Abstract
In cubic semiconductors the hole-mass ratio is small, which makes it possible to use the zero light-hole-mass limit. It was found that variational methods in this popular limit are not necessary to solve the Luttinger equation and not only the entire energy spectrum for the bound states of an acceptor and the eigenfunctions, including in momentum space, but also the behavior of the eigenfunctions at large radii can be determined to a high degree of accuracy. This approach made it possible to suggest comparatively simple relations for the lowest states of each series having different angular momenta, covering the entire range of possible mass ratios for semiconductors.
Similar content being viewed by others
References
J. M. Luttinger and W. Kohn, Phys. Rev. 97, 869 (1955).
J. M. Luttinger, Phys. Rev. 102, 1030 (1956).
D. Shechter, J. Phys. Chem. Solids 23, 237 (1962).
K. S. Mendelson and H. M. James, J. Phys. Chem. Solids 25, 729 (1964).
C. Kittel and A. H. Mitchell, Phys. Rev. 96, 1488 (1954).
E. O. Kane, J. Phys. Chem. Solids 1, 249 (1957).
L. V. Keldysh, Zh. Éksp. Teor. Fiz. 45, 364 (1963) [Sov. Phys. JETP 18, 253 (1964)].
V. I. Sheka and D. I. Sheka, Zh. Éksp. Teor. Fiz. 51, 1445 (1966) [Sov. Phys. JETP 24, 975 (1967)].
A. Baldereschi and N. O. Lipari, Phys. Rev. B 8, 2697 (1973).
A. Baldereschi and N. O. Lipari, Phys. Rev. B 9, 1525 (1974).
I. A. Merkulov and A. V. Rodina, Fiz. Tekh. Poluprovodn. 28, 321 (1994) [Sov. Phys. Semicond. 28, 195 (1994)].
Sh. M. Kogan and A. F. Polupanov, Zh. Éksp. Teor. Fiz. 80, 394 (1981) [Sov. Phys. JETP 53, 201 (1981)].
B. L. Gel’mont and M. I. D’yakonov, Fiz. Tekh. Poluprovodn. 5, 2191 (1971) [Sov. Phys. Semicond. 5, 1905 (1971)].
B. L. Gel’mont and M. I. D’yakonov, Zh. Éksp. Teor. Fiz. 62, 713 (1972) [Sov. Phys. JETP 35, 377 (1972)].
B. L. Gel’mont, V. I. Ivanov-Omskii, and M. I. Tsidil’kovskii, Usp. Fiz. Nauk 120, 337 (1976) [Sov. Phys. Usp. 19, 879 (1976)].
Yu. F. Berkovskaya, B. L. Gel’mont, and É. I. Tsidil’kovskii, Fiz. Tekh. Poluprovodn. 22, 855 (1988) [Sov. Phys. Semicond. 22, 539 (1988)].
B. L. Gel’mont and A. V. Rodina, Fiz. Tekh. Poluprovodn. 25, 2189 (1991) [Sov. Phys. Semicond. 25, 1319 (1991)].
L. D. Landau and E. M. Lifshitz, Quantum Mechanics (Pergamon Press, New York, 1974; Russian original, 4th ed., Nauka, Moscow, 1989).
Handbook of Mathematical Functions, edited by M. Abramowitz and I. A. Stegun (National Bureau of Standards Applied Mathematics Series, 1964; Nauka, Moscow, 1979).
I. S. Gradshtein and I. M. Ryzhik, Table of Integrals, Series, and Products (Academic Press, New York, 1980; Russian original, GIFML, Moscow, 1962).
Y. T. Rebane, Phys. Rev. B 48, 11772 (1993).
V. I. Sheka and D. I. Sheka, Ukr. Fiz. Zh. 14, 720 (1969).
A. V. Malyshev, I. A. Merkulov, and A. V. Rodina, Fiz. Tverd. Tela (St. Petersburg) 40, 1002 (1998) [Phys. Solid State 40, 917 (1998)].
Author information
Authors and Affiliations
Additional information
Fiz. Tverd. Tela (St. Petersburg) 41, 1556–1563 (September 1999)
Rights and permissions
About this article
Cite this article
Linnik, T.L., Sheka, V.I. Acceptor states in cubic semiconductors having a large hole-mass ratio. Phys. Solid State 41, 1425–1432 (1999). https://doi.org/10.1134/1.1131026
Received:
Issue Date:
DOI: https://doi.org/10.1134/1.1131026