Valley Degeneracies in (111) Silicon Quantum Wells

TL;DR

This paper investigates the breaking of valley degeneracy in (111) Silicon quantum wells, showing that miscut angles cause a splitting into 2 and 4 fold degeneracies through tight-binding and effective mass calculations.

Contribution

It provides a systematic analysis combining tight-binding and effective mass models to explain valley degeneracy breaking in (111) Silicon quantum wells, aligning well with experimental data.

Findings

Miscut modulates energy levels, breaking 6-fold degeneracy into 2 and 4.

Tight-binding calculations agree better with experiments than effective mass models.

Valley-minima directions are determined using an effective mass based valley-projection model.

Abstract

(111) Silicon quantum wells have been studied extensively, yet no convincing explanation exists for the experimentally observed breaking of 6 fold valley degeneracy into 2 and 4 fold degeneracies. Here, systematic sp3d5s* tight-binding and effective mass calculations are presented to show that a typical miscut modulates the energy levels which leads to breaking of 6 fold valley degeneracy into 2 lower and 4 raised valleys. An effective mass based valley-projection model is used to determine the directions of valley-minima in tight-binding calculations of large supercells. Tight-binding calculations are in better agreement with experiments compared to effective mass calculations.