Valley population of donor states in highly strained silicon

TL;DR

This paper investigates how strain in silicon affects the valley states of phosphorus donors, revealing out-of-plane valley dominance and implications for quantum device engineering.

Contribution

It combines experimental imaging and theoretical modeling to analyze valley population changes in strained silicon and their impact on quantum device properties.

Findings

Out-of-plane valleys dominate in strained silicon

Strain induces isotropic exchange and tunnel interactions

Higher orbital states influence valley population relationships

Abstract

Strain is extensively used to controllably tailor the electronic properties of materials. In the context of indirect band-gap semiconductors such as silicon, strain lifts the valley degeneracy of the six conduction band minima, and by extension the valley states of electrons bound to phosphorus donors. Here, single phosphorus atoms are embedded in an engineered thin layer of silicon strained to 0.8% and their wave function imaged using spatially resolved spectroscopy. A prevalence of the out-of-plane valleys is confirmed from the real-space images, and a combination of theoretical modelling tools is used to assess how this valley repopulation effect can yield isotropic exchange and tunnel interactions in the $xy$-plane relevant for atomically precise donor qubit devices. Finally, the residual presence of in-plane valleys is evidenced by a Fourier analysis of both experimental and theoretical images, and atomistic calculations highlight the importance of higher orbital excited states to obtain a precise relationship between valley population and strain. Controlling the valley degree of freedom in engineered strained epilayers provides a new competitive asset for the development of donor-based quantum technologies in silicon.