Valley Splitting Theory of SiGe/Si/SiGe Quantum Wells

TL;DR

This paper develops an effective mass theory for SiGe/Si/SiGe quantum wells to accurately calculate valley splitting, simplifying complex geometries and magnetic field effects with analytical solutions validated against tight binding results.

Contribution

It introduces a valley coupling parameter and provides an analytical formalism for various quantum well geometries, including magnetic fields and miscut substrates, improving computational efficiency.

Findings

Excellent agreement between effective mass and tight binding results.

Analytical solutions for complex geometries and magnetic fields.

Simplified modeling of valley splitting in quantum wells.

Abstract

We present an effective mass theory for SiGe/Si/SiGe quantum wells, with an emphasis on calculating the valley splitting. The theory introduces a valley coupling parameter, $v_v$, which encapsulates the physics of the quantum well interface. The new effective mass parameter is computed by means of a tight binding theory. The resulting formalism provides rather simple analytical results for several geometries of interest, including a finite square well, a quantum well in an electric field, and a modulation doped two-dimensional electron gas. Of particular importance is the problem of a quantum well in a magnetic field, grown on a miscut substrate. The latter may pose a numerical challenge for atomistic techniques like tight-binding, because of its two-dimensional nature. In the effective mass theory, however, the results are straightforward and analytical. We compare our effective mass results with those of the tight binding theory, obtaining excellent agreement.