Modeling tunneling through ultra-thin gate oxides

For the purpose of MOS device simulation both the numerical solution of the Schrodinger equation and the WKB approximation, which includes the numerical action integral, are too time-consuming, since the outer numerical integration is unavoidable to obtain the current. An analytical function τ(E) is desirable that takes into account the image force in a better way than by the lowering of a trapezoidal barrier. Based on the observation that the tunnel probability is mainly determined by the action of the barrier, we propose a "pseudobarrier" method.