Hole Spin Resonance and Spin-Orbit Coupling in a Silicon Metal-Oxide-Semiconductor Field-Effect Transistor

We study hole spin resonance in a $p$-channel silicon metal-oxide-semiconductor field-effect transistor. In the subthreshold region, the measured source-drain current reveals a double dot in the channel. The observed spin resonance spectra agree with a model of strongly coupled two-spin states in the presence of a spin-orbit-induced anticrossing. Detailed spectroscopy at the anticrossing shows a suppressed spin resonance signal due to spin-orbit-induced quantum state mixing. This suppression is also observed for multiphoton spin resonances. Our experimental observations agree with theoretical calculations.

Figure 1

(a) Schematic of the MOSFET device and measurement setup. (b) Potential landscape of quantum dots. (c) Intensity plot of $d{I}_D/d{V}_S$ near the subthreshold region. The spin resonance is observed in the region enclosed by the yellow dotted curve. The $d{I}_D/d{V}_S=0$ regions for $V_G\approx -0.635\mathrm{V}$ are artifacts of the current meter. (d) Schematic energy diagram for two-hole states with a $T_{+}–S$ anticrossing due to the spin-orbit interaction. The microwave-induced transitions $T_{-}–S$ (red solid lines), $T_0–S$ (blue dotted lines), $T_{+}–S$ (green dashed lines) are indicated by vertical arrows. (e) Intensity plot of $d{I}_D/dB$ measured at $V_S=25\mathrm{mV}$, $V_G=-0.597\mathrm{V}$. For $B>0$ the high-current EDSR curves due to the transitions $T_{-}–S$ (red solid lines), $T_0–S$ (blue dotted lines), $T_{+}–S$ (green dashed lines) are indicated. Plotting $d{I}_D/dB$ suppresses resonances at constant frequency due to photon-assisted tunneling enhanced by cavity modes.

Figure 2

(a) Measured and (b) calculated spin resonance spectra near the $T_{+}–S$ anticrossing point for weak microwave driving [$-40\mathrm{dBm}$ at the output of the microwave source for (a), and microwave amplitude $A=30\mu \mathrm{eV}$ for (b)]. Measured (c) and calculated (d) peak height (bright line, left axis), and background current without microwave (dark line, right axis).

Figure 3

Measured spin resonance spectra near the $T_{+}–S$ anticrossing at higher microwave powers (a) $-30\mathrm{dBm}$, (c) $-22\mathrm{dBm}$, and (e) $-20\mathrm{dBm}$ at the output of the microwave source, respectively. Results of calculation for microwave amplitude (b) $A=100\mu \mathrm{eV}$, (d) $A=200\mu \mathrm{eV}$, and (f) $A=400\mu \mathrm{eV}$.