Study of the jump conditions for the 2D MEP hydrodynamical model of charge transport in semiconductors

Abstract

Purpose

The purpose of this paper is to reply to the following question: do there exist piecewise smooth solutions to the 2D MEP hydrodynamical model of charge transport in semiconductors with smooth parts separated by a surface of strong discontinuity?

Design/methodology/approach

A standard approach is used to obtain jump conditions for the balance equations under consideration.

Findings

For the balance equations of charge transport in semiconductors based on the maximum entropy principle Rankine‐Hugoniot jump conditions were derived and studied. Considering the important case of planar discontinuity, the authors discuss the legitimacy of the introduction of surface charge and surface current in the Rankine‐Hugoniot jump conditions.

Research limitations/implications

The jump conditions are derived for the balance equations written for the case of the parabolic approximation of energy bands. However, it is possible also to perform the analysis of corresponding jump conditions for the case of Kane dispersion relation approximation.

Originality/value

The paper presents derivation and study of Rankine‐Hugoniot jump conditions for the 2D MEP hydrodynamical model of charge transport in semiconductors.

Citation

Blokhin, A.M. and Bushmanov, R.S. (2009), "Study of the jump conditions for the 2D MEP hydrodynamical model of charge transport in semiconductors", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 28 No. 2, pp. 249-271. https://doi.org/10.1108/03321640910929209