Determination of carrier diffusion length in p- and n-type GaN Shopan Hafiz* a, Sebastian Metzner b, Fan Zhang a, Morteza Monavarian a, Vitaliy Avrutin a, Hadis Morkoç a, Christopher Karbaum b, Frank Bertram b, Jürgen Christen b, Bernard Gil c, and Ümit Özgür a, a Department of Electrical and Computer Engineering, Virginia Commonwealth University, Richmond, Virginia 23284, USA b Institute of Experimental Physics, Otto-von-Guericke-University Magdeburg, Magdeburg, Germany c CNRS-University Montpellier 2, Laboratoire Charles Coulomb UMR 5221, F-34095 Montpellier, France ABSTRACT Diffusion lengths of photo-excited carriers along the c-direction were determined from photoluminescence (PL) measurements in p- and n-type GaN epitaxial layers grown on c-plane sapphire by metal-organic chemical vapor deposition. The investigated samples incorporate a 6 nm thick In 0.15 Ga 0.85 N active layer capped with either 500 nm p- GaN or 1300 nm n-gan. The top GaN layers were etched in steps and PL from the InGaN active region and the underlying layers was monitored as a function of the top GaN thickness upon photogeneration near the surface region by above bandgap excitation. Taking into consideration the absorption in the active and underlying layers, the diffusion lengths at 295 K and at 15 K were measured to be about 92 ± 7 nm and 68 ± 7 nm for Mg-doped p-type GaN and 432 ± 30 nm and 316 ± 30 nm for unintentionally doped n-type GaN, respectively. Cross-sectional cathodoluminescence line-scan measurement was performed on a separate sample and the diffusion length in n-type GaN was measured to be 280 nm. Keywords: Diffusion length, GaN, Photoluminescence, Cathodoluminescence. 1. INTRODUCTION Carrier diffusion length is an important physical parameter that directly affects the performance of electronic and optoelectronic semiconductor devices. Various experimental techniques such as electron beam induced current (EBIC), 1,2,3 junction based photocurrent, 4 surface photo-voltage spectroscopy 5 have been devised for its determination and a wide range of values ranging from 50 nm to 3.4 µm have been reported depending on the material quality, doping levels, and the techniques used. 1,2,3,4,5,6,7,8 In this study, we measured the diffusion length of the photogenerated carriers in n- and p- type GaN, along the c-direction using photoluminescence (PL) spectroscopy and compared the results with cathodoluminescence (CL) line-scan measurements. 2. EXPERIMENTAL PROCEDURE The samples used were c-plane 6 nm thick In 0.15 Ga 0.85 N double heterostructure (DH) active regions grown on a ~3.7 µmthick n-type GaN template on sapphire in a vertical low-pressure metalorganic chemical vapor deposition (MOCVD) system. A 60-nm Si-doped (2 10 18 cm -3 ) In 0.01 Ga 0.99 N underlying layer was grown just beneath the active region for improving the quality of the overgrown layers. The structures were completed with either Mg-doped (doping concentration ~ 10 19 cm -3 ) p-gan layer of 500-nm thickness or 1.30 µm thick unintentionally doped (doping concentration ~ 10 17 cm -3 ) n-type GaN layer (Fig. 1). Hole concentration in p-gan was determined to be 4 10 17 cm -3 from Hall measurements on a separate calibration sample. To mitigate the effect of Mg out-diffusion from p-gan on optical quality of the active region, a 20-nm thick In 0.01 Ga 0.99 N spacer layer was grown in between. In case of n-gan sample, the spacer layer thickness was 3 nm. Gallium Nitride Materials and Devices IX, edited by Jen-Inn Chyi, Yasushi Nanishi, Hadis Morkoç, Joachim Piprek, Euijoon Yoon, Hiroshi Fujioka, Proc. of SPIE Vol. 8986, 89862C 2014 SPIE CCC code: 0277-786X/14/$18 doi: 10.1117/12.2040645 Proc. of SPIE Vol. 8986 89862C-1
