Calculation of the direct tunneling current in a metal-oxide-semiconductor structure with one-side open boundary

Abstract

The leakage current through the oxide of an n-channel metal-oxide-semiconductor (MOS) structure with an open boundary on one side is numerically computed by applying a one-dimensional Schrödinger-Poisson self-consistent solver. By embedding the n-channel MOS structure in a well, which prevents the penetration of particles into the metallic gate, the potential profile, the bounded energy levels, and the spatial distribution of electrons in the quantized levels are calculated in the inversion regime. Penetration of electrons into the metallic gate with an open boundary results in a broadening of the discrete bound states at the interface of the substrate with the oxide, transforming the bounded energy levels to the quasibound states. Starting from the continuity equation, a qualitative formula for the current in terms of the electron lifetime in the quasibound states is derived. Based on the determination of the energy level width corresponding to the wave functions, we suggest a method to compute the lifetime, and subsequently, the tunneling current across the potential barrier. The tunneling current is computed for a MOS structure with SiO2 and Si3N4 gate dielectrics. The computational results are compared with those obtained experimentally for similar structures, yielding an excellent agreement.