A simple model for avalanche multiplication including deadspace effects

A simple Monte Carlo model (SMC) using single effective parabolic valleys and accurately accounting for deadspace effects is presented for calculating the avalanche process. Very good agreement is achieved with a range of measured electron and hole multiplication results from GaAs p ⁺-i-N⁺´s with i-region thicknesses, ω, from 1 μm down to 0.025 μm and with the excess noise factors down to 0.05 μm. While the results are insensitive to the precise values of input parameter for structures with ω⩾0.2 μm, this is not the case in thinner structures where the deadspace represents a significant fraction of the device. For ω<0.2 μm, the energy dependence of the ionization rate becomes increasingly important. The SMC model is tested against a full-band Monte Carlo model (FBMC) by comparing the mean distance between ionization events and the probability density functions, which are effectively the histograms of distances between ionization events, for equivalent material parameters. The good agreement between these suggests that the SMC, with a relatively small number of fitting parameters and much faster calculation times than the FBMC, is a useful tool for device simulation and interpreting experimental results