Quantum kinetic-equation approach to semiconductor hot-carrier screening

Abstract

The Kadanoff-Baym formulation of quantum transport is used to derive a formulation for non- equilibrium carrier screening. The approach extends the Boltzmann-equation approach for calculating carrier-screening phenomena to include quantum effects due to the spatial nonlocality of the electron. To simplify calculations, the quantum relaxation-time approximation for the collisions used by Mermin is adapted for use in this quantum transport equation. As an example, we use this formulation and the quantum relaxation-time approximation to study the linear screening of a parabolic-band semiconductor in a high electric field, and we compare the results for this formulation with the classical Boltzmann-equation formulation of nonequilibrium screening. We find that the Boltzmann-equation method gives reliable results for the susceptibility χ(q,ω) when q is much smaller than the average electron wave vector, but is unreliable for q much larger than the average electron wave vector. For q→∞, χ approaches a Lindhard-like formula for the susceptibility, but with the equilibrium distribution functions replaced by the nonequilibrium ones.