INFLUENCE OF THE QUANTUM-SIZE EFFECT FOR GRAZING ELECTRONS ON THE ELECTRONIC CONDUCTIVITY OF METAL-FILMS

The thickness dependence of the electronic conductivity of thin (5-150 nm) single-crystal (100) films of refractory metals is investigated a t different temperatures ranging from 4.2 K to room temperature. Regio ns of square-root, quasilinear, and quadratic dependences are observed . The quasilinear thickness dependence is explained by the influence o f quantum effects on the transverse motion of electrons in the case wh en electron scattering by the film surfaces dominates. For macroscopic film thicknesses 30-50 nm, much greater than the Fermi wavelength of an electron, quantum corrections to the electronic conductivity reach values of the order of 50%. This is a consequence of the quantum size effect for grazing electrons, which leads to an anomaly in electron sc attering by the film surfaces, The region of the quadratic thickness d ependence corresponds to the quantum limit, and the square-root region corresponds to the classical limit. The effect is explained in a quas iclassical two-parameter model (the effective angle alpha for small-a ngle electrons and the parameter gamma, equal to the ratio of this ang le to the diffraction angle) that takes into account the diffraction a ngular limits for grazing electrons. The effect occurs for parameters alphamuch less than 1 and gamma similar to 1 and differs from the ''o rdinary'' quantum size effect. (C) 1997 American Institute of Physics.