Defect Accumulation in Erbium Implanted Gallium Nitride

Transcription

1 Defect Accumulation in Erbium Implanted Gallium Nitride Promotor: Prof. dr. A. Vantomme Proefschrift ingediend tot het behalen van de graad van doctor in de wetenschappen door Bert Pipeleers 2005

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3 Contents Introduction 1 1 Gallium Nitride A brief history of GaN and its applications Properties of gallium nitride Growth of crystalline GaN layers Substrates Metalorganic chemical vapor deposition Molecular beam epitaxy Ion implantation into GaN Microstructural properties Electrical doping by ion implantation Optical doping by ion implantation Rare-earth elements in GaN Properties of rare-earths GaN as host material for rare-earths Rare earth doping of GaN Ion-Atom Interactions Introduction Interactions of ion beams with materials Ion-atom interactions Electronic stopping Nuclear stopping Ion distribution Ion channeling in crystals The continuum model Critical angle for channeling Ion implantation i

4 ii CONTENTS General principle Radiation damage in solids Post-implantation annealing Simulation programs for ion implantation processes Rutherford backscattering and channeling spectrometry General principle Disorder analysis by means of backscattering Experimental Details GaN layer growth Ion implantation Analysis techniques Rutherford backscattering and channeling spectrometry High-resolution X-ray diffraction Luminescence measurements Sample annealing Implantation induced damage and strain in GaN Main characteristics of defect accumulation in GaN Implantation angle dependence Experiments Implantation induced crystal damage Erbium distribution Critical angle Implantation induced strain Conclusion Erbium fluence dependence Experiments Implantation induced damage Erbium distribution Implantation induced strain Conclusion Temperature dependence Experiments Implantation induced damage Erbium distribution Implantation induced strain Conclusion Generalisation of the damage accumulation process

5 CONTENTS iii 4.6 Annealing of implantation induced damage Luminescence studies of Er implanted GaN Photoluminescence and photoluminescence excitation spectroscopy Cathodoluminescence spectroscopy Conclusion Conclusions 153 A Rutherford Backscattering and Channeling Spectrometry 159 A.1 Basic principles A.2 Physical concepts A.2.1 Kinematic factor K A.2.2 Stopping cross section A.2.3 Scattering cross section A.3 Channeling B High-Resolution X-Ray Diffraction 167 Publications 185

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7 Introduction Gallium nitride (GaN) is by far the most extensively studied semiconductor of all III-V nitrides, among which also indium nitride (InN) and aluminium nitride (AlN) are well known in this field of research. In the past decade GaN has been subject of extensive research due to the very important technological applications of this semiconductor. Blue and ultraviolet (UV) light-emitting diodes (LEDs) as well as laser diodes have already been realised and commercialised. Other examples of GaN-based applications are UV detectors and microwave power and ultra-high power switches. In the fabrication of many of these GaN-based devices, electrically or optically active dopants are introduced in the host material. For example, Ca or Mg are often used to generate p-type GaN whereas as-grown GaN is a n-type material. The production of p-type GaN is important in the fabrication of p-n junctions. On the other hand, the rare-earth elements are attractive candidates for optical GaN-based applications in the visible region, since these elements exhibit sharp optical emission lines independent of the host material. Moreover, due to the wide bandgap of GaN, luminescence is not quenched at room temperature as is the case in silicon for example. In chapter 1, progress in the research on GaN will be described to situate this work. Furthermore, the properties of this semiconductor and the growth techniques of GaN are discussed. An attractive and convenient tool to introduce dopants into the GaN lattice is the ion implantation technique, which has already proved to have outstanding advantages for doping of mature semiconductor materials, such as silicon for example. Ion implantation is characterised by a precise control of the amount of the introduced impurity, independent of the solubility of this dopant in the host material. Moreover, ion implantation also allows patterning and local and/or shallow doping of materials. However, the main disadvantage of ion implantation is the creation of radiation damage in the host material due to nuclear collisions between the impinging impurity ions and the host atoms. In this work, ion beams are not only used for the 1

8 2 Introduction introduction of erbium ions into GaN, but also as analysis technique, i.e. Rutherford backscattering and channeling spectrometry. Consequently, two types of ion beams can be distinguished: low energy, high mass and high energy, low mass ion beams. The basic concepts of the interaction of ion beams with materials will be elucidated in chapter 2 for both types of ion beams. Additionally, specific attention will be devoted to implantations along the GaN 0001 axis, i.e. channeled implantation. It has already been shown that ion implantation along a major crystal axis in silicon drastically reduces the lattice damage. The channeling effect of ions impinging along a major crystal axis will be described by various theoretical models. Accurate preparation of the substrates and a precise control of the growth conditions are very important to obtain good quality GaN layers. The high quality GaN layers used in this work were grown on sapphire substrates at the universities of Gent and Montpellier by means of metalorganic chemical vapour deposition (MOCVD). These GaN layers were implanted with erbium ions in our laboratory (IMBL). For the introduction of Er ions into GaN and especially in the case of channeled implantation, a good control of the various implantation parameters is needed. Chapter 3 elucidates the experimental details of GaN layer growth and ion implantation, as well as a variety of analysing techniques which have been applied for the structural characterisation of the implanted species. Since ion implantation induces defects which are detrimental for the optical and electrical properties of the GaN, it is important to understand the fundamental defect creation and damage accumulation processes. Chapter 4 contains a detailed study of the influence of the various implantation parameters on the damage accumulation. Simultaneously, a comparison is made between the standard random implantation process and implantations along the GaN 0001 axis for two different implantation energies. The effect of the implantation angle, i.e. the angle of the ion beam with respect to the GaN c-axis, on the damage accumulation is investigated experimentally, theoretically and by computer simulations. Next, the damage accumulation and induced lattice strain with increasing erbium fluence is studied for both random and channeled implantation. Raising the substrate temperature during annealing will enhance the mobility of the defects in the GaN crystal and enhance the dynamic recovery effect. The defect accumulation in the temperature range 23 C-700 C is investigated. Finally, we will compare the results of these implantation parameters and come to a general conclusion on the defect accumulation in GaN, independent of the specific implantation parameters.

9 Introduction 3 Finally, luminescence measurements are performed on the implanted and subsequently annealed samples. Since the implantation induced defects are detrimental for the luminescent properties of the dopants, it is important to investigate the optimal implantation parameters to obtain not only the lowest defect concentration, but also the highest luminescence intensity of the implanted species. Hence, the relationship between the induced damage and the luminescence properties will be examined.

10 4 Introduction

11 Chapter 1 Gallium Nitride 1.1 A brief history of GaN and its applications A short historical description of some of the major events in the gallium nitride (GaN) research is presented here to understand the widespread interest in this semiconductor. A more complete description can be found in literature (references [1 3]). Gallium nitride has been the subject of extensive research for a large part of the past decade. Due to outstanding physical properties such as a large and direct bandgap and thermal and chemical stability, this semiconductor has since long been viewed as a promising material for technological applications in the field of optoelectronics. Rather often GaN-based devices appeared first, like blue LED s, which stimulated researchers to understand the physical mechanisms behind this device and to improve it. GaN-based devices have opened new opportunities in short-wavelength (visible and ultraviolet (UV)) photonic devices for display and data-storage applications, solar-blind UV detectors, and high-temperature/high-power electronics. Gallium nitride was first produced in powder form in 1932 by the reaction of ammonia gas and metallic gallium at high temperatures (900 C C) by Johnson and co-workers [4]. Next reports were found nearly three decades later in which much effort was spent to grow and characterise epitaxial GaN layers. A major breakthrough in GaN research, however, occurred in 1969, when epitaxial GaN was first produced via hydride vapour phase epitaxy (HVPE) by Maruska and Tietjen [5]. The HVPE GaN film was grown on a sapphire substrate, which today remains a popular choice despite a large lattice mismatch between the two materials [1]. The HVPE technique was the basis of a worldwide substantial effort in GaN develop- 5

12 6 Gallium Nitride ment around With this technique thin GaN films with bulk-like properties could be produced, suitable for preliminary studies of many physical properties. The first light emitting device was already produced in 1971 [6]. Progress, however, was hindered for nearly two decades due to the inability to produce low Ohmic p-type material and to the contamination of the GaN films by transition metals when using the HVPE technique. The first problem was solved by Akasaki in 1989 when p-type GaN was obtained by Mg-doping [7]. This allowed the fabrication of electroluminescent diodes using p-n junctions for the first time. Another breakthrough came with the discovery that growing a buffer layer of AlN or GaN at low temperatures ( 500 ) in between the sapphire and the main GaN film greatly reduced the native defect concentration [8]. This was obtained through metalorganic chemical vapor deposition (MOCVD), a deposition technique that is still used today to grow GaN films. During the following years, luminescent efficiencies improved drastically, which opened new markets for light-emitting devices, such as vehicle break lights, highway status signs and traffic control signs. These blue and green LEDs rounded out the visible spectrum, and have had their immediate application in full-color outdoor displays and by combining the output of red, green and blue LEDs, efficient white-light sources are possible. In late 1995, Nakamura and his group, announced another major breakthrough: the pulsed operation of a blue GaN/InGaN multi-quantum-well laser diode [9]. These lasers, in turn, will be the cornerstone of major new industrial and consumer electronics goods, notably next-generation DVD player-recorders and optical data-storage systems for computers. The change from currently available red or infrared ( nm) laser diodes, to the GaN-based lasers with a wavelength of nm will significantly increase the optical-storage density up to six times the present capacity. A last area of applications that gained a lot of attention is high-temperature/high-power electronics. SiC is still the most mature technology in these devices, but GaN has almost ideal properties (a large and direct bandgap and good thermal stability) in situations where heat tolerance is critical for electronics, such as automobile engines, all-electric vehicle drive trains and avionic systems involving sensors, activators and electronics. For more information on GaN-based devices the interested reader is referred to [1, 10, 11] and references therein. Although GaN-based devices are already commercially available, many aspects of this semiconductor still remain unknown compared to the more commonly studied Si and GaAs. The most important question maybe is

13 1.2 Properties of gallium nitride 7 why heteroepitaxial nitrides work at all for photonic devices. The high defect density 1 in these films would prevent efficient light emission in other III-V materials because these defects cause the electrons to recombine with holes without creating photons and for such high densities they completely quench the optical output. A second aspect, which needs to be investigated in more detail, is the comprehension of the defect formation in GaN when introducing impurities by means of ion implantation. In this work we will investigate the defect accumulation in GaN by implantation of erbium (Er) ions and study the dependence of the damage accumulation on the erbium fluence and energy, the substrate temperature and the angle of incidence. 1.2 Properties of gallium nitride In this section, an overview of the relevant structural, thermal, electrical and optical properties are discussed, which will be used in this work. For a more extended description, we refer to [1, 2, 12, 13]. Table 1.1 summarises these basic properties of wurzite GaN. Structural properties Gallium nitride can crystallise in the zincblende as well as in the wurzite structure. The wurzite structure, however, is more common and will be used in this work. The bonding to the nearest neighbours is tetrahedral and the Bravais lattice of the wurzite structure consist of two inter-penetrating hexagonal close packed (HCP) 2 sublattices, each with one type of atoms (Ga or N), offset along the c-axis by 3/8 of the cell height. The axis perpendicular to the hexagons is usually labeled as the c-axis. Figure 1.1 shows the unit cell of the wurzite structure of GaN. The space group symmetry of this structure is C 4 6v (P6 3mc) and its point group symmetry is C 6v (6mm). For wurzite GaN, lattice parameters of a = ± Å and c = ± Å [5] are generally accepted. Thermal properties The thermal expansion of wurzite GaN has been studied in the temperature range of K by Maruska and Tietjen [5]. They reported a linear change with temperature for lattice constant a, with a mean coefficient of 1 GaN can easily have a defect density of cm 2 which is very high compared to other semiconductors like Si (10 2 cm 2 ), or GaAs (10 4 cm 2 ). 2 In a HCP lattice, the regular hexagons have a stacking sequence ABABAB...

14 8 Gallium Nitride Table 1.1: Some basic properties of GaN. Lattice parameters a = Å Ref. [5] (T = 300K) c = Å Thermal expansion coefficient a/a = /K Ref. [5] (T = 300K) c/c = /K Density ρ = 6.15 g/cm 3 Ref. [13] Atomic density at/cm 3 Bandgap E g (300K) = 3.39 ev Refs. [1, 5] E g (1.6K) = 3.50 ev Debye temperature θ D (0K) = 600K Refs. [14, 15] Melting point 2791 C Ref. [16] c a b Ga or N N or Ga Figure 1.1: Unit cell of the hexagonal wurzite structure of GaN, consisting of two interpenetrating hexagonal sublattices of Ga and N atoms. The bonding with the nearest neighbours is tetrahedral and the lattice parameters of this unit cell are a = Å and c = Å.

15 1.2 Properties of gallium nitride 9 thermal expansion of a/a = K 1 across the entire temperature range. Meanwhile, the expansion of the lattice constant c shows a superlinear dependence on temperature. The mean coefficient of thermal expansion parallel to the c-axis is c/c = K 1 and c/c = K 1 for the temperature ranges K and K, respectively. The Debye temperature (θ D ) of wurzite GaN at 0 K was calculated to be θ D 600 K [14, 15]. More thermal properties of GaN can be found in literature [2, 17] Electrical properties Control of the electrical properties remains the main obstacle for device fabrication. Unintentionally doped GaN has in all cases been observed to be n-type with a high electron concentration, even for the best samples. Since no impurities have been present in sufficient amounts to account for the carriers, this high concentration is generally believed to be caused by native defects and more specifically by nitrogen vacancies. The electrical characteristics of GaN vary widely in literature, reflecting the crystal quality and purity of the materials used. More details on the electrical properties of GaN are available in references [2, 12, 13]. Optical properties These are probably the most investigated properties of GaN, because of its great potential as light emitter. The large direct bandgap allows efficient light emission. Maruska and Tietjen [5] were the first to accurately measure the bandgap energy at room temperature to be 3.39 ev. This transition is measured between the uppermost valence band states and the lowest conduction band minimum. The calculated band structure near the direct fundamental gap (k=0) of wurzite GaN is shown in figure 1.2 at 1.6 K. The top of the valence band is split by the crystal field and by the spinorbit coupling into A, B and C states. With a bandgap of 3.39 ev, GaN is situated in the UV region as can be observed from figure 1.3. On the left hand side, one can find the more common semiconductors like Si, Ge and GaAs with a much lower bandgap energy. More about the optical properties of GaN can be found in references [1, 12, 13].

16 10 Gallium Nitride Figure 1.2: Calculated band structure near the direct bandgap (k=0) of wurzite GaN. The top of the valence band is split by the crystal field and by the spin-orbit coupling into A, B and C states [1]. Bandgap energy E (ev) g AlN Diamand AlN MgS T=300 K 4.0 ZnS GaN MgSe Ultra ZnS MgTe violet 4H-SiC ZnO GaN 3.0 violet6h-sic 2H-SiC ZnSe CdS ZnSe blue BP green AlP CdS yellow 3C-SiC 2.0 InN GaP ZnTe red AlAs CdSe Infra InN CdSe GaAs red AlSb CdTe 1.0 Si InP Ge InAs GaSb InSb BN " Italics" = indirect gap "Roman" = direct gap hexagonal structure cubic structure Lattice constant a (Angstroms) Figure 1.3: Room-temperature bandgap energy versus lattice constant of common semiconductors [18].

17 1.3 Growth of crystalline GaN layers Growth of crystalline GaN layers Maruska and Tietjen were the first who were able to grow single crystalline GaN layers on sapphire (Al 2 O 3 ) substrates by means of vapour-phase epitaxy (VPE) [5]. In the following struggle to improve the quality of the GaN layers, a number of growth techniques, such as hydride vapour-epitaxy (HVPE), metalorganic chemical vapour deposition (MOCVD) and molecular beam epitaxy (MBE) have been employed. A variety of substrates, including silicon [19], GaAs [20], silicon carbide [21, 22] and sapphire [5, 22] have been used. The MOCVD technique is nowadays the most widely used technique, since it leads to good quality GaN layers. However, doping of GaN with impurity ions is often performed by means of MBE. Both techniques will be discussed shortly below Substrates One of the major difficulties that has delayed the GaN research, is the lack of a suitable substrate material which is compatible with GaN. GaN has been grown primarily on sapphire, but in addition, also Si, GaAs, SiC, ZnO and several other materials [2] have been used as substrate. SiC appears to be an ideal candidate as a substrate for GaN, characterised by a lattice mismatch of only 3.5% and a thermal expansion coefficient of K 1, which is close to that of GaN. Moreover, SiC is a conductive substrate as opposed to sapphire, which simplifies the fabrication of LEDs or laser structures having a single top and substrate contact. In addition, GaN layers grown on SiC show superior structural and optical properties [22]. However, the high cost of SiC wafers has prevented the widespread use of this material. In contrast to SiC, the commonly used sapphire has a lattice mismatch of 16% and a large thermal mismatch (see also table 1.2) with the GaN lattice. Even for typical growth and annealing temperatures, the lattice mismatch between both materials remains approximately 16%. Additionally, sapphire is an insulator, which makes device fabrication more difficult. Despite these drawbacks, the preference towards Al 2 O 3 substrates can be attributed to its wide availability, hexagonal symmetry and its ease of handling and pregrowth cleaning. It is also stable at the high temperatures ( 1000 C) required for epitaxial growth. Due to the large thermal and lattice mismatches between sapphire and GaN, it is necessary to grow a thick epilayer (a buffer layer) to obtain good quality material. Figure 1.4 gives a schematic illustration of the lattice mismatch of a GaN(0001) film onto an Al 2 O 3 (0001) substrate.

18 12 Gallium Nitride Table 1.2: Lattice mismatch and thermal expansion mismatch for growth of GaN and AlN onto sapphire [1]. Material Lattice Thermal constant expansion a epi a Al2 0 3 a Al2 0 3 α epi α Al2 0 3 α Al2 0 3 coefficient, α (Å) (%) ( 10 6 /K) (%) GaN a = c = AlN a = c = Al 2 O 3 a = c = [1010] GaN [1210] Sapphire 3x3.189 Å Å [1210] GaN [1010] Sapphire Å : Sapphire : GaN Figure 1.4: Schematic illustration of the lattice mismatch for GaN grown onto an Al 2 O 3 (0001) surface [1].

