This paper investigates the simulation of charging a semiconductor quantum-dot cellular automata (QCA) cell in the presence of impurity atoms. The complete configuration space of the cell and the impurities is analysed using the canonical partition function. Limits on the size and location of the impurity region are determined. Within these limits, it is shown that the semiconductor QCA cell can be controllably charged. Using these results, it is shown that a short wire consisting of three QCA cells can operate with high logical correctness at cryogenic temperatures.
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