A comparison of the carrier density at the surface of quantum wells for different crystal orientations of silicon, gallium arsenide and indium arsenide

TL;DR

This study compares surface carrier densities in quantum wells made from silicon, gallium arsenide, and indium arsenide across different crystal orientations, revealing how symmetry constraints influence surface charge distribution.

Contribution

It provides a systematic analysis of how material, orientation, and well width affect carrier densities at quantum well surfaces, highlighting the role of wavefunction symmetry.

Findings

D2 states in silicon (100) wells have the lowest surface density

Carrier density shapes vary with material and orientation

Symmetry constraints influence surface charge distribution

Abstract

We report the carrier densities at the surface of single-crystal quantum wells as a function of material, orientation and well width. We include wells constructed from silicon, gallium arsenide and indium arsenide with three crystal orientations, (100), (110) and (111), included for each material. We find that the D2 states in a silicon (100) quantum well have the smallest density near the surface of the slab. Inspection of the planar average of the carrier densities reveals a characteristic shape that depends on the material and orientation, which leads to a varying degree of suppression or enhancement of the density near the surface. The physics responsible for the suppression or enhancement of the density near the surface can be traced to a constraint imposed by the symmetry of quantum well wavefunction on the phases of the bulk Bloch states of the crystal from which it can be constructed.