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.