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.

Internship opportunity for the summer of 2024

Research Council of Lithuania currently accepts student applications to do internship projects this summer at various institutions across Lithuania. One of the projects students could apply for is mine!

My project is called "Influence of the state interaction network on the statistical properties of the voter model". I would expect for the intern to take a look at the multi-state noisy voter model, and explore what happens when some of transitions between the states are forbidden (something similar was explored in AB model). You do not need to be familiar with sociophysics or opinion dynamics, though I would expect the project to have a significant numerical aspect to it (some programming skills will be required).

Intern application deadline is 29th of May.

Interns will get 1000 Eur monthly stipend. Plus, for students coming from other countries or cities to Vilnius there is possibility to get support for accommodation. Based on this call's rules I will have to give priority to students outside Vilnius University.

More details about this call is available on RCL's website: