Resistivity and Temperature Coefficient of Thin Metal Films with Rough Surface

The thickness dependence of resistivity and its temperature coefficient of thin metal films has been studied. A theory is proposed to include, the surface roughness in determining the film resistivity, in addition to the reduced mean free path to conduction electrons. The ratio of the roughness to the mean free path, h /λ, is introduced as a convenient parameter. The thickness dependence of the resistivity predicted by the present theory agrees with the well known Fuchs-Sondheimer theory if h /λ=0. If h /λ>0, the discrepancy between the two theories increases with the decrease in film thickness. Satisfactory agreement between the theoretical and experimental results can be obtained by adjusting the value of h /λ.