19 1.3 Growth of crystalline GaN layers Metalorganic chemical vapor deposition Metalorganic chemical vapour deposition (MOCVD) is a widely used growth method in semiconductor industry for preparing epitaxial structures. In this process, metalorganic compounds (called precursors) are used as source material, because they thermally decompose at lower temperatures compared to other metal containing compounds. For the growth of GaN on sapphire substrates, triethylgallium (TEGa) [Ga(C 2 H 5 ) 3 ] or trimethylgallium (TMGa) [Ga(CH 3 ) 3 ] is used as a Ga source, while ammonia (NH 3 ) is used as a nitrogen source. Both gasses flow over the substrate and react to form GaN at a temperature ideally between 970 C and 990 C. The growth of GaN layers consist of different subsequent steps which take place at atmospheric pressure. An important step in this process is the growth of a thin GaN or AlN buffer layer of inferior quality, since this layer absorbs the large lattice mismatch between sapphire and GaN. Subsequently, the sample is annealed at high temperatures before the main GaN layer is grown. More experimental details on the MOCVD growth of GaN layers are found in chapter Molecular beam epitaxy An alternative technique to grow epitaxial GaN films is molecular beam epitaxy (MBE). GaN MBE growth is a non-equilibrium process where Ga vapour from an effusion cell and an ammonia (NH 3 ) or nitrogen beam from a plasma source are directed toward a heated substrate. The MBE process is performed in an ultra-high vacuum chamber, which minimises contamination. Some drawbacks of MBE growth are the limited NH 3 flow due to a problem of pressure control and the creation of defects as a consequence of the energetic ions (in the order of ev) produced in the plasma cell. However, the major drawback of GaN MBE growth is the lower growth temperatures which are achievable ( C) because of the thermodynamic instability of GaN under vacuum: GaN decomposes at higher temperatures into metallic gallium droplets and nitrogen gas. Also the annealing of the buffer layer becomes difficult. This problem is often solved by using MOCVD grown GaN templates as substrate. Despite these drawbacks of MBE growth of GaN films, this technique also has a number of important advantages. Molecular beam epitaxy is extremely suitable to grow doped GaN layers which can be desirable to produce p-type GaN (by doping with an acceptor, like Mg or Zn) or to

20 14 Gallium Nitride introduce rare-earth elements 3 for light emitting devices. In these cases, the impurity can be used as elemental solid source in MBE and due to the lower growth temperature, the process is further away from equilibrium conditions, which increases the incorporation of impurities in the GaN film. This is in contrast with MOCVD, where a metalorganic compound of the desired impurity with a sufficiently high vapour pressure is required. On the other hand, doping of GaN with impurities can also be done ex situ, by ion implantation. This technique offers the advantage of introducing an impurity fluence which is higher than the solubility limit. 1.4 Ion implantation into GaN Ion implantation is a convenient method to incorporate impurity atoms (dopants) into the host material with precise control of the concentration and profile. It is widely used in the mature semiconductor industry for (selective area) doping or electrical isolation. Ion implantation is also expected to play an important role to introduce optical and electrical dopants in GaN and related nitrides. The first reports of the use of ion implantation to introduce dopants into GaN date back to Pankove and co-workers implanted 35 different impurities in GaN to measure their photoluminescence [23]. To remove the implantation induced damage, the samples were annealed for 1h at 1050 C in flowing ammonia. From the 35 different ion species, only Mg, Zn, Cd, Ca, As, Hg and Ag showed a characteristic spectral photoluminescence signature. Subsequent reports on ion implantation into GaN only appeared two decades later and can be divided into three major research directions: the investigation of the microstructural changes introduced by ion implantation, and the optical and electrical doping of GaN. These topics will be discussed in the following sections. For more extended reviews, the reader is referred to literature [2, 24 26] and references therein Microstructural properties In the process of ion implantation, the impinging ions will transfer kinetic energy to the host atoms in several collisions, resulting in the displacement of these atoms from their lattice site if sufficient energy is transferred. These recoiling atoms may displace other atoms, hence creating a cascade of atomic collisions. The most common defects caused by the impinging 3 See section 1.5 on rare-earths.

21 1.4 Ion implantation into GaN 15 ions are vacancies, interstitials, and extended defects such as dislocations or stacking faults. The damage concentration mainly depends on the ion mass and energy, the implantation temperature and on the structure of the host material. Rutherford backscattering and channeling spectrometry (RBS/C), transmission electron microscopy (TEM) and X-ray diffraction (XRD) are often used to investigate the crystalline quality, defect formation and lattice strain. The first study of damage accumulation in GaN after ion implantation was reported by Tan et al. [27, 28]. They demonstrated that GaN is extremely resistant to amorphisation during bombardment of 90 kev Si ions at liquid nitrogen temperature, indicating very efficient dynamic annealing. Other groups confirmed this high amorphisation threshold under a wide range of implantation conditions and with different ions species [29 40]. It was also found that for light ions, chemical effects dominate during the implantation process. These ions appear to stabilise an amorphous phase or act as an effective trap and enhance the radiation damage. Since the resulting electrical and optical properties of the implanted GaN strongly depend on the lattice site location of the impurity atoms, it is essential to know this lattice site for device processing by ion implantation. The implanted impurity atoms can occupy several lattice positions in the host lattice including substitutional and a wide variety of interstitial sites. For the determination of the lattice site of the implanted species, different techniques can be used, for example extended X-ray absorption finestructure (EXAFS), emission channeling (EC) and Rutherford backscattering and channeling spectrometry (RBS/C). It is observed that the majority of the implanted ions occupy a regular Ga site. Examples are Si [41], Ca [42], Mn [43], Fe [44, 45], Pr [46, 47], Eu [47, 48], Er [49 51], Tm [52] and Hf [53]. Annealing does not change the apparent substitutional fraction (i.e. the fraction of Er ions occupying a regular Ga site) drastically. Reference [54] reviews the different lattice location experiments on implanted GaN samples. Liu et al. [30, 32] found that a satellite peak appeared in X-ray diffraction (XRD) spectra at an angle lower than the GaN(0002) reflection after 180 kev Ca implantation in GaN at 77 K. This new peak is attributed to a local expansion of the GaN hexagonal lattice, caused by the introduced impurities and displaced host atoms onto interstitial sites. Other groups have also noticed this extra peak for Mg [55], Be [55, 56] and Er [40] implantations. From the intensity and position of this peak as a function of the implantation fluence, it was concluded that amorphisation first oc-

22 16 Gallium Nitride curs in small local regions, which increase with implantation fluence until the crystal collapses and an amorphous layer is formed. This behaviour of the crystalline lattice is already known from ion implantation studies in other semiconductors such as Si [57 60] or GaAs [61, 62]. Paine et al. [61, 62] found that the depth profile of the perpendicular lattice strain has the same shape as the calculated depth profiles of the energy deposited per ion by nuclear collisions, which is directly related to the radiation damage. Moreover, the expansion of the crystalline lattice in the implanted layer implies that the strain contribution is dominated by interstitial atoms [59, 60]. All these groups focus on the microstructural properties of the GaN crystal after implantation with the ion beam tilted several degrees of the GaN 0001 axis to minimise the channeling effect, in which the ions will enter the GaN crystal through the open channels between the rows of atoms 4. Channeling is often avoided since a good control over the ion ranges and implantation profile is difficult. Wu et al., however, demonstrated the importance of channeled implantation of Er into Si(111) substrates [63]. They found that the crystalline quality improved drastically after implantation along the Si 111 axis. We apply this approach to reduce the irradiation damage in GaN and studied the damage build-up according to this geometry Electrical doping by ion implantation The goal of electrical doping is to modify the conductivity of the semiconductor, by dopant implantation or implantation isolation. The purpose of dopant implantation is to introduce electrically active n- or p-type dopants to increase the free carrier concentration, while the aim of implantation isolation is to produce highly resistive layers by implantation of various elements, which create mid-gap levels that trap electrons and holes. Kahn and collaborators were the first to report the use of ion implantation for the modification of the electrical properties of GaN [64]. They compensated the background donor concentration by implantation of Be + or N + ions. Both ion types resulted in a significant reduction of the free carrier concentration, which implies that the induced defects are responsible for this compensation and not the chemical nature of the implanted species. This conclusion stresses the importance of a full understanding of the implantation induced defects as discussed in the previous section. 4 More information about channeling can be found in section 2.3.

23 1.5 Rare-earth elements in GaN 17 The production of n- or p-type GaN is important in device fabrication to produce p-n junctions. As grown GaN is typically n-type material due to a high free carrier concentration, which makes the production of p-type GaN difficult. Different donor and acceptor dopants are already used to achieve respectively n-type or p-type doping. Examples of donor impurities are Si [65 67] and O [68, 69] while Mg [67, 70 72], Be [71, 72], Zn [71] and Ca [39, 69, 71] are used as acceptor dopants Optical doping by ion implantation The large and direct bandgap of GaN makes it a suitable candidate as host for optical dopants. The optical properties of these dopants gained a lot of attention and can best be determined using photoluminescence (PL) or cathodoluminescence (CL) spectroscopy. The first PL studies on implanted GaN were reported by Pankove and co-workers [23]. As already mentioned, they studied the luminescence from 35 different species into GaN, but only few of them showed characteristic luminescence lines. Again, the implantation induced damage plays a crucial role, since it is detrimental for the luminescence. Numerous studies have already been performed to investigate the influence of implantation damage from various elements on the luminescence of GaN. References [24 26] give a good overview of this research. One group of elements, however, has caught the attention of many researchers: the rare-earths. The rare-earth elements are characterised by very sharp optical transitions in the visible and infrared regions, independent of the host material. This makes them extremely suitable for optoelectronic devices. Literature reports the implantation of Ce [73], Pr [47, 73 76], Nd [77, 78], Sm [79, 80], Eu [47, 81], Tb [82, 83], Dy [73, 84], Ho [79], Er [49, 81, 85 88], Tm [81, 84, 89], Lu [73] and Yb [90]. 1.5 Rare-earth elements in GaN Properties of rare-earths The rare-earth (RE) metals are the 14 lanthanide elements in group III-A of the periodic table, from cerium (Ce) to lutetium (Lu) (figure 1.5). Despite their name, the RE elements are not especially rare. Each of them is more common than silver, gold or platinum. The difficult extraction of these elements and their late discovery, lead to the name of rare-earths. RE metals have a high electrical conductivity, high melting and boiling

24 18 Gallium Nitride 58 Ce Pr Nd Pm (147) 62 Sm Eu Gd Tb Dy Ho Er Tm Yb Lu Figure 1.5: The rare-earth elements from the periodic table. points and share many common properties. This makes them difficult to distinguish from each other. Many lanthanides have played an important role in various optoelectronic and photonic applications [91], ranging from emitting elements in solid-state lasers (using Nd) and phosphors for colour lamps and displays (for example Eu or Tb) to optical fibre telecommunications (using Er or Pr). These RE elements have an electronic configuration [Xe]4f n 5d 0 6s 2 with n varying from 1 (Ce) to 14 (Lu) and they all exist as trivalent cations (RE 3+ ). Cerium (Ce), praseodymium (Pr) and terbium (Tb) also exhibit +4, while samarium (Sm), europium (Eu), thulium (Tm) and ytterbium (Yb) can form compounds with a valence of +2. As shown in figure 1.6 the partially filled 4f electron orbital of the RE is located relatively close to the nucleus and is shielded very efficiently by the outer 5s, 5p and 6s electrons. Due to this shielding, the intra 4f n shell transitions result in very sharp optical emissions at wavelengths from the ultraviolet (UV) to the infrared (IR). The wavelengths of these emissions are determined by the energy of the transition between the 4f states of the RE and are relatively independent of the host material GaN as host material for rare-earths Although the host material has almost no influence on the wavelengths of the 4f transitions as stated above, the host material does have a very strong influence on the radiative transition probability or in other words, the photoemission intensity. Conventional semiconductors like Si or GaAs doped with rare-earth ions exhibit limited photoemission at room temperature due to low RE solubility and severe quenching of the luminescence at room temperature. As shown by Favennec et al. [93], this thermal quenching decreases with the bandgap energy of the semiconductor. This conclusion resulted from PL measurements on several materials (Ga 0.38 In 0.62 As 0.84 P 0.12, Si, InP, GaAs, Al 0.17 Ga 0.83 As, ZnTe and CdS) implanted with Er ions with a different bandgap. Therefore, wide-bandgap semiconductors, such as GaN, are attractive candidates as host material for the rare-earths. The

25 1.5 Rare-earth elements in GaN 19 Figure 1.6: Approximate charge distribution of 4f, 5s, 5p, 5d, 6s and 6p electrons in different orbitals for rare-earth ions, demonstrating the shielding of the 4f electrons by outer-shell electrons [92]. 4f energy levels of some rare-earth ions (Pr, Eu, Er and Tm) are depicted together with the conduction-band edge of GaN in figure 1.7. For erbium two energy transfers result in visible light at 537 and 558 nm and one in the infrared at 1.54 µm Rare earth doping of GaN The introduction of RE ions into GaN can be accomplished by means of ion implantation or in situ doping. In situ doping requires a good understanding and control of the overall growth process and of the interaction of the RE flux with the main V/III fluxes. In most reports on in situ doping, molecular beam epitaxy (MBE) was chosen over MOCVD to introduce the RE ions, since it has the advantages of using an elemental solid source for the rare-earths and lower growth temperatures, which increases the incorporation of the RE ions. In contrast, MBE grown samples are of less crystalline quality due to the limited temperature that is achievable during

26 20 Gallium Nitride Praseodymium 3 1 P (2.528 ev) 0 D (2.063 ev) 2 GaN band edge 3.39 ev 1303 nm 1914 nm 650 nm 956 nm G (1.203 ev) 4 F 3 (0.775 ev) F 2 (0.601 ev) H 6 (0.263 ev) H (0.263 ev) 5 H 4 Europium Erbium Thullium 5 5 D 1 (2.350 ev) D (2.133 ev) nm 600 nm 621 nm 663 nm 7 F F J 537 nm 558 nm 1000 nm 1540 nm 477 nm 647 nm 801 nm 4 H 11/ 2 (2.309 ev) S 3/ 2 (2.222 ev) 4 I 11/ 2 (1.240 ev) 3 (0.263 ev) 2 (0.136 ev) 1 (0.066 ev) 4 4 I 13/ 2 (0.805 ev) I 15/ 2 G (2.600 ev) 1 4 F (1.591 ev) 3 4 H (1.052 ev) 3 5 H (0.883 ev) 3 4 H 6 3 Energy (ev) Figure 1.7: Simplified energy diagrams of the 4f levels of selected rare-earth ions (Pr, Eu, Er and Tm) in GaN. The conduction-band edge of GaN is shown [94].

27 1.5 Rare-earth elements in GaN 21 growth and the fluence of the impurity is limited by its solid solubility in GaN. An alternative approach for the incorporation of RE elements in GaN is post-growth doping by for example ion implantation. This process is widespread and has the ability to introduce rare-earths without contamination. The RE concentration can be accurately controlled independent of the growth conditions and a concentration level beyond the thermal equilibrium level can be obtained. However, the implantation approach also suffers from some disadvantages. The heavy mass of the RE ions requires a high energy and the impinging RE ions will create a significant amount of damage in the GaN crystal, which is detrimental for the electrical and optical properties. Therefore, the dependence of this defect accumulation in GaN during ion implantation is investigated in this work and the influence of the ion fluence, ion energy and lattice temperature is studied for both the channeled and random implantation geometry. In the next chapter, the interaction between impinging ions and host atoms will be discussed.

28 22 Gallium Nitride

29 Chapter 2 Ion-Atom Interactions 2.1 Introduction Ion beams play an important role in semiconductor science and in this work. They are not only used to make the desired structures but also to analyse them afterwards. Therefore this chapter will elucidate the physics behind the interaction of ion beams with host atoms. The difference between high energy, low mass (as in Rutherford backscattering spectrometry (RBS)) and low energy, high mass ions (as in ion implantation) will be discussed. Although these are different techniques, the same theory applies for both of them. For the general understanding, the accelerated charged particles will be called the ions whereas the target particles are called the atoms in this chapter. 2.2 Interactions of ion beams with materials Ion-atom interactions Ion interactions with materials depend on many parameters like ion energy (i.e. velocity) and ion and atom mass. These parameters will determine the type of interaction that will dominate during the path which the ion follows in the material. As an energetic ion penetrates a material, the following effects must be considered. The ion will lose energy in small interactions with electrons or nuclei, slow down and deviate from its original trajectory. It also undergoes major interactions such as large angle scattering, ionisation, atomic displacements, sputtering or nuclear reactions. Figure 2.1 illustrates the different interactions for low energy heavy ions, which 23

30 24 Ion-Atom Interactions (a) Low Energy, Heavy Ions Several atom layers Minor (Energy Loss) interaction Major interaction Stationary atoms Displaced target atoms Ion Trajectory Surface Thousands of atom layers (b) High Energy, Light Ions Ion Trajectory Emission products Large angle scattering Vacuum Solid Figure 2.1: Schematic illustration of minor and major interactions occurring during ion penetration of a host material for (a) low energy heavy ions and (b) high energy light ions [95]. penetrate only several tens of atomic layers while undergoing many major interactions (i.e. a nuclear interaction with energy transfer and an atomic displacement) and high energy light ions which penetrate several thousands of atom layers with occasional major interactions. A general classification of the different effects which occur during bombardment of materials with charged ions, can be made as follows: 1. Inelastic collisions with electrons of the target material. These occur when the energy of the ion equals the characteristic energy of atomic energy levels. The energy is lost in the excitation or ionisation of the atom. However, the effect on the ion is limited: the incident ion suffers from a small energy loss and negligible changes in direction.

