On the weighting field and admittance of irradiated Si-sensors

TL;DR

This study investigates the effects of proton irradiation on silicon sensors, focusing on the weighting field and admittance, revealing how irradiation alters electrical properties and how models can describe these changes.

Contribution

It provides new insights into the impact of irradiation on silicon sensors' electrical behavior and introduces models with position-dependent resistivity to explain observed frequency dependence.

Findings

Weighting field of highly irradiated sensors matches that of fully depleted sensors before irradiation.

Resistivity increase due to irradiation causes longer time constants in sensors.

Position-dependent resistivity models accurately describe frequency-dependent admittance data.

Abstract

In this paper the weighting field $E_W$ and the frequency dependence of the admittance Y of n$^+$p pad sensors irradiated by 24 GeV/c protons to equivalent fluences in the range $\Phi_{\rm eq} = 3$ to $13\times 10^{15}$ cm$^{-2}$ are investigated. 1-D TCad simulations are used to calculate $E_W$. For $\Phi_{\rm eq} < 10^{13}$ cm$^{-2}$ $E_W$ depends on position and time. However, for higher $\Phi_{\rm eq}$ the time constant $\tau$ is much longer than the typical electronics readout time and $E_W = 1/d$ ($d$ = sensor thickness). It is demonstrated that the increase of the resistivity of the Si bulk with irradiation is responsible for the increase of $\tau$. The admittance Y of irradiated pad sensors has been measured for frequencies between f = 100 Hz and 1 MHz and voltages between 1 and 1000 V at -20$^\circ$C and -30$^\circ$C. For f < 1 kHz the parallel capacitance C$_p$ shows a f dependence. A model with a position-dependent resistivity is able to describe the data. It is concluded: 1. The weighting field of a highly irradiated sensor is the same as the weighting field of a fully depleted sensor before irradiation. 2. Models with a position-dependent resistivity describe the frequency dependence of C$_p$ for irradiated sensors.