Abstract
Methods of predicting the electronic structure of disordered semiconductor alloys involving mainly isoelectronic substitution are reviewed. Special emphasis is placed on analytical methods of studying currently available models of alloys. An approximate equation for the localization threshold of electronic states in the Lifshitz model is considered, and the inaccuracy of this equation is estimated. The contributions of the perturbation potential of an individual impurity and of crystal-lattice distortions in the vicinity of the impurity center are analyzed on the basis of the Faddeev equations. The contributions of intrinsic impurity potentials and volume effects to the formation of the electronic structure of semiconductor alloys are esti- mated. Methods of calculating matrix elements of the perturbation potentials of isoelectronic impurities in alloys with consideration for deformation effects are considered. The procedure of calculating the compositional dependence of the band gap of multicomponent alloys is described. A comparative analysis of various methods for predicting the formation of electronic states bound at individual isoelectronic impurities in semiconductors is conducted. The theory of the energy spectrum of charged impurities in isoelectronic alloys is presented.
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References
V. V. Emtsev and T. V. Mashovets, Impurities and Point Defects in Semiconductors (Radio i Svyaz’, Moscow, 1981) [in Russian].
H. van Haeringen, J. Math. Phys. 24, 1274 (1983).
K. B. Tolpygo, Sov. Phys. Solid State 11, 2304 (1969).
V. A. Telezhkin and K. B. Tolpygo, Sov. Phys. Solid State 19, 1773 (1977).
V. K. Bazhenov and V. I. Fistul’, Sov. Phys. Semicond. 18, 843 (1984).
I. M. Lifshitz, Sov. Phys. Usp. 7, 571 (1964).
G. F. Koster and J. C. Slater, Phys. Rev. 95, 1167 (1954).
J. C. Slater, Insulators, Semiconductors, Metals (McGraw-Hill, New York, 1967; Mir, Moscow, 1969), rus. p. 336.
I. M. Lifshits, S. A. Gredeskul, and L. A. Pastur, Sov. J. Low Temp. Phys. 2, 533 (1976).
I. M. Lifshits, S. A. Gredeskul, and L. A. Pastur, Introduction to the Theory of Disordered Systems (Moscow, Nauka, 1982) [in Russian].
L. A. Pastur, in Probability Theory, Mathematical Statistics, and Technical Cybernetics, Vol. 25 of Results of Science and Engineering (VINITI AN SSSR, Moscow, 1987), p. 3 [in Russian].
L. A. Pastur and A. L. Figotin, Spectra of Random and Almost-Periodic Operators (Springer, Berlin, 1992; Nauka, Moscow, 1991).
G. G. Sergeeva, Sov. Phys. Solid State 7, 1578 (1965).
A. Milnes, Deep Impurities in Semiconductors (Wiley, New York, 1973; Mir, Moscow, 1977).
J. Bourgoin and M. Lanno, Point Defects in Semiconductors 1: Theoretical Aspects (Springer, Berlin, 1983; Mir, Moscow, 1985).
J. Bourgoin and M. Lanno, Point Defects in Semiconductors 2: Experimental Aspects (Springer, Berlin, 1983; Mir, Moscow, 1985).
H. Matare, Defect Electronics in Semiconductors (Wiley-Intersci., New York, 1971; Mir, Moscow, 1974).
A. M. Stoneham, Theory of Defects in Solids (Clarendon, Oxford, 1985; Mir, Moscow, 1971), Vols. 1, 2.
S. V. Bulyarsky and V. V. Fistul’, Thermodynamics and Kinetics of Interacting Defects in Semiconductors (Nauka, Fizmatlit, Moscow, 1997) [in Russian].
M. Jaros, Adv. Phys. 29, 409 (1980).
S. T. Pantelides, Rev. Mod. Phys. 50, 797 (1978).
A. B. Roitsin, Sov. Phys. Semicond. 8, 1 (1974).
R. Rennie, Adv. Phys. 26, 285 (1977).
D. Chattopadhyay and H. J. Queisser, Rev. Mod. Phys. 53, 745 (1981).
F. Bassani, G. Iadonisi, and B. Preziosi, Rep. Progr. Phys. 37, 1099 (1974).
S. Albeverio, F. Gesztesy, R. Hoegh-Krohn, H. Holden, and P. Exner, Solvable Models in Quantum Mechanics (AMS, Providence, 2005).
S. Albeverio, J. E. Fenstad, R. Hoegh-Krohn, and T. Lindstrom, Nonstandard Methods in Stochastic Analysis and Mathematical Physics, Dover Books on Mathematics (Dover, 2009; Mir, Moscow, 1990).
Yu. N. Demkov and V. N. Ostrovskii, Method of ZeroRadius Potentials in Atomic Physics (Leningr. Univ., Leningrad, 1975) [in Russian].
