Intervalley splitting and intersubband transitions in n-type Si/SiGe quantum wells: pseudopotential vs. effective mass calculation

TL;DR

This paper compares pseudopotential and effective mass methods to analyze intervalley splitting and intersubband transitions in Si/SiGe quantum wells, revealing their agreement and implications for optical device simulations.

Contribution

It demonstrates the effectiveness of the effective mass approximation compared to pseudopotential calculations for Si/SiGe quantum wells, including asymmetric structures.

Findings

Splitting oscillates with well width

Splitting is nearly independent of in-plane wave vector

Valley splitting broadens intersubband transition linewidths

Abstract

Intervalley mixing between conduction-band states in low-dimensional Si/SiGe heterostructures induces splitting between nominally degenerate energy levels. The symmetric double-valley effective mass approximation and the empirical pseudopotential method are used to find the electronic states in different types of quantum wells. A reasonably good agreement between the two methods is found, with the former being much faster computationally. Aside from being an oscillatory function of well width, the splitting is found to be almost independent of in-plane wave vector, and an increasing function of the magnitude of interface gradient. While the model is defined for symmetric envelope potentials, it is shown to remain reasonably accurate for slightly asymmetric structures such as a double quantum well, making it acceptable for simulation of multilayer intersubband optical devices. Intersubband optical transitions are investigated under both approximations and it is shown that in most cases valley splitting causes linewidth broadening, although under extreme conditions, transition line doublets may result.