Use of Fermi statistics in two-dimensional numerical simulation of heterojunction devices

The authors have developed a formalism for the use of Fermi statistics in semiconductor equations so that they can be discretised and linearised for two-dimensional device modelling. They find it important to choose the variables and the form of the boundary conditions carefully in order to use Fermi statistics consistently in both the Poisson and current continuity equations. Their method has been implemented in a two-dimensional heterojunction devices program. Using the example of an Al x Ga 1-x As/GaAs HIGFET, they show that Boltzmann statistics overestimate the carrier density and give rise to a greater variation of the potential distribution than Fermi statistics, and that Boltzmann statistics can cause significant errors in the currents at the electrodes.