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Mathematical analysis of the two-band Schrödinger model

✍ Scribed by Naoufel Ben Abdallah; Jihene Kefi-Ferhane

Publisher
John Wiley and Sons
Year
2008
Tongue
English
Weight
237 KB
Volume
31
Category
Article
ISSN
0170-4214

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✦ Synopsis

Abstract

A mathematical model for quantum transport in an interband resonant tunneling diode is studied. The wave function of electrons has two components and is a solution of a 2 × 2 matrix Schrödinger equation derived from the k.p theory. The first component represents that part of electrons living in the conduction band while the second part represents the valence band. Transparent boundary conditions are derived and the Schrödinger equation is coupled to the Poisson equation for the electrostatic potential. Using the repulsivity of the electrostatic interaction, an a priori estimate is derived and used to construct a solution of the overall problem. Copyright © 2007 John Wiley & Sons, Ltd.

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