The Atomistic Simulation of Thermal Diffusion and Coulomb Drift in Semiconductor Detectors

In order to enhance the imaging resolution of gamma cameras over standard Compton camera and coded aperture designs, one can add momentum information to the kinematics by tracking the recoil electrons that result from gamma-ray interactions. The initial direction of the recoil electron can be discerned from its meandering trajectory, as measured via the initial electron-hole charges' spatial distribution, which itself is extracted by measuring the induced current signal on the bounding electrodes of the detector. In principle, the extraction of the recoil electron direction is ultimately limited by those stochastic effects that significantly contribute to the charge motion; most notably, thermal diffusion, although for existing systems, electronic noise can contribute or even dominate the position uncertainty. Nevertheless, we neglect the effects of electronic noise in this paper in order to gauge the intrinsic uncertainty in the charges' positions. We model diffusion using two techniques: one found in the literature and based on the diffusion coefficient, the other based on the underlying physics in which the probability density function describing the random thermal motion is sampled to determine the random contribution to each charge's motion, which depends on its drift state as well as the surrounding crystallographic environment. As is shown, the effect of diffusion is always significant, but its effect can be mitigated if the charges drift with alacrity. Coulomb drift, which refers to the dynamic charge motion due to the electromagnetic forces of the space charge created during the radiation event, is usually neglected; however, it can also be important for highly ionizing particles. We thus quantify the effect of Coulomb drift and suggest methods by which its impact can be extracted from the overall charge-track reconstruction.