Analytical Solution to the Density-Gradient Equation for MOS Quantum Tunneling

Engineering-oriented simulations of quantum mechanical tunneling are often based on density-gradient(DG) theory.This paper presents an analytical solution to the DG equation for quantum tunneling through an ultra-thin oxide in a MOS capacitor with an n+ poly-silicon gate obtained using the method of matched asymptotic expansions.Tunneling boundary conditions extend the approximation into the entire region of the poly-silicon gate,oxide barrier,and substrate.An analytical solution in the form of an asymptoti...