Study of the transport of charge carriers in materials with degenerate electroc gas

Abstract

This study is addressed to the stochastic description of the effective density of the randomly moving (RM) electrons in metals and other materials with degenerate electron gas. It is written in the accessible form for researchers, engineers and students without an extensive background of quantum mechanics of solid-state physics. The chapter begins with the interpretation of the basic transport characteristics of the metals, superconductors in the normal state, and very strongly doped semiconductors with degenerate electron gas. An application of the effective density of RM electrons leads one simply to explain the conductivity of metals, and the electron transport characteristics such as the average diffusion coefficient, the average mobility, the mean free path, and the electron scattering mechanisms in very wide temperature range. The generalized expressions for basic electron transport characteristics, which are valid for materials both with non-degenerate and degenerate electron gas, are presented. It is well known that electrons obey the Pauli principle and they are described by the Fermi-Dirac statistics, and using the total density of free valence electrons for estimation of transport characteristics of electrons in materials with degenerate electron gas is unacceptable with respect to Fermi-Dirac statistics, because all these characteristics are determined by RM electrons near the Fermi level energy. An application of the classical statistics leads to colossal errors in the estimation of transport characteristics of electrons in materials with degenerate electron gas. It is shown that the Einstein’s relation between the diffusion coefficient and drift mobility of RM electrons is held at any level of degeneracy of electron gas. The presented general expressions are applied for estimation of the carrier transport characteristics in the superconductor YBa2Cu3O7-x in the normal state, especially for description of the Hall-effect. It is shown that drift mobility of electrons in materials with degenerate electron gas can be tens or hundred times larger than the Hall mobility. The calculation results of the resistivity and other transport characteristics for elemental metals in temperature range from 1 K to 900 K are represented and compared with the experimental data.