The DC and RF resistivity of discontinuous metal films: a size effect theory

Abstract

A model based on the Mayadas-Shatzkes theory of polycrystalline films is proposed to represent discontinuous films in which island boundaries are considered to be partially reflecting planes, the coefficient of reflection at the boundaries being equivalent to the energy associated with charge transfer from one island to the neighbouring one. The relation between DC resistivity and the thickness of discontinuous films is discussed, and a quantitative picture is presented. The resistivity at radio frequencies, at which islands are effectively AC-shunted, is also considered. The coefficient of reflection at these frequencies is significantly different from that for DC measurements, and its value depends on the nature of the crystallinity of the islands. Thickness-dependent DC and RF resistivities of polycrystalline, discontinuous bismuth films have been studied, and the results are presented. The agreement of the data with our model is quite satisfactory.