An analysis technique for extraction of thin film stresses from x-ray data

We demonstrate a technique for experimentally determining stresses in crystalline thin films without any knowledge of the elastic properties of the thin film material. The results are obtained from interplanar spacing versus ${\sin }^2\mathrm{\hspace{0.17em}\Psi }$ plots for different stress states. The interplanar spacings are measured by non-symmetric x-ray diffraction. The different stress states are produced by annealing the thin film/substrate samples at elevated temperatures in air and by cooling them in liquid nitrogen. Poisson’s ratio for isotropic films or a similar quantity for anisotropic films can be found through the use of this technique. An extension of this technique also permits the measurement of the coefficient of thermal expansion without removing the film from the substrate.