Homogenization theory for the cumulative effect of Te inclusions in CdZnTe radiation detectors

In this paper, homogenization theory based on a multiple scale perturbation of the charge-transport equation is used to derive a mathematical framework for modeling the cumulative effect of Te inclusions in radiation detectors based on semi-insulating cadmium zinc telluride (CdZnTe). The derived framework naturally incorporates a wide range of physical models that may posit either a reduced electron lifetime due to enhanced trapping at inclusions, or an altered carrier speed due to a distorted electric field at inclusions, or both. The new framework is applied to a simplified version of the geometric model introduced by Bolotnikov [Nucl. Instrum. Methods Phys. Res. A 571, 687 (2007)], and it is shown that this results in a closed-form approximation to the reduced electron trapping time that depends in a rather simple way on fundamental inclusion parameters such as their mean size and number density. It is also demonstrated that this effective trapping time compares well with previously published simulation data for the geometric model. Further, the electron mobility-lifetime product that results from the reduced carrier lifetime is easily incorporated into Monte Carlo device simulation. Examples of simulated induction maps and pulse-height spectra for pixelated detectors that contain inclusions of various mean sizes and number densities are presented.