Fast calculation of capacitances in silicon sensors with 3D and 2D numerical solutions of the Laplace's equation and comparison with experimental data and TCAD simulations

We have developed a software for fast calculation of capacitances in planar silicon pixel and strip sensors, based on 3D and 2D numerical solutions of the Laplace's equation. The validity of the 2D calculations was checked with capacitances measurements on Multi-Geometry Silicon Strip Detectors (MSSD). The 3D calculations were tested by comparison with pixel sensors capacitance measurements from literature. In both cases the Laplace equation results were compared with simulations obtained from the TCAD Sentaurus suite. The developed software is a useful tool for fast estimation of interstrip, interpixel and backplane capacitances, saving computation time, as a first approximation before using a more sophisticated platform for more accurate results if needed.