Semi-classical Charge Transport in Semiconductor Devices

Abstract

This chapter gives an introduction to the semi-classical modeling of charge transport in semiconductor devices based on the van Roosbroeck system. The model equations are explained in detail, including a survey on boundary conditions, recombination rate models, carrier and current density expressions. The focus of this thesis is on the modeling of charge transport in quantum optical devices, that are typically operated at extremely low temperatures. Therefore, a particular focus is put on the thorough inclusion of degeneration effects due to Fermi–Dirac statistics in all relevant parts of the model system–ranging from nonlinear diffusion to boundary conditions and a generalized structure of the standard recombination rate models. The approximations underlying the van Roosbroeck system are discussed by outlining its derivation from the semi-classical Boltzmann transport equation. Finally, the chapter provides a detailed discussion of the van Roosbroeck system from the viewpoint of non-equilibrium thermodynamics. The consistency with fundamental laws of thermodynamics is regarded as a major principle for the construction of a hybrid quantum-classical model system in a later chapter.