The effective density of randomly moving electrons and related characteristics of materials with degenerate electron gas

Abstract

Interpretation of the conductivity of metals, of superconductors in the normal state and of semiconductors with highly degenerate electron gas remains a significant issue if consideration is based on the classical statistics. This study is addressed to the characterization of the effective density of randomly moving electrons and to the evaluation of carrier diffusion coefficient, mobility, and other parameters by generalization of the widely published experimental results. The generalized expressions have been derived for various kinetic parameters attributed to the non-degenerate and degenerate electron gas, by analyzing a random motion of the single type carriers in homogeneous materials. The values of the most important kinetic parameters for different metals are also systematized and discussed. It has been proved that Einstein's relation between the diffusion coefficient and the drift mobility of electrons is held for any level of degeneracy if the effective density of randomly moving carriers is properly taken into account.