In-face films were measured and used to identify favourable MBE growth conditions. The transport properties were extracted from the measurement of Hall and resistivity voltages at multiple magnetic fields, between 20 and 300 K. It was found that the best bulk transport properties were obtained in epilayers grown at the highest temperature in the series, at 470 C rather than at 440 C or 450 C. However at similar growth temperatures, growth in the In-rich regime (having an In/N flux ratio greater than one in the chamber) was preferable for the best transport results. Once the low mobility surface electron species was extracted from the data, it was shown that the bulk electron concentrations were very similar in all of the films at 300 K, at cm 3, though the mobilities varied by a considerable amount, between 1730 and 2430 cm 2 /Vs at 300 K. This result suggests non-uniform impurity and defect incorporation during growth, leading

166 146 Chapter 5: InN Characterisation Results to different doping and scattering mechanisms between the three samples. The surface roughness of the samples varied significantly and correlated with the sheet concentration of the low mobility surface electron species, with a rougher surface resulting in a greater concentration of low mobility electrons and a lower mobility for the species, varying between 200 and 600 cm 2 /Vs. In the third experiment, the transport properties of multiple electron species were measured in N-face InN, which has the opposite crystal polarity in the c-plane to the In-face InN samples investigated in the first two experiments. N-face InN has a higher temperature stability than In-face InN, potentially making it more compatible with GaN and AlN alloys (which require higher temperature growth) for heterostructure devices. N-face InN samples of different thickness and different growth regime (In- or N-rich flux conditions) were measured. The influence of the measurement method was also considered by measuring samples in both the van der Pauw and Hall bar device structures. N-face InN was shown via QMSA to exhibit bulk and surface electron species. The transport properties were compared with those of In-face InN. The bulk electron characteristics were comparable to or better than that of In-face InN, with a very low electron concentration in the thickest (2 µm) N-face InN sample of only cm 3 at 300 K and potentially as low as high cm 3 at lower temperatures (at the limits of the measurement resolution due to the high mobility of the surface electron species). The surface electron species in the N-face InN exhibited very high mobilities, between 600 and 1400 cm 2 /Vs, which is up to over twice the measured mobilities of the surface accumulation electron species in In-face InN. The surface electron transport properties of N-face InN also exhibited a much stronger thickness dependence than for In-face InN, with thicker samples having higher surface species electron mobility. This is a significant result for the realisation of InN-based devices in which the surface electron species conduction is unavoidable. For the thickest (2 µm) sample, however, the high mobilities of the surface electron species affected the ability to separate out the properties of the two electron species, as the peaks of the two species were seen to overlap in the mobility spectrum. Growth in the In-rich flux regime, as for the case of In-face InN, was found to result in higher bulk mobilities, even though the bulk electron concentrations were comparable. This reiterates the conclusion that In-rich growth is preferable for InN.

167 Chapter 6 Aluminum Gallium Nitride/Gallium Nitride High Electron Mobility Transistors 6.1 Introduction Gallium nitride-based high electron mobility transistors (AlGaN/GaN HEMTs) present new options in power electronics. The III-nitride semiconductors feature material properties favourable for new applications over the properties of existing mature technologies such as silicon and other III-Vs. These favourable properties include large band gaps and correspondingly high breakdown voltages (for high power applications), extremely high saturation and peak electron velocities (for high speed devices), and strong chemical bonding (for high temperature and radiation hard environments). Additionally, the III-nitrides exhibit some more interesting material properties, such as being highly piezoelectric, which extend device design possibilities in ways unavailable to other material systems. There are, however, materials issues that affect device performance, such as electrically active surface states, that must be addressed in the device designs by the inclusion of elements such as surface passivation and/or metal field-plates. The layer structure of AlGaN/GaN HEMTs is unlike traditional silicon field effect transistors (FETs), in which carriers are accumulated in the same region of the device as their dopant atoms. In a standard FET, dopant atoms within and close to the channel region act as charged impurity centers, which affect the flow of electrons. AlGaN/GaN HEMTs, in contrast, use a structure in which charge carriers can be accumulated in a region that is 147

