Calculation of pixel detector capacitances through three dimensional numerical solution of the Laplace equation

Abstract

A method for the solution of the three dimensional Laplace equation is presented. The method applies to planar geometry cases, such as pixel detector devices, characterized by mixed boundary conditions. Through this algorithm the capacitances associated with pixel detectors are calculated. These capacitances, which are the pixel to substrate and the interpixel capacitances, are of great importance in the design of a pixel detector since they influence the noise and the cross talk effects between pixels. Capacitances for various pixel and interpixel dimensions are presented along with an analytical approximation for the calculation of the total pixel capacitance.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>