Abstract
A solution to the Liouville equation for a one-electron density matrix in relation to a homogeneous semiconductor in a magnetic field is obtained using perturbation theory. Expressions for the conductivity tensor and electron-momentum relaxation rate are obtained for the case of scattering by ionized impurities. These expressions provide a sufficiently accurate description of the concentration and magnetic field dependences of the longitudinal conductivity of a nondegenerate electron gas in the quantum limit that have been observed in some studies. No explanation for these dependences is found in the context of the current theory of magnetoresistivity. An explanation of the temperature dependences of the components of the conductivity tensor is suggested for a degenerate electron gas in magnetic fields that correspond to the quantum limit.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
E. N. Adams and T. D. Holstein, J. Phys. Chem. 10, 254 (1959); in Problems in Quantum Theory of Irreversible Processes (Inostrannaya Literatura, Moscow, 1961), p. 255.
R. Kubo, H. Hesegawa, and N. Hashitdume, J. Phys. Soc. Jpn. 14, 56 (1959); in Problems in Quantum Theory of Irreversible Processes (Inostrannaya Literatura, Moscow, 1961), p. 89.
P. N. Agryes and L. M. Roth, Phys. Chem. Solids 12, 89 (1959).
S. S. Murzin, Usp. Fiz. Nauk 170, 387 (2000) [Phys. Usp. 43, 349 (2000)].
V. F. Gantmakher and I. B. Levinson, Scattering of Carriers in Metals and Semiconductors (Nauka, Moscow, 1984; North-Holland, Amsterdam, 1987), Chap. 14.
S. S. Murzin and P. V. Popov, Pis’ma Zh. Éksp. Teor. Fiz. 58, 280 (1993) [JETP Lett. 58, 289 (1993)].
V. É. Kaminskii, Fiz. Tekh. Poluprovodn. (St. Petersburg) 36, 1360 (2002) [Semiconductors 36, 1276 (2002)].
V. É. Kaminskii, Phys. Rev. B 67, 085201 (2003).
L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics, Vol. 3: Quantum Mechanics: Non-Relativistic Theory, 4th ed. (Nauka, Moscow, 1989; Pergamon, Oxford, 1977), Chap. 15.
A. I. Akhiezer and S. V. Peletminskii, Methods of Statistical Physics (Nauka, Moscow, 1977; Pergamon, Oxford, 1981), Chaps. 3–5.
A. I. Ansel’m, Introduction to the Theory of Semiconductors (Nauka, Moscow, 1977), Chap. 7.
L. M. Falicov and M. Quevas, Phys. Rev. 164, 1025 (1967).
Author information
Authors and Affiliations
Additional information
__________
Translated from Fizika i Tekhnika Poluprovodnikov, Vol. 39, No. 5, 2005, pp. 543–549.
Original Russian Text Copyright © 2005 by Kaminskii.
Rights and permissions
About this article
Cite this article
Kaminskii, V.E. The conductivity tensor and frequency of electron momentum relaxation in the case of scattering by ionized impurities in a magnetic field: The density matrix method. Semiconductors 39, 514–520 (2005). https://doi.org/10.1134/1.1923556
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1134/1.1923556