Charge collection efficiency in the presence of non-uniform carrier drift mobilities and lifetimes in photoconductive detectors

Abstract

We consider the charge collection efficiency (CCE) for semiconductors in which the charge transport parameters, the drift mobility μ, and the carrier lifetime τ have spatial dependence, i.e., μ = μ(x) and τ = τ(x), where x is the distance from the radiation receiving top electrode toward the rear electrode. The small signal carrier packet drift analysis (CPDA) is re-examined, and the CCE efficiency for electrons and holes is formulated in terms of μ(x)τ(x)F(x), where F is the field. We use two model mobility and lifetime variations that are linear and exponential and then calculate and compare CCE determined from the CPDA equation, numerical solution of the continuity equation and Monte Carlo simulations as a function of the parameters characterizing the linear and exponential changes. The use of standard CCE equations for nonuniform samples is extensively examined, and errors are quantified by introducing a spatial average (SA) ⟨τ(x)⟩, average inverse (AI) ⟨1/τ(x)⟩, a new effective lifetime, and a kth order average. The SA lifetime works best when τ(x) monotonically decreases with x and AI works best when τ(x) monotonically increases with x. Stabilized a-Se x-ray photoconductors were considered as a practical application of this work. Both hole and electron lifetimes decrease in a-Se upon x-ray irradiation. Using the empirical equations derived recently for τh(x) and τe(x) as a function of dose D(x) in the sample, the CCE for two a-Se samples corresponding to a low-end device quality and the “best” was determined as a function of applied field.