A hydrodynamical model for holes in silicon semiconductors: The case of parabolic warped bands

Abstract

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 equations 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.

Citation

Mascali, G. and Romano, V. (2012), "A hydrodynamical model for holes in silicon semiconductors: The case of parabolic warped bands", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 31 No. 2, pp. 552-582. https://doi.org/10.1108/03321641211200581