168 148 Chapter 6: AlGaN/GaN High Electron Mobility Transistors optional doped layer AlGaN:Si optional AlN interlayer GaN:Fe nucleation layers 2D electron gas AlGaN UID GaN sapphire substrate (0001) z Figure 6.1: Layer structure of the AlGaN/GaN heterostructure used in a UCSB Al- GaN/GaN HEMT, showing growth nucleation and Fe:doped layer, and optional design variations in the AlGaN barrier layer. physically separated from any ionized dopant atoms, an idea similar in part to modulation doped AlGaAs/GaAs FETs. The fundamental material properties of GaN and AlGaN, however, can be exploited to generate accumulations of electrons without any doping. An example of the AlGaN/GaN heterostructure used in a HEMT is shown in Fig The most commonly used substrate for the growth of AlGaN/GaN HEMTs is sapphire. Sapphire substrates are available at low cost and in large sizes; silicon carbide (SiC) is also used as an AlGaN/GaN HEMT substrate but is more expensive. In this work, all AlGaN/GaN heterostructures were grown by MOCVD on sapphire at the University of California, Santa Barbara (UCSB) [66]. The growth of the high quality GaN template first requires the growth of nucleation and buffer layers onto the substrate, including (for devices grown at UCSB) an Fe-doped GaN layer which is believed to inhibit the migration of oxygen from the sapphire substrate [224]. The unintentionally-doped (UID) GaN layer grown above is then semi-insulating (SI) as a result of the Fe-doped buffer. A semi-insulating buffer greatly reduces any current paths through the bulk of the GaN buffer layer. On top of the GaN is the AlGaN barrier layer, usually designated with the Al x Ga 1 x N notation to specify the percentage concentration of AlGaN composition, or Al mole fraction, x. Typical x values are between 0.1 and 0.4. The carriers (electrons) in the channel of the device collect in the GaN layer near the AlGaN interface, and are quantised into a two-dimensional electron gas (2DEG), indicated by the dotted line in Fig In some HEMT designs a Si-doped layer is included in the AlGaN barrier layer, as in a more traditional modulation doped structure (however this doping is not required to form a 2DEG). Often also a thin AlN interlayer is included between the GaN and AlGaN in order to increase the band offset at the interface, thereby increasing electron confinement and reducing wave function penetration into the AlGaN, which reduces alloy scattering and therefore increases the mobility of the 2DEG [225].

169 6.1: Introduction 149 Figure 6.2: Band diagram (conduction band) of the AlGaN/GaN heterojunction interface [77]. At the AlGaN/GaN heterointerface, the band offsets of the AlGaN and GaN layers, given a suitable barrier thickness and Al mole fraction, led to the formation of an approximately triangular potential well in the conduction band in the GaN layer near the interface, as seen in Fig The width of the triangular potential well containing the 2DEG is generally on the order of, or less than, the electron de Broglie wavelength ( 260 Å at RT). As a result of the well width and electron confinement, there is a quantisation of energy states in the well, forming subbands. At the interface there is also a fixed positive charge due to two forms of polarisation, which contribute electric fields that attract electrons into the well and increase the density of the 2DEG. Within the material there is a spontaneous electrical polarisation, P SP, due to the irregularity of the arrangement of gallium/aluminum (large) and nitride (small) atoms within the unit cell [143]. The abrupt boundary of the crystal at the surface and AlGaN/GaN interfaces means that the charges on the atoms no longer cancel out and the result is the presence of fixed polarisation charge at each interface. The spontaneous polarisation [76, 226, 227] is very large in wurtzite group-iii nitrides, with AlN having a spontaneous polarisation almost three times as large as either InN or GaN [226], due to the increased non-ideality of the crystal structure [227]. The spontaneous polarisation therefore increases with the Al mole fraction. Piezoelectric polarisation charges are also present due to the strain in the AlGaN layer, resulting from the lattice mismatch between AlGaN and GaN; a 2.4 % difference between AlN and GaN at 300 K [78]. As the lattice spacing in AlGaN is smaller than in GaN, if

170 150 Chapter : AlGaN/GaN J. Appl. Phys., High Vol. 85, Electron No. 6, Mobility 15 March Transistors 1999 (a) (b) (c) (d) 2DEG with the AlGaN interface ro will For a Ga A calculated charge is p relaxed A fined at the ous polariz grown pseu tion of the difference charge N-face AlG piezoelectr parison to Figure 6.3: The directions of spontaneous and piezoelectric polarisation in Ga- (subfigures sheet charg (a) and (b)) and N-face (subfigures (c) and (d)) AlGaN/GaN heterostructures, for cases this interfa in which the AlGaN is either relaxed (subfigures (a) and (c)) or pseudomorphic and under tures, elect tensile strain (as a(aln) < a(gan)) (subfigures (b) and (d)). In all cases the polarisations are aligned [227]. AlGaN, du All samples measured in this work are Ga-face with pseudomorphic AlGaN barrier formed layersin (subfigure (b)). becomes ob the C V-p FIG. 7. Polarization induced sheet charge density and directions of the spontaneous and piezoelectric polarization in Ga- and N-face strained and structure A relaxed AlGaN/GaN heterostructures. different p PIMBE N which is co the AlGaN barrier was layer foundis to pseudomorphic be negative, (i.e. 14 meaning not relaxed) that it for will Ga Al -face be under tensile for strain. heteros heterostructures the spontaneous polarization is pointing towards the substrate Fig. 7. As a consequence, the alignment heterostruc hole accum AlGaN barrier layers are pseudomorphic for most standard AlGaN/GaN heterostructures (where the thickness of the piezoelectrical d AlGaN < 65 nm and [227], spontaneous x < 0.38 polarization [227], though is researchers parallel at and UCSB an AlG have maintained the pseudomorphic case of tensile AlGaN strain, overand theantiparallel entire composition in the case range of0 < arguments, x < 1 compressively strained top layers. If the polarity flips over and n [66]). All AlGaN layers in heterostructures studied in this work are pseudomorphic. from Ga-face to N-face material, the piezoelectric, as well as To Thecal piezoelectric polarisation, the spontaneous P PE, inpolarization the AlGaN/GaN changes system its sign. is more In than Fig. five 7, the times the sheet value charg directions of the spontaneous and piezoelectric polarization interfaces in an AlGaAs/GaAs heterostructure [76]. The piezoelectric polarisation also increases with are given for Ga-face, N-face, strained, unstrained AlGaN/ Al x Ga 1 x N x; the piezoelectric coefficients increase with the Al mole fraction, while also the strain in the AlGaN layer is increased due to increased lattice mismatch with the GaN layer. In this work all AlGaN/GaN heterostructures studied were grown in the Ga-face crystal orientation. As shown in Fig. 6.3, subfigure (b), in a Ga-face heterostructure the spontaneous and piezoelectric polarisations are aligned, contributing to a large positive (fixed) charge at the AlGaN/GaN interface. The directions of polarisations for a range of cases are shown in Fig. 6.3 [76]. This fixed positive polarisation-induced charge at the AlGaN/GaN interface induces an excess of free electrons in the GaN layer at the interface [76,143]. The channel of the transistor is thus present without any specific doping or applied gate bias.

