Impact ionization model for full band Monte Carlo simulation

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Abstract
The impact ionization rate in silicon is numerically derived from wave functions and energy band structure based on an empirical pseudopotential method. The calculated impact ionization rate is well fitted to an analytical formula with a power exponent of 4.6, indicating soft threshold of impact ionization rate, which originates from the complexity of the Si band structure. The calculated impact ionization rate shows strong anisotropy at low electron energy (ε<3 eV), while it becomes isotropic at higher energy. Numerical calculation also reveals that the average energy of secondary generated carriers depends linearly on the primary electron energy at the moment of their generation. A full band Monte Carlo simulation using the newly derived impact ionization rate demonstrates that calculated quantum yield and ionization coefficient agree well with reported experimental data.