Square-Mean-Root Approximation for Evaluating Asymmetric Tunneling Characteristics

A new method of approximating the basic tunnel integral is used to calculate the asymmetric characteristics of the tunnel effect between two dissimilar electrodes separated by a thin insulating film. The method is to approximate the true potential barrier by an equivalent rectangular barrier whose height is determined by the square-mean-root value of the true barrier. Even for barriers of trapezoidal shape, the calculation gives the polarity dependence of the J—V characteristics in the low-voltage region, as well as in the higher-voltage region. The asymmetry at low voltage for trapezoidal barriers has not been predicted in previous calculations.