This work reports the measurement of electron $g$-factor anisotropy $\left(\left|\mathrm{\Delta }g\right|=|g_{001}-g_{1\overline{1}0}|\right)$ for phosphorous donor qubits in strained silicon (sSi = Si/${\mathrm{Si}}_{1-x}{\mathrm{Ge}}_x)$ environments. Multimillion-atom tight-binding simulations are performed to understand the measured decrease in $\left|\mathrm{\Delta }g\right|$ as a function of $x$, which is attributed to a reduction in the interface-related anisotropy. For $x<7\%$, the variation in $\left|\mathrm{\Delta }g\right|$ is linear and can be described by ${\eta }_{x}x$, where ${\eta }_x\approx 1.62\times {10}^{-3}$. At $x=20\%$, the measured $\left|\mathrm{\Delta }g\right|$ 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 $\left|\mathrm{\Delta }g\right|$. Our results provide useful insights on the spin properties of sSi:P for spin qubits, and more generally for devices in spintronics and valleytronics areas of research.

• Received 18 December 2017
• Revised 1 June 2018

DOI:https://doi.org/10.1103/PhysRevB.98.035432