Characterization of multiple carriers in GaN using ... - Springer Link

JEM_1021-S6

4/15/04

4:43 PM

Page 412

Journal of ELECTRONIC MATERIALS, Vol. 33, No. 5, 2004

Special Issue Paper

Characterization of Multiple Carriers in GaN Using Variable Magnetic-Field Hall Measurements C.H. SWARTZ,1 R.P. TOMPKINS,1 T.H. MYERS,1,4 D.C. LOOK,2,3 and J.R. SIZELOVE3 1.—Department of Physics, West Virginia University, Morgantown, WV 26506. 2.—Semiconductor Research Center, Wright State University, Dayton, OH 45435. 3.—Air Force Research Laboratory, Materials and Manufacturing Directorate, Wright-Patterson Air Force Base, OH 45433. 4.—E-mail: [email protected]

Variable magnetic-field Hall-effect measurements were performed on two thick GaN samples grown by hydride vapor-phase epitaxy (HVPE), one freestanding and one attached to the sapphire substrate. Results are compared to those obtained using the more standard, single magnetic-field Hall measurements. In both samples, a second low-mobility electron was indicated that significantly influenced interpretation of single-field Hall measurements, particularly at low temperatures. Extraction of the bulk carrier using fits to the variable-field Hall data allowed a more accurate determination of the temperature dependence of the bulk electrical properties and, hence, basic physical parameters. In addition, the quantitative mobility-spectrum analysis (QMSA) technique, reported here for the first time on GaN, indicated a continuous and significant spread in mobility for the bulk electron, likely with sample thickness. Thus, even the “improved” results, based on modeling the multiple-carrier fitting (MCF) analysis, obtained in this study should be viewed with some suspicion, as they clearly represent an average over an electrically inhomogeneous sample. Key words: Hydride vapor-phase epitaxy (HVPE), GaN, variable magneticfield Hall measurements, quantitative mobility-spectrum analysis (QMSA)

INTRODUCTION Interest in hydride vapor-phase epitaxy (HVPE) growth of GaN has been revitalized by the significant improvements obtained in structural, electrical, and optical properties through the growth of thick (200 µm) layers.1–4 The thick layers can be delaminated from the substrate by backside laser irradiation, providing a “freestanding” layer that can then be used as a homoepitaxial substrate.5,6 Electrical characterization using Hall measurements is one of the cornerstone techniques for evaluating the quality and reproducibility of these materials. Mixed conduction effects can have a strong influence on magneto-transport in HVPE material, complicating interpretation of the Hall measurements. This is particularly true for as-grown layers, as the growth (Received November 3, 2003; accepted January 6, 2004) 412

of GaN on sapphire leads to the formation of defects caused by the lattice and thermal expansion mismatch between film and substrate. In addition, oxygen from the sapphire substrate tends to diffuse into the growing layer. Thus, an electrically degenerate “interfacial” layer ranging in thickness from 0.25 µm to greater than 20 µm forms at the sapphire/GaN interface, depending on growth parameters.7 Conduction at such a substrate/epilayer interface, or potentially at surfaces, can dominate the transport.8,9 Variable magnetic-field Hall measurements can be used to determine, in principle, the influence of the various carriers and as such is a powerful characterization tool.10,11 On the other hand, variable-field measurements add a significant degree of complexity to the process of sample characterization, which directly translates into increased time and characterization costs. Thus, each situation should be

JEM_1021-S6

4/15/04

4:43 PM

Page 413

Characterization of Multiple Carriers in GaN Using Variable Magnetic-Field Hall Measurements