171 6.2: Surface States 151 The strong electric field leads to a narrow confinement of the 2DEG, becoming narrower as the fields increase with increased Al mole fraction [76]. The structure as a whole, of course, remains charge neutral in the absence of any applied external electric fields. The nature of each (and the total) polarisation is that of a dipole, with a net charge contribution of zero, and so the positive polarisation charge at the AlGaN/GaN interface is matched by a fixed negative charge at the top of the AlGaN layer. Free carriers will not accumulate at the AlGaN surface due to the band energies. As discussed further in section 6.2, however, the surface does counteract the negative polarisation charge through the formation of positive donor-like surface states, which donate their electrons to the 2DEG. By considering the charge balance it will be shown that the primary source of the 2DEG electrons in a nominally undoped HEMT is from such surface states, and as such the surface plays a critical role in device performance, via the properties of the 2DEG. 6.2 Surface States Keller et al. (2001) [66] suggested that in order to reach charge neutrality against the fixed (negative) charge present at the AlGaN surface due to spontaneous and piezoelectric polarisations, a significant concentration of charged defects form on the surface of the AlGaN layer. Smorchkova et al. (1999) [78] considered the scenario where deep surface donor-like states are responsible for both neutralising the negative surface polarisation charge, and as the source of the 2DEG electrons. Their calculations used measured values of carrier concentration versus barrier thickness to calculate the surface barrier height, eφ b, using equations presented in the following section. Their results supported the surface state hypothesis, locating the donor-like surface states at 1.42 ev below the Al x Ga 1 x N (x = 0.27) conduction band edge. Ibbetson et al. (2000) [77] demonstrated that surface states are the only possible source of 2DEG electrons in undoped AlGaN/GaN HEMTs. They favoured a model in which a single surface state is responsible for donating the electrons, though remark that a pinned surface potential (formed from a combination of donor- and acceptor- like states) could also explain the results. They stressed that the 2DEG electrons come from donor-like surface states in either scenario; that the existence of a polarisation dipole alone is not sufficient for a 2DEG to form in the GaN channel.

172 152 Chapter 6: AlGaN/GaN High Electron Mobility Transistors AlGaN GaN!AlGaN 2DEG qns!surface EC EF!+ PZ(AlGaN)!- PZ(AlGaN)!- PZ(GaN)!+ PZ(GaN)!buffer Figure 6.4: Band diagram of the AlGaN/GaN heterojunction interface highlighting regions of space charge [77]. Figure 6.4 shows the schematic conduction band diagram for an AlGaN/GaN HEMT, grown in the (0001) orientation (Ga-face) and with an abrupt junction [77]. Indicated are the following space charge regions: the negative charge due to the N s electrons in the 2DEG (qn s ); the polarisation induced charges on either side of the AlGaN barrier layer and GaN buffer; i.e. at the junction and at the surface (±σ PZ,AlGaN ) and at the junction and the substrate interface (±σ PZ,GaN ); the integrated sheet charge due to ionised donors in the AlGaN (σ AlGaN ); charge due to ionized surface states (σ surface ); and any charge stored in the GaN buffer (σ buffer ). The formation of the 2DEG and the role of the surface states is governed by some simple observations [77]. Most importantly, the sum of all the various space charges is zero, as the structure must be charge neutral in the absence of an externally applied electric field. From the physicality, the polarisation charges (spontaneous and piezoelectric combined, for AlGaN and GaN alike) constitute a dipole for which the net contribution to the total space charge is exactly zero. Ibbetson et al. (2000) [77] note that this implicitly rules out the notion of polarisation doping, a term floated in early publications on this topic, suggesting the source of the 2DEG electrons is the polarisations. The space charge in the GaN buffer must be zero or else the 2DEG would not be confined. Furthermore, a well designed HEMT would ensure the buffer charge is as small as possible (which in this work is achieved by the growth of a GaN:Fe layer which enables the bulk to be semi-insulating),

