Donor states in modulation-doped Si/SiGe heterostructures

TL;DR

This paper introduces a comprehensive, non-variational method to calculate the properties of shallow donors in Si/SiGe heterostructures, including energies, wave functions, and optical spectra, considering strain and central-cell effects.

Contribution

A unified approach for calculating donor states in heterostructure quantum wells, capable of determining energies, wave functions, and optical properties with consideration of strain and central-cell effects.

Findings

Calculated binding energies and wave functions for donors in Si/SiGe wells.

Analyzed the impact of donor position on impurity states.

Predicted optical absorption spectra with anisotropic features.

Abstract

We present a unified approach for calculating the properties of shallow donors inside or outside heterostructure quantum wells. The method allows us to obtain not only the binding energies of all localized states of any symmetry, but also the energy width of the resonant states which may appear when a localized state becomes degenerate with the continuous quantum well subbands. The approach is non-variational, and we are therefore also able to evaluate the wave functions. This is used to calculate the optical absorption spectrum, which is strongly non-isotropic due to the selection rules. The results obtained from calculations for Si/Si$_{1-x}$Ge$_x$ quantum wells allow us to present the general behavior of the impurity states, as the donor position is varied from the center of the well to deep inside the barrier. The influence on the donor ground state from both the central-cell effect and the strain arising from the lattice mismatch is carefully considered.