Matching Conditions in Effective-Mass Theory

TL;DR

This paper demonstrates that the traditional wavefunction matching conditions in effective-mass theory are qualitatively incorrect, proposing a revised matching condition that significantly alters the understanding of wavefunction behavior at material interfaces.

Contribution

The paper clarifies the correct matching conditions in effective-mass theory and shows that traditional methods are qualitatively wrong through a simple example.

Findings

Traditional matching is qualitatively incorrect

Revised matching conditions significantly change wavefunction behavior

Impacts modeling of heterostructures and quantum devices

Abstract

It has been shown that the traditional matching of wavefunctions between regions of different effective mass (matching {\psi} and (1/m*)\partial{\psi}/\partialx) is not correct, but that one should match (1/\surdm*){\psi} and (1/\surdm*)\partial{\psi}/\partialx. It has not been clear how serious is the error in using the traditional formula. We apply the two sets of conditions to a simple, but rather general, example and find that the traditional matching is not even qualitatively correct.