Orbital and valley state spectra of a few-electron silicon quantum dot

Understanding interactions between orbital and valley quantum states in silicon nanodevices is crucial in assessing the prospects of spin-based qubits. We study the energy spectra of a few-electron silicon metal-oxide-semiconductor quantum dot using dynamic charge sensing and pulsed-voltage spectroscopy. The occupancy of the quantum dot is probed down to the single-electron level using a nearby single-electron transistor as a charge sensor. The energy of the first orbital excited state is found to decrease rapidly as the electron occupancy increases from $N=1$ to 4. By monitoring the sequential spin filling of the dot we extract a valley splitting of $\sim 230\mu$eV, irrespective of electron number. This indicates that favorable conditions for qubit operation are in place in the few-electron regime.

Figure 1

(a) SEM image of a quantum dot integrated with a SET and the measurement setup. Only colored gates are used in the experiments. (b) and (c) Schematic energy diagrams during pulsing of gate P with two different $V_{\mathrm{P}}$ offsets.

Figure 2

(a) SET sensor lock-in current $I_{\mathrm{S}}$ vs $V_{\mathrm{P}}$ and $V_{\mathrm{RB}}$, mapping out the charge stability plot of the quantum dot. Dynamic compensation is applied to the SET sensor. (b) Measured pulse lock-in signal $I_{\mathrm{pulse}}$ from SET sensor with a symmetric square wave of peak-to-peak voltage $V_{\mathrm{pulse}}=2$ mV applied to dot plunger P at $f_{\mathrm{pulse}}=487$ Hz. The first charge transition is not visible because the tunnel rate into/out of dot is too low with respect to $f_{\mathrm{pulse}}$. (c) Lock-in detection signal, with $V_{\mathrm{pulse}}=20$ mV, at $f_{\mathrm{pulse}}=444$ Hz for $N=2\leftrightarrow 3$ transition, extracted along the yellow dashed line in (d) at $V_{\mathrm{pulse}}=20$ mV. The red arrow indicates the orbital excited state. (d) Derivative of the detection signal with respect to $V_{\mathrm{P}}$. Orbital ground and excited states are observed at the loading edge as white parallel lines.

Figure 3

(a) Lock-in signal from sensor S with $V_{\mathrm{pulse}}=40$ mV at $f_{\mathrm{pulse}}=487$ Hz applied to gate P, as a function of $V_{\mathrm{P}}$ and $V_{\mathrm{LB}}$. Here we apply a linear scaling of the lock-in output to directly indicate the excess electron occupancy $\Delta N$ on the dot. (Inset) different region focusing on the first transition shown to enhance visibility of both excited state and unloading edge. (b) Orbital excited-state energy of the first four electrons at $V_{\mathrm{LB}}=0.3$ V. (c) Positions of $\Delta N=0.5$ for ground states (GS) and first excited states (OS). These points are extracted from panel (a) where the tunnel rate from the reservoir to the dot is around 974 Hz.

Figure 4

(a) Grayscale plot of the QD differential occupancy (${\Delta }^{2}N$) in magnetic field for the first four electron transitions at $V_{\mathrm{pulse}}=20$ mV and $f_{\mathrm{pulse}}=487$ Hz. Orbital excited states, Zeeman splittings and valley-orbit splitting are observed. $V_{\mathrm{P}}^{\prime }$ represents arbitrarily shifted $V_{\mathrm{P}}$. (b) Schematic of the evolution of two nondegenerate valley eigenstates for positive $B$ field. V${}_1$ (V${}_1$’) and V${}_2$ (V${}_2$’) represent loading (unloading) edge states. Each valley state Zeeman splits into two levels at finite $B$ fields. The blue dots represent already-occupied electron states.