Statistical modeling of charge collection in semiconductor gamma-ray spectrometers

Charge collection efficiency and the variance of the collected charge of semiconductor gamma-ray spectrometers are analytically modeled for the case of a uniform electric field. The model is based on a rigorous statistical approach. In contrast to previously reported models for the variance of the collected charge, the present statistical model simultaneously takes into account a random point of photon absorption (i.e., a nonuniform absorption) and a random drift time for each generated carrier. Analytical expressions are obtained for the variance of the collected charge as a function of photon energy, applied bias voltage, electron and hole mobility-lifetime products, and the direction of irradiation. Since at present the performance of high-Z room-temperature spectrometers is mainly limited by the charge transport properties of the semiconductors, it is interesting to calculate the limit for the expected resolution. The statistical model presented here yields physical insight and determines quantitatively the expected spectrometer resolution as a function of the semiconductor transport parameters and device parameters, as well as the radiation parameters. Several limiting cases are calculated and discussed. The methodology presented here, which is based on conditional probabilities, can be extended to spectrometers with nonuniform fields. (C) 1999 American Institute of Physics. [S0021-8979(98)00524-6].