Statistical models for charge collection efficiency and variance in semiconductor spectrometers

Charge collection efficiency and the variance in the collected charge of semiconductor spectrometers are modeled. The model is based on a statistical approach and the extended Ramo theorem. The model yields an expression for variance in charge collection efficiency as a function of photon energy, bias voltage, and semiconductor parameters. These calculations as a function of absorption depth are particularly important in semiconductors with high atomic numbers, such as CdZnTe, since in these materials a uniform absorption cannot be assumed for a wide range of energies. Three different spectrometer configurations were considered: resistive, partially depleted Schottky barrier, and fully depleted Schottky barrier. An analytical model for the resistive configuration is presented and the results are compared to numerically obtained results of the Schottky configuration.