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_G 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_G = 1/C_OX + N_G/C_DOS + N_G/ηC_WF, where N_G is the number of gates, C_OX is the oxide capacitance per unit area, C_DOS is the density-of-states capacitance per unit area, C_WF is the wave function spreading capacitance per unit area, and η is a constant on the order of 1