A semi-analytic approximation of charge induction in monolithic pixelated CdZnTe radiation detectors

A semi-analytic approximation to the weighting potential within monolithic pixelated CdZnTe radiation detectors is presented. The approximation is based on solving the multi-dimensional Laplace equation that results upon replacing rectangular pixels with equal-area circular pixels. Further, we utilize the simplicity of the resulting approximate weighting potential to extend the well-known Hecht equation, describing charge induction in a parallel plate detector, to that approximating the multi-dimensional charge induction within a pixelated detector. These newly found expressions for the weighting potential and charge induction in a pixelated detector are compared throughout to full 3D electrostatic and monte carlo simulations using eVdsim (eV Microelectronics Device SIMulator). The semi-analytic expressions derived in this paper can be evaluated quickly, and can therefore be used to efficiently reduce the size and dimensionality of the parameter space on which a detailed 3D numerical analysis is needed for pixelated detector design in a wide range of applications.