Definition of curve fitting parameter to study tunneling and trapping of electrons in Si/ultra-thin SiO2/metal structures

The tunneling of electrons through metal–oxide–silicon (MOS) structures with ultra-thin oxide is modeled using a linear model for the electron potential energy, an approach which simplifies the computation of both the interface potential and the field penetration distance in the substrate. The one-particle quantum problem is split into finding the metastable states induced by the internal field penetration in the substrate and the running states in the gate region. The two states are assumed to be connected by the condition for the continuity of the probability density at the substrate–dielectric interface. The electron probability current and the total gate current density are obtained for different gate voltages. As the model yields excellent fittings with experimental current–voltage (I–V) data for MOS structures, it was further applied to constant current stressing analysis in order to obtain values for important electron trapping parameters in the oxide. The resultant estimates of the electron trapping cross-section fall in the range of other independent determinations in the literature.