Electrical operation of hole spin qubits in planar MOS silicon quantum dots

Silicon hole quantum dots have been the subject of considerable attention thanks to their strong spin-orbit coupling enabling electrical control, a feature that has been demonstrated in recent experiments combined with the prospects for scalable fabrication in CMOS (complementary metal-oxide-semiconductor) foundries. The physics of silicon holes is qualitatively different from germanium holes and requires a separate theoretical description, since many aspects differ substantially: the effective masses, cubic symmetry terms, spin-orbit energy scales, magnetic field response, and the role of the split-off band and strain. In this work, we theoretically study the electrical control and coherence properties of silicon hole dots with different magnetic field orientations, using a combined analytical and numerical approach. We discuss possible experimental configurations required to obtain a sweet spot in the qubit Larmor frequency to optimize the electric dipole spin resonance (EDSR) Rabi time, the phonon relaxation time, and the dephasing due to random telegraph noise. Our main findings are as follows. (i) The in-plane $g$ factor is strongly influenced by the presence of the split-off band, as well as by any shear strain that is typically present in the sample. The $g$ factor is a nonmonotonic function of the top gate electric field, in agreement with recent experiments. This enables coherence sweet spots at specific values of the top gate field and specific magnetic field orientations. (ii) Even a small ellipticity (aspect ratios $\sim 1.2$) causes significant anisotropy in the in-plane $g$ factor, which can vary by $50\%–100\%$ as the magnetic field is rotated in the plane. This is again consistent with experimental observations. (iii) EDSR Rabi frequencies are comparable to Ge and the ratio between the relaxation time and the EDSR Rabi time $\sim {10}^5$. For an out-of-plane magnetic field the EDSR Rabi frequency is anisotropic with respect to the orientation of the driving electric field, varying by $\approx 20\%$ as the driving field is rotated in the plane. Our work aims to stimulate experiments by providing guidelines on optimizing configurations and geometries to achieve robust, fast, and long-lived hole spin qubits in silicon.