Fast tools for 3-D design problems in semiconductor detectors

In this paper we present a practical method to obtain the three dimensional solution of the Poisson equation in closed form in fully depleted semiconductor detectors. The method applies to detectors with planar geometry with possible mixed boundary conditions. The obtained potential and electric field distribution inside the detector volume is expressed by a series of elementary functions. The motion of an electron cloud in a drift detector, the current signals induced on the collecting anodes and electrode capacitance calculations are presented.