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

TL;DR

This paper introduces a software tool that rapidly calculates capacitances in silicon sensors using 2D and 3D solutions of Laplace's equation, validated against experimental data and TCAD simulations, aiding quick estimations in sensor design.

Contribution

The paper presents a novel software for fast capacitance calculations in silicon sensors using numerical Laplace solutions, validated against measurements and TCAD simulations.

Findings

2D calculations agree with measurements on silicon strip detectors.

3D calculations are consistent with literature data.

Software significantly reduces computation time for capacitance estimation.

Abstract

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.