Zur berechnung des tunnelstroms durch eine trapezförmige potentialstufe

Abstract

The transmission coefficient D( V) and the tunnel current I( V) for a trapezoidal potential barrier is calculated as a function of applied voltage V. In earlier works the WKB approximation was used evaluating the transmission coefficient and therefore only the barrier between the classical turning points was considered. The WKB transmission coefficient of a trapezoidal potential barrier is a monotonically decreasing function of applied voltage. In the present paper the exact treatment of the whole barrier shows that the transmission coefficient D( V) can be a function with superposed periodic oscillations. These oscillations are caused by partial reflection and interference of electron waves in the part of the trapezoidal barrier, where the potential energy is less than the kinetic energy of the electron. Also the calculated tunnel current I( V) can have a noticeable superposed oscillation. For observing this oscillation in metal-insulator-metal films the conditions are large electron mean free path (probable some hundred AE) in the dielectric layer and specular reflection from the barrier boundaries.