Spatial description theory of narrow-band single-carrier avalanche photodetectors

The avalanche is the foundation of the understanding and vast applications of the breakdown of semiconductors and insulators. Present numerical theories analyzing the avalanche photodetectors are mainly split into two categories: the macroscopic empirical model with fitting parameters and the microscopic process simulation with statistical estimations. Here, we present a parameter-free analytic theory of the avalanche for a narrow-band material, HgCdTe, originated from quantum mechanics, avoiding any fitting parameter or any statistical estimation while taking advantage of both categories. Distinct from classical theory, we propose a full spatial description of an avalanche with basic concepts such as transition rate and equation of motion modified. As a stochastic process, the probability density function (PDF) of impact ionization is utilized in a generalized history-dependent theory. On account of different carrier generation character of light and leakage current, we suggest that carrier generated at different positions should be considered separately, which is done by generalized history-dependent theory in our work. Further, in our calculation, the reason for the abnormal rise of excess noise factor (ENF) observed in the experiment in single-carrier avalanche photodetectors is clarified.