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The island size dependence of the capacitance components of single-electron transistors (SETs) based on gate-induced Si islands was extracted from the electrical characteristics. In the fabricated SETs, the sidewall gate tunes the electrically induced tunnel junctions, and controls the phase of the Coulomb oscillation. The capacitance between the sidewall gate and the Si island extracted from the Coulomb oscillation phase shift of the SETs with sidewall depletion gates on a silicon-on-insulator nanowire was independent of the Si island size, which is consistent with the device structure. The Coulomb oscillation phase shift of the fabricated SETs has the potential for a complementary operation. As a possible application to single-electron logic, the complementary single-electron inverter and binary decision diagram operation on the basis of the Coulomb oscillation phase shift and the tunable tunnel junctions were demonstrated.