Detrapping rates arising from Fermi-Dirac statistics

Have you ever wondered how Fermi-Dirac statistics arises? I already have in the previous couple of posts, but the more important question is why I suddenly started to care about Fermi-Dirac statistics. It is still all related to [1]. Reviewers raised doubts about our assumption about uniform detrapping rates, asking us to provide experimental evidence for our claim. As far as I am able to read the experimental works, it doesn't seem possible to provide any direct evidence. Still as a theoretician I can provide theoretical justification which is indirectly supported by experimental works.

This is why in this post we'll talk about detrapping rates arising from a simple model explored in an earlier post.

Fermi-Dirac statistics with single conduction level

Have you ever wondered how Fermi-Dirac statistics arises? I may have wondered during my bachelor degree studies, but now I only remember derivation done by the means of combinatorics. In this post I continue my wandering from a perspective of numerical simulation of a highly simplified system.

In the previous post we have built a model in which particles may freely jump between the energy levels (restricted only by the Pauli exclusion principle and Boltzmann statistics). This is not necessarily possible in real life systems. In semiconductors individual traps may have a single characteristic trap depth, or multiple depths which would not span full spectrum of available trap depths. In such case we need to assume existence of a conduction band energy level, which allows particles to travel between different traps.

Let us examine this particular case in this post.