173 6.2: Surface States 153 and thus for clarity it is neglected and the Fermi level is assumed to be close to the GaN conduction band edge in the buffer. Starting from the total charge description qn s + σ + PZ σ - PZ + σ AlGaN + σ surface + σ buffer = 0, (6.1) setting the buffer charge to zero, and cancelling out the polarisation dipole (±σ PZ ) gives [77] σ surface + σ AlGaN qn s = 0, (6.2) which is the statement that defines the source of the 2DEG electrons. Positive donor states in the AlGaN barrier are as per conventional modulation doping. Any positive surface states must be due to the transfer of electrons from the surface into lower energy states in the GaN. Any negative surface charge has states accepting electrons at the expense of the 2DEG. For a truly undoped barrier layer, it follows that any 2DEG electrons come from donor-like surface states. Note that the emptied surface states counteract the negative charge at the surface from the polarisation dipole. Without any treatment of the free AlGaN surface, these positive donor-like surface states may be filled by any electrons with sufficient energy. The filling of these states, and consequential depletion of the 2DEG, is referred to, in reference to HEMT operation, by the term dispersion or current collapse, and is discussed in section 6.5. Again, filling of the donor-like surface states (making them charge neutral) has the net effect of causing the surface to be negative due to the fixed negative polarisation charge there. The surface states themselves (if purely donor-like, as is the more favoured explanation) will not be the source of the negative surface charge, a common misrepresentation in the literature. To prevent filling of the states, and depletion of the 2DEG, much work has been focused on the passivation of the surface with a thin film dielectric. However in addition to prevention of the 2DEG depletion through passivation of the surface states, surface passivation with a thin film dielectric material affects the transport properties of the 2DEG. Ultimately, the dielectric used for passivation can be optimised, and one approach to such optimisation is by considering how it affects the transport properties of the 2DEG, which is the focus of work in this thesis in Chapter 7.

174 154 Chapter 6: AlGaN/GaN High Electron Mobility Transistors 6.3 2DEG Carrier Concentration The carrier concentration, N s, of the 2DEG is an important transport parameter of an AlGaN/GaN heterostructure. The concentration of electrons in the 2DEG relates directly to the possible current output, I DS. The carrier concentration in an undoped HEMT can be predicted by calculating the polarisation charges at the interface, as ideally the (maximum) 2DEG charge will equal the net fixed positive charge at the interface, if all surface states are depleted. In a polarisation analysis, we calculate the piezoelectric and spontaneous polarisation charge densities. The spontaneous polarisation for GaN and AlN is negative (directed towards the substrate, i.e. the positive side of the dipole is at the substrate) and increases in magnitude from GaN to AlN [76, 78]. The spontaneous polarisation, as a function of the Al mole fraction, x, is defined by P SP (x) = ( 0.052x 0.029) C/m 2 (6.3) The piezoelectric polarisation is dependent on the strain in the AlGaN barrier (we assume the AlGaN is pseudomorphic and under tensile stress for all thicknesses and concentrations in this work) and is also dependent on the Al mole fraction of the Al x Ga 1 x N composition. The piezoelectric tensor has three independent components: e 33 and e 31, which apply to the strain along the c axis and in-plane strain respectively, and e 15, which is related to polarisation induced by shear strain which is not relevant to this model. The total piezoelectric polarisation in the AlGaN is defined by the change in polarisation induced by variations in the wurtzite lattice constants a and c, as [76] P PE = e 33 ɛ z + e 31 (ɛ x + ɛ y ) (6.4) where ɛ z = (c c 0 )/c 0 is the strain along the c axis, the in-plane strain ɛ x = ɛ y = (a a 0 )/a 0 is assumed to be isotropic, e 33 and e 31 are the piezoelectric coefficients, and a and c are the lattice constants of the strained (AlGaN) layer. This equation is valid in the linear regime for small strain values. The relationship between the lattice constants in the hexagonal AlGaN system is given by [76] c c 0 c 0 = 2 C 13 C 33 a a 0 a 0 (6.5) where C 13 and C 33 are the elastic constants. Combining the previous two equations the amount of piezoelectric polarisation in the direction of the c axis can be determined by [78, 227] P PE = 2 a a 0 a 0 ( ) C 13 e 31 e 33 C 33 (6.6)

