Statistical modeling of the spectral performance of a two-dimensional array of gamma-ray spectrometers

We develop a statistical model for the calculation of the spectral performance of two-dimensional (2D) array of gamma-ray spectrometers. We consider a nonuniform field in the device, determined by the geometrical design of the anodes. The induced charge is calculated by solving the Poisson’s equation with the appropriate boundary conditions. Furthermore, the presented model simultaneously considers a random point of photon absorption and a random drift length for each carrier, taking into account the effect of multiple trapping and detrapping. The model developed in this article enables the optimal geometrical design of the 2D array of anodes according to the electrical properties of the given semiconductor material, in order to achieve optimal results for the spectral performances. The model consists of three parts. The first is the calculation of the potential at each point of a three-dimensional (3D) map of the device. The second is the calculation of the charge induced on the anode by a point charge positioned in the device (for each point of a 3D map). The third is the statistical calculation of the pulse height spectrum. Finally, the pulse height spectrum is calculated as a function of the geometrical design, photon energy, electron and hole mobility, lifetime, mean detrapping time and applied voltage as well as the shaping time.