On the effect of non local impact ionization on avalanche multiplication for uniform electric fields

TL;DR

This paper introduces a new model for non local impact ionization in avalanche multiplication, revealing the dead space and resonance effects at different electric fields through Monte Carlo simulations.

Contribution

It proposes a novel definition and model for the non local impact ionization coefficient and derives an expression for avalanche multiplication incorporating these effects.

Findings

Identification of dead space effect in avalanche multiplication

Discovery of resonance effect at higher electric fields

Quantitative results matching Monte Carlo simulations

Abstract

An alternative definition for the non local impact ionization coefficient is given and its relationship to the ionization pathlength probability distribution function (PDF) is determined. A model for the ionization pathlength PDF is proposed and the resultant non local ionization coefficient is derived. An expression for the avalanche multiplication is derived. Results are calculated using non local ionization coefficients for two electric field values using fits to ionization pathlength PDFs calculated using Monte Carlo techniques. These results show two features: the well known dead space effect and at the higher field value a resonance effect. The resonance effect gives rise to level sections in the multiplication curve for multiplications of 2, 4, 8 and 16 if the ionization coefficient ratio is small.