Electron tunneling through thin oxide–nitride–oxide films under electric field concentration

Abstract

Electron tunneling through the thin ONO films formed on the rough poly-Si surface, which grain sizes are nonuniform, is investigated theoretically considering the model for the electric field concentration at the convex edge of the plate electrode. Assuming the normal distribution of the curvature radius for the convex edge of the plate electrode, the leakage currents are calculated from the direct-tunneling (DT) current that is introduced from the WKB approximation method. The fitting of the calculated leakage current to the measured one is performed by considering a coefficient of the electric field concentration at the convex edge, the effective mass of the electron and the standard deviation of the normal distribution for the curvature radius. By solving the Schrödinger equation numerically, the wave functions are calculated both for the condition with the electric field concentration and for the condition without it. The relationship between the transmission coefficient of the electrons and the electric field concentration indicates that the electric field concentration at the convex edge enhances the DT of the electrons through the ONO films. The transmission coefficient shows the peaks at the particular potential energies, and they are due to the resonant-tunneling (RT). It is found that the electric field concentration also enhances the RT. It is thought that DT mechanism at the convex edge of the plate electrode occurs in the low voltage range and the RT mechanism occurs in the high voltage range.