Electrical conductivity

Theory behind electron simulations

Essentially, we want to solve the Boltzmann transport equation:

We use the relaxation time approximation to compute the collision term:

And we can compute the average time of flight $\tau _s$ i.e. the time it takes for an electron to travel from one side of the structure to another. Once $\tau _s$ is known, we can compute the physical quantities:

Also, we want our prediction to match the bulk electron conductivity before we proceed to the calculations on nanostructures, so we need to compute the mapping constant as:

See additional details in the Ref. [1].

References

1. Priyadarshia and Neophytou, J. Appl. Phys. 133, 054301 (2023)