175 6.3: 2DEG Carrier Concentration 155 where the elastic constants can be linearly interpolated as [76] C 13 (x) = (5x + 103) GPa (6.7) C 33 (x) = ( 32x + 405) GPa (6.8) and a 0 can be linearly interpolated as [76] a 0 (x) = ( 0.077x ) Å (6.9) The influence of non-linearity in the calculated polarisation induced sheet charge is negligible [76]. The piezoelectric polarisation is negative for tensile strained AlGaN barriers, as [e 31 e 33 (C 13 /C 33 )] < 0 for all AlGaN compositions. The spontaneous polarisation is also negative. As shown in Fig. 6.3, in the case of an AlGaN barrier layer under tensile strain the two polarisations are aligned, and the value of the total polarisation across the AlGaN layer is the sum of the piezoelectric and spontaneous polarisations. Also present is a spontaneous polarisation in the GaN layer, in the same direction as the AlGaN and thus reducing the net polarisation charge at the interface. Associated with the abrupt changes of the polarisation field at the AlGaN/GaN interface is a polarisation-induced charge density, σ(x), equal to the contributions of the piezoelectric and spontaneous polarisations in the AlGaN and the spontaneous polarisation in the GaN [76 78] σ(x) = P PE (Al x Ga 1 x N) + P SP (Al x Ga 1 x N) P SP (GaN) (6.10) Therefore at the interface is a positive polarisation charge on the AlGaN layer side and a negative polarisation charge on the GaN side. As the spontaneous polarisation of AlN is nearly three times that of GaN, and the piezoelectric polarisation is also very large, the spontaneous polarisation charge in the GaN layer has a minimal effect on the total space charge at the interface. For an undoped Ga-face AlGaN/GaN HEMT structure, the sheet electron concentration N s (x) can be calculated using the total bound sheet charge σ(x) as [227, 236, 237] n s (x) = σ(x) e ɛ 0ɛ(x) d AlGaN e 2 [eφ b(x) + E F (x) E C (x)] (6.11) where ɛ(x) is the dielectric constant of the Al x Ga 1 x N, d AlGaN is the thickness of the barrier layer, eφ b (x) is the surface barrier height, E F is the Fermi level with respect to the GaN conduction-band-edge energy and E C is the conduction band offset at the AlGaN/GaN interface.

176 156 Chapter 6: AlGaN/GaN High Electron Mobility Transistors Table 6.1: Values of constants, coefficients and variables required for the calculation of the 2DEG concentration in AlGaN/GaN HEMTs in a polarisation-charge based analysis. Variable Value Units Reference Lattice, Dielectric and Elastic Constants a 0 (GaN) Å [76] a 0 (AlN) Å [76] c 0 (GaN) Å [76] c 0 (AlN) Å [76] c 0 /a 0 (GaN) [76] [226] c 0 /a 0 (AlN) [76] [226] ɛ 11 (GaN) [228] ɛ 11 (AlN) [229] ɛ 33 (GaN) [228] ɛ 33 (AlN) [229] C 13 (GaN) 103 GPa [76] C 33 (GaN) 405 GPa [76] C 13 (AlN) 108 GPa [76] C 33 (AlN) 373 GPa [76] Polarisation Constants P SP (GaN) C/m 2 [226] P SP (AlN) C/m 2 [226] e 33 (GaN) 0.73 C/m 2 [226] 1 C/m 2 [230] 0.65 C/m 2 [231] 0.63 C/m 2 [232, 233] e 31 (GaN) C/m 2 [226] C/m 2 [230] C/m 2 [231] C/m 2 [232, 233] e 33 (AlN) 1.46 C/m 2 [226] 1.55 C/m 2 [229] 1.29 C/m 2 [232, 233] e 31 (AlN) C/m 2 [226] C/m 2 [229] C/m 2 [232, 233] ɛ(x) 0.3x [76, 78] eφ b (x) ev [234] 1.7 ev (for d > 20 nm) [234] 1.42 ev by fit [78] (1.3x ) ev Ni barrier [76] E F mid-gap [76] E C 0.75 E G [78, 235] 0.7 E G [76]

177 6.4: 2DEG Mobility 157 Table 6.1 gives the values of these variables and relevant polarisation constants and other coefficients as used in the literature. actual values of some constants. There remains a degree of uncertainty as to the The band gap of AlGaN is measured [238] to be E g (x) = x E g (AlN) + (1 x) E g (GaN) x (1 x) 1.0 ev = 6.13 x (1 x) x (1 x) ev (6.12) The value of the surface barrier height is one of the more uncertain parameters. Smorchkova et al. (1999) [78] used the barrier height as a fitting parameter for AlGaN-thickness dependent values of 2DEG concentration, and yielded the value of 1.42 ev for the surface barrier height eφ b (x). Ambacher et al. (2000) [76] used the barrier height of Ni on the AlGaN surface. The most thorough investigation of the barrier height was conducted by Koley and Spencer (2005) [234] in which they used UV laser induced transients to measure the bare surface barrier heights, for a range of heterostructures with different barrier thicknesses. They found that the bare surface barrier height increased with AlGaN thickness, and had a thickness variation very similar to the 2DEG density. The surface barrier height was found to have values between 1.0 and 1.7 ev, becoming constant at around 1.7 ev for AlGaN layers of 20 nm and above. These results would seem to invalidate the findings of Smorchkova et al. as they had assumed a constant barrier height with thickness, including thicknesses below 20 nm, which is an incorrect assumption based on Koley and Spencer s measurements. For this work, all AlGaN layers are thicker than 20 nm, and so a value of 1.7 ev would be applicable. The carrier concentration can also be calculated via a self-consistent solution to the Schrödinger and Poisson equations that govern the potential well, using a 1D Schrödinger- Poisson solver [239]. In such a simulation program, polarisation charges can be represented by incorporating thin layers of charge, as used by Ambacher et al. (2000) [76] to calculate the 2DEG density and carrier distribution profile in various HEMT structures. They incorporated thin (6 Å) layers of charge to simulate the polarisation bound sheet charge densities DEG Mobility The electron mobility of the 2DEG is an important transport parameter in the performance of HEMT devices [240]. The mobility is one of the major limiting factors for operating

