A hydrodynamical model for holes in silicon semiconductors The case of parabolic warped bands
Purpose - This paper intends to present a hydrodynamical model which describes the hole motion in silicon and couples holes and electrons. Design/methodology/approach - The model is based on the moment method and the closure of the system of moment equation S is obtained by using the maximum entropy principle (hereafter MEP). The heavy, light and split-off valence bands are considered. The first two are described by taking into account their warped shape, while for the split-off band a parabolic approximation is used. Findings - The model for holes is coupled with an analogous one for electrons, so obtaining a complete description of charge transport in silicon. Numerical simulations are performed both for bulk silicon and a p-n junction. Research limitations/implications - The model uses a linear approximation of the maximum entropy distribution in order to close the system of moment equations. Furthermore, the non-parabolicity of the heavy and light bands is neglected. This implies an approximation on the high field results. This issue is under current investigation. Practical implications - The paper improves the previous hydrodynamical models on holes and furnishes a complete model which couples electrons and holes. It can be useful in simulations of bipolar devices. Originality/value - The results of the paper are new since a better approximation of the band structure is used and a description of both electron and hole behavior is present, therefore the results are of a certain relevance for the theory of charge transport in semiconductors.
hydrodynamical models silicon hole transport diodes