Measurement of the lattice thermal expansion coefficients of thin metal films on substrates

A difference in thermal expansion between a thin film and its substrate causes mechanical stresses in the film. Therefore, knowledge of the thermal expansion coefficients of thin films are important for their technological applications. In this article, we present an analysis which can be used to extract the thermal expansion coefficient of a thin film material using a commonly used x-ray technique. The major advantage of our approach is that it is not necessary to remove the film from the substrate. The knowledge of the elastic constants of the thin film material and their temperature dependence is not required, which is particularly useful when thin film alloys are studied whose thermal and elastic properties are not available. For verification of the method, we investigated thin Al films because the thermal and elastic properties of bulk Al are well known. The comparison of our results with the bulk properties shows a reasonable agreement, indicating the validity of the new method.