Stark Tuning of Donor Electron Spins in Silicon

We report Stark shift measurements for ${}^{121}\mathrm{Sb}$ donor electron spins in silicon using pulsed electron spin resonance. Interdigitated metal gates on a Sb-implanted ${}^{28}\mathrm{Si}$ epilayer are used to apply the electric fields. Two quadratic Stark effects are resolved: a decrease of the hyperfine coupling between electron and nuclear spins of the donor and a decrease in electron Zeeman $g$ factor. The hyperfine term prevails at magnetic fields of 0.35 T, while the $g$ factor term is expected to dominate at higher magnetic fields. We discuss the results in the context of the Kane model quantum computer.

Figure 1

(a) Micrographs of the interdigitated gate structure used in this work to measure the donor electron spin resonance Stark effect. Bonding pads for the two gates are labeled G1 and G2. Gate lines are oriented along a long side of the sample, a [100] axis. (b) Calculated electric field distribution at donor sites for 2 V applied between the interdigitated gates. Two peaks arise from the finite depth of the implanted antimony and the finite width of the gate lines.

Figure 2

Pulsed ESR sequences for measuring Stark effect in the ${}^{28}\mathrm{Si}:\mathrm{Sb}$ epilayer. (a) Two microwave pulses, with rotation angles $\pi /2$ and $\pi$ and a constant interpulse delay $\tau$, generate a Hahn echo signal at time $2\tau$. (b) Voltage pulses applied between gates G1 and G2 (Fig. 1) are time correlated with the microwave pulses.

Figure 3

Traces of the two-pulse (Hahn) echo signals measured on the $M_I=+1/2$ hyperfine line for ${}^{28}\mathrm{Si}:\mathrm{Sb}$ at 6.2 K and the interpulse delay $\tau =40\mu \mathrm{s}$. In each plot the two signals represent the in-phase and quadrature channels of the microwave quadrature detector. (a) No gate voltage is applied (sequence I) and the detector is adjusted to produce a purely in-phase echo signal. (b) A bipolar pulse, $\pm 2\mathrm{V}$, is applied (sequence IV) during the defocusing period, and the echo signal rephases with amplitudes in both the in-phase and quadrature channel, corresponding to a phase shift of 49°.

Figure 4

Phase shift of the echo signal plotted as a function of the applied gate voltage for ${}^{28}\mathrm{Si}:\mathrm{Sb}$ at 6.2 K. Bipolar electrical pulse sequences IV and VI [Fig. 2b] were used with interpulse delay $\tau =40\mu \mathrm{s}$. Data (points) and numerical fits (lines) are shown for the $M_I=\pm 1/2$ (a) and $M_I=\pm 5/2$ (b) hyperfine lines of the six line ESR spectrum of ${}^{121}\mathrm{Sb}$. Note that phase shifts for the $M_I=\pm 5/2$ lines are extended beyond 1.5 V with the differential voltage sequence (experiment VI). For the $M_I=-1/2$ line, the data in the 2–3 V range were obtained using both the standard bipolar (IV) and differential (VI) voltage sequences. The small oscillations in the calculated curves arise from the second, higher field peak in the electric field distribution [Fig. 1b].