Determination of the dispersion relation in tunnel structures: Influence of the barrier shape and validity of the WKB approximation

Abstract

A simulation study has been made of the way in which the shape of the barrier influences the determination of the energy-momentum relationship in the insulator forbidden band of M-I-M tunnel junctions. It is shown that the method which analyses current-voltage data for different insulator thicknesses (Stratton, Lewicki, Mead) is rather insensitive to the barrier shape. Analysis of current-voltage data for only a single insulator thickness (Korneffel, Ludwig) is found to be less appropriate because the dispersion relationship is strongly affected by the barrier shape. Some consequences are discussed. Application of an exact expression for the transmission probability indicates that the error involved by the use of the WKB approximation is small. © 1973.