A More Exact Treatment of the Equations Describing Dielectric Relaxation and Carrier Motion in Semiconductors

Abstract

Previous treatments of the linearized equations describing hole and electron flow in a homogeneous semiconductor have not been wholly satisfying mathematically. An exact treatment of these equations is undertaken and it is demonstrated that the departure from complete local charge neutrality implicit in the equations corresponds to a polarization attributable to local variations of conductivity. The dielectric relaxation is described and exact expressions for the effective mobility and diffusion coefficients are obtained. The corrections to the older values are of magnitude τ_r/τ, where τ_r is the relaxation time and τ the lifetime. For semiconductors, these corrections are negligible.