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Excitation spectrum of point defects in semiconductors studied by time-dependent density functional theory

Published online by Cambridge University Press:  24 January 2012

Adam Gali
Adam Gali*
Affiliation:
Institute for Solid State Physics and Optics, Wigner Research Center for Physics, Hungarian Academy of Sciences, Budapest, H-1525; and Department of Atomic Physics, Budapest University of Technology and Economics, Budapest, H-1111, Hungary
*
a)Address all correspondence to this author. e-mail: agali@eik.bme.hu
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Abstract

A common fingerprint of the electrically active point defects in semiconductors is the transition among their localized defect states upon excitation, which may result in characteristic absorption- or photoluminescence spectrum. Identification of such point defects by means of density functional theory (DFT) calculations with traditional (semi) local functionals suffers from two problems: the “band gap error” and the many-body nature of the electron-hole interaction of the excited state. We show that non local hybrid density functionals may effectively mimic the quasiparticle correction of the band edges and the defect levels within the band gap in group-IV semiconductors, thus they can effectively heal the “band gap error.” The electron-hole interaction can be calculated by time-dependent DFT (TD-DFT) method. Here, we apply TD-DFT on three topical examples: nitrogen-vacancy defect in diamond, silicon-vacancy and divacancy defects in silicon carbide that are candidates in effective development of solid-state quantum bits.

Keywords

DefectsNanostructurePhotoemission

Information

Type
Invited Feature Paper
Information
Journal of Materials Research , Volume 27 , Issue 6 , 28 March 2012 , pp. 897 - 909
Copyright
Copyright © Materials Research Society 2012

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References

REFERENCES

1.de Walle, C.G.V. and Neugebauer, J.: First-principles calculations for defects and impurities: Applications to III-nitrides. J. Appl. Phys. 95, 3851–3879 (2004).CrossRefGoogle Scholar
2.Estreicher, S.K., Backlund, D., Gibbons, T.M., and Doçaj, A.: Vibrational properties of impurities in semiconductors. Modell. Simul. Mater. Sci. Eng. 17, 084006 (2009).CrossRefGoogle Scholar
3.Blöchl, P.E.: First-principles calculations of defects in oxygen-deficient silica exposed to hydrogen. Phys. Rev. B Condens. Matter 62, 6158 (2000).CrossRefGoogle Scholar
4.Son, N.T., Carlsson, P., ul Hassan, J., Janzén, E., Umeda, T., Isoya, J., Gali, A., Bockstedte, M., Morishita, N., Ohshima, T., and Itoh, H.: Divacancy in 4H-SiC. Phys. Rev. Lett. 96, 055501 (2006).CrossRefGoogle ScholarPubMed
5.Umeda, T., Son, N.T., Isoya, J., Janzén, E., Ohshima, T., Morishita, N., Itoh, H., Gali, A., and Bockstedte, M.: Identification of the carbon antisite-vacancy pair in 4H-SiC. Phys. Rev. Lett. 96, 145501 (2006).CrossRefGoogle ScholarPubMed
6.Ceperley, D.M. and Alder, B.J.: Ground state of the electron gas by a stochastic method. Phys. Rev. Lett. 45, 566 (1980).CrossRefGoogle Scholar
7.Perdew, J.P. and Zunger, A.: Self-interaction correction to density-functional approximations for many–electron systems. Phys. Rev. B Condens. Matter 23, 5048 (1981).CrossRefGoogle Scholar