evaluated on a case-by-case basis to determine whether the added complexity is justified. For example, standard single-field Hall measurements are often adequate as a process control when many identical layers (or even structures) are grown and what is desired is a measure of reproducibility. However, to correctly interpret the parameters measured by standard Hall data or to derive absolute values for mobility or carrier concentrations, variable-field measurements become necessary. The results of the present study indicate that variable-field Hall techniques are essential for evaluating multiple-carrier transport in both unseparated and freestanding HVPE GaN. EXPERIMENTAL Two HVPE GaN samples were investigated using variable magnetic-field measurements: a 30-µmthick layer on sapphire from TDI, Inc. (Silver Springs, MD) and a 245-µm-thick freestanding layer from Samsung Advanced Institute of Technology (Suwon, Korea). The HVPE GaN grows with a Gapolar (0001) orientation. Separation from the substrate by irradiating the N-polar face through the sapphire substrate still leaves the degenerate layer discussed earlier,11 potentially coupled with laserinduced damage. Mechanical polishing followed by reactive ion etching was used to remove material from both faces in order to flatten the sample. Removal of the material from the N-polar face of the sample also attempts to eliminate the degenerate layer, leaving a total thickness of 245 µm.4 Because the delaminated sample is initially convex due to stress release, the possibility exists that varying amounts of the degenerate layer may remain.7 Resistivity and Hall measurements were made at West Virginia University (WVU) as a function of temperature and magnetic field up to 4.5 T. The van der Pauw technique12 was used with soldered In contacts. Measurements were taken in a Janis SuperOptiMag System powered by a Cryomagnetics IPS-100 supply. At a given temperature, measurements were made at each of 22 logarithmically spaced values of the magnetic field. All contact configurations and both current directions were measured by the use of a Keithley 7001 switching unit (Cleveland, OH) with a 220 current source and 197 A voltmeter. The Hall and resistivity values were converted to the conductivity tensor components σxx and σxy; then, quantitative mobility-spectrum analysis (QMSA) and multiple-carrier fitting (MCF) were performed using standard techniques.13,14 It should be noted that QMSA is a recently developed approach that does not depend on any a priori assumptions about the type and number of carriers and can actually reveal information about potential nonuniformity, or spread, in mobility for a given carrier. This study represents the first time that QMSA has been applied to analysis of Hall results in GaN. The temperature dependence of the electron mobility and carrier concentration for each sample was analyzed

413

at Wright-Patterson Air Force Base using the full Boltzman transport equation model.15,4 RESULTS AND DISCUSSION Typically, the interface layer present in GaN grown on sapphire is accounted for by assuming its electrical properties are degenerate and, thus, exhibit little temperature dependence.9 Because the bulk carrier exhibits freeze-out, Hall-effect measurements at very low temperature should reflect primarily the interfacial layer. Thus, the values obtained for the lowest temperature are “subtracted” from the Hall results at all other temperatures to obtain a “corrected” value of mobility and carrier concentration. In reality, this assumption (and approach) may not be strictly valid. The expected conduction from the interface layer in the 30-µm-thick sample on sapphire was unambiguously indicated by QMSA analysis of variable-field Hall measurements at 60 K, as shown in Fig. 1. There is a lower mobility electron with an average mobility of 200 cm2/Vs and a higher mobility electron with an average mobility of 3,000 cm2/Vs indicative of “bulk” conduction. What is interesting is that there appears to be a spread in the electron mobility associated with both carriers, implying nonuniformity with depth. At temperatures above 70 K, the magnetic-fielddependent contribution of the low mobility carrier was not high enough at the maximum magnetic field available at WVU to allow accurate determination of both the carrier concentration and the mobility. The MCF analysis at temperatures below this where both carriers could be clearly separated indicated no evidence of carrier freeze-out for the degenerate interfacial layer between 10 K and 50 K. Thus, we

Fig. 1. The QMSA spectrum of HVPE GaN on sapphire, indicating a bulk and interface electron.

JEM_1021-S6

4/15/04

4:43 PM

Page 414

414

Swartz, Tompkins, Myers, Look, and Sizelove

Fig. 2. Comparison of the mobility of each electron in HVPE GaN on sapphire obtained from a two-carrier MCF to the variable-field Hall data with that from the corrected, single-field Hall mobility.

previously obtained single-field Hall results for carrier concentration. Both sets of results were analyzed using the approach described previously. Modeling of the temperature variation of the single-field mobility indicated a net acceptor concentration of NA 3.1  1016 cm3. This could be used to analyze the temperature dependence of the carrier concentration, which strongly suggested two donor impurities: one with an activation energy of ED  15 meV and donor concentration of ND  5.9  1016 cm3 and the other with an activation energy of ED  59 meV and donor concentration of ND  9.3  1015 cm3. However, fitting to the temperature dependence of the bulk carrier mobility obtained by MCF analysis resulted in a lower value for NA, 1.8  1016 cm3, and the fit to the associated carrier concentration indicated only a single donor with ED  23 meV and ND  3.9  1016 cm3. This donor energy is much closer to what is expected either for oxygen or for silicon, the typical n-type impurities in HVPE GaN. Thus, ignoring the temperature dependence of the electrical properties of the interfacial layer resulted in a factor of 1.5 inaccuracy in the primary, n-type impurity-ionization energy, as well as needing to assume two different types of n-type impurities to explain the temperature dependence of the carrier concentration. The use of variable magnetic-field analysis appears to be clearly required to cleanly interpret the electrical properties of thick HVPE GaN on sapphire. The 245-µm-thick freestanding GaN from Samsung also exhibited conduction caused by two electrons—one with a significantly lower mobility. Figure 4 is the 50-K spectra obtained from QMSA of the variable-field measurements, indicating

