Stresses in textured and polycrystalline cubic films by Raman spectroscopy: Application to diamond

Abstract

The determination of the stress/strain level in cubic films is carried out here by polarized Raman spectroscopy. The Voigt-Reuss-Hill averaging technique has been used for calculating the phonon deformation potentials in textured cubic films, especially here in diamond. With the corresponding elastic constants known, the resolution of the secular equation has allowed us to calculate the strain/stress configuration from the shifts and splitting of textured diamond polycrystalline films. For isotropic polycrystalline films, the results obtained by averaging over the different textures compare very well to the results obtained with the complete averaging procedure of Anastassakis [J. Appl. Phys. 86, 249 (1999)]. With both averaging methods, the stress/strain level in polycrystalline films are evaluated with a fairly good accuracy, either for biaxial isotropic in-plane stresses due to thermal expansion mismatch between the film and the titanium alloy substrates or for anisotropic stresses induced by permanent deformations of titanium tensile specimens. The difference between these averaging procedures and a method using the addition of the contributions of different textures is shown for evaluating the strains/stresses in diamond films. A slightly more accurate method is obtained because of the different influences of the various textures on the Raman shifts. However, the textured polycrystalline state being averaged with a method that results in an effective hexagonal symmetry, this approach is still insufficient to take into account the influence of the in-plane orientation of each crystallite relative to strong anisotropic biaxial stresses, an influence which is shown experimentally and theoretically for one texture, along the [110] direction of growth.