8.Perdew, J.P. and Wang, Y.: Accurate and simple analytic representation of the electron-gas correlation energy. Phys. Rev. B Condens. Matter 45, 13244–13249 (1992).CrossRefGoogle ScholarPubMed
9.Perdew, J.P., Burke, K., and Ernzerhof, M.: Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865–3868 (1996).CrossRefGoogle ScholarPubMed
10.Deák, P.: Modeling of defects in solids. Phys. Status Solidi B 217, 9 (2000).3.0.CO;2-6>CrossRefGoogle Scholar
11.Baraff, G.A. and Schlüter, M.: Calculation of the total energy of charged point defects using the Green’s-function technique. Phys. Rev. B Condens. Matter 30, 1853 (1984).CrossRefGoogle Scholar
12.Aradi, B., Gali, A., Deák, P., Lowther, J.E., Son, N.T., Janzén, E., and Choyke, W.J.: Ab initio density-functional supercell calculations of hydrogen defects in cubic SiC. Phys. Rev. B Condens. Matter 63, 245202 (2001).CrossRefGoogle Scholar
13.Deák, P., Frauenheim, T., and Gali, A.: Limits of the scaled shift correction to levels of interstitial defects in semiconductors. Phys. Rev. B Condens. Matter 75, 153204 (2007).CrossRefGoogle Scholar
14.Hedin, L. and Lundqvist, S.: Solid State Physics. (Academic, 23, New York, NY, 1969).Google Scholar
15.Furthmüller, J., Cappellini, G., Weissker, H.C., and Bechstedt, F.: GW self-energy calculations for systems with huge supercells. Phys. Rev. B Condens. Matter 66, 045110 (2002).CrossRefGoogle Scholar
16.Ma, Y., Rohlfing, M., and Gali, A.: Excited states of the negatively charged nitrogen-vacancy color center in diamond. Phys. Rev. B Condens. Matter 81, 041204 (2010).CrossRefGoogle Scholar
17.Bockstedte, M., Marini, A., Pankratov, O., and Rubio, A.: Many–Body effects in the excitation spectrum of a defect in SiC. Phys. Rev. Lett. 105, 026401 (2010).CrossRefGoogle ScholarPubMed
18.Gali, A., Deák, P., Ordejón, P., Son, N.T., Janzén, E., and Choyke, W.J.: Aggregation of carbon interstitials in silicon carbide: A theoretical study. Phys. Rev. B Condens. Matter 68, 125201 (2003).CrossRefGoogle Scholar
19.Gali, A., Deák, P., Rauls, E., Son, N.T., Ivanov, I.G., Carlsson, F.H.C., Janzén, E., and Choyke, W.J.: Correlation between the antisite pair and the DI center in SiC. Phys. Rev. B Condens. Matter 67, 155203 (2003).CrossRefGoogle Scholar
20.Deák, P., Gali, A., Sólyom, A., Buruzs, A., and Frauenheim, T.: Electronic structure of boron-interstitial clusters in silicon. J. Phys. Condens. Matter 17, S2141 (2005).CrossRefGoogle Scholar
21.Knaup, J.M., Deák, P., Frauenheim, T., Gali, A., Hajnal, Z., and Choyke, W.J.: Defects in SiO2 as the possible origin of near interface traps in the SiC/SiO2 system: A systematic theoretical study. Phys. Rev. B Condens. Matter 72, 115323 (2005).CrossRefGoogle Scholar
22.Knaup, J.M., Deák, P., Frauenheim, T., Gali, A., Hajnal, Z., and Choyke, W.J.: Theoretical study of the mechanism of dry oxidation of 4H -SiC. Phys. Rev. B Condens. Matter 71, 235321 (2005).CrossRefGoogle Scholar
23.Gali, A., Son, N.T., and Janzén, E.: Electrical characterization of metastable carbon clusters in SiC: A theoretical study. Phys. Rev. B Condens. Matter 73, 033204 (2006).CrossRefGoogle Scholar
24.Gali, A.: Ab initio study of nitrogen and boron substitutional impurities in single-wall SiC nanotubes. Phys. Rev. B Condens. Matter 73, 245415 (2006).Google Scholar
25.Deák, P., Buruzs, A., Gali, A., and Frauenheim, T.: Strain-free polarization superlattice in silicon carbide: A theoretical investigation: Phys. Rev. Lett. 96, 236803 (2006).CrossRefGoogle ScholarPubMed
