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 position-dependent 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).

通过雪崩过程进行的电荷倍增通常用于检测高能物理及其他领域中的单个光子或带电粒子。在此报告中，我们将详细讨论由两种电荷载流子驱动的雪崩特性，例如，电子和半导体中暴露于电场的空穴。我们推导出描述在依赖位置的电场中发生雪崩的一般情况的方程，并给出其对恒定场的解析解。我们讨论了在击穿极限以上工作的检测器（例如单光子雪崩二极管（SPAD）和硅光电倍增管（SiPM））可实现的时间分辨率的后果。