The statistics of electron-hole avalanches

TL;DR

This paper provides a comprehensive analysis of electron-hole avalanche processes in semiconductors, deriving equations for inhomogeneous fields and discussing implications for detector time resolution and gain in various photodetectors.

Contribution

It introduces analytical solutions for avalanche development in inhomogeneous electric fields and discusses their impact on detector performance, a novel approach in the study of charge multiplication.

Findings

Analytical solutions for avalanches in constant electric fields.

Implications for time resolution in single-photon detectors.

Descriptions of avalanche behavior in low-gain and high-gain detectors.

Abstract

Charge multiplication through avalanche processes is commonly employed in the detection of single photons or charged particles in high-energy physics and beyond. In this report, we provide a detailed discussion of the properties of avalanches driven by two species of charge carriers, e.g. electrons and holes in a semiconductor exposed to an electric field. We derive equations that describe the general case of avalanches developing in inhomogeneous electric fields and give their analytical solutions for constant fields. We discuss consequences for the time resolution achievable with detectors that operate above the breakdown limit, e.g. single-photon avalanche diodes (SPADs) and silicon photomultipliers (SiPMs). Our results also describe avalanches that achieve finite gain and are important for avalanche photodiodes (APDs) and low-gain avalanche detectors (LGADs).