Modified Airy function method for modeling of direct tunneling current in metal-oxide-semiconductor structures

Using a modified Airy function (MAF) to solve the Schrodinger equation in t he whole metaloxide-semiconductor structure, a fully quantum-mechanical mod el of direct tunneling current from an inverted p-Si substrate through ultr athin oxides is presented. The effects of tunneling on the electrostatic po tential and the distribution of electrons are also included when self-consi stently solving the Schrodinger and Poisson equations in silicon. Due to th e semianalytical nature of the MAF method, the model has Iii-h efficiency. Model results are compared with experimental data and show excellent agreem ent. Moreover, an approximately linear relationship between the logarithm o f the direct tunneling current and oxide thickness is found out. (C) 2001 A merican Institute of Physics.