Multiple-Scale Analysis of Charge Transport in Semiconductor Radiation Detectors: Application to Semi-Insulating CdZnTe

The transport, trapping, and subsequent detrapping of charge in single crystals of semi-insulating cadmium zinc telluride (CdZnTe) has been analyzed using multiple-scale perturbation techniques. This method has the advantage of not only treating impulse charge generation typical in spectroscopic analysis, but also a large class of continuous generation sources more relevant to high-flux x-ray imaging applications. We first demonstrate that the multiple-scale solutions obtained for small-current transients induced by an impulse generation of charge are consistent with well-known exact solutions. Further, we use the multiple-scale solutions to derive an analytic generalization of the Hecht equation that incorporates detrapping over times much longer than the carrier transit time (i.e., delayed signal components). The method is then applied to a continuous charge generation source that approximates that of an x-ray source. The space–time solutions obtained are relevant to detector design in high-flux x-ray imaging applications. Throughout this work the multiple-scale solutions are compared with exact solutions as well as full numerical solutions of the fundamental charge conservation equations.