Spacer layer - Active region - Underlying layers '-' - p-/n-gan (500nm/1.3µm) In0.01Ga0.99N (20nm/3nm) Ino.1sGao.ssN (ónm ) In0.01Ga0.99N (60nm) n-gan (^'3.7µm) Fig. 1. Cross-sectional schematic of the InGaN-based DH samples investigated. To achieve n- and p-type layers with different thickness, selective area inductively coupled plasma (ICP) etching was used in multiple steps. Etched thickness of the top layer was determined after each etching step using a surface profiler. PL measurements were carried out on regions with different p-gan/n-gan thicknesses using He-Cd laser (325 nm) excitation (excitation density of 4 kwcm -2 to 25 kwcm -2 ). As the absorption coefficient at the wavelength of the exciting laser is large, photogeneration of carriers takes place near the surface region of the sample and upon diffusion of carriers away from the surface the resulting PL from the active region, spacer layer and underlying n-gan is measured. The thicker the top layer, the less intense the PL from underlying layers. The PL intensity of the etched region was always compared with that from the corresponding un-etched reference region to minimize the effect of any variation across the sample. As the top GaN layer becomes thinner, PL contribution from photogenerated carriers due to direct absorption of light increases and becomes significant compared to the PL from diffused carriers. For CL measurement, a light emitting diode (LED) structure with an active region composed of four 3 nm-thick DHs separated by 3 nm In 0.06 Ga 0.94 N barrier (quad 3-nm DH) and 100 nm p-gan on top was used. 3. EXPERIMENTAL RESULT Fig. 2 shows the representative room temperature PL spectra for different top p-gan thicknesses when the detector side was optimized for n-gan luminescence. With decreasing p-gan thickness, PL intensity of underlying n-gan and spacer layer increase. Proc. of SPIE Vol. 8986 89862C-2
PL intensity (arb. units) 10 6 10 5 10 4 10 3 n-gan Sapcer layer p-gan thickness (nm) 500 200 400 150 350 100 300 50 Active region 250 0 10 2 360 380 400 420 440 460 Wavelength (nm) Fig. 2. Room temperature PL spectra of underlying n-gan and spacer layer for different p-gan thickness Fig. 3 shows the integrated PL intensity of underlying n-gan, spacer layer, and the active region plotted as a function of p-gan thickness at 295 K and at 15 K, taking into account the absorption in the active region and underlying layer using the absorption coefficients of InGaN and GaN calculated from their square root dependence on photon energy. 9 With increasing p-gan thickness, the normalized PL intensity from the Ldiff underlying n-gan layer exhibits an exponential decay, where x is the p-gan thickness and L diff is the diffusion length. The diffusion lengths in p-gan extracted from the fit are 92 ± 7 nm and 68 ± 7 nm at 295 K and 15 K, respectively. The same values within the error bars were obtained from the fits to the integrated PL intensities from the active region and the spacer layer. It should be noted that due to high Mg content, there is negligible near band edge emission from the p-gan layer. Moreover, it is noticeable that the active region emission is weaker than spacer layer and underlying n-gan emission. As the top p-gan layer is grown at a higher temperature (1000 C) compared to that for the active region (680 C) for a long period of time to achieve the desired thickness of 500 nm, the active region optical quality noticeably degrades as compared to conventional LED structure having thickness of the p-gan layer of only around 100 nm, possibly due to straindriven Indium diffusion. This effect is much higher for the active region because of its higher Indium composition compared to spacer layer. x e Proc. of SPIE Vol. 8986 89862C-3
