CURRENT-VOLTAGE CHARACTERISTIC AND DIFFERENTIAL CONDUCTANCE OF A POINT-CONTACT AND PLANAR TUNNEL CONTACT BETWEEN AN ORDINARY METAL AND SUPERCONDUCTOR IN REALISTIC 3-DIMENSIONAL GEOMETRY - COMPARISON WITH A ONE-DIMENSIONAL CASE

Current-voltage characteristic for a point or planar tunnel contact of the structure ordinary metal-finite-thickness barrier-ordinary superc onductor was derived taking into account a realistic three-dimensional (3D) geometry of the problem. Ordinary and Andreev reflection coeffic ients were obtained by means of a so-called transmission matrix for re gions with varying model parameters. The model with a sharp barrier-su perconductor interface was investigated in detail. For contacts with a barrier transmissivity clearly dependent on the incident electron ene rgy for electrons from the chemical potential vicinity, differential c onductances are very different from the curves usually provided by the commonly used one-dimensional (1D) theories. Due to a relevant influe nce of an applied voltage on the barrier shape and height, the differe ntial conductance as a function of voltage is a rough curve with a num ber of peaks at various voltage values. For contacts with a barrier tr ansmissivity practically independent on the incident electron energy, expressions for ordinary and Andreev reflection coefficients are forma lly the same as in 1D theories. But in our approach the barrier charac ter is described by an increasing function of an electron incidence an gle instead of a single parameter (barrier strength Z) in 1D cases. Du e to this difference, the differential conductance calculated within t he 3D approach reveals more tunnel character than the one obtained for the same barrier from a 1D theory. (C) 1997 Elsevier Science B.V.