31 2.2 Interactions of ion beams with materials Inelastic collisions with nuclei. These interactions are the least common since they require very high energies. Inelastic nuclear collisions cause Bremsstrahlung, nuclear excitation or nuclear reactions. 3. Elastic collisions with bound electrons are only important for very low energies (< 1 kev, depending on ion and target mass). 4. Elastic collisions with nuclei or atoms. For small impact parameters, the incident ion undergoes a major change in direction and part of the kinetic energy of the ion is transferred to the atoms involved in the collision. From these effects, inelastic collisions with electrons and elastic nuclear collisions are the dominant processes for slowing down the impinging ions. The slowing down process is governed by two mechanisms, electronic and nuclear stopping, and characterised by the stopping power de/dx, the energy loss per distance unit. The total stopping power can be written as the sum of both electronic and nuclear stopping: de dx = ( de dx ) e + ( de dx ) n (2.1) The energy dependence of both stopping powers is depicted in figure 2.2, which shows that both increase with energy, reach a maximum and then decrease again. The probability of each particular kind of stopping, is given by the stopping cross-section, ɛ, and is defined as: ɛ = 1 ( ) de (2.2) N dx in which N is the density of the material. In the following sections, electronic and nuclear stopping will be treated briefly. A more detailed discussion can be found in references [95 97] Electronic stopping As the accelerated ion penetrates the material, it suffers many inelastic collisions with electrons and only small deflections from the initial path take place. Due to the large number of electrons, these interactions can be approximated by a continuous energy loss process. Two regimes can be considered for electronic stopping: the Lindhard region and the Bethe-Bloch region. The boundary between these two regimes e,n

32 26 Ion-Atom Interactions Lindhard region Bethe-Bloch region de/dx Electronic Nuclear Velocity Figure 2.2: Schematic graph of typical electronic and nuclear energy loss as a function of energy. is given by the following criterium: v 1 = Z 2/3 1 e 2 /, where Z 1 is the atomic number of the ion and the ratio v 0 = e 2 / is known as the Bohr velocity. In the high energy regime, which is valid in Rutherford backscattering (RBS 1 ), an incoming ion will have a high probability of being fully stripped of its electrons since it is moving at velocities greater than its orbital velocity. The electronic stopping in this region is described by the Bethe-Bloch formula: ( ) ( de = 4πZ2 1 e4 N 2me v 2 ) dx e m e v 2 Z 2 ln (2.3) I In this formula, I is the average excitation energy of the electrons in the target and is proportional to Z 2. The proportionality factor varies with Z 2 and has roughly a value around 10 ev. In the low energy regime (energies used for ion implantation), the stopping power increases linearly with the ion velocity as can be seen in figure 2.2. This dependence can be described by the LSS theory (Lindhard- Scharff-Schiøtt) using a Thomas-Fermi atomic model. The stopping power then becomes: ( ) de = ξ e 8πe 2 Na 0 Z 1 Z 2 (Z 2/3 1 + Z 2/3 2 ) 3/2 v/v 0 (2.4) dx e 1 See appendix A for more information on RBS.

33 2.2 Interactions of ion beams with materials 27 Projectile Ion M 1 E 1 Impact parameter p Initial Position of Target Atom M 2 Figure 2.3: A typical two-body scattering process with an impact parameter p. where a 0 is the Bohr radius, v 0 the Bohr velocity and ξ e a dimensionless constant of the order Z 1/ Nuclear stopping Nuclear stopping becomes the dominating process at low ion velocities as depicted in figure 2.2. The incoming ions lose energy due to elastic collisions with the target atoms and the specific energy loss can be derived by considering these interactions as independent two-body interactions with impact parameter p. The incident ion is deflected through an angle θ 1, transferring an energy T to the struck atom, which recoils at an angle θ 2 (see figure 2.3). The energy loss de of an ion in a layer dx is given by ( ) de Tmax = N T (E, p)2πpdp = N T dσ(e, T ) (2.5) dx T min n 0 where dσ (dσ = 2πpdp) is the differential cross section and T min and T max are respectively the minimum and maximum energy transfer. The form of T (E, p) and dσ(e, T ) depends on the interaction potential V (r) between the two particles. The choice of the interaction potential is determined by the interaction radii and thus by the energy of the incoming ion. In the case of high energy low mass ions, the screening effect of the electrons can be neglected and V (r) can be directly written as the Coulomb potential.

34 28 Ion-Atom Interactions This situation is applicable for the classical case of Rutherford scattering of α-particles. For heavy particles of low energy, as is the case in ion implantation, the screening effect cannot be neglected and the interaction potential is written as: V (r) = Z 1Z 2 e 2 ( r ϕ r a) (2.6) with ϕ(r/a) a suitable screening function and a the Thomas-Fermi screening length. Different approximations have been made for this screening function and a more detailed description can be found in literature [96, 97] Ion distribution The total path length of an ion penetrating a solid can be calculated according to the energy loss equation (equation 2.1). However, this is not very useful since frequent collisions cause a departure from linearity of the ion trajectory and also gives rise to a statistical distribution in path lengths. The projection of the path length (R t ) on the original ion direction is known as the projected range (R p ) and is most useful in practice. Fluctuations in the shape of the ion trajectories affect the ratio of projected range to path length and introduce distributions in both projected range and lateral displacement. Therefore, the ion distribution as a function of depth can be typically described by a Gaussian distribution characterised by two quantities: the projected range R p and the straggle R p (figure 2.4), which is directly related to the standard deviation of the distribution. As shown in figure 2.4(a), high energy light ions will penetrate deeply into the sample before they are stopped. In this process, electronic stopping mainly dominates. A technique in which high energy light ions are used is, for example, Rutherford backscattering spectrometry (RBS). However, this technique is based on the fact that (very) few α-particles (much less than 1 out of 10 4 ) undergo an elastic nuclear collision (the nuclear stopping power is small, but not zero at high energies!) and are scattered out of the sample. Of these, only a small fraction is incident on the detector. A more comprehensive description of RBS can be found in appendix A. On the other hand, low energy heavy ions such as used in ion implantation, will penetrate only tens of atom layers before they are stopped principally by nuclear stopping. In this case, a significant fraction of host atoms and implanted ions can be scattered out of the surface (i.e. sputtering) and as a consequence, the ion distribution is found close to the surface and is asymmetrical and truncated (figure 2.4(b)).

35 2.2 Interactions of ion beams with materials 29 (a) High energy, light ions Vacuum Incident Ion Solid R t Ion Range (~ m) R l Lateral Distance R p 1 Ion Concentration 1/e 1 1/e R p Ion Concentration Depth ( m) (b) Low energy, heavy ions Vacuum Solid Incident Ion R l Lateral Distance R p Ion Range (tens of atom layers) Ion Concentration 1 1/e 1 1/e R p Ion Concentration Surface Depth (Å) Figure 2.4: Illustration of the path length (R t ), the projected range (R p ) and the range straggling ( R p ) for (a) high energy light ions and (b) low energy heavy ions [95].

36 30 Ion-Atom Interactions (a) (b) (c) Figure 2.5: Different orientations of a crystal: (a) random, (b) planar channeling and (c) axial channeling. 2.3 Ion channeling in crystals Channeling in crystal lattices occurs when the trajectory of an accelerated charged particle is aligned with a major crystal direction. In these directions, open spaces are found between the the rows or planes formed by the target atoms as shown in figure 2.5. As a consequence, ions incident parallel to such rows or planes will penetrate the crystal lattice to anomalous depths. Although the possibility of this effect was already pointed out by Stark in 1912 [98], his ideas were rejected. For a long time it was assumed that ion penetration in crystalline materials would not differ substantially from that in amorphous media. Until in the early 1960 s, low sputtering ratios were reported for ion beams incident along a low-index crystal direction [99]. These effects, however, could not be explained until 1963 when Robinson en Oen predicted by means of a computer simulation, that when a copper crystal is bombarded with neutrons, a proportion of the recoiled Cu atoms will become channeled in the crystal [100]. Experimental evidence in support of this phenomenon followed shortly afterwards by several independent groups [101, 102]. Hereafter, in 1965, Lindhard published his channeling theory, which still forms the basis of modern channeling analysis [103]. In the next section, the channeling theory will be discussed for an ion incident along a major crystal axis (i.e. axial channeling). Since it is outside the scope of this work, planar channeling (figure 2.5(b)), in which the ion penetrates along crystal planes, will not be discussed here, but the interested reader is referred to [96, 97, 104, 105] The continuum model When the channeling effect occurs, the regular atomic rows and planes in a single crystal steer the incoming ions into stable trajectories down the

37 2.3 Ion channeling in crystals 31 Shadow Cone ~5Å ~100Å Figure 2.6: Schematic image of ion trajectories undergoing scattering at the surface and channeling within the crystal [105]. open channels between them. This is illustrated in figure 2.6. The ordered structure of the crystal is a crucial factor in determining both the path and properties of the ion s motion. In order for an ion to be channeled, three essential conditions must be fulfilled: 1. Transparency: the ion must find an open channel between the atomic rows. 2. Steering: a force has to act on the incoming ion, which steers it towards the middle of the channel. 3. Stability: the ion cannot approach the rows of atoms too closely, otherwise the gentle steering effect of many glancing collisions will be replaced by a wide angle deflection. Instead of considering the target atoms as individual point charges, Lindhard proposed to approximate the lattice atoms as a continuous string with an average screened nuclear charge. In the continuum model, only the interactions of the incoming ion with this string is considered. The continuum potential U(r) felt by an accelerated ion at a distance r from the string of atoms, is the atomic potential V (R) averaged along the atomic row with atomic spacing d with R the spherical radial coordinate, R 2 = z 2 + r 2. U(r) = 1 d V ( z 2 + r 2 )dz (2.7) Lindhard used the Thomas-Fermi potential for V (R) which is valid if R is not much larger than a, where a is the Thomas-Fermi screening length

38 32 Ion-Atom Interactions given by: a 0 a = ( ) Z 2/3 1 + Z 2/3 1/2 (2.8) 2 in which a 0 = Å represents the Bohr radius. V (R) is given by equation 2.6 in which ϕ(r/a) is the Thomas-Fermi screening function. The expression for the continuum potential now becomes [ (Ca U(r) = Z 1Z 2 e 2 ) 2 ln + 1] (2.9) d r where Z 1 the atomic number of the projectile, Z 2 is the atomic number of the target atoms, e is the charge of an electron and C Critical angle for channeling In order to remain channeled, the transverse energy E sin 2 ψ (E is the initial ion energy and ψ the angle between the incident beam and the channel direction (Fig. 2.7)) of the incident ion must not exceed the barrier to the neighbouring channel. Using the continuum potential (equation 2.9) and conservation of the total energy, it is possible to find the critical angle for channeling by equating the transverse energy at the turning point U(r min ) (in which r min is the distance of closest approach) to the transverse energy at the midpoint. U(r min ) = E sin 2 ψ c (2.10) This is allowed since the transverse energy is conserved in this approximation. By using a small angle approximation, ψ c can be found from: U(rmin ) ψ c = (2.11) E Substituting U(r) by the Lindhard potential given in equation 2.9 leads to two expressions for the critical angle, depending on the energy of the incoming ion: ( 2Z1 Z 2 e 2 ) 1/2 ψ 1 = (2.12) Ed and ψ 2 = ( ψ 1 Ca 2d ) 1/2 (2.13) The first equation is valid for ψ 1 a/d or E E = 2Z 1 Z 2 e 2 d/a 2, which is

39 2.3 Ion channeling in crystals 33 d r min Figure 2.7: Schematic picture of an ion path in a channel for ψ ψ c. the case for high energy, low mass ions, while the latter is valid for ψ 1 > a/d or E < E namely for low energy, high mass ions. In the derivation of the critical angle, a perfect crystal lattice is assumed and the effect of thermal vibrations is not included. To take the effect of substrate temperature into account, r min in equation 2.9 has to be replaced by ρ, the two-dimensional (2D) thermal vibration amplitude of the lattice atoms. This modifies the critical angle to: [ (Ca ψ c (ρ) = ψ ) ]) 2 1/2 1 (ln + 1 (2.14) 2 ρ The relationship between the mean square of the 2D thermal vibration amplitude and the temperature can be calculated according to the Debye model, and is given by: ρ 2 = 2 < u 2 x > (2.15) in which < u 2 x > is the one-dimensional thermal vibration amplitude, given by ( ( ) < u 2 x >= 3 2 T ΘD M 2 k B Θ 2 ϕ + Θ ) D (2.16) D T 4T where M 2 is the mass of the target atom, k B the Boltzmann constant, Θ D the Debye temperature and ϕ(x) the Debye function defined as: ϕ(x) = 1 x x 0 tdt e t 1 (2.17)

40 34 Ion-Atom Interactions Values of the root-mean-square (rms) lattice vibrations of Ga and N atoms in GaN were determined experimentally at room temperature by extended X-ray absorption fine structure (EXAFS) spectroscopy by Yoshiasa et al. [106]. They found values of ± 0.03 Å and ± 0.02 Å for Ga and N atoms in GaN respectively. When using these rms displacements in equation 2.16, the Debye temperatures for Ga and N atoms in a GaN lattice can be calculated. This results in values of Θ D = 347 ± 10 K and Θ D = 753 ± 60 K for Ga and N atoms respectively. Since the critical angle derived by Lindhard in equation 2.12 typically overestimates the experimental value by about 20%, a refinement was made by Barrett [107] for high energy, low mass ions. He used the approach of binary collisions in stead of the continuum model like Lindhard and by means of Monte Carlo simulations, Barrett was able to correct the value of the critical angle ψ 1 as follows: ψ B = 0.8F RS (ξ)ψ 1 (2.18) in which ξ = 0.85 ρ (2.19) a is the normalised distance of closest approach. A graph of F RS is given in figure 2.8. For low energy, heavy ions such as those used in ion implantation, channeling causes a deep tail in the depth profile, which is highly orientation sensitive and makes it difficult to reproduce implantation profiles. Generally, the ion beam is tilted several degrees to minimise the channeling effect. To our knowledge, no detailed study of channeled implantation in GaN has been carried out for heavy ions. In this work, channeled implantation will be used in an attempt to minimise the defect accumulation in GaN. The results of this research are reported in chapter 4. Table 2.1 lists values of the critical angle along the GaN 0001 axis for two different ion beam techniques, namely RBS/C and ion implantation as an example for high energy, light ions and low energy, heavy ions respectively. They are compared with the value of the critical angle which was determined experimentally in this work. In the calculations of these critical angles, average values are used for both Z 2 and d since the atomic rows along this direction consist of alternating Ga and N atoms with uneven lattice spacings. 1 The experimental determination of this critical angle can be found in reference [108].

41 2.3 Ion channeling in crystals 35 Figure 2.8: The value of F RS as a function of the normalised distance of closest approach ξ [107]. Table 2.1: Critical angle for (a) high energy, low mass ions and (b) low energy, high mass ions along the GaN 0001 axis. ψc L and ψc B represent the critical angles predicted by respectively Lindhard s and Barret s formula. Method Ion Energy ψ L c ψ c (ρ) ψ B c ψ exp c (kev) RBS/C He (Eq. 2.12) Ion 166 Er implantation (Eq. 2.13)

42 36 Ion-Atom Interactions Previously, the general theory of ion-atom interactions is described, both for low energy ion beams as used in ion implantation as well as for high energy, light ions like in RBS/C. In the next sections these two techniques will be elucidated. 2.4 Ion implantation General principle Ion implantation is a widespread technique to incorporate foreign ions into a host material. The principle is simple: atoms or molecules are ionised in an ion source and accelerated in an electrostatic field to an energy between a few thousand electron volt (kev) and several million electron volt (MeV). Subsequently, the ions are separated by mass, using an analysing magnet. After passing through quadrupole magnets for focussing, they are implanted into the desired material. The whole implantation process is executed in high vacuum. This technique has applications in several research fields like ion beam synthesis, electrical and optical doping, and the introduction of radioactive probes. Implantation offers a number of advantages: 1. Speed, homogeneity and reproducibility of the doping process. 2. Exact control of the implantation fluence by integration of the beam current. 3. Isotopically pure ion beams due to mass separation. 4. Possibility to implant fluences higher than the solubility limit. 5. Simple masking methods to make patterns for devices. However, as a result of bombardment with heavy particles, many atomic displacements will occur causing a degradation of the crystalline structure, until amorphisation is reached. Amorphisation of the crystalline lattice is generally undesirable since the electrical and optical properties of the material will be altered as described in section 1.4. For example, this can lead to quenching of the luminescence. To restore the crystal lattice, hightemperature annealing is the standard method, but also implantation at elevated temperature and channeled implantation are used in this work to avoid damage accumulation in the target material. The results are described in chapter 4.

43 2.4 Ion implantation Radiation damage in solids As discussed earlier in this work, ion beams impinging on a solid will suffer many collisions with electrons and substrate atoms. The electronic excitations mainly serve as an energy-loss mechanism which slows down the ion, but do not create structural damage in this energy range. More important are the elastic collisions with the lattice atoms that lead to defect production. Due to the high mass and low energy (and thus a large nuclear stopping power) of the ions used in ion implantation, defect creation will be a more important issue to deal with then in backscattering experiments (RBS/C) in which light ions with high energy are used. The endothermal formation of atomic defects in solids requires the transfer of energy which can be achieved by irradiation, a process far from thermodynamic equilibrium. The energy transfer depends on the energy and mass of the impinging ion and on the mass of the target atoms. The displaced atoms themselves can also displace other atoms, resulting in collision cascades and leading to the accumulation of vacancies and interstitial atoms (Frenkel defects) but also to complex lattice defects along the ion path. With increasing ion fluence, amorphisation of the crystal lattice can occur. Radiation-induced amorphisation can be caused by a collapse of the crystal lattice due to accumulation of individual point defects when reaching a critical value (i.e. homogeneous amorphisation) or by superposition of amorphous zones (i.e. heterogeneous amorphisation). Radiation-induced defects By a crystalline defect one generally means any region where the microscopic arrangement of atoms differs drastically from that of a perfect crystal. Defects are labelled surface, line or point defects, according to the dimensionality of the defect. In this paragraph a brief overview of the types of radiation-induced defects, their migration and agglomeration is given. For a more detailed survey, one refers to [109, 110] and references therein. The most simple defects in solids are point defects. These can be vacancies, created by a missing atom A (V A ), substitutional ions, which are impurity ions B replacing an atom A (B A ) or interstitials, which are impurity ions or lattice atoms C occupying an interstitial site (I C ). Moreover, various interstitial formations are possible according to the occupied lattice or non-regular site and to the number of atoms involved. Combinations of these three kinds of defects are also possible and among

44 38 Ion-Atom Interactions them Frenkel pairs, which are V A -I A complexes formed by an atom displaced from a lattice site to a nearby interstitials site, are of most frequent occurrence during irradiation of solids. Frenkel pairs created during irradiation with particles above the threshold energy, can either recombine spontaneously or become stable when the interstitial-vacancy separation exceeds a critical distance, called the recombination or capture radius R C. Hence, recombination occurs when interstitials and vacancies are within a sphere of volume 4 3 πr3 C. The recombination radius of such a V A-I A pair in a crystal, however, is often anisotropic and displays maxima along close-packed directions. Through the operation of replacement collision sequences, the separation of interstitial and vacancy is aligned predominantly along closepacked directions. A typical value of the maximum capture radius in Si is 2.33 Å [111]. To our knowledge, no data on the capture radius of point defects in GaN is available yet. Single point defects disappear either by annihilation with a point defect of opposite nature or form clusters by aggregation to defects of the same nature. Furthermore, point defects can disappear at sinks such as the surface of the crystal or extended crystallographic defects. The defect evolution is governed by the mobilities of interstitials and vacancies which depend on the temperature. The temperature dependence of the diffusivity D of a vacancy or an interstitial follows an Arrhenius law: D = D 0 exp( E m /k B T ) (2.20) where D 0 is the pre-exponential factor (containing the migration entropy), E m is the migration energy, k B is Boltzmann s constant and T is the temperature. Generally, the mobility of interstitials is larger than the mobility of vacancies, hence, they become mobile at lower temperatures. The development of the defect concentrations can be calculated by a set of diffusion equations or by applying reaction rate theory. Under continuous irradiation, already existing defects will accumulate and new defects form clusters or recombine with existing defects. Thus, the damage rate decreases when new defects are generated within the recombination volume of an already existing defect or cluster with opposite nature. Interstitials and vacancies have a tendency to aggregate into clusters to reduce their free energy, which can lead to extended defects. For example, the clustering of interstitials leads to dislocation loops on close-packed planes. Such extended defects will hinder the migration of point defects and are stable up to high temperatures.

