Three-dimensional simulation of charge transport in pixel detectors

The simulation of the charge transport and collection following ionization in the depleted bulk of a semiconductor pixel detector requires the three-dimensional calculation of the potential and the electric field strength. In this paper, a Fourier transform-based method is presented for the three-dimensional numerical solution of the Poisson equation for the field in a fully depleted detector. The carrier positions due to drift and diffusion are calculated as functions of position and time. These functions provide the time evolution of the charge collected by the pixels and the charge splitting between neighboring pixels.