Impact ionization model for full band Monte Carlo simulation

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.

Characteristics of impact ionization rates in direct and indirect gap semiconductors

“…21,22 Expressions of the form of Eq. ͑8͒ were also fitted to the volume of phase space ͑i.e., the rate calculated by setting the matrix elements to 1͒ for each material.…”

Impact ionization rate calculations in wide band gap semiconductors

“…3,14,20,21,32,33 The mean rate at a particular impacting carrier energy is obtained by averaging the rate due to carriers at all k vectors at that energy:…”

“…Kane 17 performed a more thorough calculation for Si in which he numerically integrated the rate obtained through Fermi's Golden Rule over all energy and momentum conserving transitions, obtaining a significantly different rate to that of Keldysh. Several other workers 12,14,[18][19][20][21][22] have applied methods similar to Kane's to obtain impact ionization rates including the effect of realistic band structure for several semiconductors.…”

Numerical Simulation of Electric Characteristics of Deep Submicron Silicon-on-Insulator Mos Transistor

“…These types of models usually have no fitting parameters, but their implementation is restricted by the complexity of scattering rate calculation and definition of the particle final states which result in too much computational effort. Basing on the full-band approach in [32] the expression for impact ionization scattering rate for silicon was derived in a rather simple fitted form: (7) where electron energy E is in eV. Moreover, the calculation revealed that the average energy of secondary generated particles depends linearly on the primary electron energy after the scattering event.…”

“…By now more sophisticated models of impact ionization process based on full-band calculations have been developed [25,[30][31][32]. These types of models usually have no fitting parameters, but their implementation is restricted by the complexity of scattering rate calculation and definition of the particle final states which result in too much computational effort.…”