The effect of linear thermal expansion on the temperature coefficient of resistance of double-layer thin metallic films

A general theoretical expression for the temperature coefficient of resistance of double-layer thin metallic films, based on the well known Fuchs-Sondheimer model, is derived. This expression includes the linear thermal expansion coefficients and Poisson's ratios of the double layers and the substrate, also the film dimensions and temperature coefficient of resistance of the double-layer thin film, with and without the thermal expansion of both the film layers and the substrate. Numerical calculations are carried out for gold-silver double-layer films deposited on a glass substrate, where variations in the temperature coefficient of resistance depending on thermal expansion are studied as a function of reduced film thickness. The computed numerical results, using the derived new expression for the temperature coefficient of resistance of the double-layer thin metallic films, show that the thermal expansion decreases the value of the temperature coefficient of resistance.