Effective Conductivity and Microwave Reflectivity of Thin Metallic Films

Thin metallic films have reduced conductivity when thickness is not larger than electron mean free path, a phenomenon studied by Lord Thompson. Formulas given by Liao are valid for small thickness; a general formula is available for all ranges of film thickness. The result is in terms of an exponential integral which is easily computed, and is graphed. A simple and accurate formula for calculating microwave reflection from a thin metallic film is developed. The equivalent circuit has the film surface resistivity in shunt with 120 pi (or the substrate impedance). Examples of surface resistivity and reflection coefficient for a gold film are given graphically.