Fig. 3. The carrier concentration of the bulk electron in HVPE GaN on sapphire, from a two-carrier MCF to the variable-field Hall data, compared with the corrected, single-field Hall concentration.

Fig. 4. The QMSA spectrum of freestanding GaN, indicating the presence of two types of conduction electrons.

assumed the interfacial carrier concentration to be constant at a value of 1.6  0.3  1014 cm2 at all temperatures. As can be seen from MCF analysis, the mobility of the interfacial layer did exhibit temperature dependence, as shown in Fig. 2. Taking this into consideration, we can obtain improved values for the bulk electron’s mobility and carrier concentration. As also shown in Fig. 2, the MCF determination of the bulk electron mobility indicates a much reduced “die-off” at low temperature. Figure 3 compares the results of the MCF analysis and the

JEM_1021-S6

4/15/04

4:43 PM

Page 415

Characterization of Multiple Carriers in GaN Using Variable Magnetic-Field Hall Measurements

Fig. 5. Two-carrier MCF analysis for freestanding GaN, showing the effective conductivity of high mobility (bulk) electron and low mobility electron.

conduction from these two electrons. At most temperatures, the contribution of the low mobility carrier was too small to allow accurate determination of both the carrier concentration and the mobility. However, the “conductivity” of the lower mobility carrier was a robust result. Figure 5 illustrates the temperature dependence of the conductivity of both the lower and the higher mobility carriers. Though the contribution of the lower mobility carrier is much less significant than the interfacial layer of the previous sample, its effect becomes considerable below 80 K. Based on this result, MCF analysis was used to separate the lower mobility conductivity from the higher, allowing a more accurate determination of the variation in carrier concentration. The MCF results are compared to that resulting from single-field measurements on the same sample in Figs. 6 and 7. Figure 6 compares the mobilities for the bulk carrier. As can be seen, MCF analysis gives essentially the same mobilities at higher temperature but indicates a slight reduction in mobility at lower temperatures. Because NA is mainly determined by modeling of the low temperature mobility and depends only weakly on carrier concentration, both measurements indicate similar values with NA  2.2  1015 cm3 for MCF analysis and NA  1.8  1015 cm3 for single-field analysis. More important, though, is the effect on the “measured” carrier concentration as indicated in Fig. 7. The effect of the low mobility carrier in the analysis of the single-field, single carrier measurement strongly suggests the presence of two n-type dopants, one with ND  2.3  1016 cm3 and ED  24.4 meV and another with ND  2.7  1015 cm3 and ED  77.7 meV. In contrast, by separating out the lower mobility conduction, the carrier concentration is easily explainable with a single n-type impurity with ND  1.6  1016 cm3 and ED  27.1 meV.

415

Fig. 6. The mobility of the bulk electron in freestanding GaN, from a two-carrier MCF to the variable-field Hall data, compared with that obtained from single-field Hall measurements.

Fig. 7. The carrier concentration of the bulk electron in freestanding GaN, from a two-carrier MCF to the variable-field Hall data, compared with the single-field Hall concentration.

The origin of the lower mobility conductivity is not clear. One interesting result is suggestive. Initially, In contacts were applied to the Ga face of the sample and were ohmic at room temperature. Upon cooling, however, the contacts became highly nonohmic below 175 K. When changed to the N-polar face, the contacts were ohmic down to 30 K, where the sample became quite insulating, and our measurements were terminated. Thus, it may be that there was incomplete removal of the interfacial layer that occurred during growth, indicating more material needs to be removed from the N-polar face.

