Experimental verification of new theoretical equation describing electrical conductivity of thin films

Abstract

Polycrystalline thin films exhibit three kinds of electronic properties: bulk properties, that are induced by the surface, and properties that are connected with the crystal arrangement and the size of the aggregates. The first analysis of electrical measurement data for thin films was carried out by Fuchs [1 ] and developed by Sondheimer [2]. In this model, the film is considered to be of uniform thickness d and limited by plane surfaces, which introduce boundary conditions on the distribution function of the electrons. The general theory assumes that a fraction p of the electrons are reflected specutarly at the surfaces while the rest are scattered diffusely. The main objections one can find in this theory is that the film approximates a planeparallel single crystal of metal. When the electron scattering at external surfaces becomes specular (p~l), this model indicates that the film conductivity reduces to the conductivity of the bulk metal. In practice, this is not the case because evaporated or sputtered films are Composed of polycrystallites, which is ignored in the FuchsSondheimer model. The grain boundary scattering gives a resistivity which varies inversely with the sample thickness. This type of dependence on thickness is precisely the form expected from the approximate expression for Fuchs theory. The influence of grain boundaries on conductivity was first studied by Mayadas and Shatzkes [3]. In their model, Mayadas and Shatzkes consider the conductivity to be due to isotropic electron scattering (caused by point defects and phonons), to surface scattering (FS effect), and to grain boundary scattering. These authors started from the assumption that an evaporated or sputtered film is made of grains that grow in a column like fashion extending from the substrate to the top of a film. With this hypothesis, grain boundaries are represented by a series of randomly electron-reflecting parallel planes oriented