Anelasticity and damping of thin aluminum films on silicon substrates

A new dynamic measurement system has been developed to investigate damping in thin metal films. This system includes a vacuum chamber, in which a free-standing bilayer cantilever sample is vibrated using an electrostatic force, and a laser interferometer to measure the displacement and velocity of the sample. With this equipment, internal friction as low as 10^-5 in micrometer thick metal films in a temperature range from 300 to 750 K can be measured. Free-standing cantilevers with different frequencies have been fabricated using well-established integrated circuit (IC) fabrication processes. The cantilevers consist of thin metal films on thicker Si substrates, which exhibit low damping. From measurements of internal friction of Al thin films at various temperatures and frequencies, it is possible to study relaxation processes associated with grain boundary diffusion. The activation energy calculated from the damping data is 0.57 eV, which is consistent with previous research. This value suggests that the mechanism of internal friction in pure Al films involves grain boundary diffusion controlled grain boundary sliding. A model to describe these damping effects has been developed. By deriving an expression for the diffusional strain rate using a two-dimensional (2-D) Coble creep model, and modifying the conventional standard linear solid model for the case of bending, it is possible to give a good account of the observed damping.