Fig. 3: Variability of the spin–orbit coupling.
From: Bounds to electron spin qubit variability for scalable CMOS architectures
a, b Comparison between g-factor variability in atomistic simulations and measurements in devices A to E under a varying magnetic field angle. On each device and configuration we measured two qubits. In a we compare the difference between the Larmor frequencies of the two-qubit qubits measured in each device (g1−g2)μB vs the differences between the frequency of neighbouring dots simulated atomistically (Fig. 1b). The marker for experimental data is associated with the device (A to E). In b, we compare the top gate Stark shift dg/dV measured in the two qubits of each device, with atomistic simulations of the dots (methods). Two qubits in a device have a different Stark shift dg/dV due to variations in surface roughness. Filled markers represent the data for the first qubit and empty makers for the second qubit (e.g. the empty purple triangles represent the Stark shifts measure on the second qubit of device E). c, d Distribution of simulated Dresselhaus β (c) and Rashba α (d) spin–orbit terms versus vertical electric field Ez. Box plots indicate the median (middle line), 25th, 75th percentile (box) and 5th and 95th percentile (whiskers), as well as outliers (single points). e, f Schematic table showing that the sinusoidal dependence of the g-factors versus in-plane magnetic angle (e) follows from the anisotropy in the silicon lattice near the interface shown in (f). In an ideal flat surface, the border of silicon must end in one of the two possible sublattices A (black circles) or B (grey circles) and the interface looks different when observed from the [110] and the \(1\bar{1}0\) lattice orientations. In a realistic rough surface, the border is a mixture of both A and B sub-lattice terminations, which explains the observed g-factor variability g Distribution of qubit frequencies for two magnetic field orientations: [110] and [100]. Qubits affected by near-valley degeneracies in the simulation are not included in this figure. The bars show an estimate for the maximum gate tunability of the g-factors with the top gate and a lateral gate (methods). The typical range of tunability for this gate is about 0.2 V for these devices. A higher potential bias could induce a charge transition, thus ruining the two-qubit system. h Zoom to the [100] data in (g). Source data are provided in the Source Data file.