26.Gali, A., Hornos, T., Son, N.T., Janzén, E., and Choyke, W.J.: Ab initio supercell calculations on aluminum-related defects in SiC. Phys. Rev. B Condens. Matter 75, 045211 (2007).CrossRefGoogle Scholar
27.Rurali, R., Aradi, B., Frauenheim, T., and Gali, A.: Accurate single-particle determination of the band gap in silicon nanowires. Phys. Rev. B Condens. Matter 76, 113303 (2007).CrossRefGoogle Scholar
28.Saunders, V.R., Dovesi, R., Roetti, C., Causá, M., Harrison, N.M., Orlando, R., and Zicovich-Wilson, C.M.: CRYSTAL98 User’s Manual (University of Torino, Torino, 1998).Google Scholar
29.Becke, A.D.: Density-functional thermochemistry. IV. A new dynamical correlation functional and implications for exact-exchange mixing. J. Chem. Phys. 104, 1040–1046 (1996).CrossRefGoogle Scholar
30.Ernzerhof, M. and Scuseria, G.E.: Assessment of the Perdew–Burke–Ernzerhof exchange-correlation functional. J. Chem. Phys. 110, 5029–5036 (1999).CrossRefGoogle Scholar
31.Heyd, J., Scuseria, G.E., and Ernzerhof, M.: Hybrid functionals based on a screened Coulomb potential. J. Chem. Phys. 118, 8207–8215 (2003).CrossRefGoogle Scholar
32.Heyd, J. and Scuseria, G.E.: Assessment and validation of a screened Coulomb hybrid density functional. J. Chem. Phys. 120, 7274–7280 (2004).CrossRefGoogle ScholarPubMed
33.Kresse, G. and Hafner, J.: Ab initio molecular-dynamics simulation of the liquid-metal–amorphous-semiconductor transition in germanium. Phys. Rev. B Condens. Matter 49, 14251 (1994).CrossRefGoogle ScholarPubMed
34.Kresse, G. and Furthmüller, J.: Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B Condens. Matter 54, 11169 (1996).CrossRefGoogle ScholarPubMed
35.Giannozzi, P., Baroni, S., Bonini, N., Calandra, M., Car, R., Cavazzoni, C., Ceresoli, D., Chiarotti, G.L., Cococcioni, M., Dabo, I., Dal Corso, A., de Gironcoli, S., Fabris, S., Fratesi, G., Gebauer, R., Gerstmann, U., Gougoussis, C., Kokalj, A., Lazzeri, M., Martin-Samos, L., Marzari, N., Mauri, F., Mazzarello, R., Paolini, S., Pasquarello, A., Paulatto, L., Sbraccia, C., Scandolo, S., Sclauzero, G., Seitsonen, A.P., Smogunov, A., Umari, P., and Wentzcovitch, R.M.: QUANTUM ESPRESSO: A modular and open-source software project for quantum simulations of materials. J. Phys. Condens. Matter 21, 395502 (2009).CrossRefGoogle ScholarPubMed
36.Marsman, M., Paier, J., Stroppa, A., and Kresse, G.: Hybrid functionals applied to extended systems. J. Phys. Condens. Matter 20, 064201 (2008).CrossRefGoogle ScholarPubMed
37.Wadehra, A., Nicklas, J.W., and Wilkins, J.W.: Band offsets of semiconductor heterostructures: A hybrid density functional study. Appl. Phys. Lett. 97, 092119 (2010).CrossRefGoogle Scholar
38.Deák, P., Aradi, B., Frauenheim, T., Janzén, E., and Gali, A.: Accurate defect levels obtained from the HSE06 range-separated hybrid functional. Phys. Rev. B Condens. Matter 81, 153203 (2010).CrossRefGoogle Scholar
39.Komsa, H.P., Broqvist, P., and Pasquarello, A.: Alignment of defect levels and band edges through hybrid functionals: Effect of screening in the exchange term. Phys. Rev. B Condens. Matter 81, 205118 (2010).CrossRefGoogle Scholar
40.Casida, M.E.: All-Electron Local and Gradient-Corrected Density-Functional Calculations of Nan Dipole Polarizabilities for n=1-6. In Recent Advances in Density Functional Theory; Chong, D.P., ed, World Scientific: Singapore, 1995; p. 155.CrossRefGoogle Scholar