45 2.4 Ion implantation 39 Collision cascades When an energetic ion collides with an atom in a crystal lattice and transfers enough energy to it, the lattice atom will collide with other lattice atoms, resulting in a large number of successive collisions. All the atomic collisions initiated by a single ion are called a collision cascade. An illustration of an impinging ion creating several collision cascades is presented in figure 2.9. A collision cascade can be divided into three phases [113]. The initial stage, during which atoms collide strongly, is called the collisional phase, and typically lasts about ps. As a result of the collisions, one can assume that all atoms near the initial ion path are in thermal motion at a high temperature. The high temperature will spread and be reduced in the crystal by heat conduction. This phase is called the thermal spike, and lasts roughly 1 ns. When the thermal spike has cooled down, a large quantity of defects will usually remain in the crystal. The defects can range from vacancies and interstitial atoms to complex interstitial-dislocation loops and volume defects. If the lattice temperature is high enough, many of these defects will relax by thermally activated migration. This is the so called relaxation phase of the collision cascade. During ion implantation, electronic slowing down dominates the stopping of an implanted ion at high ion energies. However, when the ion has slowed down sufficiently, nuclear stopping will become significant. Thus, collision cascades will be present and produce lattice damage near the ion end-of-range (EOR) region. The type of damage produced during ion implantation may be very complex and varies a great deal for different ion types, sample materials and implantation conditions. The density of collision cascades plays an important role in the type of damage that is created. For low density collision cascades, simple point defects are formed, such as gallium or nitrogen vacancies (V Ga or V N ) and interstitials. These interstitials can be nitrogen (I N ) or gallium (I Ga ) atoms which were displaced from their lattice site and are now occupying a nonlattice position in the crystal (so called self-interstitials). The implanted Er ions can occupy a non-regular lattice position as well, i.e. impurity interstitials. Not all defects are considered to be on a non-lattice position. Also substitutional point defects exist. In this case the implanted Er possesses a Ga- or N-lattice site, or a N atom can be replaced by a Ga atom and vice-versa. As a result of the forward peaking nature of the momentum of an incoming ion, a vacancy-rich zone is found extending from the surface down to the maximum of the damage distribution (R p ) whereas between R p and 2R p, an interstitial-rich zone is formed.

46 40 Ion-Atom Interactions Ion Figure 2.9: Schematic representation of a collision cascade induced by an energetic ion impinging on a crystalline solid. The open circles represent vacancies while the closed circles are both interstitial and substitutional atoms [112].

47 2.4 Ion implantation 41 When the collision cascades become more dense, more complex defects are being formed. The amount of point defects increases and small, highly defected regions in the crystalline lattice are formed. When many of these amorphous clusters are formed, they start to overlap and finally form an amorphous layer. In silicon, already many studies are performed on implantation induced damage [60, 114]. However, implantation induced defects in GaN are still not well understood, especially in the case of channeled implantation. Number of displaced atoms A recoiling lattice atom can be removed from its lattice site to become permanently displaced within the solid if the atom receives an energy from the impinging ion in excess of a minimum value, called the displacement energy, E d. The exact magnitude of the displacement energy not only depends on the solid in question, but also on the recoil direction in the crystal, i.e. ions can be displaced more easily in certain directions. However, few reports have been found on the displacement energy of Ga and N atoms in GaN. Experimental values for the threshold displacement energy differ from 19 ev to 25.5 ev for Ga and from 10.8 ev to 22 ev for N [ ]. Recently, Nord et al. [119] calculated the threshold displacement energy for all recoil directions by means of molecular dynamics (MD) computer simulations. These distributions of the different energies for both atom types are shown in figure Although the lowest values for the displacement energies are rather small (18±1 ev for Ga and 22±1 ev for N), the average values are considerably high (45±1 ev for Ga and 109±1 ev for N), which indicates that GaN is highly resistant against radiation induced damage. The lowest values found for the threshold displacement energy for nitrogen is in a direction about 10 off the c-axis. For Ga, the minimum value is obtained toward the second-nearest Ga neighbour. Knowing the threshold energy needed to displace a substrate atom, it is possible to calculate the total number of displacements per atom with the Kinchin-Pease formula [120]. ( ) E N D = (2.21) 2E d This formula is valid for E > 2E d, while for E d E 2E d, N D =1. Unfortunately, the original Kinchin-Pease model failed to account for the electronic stopping power of the material, since the model considers the mobile atoms to be hard spheres. Therefore, a correction factor, κ, is

48 42 Ion-Atom Interactions Figure 2.10: Distribution of different threshold displacement energies for Ga and N recoils in wurzite GaN [119]. applied for energies greater than 2E d such that the modified Kinchin-Pease equation for the damage function becomes 0 0 < E < E d N D = 1 E d E < 2E d /κ (2.22) ( ) κ E 2E d 2E d /κ E < Both analytical and computer simulations predict the value of the correction factor to be κ = 0.8. Not all defects as calculated with this formula, however, will remain after implantation, since the defects might recombine during implantation, a process called dynamic annealing. The modified Kinchin-Pease formula will therefore overestimate the number of displaced atoms. Another possibility is to calculate the number of displacements with the SRIM program 2. As an example: for 80 kev 166 Er ions implanted into GaN, SRIM results in 1632 displacements/ion of which 612 are displaced N atoms and 1020 displaced Ga atoms, using threshold displacement energies 2 SRIM is a computer code to calculate ion and defect distributions for ion implantation into different media. See section for more information.

49 2.4 Ion implantation 43 of 18 ev for Ga and 22 ev for N, which were obtained from reference [119]. SRIM showed also the same depth distribution for both Ga and N displacements. Factors influencing defect production The retained defect concentration in semiconductors by ion implantation depends on many different parameters. First of all, the cross-section for nuclear collisions is strongly dependent on the atomic number of the projectile (Z 1 ) and of the substrate atom (Z 2 ). As a consequence, the collision cascades will be very dense for heavy atoms like erbium. Kucheyev et al. [38] studied the influence of a wide range of ion species on the damage accumulation in GaN. It was found that for light ions, chemical effects enhance the damage build-up, due to (1) trapping of ion-beam-generated migrating point defects by implanted impurity atoms, (2) second phase formation and associated lattice distortion, and/or (3) enhanced stability of irradiationinduced defects in GaN. For heavy ions, chemical effects are negligible but an increase in the density of the collision cascades strongly increases the level of implantation induced lattice disorder. Also the implantation parameters play an important role, like the particle energy, the beam flux, the implantation fluence and geometry, and the substrate temperature. The effect of these different parameters will be discussed in the next paragraphs. Ion Energy Increasing the ion energy will result in a deeper penetration depth of the impinging ions. Due to the energy straggling, the ions will be spread over a more extended region. This effect is clearly illustrated in figure 2.11, in which the depth profile obtained by RBS measurements of 166 Er ions implanted into GaN is depicted for implantation energies of 80 kev and 170 kev. The projected range R p and the straggling R p are determined from these profiles by fitting them with a Gaussian curve and tabulated in table 2.2. The projected range and straggling found experimentally are in good agreement with the values found by SRIM calculations. As a consequence of the increased penetration depth of the implanted ions for higher energies, the defect distribution will also be spread over a greater depth range. Additionally, higher energy ions will cause more defects in the crystalline lattice compared to lower energy ions, since they have more energy to transfer in nuclear collisions. This is confirmed by the defect concentration calculated from the RBS/C spectra for the aforementioned samples which are presented in table 2.2.

50 44 Ion-Atom Interactions Table 2.2: Projected range R p and straggling R p of the Er distribution after implantation at 80 and 170 kev to a fluence of at/cm 2, determined from the profiles of figure The calculated defect concentration of both is presented in the last column. Ion energy R p (Å) R p (Å) C D (kev) Exp. SRIM Exp. SRIM ( cm 2 ) Figure 2.11: Erbium profile for 80 ( ) and 170 ( ) kev random implantations into GaN to a fluence of at/cm 2. Orientation of the ion beam with respect to the sample The orientation of the beam plays an important role, both in the implanted ion profile as in the resulting defect distribution. In a standard implantation experiment, the ion beam is tilted a few degrees off the crystal main axis (typically 10 for GaN) to minimise channeling of the ion beam, i.e. random implantation. The ion distribution has a Gaussian shape with a projected

51 2.4 Ion implantation 45 Figure 2.12: Marlowe simulation of 80 kev 166 Er ions implanted in GaN with the ion beam respectively aligned along the GaN<0001> axis ( ) and tilted by 10 off this axis ( ). range R p which can be calculated with the SRIM program. For implantations along a major crystal axis, i.e. channeled implantation, the nuclear stopping is much lower compared to random implantations, resulting in a much larger penetration depth of the ions and a lower defect concentration. The ions are hence steered through the crystal by the atomic rows and this affects the ion and defect distribution drastically. This is observed experimentally for Er implantations in Si(111) [63] and confirmed by Marlowe simulations [121]. Figure 2.12 shows an example of a Marlowe simulation for Er implanted into GaN along the GaN c-axis and 10 off the axis. It can be clearly seen that the ions travel several hundreds of ångström through the crystal in the case of channeled implantation, while the random implantation is rather shallow. Ion fluence As the fluence of the implanted ions increases, the total energy deposited in the GaN crystal increases, and as a consequence a higher defect concentration for high fluence implantations is observed. Several examples of the influence of the ion fluence on the defect concentration can be found in

52 46 Ion-Atom Interactions literature [39, 52, 122]. In the case of channeled implantation, the ions can be scattered from interstitial ions or atoms in the crystalline lattice. For low fluences, the defect concentration will not increase drastically, since only ions which entered a damaged channel will be scattered and cause extra defects as is observed experimentally. This will be treated in more detail in section 4.2. As the fluence increases, more ions become dechanneled and suffer nuclear collisions, thereby increasing the defect concentration in the lattice until amorphisation is reached and the channeling effect completely disappears. As an example, computer simulations using Crystal-TRIM 3 of room temperature implantation of 200 kev phosphorus ions into single-crystalline Si show that the accumulation of radiation damage leads to enhanced dechanneling [123]. Therefore the shape of the range profiles is dependent on the implantation fluence. The increase in defect accumulation and the reduction of the channeling effect with increasing ion fluence is also observed experimentally for implantation of erbium ions into crystalline Si [124]. In this work, the influence of the erbium fluence on the defect concentration in GaN will be studied for channeled implantations to investigate the damage build-up. Beam flux An increase in the beam flux decreases the average time interval between collision cascades which spatially overlap. Such an increase in the generation rate of point defects with increasing beam flux enhances the rate of interactions between mobile defects and, therefore, enhances the formation of defect complexes. Kucheyev et al. [122] found that an increase in beam flux from cm 2 s 1 to cm 2 s 1 of 300 kev Au ions into GaN slightly changed the defect profile as measured by RBS/C: an increased yield is found in the GaN film, while the surface defect peak decreases in magnitude. The overall damage fraction, however, does not change drastically. The increase in beam flux enhances the formation of defect complexes in the crystal bulk. Hence, fewer point defects generated in this region can reach the surface. In this work, typically beam fluxes of cm 2 s 1 are used for 80 and 160 kev 166 Er ions. Since the overall damage fraction remains the same as found by Kucheyev and co-workers, the effect is neglected in our studies. 3 The program Crystal-TRIM simulates ion implantation into single-crystalline silicon. Not only atomic ions but also molecular ions may be considered. Dynamic simulation of damage accumulation in the single-crystalline substrate, including the formation of amorphous layers, is possible.

53 2.4 Ion implantation 47 Substrate temperature Atoms that are removed from their lattice site due to collisions with the incoming ions, will create vacancies and interstitials in the crystalline lattice. These vacancy-interstitial pairs can recombine and thereby recover part of the induced damage, an effect that is called dynamic annealing and which depends on the mobility of the defects in the material. Dynamic annealing can be affected by the substrate temperature during implantation. High temperatures will enhance this process and reduce the retained lattice damage while lowering the substrate temperature will have the opposite effect. This is confirmed by several reports on ion implanted GaN in a temperature range from liquid nitrogen temperature to 1000 C [32, 52, 122, ]. Irradiation of GaN at 15 K indicates that the defect formation is dominated by a pronounced recombination of the produced defects within the primary collision cascades [128]. Additionally, Jiang et al. [126] observed a significant dynamic recovery effect on the disorder accumulation in GaN in the temperature range 210 to 250 K after bombardment with 1.0 MeV Au 2+ ions. They also noticed an excess disorder along the GaN 1011 axis relative to that along the GaN 0001 axis [127], particularly for the N sublattice. This indicates the presence of (planar) defects that are well aligned with the 0001 axis in GaN. This surplus disorder increases for temperatures below 600 K and tends to saturate at higher temperatures. Implantation at elevated temperatures will also influence the channeling effect. Higher substrate temperatures will cause the lattice atoms to vibrate more vehemently around their lattice site positions. Due to the larger thermal vibration amplitudes, the probability for an ion to be dechanneled will increase and as a consequence the defect concentration will be affected Post-implantation annealing The recovery of the GaN lattice after ion implantation, can be realised by heating the sample to increase the defect mobility and facilitate the damage removal. For a complete recovery of the crystalline structure of compound semiconductors after implantation, an annealing temperature of two-third of the melting point is required by rule of thumb [24]. Since the melting point of GaN is 2791 C [16], an annealing temperature up to 1600 C is required for a full lattice recovery. It is also known that, although annealing of the implanted damage in GaN starts around 600 C, no significant recovery is observed up to temperatures of 900 C [50, 129] and since the GaN structure starts to decompose at temperatures above 900 C

54 48 Ion-Atom Interactions [130], other annealing techniques are required. Many different techniques have already been used and these procedures can be divided into four main groups. Firstly, implanted GaN samples have been annealed in a nonreactive ambience, but with limited success. Vacuum annealing offers the cleanest solution, but only temperatures of C can be reached for several minutes without degradation of the sample [130, 131]. Slightly higher temperatures can be reached under Ar or N 2 flows, while temperatures up to 1200 C [131, 132] and a significant recovery of the implantation induced damage can be obtained by using high N 2 overpressures (1 GPa). On the other hand, by reducing the annealing time in rapid thermal annealing (RTA) systems, higher annealing temperatures can be used for the recovery of GaN crystals. For this work, the maximum annealing temperature by RTA was investigated by annealing virgin GaN layers under N 2 atmosphere and measuring the thickness of these layers before and after annealing by means of backscattering experiments. Once nitrogen starts to escape from the GaN surface, the thickness of the total GaN layer will change. One set of samples was covered with other GaN pieces (i.e. proximity caps) to prevent nitrogen from escaping the GaN surface. The results of this test are shown in figure It is seen from this figure that a maximum temperature of 1000 C can be reached before decomposition of the GaN layer starts. When protecting the virgin GaN samples by another piece of GaN, temperatures up to 1100 C could be reached. In literature, reports are made of a maximum RTA annealing temperature of 1150 C under nitrogen atmosphere [133]. Secondly, implanted GaN samples have been annealed under a reactive ambience, like ammonia (NH 3 ). Temperatures up to 1100 C for 1 hour can be obtained under these conditions [23, 56]. A third way to protect the GaN surface is to deposit a capping layer which is stable at high temperatures, but that must be removed after annealing. A maximum of 1300 C was achieved with epitaxially grown AlN caps on top of the GaN sample and subsequent vacuum annealing for 15 minutes [134]. Finally, laser processing is an additional annealing technique that uses short processing times. However, few experiments with laser annealing on implanted GaN are known [135].

55 2.4 Ion implantation 49 Figure 2.13: Remaining fraction of the GaN layer thickness after RTA annealing at different temperatures. One set of samples was capped with a piece of GaN for protection. The solid lines are meant as a guide to the eye Simulation programs for ion implantation processes Computer simulation methods to calculate the motion of ions in a medium have been developed since the 1960 s. The first computer programs were based on the binary collision approximation (BCA), which treats the interaction between the ion and the target atoms by successive two-body interactions. This method provide a fairly efficient means for calculating ion ranges. On the other hand, molecular dynamics (MD) methods described the interactions involved in ion implantation more realistically, but require much larger amounts of computer capacity than BCA methods. In both BCA and MD simulations the interaction between the projectile i and a lattice atom j at a distance r from one another, is described with an interatomic potential given by: V ij (r) = Z iz j e 2 φ(r) (2.23) r The first factor describes the Coulomb repulsion between two bare nuclei and the effect of screening is taken into account by the screening function

56 50 Ion-Atom Interactions φ(r). The electronic stopping is usually taken into account as a frictional force. Two broad classes of simulation models are used to simulate ion implantation processes. In one class, termed molecular dynamics (MD) models, the equations of motion of many atoms are integrated simultaneously. Models of the other class are based on the binary collision approximation (BCA). The trajectories of energetic particles are represented as series of two-body encounters in which the other particles are mere spectators. There are two distinct types of BCA model. Models for crystalline targets, termed BC (binary crystal) models and models for structureless media, named Monte Carlo (MC) models. The most widely used codes are TRIM (a MC code) and MARLOWE (a BCA code) will be described in more detail. SRIM SRIM (the Stopping and Range of Ions in Matter) is a group of programs which calculate the stopping and range of ions (up to 2 GeV/amu) into matter using a quantum mechanical treatment of ion-atom collisions. TRIM (the Transport of Ions in Matter) is the most comprehensive program included. This is a Monte Carlo program developed by J.F. Ziegler and J.P. Biersack [136], which will calculate both the final three dimensional distribution of the ions and also all kinetic phenomena associated with the ion s energy loss: target damage, sputtering, ionisation and phonon production. As with other Monte Carlo programs, the program follows a large number of individual ion histories in a target. Each history starts with a certain energy, position and direction. The particle or recoiling atom is assumed to change direction in binary collisions with target atoms and to move in straight free-flight-paths between the collisions. The ion energy reduces due to nuclear and electronic energy losses, and the history ends when the energy drops below a specified value or when it leaves the target. The target is considered to be amorphous with atoms at random positions and hence the crystalline structure of the target lattice is ignored. Although the crystal structure is not taken into account, accurate range profiles are obtained for the random implantations performed in this work. An example of the ion distribution calculated with SRIM is given in figure In this simulation, 80 kev 166 Er ions were implanted into a GaN layer under an angle of 10 with respect to the sample normal. The ion distribution exhibits a Gaussian shape with a maximum at a depth of R p = 192 Å and a straggling of R p = 67 Å and is in agreement with the experimental Er profile (solid line).