V. B. Belyaev, Lectures in the Theory of Few-Particle Systems (Energoatomizdat, Moscow, 1986) [in Russian].
B. F. Haas, T. Frederico, B. V. Carlson, and F. B. Guimarães, Nucl. Phys. A 728, 379 (2003).
P. W. Anderson, Phys. Rev. 109, 1492 (1958).
J. Ziman, Models of Disorder: The Theoretical Physics of Homogeneously Disordered Systems (Cambridge Univ., Cambridge, New York, 1979; Mir, Moscow, 1982).
T. Ziman, Phys. Rev. B 26, 7066 (1982).
A. Eilmes and R. A. Römer, Phys. Status Solidi B 241, 2079 (2004).
J. M. Luttinger and R. Tao, Ann. Phys. (N.Y.) 145, 185 (1983).
P. Lloyd, J. Phys. C: Solid State Phys. 2, 1717 (1969).
J. T. Edwards and D. J. Thouless, J. Phys. C: Solid State Phys. 4, 453 (1971).
D. J. Thouless. Phys. Rep. 13, 93 (1974).
M. Saitoh, Phys. Lett. A 33, 44 (1970).
M. Saitoh, Progr. Theor. Phys. 45, 746 (1971).
F. Wegner, Z. Phys. B 44, 9 (1981).
F. Constantinescu, J. Fröhlich, and T. Spencer, J. Stat. Phys. 34, 571 (1984).
L. A. Pastur, Comm. Math. Phys. 75, 179 (1980).
F. Delyon and B. Souillard, Commun. Math. Phys. 94, 289 (1984).
W. Craig and B. Simon, Commun. Math. Phys. 90, 207 (1983).
D. Simon, M. Taylor, and T. Wolff, Phys. Rev. Lett. 54, 1589 (1985).
N. F. Mott, Adv. Phys. 16 (61), 49 (1967).
A. I. Baz’, Ya. B. Zel’dovich, and A. M. Perelomov, Scattering Reactions and Decays in Nonrelativistic Quantum Mechanics (Nauka, Moscow, 1971; Plenum, New York, 1975).
A. L. Efros, Sov. Phys. Usp. 21, 746 (1978).
M. V. Sadovskii, Sov. Phys. Usp. 24, 96 (1981).
V. L. Bonch-Bruevich, Sov. Phys. Usp. 27, 664 (1984).
V. L. Bonch-Bruevich, I. P. Zvyagin, R. Kaiper, A. G. Mironov, et al., Electronic Theory of Disordered Semiconductors (Nauka, Moscow, 1981) [in Russian].
T. C. Lubensky, Lect. Notes Phys. 149, 199 (1981).
K. B. Efetov, A. I. Larkin, and D. E. Khmel’nitskii, Sov. Phys. JETP 52, 568 (1980).
K. B. Efetov, Sov. Phys. JETP 55, 514 (1982).
K. B. Efetov, Adv. Phys. 32, 53 (1983).
K. B. Efetov, Supersymmetry in Disorder and Chaos (Cambridge Univ. Press, Cambridge, 1999).
R. Newton, Scattering Theory of Waves and Particles (Springer, Berlin, 1982; Mir, Moscow, 1969).
G. Ehrenreich and L. Schwartz, The Electronic Structure of Alloys, Solid State Physics, Vol. 31 (Academic Press, New York, San Francisco, London, 1976; Mir, Moscow, 1979).
A. Yu. Zakharov and Ya. Ya. Shcherbak, Sov. Phys. Semicond. 10, 461 (1976).
A. Yu. Zakharov and Ya. Ya. Shcherbak, Sov. Phys. Semicond. 13, 1112 (1979).
P. Soven, Phys. Rev. 156, 809 (1967).
F. Yonezawa, Progr. Theor. Phys. 31, 357 (1964).
F. Yonezawa and T. Matsubara, Progr. Theor. Phys. 35, 357 (1966); Progr. Theor. Phys. 35, 759 (1966).
F. Yonezawa, Progr. Theor. Phys. 40, 734 (1968); Progr. Theor. Phys. 39, 1076 (1968).
F. Yonezawa and R. Morigaki, Progr. Theor. Phys. Suppl., No. 53, 1 (1973).
T. Matsubara, Progr. Theor. Phys. Suppl., No. 46, 326 (1970).
G. L. Bir and G. E. Pikus, Symmetry and StainInduced Effects in Semiconductors (Nauka, Moscow, 1972; Wiley, New York, 1975).
A. Blacha, H. Presting, and M. Cardona, Phys. Status Solidi B 126, 11 (1984).
A. Yu. Zakharov and M. V. Kravchenko, Sov. Phys. Semicond. 16, 974 (1982).
A. Yu. Zakharov and M. V. Kravchenko, Sov. Phys. Solid State 26, 1585 (1984).
M. A. Krivoglaz, X-Ray and Neutron Diffraction in Nonideal Crystals (Nauk. dumka, Kiev, 1983; Springer, Berlin, 1996).
L. D. Faddeev, Mathematical Questions in the Quantum Theory of Scattering for a System of Three Particles, Tr. Matem. Inst. V. A. Steklova AN SSSR, Vol. 63 (Akad. Nauk SSSR, Moscow, Leningrad, 1963) [in Russian].
