A single electron tunneling device consisting of a double junction with inductance, resistance and capacitance (Z-SET) is considered. Current-voltage characteristics are calculated using a self-consistent treatment of the environmental impedance.It is shown that the single electron tunneling can be controlled by modulating the resistive environmental impedance. It is also shown that the controllability of the device is strongly degraded when the capacitance becomes large. This suggests theimportance of the careful design of Z-SET against the stray capacitance inevitable in the actual device. The critical value of stray capacitance for controllability of Z-SET is estimated.
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