$\Psi=0$ at a sharp semiconductor/insulator interface. Is this correct?

TL;DR

This paper investigates the impact of interface levels on the hole spectrum in semiconductor quantum dots, challenging the common assumption that the wave function component $$ vanishes at the interface.

Contribution

It introduces generalized boundary conditions accounting for interface structure, revealing the significant influence of interface levels on the hole spectrum.

Findings

Interface levels near the valence band top affect hole states.

Standard boundary conditions are valid only without interface levels.

Interface structure must be considered for accurate modeling.

Abstract

The generalized boundary conditions for the envelope wave function that take into account the real structure of an interface were used to investigate the hole spectrum of the semiconductor quantum dot embedded in an insulator matrix. An essential influence of the interface levels, which could exist at the top of the valence band, on the hole spectrum has been demonstrated. It is found that usually applied boundary conditions, wherein all components of the envelope wave function vanish at the interface, can be used only in the absence of the interface levels close to the band edge.