E. Schmid and H. Ziegelmann, The Quantum Mechanical Three-Body Problem, Vieweg Tracts in Pure and Applied Physics (Vieweg, Braunschweig, 1974; Nauka, Moscow, 1979).
A. Yu. Zakharov, Sov. Phys. Semicond. 9, 282 (1975).
A. Yu. Zakharov, Sov. Phys. Solid State 15, 864 (1975).
A. Yu. Zakharov and L. P. Mironenko, Ukr. Fiz. Zh. 35, 119 (1990).
A. Yu. Zakharov and L. P. Mironenko, Izv. Vyssh. Uchebn. Zaved., Ser. Fiz. 33 (3), 58 (1990).
Solids under High Pressure, Ed. by W. Paul and D. M. Warschauer (McGraw-Hill, New York, 1963; Mir, Moscow, 1966), p. 205.
P. I. Baranskii, V. P. Klochkov, and I. V. Potykevich, Semiconductor Electronics. The Manual (Nauk. Dumka, Kiev, 1975) [in Russian].
Physicochemical Properties of Semiconductor Materials, The Handbook (Nauka, Moscow, 1978) [in Russian].
Semiconductors and Semimetals (Academic Press, Elsevier, 1966–2013), vols. 1–89.
G. N. Watson, Quart. J. Math. (Oxford) 10, 266 (1939).
E. Montroll, in Applied Combinatorial Mathematics, Ed. by E. Beckenbach, Collection of Articles (Wiley, New York, 1964; Mir, Mosccow, 1968), p. 9.
G. S. Joyce, J. Phys. A: Math. Theor. 44, 315202 (2011).
R. A. Faulkner, Phys. Rev. 175, 991 (1968).
J. W. Allen, J. Phys. C: Solid State Phys. 4, 1936 (1971).
W. Czaja, Festkörperprobleme (Adv. Solid State Phys.) 11, 65 (1971).
A. Baldereschi and J. J. Hopfield, Phys. Rev. Lett. 28, 171 (1972).
C. A. Coulson, L. B. Redei, and D. Stocker, Proc. R. Soc. London A 270 (1342), 357 (1962).
L. B. Redei, Proc. R. Soc. London A 270 (1342), 383 (1962).
D. Stocker, Proc. R. Soc. London A 270 (1342), 397 (1962).
Yu. A. Bratashevskii, A. Yu. Zakharov, and Yu. M. Ivanchenko, Solid State Commun. 15, 1777 (1974).
F. Stern, in Solid State Physics, Vol. 15, Ed. by F. Seitz and D. Turnbull (Academic Press, New York, 1963), p. 300.
K. Hübner, Phys. Lett. 31, 365 (1970).
A. Yu. Zakharov and L. P. Mironenko, Ukr. Fiz. Zh. 34, 421 (1989).
P. Vogl, Adv. Electron. Electron Phys. 62, 101 (1984).
N. A. Goryunova, Solid Substitution Solutions in Compounds with ZnS Structure (Akad. Nauk SSSR, Moscow, 1955) [in Russian].
N. A. Goryunova, Complex Diamond-Like Semiconductors (Sov. Radio, Moscow, 1968) [in Russian].
A. B. Almazov, Electronic Properties of Semiconductor Solid Solutions (Nauka, Moscow, 1966) [in Russian].
Yu. M. Ivanchenko and A. A. Lisyanskii, Physica A 107, 567 (1981).
Yu. M. Ivanchenko, A. I. Kozinskaya, and A. A. Lisyanskii, Solid State Commun. 38, 297 (1981).
S. B. Borisov, Yu. A. Genenko, A. Yu. Zakharov, and Ya. Ya. Shcherbak, in Semiconductor Doping (Nauka, Moscow, 1982), p. 5 [in Russian].
A. Yu. Zakharov and Yu. M. Ivanchenko, Solid State Commun. 19, 533 (1976).
A. Yu. Zakharov and Yu. M. Ivanchenko, Sov. J. Low Temp. Phys. 4, 19 (1978).
A. Yu. Zakharov, Trans. Theory Stat. Phys. 37, 613 (2008).
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Dedicated to the memory of my Teachers, Prof. Yuli Mikhailovich Ivanchenko (December 18, 1938–December 26, 2014) and Corresponding Member of the Ukrainian Academy of Sciences, Prof. Kirill Borisovich Tolpygo (May 3, 1916–May 13, 1994).
Original Russian Text © A.Yu. Zakharov, 2015, published in Fizika i Tekhnika Poluprovodnikov, 2015, Vol. 49, No. 7, pp. 865–886.
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Zakharov, A.Y. Theory of the electronic structure of substitutional semiconductor alloys: Analytical approaches. Semiconductors 49, 843–866 (2015). https://doi.org/10.1134/S1063782615070246
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DOI: https://doi.org/10.1134/S1063782615070246