JEM_1021-S6

4/15/04

4:43 PM

Page 416

416

That is, incomplete removal of the heavily doped region occurring near the sapphire substrate during growth after separation would leave a more conductive N-polar surface, which would allow contacts to remain ohmic at lower temperatures. Another possibility is that damage was introduced on either surface during the reactive ion etching. Other possibilities include an accumulation layer caused by an N-face polarization charge16 or edge conduction— the samples were sawn into squares with no attempt to remove the resulting damage on the edges. For the 245-µm-thick sample studied, the sawn edges represent approximately 5% of the sample’s surface area. As such, it could be a significant source of conductivity. Irrespective of the origin, there is a distinct low-mobility conduction channel that must be accounted for to obtain correct analysis of the electrical properties of the sample. Further investigation will be made to try to identify its source. Unlike MCF, QMSA can measure the spread in mobility for a given electron in a sample. Such a continuous distribution of mobility for the higher mobility electron in the freestanding sample was shown in Fig. 4. In Fig. 8, the average value of the mobility as determined from QMSA, corresponding to the bulk electron, is shown for both samples. At higher temperatures, there was little spread in mobility. This is consistent with mobilities at temperatures 200 K being primarily limited by intrinsic lattice scattering.4 There was a much larger spread at lower temperatures where mobility is more influenced by extrinsic influences, such as defects and impurities. This spread is represented in Fig. 8 by the standard deviation of the QMSA spectrum at the peak mobility, indicating the absolute width of the QMSA

Swartz, Tompkins, Myers, Look, and Sizelove

peak. This suggests that the peak mobility for the bulk electrons in the Samsung sample ranges from roughly 4,000 cm2/Vs to 10,000 cm2/Vs, and thus, the layer mobility is nonuniform, most likely with depth. The MCF value, determined for the mobilities, clearly represents an average value for this sample. If the carrier concentration is reasonably uniform throughout the sample (not necessarily a valid assumption), the change in mobility is likely due to thickness-dependent changes in background acceptor concentrations or possibly defects. This should not be surprising as various studies indicate a continuously decreasing concentration of dislocations,17–19 impurities,20,21 deep level defects,22 and Ga vacancies18,23 with increasing HVPE-GaN layer thickness. For example, the study by Oila et al.18 indicates that the Ga vacancy concentration may decrease by a factor of 10 over the thickness typical of the freestanding HVPE sample. If Ga vacancies are the primary residual acceptors as suggested by that study, this would easily predict the large spread in mobility suggested by the QMSA results. SUMMARY Multiple carrier analysis of variable magnetic-field Hall measurements is essential to determine the “true” electrical properties of both HVPE samples investigated: a 30-µm-thick GaN layer on sapphire and a 245-µm-thick freestanding GaN layer. Ignoring the temperature dependence of the electrical properties of the interfacial layer in the sample on sapphire led to significant error in determining both the number of donor impurities and the activation energy of the primary donor impurity in the sample. Ignoring the presence of a small but finite lower mobility “surface” electron led to similar errors in interpreting the electrical properties of the freestanding sample. Perhaps the most important result is that QMSA of the variable-field Hall measurements indicates that both samples contain a large spread in electron mobility values, likely with depth. Thus, even the improved results based on modeling the MCF analysis obtained in this study should be viewed with some suspicion, as they clearly represent an average over an electrically inhomogeneous sample. ACKNOWLEDGEMENTS

Fig. 8. The average of the mobility, weighted by the carrier concentration, of the bulk electron peak from the QMSA of each sample with bars illustrating a range of one standard deviation above and below the mean.

The freestanding and as-grown HVPE samples were provided through the Wood–Witt program by S.S. Park and K.Y. Lee, Samsung Advanced Institute of Technology (Suwon, Korea), and by V. Dmitriev and K. Tsvetkov, TDI, Inc. (Silver Springs, MD), respectively. We thank T.A. Cooper, WSU, for the single-field Hall-effect measurements. The work at WSU was supported by ONR Grant No. N00014-03-1-0467 (monitored by C. Wood), AFOSR Grant No. F4962003-1-0197 (monitored by G. Witt), and United States Air Force Contract No. F33615-00-C-5402 (monitored by J. Brown). Work at West Virginia University was supported by ONR Grant Nos. N00014-02-1-0974 and N00014-01-1-0571, both monitored by C. Wood.