57 2.4 Ion implantation 51 Figure 2.14: The ion distribution of 80 kev 166 Er implanted GaN as calculated with SRIM. The distribution has a Gaussian shape with R p = 192Å and R p = 67Å. The experimentally determined Er profile is shown as a solid curve. MARLOWE MARLOWE is the successor of the computer code by which channeling was first discovered [100]. The program simulates atomic collisions in crystalline targets using the binary collision approximation. MARLOWE is used to study phenomena governed by such collisions, including the sizes and shapes of displacement cascades, sputtering and ion ranges. The path of an ion is determined by binary encounters with target atoms. For each individual collision, the BCA code solves the classical scattering integral by numerical integration. The program follows the slowing-down of the primary energetic atomic particle and that of all target particles which are displaced from their lattice sites, until they either leave the target or fall below a selected low kinetic energy. Although the BCA methods have been successfully used in describing many physical processes, there are some obstacles in describing the slowing-down process of energetic ions realistically. Due to the assumption that collisions are binary, problems arise when trying to take multiple interactions into account. Additionally, the form of

58 52 Ion-Atom Interactions the scattering integral does not allow the incorporation of angle-dependent potentials, which are necessary to describe covalently bonded materials. These factors make it difficult to describe collision cascades realistically in BCA simulations. More information on MARLOWE can be found in reference [137]. Molecular dynamics simulations Molecular dynamics (MD) simulations consider the interaction of the incoming ion with a number of atoms in its vicinity. This simulation code calculates the time evolution of a system of atoms by solving the equations of motion numerically. Contrary to the BCA methods, all interactions by an ion in MD simulations are taken into consideration simultaneously. This is more realistic compared to the binary collision model used in MARLOWE, but it requires much larger computing capabilities. More information on MD simulations can be found in reference [138]. An example of MD simulations is the MDRange program which is described in detail in reference [139]. MDRange is capable of determining the range of ions for implantations in the kev energy range. Moreover, it also calculates the deposited energies and the primary recoil spectrum for any ion and sample element. Typically, unit cells of atoms are considered and thermal vibrations can be taken into account. 2.5 Rutherford backscattering and channeling spectrometry General principle Rutherford backscattering and channeling spectrometry (RBS/C) is an analysis technique used for material characterisation. It is based on Rutherford s famous experiment from which he proposed a new atomic model [140, 141]. Charged particles (usually 4 He + ) are generated in an ion source and accelerated by means of an accelerator to an energy of several MeV. After passing through a series of quadrupole magnets and electrostatic lenses for the focus and collimation of the beam, the generated He-beam strikes the target to be investigated. A fraction of the impinging He-ions is backscattered and detected in the detector. By determining the energy of the detected particles, a backscattering spectrum can be composed which contains information on the target composition as a function of depth from the surface.

59 2.5 Rutherford backscattering and channeling spectrometry 53 Figure 2.15: RBS/C spectra of a virgin GaN sample ( ) and after implantation of Er/cm 2 at 80 kev ( ). When the He + beam is aligned with a major axis of a crystalline target material, the ions become channeled (see section 2.3) and the backscattering yield decreases drastically. By means of RBS channeling, extra information can be obtained on the crystalline quality of the analysed material. For example defect profiles, elastic strain and the lattice location of impurities can be determined. The non-destructive character of Rutherford backscattering in combination with channeling, makes it a very powerful tool in material characterisation. RBS/C is explained in more detail in appendix A Disorder analysis by means of backscattering RBS spectra, measured along the GaN 0001 axis from GaN samples implanted with 80 kev 166 Er ions, exhibit an increased backscattering yield close to the surface due to the implantation induced damage as depicted in figure As can be seen in this figure, the backscattering yield of the undamage crystal (below 1.25 MeV) is higher in comparison with that of a virgin GaN sample due to dechanneling of the 4 He-ions on the defects in the damaged area. This should be taken into account when analysing

60 54 Ion-Atom Interactions Figure 2.16: Rutherford backscattering and channeling spectra before and after Rutherford correction, which is applied to remove the energy dependence of the Rutherford scattering cross section such disorder profiles. Furthermore, to obtain a qualitative analysis, one is interested in the depth distribution of the induced damage and hence, the energy scale should be converted to a depth scale. The specific analysis of these effects are scrutinised in detail in literature [ ], but will be discussed in detail here since it plays an important role in this work. In the next paragraphs, each of these complications will be discussed separately, focussed on the Ga signal of the RBS/C spectra. As a result, only the damage in the Ga sublattice of the GaN crystal is determined. The RBS signal of the N atoms is not taken into account since it is too small due to its low scattering cross section. This has to be kept in mind during the analysis of the RBS/C spectra. To investigate the disorder in the N sublattice, analysis techniques which are based on non-rutherford cross-sections should be used, for example nuclear reaction analysis (NRA). Rutherford correction A correction is applied on the measured RBS/C spectra to remove the energy dependence of the Rutherford scattering cross section. In other

61 2.5 Rutherford backscattering and channeling spectrometry 55 words, the yield y(i) in channel i is related to the yield y (i) before correction by [144]: y [ ] (i) y(i) = 1 E 1 /(K E 0 ) 2 1 (2.24) 1 + S(K E 0 )/[K S(E 0 ) cos θ] where E 0 is the incident beam energy, E 1 is the energy of the detected particle and θ is the scattering angle. S(E) is the appropriate stopping cross-section for an energy E and K is the kinematic factor (see appendix A). S(E) is given by [ K de S(E) = + 1 de ] (2.25) cos θ 1 dx Ein cos θ 2 dx Eout in which θ 1 and θ 2 are respectively the incident and exit angles of the impinging ion with respect to the surface normal and K is the kinematic factor (see appendix A on RBS). For use in computer calculations, the ZBL (Ziegler, Biersack and Littmark) stopping powers [136] for 4 He + ions incident on GaN, which are also used as input for the SRIM program, were approximated by de dx = N ( E 70.1E E E E 5 ) (2.26) with N the atomic density of GaN. The influence of this Rutherford correction will be small, since it mainly influences the yield at low energies while the measured profile of the disorder distribution lies close to the surface. To give an idea about the magnitude of this effect on an RBS spectrum, figure 2.16 presents measured RBS/C spectra before and after applying the Rutherford correction. Dechanneling analysis In a damaged crystal, part of the incident channeled particles will be scattered by displaced atoms over a small angle, which is greater than the critical angle. As a consequence, these ions are no longer channeled and the atoms in the crystal act on them with random backscattering probability. The principles of dechanneling are shown in figure In the following analysis the assumption of single scattering is made, which means that each 4 He + ion has only scattered once before it is detected. When an atom in the analysed layer is not on a lattice site, the number of impinging He-ions backscattered by this atom (n i ), is proportional to the number of particles which are first dechanneled by this atom

62 56 Ion-Atom Interactions n i d i CHANNEL i OF THE MCA Figure 2.17: The various possibilities for the backscattering of channeled particles in a crystal. and are backscattered in a next scattering event (d i ). C = d i n i (2.27) in which the index i refers to the channel i of the multichannel analyser (MCA) of the RBS/C system. Figure 2.18 depicts schematically the analysis, in which y r is the random spectrum and y c is the channeled spectrum of an implanted sample. Line d separates the directly backscattered particles from the dechanneled particles and d i+1 are the registered particles which are dechanneled before and detected in channel i + 1 of the MCA. At a depth t a (channel a in the MCA), where the sample is undamaged, the backscattering yield is y c(a). For a depth t i (channel i in the MCA), this results in: y c(i) n i = b k=i+1 d k + d i 2 (2.28) The left-hand side of this equation represents the particles which are backscattered from a random direction and registered in channel i of the MCA. These particles have been dechanneled and that is described by the righthand side of equation The term d i /2 is added to avoid shifting the backscattering event of a disordered region with respect to its dechanneling effect. This principle is illustrated in figure Combining equations 2.27

63 2.5 Rutherford backscattering and channeling spectrometry 57 y r Scattering Yield y' c n i d i+1 Line d Channel number a i b Figure 2.18: Schematic drawing for the calculation of the number of n i particles which are backscattered directly out of the channel direction. y r and y c are the random and channeled energy spectra of the backscattered ions. d i+1 are the registered particles which are first dechanneled before detection in channel i + 1 of the MCA. n i d i d/2 i i-1 i i+1 CHANNEL NUMBER Figure 2.19: The dechanneling effect of a damage cluster. In the case of channel i a dechanneling rate of d i /2 would be assumed.

64 58 Ion-Atom Interactions and 2.28 results in: or n i = y c(i) b k=i+1 n k C n i C 2 n i = y c(i) b k=i+1 n k C 1 + C 2 The line d in figure 2.18 can now be evaluated by: y c(i) n i = b k=i+1 n k C + n i C 2 (2.29) (2.30) (2.31) Starting at the surface of the sample (channel i = b), the particles which are backscattered directly out of the channel direction (n i ), are now evaluated step by step by means of equation For the first step one obtains: n i=b = y c(b) 1 + C 2 (2.32) since no dechanneled ions can be registered at the sample surface. At a depth t a, corresponding to channel a in the MCA, the sample is free of damage and hence the backscattering yield only consists out of dechanneled particles. This condition is written as follows: y c(a) = Substitution of equation 2.27 in equation 2.33 results in: C = a d i (2.33) i=b y c(a) a i=b n i (2.34) A first approximation of C can be obtained by replacing the line d in figure 2.18 by a straight connection line between the start and end points in channel a and b of the MCA. The total number of He-ions directly backscattered from defects in the interval [a,b], i.e. a i=b n i, can now be found by subtracting the surface below the straight line from the total surface below the channeled spectra in this interval. This results in: a a ( ) y n i y c(i) c (a) (b a) (2.35) 2 i=b i=b

65 2.5 Rutherford backscattering and channeling spectrometry 59 Combining equations 2.35 and 2.34 yields: [ ( a ( ) )] 1 1 y C y c(a) y c(i) c (a) (b a) 2 i=b (2.36) Using equations 2.30 and 2.36, the distribution n i = f(i) can be evaluated step by step. The distribution N i of the fraction of displaced atoms in the sample results from this by: N i = n i y r b k=i+1 d k d i 2 (2.37) Although the approximation for the evaluation of C made in equation 2.36 results in quite acceptable solutions, it turns out to be favorable to evaluate the exact value of C by an iteration. Starting with the linear approximation for C from equation 2.35, n i and d i are evaluated as a function of channel i. If the condition 2.33 is not fulfilled, C can be recalculated according to equation 2.34 with the sum of the new n i. This is repeated until b i=a d i = y c(a). Typically, four or five iterations are required for satisfactory convergence. An example of the defect fraction obtained with this method is shown in figure Energy-depth scale In RBS/C experiments, the number of backscattered 4 He + particles is measured as function of their energy. This energy scale can be converted to a depth scale by means of the stopping power de/dx (see section 2.2.1). The energy-depth relation is given by: where E = [S] x (2.38) E = KE 0 E 1 (2.39) The energy KE 0 corresponds to the energy of the particles scattered from atoms at the surface, while E 1 is the measured energy of a particle scattered at depth x. [S] is the appropriate stopping cross-section, given by equation 2.25 and are obtained in the same way as discussed earlier. The depth profile of the defect distribution obtained in Fig is calculated and the result is presented in figure 2.21 which depicts the defect fraction, i.e. the fraction of disorder compared to the random level of the Ga

66 60 Ion-Atom Interactions Figure 2.20: The disorder profile as measured with RBS ( ) and after substraction of the dechanneled ions ( ). Figure 2.21: The calculated defect profile after conversion of the energy scale to a depth scale.

67 2.5 Rutherford backscattering and channeling spectrometry 61 signal in the RBS spectra, as a function of depth. These depth calculations were performed, assuming that the 4 He-ions impinge in a non-channeling direction or into an amorphous material, since the stopping powers for channeled ions into GaN are not well known. This can lead to deviations in depth scale from the actual situation, although it will be shown later in this work that the calculations of the depth scale are in good agreement with results obtained from transmission electron microscopy measurements. Complete method The RBS/C spectra measured in this work are treated following the described analytical operations in the the following sequence: Rutherford correction, dechanneling analysis and energy-to-depth scale conversion. A Fortran computer program was written for this purpose. The random spectrum in this analysis is assumed to be constant for all the channels of the MCA and is taken to be the average over the region of interest. At the surface of the sample, the slopes of y c and y r are not vertical due to the detector resolution, which is typically of the order of 15 kev. As comparison: a resolution of 15 kev for a detector positioned at a scattering angle of 105 during an RBS measurement with 1.57 MeV 4 He + ions impinging on a GaN sample, corresponds to a thickness of 60 Å. Consequently, the disorder density calculated at this point is not accurate and assuming y r to be constant solves this problem.

68 62 Ion-Atom Interactions

69 Chapter 3 Experimental Details This chapter deals with the details of the experimental techniques used in this work. First the growth of GaN layers by metalorganic chemical vapour deposition and ion implantation of rare-earths in GaN are discussed. Secondly, the details of the analysis techniques are described. 3.1 GaN layer growth GaN layers grown on sapphire were obtained from two institutes, the semiconductor group (GES) at the university of Montpellier and the department of information technology (Intec) at the university of Gent. The growth of the GaN layers was performed with the same method for both institutes: metalorganic chemical vapour deposition (MOCVD) (see section 1.3.2), and with the same growth procedure. Triethylgallium (TEGa) [Ga(C 2 H 5 ) 3 ] or trimethylgallium (TMGa) [Ga(CH 3 ) 3 ] is used as metalorganic compound for the supply of gallium, while ammonia is used as nitrogen source. Both gasses flow over a sapphire substrate and react to form GaN. The complete MOCVD growth process comprises a number of consecutive steps, executed at atmospheric pressure. These different steps are shown schematically in figure 3.1. In a first step, the nitridation step, the substrate is heated to 1100 C under a NH 3 flow to remove the absorbed impurities from its surface, preparing the substrate for deposition. A small AlN layer is formed, which partially reduces the lattice mismatch. This will promote the two-dimensional growth and improve the crystalline quality of the buffer layer [148]. After nitridation the substrate temperature is decreased to 550 C to grow a thin (approximately 250 Å) GaN buffer layer. The buffer layer exhibits a low crystalline quality, but it is a critical step 63

70 64 Experimental Details Temperature Nitridation Buffer growth Annealing GaN layer growth Time Figure 3.1: The different steps in the growth of a GaN layer by MOCVD. in obtaining high quality layers. Next, the sample is annealed for a few minutes at 1070 C and finally, the GaN film is grown at an ideal temperature between 970 C and 990 C. The growth of this layer starts with the formation of GaN islands on the buffer layer. These islands grow laterally until they start to coalesce and form a continuous layer. The layers grown by both institutes are of high crystalline quality with a thickness of approximately 1 µm and no difference is observed in the results between GaN layers grown at Monpellier or at Gent. 3.2 Ion implantation Ion implantations are performed in the Ion and Molecular Beam Lab (IMBL) at the K.U.Leuven, from which a schematic map is shown in figure 3.2. The ion implantation setup is shown at the left side of the map. A Nielsen plasma source containing ErCl 3 is used to create the ions. Electrons escaping from a tungsten filament are moving in an magnetic field inside the source and ionise the erbium and chloride atoms. Subsequently, the ions are extracted from the source by a electric field of approximately 15 kv. Next, the ion beam is accelerated to 80 kev and separated by mass by

71 3.3 Analysis techniques 65 means of the analysis magnet. The most abundant 166 Er ions are chosen for implantation in the GaN layers. Unless stated otherwise, 80 kev 166 Er + ions or 160 kev 166 Er 2+ ions are used in this work. The 166 Er ions are transmitted towards the implantation chamber by focussing magnets and electrostatic lenses. The samples are mounted on a two-axes goniometer (schematised in figure 3.3) which can be translated in three perpendicular directions. The channeling direction of the goniometer was established previously by measuring the RBS/C channeling direction of a silicon wafer with an accuracy of ±0.5 using a 160 kev 4 He 2+ beam. Since the critical angle for channeling of Er ions into GaN is several degrees, reproducible implantations can be performed. For random implantations, the goniometer was turned 10 off this direction, to minimise channeling. The beam diameter is approximately 2 mm 2 with current densities between 0.05 µa/cm 2 and 2 µa/cm 2. To achieve homogeneous implantations an electrostatic sweep mechanism is used to steer the beam over the surface. Two inch MOCVD grown GaN wafers were implanted and by using a diaphragm with an aperture of 7 7 mm 2, multiple implantations could be performed on one GaN wafer by translating the wafer vertically and horizontally, as can be seen in figure 3.4. The sample stage is equipped with a resistive heating element, which allows implantations at temperatures from room temperature up to 800 C. The temperature can be controlled within a ±5 C error margin. During implantation, the pressure in the implantation chamber always remained below 10 9 Torr. To ensure a good heat homogeneity and to avoid post-implantation annealing when performing multiple implantations on the same wafer, the implantations at high temperatures were done on separate GaN pieces, cut from a 2 inch wafer and placed in the middle of the heating element. 3.3 Analysis techniques To investigate the defects introduced in the implanted GaN layers, the samples were characterised by Rutherford backscattering and channeling spectrometry (RBS/C) since this is a non-destructive technique which allows depth determination of the distribution of ions and defects present in the sample. High-resolution X-ray diffraction (HRXRD) is used to determine the elastic strain induced in the samples after implantation. The principles of these techniques can be found in the appendices. Furthermore, cathodoluminescence (CL), photoluminescence (PL) and photoluminescence excitation (PLE) measurements are carried out on the implanted samples to

72 66 Experimental Details Leuven ion separator ion source analysis magnet switching magnet co-evaplantation standard RBS analysis chamber standard implantation channeling implantation chamber STM MBE 2 MBE 1 annealing chamber CEMS sputter and surface analysis chamber magnet Pelletron accelerator RF source SNICS source 1 m wet bench RBS / PIXE / NRA analysis chamber Figure 3.2: Schematic view of the Ion and Molecular Beam Lab (IMBL) at the Katholieke Universiteit of Leuven. The used implantation and RBS setups are shown in black.

