Electric fields, weighting fields, signals and charge diffusion in detectors including resistive materials

TL;DR

This paper analyzes electric and weighting fields in layered detectors with resistive materials, deriving Green's functions and studying charge diffusion, signal formation, and crosstalk effects in various detector configurations.

Contribution

It provides a comprehensive derivation of Green's functions and weighting fields in layered resistive detectors, including effects of resistivity on signals and charge spreading, which was not previously detailed.

Findings

Resistive layers influence signal shapes and crosstalk.

Derived Green's functions for complex layered geometries.

Analyzed charge diffusion and its impact on detector signals.

Abstract

In this report we discuss static and time dependent electric fields in detector geometries with an arbitrary number of parallel layers of a given permittivity and weak conductivity. We derive the Green's functions i.e. the field of a point charge, as well as the weighting fields for readout pads and readout strips in these geometries. The effect of 'bulk' resistivity on electric fields and signals is investigated. The spreading of charge on thin resistive layers is also discussed in detail, and the conditions for allowing the effect to be described by the diffusion equation is discussed. We apply the results to derive fields and induced signals in Resistive Plate Chambers, Micromega detectors including resistive layers for charge spreading and discharge protection as well as detectors using resistive charge division readout like the MicroCAT detector. We also discuss in detail how resistive layers affect signal shapes and increase crosstalk between readout electrodes.