JEM_1021-S6

4/15/04

4:43 PM

Page 417

Characterization of Multiple Carriers in GaN Using Variable Magnetic-Field Hall Measurements

REFERENCES 1. S. Nakamura et al., Appl. Phys. Lett. 26, 461 (1975). 2. D.C. Reynolds, D.C. Look, B. Jogai, A.W. Saxler, S.S. Park, and J.Y. Han, Appl. Phys. Lett. 77, 2879 (2000). 3. Z.-Q. Fang, D.C. Look, P. Visconti, D.-F. Wang, C.-Z. Lu, F. Yun, H. Morkoç, S.S. Park, and K.Y. Lee, Appl. Phys. Lett. 78, 2178 (2001). 4. D.C. Look and J.R. Sizelove, Appl. Phys. Lett. 79, 1133 (2001). 5. E. Oh, S.K. Lee, S.S. Park, K.Y. Lee, L.J. Song, and J.Y. Han, Appl. Phys. Lett. 78, 273 (2001). 6. M.K. Kell, R.P. Vando, V.M. Phanse, L. Gorgens, O. Ambacher, and M. Stutzmann, Jpn. J. Appl. Phys. Part II 38, L217 (1998). 7. D.C. Look, R.L. Jones, X.L. Sun, L.J. Brillson, J.W. Ager, S.S. Park, J.H. Han, R.J. Molnar, and J.E. Maslar, J. Phys.: Condens. Matter 14, 13337 (2002). 8. W. Götz, J. Walker, L.T. Romano, N.M. Johnson, and R.J. Molnar, Mater. Res. Soc. Symp. 449, 525 (1997). 9. D.C. Look and R.J. Molnar, Appl. Phys. Lett. 70, 3377 (1997). 10. J.R. Meyer, C.A. Hoffman, F.J. Bartoli, D.A. Arnold, S. Sivananthan, and J.P. Faurie, Semicond. Sci. Technol. 8, 805 (1993). 11. A. Saxler, D.C. Look, S. Elhamri, J. Sizelove, W.C. Mitchell, C.M. Sung, S.S. Park, and K.Y. Lee, Appl. Phys. Lett. 78, 1873 (2001). 12. L.J. van der Pauw, Philips Technol. Rev. 20, 220 (1958).

417 13. I. Vurgaftman, J.R. Meyer, C.A. Hoffman, D. Redfern, J. Antoszewski, L. Farone, and J.R. Lindemuth, J. Appl. Phys. 84, 4966 (1998). 14. J.R. Meyer, C.A. Hoffman, F.J. Bartoli, D.A. Arnold, S. Sivananthan, and J.P. Faurie, Semicond. Sci. Technol. 8, 805 (1993). 15. D.L. Rode, Semicond. Semimet. 10, 1 (1975). 16. J.J. Harris, K.J. Lee, J.B. Webb, H. Tang, I. Harrison, L.B. Flannery, T.S. Cheng, and C.T. Foxon, Semicond. Sci. Technol. 15, 413 (2000). 17. Z.Q. Fang, D.C. Look, J. Jasinski, M. Benamara, Z. LilientalWeber, and R.J. Molnar, Appl. Phys. Lett. 78, 332 (2001). 18. J. Oila, J. Kivioja, V. Ranki, K. Saarinen, D.C. Look, R.J. Molnar, S.S. Park, S.K. Lee, and J.Y. Han, Appl. Phys. Lett. 82, 3433 (2003). 19. G. Nootz, A. Shulte, L. Chernyak, A. Osinsky, J. Jasinski, M. Benamara, and Z. Liliental-Weber, Appl. Phys. Lett. 80, 1355 (2002). 20. D.C. Look, C.E. Stutz, R.J. Molnar, K. Saarinen, and Z. Liliental-Weber, Solid State Commun. 117, 571 (2001). 21. X.L. Sun, S.H. Gross, L.J. Brillson, D.C. Look, and R.J. Molnar, J. Appl. Phys. 91, 6729 (2002). 22. A.Y. Polyakov, N.B. Smirnov, A.V. Govorkov, Z.Q. Fang, D.C. Look, R.J. Molnar, and A.V. Osinsky, J. Appl. Phys. 91, 6580 (2002). 23. L. Chernyak, A. Osinsky, G. Nootz, A. Schulte, J. Jasinski, M. Benamara, Z. Liliental-Weber, D.C. Look, and R.J. Molnar, Appl. Phys. Lett. 77, 2695 (2000).