Valley splitting in strained silicon quantum wells

TL;DR

This paper develops a localized-orbital theory and tight-binding model to analyze valley splitting in strained silicon quantum wells, revealing oscillatory behavior and decay characteristics relevant for quantum computing devices.

Contribution

It introduces a new analytical and numerical framework for understanding valley splitting, including oscillations and decay, in silicon quantum wells relevant for quantum computing.

Findings

Valley splitting oscillates with the number of layers in the quantum well.

Splitting persists even without electric field, contrary to previous assumptions.

Splitting envelope decays as the cube of the number of layers.

Abstract

A theory based on localized-orbital approaches is developed to describe the valley splitting observed in silicon quantum wells. The theory is appropriate in the limit of low electron density and relevant for proposed quantum computing architectures. The valley splitting is computed for realistic devices using the quantitative nanoelectronic modeling tool NEMO. A simple, analytically solvable tight-binding model is developed, it yields much physical insight, and it reproduces the behavior of the splitting in the NEMO results. The splitting is in general nonzero even in the absence of electric field in contrast to previous works. The splitting in a square well oscillates as a function of S, the number of layers in the quantum well, with a period that is determined by the location of the valley minimum in the Brillouin zone. The envelope of the splitting decays as $S^3$. Finally the feasibility of observing such oscillations experimentally in modern Si/SiGe heterostructures is discussed.