Study of Balance Equations for Hot-Electron Transport in an Arbitrary Energy Band (III)

TL;DR

This paper revises and extends previous calculations of hot-electron transport by using a different initial state, deriving new distribution functions, and numerically analyzing nonlinear resistance in a degenerate electron gas at high electric fields.

Contribution

It introduces a new approach to calculating electron distribution functions and nonlinear resistance, improving accuracy at high electric fields.

Findings

New closed-form expression for electron distribution function.

Significant differences in resistance calculations at high electric fields.

Enhanced understanding of high-field hot-electron transport.

Abstract

By choosing an electron gas resting instead of drifting in the laboratory coordinate system as the initial state, the first order perturbation calculation of the previous paper (Phys. Stat. Sol. (b) 198, 785(1996)) is revised and extended to include the high order field corrections in the expression for the frictional forces and the energy transfer rates. The final expressions are formally the same as those in first order in the electric field, but the distribution functions of electrons appearing in them are defined by different expressions. The problems relative to the distribution function are discussed in detail and a new closed expression for the distribution function is obtained. The nonlinear impurity-limited resistance of a strong degenerate electron gas is computed numerically. The result calculated by using the new expression for the distribution function is quite different from that using the displaced Fermi function when the electric field is sufficiently high.