Modeling of charge quantization and wave function penetration effects in a metal–oxide–semiconductor system with ultrathin gate oxide

We investigated the charge quantization and wave function penetration effects in a metal–oxide–semiconductor structure using an in-house developed quantum mechanical (QM) capacitance–voltage (C–V) simulator (denoted as NUSQM), which solves the Schrödinger and Poisson equations self-consistently. The C–V results obtained from the NUSQM simulator were compared with those obtained from other QM simulators in the literature (i.e., U.C. Berkeley, U.T. Quant, NEMO, and North Carolina State University). The results in the present work are generally in good agreement with the other simulators in the inversion region while some discrepancies exist among the different simulators in the accumulation region. It was found that the wave function penetration has a non-negligible effect on the gate capacitance and resulting C–V curves when the oxide thickness decreases to 1 nm and below.