178 158 Chapter 6: AlGaN/GaN High Electron Mobility Transistors J. Appl. Phys., Vol. 95, No. 3, 1 February 2004 Asgari, Kalafi, and Faraone 1189 FIG. 5. The total 2DEG mobility of an AlGaN/GaN heterostructure with 350 Å AlGaN barrier thickness vs Al mole fraction at 10, 80, 120, 150, 180, 220, 250, 300, and 400 K, respectively. pancy. As evident from these figures, the intersub-band scattering increases when the number of occupied sub-bands is increased, which leads to a decrease in the total mobility. Furthermore, Fig. 4 directly compares our calculated results of the total mobility by taking into account the occupation of higher sub-bands, with the experimental results taken from Ref. 18. This comparison produces a remarkably good fit between theoretical calculations and experimental results, which could not have been obtained without taking into consideration the effect of partially occupied sub-bands. For the AlN/GaN heterostructure with 35 Å barrier thickness at T 300 K, the total calculated mobility for one occupied sub- The results of this study indicate that in Al x Ga 1 x N/GaN power, needs to be applied to get electrons moving at a given velocityheterostructures, through the forchannel higher Al mole fraction and thick Al x Ga 1 x N layers, more than one sub-band will be occupied. band is 1475 cm 2 /V s, whereas for multi-occupied sub-bands Thus, intrasub-band and intersub-band scattering will be important in these heterostructures and, hence in calculating the of the device (i.e. for a given frequency). A large mobility is thus desirable. it is 1033 cm 2 /V s, corresponding to a difference of approximately 50% between the two models. 2DEG mobility all of the fully occupied and partially occupied sub-bands need to be considered. Our results We have calculated the mobility of the 2DEG for the indicate Al x Ga 1 x N/GaN heterostructure for all x between 0 and 1 for an Al x Ga 1 x N barrier thickness of 350 Å, which was chosen to ensure that the 2DEG can be developed for all values of x. 16 This calculation is based on including all higher sub-bands occupancy in the model. The results in Fig. 5 show the mobility of the 2DEG for all values of x at different temperatures, which indicates that the mobility decreases rapidly with increasing x value. This rate of decrease is more pronounced for both the lower values of x, such as between 0 and 0.4 at low temperatures, and also for higher values of x at high temperatures (T 200 K). This behavior is related to the temperature dependence of the different scattering mechanisms on x-value, 2DEG density, and occupancy of the higher subbands. At low temperature, many of the FIG. 6. The total mobility of AlGaN/GaN heterostructures with 350 Å Al- GaN barrier thickness vs Al mole fraction at temperatures of 10 and 400 K for both single and multisub-band occupancy models. Figure 6.5: The total 2DEG mobility of an AlGaN/GaN heterostructure with 350 Å AlGaN barrier thickness vs Al mole fraction at 10, 80, 120, 150, 180, 220, 250, 300, and 400 K, respectively [241]. scattering mechanisms such as surface roughness and alloy scattering have a strong dependence on x value and 2DEG density. In contrast, the optical phonon scattering mechanism, which dominates at high temperature, has a weak dependence on x value but is strongly dependent on higher sub-band occupancy and related scattering mechanisms. To study the effect of sub-band occupancy on the Al x Ga 1 x -N/GaN heterostructure, we have calculated the total mobility with either a single level or multiple sub-band occupancy for different x values at two different temperatures, 10 and 400 K. As evident from Fig. 6, the inclusion of multisub-band occupancy has its greatest impact on mobility at high x value and at high temperatures. This is to be expected since there is a higher probability of sub-band occupancy at higher x values and higher temperatures. speed. Since the electron mobility, µ, is the relationship between electric field, E, and IV. CONCLUSIONS electron velocity, v, where v = µe, a greater mobility means less voltage, and hence The mobility of the 2DEG is dependent on the density of the 2DEG and therefore on that at room temperature there is approximately a 50% difference between the 2DEG total mobility as calculated using only a single sub-band, in comparison to when multisubband occupancy is included. Furthermore, this difference is greater as the number of occupied sub-bands increases. Evidence for the applicability of the developed model is provided by the fact that the 2DEG total mobility calculated for multisub-band occupancy shows good agreement with published experimental data. the Al mole fraction of the AlGaN barrier layer (as the x mole fraction dictates a large part of the 2DEG density value) though also due to the penetration of the electron wave functions into the barrier layer (alloy scattering). While the 2DEG mobility is dictated by a number of scattering mechanisms depending on the layer structure of the HEMT, an example of the dependence of the mobility on Al mole fraction is given in Fig ACKNOWLEDGMENTS The authors wish to thank the Research Institute for Fundamental Sciences RIFS and the Australian Research Council ARC for financial support of this work. The mobility of the 2DEG is dictated by a number of scattering mechanisms which deflect electrons from their path in various directions on their way to being collected at the drain of the transistor, thus reducing their speed through the device. 1 O. Aktas, Z. F. Fan, A. Botchkarev, S. N. Mohammad, M. Roth, T. Jenkis, L. Kehias, and H. Morkoc, IEEE Electron Device Lett. 18, M. S. Shur and M. A. Kahn, MRS Bull. 22, The dominant 3 U. K. Mishra, Y. F. Wu, B. P. Keller, S. Keller, and S. P. DenBaars, IEEE Trans. Microwave Theory Tech. 46, J. M. Redwing, M. A. Tischler, J. S. Flynn, S. Elhamori, M. Ahoujja, R. S. Newrock, and W. C. Mitchel, Appl. Phys. Lett. 69, R. Gaska, J. W. Yang, A. Osinski, Q. Chen, M. A. Kahn, A. O. Orlov, L. scattering mechanism in AlGaN/GaN HEMTs above 150 K is polar optical phonon (POP) scattering [242]. Polar optical phonon scattering is difficult to model as it is an Downloaded 14 Oct 2009 to Redistribution subject to AIP license or copyright; see inelastic process, and the energy of POPs in GaN is quite high compared to the thermal energy, at around 90 mev. At low temperatures, below perhaps 40 K, interface roughness and scattering from interface charges have been shown to be the dominant mechanisms limiting electron mobility [242]. Improving the mobility by reducing, where possible, electron scattering mechanisms is important for improving HEMT device performance. It is also important to limit reductions in the mobility that can occur during processing, for example by the deposition of a surface passivation layer. This work seeks to find surface passivation that either improves the 2DEG mobility, or limits any unavoidable reduction.

