Electroelastic Hyperfine Tuning of Phosphorus Donors in Silicon

We demonstrate an electroelastic control of the hyperfine interaction between nuclear and electronic spins opening an alternative way to address and couple spin-based qubits. The hyperfine interaction is measured by electrically detected magnetic resonance in phosphorus-doped silicon epitaxial layers employing a hybrid structure consisting of a silicon-germanium virtual substrate and a piezoelectric actuator. By applying a voltage to the actuator, the hyperfine interaction is changed by up to 0.9 MHz, which would be enough to shift the phosphorus donor electron spin out of resonance by more than one linewidth in isotopically purified ${}^{28}\mathrm{Si}$.

Figure 1

Illustration of a modified architecture for a spin-based Si quantum computer with electroelastic $A$ gates, realized by piezoelectric nanoactuators. These actuators strain the crystal in the vicinity of the donor, which alters the hf coupling between nuclear spin (small red arrow) and electronic spin (large blue arrow) and thus allows us to shift the donor spins in and out of resonance. The isolines show the distribution of the out-of-plane strain ${\epsilon }_{33}$, normalized to its maximum value, as described in the text. The ${}^{28}\mathrm{Si}$ layer is grown on a virtual SiGe substrate to enhance the efficiency of the electroelastic gates.

Figure 2

Hyperfine splitting as a function of the out-of-plane strain according to VRM (dashed line) and DFT (solid squares) calculations; the solid line is a guide to the eye. The hf interaction of the sample studied with EDMR (open circle) is reproduced by the DFT calculations.

Figure 3

The hybrid device used for the EDMR measurements allows for on-chip microwave magnetic field generation by a loop-terminated CPS, photoconductivity measurements, and application of voltage-controlled strain. Strain along the [110] direction results in in- and out-of-plane strain components.

Figure 4

The EDMR spectra obtained at actuator voltages $V_p=\pm 200\mathrm{V}$ are shown in (b). In (a) the low-field ${}^{31}\mathrm{P}$ resonance is magnified, demonstrating the actuator tuning of the hf interaction, which is a linear function of $|\Delta V_p|$, as shown in the inset. The spectra in (b) have been fitted by Lorentzian lines, and the difference of the fits is shown in (c) together with the difference of the measured data.