73 3.3 Analysis techniques 67 x y z Figure 3.3: Schematics of the goniometer setup used for ion implantation. Figure 3.4: Multiple implantations of a GaN wafer with 170 kev 166 Er ions. The implanted area becomes darker due to an increasing defect density.

74 68 Experimental Details investigate the influence of the implantation parameters on the luminescence from the erbium ions. Finally, also transmission electron microscopy (TEM) measurements were carried out to confirm the RBS/C results and to receive more information on the kind of defects that are formed in the GaN layer Rutherford backscattering and channeling spectrometry The principles of Rutherford backscattering are discussed in appendix A, while the defect analysis from the RBS/C spectra was reported in section In this paragraph we would like to present the conditions for the RBS/C setup used in this work. This setup is depicted at the right hand side of the schematic map of the IMBL (figure 3.2). RBS/C measurements were achieved with a 1.57 MeV 4 He + beam with a beam diameter of 1 mm. The 4 He + ions were created in a radiofrequency source and subsequently accelerated by a Van de Graaff tandem accelerator (Pelletron) towards the standard RBS chamber, which contains a three-axis goniometer that allows the determination of the channeling directions of the GaN crystal with an accuracy of The 4 He + ions which impinge on the target and are backscattered, are detected with two silicon barrier detectors which have a detector resolution of approximately 15 kev. One detector is positioned at a fixed scattering angle of 170 and is called the annular detector. Due to this large scattering angle, it has a very good mass resolution. The second detector, called glancing detector, has a variable position and is often set at a grazing exit angle, in which case the detected 4 He + ions have traveled a larger distance through the sample. Therefore, this detector has a superior depth resolution but a lower mass resolution. The backscattered 4 He + ions which collide with the detector generate an electric pulse proportional to the energy of the ion. The signal from the detector passes through an amplifier, coupled to a multichannel analyser, which divides the selected energy range up into smaller channels each spanning a range of a several kev. The number of ions entering the detector in each energy range is summed during the measurement thereby generating an RBS spectrum which is simply the number of backscattered particles as a function of energy. For the experiments carried out in this work, an angle of 75 with respect to the incoming 4 He + beam (i.e. a scattering angle of 105 ) is chosen for the glancing detector. In this case, an optimal depth resolution is obtained without creating an overlap of the Ga and Er signals in the spectra.

75 3.3 Analysis techniques 69 The defect distribution and concentration in the implanted GaN samples were calculated from the spectra of the glancing detector because of its good depth resolution. The calculations were carried out by means of the computer code RUMP [149] and a Fortran program which performs the disorder analysis as described section The normalised defect distribution as a function of depth is acquired by taking into account the dechanneling of the 4 He + ions at the defects. Figure 3.5(a) shows the RBS/C spectrum of a typical GaN sample implanted with 166 Er ions and the defect distribution as function of depth which is deduced from this spectrum, is shown below (fig. 3.5(b)). To obtain the absolute defect concentration, the normalised defect distribution is integrated and multiplied by the atomic density of the Ga sublattice, which equals atoms/cm 2 (which is half the atomic density of GaN, i.e. ρ = atoms/cm 2, due to the stoichiometry) High-resolution X-ray diffraction The defects resulting from ion implantation cause strain in the GaN lattice as will be shown later in chapter 4. This strain can be determined when measuring the lattice constants by means of high-resolution X-ray diffraction (HRXRD). The equipment used here to determine the GaN lattice constants, is the D8 Discover from Bruker. A Cu source operating at 40 kv and 40 ma is used to generate the X-rays. To improve the angular resolution of the measurement, a monochromator with four Ge(002) crystals is placed directly behind the X-ray source. As a consequence, only Cu K α1 radiation is selected. The sample is mounted on a goniometer which is able to translate along and rotate around three perpendicular axis. X- rays reflected on the sample pass 0.6 mm and 0.2 mm slits before they are detected with a scintillator detector. A computer registers the number of counts for every sample and/or detector position. The c lattice parameter, which is perpendicular to the surface as shown in figure 1.1, can be determined by symmetric θ-2θ scans 1 around the GaN(000n) reflections (with n an even number). Although the GaN(0004) and GaN(0006) reflections have a better angular resolution, the intensity was often too low for a good determination of the lattice parameter. Therefore, the GaN(0002) peak from a θ-2θ scan was chosen to calculate the c-parameter, using Bragg s law (see also appendix B). 1 For more information of the θ-2θ scan type, see appendix B.

76 70 Experimental Details Figure 3.5: (a) RBS/C spectrum of an 170 kev 166 Er random implanted GaN sample to a fluence of Er/cm 2. The channeled spectrum (open circles) shows an increased yield close to the surface, indicating a damaged area. (b) The calculated defect distribution in function of depth from this RBS/C spectra. The depth scale is inversely proportional to the energy scale, since the He-ions that are scattered deeper into the crystal will lose more energy due to a longer path length in the sample compared to 4 He-ions scattered at the surface.

77 3.3 Analysis techniques Luminescence measurements To measure the luminescence of the implanted Er ions, photoluminescence (PL), PL excitation (PLE) and cathodoluminescence (CL) spectroscopy measurements where performed. Photoluminescence spectroscopy is a contactless, nondestructive method of probing the electronic structure of materials [150]. Light is directed onto a sample, where it is absorbed and imparts excess energy into the material in a process called photo-excitation. More specifically, photo-excitation causes electrons within the material to move into permissible excited states. When these electrons return to their equilibrium states, the excess energy is released and may include the emission of light (a radiative process) or not (a non-radiative process). The energy of the emitted light - or photoluminescence - is related to the difference in energy levels between the two electron states involved in the transition, i.e. between the excited state and the equilibrium state. The intensity of the emitted light is related to the relative contribution of the radiative process. The difference between PL and PLE spectroscopy is determined by the excitation and detection wavelengths. In the case of PL spectroscopy, the electrons are excited through laser light with a fixed wavelength and the emitted light is measured over the whole wavelength region. In PLE spectroscopy, on the other hand, light with a fixed wavelength is detected while the excitation wavelength varies. In the latter case, an absorption spectrum is measured. In this work, a combination of PL and PLE spectroscopy is used to determine different types of Er-related defects and their concentration in the implanted material. These measurements were performed at the ENSICAEN research center in Caen (France). The setup used is shown in figure 3.6. The samples were cooled down to 7 K in a liquid helium cryostat. PL and PLE studies were performed by exciting the GaN:Er samples with a CW tunable Ti:Sapphire laser or Ar laser. The laser beam was pulsed by means of a chopper and focussed on the sample. Infrared luminescence was recorded using a 0.75 m-monochromator equipped with a thermo-electric cooled In- GaAs photodiode. The monochromator resolution was kept below 0.6 nm for all spectra. A lock-in amplifier, which is coupled to the chopper, is placed between the detector and the computer to filter the detected light. Hence, only the signal coming from the detector which is in agreement with the frequency of the chopper is allowed to pass. As a result of this method, the background is reduced in the final spectra. Cathodoluminescence (CL) spectroscopy is a similar process as PL spectroscopy, except for the excitation mechanism for which electrons are used

78 72 Experimental Details Figure 3.6: Experimental PL(E) setup used at ENSI-Caen to obtain the PL and PL excitation spectra in this work. instead of photons. Additionally, CL uses higher excitation energies (several kev) whereas PL utilises laser radiation with considerably lower excitation energies (several ev photons). As a consequence, CL generates greater densities of electron-hole pairs. Additionally, also depth-resolved measurements are possible with CL. Electron penetration can be readily varied by changing accelerating voltage. In this work, CL spectroscopy was carried out at the university of Strathclyde (UK) by means of a Cameca SX100. The setup is shown schematically in figure 3.7. An electron beam with a beam voltage of 10 kv and a current of 30 na irradiates the sample. The radiation emitted by the sample is guided to a spectrometer which is connected to a CCD camera. 3.4 Sample annealing After implantation, the samples are annealed to reduce the implantation induced damage. As discussed in section 2.4.3, temperatures up to 1600 C are required to completely recover the crystalline structure. However, the GaN lattice already starts to decompose at annealing temperatures above 900 C under vacuum. A classical tube furnace is used to anneal the samples at a temperature of 950 C under flowing nitrogen gas under atmospheric

79 3.4 Sample annealing 73 Figure 3.7: Schematic picture of the Cameca SX100 setup used for cathodoluminescence spectroscopy in this work at the university of Strathclyde. pressure. The N 2 gas first passed through a bath of liquid nitrogen to remove residual impurities present in the gas. After annealing for 30 minutes, the samples are taken out of the furnace, but kept under a nitrogen atmosphere to cool down.

80 74 Experimental Details

81 Chapter 4 Damage Accumulation and Induced Strain in GaN under Different Implantation Conditions In the process of ion implantation, ions are accelerated to an energy of several tens of kev, before they impinge on the target material. These ions will transfer their energy to the lattice atoms in several encounters, which will result in displaced lattice atoms and damage of the crystalline structure. This chapter will start with an example to understand the main characteristics of defect accumulation in ion implanted GaN. Subsequently, the influence of the incident angle, the erbium fluence and the substrate temperature are discussed. 4.1 Main characteristics of defect accumulation in ion implanted GaN The main characteristics of defect accumulation in GaN implanted with erbium ions are illustrated with two 170 kev 166 Er 2+ implanted GaN samples. The implantations were performed at room temperature to a fluence of at/cm 2 with the ion beam respectively tilted 10 (i.e. random implantation) and 0 (i.e. channeled implantation) off the GaN 0001 axis. The implantation induced lattice damage and elastic strain where investigated by means of Rutherford backscattering and channeling spectrometry 75

82 76 Implantation induced damage and strain in GaN (RBS/C) and high-resolution X-ray diffraction (HRXRD). Figure 4.1(a) depicts the RBS/C spectra of the above-mentioned GaN samples while the deduced defect distribution is presented in figure 4.1(b). When the RBS channeling spectrum (open circles) of the randomly implanted sample is compared to that of a virgin GaN sample (solid line), a drastic increase of the backscattering yield is observed after implantation, which is a direct indication of the reduced crystalline structure and the accumulation of damage in the GaN sample. The spectrum exhibits one broad peak around 300 Å. This depth coincides with the end of range of the implanted Er ions, which corresponds to a value of R p = 329 Å for the projected range as calculated with SRIM. In this region the erbium ions lose most of their energy in nuclear collisions, causing many displacements in the lattice. The damage build-up will be dominated by simple point defects (Ga and N interstitials and vacancies), which survive after quenching of the collision cascades [122]. The amount of lattice disorder predicted by calculations (such as SRIM), is much higher compared to the experimentally determined disorder [151], indicating that these defects are mobile at room temperature and experience annihilation. However, defect annihilation is far from complete and point defect clusters and a dense network of large planar defects, including basal-plane dislocation loops and stacking faults, will appear after implantation [122, 126, 152]. A second peak, which appears close to the surface, can be observed in the spectra and is presented in figure 4.1. It reflects the presence of a thin, highly disordered layer at the surface of the GaN film. Transmission electron microscopy (TEM) studies confirm the presence of this highly disordered surface region of a few nanometres thickness [153], which consist of amorphous zones and small crystalline domains arranged in random orientations [126]. For the case of 80 kev random implantations to a fluence of Er/cm 2, a TEM image is presented in figure 4.2. It confirms the presence of two damage regions in the GaN crystal. The dark zone visualises the defect region at the maximum of the nuclear energy loss and it extends to a depth of 50 nm. At the surface (indicated by the black arrow) an amorphous zone (between the arrows) is observed with a thickness of 10 nm. This second peak may be unexpected since ion implantation usually creates most defects at a depth corresponding to the maximum of the nuclear stopping cross section. A similar phenomenon has previously been observed for ion implantation in silicon [ ]. Titov et al. [157] ascribes the near surface disorder production to a combination of two effects. An efficient atomic displacement or rearrangement process at

83 4.1 Main characteristics of defect accumulation in GaN 77 (a) Depth (Å) Ga surface Normalised Yield Random spectrum Random implantation Channeled implantation Virgin GaN Er (b) Defect Fraction ,0 0,9 0,8 0,7 0,6 0,5 0,4 0,3 0,2 0,1 Energy (MeV) 0, Depth (Å) Random implantation Channeled implantation Er distribution (SRIM) Vacancy distribution (SRIM) Figure 4.1: (a) Rutherford backscattering and channeling spectra of a GaN sample implanted with 170 kev 166 Er ions to a fluence of at/cm 2 for a random (open circles) and channeled (open triangles) implanted sample. For comparison, the spectrum of a virgin GaN sample is also depicted (solid line). (b) The defect distribution calculated from the RBS/C spectra shown above.

84 78 Implantation induced damage and strain in GaN Figure 4.2: TEM image of an 80 kev 166 Er implantation in the random geometry with a fluence of Er/cm 2. An amorphous layer is observed (between the arrows) at the GaN surface. the silicon-vacuum boundary accounts for the majority of the near surface peak growth, while a minor component of the surface peak results from migrating point defects, which become trapped at the Si surface. In the case of GaN, Kucheyev et al. suggested that the origin of the surface defect peak can be attributed to a highly disordered layer formed due to trapping of migrating point defects at the semiconductor surface which acts as a sink [159], similar to the effect in Si. It is not yet clear whether N loss in the near surface region, due to heavy ion irradiation, plays a role in the trapping of point defects. Kucheyev et al. investigated 450 kev 197 Au + implantations into GaN capped with a 300 Å SiO x or Si x N y layer [159]. As a result of the capping layer only a small decrease in the intensity of the surface damage peak as observed by RBS/C. They concluded from these experiments that the loss of N from the GaN surface during ion irradiation might not be the main reason for preferential disordering in the near surface region of GaN. On the other hand, Lorenz et al. performed similar experiments with 300 kev Eu ions into GaN layers capped with an AlN film of 100 Å [160]. No surface damage peak is observed after implantation, indicating that preferential sputtering of N causes this disordered surface region.

85 4.1 Main characteristics of defect accumulation in GaN 79 When ion implantation is performed along a major crystal axis, i.e. channeled implantation, a drastically lower defect distribution is found from RBS/C analysis compared to random implantation. Due to the channeling effect, the Er ions will be steered through the crystal channels and suffer less nuclear collisions compared to random implantation. As a result, the implanted ions will penetrate the GaN crystal more deeply and a lower defect concentration is observed in the RBS/C spectra in figure 4.1. Although the backscattering yield for channeled implantation (open triangles) is still higher compared to that of the virgin sample, it is remarkably lower compared to the random implantation. Moreover, for channeled implantation only a damage peak at the surface is observed. As will be discussed later in this chapter, the defect production in the case of channeled implantation is lower and spread over a more extended region compared to random implantation since a channeled ion spends a considerable part of its energy in electronic losses which do not lead to damage under these conditions. As a result, less damaging nuclear energy losses occur and are spread over a larger range. Hence, the majority of the created point defects experience annihilation while less extended defects are created in the case of channeled implantation. This results in a low defect concentration and is an indication that channeled implantation can be an advantageous method to introduce ions into the GaN lattice in a less destructive manner compared to random implantation. In addition, the lattice strain in the GaN crystal was determined by means of high-resolution X-ray diffraction (HRXRD). In contrast to RBS/C which registers backscattering from defects which are displaced in a direction perpendicular to the GaN c-axis, HRXRD measurements of the GaN(0002) reflections are sensitive to changes in a direction parallel to the GaN c-axis. A typical HRXRD measurement of the GaN(0002) reflection before and after random Er implantation is shown in figure 4.3. A satellite peak appears at the low angle side of the main GaN(0002) reflection, which originates from non-implanted and therefore undamaged GaN. It can be derived that ion implantation induces an expansion of the lattice in a direction perpendicular to the GaN surface. Similar results were observed after implantation of Ca + and Ar + ions into GaN which excludes the possibility of the formation of a new phase, because Ar is an inert element [30, 32]. The lattice expansion can neither be caused by the heavy erbium ions which principally occupy a regular Ga position after implantation, as will be discussed later in this chapter, since the ionic radius of Ga 3+ and Er 3+ in a tetrahedral bonding are of the same order of magnitude (0.62 Å

86 80 Implantation induced damage and strain in GaN Figure 4.3: Example of HRXRD spectra of a virgin GaN sample (solid line) and an Er-implanted GaN sample (open circles). and 0.88 Å respectively [161]). However, the elastic strain induced during the implantation process is believed to be caused by the formation of interstitial atoms (these can be both lattice or dopant atoms) in the GaN lattice during the implantation process. As a consequence, the strain distribution in the GaN lattice is expected to exhibit the same depth profile as the defect distribution which makes the determination of the induced strain in the implanted layers more complicated. Bai et al. observed the same effect in the XRD spectra of self-implanted Si. They came to the conclusion that the strain contribution is dominated by interstitial-like defects [114]. These defects act as dilatational centres which induce strain. In most semiconductors such as Si, Ge and GaAs, the strain is positive, indicating that the damage causes volume expansion [162]. How this satellite peak arises is explained by means of figure 4.4. Since the strain is caused by the implantation induced defects, the strain profile will have the same distribution as the defects in the GaN crystal as a function of depth. We consider the case of a defect peak near the end of range region. As a result of the statistical nature of the ion implantation process, the distribution of the implanted Er ions will have a Gaussian shape and so does the defect distribution as shown by RBS/C spectra (figure 4.1(a)) and a SRIM simulation shown in figure 4.4(a). The implantation induced

