Analysis of mechanism for resonant tunneling via localized states in thin SiO2 films

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Abstract
In this work we use transfer matrix and Airy function approaches to investigate the distribution of carriers within thin SiO2 films containing localized states for Si/SiO2/Si structure in detail. We show that the distribution of the probability density ‖ψ‖2 within oxide films has a shape with, at first, a monotonically exponential decrease from the Si/SiO2 interface, then arriving at a valley, and followed by a peak at the center for the case of ‘‘off’’ resonance. When the carrier energy matches that of the eigenstate the probability density is exponentially decreased from the localized center on both sides. We show that there are two kinds of probability densities corresponding to resonant tunneling via a localized state within the barrier. On increasing the reverse applied field, the localization degree of the wave function decreases.