Determination of elastic constants of thin films from phase velocity dispersion of different surface acoustic wave modes

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Abstract
We have carried out a systematic investigation of the achievable accuracy in the determination of the independent elastic constants c11 and c12 and the related constant c44 of thin isotropic films from the phase velocity dispersion of surface acoustic waves (SAWs). As a model system SiO2 and Au films deposited on Y-cut LiNbO3 were considered. The phase velocity dispersion was calculated for real elastic constants in dependence on the film thickness. These input data were used to determine the least-squares fits of the input dispersion and the phase velocity obtained by modifying c11 and c12. The minimum of this error field describes the solution of the inverse wave propagation problem. Error fields of the least-squares fits were calculated with ±5% variation for c11 and ±30% for c12. Different functional behavior and various magnitudes of the dispersion were compared. When simulating a small measuring uncertainty for the phase velocity the solution of the inverse problem becomes unstable which results in an insufficient accuracy of the interesting elastic constants. By superposition of two SAW modes the inaccuracy was significantly reduced. For the model system each independent SAW mode offers the ability to determine one elastic constant or one relation between different elastic parameters.