Intervalley splittings of Si quantum wells

TL;DR

This paper develops a multi-valley effective mass theory for silicon quantum wells, deriving the phenomenological delta potential self-consistently and validating it against experimental valley splitting data.

Contribution

It introduces a self-consistent derivation of the delta potential in multi-valley effective mass theory for silicon quantum wells.

Findings

The delta function potential can be derived from the multi-valley effective mass theory.

Theoretical predictions agree well with experimental valley splitting measurements.

Finite element method effectively solves the multi-valley equations.

Abstract

Multi-valley effective mass theory for silicon quantum well structure is studied taking into account the external fields and the quantum interfaces. It is found that the phenomenological delta function potential, employed to explain the valley splitting caused by the quantum well interface in the previous work [Ref. 10], can be derived self-consistently from the multi-valley effective mass theory. Finite element method is used to solve the multi-valley effective equations. Theoretical predictions are in a reasonably good agreement with the recent experimental observation of valley splitting in a SiO_{2}/Si/SiO_{2} quantum well, which prove the validity of our approach.