Resonance ultrasound spectroscopy with laser-Doppler interferometry for studying elastic properties of thin films.

We propose an advanced method to determine the elastic-stiffness coefficients Cij of thin films using resonance ultrasound spectroscopy (RUS). It uses free-vibration resonance frequencies of a film/substrate layered solid and derives inversely the film's Cij from the resonance frequencies. We develop a piezoelectric tripod consisting of two pinducers and one support to place the specimen on it and measure the resonance frequencies with high enough accuracy. Furthermore, we achieve mode identification by measuring deformation distributions on the vibrating specimen surface using laser-Doppler interferometry. Accurate measurements of frequencies and correct mode identification are the keys for deducing reliable Cij of the film. We applied this technique to copper thin films deposited of Si substrates. The resulting film's Cij are considerably smaller than the bulk's Cij and show anisotropy between the out-of-plane direction and in-plane direction.