Effects of residual stress on the thin-film elastic moduli calculated from surface acoustic wave spectroscopy experiments

We describe a method to examine how residual stress affects the values of thin-film elastic moduli determined from surface acoustic wave spectroscopy experiments. To illustrate our approach, we apply it to the case of an elastically isotropic thin film under equibiaxial stress. The five test samples consisted of TiN films deposited on single-crystal Si substrate (film thickness 0.287-3.330 μm and assumed compressive stress 0.5-5.4 GPa). With increasing thickness and decreasing stress, the effective second-order moduli C11 increased and C13 decreased. The natural second-order elastic moduli c11 and c13 and the natural third-order elastic moduli c111, c112, and c123 in the unstressed state were computed by fitting the model equations to the measured data. Our results show how surface acoustic wave measurements may be analyzed to obtain additional information about the mechanical properties of thin films with residual stress.