Diffusive semiconductor moment equations using Fermi-Dirac statistics
Extending a previous work, the authors formulate a diffusive moment model for charge transport in semiconductors using a Fermi-Dirac statistics instead of the previously employed Maxwell-Boltzmann one. The balance equations are derived by using the moments of the Boltzmann equation written in the diffusion scaling. The closure relations are obtained by applying the maximum entropy principle with a generalized Fermi-Dirac statistics, and by performing a Chapman-Enskog expansion. The weight functions entering in the definition of the moments are taken as powers of the energy. Under the main assumption that the collision term can be split into the sum of a dominant term conserving the basic moments and a second-order correction, along with some technical assumptions, a general model of diffusive macroscopic equations is obtained. A symmetric formulation is also deduced with the introduction of appropriate entropic variable. This allows to get an entropy-entropy dissipative relation. For particular choices of the energy band and moments, explicit drift-diffusion and energy transport models are obtained, and their degeneracy limit is studied.
scientific article; zbMATH DE number 6134348
scientific article