Modified Poisson solver for the simulation of the silicon–oxide interface in semiconductor detectors

We present a modified Poisson solver for depleted semiconductor detectors that takes into account the effects of possible accumulation of mobile charge at the silicon–oxide interfaces. The solver is based on a physical model that closely approximates the correct boundary condition at the silicon–oxide interface. The model assumes that the silicon–oxide interface is divided into an equipotential region, where the electron layer is located, and a fully depleted region. The actual extension and potential of the electron layer region are approximated with the desired accuracy by an iterative procedure. This model has been implemented in 2- and 3-D Poisson solvers. The comparison with a 2-D drift–diffusion simulator has shown the accuracy of the proposed method. The modified Poisson solver has shown to be useful in giving accurate solutions to 3-D design problems at high CPU speed.