Exactly solvable model for metal-insulator -metal stepped boundary tunnel junctions

摘要

An exactly solvable model, which treats the effective barrier potential of the biased metal-insulator-metal tunnel junctions as a trapezoidal potential with an ideal stepped boundary, is presented. Thus, the exact analytic expressions for the electron wave functions and the tunneling probabilities were obtained by solving Schrodinger's equation strictly. It is found that if the longitudinal kinetic energy of the electron, E_x, is greater than the shorter side of the trapezoidal potential, in the barrier region Schordinger equation has to be solved in the two subregions: where E_x is lower and higher than the barrier height, respectively.