Normalized integrated PL intensity 1.0 0.5 0.0 295K underlying n-gan spacer layer active region 15K underlying n-gan 0 100 200 300 400 500 p-gan thickness (nm) Fig. 3. Integrated PL from underlying GaN, spacer layer, and the active region at 15 and 295 K as a function of p-gan thickness. In case of n-gan capped sample, as the emission from the underlying n-gan layer cannot be differentiated, intensities of PL from the active region and underlying InGaN (only at 15 K) were monitored to determine the diffusion length. In Fig. 4 integrated active region PL intensity is plotted as a function of top n-gan thickness. Using an exponential decay fit as was done for p-gan, diffusion length in n-gan was found to be 432±30 nm at 295 K and 316±30 nm at 15 K. Underlying InGaN PL spectra could not be used for room temperature diffusion length estimation as emission from n- GaN was so strong that no distinct peak of InGaN emission was observed for a top n-gan thickness of 450 nm or more. Normalized integrated PL intensity 1.0 0.5 0.0 295K active region 15K active region underlying InGaN 0 300 600 900 1200 n-gan thickness (nm) Fig. 4. Integrated PL from the active region and spacer layer at 15 and 295 K as a function of p-gan thickness. Proc. of SPIE Vol. 8986 89862C-4
Cross-sectional CL line scan was performed on quad DH sample at 5 K. Electron beam was focused on the underlying n- GaN and as the excitation gets closer to the active region, CL intensity starts increasing exponentially. Using the slope of this increase for exponential fitting, diffusion length in n-gan was measured to be 280 nm (Fig. 5) which is consistent with the PL measurement value. 10 3 1 CL Intensity (arb. units) 10 2 10 1 10 0 normalized to n-gan active region (DH) underlying n-gan 0.1 λ DH =280 nm 10-1 10-2 1 2 3 4 5 Linescan Position (µm) 4.6 4.8 5.0 5.2 Fig. 5. Cross-sectional CL line-scan for quad DH at 5K The carrier diffusion lengths measured were found to be independent of the photogenerated carrier density within the range employed from 1.4 10 17 cm -3 to 4 10 17 cm -3 (calculated using radiative recombination coefficient, B = 1.1 10-8 cm 3 s -1 ) 10 and the results for the highest excitation density are presented above. G. P. Yablonskii et al. 11 also reported little change in diffusion length for carrier density up to 6.2 10 17 cm -3. Moreover, carrier diffusion length in p-gan is smaller than in n-gan, in agreement with previous studies. 2,3 This is expected because of a large concentration of Mg atoms required to achieve p-type doping due to the relatively deep Mg acceptor level. These substitutional Mg atoms act as traps for carriers and give rise to trap assisted recombination which eventually becomes the dominant recombination mechanism. The diffusion length has been reported 7 to decrease drastically from 950 nm to 220 nm with increasing Mg concentration from 4 x 10 18 cm -3 to 3 x 10 19 cm -3 for low dislocation densities of less than 10 8 cm -2. However, for relatively high dislocation density above 10 9 cm -2, diffusion length of electrons in p-gan was reported to be independent of Mg doping concentration. The decrease in diffusion length at low temperature in both n- and p-gan is due to the increased ionized impurity scattering which is dominant at low temperatures because, as the thermal velocity of the carriers reduces, the effect of long-range Coulomb interactions on their motion increases. This temperature dependence of diffusion length is also consistent with data available in literature, 1,12 although the specific values of diffusion lengths differ from those reported here due to different measurement techniques and varying layer quality. L. Chernyak et al. reported 1 the diffusion length in n-gan (electron concentration ~ 2 10 18 cm -3 ) to be 1.25 µm at 300 K and 3 µm at 525 K while J. Y. Duboz et al. reported 12 120nm at 5 K and 320 nm at 80 K in unintentionally doped n-gan. 4. CONCLUSION In conclusion, carrier diffusion lengths in p-type and n-type GaN were determined by measuring the PL spectra of InGaN-based double heterostructures with different top n-gan and p-gan thickness and by the subsequent exponential fitting of the experimental data. As the photoexcited carrier concentration is in the same order of magnitude as the background carrier concentration, the estimated values of carrier diffusion lengths are ambipolar in nature. However, this method is also applicable for determination of minority carrier diffusion length by using lower photo-excitation density. Proc. of SPIE Vol. 8986 89862C-5