41.Reining, L., Olevano, V., Rubio, A., and Onida, G.: Excitonic effects in solids described by time-dependent density-functional theory. Phys. Rev. Lett. 88, 066404 (2002).CrossRefGoogle ScholarPubMed
42.Onida, G., Reining, L., and Rubio, A.: Electronic excitations: Density-functional versus many-body Green’s-function approaches. Rev. Mod. Phys. 74, 601–659 (2002).CrossRefGoogle Scholar
43.Uchino, T., Takahashi, M., and Yoko, T.: Structure and formation mechanism of Ge E′ center from divalent defects in Ge-doped SiO2 glass. Phys. Rev. Lett. 84, 1475–1478 (2000).CrossRefGoogle Scholar
44.Raghavachari, K., Ricci, D., and Pacchioni, G.: Optical properties of point defects in SiO2 from time-dependent density functional theory. J. Chem. Phys. 116, 825–831 (2002).CrossRefGoogle Scholar
45.Zyubin, A.S., Mebel, A.M., and Lin, S.H.: Photoluminescence of oxygen-containing surface defects in germanium oxides: A theoretical study. J. Chem. Phys. 123, 044701 (2005).CrossRefGoogle ScholarPubMed
46.Zyubin, A.S., Mebel, A.M., Hayashi, M., Chang, H.C., and Lin, S.H.: Quantum chemical modeling of photoadsorption properties of the nitrogen-vacancy point defect in diamond. J. Comput. Chem. 30, 131 (2009).CrossRefGoogle ScholarPubMed
47.Zyubin, A.S., Mebel, A.M., Hayashi, M., Chang, H.C., and Lin, S.H.: Quantum chemical modeling of photoabsorption properties of two- and three-nitrogen vacancy point defects in diamond. J. Phys. Chem. C 113, 10432–10440 (2009).CrossRefGoogle Scholar
48.Paier, J., Marsman, M., and Kresse, G.: Dielectric properties and excitons for extended systems from hybrid functionals. Phys. Rev. B Condens. Matter 78, 121201 (2008).CrossRefGoogle Scholar
49.Blöchl, P.E.: Projector augmented-wave method. Phys. Rev. B Condens. Matter 50, 17953 (1994).CrossRefGoogle ScholarPubMed
50.Kresse, G. and Joubert, D.: From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B Condens. Matter 59, 1758 (1999).CrossRefGoogle Scholar
51.Gali, A., Fyta, M., and Kaxiras, E.: Ab initio supercell calculations on nitrogen-vacancy center in diamond: Electronic structure and hyperfine tensors. Phys. Rev. B Condens. Matter 77, 155206 (2008).CrossRefGoogle Scholar
52.Sanchéz-Portal, D., Ordejón, P., Artacho, E., and Soler, J.M.: Density-functional method for very large systems with LCAO basis sets. Int. J. Quantum Chem. 65, 453 (1997).3.0.CO;2-V>CrossRefGoogle Scholar
53.Troullier, N. and Martins, J.L.: Efficient pseudopotentials for plane-wave calculations. Phys. Rev. B Condens. Matter 43, 1993 (1991).CrossRefGoogle ScholarPubMed
54.Gali, A., Janzén, E., Deák, P., Kresse, G., and Kaxiras, E.: Theory of spin-conserving excitation of the N–V– center in diamond. Phys. Rev. Lett. 103, 186404 (2009).CrossRefGoogle Scholar
55.Ahlrichs, R., Bär, M., Häser, M., Horn, H., and Kölmel, C.: Electronic structure calculations on workstation computers: The program system turbomole. Chem. Phys. Lett. 162, 169 (1989).CrossRefGoogle Scholar
56.Schuchardt, K.L., Didier, B.T., Elsethagen, T., Sun, L., Gurumoorthi, V., Chase, J., Li, J., and Windus, T.L.. Basis set exchange: A community database for computational sciences. J. Chem. Inf. Model. 47, 1045 (2007).CrossRefGoogle ScholarPubMed
57.Gruber, A., Drabenstedt, A., Tietz, C., Fleury, L., Wrachtrup, J., and Borczyskowski, C.: Scanning confocal optical microscopy and magnetic resonance on single defect centers. Science 276, 2012 (1997).CrossRefGoogle Scholar
