Probability Theory of Single-Carrier Avalanche in HgCdTe APDs as a Stochastic Process

Recent researches have proven that HgCdTe is a good material to acquire both high multiplication and low excess noise factor at the same time in avalanche photodiodes (APDs). As a pseudo-binary narrow bandgap semiconductor material, HgCdTe exhibits high conduction band nonparabolicity as well as strong alloy scattering, especially for hot electrons, which changes the dynamics of hot electrons in a fundamental manner. Here, we propose a different scheme to characterize the scattering event and establish the probability theory, spatial description theory, to discuss the dynamics of electrons in HgCdTe APDs with the large nonparabolicity and the strong alloy scattering included. The spatial description theory is then compared with current analytic theory and the Monte Carlo method.