179 6.5: Current Collapse 159 Values of the mobility measured in the AlGaN/GaN heterostructure increased as the materials and structure were grown with increased purity and quality. The incorporation of an AlN interlayer in some device designs (Fig. 6.1) reduces alloy scattering and therefore also helps to improve the mobility of the 2DEG. Very high mobility values can now be achieved, with measured results at 300 K such as a 2DEG mobility of 2200 cm 2 /Vs at a 2DEG density of cm 2 [243], 2170 cm 2 /Vs at cm 2 [244], 2175 cm 2 /Vs at cm 2 [244] and 2215 cm 2 /Vs at cm 2 [245]. At lower temperatures the mobility increases significantly, with reported values of cm 2 /Vs at cm 2 at 15 K [244], cm 2 /Vs at 12 K and cm 2 /Vs at 77 K [246] and cm 2 /Vs at 13 K for an x mole fraction of 0.09 (9 %) [78]. Polyakov et al. [247] have calculated through Monte Carlo modelling the maximum mobility in an undoped AlGaN/GaN heterostructure 2DEG to have an intrinsic limit of 2700 cm 2 /Vs at cm 2 for an x mole fraction of Current Collapse One of the driving issues behind the use of passivation for AlGaN/GaN HEMT devices is the phenomena of current collapse. The measured output power of early AlGaN/GaN HEMTs under high biases and high frequencies of interest was frequently observed to be much lower than that expected from static current voltage characteristics [66, 105, 248]. The following equation gives the expected power output of a HEMT at any frequency, based on DC characteristics [69] P = 1 8 I DS,MAX ( V BREAKDOWN V KNEE ) (6.13) where I DS,MAX, V BREAKDOWN and V KNEE are the maximum drain current, breakdown voltage and knee voltage, respectively, measured during DC operation. Thus when a reduction in I DS from I DS,MAX, a reduced value for V BREAKDOWN, or an increase in V KNEE occurs, the output power is reduced. In general the most significant factor affecting output power at high frequencies in standard HEMT designs is a reduction in the drain current, I DS, though often an increase in knee voltage is also seen. The combined result is a phenomenon referred to as current collapse, though also occasionally as dispersion, current compression or current slump [69]. An example of reduced performance under AC conditions, current collapse, is shown in Fig. 6.6.

