A model for forming the monophoton response in an avalanche photodiode

An analytical model describing the electron and hole multiplication process in the space charge region of the avalanche photodiode (APD) is proposed. It is shown that the commonly used McIntyre theory of avalanche multiplication imposes severe restrictions on the distribution of distances between subsequent ionizations. The model developed takes into account the probability distribution of ionization points and enables one to obtain characteristics of the number of charges in the monophoton response of the avalanche photodiode. The systems of integral equation for determining the photodiode gain and noise factor are derived. A simulation model and computer codes for the charge multiplication process in the APD are developed and implemented. The noise factor values are plotted as a function of the charge multiplication factor for the particular distribution function.