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

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.