Inversion gate capacitance of undoped single-gate and double-gate field-effect transistor geometries in the extreme quantum limit

We present first-principle analytical derivations and numerically modeled data to show that the gate capacitance per unit gate area C of extremely thin undoped-channel single-gate and double-gate field-effect transistor geometries in the extreme quantum limit with single-subband occupancy can be written as 1/C=1/C+N/C+N/ηC, where N is the number of gates, C is the oxide capacitance per unit area, C is the density-of-states capacitance per unit area, C is the wave function spreading capacitance per unit area, and η is a constant on the order of 1.