180 160 Chapter 6: AlGaN/GaN High Electron Mobility Transistors 3074 Appl. Phys. Lett., Vol. 81, No. 16, 14 October 2002 GaN HEMT if the by a surface hole gas. MT if the polarization deep donor. nd SiC, but AlN, Si, and also emerge as viable. The own entirely by molecular chemical vapor deposition uffer grown by vapor phase tly, is less common. Hetice-mismatched substrates the most critical aspects of bstrate, the nucleation layer at a low temperature (typated up to the growth temhe GaN and AlGaN layers t growth rates of 1 m/h. rformed using AlN grown s device behavior and may the film is the polar nature Fig. 9. Dispersion between the large-signal ac and dc HEMT characteristics simulated by a 80 s pulse on the gate. Figure 6.6: Current collapse can be seen as a reduction in the output current in the AC characteristics, from the characteristics measured at DC, in the I D /V D curves. Also present is a reduction in knee voltage [106, 248]. The reduction in I DS is a result of a depletion of the 2DEG. This occurs most significantly Fig. 10. Proposed mechanism for large-signal dispersion. Occupancy of surface traps under negative bias. due to re-occupation of the donor-like surface states. FIG. 1. Measured dc and ac I DS V DS characteristics for different drain of the GaN and AlGaN. Fig. 5 shows the crystal structure sweep voltages V DS 4, 8, 12, 15, and 20 V of AlGaN/GaN HEMTs on a sapphire and b SI SiC substrates. Top trace was at V of Ga-polarity or Ga-face GaN. Currently, all high-quality GS 1.5 V step voltage was 1.0 V. material is grown with this polarity. The sense of the spontaneous polarization is indicated on the diagram. The band diagram and piezoelectric constants versus lattice constant HEMTs. 7 However, three deep trap activation energies of for the (Al, Ga, In, N) system is shown in Fig. 6. The tensile E 1.23, 0.61, and ev were observed on the strain caused by the growth of Al Ga N on GaN results sapphire-based HEMTs. These deep trap activation energies in a piezoelectric polarization that adds to the net spontaneous polarization in a manner given by [3] density has been realized on GaN epilayers grown on SiC are related with the material defects/dislocations. Low defect substrates ( cm 2 ) when compared with the GaN epilayers on sapphire substrates ( cm 2 ). The low dislocation density of GaN on SiC is related to its small lattice cm mismatch and thermal expansion coefficient with GaN. Moreover, low radiative recombination centers have also where is the net total polarization. This results in a been net observed on the SiC grown GaN using electron beam positive charge at the AlGaN/GaN interface, as shown in Fig. 7(a). The compressive strain caused by the growth of In Ga N on GaN causes a net negative piezoelectric polarization charge at the In Ga N GaN interface, as shown in Fig. 7(b). The magnitude of the charge follows [3] Western Australia. Downloaded on October 14, 2009 at 01:53 from IEEE Xplore. Restrictions apply. cm PROCEEDINGS OF THE IEEE, VOL. 90, NO. 6, JUNE 2002 The filling of the surface states, which become charge neutral, leaves a net negative charge on the surface as a result of the fixed negative polarisation charge at the surface. This process depletes the 2DEG and therefore reduces the drain current, resulting in reduced output power and an observable current collapse. The surface states can only capture and emit electrons at certain rates, depending on a complex interaction of conditions. Vetury et al. [69, 72] determined the trapping and detrapping time constants and found the more significant detrapping time constant to be on the order of seconds, making it difficult to discharge the surface states quickly. Surface state trapping, then, leads to a slow large-signal response time, which restricts output microwave power because the maximum drain current cannot follow the applied AC gate signal [65], i.e. at high frequencies the channel modulation is severely degraded. The filling of surface states reduces the 2DEG density and reduces the influence of the gate. This effect was first measured by Vetury [69, 71] by measuring the surface potential FIG. 3. Activation energy plot of drain leakage c the gate voltage of V g 5 V and drain voltage induced current EBIC measurements. 1 mobility and sheet carrier density ( H high for AlGaN/GaN heterostructures o Figure 4 shows the dc I DS V DS chara measured at V g 0 V under dark and tion. The increase in percentage of drai light illumination was high for sap 33% when compared with the SiC- The white-light illuminated I DS V DS c the existence of more number of traps HEMTs. The ac I DS V DS curve of sap shows see Fig. 1 a large hysteresi when compared with the HEMTs ( 310 mv). Large values of hysteres presence of more deep traps located ad which increases the device capacitance. conductivity of sapphire and an additio deep trap ( E 0.61 ev) level located band severely degraded the drain curre HEMTs see Figs. 1 a and 3. These agreement with the low dislocation d H n s and small number of radiative r of GaN on SiC substrates, which was force microscopy, Hall effect, an elsewhere FIG. 2. Maximum drain current (I Dmax ) of AlGaN/GaN HEMTs on sapphire and SI SiC substrates as a function of ac drain sweep voltages for different FIG. 4. dc I DS V DS characteristics of AlGaN/Ga gate voltages ( 1.5, 0.5, and 0.5 V). SiC substrates measured under dark and white-li Downloaded 16 Jun 2004 to Redistribution subject to AIP license or copyright, see along the gate-drain access region using floating gates as potential probes. A region of negative charge appears over the gate-drain access region: a second virtual gate is formed, which modulates the channel and is outside the control of the actual gate. The output drain current is now controlled by the mechanisms that supply and remove charge from the virtual gate, in addition to the applied gate bias [69]. Current collapse is explained and modelled by this concept of a virtual gate [69, 72]. A diagram of the virtual gate in the gate-drain access region, and as a schematic circuit element in series with the actual gate, are shown in Fig Vetury et al. [69, 72] outlined that the virtual gate model