Energy-Dependent Tunneling from Few-Electron Dynamic Quantum Dots

We measure the electron escape rate from surface-acoustic-wave dynamic quantum dots (QDs) through a tunnel barrier. Rate equations are used to extract the tunneling rates, which change by an order of magnitude with tunnel-barrier-gate voltage. We find that the tunneling rates depend on the number of electrons in each dynamic QD because of Coulomb energy. By comparing this dependence to a saddle-point-potential model, the addition energies of the second and third electron in each dynamic QD are estimated. The scale ($\sim$ a few meV) is comparable to those in static QDs as expected.

Figure 1

Upper panel: Schematic of the device design. Lower panel: Electron micrograph of the device’s surface gates. The dark shaded gates were grounded.

Figure 2

$I_{\mathrm{in}}$ (dotted line) and $I_{\mathrm{out}}$ (solid lines) dependence on injector gate voltage for a range of barrier-gate voltages. Plateaus occur when an integer number ($N$) of electrons occurs in each SAW minimum. $I_t$ is the difference between the two curves.

Figure 3

The ratios $I_{\mathrm{in}}/I_{\mathrm{out}}$ as a function of barrier-gate voltage, taken from the $I_{\mathrm{in}}$ plateau corresponding to $N=1$ (■), $N=2$ (○), and $N=3$ (×). Inset: Schematic of tunneling of electrons from the dynamic QD across the barrier into the reservoir—energies of the electrons within the dot are dependent on $n$, leading to $n$-dependent tunneling rates.

Figure 4

Dependence of the calculated tunneling rates ${\Gamma }_n$ on barrier-gate voltage for one (■), two (○), and three (×) electrons in the dynamic QD, normalized by the tunneling time ${\tau }_n$. The solid lines show fits based on the tunneling probability of noninteracting electrons incident on a saddle-point potential, as described in the text. Inset: Example of the time evolution of $P_n$ for $3ef$ injection, using tunnel rates for $V_T=-0.575\mathrm{V}$.