Size Effects on Thermal Properties of Thin Metal Films With Rough Surfaces

By calculating the effects of electronic scattering at rough surfaces by means of a combined Soffer-Cottey model, general theoretical expressions for the size effects in thermal properties of thin metal films are proposed. Simple analytical expressions for the thermoelectric power, Sf, and the thermal conductivity, ℒf, are given under the assumption that the energy dependence of the electronic relaxation time in bulk material may be written in the form τo∼Wm . The size effects in the thermoelectric power are found to depend on the value of m. However, a decrease in the overall size effects is observed in all transport parameters with respect to the predictions of classical theories based on the Fuchs-Sondheimer or the Cottey models. A comparison with data on the thermoelectric power of thin copper, silver and tin films from previous experiments by various workers shows that a combined Soffer-Cottey model is convenient to analyze size effects in thermoelectric properties. The values of the r.m.s, surface roughness obtained from data are physically consistent.