Fluctuations in induced charge introduced by Te inclusions within CdZnTe radiation detectors

Recently, homogenization theory based on a multiple-scale perturbation of the electron transport equation has been used to derive a mathematical framework for modeling the excess charge lost to Te inclusions within radiation detectors based on semi-insulating cadmium zinc telluride (CdZnTe). In that theory, the heterogeneous material is mathematically replaced by a homogenized CdZnTe crystal whose effective electron attenuation length incorporates the additional uniform electron trapping caused by the inclusions. In this paper, the homogenization theory is extended to incorporate fluctuations in the induced charge (i.e., charge collection nonuniformities) introduced by the random position and size distributions of a noncorrelated population of small (i.e, <20 μm) Te inclusions. Analysis of the effective parameters derived within the homogenized framework is used to develop a probability distribution of effective electron attenuation lengths, and therefore effective mobility-lifetime products, as a function of both the position and size distribution of Te inclusions. Example distributions are detailed for the case of an exponential size distribution at various number densities. Further, it is demonstrated that the inclusion-induced material nonuniformities derived in this paper can be numerically sampled efficiently, making them applicable to Monte Carlo device simulation of realistic CdZnTe detectors. Simulated charge induction maps and pulse-height spectra are presented and compared to recently published measurements.