87 4.1 Main characteristics of defect accumulation in GaN 81 (a) # Vacancies (a.u.) (c) Strain e max (%) Depth (Å) Defect distribution Er distribution 1,3 1,2 1,1 1,0 0,9 0,8 0,7 0,6 0,5 0,4 0,3 0,2 0,1 0, Depth (Å) (b) Lattice parameter c (Å) 5,26 5,25 5,24 5,23 5,22 5,21 5,20 5,19 5,18 Bulk GaN 5,17 5,16 5, (d) 17,30 Bragg ( ) 17,25 17,20 17,15 17,10 Bulk GaN Depth (Å) 17, Depth (Å) Figure 4.4: (a) The Er and defect distribution after implantation as simulated by SRIM show a Gaussian shape. These defects locally extend the lattice which results in a distribution of lattice parameters (b). As a consequence the lattice strain (c) and Bragg angle (d) will vary between the values for bulk GaN and an extreme. defects cause an expansion of the crystalline lattice and the c lattice parameter alters continuously between a maximum value, coinciding in depth with the maximum of the defect distribution, and the bulk GaN lattice constant, originating from regions in the crystal that are not damaged (figure 4.4(b)). As a result, a strain profile will be present in the implanted GaN layer (figure 4.4(c)) and the Bragg angle, calculated with Bragg s law, varies between the angle for bulk GaN and a minimum value which corresponds to the maximum lattice parameter c (figure 4.4(d)). For each value of the Bragg angle in this depth profile, there will be constructive interference of the incident X-rays which contribute to the final HRXRD spectra. It is important to point out that the Gaussian distribution of the strain is not the same as the profile of the satellite peak, but both are directly related. Since no simulation programs exist for hexagonal crystal structures, we

88 82 Implantation induced damage and strain in GaN Figure 4.5: Reciprocal space map of the GaN(1015) reflection after 80 kev 166 Er implantation to a fluence of at/cm 2 along the GaN were not able to acquire the strain profile from such a HRXRD spectrum. However, the maximum lattice parameter can be calculated by determination of θ, the difference between the minimum diffraction angle in the spectra and the Bragg angle for the undamaged GaN(0002) reflection. A consistent approach to obtain the minimum angle, θ min, is to determine the angle θ for which the measured spectrum intersects a horizontal line with an intensity of two times the background. The maximum elastic strain in the perpendicular direction, e max, can now be determined with the following formula: e max = c max c bulk c bulk (4.1) in which c max is the maximum lattice parameter in the implanted area and c bulk, the lattice parameter for bulk GaN. In order to determine the influence of ion implantation on the parallel elastic strain (i.e. along the a lattice parameter) an asymmetric XRD scan

89 4.1 Main characteristics of defect accumulation in GaN 83 should be performed. For this purpose, reciprocal space mappings (RSM) around the GaN(1015) reflection were made. This type of XRD measurements 1 allow a simultaneous analysis of both the c and a lattice parameter and give direct information on the lattice strain. Figure 4.5 shows an example of a RSM around the GaN(1015) reflection after implantation of 80 kev 166 Er ions along the GaN c-axis to a fluence of at/cm 2. An intens Bragg peak is found at (q x, q z )=(3.613, 9.648) nm 1 in which q x and q z correspond to respectively the reciprocal of the a lattice parameter and the reciprocal of the c lattice parameter. A second reflection appears after implantation at (q x, q z )=(3.613, 9.597) nm 1 directly below the main peak and hence corresponds to the lattice deformation in the implanted region. The smaller q z value found for this peak indicates a lattice expansion along the GaN c-axis, which was already stated earlier in this chapter. Additionally, one can conclude that no lattice deformation in the a direction is found because the same q x value is found and hence, the parallel elastic strain is zero. Since the GaN lattice matches the substrate lattice in the a-direction, the creation of strain along this direction is more difficult than in the formation of strain in the c-direction, which explains this result. As already mentioned in section 1.4, the implantation induced damage is detrimental for the optical and electrical properties of gallium nitride. Moreover, implantation induced damage is difficult to remove in GaN (see section 2.4.3). Therefore, a good understanding of the ion implantation process and the influences of the different implantation parameters on the damage formation is important. Therefore, the influence of the implantation fluence, energy and substrate temperature on the accumulation of defects in GaN and the induced lattice strain after bombardment of erbium ions is investigated in this chapter. The role of these parameters on the defect generation is compared for random and channeled ion implantation. For a good understanding of the implantation geometry, this chapter will first discuss the influence of the incident angle on the defect accumulation and the induced strain. RBS/C and HRXRD are the main techniques used for this analysis, together with computer simulations. 1 For more information on reciprocal space mappings, see appendix B.

90 84 Implantation induced damage and strain in GaN 4.2 Implantation angle dependence As already discussed in section and in the previous paragraph, channeled implantation can have a major influence on the defect concentration in semiconductors. In this section, the influence of the implantation angle on the defect accumulation, erbium distribution, and lattice strain will be investigated. The results will be compared with theory and computer simulations Experiments Two series of samples were produced in order to investigate the influence of the implantation angle on the damage accumulation and strain in GaN. A first series of GaN samples was implanted with 80 kev 166 Er + ions to a fluence of at/cm 2. By varying the angle between the incident ion beam and the GaN 0001 axis between 1.5 and 10, 11 samples were made at room temperature. The two defect regions however, were hard to distinguish since the implantations are rather shallow for these heavy mass ions and energy, which results in an overlap of both defect regions. A higher energy is therefore chosen for the erbium ions to penetrate deeper into the GaN layer. The second series of samples was made with 160 kev 166 Er 2+ ions implanted into GaN. The implantations were performed at room temperature to a fluence of at/cm 2. This erbium fluence was chosen to obtain a comparable defect concentration with the samples in the first series, taking into account the greater penetration depth of the 160 kev 166 Er ions Implantation induced crystal damage The defect distribution as a function of depth obtained from the RBS/C measurements on the 80 kev and 160 kev 166 Er implantations for the different incident angles is shown in figure 4.6. The two damage regions, as discussed in the previous section are perceived in this figure. At the surface, mobile point defects are trapped and form a highly disordered surface layer. The second region is centred around a depth of approximately 180 Å or 300 Å for the 80 kev and 160 kev implantations respectively and corresponds to the maximum of the nuclear energy loss profile. These values are in good correspondence with the projected range R p of the implanted Er ions, respectively 192 Å and 315 Å for ion energies of 80 and 160 kev, calculated with SRIM. Highly disordered domains, dislocation loops and

91 4.2 Implantation angle dependence 85 stacking faults are the main types of defects in this area for random implantation [122, 152]. For implantation angles close to the GaN c-axis, the defect distributions are nearly identical. This is not unexpected since for small incident angles the impinging erbium ions are channeled and they will only undergo electronic stopping which does not strongly vary with the implantation angle. However, when increasing the angle of the incident Er beam above 4 for 80 kev or 2 for 160 kev, the amount of defects also increases, which is observed as an increase in the defect profile. In the case of the 160 kev implantations, figure 4.6(b) shows that the bulk damage peak saturates at a value of 50% with increasing implantation angle while the surface defect peak rises to a value of 1, indicating amorphisation. The saturation of the bulk peak is caused by migration of defects towards the GaN surface and dynamic recovery. By further increasing the incident angle, layer-by-layer amorphisation of the GaN crystal appears from the surface. Kucheyev et al. also observed a saturation of the defect concentration in the end of range region after implantation of 300 kev Au ions into GaN for different ion fluences [122]. This will be treated in more detail in section 4.3. The effect of greater penetration depths attained by channeled implanted Er ions can also be observed very clearly for the high energy implantations in figure 4.6(b). For an implantation angle of 3, for example, the defect distribution reaches a depth of 700 Å before it drops to zero. According to this, Er ions penetrate the GaN lattice at least 700 Å before they have lost all their energy. This is much deeper compared to randomly implanted Er ions, which reach a maximum of 500 Å as can be observed from the defect distribution of the implantation at 10. Hence, it can be concluded that the implantation induced damage for channeled implantation is spread over a broader region compared to random implantation. For a quantitative analysis, the defect distributions were integrated to calculate the absolute defect concentration which is plotted against the implantation angle in figure 4.7 for both implantation energies. The solid line is meant as a guide to the eye. For angles around the channeling direction (with an incident angle of 0 ), the defect concentration remains constant at a very low value due to the invariance of the electronic stopping as explained above. When increasing the incident angle of the Er ions, the defect concentration starts to increase, due to the gradual disappearance of the channeling effect. As a result, more nuclear collisions will occur and the crystal damage increases. For 80 kev this effect takes place when the in-

92 86 Implantation induced damage and strain in GaN Figure 4.6: Defect distribution for (a) 80 kev and (b) 160 kev 166 Er implanted GaN samples under different incident angles, ranging from 0 until 10 with respect to the GaN 0001 direction. For clarity, not all spectra are shown.

93 4.2 Implantation angle dependence 87 Figure 4.7: Defect concentration calculated from the distributions in figure 4.6 as a function of the implantation angle for (a) 80 kev and (b) 160 kev implantations. The solid line is meant as a guide to the eye.

94 88 Implantation induced damage and strain in GaN cident angle exceeds a value of 4, while for the high energy implantation this gradual increase already starts for angles larger than 2. The reason for this is a difference in critical angle and will be discussed in more detail in section Finally, the defect concentration reaches saturation for the random implantation geometry (implantation angle of 10 ), at a value approximately five times higher compared to channeled implantation. In the case of channeled implantation, defects are produced over a broader region compared to random implantation. As a result, the damage concentration for the former geometry is smaller and more scattered. This can be seen in figure 4.6(b) for the 160 kev implantations, in which the defect concentration for small incident angles extends to more than 700 Å. In contrast, no defect concentration is observed deeper than 500 Å for implantations with an incident angle of 10. When comparing the results of the 80 kev and 160 kev implantations in figure 4.7, a factor of two increase in defect concentration is observed when doubling the ion energy. Moreover, the Er fluence is also doubled and hence, a factor of four difference is expected between both experiments. This is rather unexpected, but this may suggest that a more effective dynamic annealing process appears in the case of 160 kev implantations. Another remarkable effect is the difference in slope between the curves of both energies in figure 4.7. For low energies a rather gradual change from channeled to random implantation is observed, while for 160 kev, the change is rather abrupt. This difference is rather unexpected and a more extended investigation has to be performed to find the reason for this difference. To complement the experimental data, molecular dynamics (MD) simulations were carried out [163] to study the influence of the implantation angle on the defect concentration. The results of these simulations are compared with the results of the 80 kev implantations. Wurzite GaN was bombarded with 5 kev Er ions with incident angles from 0 to 22. Although the ion energy used in the simulations is different from the experimental ion energy due to computer capacity limitations, the use of this energy is justified since MD range calculations [138] show that the effective channel width (i.e. the region between the atomic rows in which dechanneling does not occur) for damage production is roughly the same for both energies. Fig. 4.8 depicts the angular dependence of the experimental defect density along with the number of interstitials and number of interstitials in clusters produced in the simulations with different angles. Qualitatively, both the simulated and the experimentally determined damage concentration behave in similar way: the number of defects increases when the implantation angle

95 4.2 Implantation angle dependence 89 (a) (b) Figure 4.8: Comparison between the experimental defect density (dotted line) in Er bombarded GaN and the total number of interstitials I (a) as well as the number of interstitials in clusters I clus (b) derived from molecular dynamics simulations [163]. The energy of the incident Er ions is 80 kev and 5 kev for respectively the experiment and the simulation. is raised from 5 to 10, and is almost constant for smaller angles. However, the increase in the total number of interstitials in the simulations (a factor of 2) is clearly smaller compared to the experimentally observed increase in defect density (a factor of 4). Moreover, if one only analyses the number of interstitials in clusters, an identical angular dependence as in the experiments is obtained (within the statistical uncertainty) - see figure 4.8(b). The excellent agreement indicates that most of the single interstitials recombine, since interstitials in GaN are mobile at room temperature [164], and hence that the experimentally observed defect profile is mainly due to interstitials or clusters produced by the primary recoil. As a result, one can conclude that there are two main reasons for the experimentally observed suppression of damage production during channeled implantation.

96 90 Implantation induced damage and strain in GaN First, the total damage production decreases at small angles, and second, the damage is more scattered for channeled implantations. The simulations also show the formation of a surface peak of large damage clusters (not depicted) for both small angle and large angle implantations [163]. The effect, however, is much stronger for larger angles Erbium distribution As an effect of the statistical nature of the implantation process, the implanted erbium ions exhibit a Gaussian distribution, with the maximum centred around a certain depth, called the projected range R p (2.2.4). The projected range of the implanted Er ions is experimentally determined from the RBS spectra by fitting the Er profile with a Gaussian curve as shown in figure 4.9. The projected range as a function of the implantation angle is shown in figure For random implantation at 80 kev, a projected range around 180 Å is found, which is in good agreement with the value of R p = 192 Å obtained from SRIM simulations. However, when aligning the erbium ion beam with the GaN 0001 axis, the total stopping power will be smaller and as a consequence, larger penetration depths will be reached. This is presented by an increase in projected range as seen from figure 4.10, in which R p reaches values around 240 Å for 80 kev implantations executed in (or close to) the channeling geometry. The deeper penetration in the case of channeled implantation is also clear from figure 4.9 which shows the Er profiles as measured with RBS after 80 kev implantation to a fluence of at/cm 2. The effect of the implantation angle on the Er distribution is also investigated by means of MARLOWE simulations. Implantation profiles of 80 kev 166 Er ions in GaN at 300 K to a fluence of Er/cm 2 were simulated for different incident angles using a Debye temperature of 600 K. The Debye temperature is an important parameter in these simulations, since it determines the thermal lattice vibrations. Morgan and Van Vliet claimed that in the low energy regime (which is the case for 80 kev 166 Er implantations) the thermal lattice vibrations do not strongly alter the fraction of ions that initially experience a channeling effect. However, they do control, in conjunction with the energy loss mechanism, the depth over which the channeling actually persists [165] and hence the projected range. Furthermore, two models for the electronic energy loss of the Er ions due to interactions with the Ga and N atoms in the GaN crystal were tested. These methods differ in the contribution of the local and non-local components of the electronic energy loss. The local electronic energy loss depends on the

97 4.2 Implantation angle dependence 91 Figure 4.9: Erbium profile of 80 kev implantations to a fluence of at/cm 2 for channeled (full circles) and random (empty circles) implantation. The solid lines are a Gaussian fit of the measured points. local electron density at the point of interaction and hence on the impact parameter. Large energy losses occur for very small impact parameters. On the other hand, non-local energy loss depends on the average electron density in the crystal and is usually an overestimation in a channeled direction. In the first model used, the total electronic energy loss per collision is a combination of 50% local and 50% non-local component. The total electronic energy loss in the second model depends on a maximum impact parameter. For smaller impact parameters, the energy loss is described by the local component only, while for larger impact parameters, that do not result in any collision, the energy loss is given by the non-local component only. Figure 4.11(a) depicts the implantation profiles obtained from MAR- LOWE simulations using the first model which uses a combination of both components. As can be seen, the ions penetrate very deep into the crystal for low incident angles, resulting in a deep channeling tail. The channeling tail diminishes with increasing the incident angle, indicating a reduction of the number of channeled particles. The fraction of channeled ions further

98 92 Implantation induced damage and strain in GaN Figure 4.10: The derived projected range from the implanted Er profiles obtained from the RBS spectra for implantation angles ranging from -1.5 until 10 and implantation energy of 80 kev to a fluence of at/cm 2. The projected range was determined from the maximum of a Gaussian plot of the Er signal. The solid line is a guide to the eye. decreases until the channeling tail completely vanishes for incident angles above 5-6. The depth of the Er ions in these simulations, however, may be overestimated, which indicates that the local component of the electronic energy loss is larger than the non-local component. On the other hand, MARLOWE simulations with the second model (local electronic stopping depending on the impact parameter) in figure 4.11(b) show a smaller penetration depth of the ions but a much stronger channeling peak compared to the simulations which uses the first model. This channeling peak is not expected in comparison with the experimental results since no increased defect concentration is observed at such depths. MARLOWE simulations, however, do not take defect accumulation into account and as a result, each impinging ion is channeled in a perfect crystal which is not corresponding to reality. Moreover, the channeling tail is also strongly dependent on the Debye temperature chosen in the MARLOWE simulations and small changes in the Debye temperature can result in large differences in channeling tails.

99 4.2 Implantation angle dependence 93 Figure 4.11: MARLOWE simulations of the Er distribution as a function of depth using two different models for the electronic energy loss: (a) a combination of local and non-local components of the electronic stopping and (b) only local component depending in a maximum impact parameter. Implantation of 80 kev 166 Er ions into GaN at 300K for different implantation angles from 0 until 10 are simulated. The inset in (a) shows the projected range R p extracted from these implantation profiles

100 94 Implantation induced damage and strain in GaN Figure 4.12: The Er depth profile after implantation of 80 kev 166 Er + ions at 650 C into Si for fluences between at/cm 2 and at/cm 2. Hence, it is believed that the real Er profile for channeled implantation corresponds closer to the simulations in figure 4.11(a). This is confirmed by channeled implantations of Er into Si, shown in figure 4.12 from reference [124]. The measured Er profile indeed shows a channeling tail deeper into the crystal but without strong channeling peak. This channeling tail overlaps for all Er fluences used in these experiments, indicating that the channels already become blocked by defects for low ion fluences and that the channeling effect disappears due to the blocking of the channels. A high substrate temperature (650 C) and a large mass difference between Er and Si, made it possible to observe this effect in silicon by means of RBS. Due to the low ion fluences used at room temperature in our experiments with GaN and the smaller mass difference, RBS measurements could not confirm the result in Si, nor the MARLOWE simulations on GaN. Hence, a more sensitive technique such as secondary ion mass spectroscopy (SIMS) should be used to verify the correct model used by MARLOWE. From this distribution in figure 4.11(a) the projected range R p could be calculated and the results are presented in the inset of Fig. 4.11(a). Although the simulated ion ranges are much deeper than the experimentally

101 4.2 Implantation angle dependence 95 determined values due to an underestimation of the electronic stopping in the models described above, this figure shows a decreasing projected range with increasing angle having a similar tendency as the experimentally determined ranges in figure As discussed earlier in section 1.4, implanted ions can occupy several positions in the GaN lattice. The determination of this lattice site position can be done with RBS channeling measurements. For small impurity concentrations, < 1%, the presence of the impurities does not affect the channeling properties of the host material. The fraction f of ions occupying a regular lattice site along a certain direction, is then given by: f = 1 χ min(impurity) 1 χ min (Ga) (4.2) where 1 χ min (Ga) represents the fraction of the incident aligned 4 He + beam that is channeled. This channeled fraction is calculated from the RBS/C Ga-signal at the position corresponding in depth with the implanted Er ions. Determination of the lattice site positions of the implanted species has to be performed by channeling experiments in three independent lattice directions and combining these results. More information on the determination of lattice site positions by RBS/C can be found in references [104, 105, 166]. For implantation of erbium in GaN, emission channeling [51] and RBS/C [49, 50] experiments found that the majority of the implanted Er ions always occupy regular Ga sites. The driving force for Er (and other impurities) to occupy immediately after implantation a regular Ga-site is not yet clear, but it is believed that chemistry plays an important role here. In this work, only channeling experiments along the GaN 0001 axis were performed which only allows the determination of the fraction of Er ions that are situated inside the string of alternating Ga and N atoms. Since no simulation programs, such as FLUX 2, are used in the analysis, these results are not sensitive to small deviations. However, these results compare well with the above-mentioned studies in literature and hence, are a good representation of the real fraction of Er ions occupying a regular Ga site. In this work, we will define the fraction of Ga ions occupying a regular Ga site as the substitutional fraction of Er. As an example, we will calculate the Er substitutional fraction of a GaN sample implanted with 160 kev 166 Er ions at an angle of FLUX is a binary collision simulation code that simulates the trajectories of high energy ions in single crystals in a channeling, or near channeling, direction.

