Anisotropic biaxial stresses in diamond films by polarized Raman spectroscopy of cubic polycrystals

Abstract

The anisotropic stresses in diamond films induced by permanent deformations of titanium tensile substrates are studied by polarized Raman spectroscopy. The influence of the in-plane orientation of each grain relative to the stress directions is shown experimentally and theoretically. Considering the dynamical equations under small strains, the solutions of the secular equation permit the determination of the triply degenerate phonon frequency of polycrystalline diamond, which splits into three singlets for each crystallite. The calculation is carried out here for six growth directions, along [001], [110], [111], [112], [113], and [331], and for all in-plane orientations normal to these textures. In the case of anisotropic stresses, it is shown how the relative values of the two stresses induce different shapes in the Raman spectra. For an isotropic polycrystalline diamond film, this Raman spectroscopy of strained cubic polycrystals approximates the complete solution for all crystallite orientations relative to the anisotropic biaxial stresses. It allows calculating theoretical Raman spectra that fairly well compare to the experimental ones. The determination of the anisotropic stresses is obtained with a better accuracy when the influence of all orientations is taken into account than with the previous average procedures used for isotropic cubic polycrystalline materials. Partially or completely textured films along one of the growth directions can also be studied. If the stresses along the two directions are identical, the particular case of isotropic biaxial stresses is also studied with a better accuracy.