Carrier trajectory tracking equations for Simple-band Monte Carlo simulation of avalanche multiplication processes

Abstract

Avalanche photodiodes (APDs) with steep electric field gradients generally have low excess noise that arises from carrier multiplication within the internal gain of the devices, and the Monte Carlo (MC) method is among popular device simulation tools for such devices. However, there are few articles relating to carrier trajectory modeling in MC models for such devices. In this work, a set of electric-field-gradient-dependent carrier trajectory tracking equations are developed and used to update the positions of carriers along the path during Simple-band Monte Carlo (SMC) simulations of APDs with non-uniform electric fields. The mean gain and excess noise results obtained from the SMC model employing these equations show good agreement with the results reported for a series of silicon diodes, including a p+n diode with steep electric field gradients. These results confirm the validity and demonstrate the feasibility of the trajectory tracking equations applied in SMC models for simulating mean gain and excess noise in APDs with non-uniform electric fields. Also, the simulation results of mean gain, excess noise, and carrier ionization positions obtained from the SMC model of this work agree well with those of the conventional SMC model employing the concept of a uniform electric field within a carrier free-flight. These results demonstrate that the electric field variation within a carrier free-flight has an insignificant effect on the predicted mean gain and excess noise results. Therefore, both the SMC model of this work and the conventional SMC model can be used to predict the mean gain and excess noise in APDs with highly non-uniform electric fields.