A general review of drift mobility, diffusion coefficient of randomly moving charge carriers in metals and other materials with degenerate electron gas

Abstract

In this short review some aspects of applications of free electron theory on the ground of the Fermi statistics will be analysed. There it is an intention to attempt somebody’s attention to problems in widespread literature of interpretation of conductivity of metals, superconductor in the normal state and semiconductors with degenerate electron gas. In literature there are many cases when to these materials the classical statistics is applied. It is well known that the electron heat capacity and thermal noise (and as a consequence the electrical conductivity) are determined by randomly moving electrons, which energy is close to the Fermi energy level, and the other part of electrons, which energy is well below the Fermi level cannot be scattered and change its energy. Therefore, there was tried as simple as possible on the ground of Fermi distribution, and on random motion of charge carriers, and on the well-known experimental results to take general expressions for various kinetic parameters which are applicable for materials both without and with degenerate electron gas. It is shown, that drift mobility of randomly moving charge carriers, depending on the degree degeneracy, can considerably exceed the Hall mobility. It also is shown that the Einstein relation between the diffusion coefficient and the drift mobility of charge carriers is valid at any degree of degeneracy. There are presented the main kinetic parameter values for elemental metals.