The diffusion lengths at 295 K and at 15 K were measured to be 92 ± 7 nm and 68 ± 7 nm in p-type GaN and 432 ± 30 nm and 316 ± 30 nm in unintentionally doped n-type GaN, respectively and were independent of excitation density ranging from 4 kwcm -2 to 25 kwcm -2. Moreover, from cross-sectional CL line scan measurement, the diffusion length in n-type GaN was found to be 280 nm. Both of these methods of diffusion length estimation are simple, direct and require no contact formation unlike EBIC technique and yet give reliable values quite consistent with the literature. ACKNOWLEDGEMENTS The work at VCU was supported by NSF (grant number EPMD 1128489 under direction of Dr. J. Zavada). The work at Magdeburg University is funded by the German Research Foundation DFG in the frame of the research unit FOR 957 PolarCoN. B. G. acknowledges support from GANEX (ANR-11-LABX-0014). REFERENCES [1] Chernyak, L., Osinsky, A., Temkin, H., Yang, J. W., Chen, Q. and Khan, M. A., Electron beam induced current measurements of minority carrier diffusion length in gallium nitride, Appl. Phys. Lett. 69, 2531 (1996) [2] Bandic, Z. Z., Bridger, P. M., Piquette, E. C. and McGill, T. C., Minority carrier diffusion length and lifetime in GaN, Appl. Phys. Lett. 72, 3166 (1998) [3] Bandic, Z. Z., Bridger, P. M., Piquette, E. C. and McGill, T. C., Electron diffusion length and lifetime in p -type GaN, Appl. Phys. Lett. 73, 3276 (1998) [4] Wee, D., Parish, G. and Nener, B., Investigation of the accuracy of the spectral photocurrent method for the determination of minority carrier diffusion length, J. Appl. Phys. 111, 074503 (2012) [5] Park, S. E., Kopanski, J. J., Kang, Y. S. and Robins, L. H., Surface photovoltage spectroscopy of minority carrier diffusion lengths in undoped and Si-doped GaN epitaxial films, Phys. Stat. Sol (c), 2, 2433 (2005) [6] Gonzalez, J. C., Bunker, K. L. and Russell, P. E. Minority-carrier diffusion length in a GaN-based light-emitting diode, Appl. Phys. Lett. 79, 1567 (2001) [7] Kumakura, K., Makimoto, T., Kobayashi, N., Hashizume, T., Fukui, T. and Hasegawa, H., Minority carrier diffusion length in GaN: Dislocation density and doping concentration dependence, Appl. Phys. Lett. 86, 052105 (2005) [8] Miyajima, T., Ozawa, M., Asatsuma, T., Kawai, H. and Ikeda, M., Minority carrier diffusion length in GaN and ZnSe, J. Cryst. Growth 189, 768 (1998) [9] Schubert, E. F., [Light-Emitting Diodes], 2 nd ed., Cambridge University Press, Cambridge, (2006) [10] Muth, J. F., Lee, J. H., Shmagin, I. K., Kolbas, R. M., Casey, H. C., Keller, B. P., Mishra, U. K. and DenBaars, S. P., Absorption coefficient, energy gap, exciton binding energy, and recombination lifetime of GaN obtained from transmission measurements, Appl. Phys. Lett. 71, 2572 (1997) [11] Yablonskii, G. P., Gurskii, A. L., Pavlovskii, V. N., Lutsenko, E. V., Zubialevich, V. Z., Shulga, T. S., Stognij, A. I., Kalisch, H., Szymakowski, A., Jansen, R. H., Alam, A., Schineller, B. and Heuken, M., Carrier diffusion length measured by optical method in GaN epilayers grown by MOCVD on sapphire substrates, J. Cryst. Growth 275, E1047 (2005) [12] Duboz, J. Y., Binet, F., Dolfi, D., Laurent, N., Scholz, F., Off, J., Sohmer, A., Briot, O., Gil, B., Diffusion length of photoexcited carriers in GaN, Mat. Sci. Eng. B 50, 289 (1997) Proc. of SPIE Vol. 8986 89862C-6