58.Drabenstedt, A., Fleury, L., Tietz, C., Jelezko, F., Kilin, S., Nizovtzev, A., and Wrachtrup, J.: Low-temperature microscopy and spectroscopy on single defect centers in diamond. Phys. Rev. B Condens. Matter 60, 11503 (1999).CrossRefGoogle Scholar
59.Jelezko, F., Popa, I., Gruber, A., Tietz, C., Wrachtrup, J., Nizovtsev, A., and Kilin, S.: Single spin states in a defect center resolved by optical spectroscopy. Appl. Phys. Lett. 81, 2160 (2002).CrossRefGoogle Scholar
60.Jelezko, F., Gaebel, T., Popa, I., Gruber, A., and Wrachtrup, J.: Observation of coherent oscillations in a single electron spin. Phys. Rev. Lett. 92, 076401 (2004).CrossRefGoogle Scholar
61.Jelezko, F., Gaebel, T., Popa, I., Dunham, M., Gruber, A., and Wrachtrup, J.: Observation of coherent oscillation of a single nuclear spin and realization of a two-qubit conditional quantum gate. Phys. Rev. Lett. 93, 130501 (2004).CrossRefGoogle ScholarPubMed
62.Epstein, R.J., Mendoza, F., Kato, Y.K., and Awschalom, D.D.: Anisotropic interactions of a single spin and dark-spin spectroscopy in diamond. Nat. Phys. 1, 94 (2005).CrossRefGoogle Scholar
63.Hanson, R., Mendosa, F.M., Epstein, R.J., and Awschalom, D.D.: Polarization and readout of coupled single spins in diamond. Phys. Rev. Lett. 97, 087601 (2006).CrossRefGoogle ScholarPubMed
64.Brouri, R., Beveratos, A., Poizat, J.P., and Gragier, P.: Photon antibunching in the fluorescence of individual color centers in diamond. Opt. Lett. 25, 1294 (2000).CrossRefGoogle ScholarPubMed
65.Beveratos, A., Brouri, R., Gacoin, T., Poizat, J.P., and Grangier, P.: Nonclassical radiation from diamond nanocrystals. Phys. Rev. A: At. Mol. Opt. Phys. 64, 061802(R) (2002).CrossRefGoogle Scholar
66.Childress, L., Taylor, J.M., Sørensen, A.S., and Lukin, M.D.: Fault-tolerant quantum communication based on solid-state photon emitters. Phys. Rev. Lett. 96, 070504 (2006).CrossRefGoogle ScholarPubMed
67.Jiang, L., Hodges, J.S., Maze, J.R., Maurer, P., Taylor, J.M., Cory, D.G., Hemmer, P.R., Walsworth, R.L., Yacoby, A., Zibrov, A.S., and Lukin, M.D.: Repetitive readout of a single electronic spin via quantum logic with nuclear spin ancillae. Science 326, 272 (2009).CrossRefGoogle ScholarPubMed
68.Childress, L., Gurudev Dutt, M.V., Taylor, J.M., Zibrov, A.S., Jelezko, F., Wrachtrup, J., Hemmer, P.R., and Lukin, M.D.: Coherent dynamics of coupled electron and nuclear spinqubits in diamond. Science 314, 281 (2006).CrossRefGoogle Scholar
69.Gurudev Dutt, M.V., Childress, L., Jiang, L., Togan, E., Maze, J., Jelezko, F., Zibrov, A.S., Hemmer, P.R., and Lukin, M.D.: Quantum register based on individual electronic and nuclear spin qubits in diamond. Science 316, 312 (2007).Google Scholar
70.du Preez, L.: Ph.D. Dissertation, University of Witwatersrand, (1965).Google Scholar
71.Davies, G. and Hamer, M.F.: Optical studies of the 1.945 eV Vibronic band in diamond. Proc. R. Soc. London Ser. A 348, 285 (1976).Google Scholar
72.Loubser, J.H.N. and van Wyk, J.P.: Electron Spin Resonance in Annealed Type 1b Diamond. (Diamond Research (London), London, 1977; p. 4–7).Google Scholar
73.Loubser, J.H.N. and van Wyk, J.A.: Electron spin resonance in the study of diamond. Rep. Prog. Phys. 41, 1201 (1978).CrossRefGoogle Scholar
74.Collins, A.T.: Luminescence decay time of the 1.945 eV centre in type Ib diamond. J. Phys. C: Solid State Phys. 16, 2177 (1983).CrossRefGoogle Scholar
