Theory of Electrical Resistance with Simple Application to Hot Electron Problem

Abstract

A method is proposed to derive the electrical resistance from calculating an average frictional force exerted on a conduction electron system of a given drift velocity., which is ·in contrast with the customary method by which the electrical conductivity is derived from calculating an average drift velocity of that system in a given driving field. It is shown that, except for the perfectly degenerate case, a slight difference arises in the results of the two methods. The reason for it is discussed. Then an energy transfer problem in that system is considered to study a non-Ohmic effect, and Shockley's treatment of hot electron problem is shown to be consistent provided m*V2/KT. is much smaller than unity, which is the case in practice, where m* is the iso­ tropic effective electron mass, V the drift velocity, K the Boltzmann constant and T. the electron temperature. It is further pointed out that Fourier components of scattering potentials, ·which are essential for qualitative features of related kinetic coefficients especially in non-degenerate cases, are only imperfectly known at present.