Quantum charge transportation in metal-oxide-Si structures with ultrathin oxide

Abstract

Quantum electron dynamics in metal-oxide-silicon structures with ultrathin oxide is calculated. A linear model of the surface-potential energy is used in the calculation. This treatment simplifies the computation for both the interface potential and the field penetration distance in the substrate. The electronic metastable states induced by the internal field penetration in the substrate and the running states in the gate region are then treated separately, with a weak condition for the continuity of the probability density at the substrate-dielectric interface. The probability current in the gate and then the total tunneling current are obtained for different gate voltages. While the spectrum of the transverse energy in the metastable states is assumed as continuous, the emerging probability current is shown to vanish for a finite number of values of the transverse energy, which may be interpreted as standing (bound) states in the structure. This model yields excellent fittings for the experimental data obtained from metal-oxide-semiconductor structures with different ultrathin gate dielectrics.