Measurements and atomistic theory of electron $g$ factor anisotropy for phosphorus donors in strained silicon

TL;DR

This study combines experimental measurements and atomistic simulations to analyze how strain affects the electron g-factor anisotropy in phosphorus donors within silicon, providing insights relevant for quantum and spintronic devices.

Contribution

It offers the first combined experimental and theoretical analysis of g-factor anisotropy in strained silicon phosphorus donors, revealing how strain reduces anisotropy and predicting effects of combined strain and electric fields.

Findings

g-factor anisotropy decreases with strain, linearly for x<7%

Measured anisotropy at 20% strain is 1.2×10^{-3}, matching simulations

Strain dominates over electric fields in affecting g-factor anisotropy

Abstract

This work reports the measurement of electron $g$ factor anisotropy ($| \Delta g |$ = $| g_{001} - g_{1 \bar 1 0} |$) for phosphorous donor qubits in strained silicon (sSi = Si/Si$_{1-x}$Ge$_x$) environments. Multi-million-atom tight-binding simulations are performed to understand the measured decrease in $| \Delta g |$ as a function of $x$, which is attributed to a reduction in the interface-related anisotropy. For $x <$7\%, the variation in $| \Delta g |$ is linear and can be described by $\eta_x x$, where $\eta_x \approx$1.62$\times$ 10$^{-3}$. At $x$=20\%, the measured $| \Delta g |$ is 1.2 $\pm$ 0.04 $\times$ 10$^{-3}$, which is in good agreement with the computed value of 1$\times 10^{-3}$. When strain and electric fields are applied simultaneously, the strain effect is predicted to play a dominant role on $| \Delta g |$. Our results provide useful insights on spin properties of sSi:P for spin qubits, and more generally for devices in spintronics and valleytronics areas of research.