75.Goss, J.P., Jones, R., Breuer, S.J., Briddon, P.R., and Öberg, S.: The twelve- line 1.682 eV luminescence center in diamond and the vacancy—silicon complex. Phys. Rev. Lett. 77, 3041 (1996).CrossRefGoogle ScholarPubMed
76.Larsson, J.A. and Delaney, P.: Electronic structure of the nitrogen-vacancy center in diamond from first-principles theory. Phys. Rev. B Condens. Matter 77, 165201 (2008).CrossRefGoogle Scholar
77.Watts, R.K.: Point Defects in Crystals (Wiley-Interscience Publication, New York, 1977).CrossRefGoogle Scholar
78.Weber, J.R., Koehl, W.F., Varley, J.B., Janotti, A., Buckley, B.B., de Walle, C.G.V., and Awschalom, D.D.: Quantum computing with defects. Proc. Natl. Acad. Sci. U S A 107, 8513–8518 (2010).CrossRefGoogle ScholarPubMed
79.Vörös, M. and Gali, A.: Optical absorption of diamond nanocrystals from ab initio density-functional calculations. Phys. Rev. B Condens. Matter 80, 161411 (2009).CrossRefGoogle Scholar
80.Sörman, E., Son, N.T., Chen, W.M., Kordina, O., Hallin, C., and Janzén, E.: Silicon vacancy related defect in 4H and 6H SiC. Phys. Rev. B Condens. Matter 61, 2613–2620 (2000).CrossRefGoogle Scholar
81.Baranov, P.G., Bundakova, A.P., Soltamova, A.A., Orlinskii, S.B., Borovykh, I.V., Zondervan, R., Verberk, R., and Schmidt, J.: Silicon vacancy in SiC as a promising quantum system for single-defect and single-photon spectroscopy. Phys. Rev. B Condens. Matter 83, 125203 (2011).CrossRefGoogle Scholar
82.Mizuochi, N., Yamasaki, S., Takizawa, H., Morishita, N., Ohshima, T., Itoh, H., and Isoya, J.: Continuous-wave and pulsed EPR study of the negatively charged silicon vacancy with S = 3/2 and C3ν symmetry in n -type 4H–SiC. Phys. Rev. B Condens. Matter 66, 235202 (2002).CrossRefGoogle Scholar
83.Mizuochi, N., Yamasaki, S., Takizawa, H., Morishita, N., Ohshima, T., Itoh, H., Umeda, T., and Isoya, J.: Spin multiplicity and charge state of a silicon vacancy (T V2a) in 4H -SiC determined by pulsed ENDOR. Phys. Rev. B Condens. Matter 72, 235208 (2005).CrossRefGoogle Scholar
84.Isono, H., Tajima, M., Hoshino, N., and Sugimoto, H.: Rapid Characterization of SiC Crystals by Full-Wafer Photoluminescence Imaging under Below-Gap Excitation. Mater. Sci. Forum 600–603, 545 (2009).Google Scholar
85.Janzén, E., Gali, A., Carlsson, P., Gällström, A., Magnusson, B., and Son, N.T.: The silicon vacancy in SiC. Physica B 404, 4354 (2009).CrossRefGoogle Scholar
86.Janzén, E., Gali, A., Henry, A., Ivanov, I.G., Magnusson, B., and Son, N.T.: Defects in SiC. in Defects in Microelectronic Materials and Devices Fleetwood, D.M., Pantelides, S.T., and Schrimpf, R.D., eds, Taylor & Francis Group: Boca Raton, FL, 2009; p. 615. Chapter 21.Google Scholar
87.Magnusson, B. and Janzén, E.: Optical characterization of deep level defects in SiC. Mater. Sci. Forum 483–485, 341 (2005).CrossRefGoogle Scholar
88.Lowther, J.E.: Excited states of the vacancy in diamond. Phys. Rev. B Condens. Matter 48, 11592–11601 (1993).CrossRefGoogle ScholarPubMed
89.Vörös, M., Deák, P., Frauenheim, T., and Gali, A.: The absorption spectrum of hydrogenated silicon carbide nanocrystals from ab initio calculations. Appl. Phys. Lett. 96, 051909 (2010).CrossRefGoogle Scholar
90.Madelung, O., ed: Semiconductors. Group IV Elements and II-V Compounds, (Data in Science and Technology) (Springer, Berlin, 1991).Google Scholar
91.Levinshtein, M.E., Rumyantsev, S.L., and Shur, M.S., eds: Properties of Advanced Semiconductor Materials: GaN, AlN, InN, BN, SiC, and SiGe (John Wiley and Sons, New York, NY, 2001).Google Scholar