Intervalley splitting and intersubband transitions inn-typeSi∕SiGequantum wells: Pseudopotential vs. effective mass calculation

Abstract

Intervalley mixing between conduction-band states in low-dimensional $\mathrm{Si}∕\mathrm{Si}\mathrm{Ge}$ 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.