Semiconductor multiple-quantum-dot devices have been attracted as a single-electron pump and quantum bits (qubits) [1, 2]. In particular, silicon-based coupled-quantum-dot has been paid attentions for the applications as qubits in solid state quantum computers due to their long coherent time of electron spins [3]. In the previous reports, these devices have been demonstrated by the use of two-dimensional electron gas (2DEG) and multiple control gates, where many gates were used to form tunnel barriers. This device concept makes it difficult to integrate quantum dots (QDs) due to the interference of many gates. For the applications in quantum computing, development of coupled QDs with a smaller number of control gates is considered.

We have already succeeded in the fabrication of serially coupled Si triple-quantum-dots (TQD) by pattern-dependent oxidation (PADOX) method [4] and additional oxidation of the silicon nanowire on a SOI wafer with three control gates [5, 6]. The formation of a Si TQD, where each QD is formed just under each control gate, was confirmed experimentally.

The equivalent circuit of the fabricated TQD is shown in Fig. 1 (a). The device has nine gate capacitances and two inter-dot coupling capacitances. It is crucial to know these capacitances for controlling the potential and the number of electrons of each dot. It is well known that the nine gate capacitances can be evaluated from the stability diagram that consists of boundary of the charge transition in the QDs. If the distance between the three gates is relatively long enough to ignore the influence of non-adjacent QD, it is easy to get the stability diagrams of charges. However, when the TQD become compact in size, the outer QD cannot be ignored because the center gate strongly couples to all three QDs, i.e., C₂₃ or C₂₁ is comparable to C₂₂. The stability diagram of such TQD usually shows very complicated behavior because three boundaries of the charge transition lines of individual QDs are superimposed. Fig. 1(b) shows the stability diagram which is the contour plot of current of TQD at 10 K simulated as a function of the two gate voltages V₁ and V₂ by the use of Monte Carlo method. Green dotted lines in the figures are the boundaries of charge transition of QD3, which are difficult to determine from the diagram. In addition, the coupling capacitance between the QDs also makes the stability diagrams complicate. Figs. 1(c) and (d) show stability diagrams of the TQD when the coupling capacitances, C₂ and C₃, become larger. As shown in the figures, the current peaks (white regions) are split as coupling capacitance C₂ and C₃ increase.

In this study, we propose a simple analyzing method to evaluate the TQD by defining the contributions from each QD in stability diagrams. In order to divide the complicated stability diagram of TQD into the diagram of each QD, we employ the simultaneous scanning of three gate voltages with different sweeping ratios [7]. The effectiveness of the method is also confirmed even when the inter-dot coupling capacitance is large as shown in Fig. 1(c) and (d). The analysis using this method was applied to a Si TQD device fabricated on SOI wafer and successfully achieved the nine gate capacitances of the TQD.

Acknowledgement

This work was partly supported by JSPS KAKENHI (nos. 25420279, 26630141, 15H01706, 16H04339 and 16K18073).

References

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