Single-electron pumping in common-gate triple-dot devices is examined for arbitrary asymmetric gate capacitance distributions. Here, the ratio of the three gate capacitances is assumed to be a + d/2:1:a − d/2, where a and d are arbitrary positive real numbers. To ensure that pumping occurs, the gate voltage should be swung such that the set of excess electron numbers in the three dots is (ns, nc, ns) at low gate voltage and (ns, nc + 1, ns) or (ns + 1, nc − 1, ns + 1) at high gate voltage, where ns and nc are arbitrary integers. Moreover, (a, d) should be within a region that depends on the set of excess electron numbers at high and low gate voltages. Thus, the regions for pumping in the a–d plane are revealed. The absolute value of the bias voltage for pumping is limited to a maximum value, called the critical voltage. The critical voltage is also demonstrated as a function of a and d. The largest critical voltage obtained in this study is 2.5 times that reported in previous work for common-gate triple-dot devices.
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The derivations of the CB conditions as linear inequalities of Vsd, Vg, and n1 to n3 are similar to those for quadruple-dot SE devices described in Appendices A and B of Ref. . Thus, only the results for triple-dot devices are presented here because the derivation procedure is very long.
Here, Q1, Q2, and Q3 are defined as follows.
The source and drain voltages are defined as follows.
The total capacitances are as follows.
The parallel capacitances CLgi and CRgi in the coefficients and the series capacitances CLi and CRi are obtained inductively as follows.
In this paper, the junction capacitances C(k+1)k are uniform and equal to Cj.
Tunneling event Tkk′ can occur when CTk′k (Vk′ − Vk) is greater than e/2, where CTk′k is equal to CTkk′ if k = k′ + 1. Here, (Vk′ − Vk) is explained to be the dominant factor that determines which of Tkk′ and T(4–k′)(4–k) is preferable when the operating point leaves an SR along the V′g axis.
If d > 0, that is, Cg1 > Cg3, then V1 is always greater than V3 for Vsd = 0, Vg > 0, n1 = n3 ≥ 0 and n2 ≥ 0. The reason is as follows. If Vg is positive and no excess electrons exist at the three islands, then V1 is increased by Vg more strongly than V3 because island I1 is capacitively coupled with the gate electrode more strongly than island I3 is. If excess electrons exist in the three islands symmetrically (n1 = n3) and Vg is zero, then V1 is decreased from zero by excess electrons more weakly than V3 because island I1 is capacitively coupled with the zero-biased gate electrode more strongly than island I3 is. Thus, if Vg is positive and excess electrons exist, then V1 is always greater than V3 because of the principle of superposition.
Thus, V1 − V2 > V3 − V2, V2 − V3 > V2 − V1, V1 − V0 > V3 − V4, and V4 − V3 > V0 − V1 because V0 = V4 = 0. If (Vk′ − Vk) is the dominant factor, then these inequalities are consistent with the fact that T21, T32, T01, and T34 are preferred over T23, T12, T43, and T10, respectively. Consequently, b21, b32, b01 and b34 are chosen as the boundary segments of an SR.
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Imai, S., Takanoya, R. Single-electron pumping in common-gate triple-dot devices with arbitrary asymmetric gate capacitance distributions. J Comput Electron (2020). https://doi.org/10.1007/s10825-020-01552-z
- Single-electron pumping
- Common-gate triple-dot structure
- Stability regions
- Coulomb blockade