102 96 Implantation induced damage and strain in GaN Example The minimum yield of the Er signal, χ min (Er) is calculated as follows: χ min (Er) A chan A rand = (852 ± 42) = (0.48 ± 0.02) (1778 ± 29) with A chan and A rand the area under the Er signal of respectively a channeled and random RBS measurement. The minimum yield of the Ga signal is given by: χ min (Ga) H chan H rand = (150 ± 3) = (0.095 ± 0.002) (1576 ± 29) with H chan and H rand the height of the Ga signal of respectively a channeled and random RBS measurement. The fraction of Er ions occupying a lattice position along the GaN 0001 axis is calculated with formula 4.2 and results in: f = (58 ± 3)%. Figure 4.13 presents the fraction of Er ions occupying substitutional Ga-sites along the GaN 0001 axis for different implantation angles and an implantation energy of respectively 80 and 160 kev. When the implantations are performed close to the GaN c-axis, almost all Er ions are found on a Ga lattice site position. This fraction decreases down to (73 ± 4)% or (58 ± 3)% for an ion energy of respectively 80 kev or 160 kev when increasing the incident angle. A few studies on lattice site determination of Er in GaN are reported in literature. Values of 90 to 95% for the Er substitutional fraction are found by emission channeling [51] for 60 kev implantations to a fluence of at/cm 2, while RBS/C studies report values of 70% substitutional erbium [49, 50] for 160 kev implantations to a fluence of at/cm 2. These differences can be explained by the different erbium fluences used in both techniques. As will be discussed in section 4.3, the fraction of erbium ions occupying a Ga lattice site strongly depends on the implantation fluence Critical angle The critical angle is defined as the maximum angle of incidence for which the incident ions will still be channeled. The conditions for channeling determined by this angle are derived in section For low energy, high

103 4.2 Implantation angle dependence 97 Figure 4.13: Fraction of Er ions occupying a Ga-site in the GaN crystal after implantation of (a) 80 kev and (b) 160 kev 166 Er ions under different incident angles and fluences of respectively at/cm 2 and at/cm 2.

104 98 Implantation induced damage and strain in GaN Table 4.1: Critical angles for implantation of 80 and 160 kev 166 Er ions into GaN(0001). ψc L represents the critical angle predicted by Lindhard s formula, ψc exp is experimentally determined and also the critical angle extracted from MARLOWE and molecular dynamics (MD) computer simulations are presented. Ion energy ψc L ψc exp MARLOWE MD 80 kev kev mass ions such as those used in ion implantation, the determination of this angle is not straightforward. However, the critical angle can indirectly be extracted from the experiments since it is related to the process of dechanneling. The dechanneling of the impinging ions will be enhanced when the incident angle is increased to angles higher than the critical angle. For light ions with high energy, such as 4 He ions used for RBS/C, dechanneling of the ions will lead to backscattering. Hence, an experimental half-angle ψ 1/2 can be obtained from the angular yield profile. An example of an angular yield profile is shown in figure 4.14 and is obtained by plotting the RBS/C yield from the near-surface region as a function of the incident angle relative to the channeling direction. The half-angle, which is correlated with the critical angle via the dechanneling process, is defined as the width of this channeling dip at half the height between the minimum yield χ min (the lowest point of the dip) and the yield for random incidence (normalised to 1 in this figure). As an example, the half-angle ψ 1/2 for 1.57 MeV 4 He + ions incident on GaN in the 0001 direction at room temperature is ψ min = The respective calculations as described in section give ψ 1 = 0.81, ψ c (ρ) = 0.90 and ψ B = 0.70 (see also table 2.1). On the other hand, dechanneling of low energy, heavy ions such as 166 Er ions used in ion implantation with a mass larger than the mass of a target atom, will not lead to backscattering, but will create displacements and consequently lattice damage in the crystal. An estimate of the critical angle can be obtained by plotting the defect concentration as a function of the incident angle and determining the half-angle. From the defect concentration plotted in figure 4.7, a half-angle angle of 6.5 can be derived for implantation of 80 kev 166 Er ions and of 3 for implantation of 160 kev 166 Er ions. The critical angles predicted by Lindhard s formula (as given in equa-

105 4.2 Implantation angle dependence 99 Figure 4.14: Normalized angular yield for backscattered 4 He ions with an energy of 1.57 MeV which were incident on GaN The experimental definition of the angular width ψ 1/2 and the minimum yield χ min is given. tion 2.13), 7.5 and 4.2 for respectively 80 and 160 kev 166 Er ions, are in reasonable agreement with the values that were found experimentally. The smaller critical angle for the high energy implantations can be attributed to a closer approach of the impinging ions to the string of atoms at higher energies. As a result, the ions become more easily dechanneled and nuclear collisions will be more likely. Hence, the increase in defect concentration will appear at lower incident angles. Additionally, the critical angle can also be assessed by simulations with MARLOWE (Fig. 4.11) and the MD computer calculations (Fig. 4.8). From the defect density calculated with molecular dynamics simulations in figure 4.8 a half-angle of 6 is found which is in good agreement with the values extracted from the experimental results. On the other hand, determining the critical angle from implantation profiles calculated with MARLOWE is difficult. However, a half-angle of 4 can be obtained when plotting the projected range of these simulated profiles as a function of the incident angle (inset figure 4.11(a)). This value is smaller compared to the calculated and experimentally determined half-angles, but closer examination of the

106 100 Implantation induced damage and strain in GaN implantation profiles shows that a significant fraction of Er ions is channeled up to 6. Hence, it can be concluded that the experimentally obtained critical angle for 80 kev 166 Er ions is in good agreement with the theoretical predictions as well as with the computers simulations. Finally, it should be noted that the critical angle can not only be derived from the defect distribution, but also the projected range (Fig. 4.10) and the Er substitutional fraction S Ga (Er) (Fig. 4.13) are related to dechanneling of the Er ions at high implantation angles and can hence be used for the determination of the maximum angle for channeling. From the dependency of these quantities on the incident angle, values around 6.5 for the critical angle can be deduced, which are in agreement with the values of the critical angle found previously Implantation induced strain Figure 4.15 depicts the GaN(0002) reflection for HRXRD after erbium implantation under different incident angles for both ion energies. The HRXRD spectrum of a virgin GaN sample is given as reference. At the low-angle side of the main GaN(0002) peak, which originates from nonimplanted and hence undamaged GaN, a satellite peak appears. Expansion of the GaN crystal lattice in the implanted region due to implantation induced interstitials accounts for this phenomenon. The interstitial atoms cause stress in the crystalline lattice which becomes strained. When the implantation angle increases, the tail of this peak shifts towards lower angles and at the same time its intensity decreases, caused by the increasing defect concentration in the implanted area and gradual amorphisation of the GaN lattice. As explained previously in section 4.1, this peak actually is composed by several contributions of a strain profile which is correlated to the defect distribution and both profiles will exhibit the same shape. However, since it is difficult to extract the strain profile from these HRXRD spectra, only the maximum induced strain, corresponding with the extreme minimum Bragg angle of this satellite peak, is deduced and presented in figure The maximum perpendicular strain increases gradually with increasing implantation angle, sharing a similar sigmoidal trend as seen from the defect concentration. The apparent saturation of the perpendicular strain, however, is caused by a decrease in intensity of this satellite peak due to gradual amorphisation of the GaN lattice for higher implantation angles.

107 4.2 Implantation angle dependence 101 Figure 4.15: High-resolution XRD spectra of the GaN(0002) reflection measured after implantation of (a) 80 kev and (b) 160 kev 166 Er ions for different implantation angles ranging from -1.5 until 10. For clarity only some of the spectra are shown. A virgin GaN sample was measured (solid line) as reference.

108 102 Implantation induced damage and strain in GaN Figure 4.16: The maximum induced perpendicular strain as a function of implantation angle for (a) 80 kev and (b) 160 kev 166 Er implantations for fluences of respectively Er/cm 2 and Er/cm 2.

109 4.2 Implantation angle dependence Conclusion Erbium implantation along the GaN 0001 axis drastically suppresses the induced damage as well as the elastic strain in the crystalline lattice. For small angles around the channeling direction, the majority of the impinging Er ions is channeled due to a smaller potential in the channeling direction. As a consequence, these ions penetrate deep into the GaN crystal and reduce the lattice damage and perpendicular strain. The majority of the implanted ions occupy a substitutional Ga site. As the incident angle with respect to the channeling direction is increased, the fraction of fully channeled ions gradually decreases and the long channeling tail observed in the MARLOWE simulations diminishes. Hence, the projected range becomes more shallow and the defect concentration in the implanted area increases. The gradual degradation of the crystalline structure leads to worse defined lattice sites which results in a lower erbium substitutional fraction. The channeling effect has nearly completely vanished for incident angles larger than 6.5 for 80 kev 166 Er ions or larger than 3 for 160 kev 166 Er ions. These experimentally determined half-angles are confirmed by computer simulations and are in good agreement with the theoretical calculations of the critical angle. In order to reduce the implantation induced damage and elastic strain, the implantation angle should not be higher than this critical angle.

110 104 Implantation induced damage and strain in GaN 4.3 Erbium fluence dependence Implantation along the GaN 0001 axis suppresses the implantation induced damage. When the implantation fluence increases, channels become blocked by the induced lattice damage and the channeling effect will gradually disappear. In this section, the behaviour of the implantation damage and lattice strain with increasing erbium fluence is investigated Experiments To investigate the dependence of the erbium fluence on the implantation induced defects and strain, two series of implantations were performed at room temperature for two different energies. In the first series, 80 kev 166 Er + ions are implanted into GaN to fluences ranging from at/cm 2 to at/cm 2. For every fluence, one implantation was performed with the ion beam along the GaN 0001 axis and a second one with the ion beam tilted 10 off this axis. For the second series of samples, 170 kev 166 Er 2+ ions were implanted to fluences ranging from at/cm 2 to at/cm 2 and along both implantation geometries for each fluence. The high energy implantations were performed to obtain a better resolution of the two defect regions present in the GaN after implantation as discussed earlier in this chapter Implantation induced damage The defect distributions of the GaN samples implanted with different 166 Er fluences, extracted from the RBS/C measurements, are presented in figure 4.17 for both 80 kev and 170 kev ion implantations. The difference in profile for both ion energies attracts attention: one broad defect distribution is observed for the 80 kev Er ions while two defect regions are observed in the 170 kev implantations. The reason for this difference is twofold: firstly, the 170 kev 166 Er ions have more energy and are therefore able to penetrate deeper into the crystal. As a result, the defect region corresponding to the maximum of the nuclear stopping is found deeper in the crystal compared to the 80 kev 166 Er implantations. Secondly, the detector was positioned at a higher angle (hence, lower scattering angle) and had a better resolution for the RBS/C measurements of the 170 kev implantations, which results in an enhanced depth resolution. Hence, the following discussion is mainly based on the results of the high-energy implantations. For erbium fluences below Er/cm 2, almost no damage is found

111 4.3 Erbium fluence dependence kev implantations 170 kev implantations Figure 4.17: Defect distributions of 80 kev and 170 kev 166 Er implantations for fluences ranging from at/cm 2 to at/cm 2. The spectra are presented for both the random (a) and (c) and channeled (b) and (d) implantation geometry.

112 106 Implantation induced damage and strain in GaN in the end of range (EOR) region. The damage build-up during ion implantation for such low erbium fluences is mainly dominated by simple point defects (gallium and nitrogen vacancies and interstitials), which survive after quenching of the collision cascades, and the formation of small planar defects. Most of these defects experience annihilation which accounts for the high amorphisation threshold [122]. A second defect region is found within a thin surface layer with an estimated maximum thickness of 100 Å obtained from figure It is believed that migration and trapping of point defects is responsible for the defect accumulation at the surface. The presence of this thin surface layer and its thickness is confirmed by transmission electron microscopy (TEM) measurements, presented in figure 4.20(a). With increasing ion fluence, the EOR defect peak rises monotonically due to the formation of extended defects, like point-defect clusters and larger planar defects such as stacking faults and pyramidal dislocation loops [122, 126, 152]. Finally, this defect peak saturates at a level of 60% for erbium fluences above Er/cm 2 which is below the amorphisation level. The saturation is believed to be associated with both defect migration towards the surface and an efficient dynamic recovery process [167]. Meanwhile defects accumulate at the surface until amorphisation is reached. From that point on, the damage builds up layer by layer starting from the surface deeper into the GaN crystal. In the case of channeled implantation, less nuclear collisions and a larger penetration depth result in a lower and more evenly spread defect concentration compared to random implantation. The defect distributions for channeled implantation, presented in figure 4.17(b) and (d), show a resemblance with the profiles obtained after random implantation. However, higher fluences can be implanted before the same damage level is reached as in the random geometry. Up to a fluence of Er/cm 2, the defect fraction in the GaN crystal remains low for both 80 kev and 170 kev implantation energies and only a small defect peak at the GaN surface is observed. With higher fluences, a gradual increase in defect fraction is observed in the case of channeled implantation as well. The sharp increase for ion fluences higher than Er/cm 2 is caused by blocking of the channels. Initially, the channeled ions penetrate deeply into the substrate. In the end of range region, however, the channeled ions will lose their energy in nuclear collisions with substrate atoms and as a result, they cause atomic displacements. Channeling is hence suppressed even for low implantation fluences. With increasing ion fluence, the fraction of dechanneled erbium ions will become larger due to the initially created defects which leads to

113 4.3 Erbium fluence dependence 107 Defect Concentration ( Ga-defects/cm 2 ) Random - 80 kev Channeled - 80 kev Random kev Channeled kev Displacements Per Atom (dpa) Figure 4.18: Defect concentration as a function of the number of displacements per atom for 80 kev and 170 kev 166 Er implantations into GaN. The defect concentrations are calculated by integrating the defect distributions in figure The solid lines are a guide to the eye. the creation of more defects. Finally, the channeling effect vanishes completely, resulting in a sharp increase in the defect concentration. Hogg et al. observed the same effect for channeled implantation of Er in Si(111) [124] where vanishing of the channeling effect resulted in a compression of the implantation profile. This effect is also illustrated in figure In this figure, the defect concentration is presented as a function of the number of displacements per atom. The defect concentration is obtained by integration of the defect distribution peak in figure In order to compare both implantation energies, the ion fluence was converted to the number of displacements per atom (dpa) according to equation 4.3. dpa = F luence N vac Max (4.3) n at in which n at equals at/cm 3, the atomic density of GaN, and N Max vac

114 108 Implantation induced damage and strain in GaN the number of vacancies in the maximum of the nuclear energy loss profile as calculated with SRIM. This formula results in a conversion factor of 0.53 or 0.60 for the 80 kev or 170 kev implantations respectively. It should be noted that the value of Nvac Max obtained by SRIM is only valid for random implantations. For channeled implantations, however, SRIM will overestimate the number of vacancies. Figure 4.18 shows that the damage build-up has a sigmoidal shape independent of the implantation energy. The sharp increase (or strong sigmoidality) is a characteristic feature of nucleationlimited amorphisation, where the initial stage of ion bombardment results in the formation of nucleation sites for amorphisation [151]. When such nucleation sites are formed, subsequent irradiation of a pre-damaged crystal leads to a very fast increase in the damage level with increasing ion fluence. Kucheyev et al. found that the onset of the fast growth coincides with the formation of planar defects, which may suggest that this kind of defect is a plausible candidate for the nucleation sites [122]. Literature reports the same dependence of the implantation damage on the ion fluence for random implantations of other elements, such as C and Au[122], Si [28], Ar and Ca [32, 39] and Eu [168] into GaN. However, no report on channeled implantations in GaN are found. Figure 4.18 presents a substantial difference in defect concentration between both implantation geometries in the fluence region between 1 and 10 dpa. For the same number of displacements in this region, random implantation results in twice as many Ga-defects compared to channeled implantation. However, the conversion from erbium fluence to dpa for channeled implantations is probably overestimated and it is possible that both geometries result in the same defect concentration for an equal number of displacements per atom. Performing the implantations along a major GaN axis remains still beneficial, since a higher erbium fluence can be implanted in the case of channeled implantation, before the same dpa value is obtained compared to random implantations. Bright-field TEM images of two samples with different implantation geometries to a fluence of Er/cm 2 and Er/cm 2 for respectively random and channeled implantation are depicted in figure These bright-field TEM images were taken with a Topcon 002B electron microscope at SIFCOM in Caen (France). Although these two samples appear to have the same defect concentration as observed with RBS/C (figure 4.19(a)), their HRXRD spectra and TEM images show remarkable differences. In both cases, the TEM images show a small amorphous layer at the GaN surface with below the second defect region, which consists out of

115 4.3 Erbium fluence dependence 109 Figure 4.19: (a) Defect distribution in GaN implanted with 80 kev 166 Er ions for the case of random implantation and channeled implantation to a fluence of respectively Er/cm 2 and Er/cm 2. (b) HRXRD spectra of the GaN(0004) reflection of the above-mentioned samples.

116 110 Implantation induced damage and strain in GaN (a) Random implantation (b) Channeled implantation Figure 4.20: Cross-sectional bright field TEM images taken from GaN implanted with 80 kev 166 Er ions for the case of (a) random implantation and (b) channeled implantation to a fluence of respectively Er/cm 2 and Er/cm 2. The black arrow indicates the surface of the samples and the thin, highly defective surface layer is shown between the two arrows.