Nondestructive separation of residual stress and composition gradients in thin films by angle- and energy-dispersive X-ray diffraction. I. Theoretical concepts

Different X-ray measurement and data evaluation concepts are presented, which allow for residual stress analysis in thin films with pronounced gradients in chemical composition. These gradients lead to a variation in the strain-free lattice parameter a₀ with respect to the film thickness and superimpose the lattice strain induced by the film's inherent stresses. Non-consideration of a₀(z) gradients is shown to lead to considerable errors (`ghost stresses') in the residual stress depth profiles. With the simulated example of a TiC_xN_1−x film with a pronounced carbon gradient, the first part of this series introduces four approaches, which permit the separation of residual stress and composition depth distributions at different levels of approximation. They are based on lattice spacing depth profile measurements performed in either the sin²ψ mode or the scattering vector mode, or in combinations of these two scanning modes. Depending on the approach used for separating the residual stress and composition gradients, angle- or energy-dispersive diffraction has to be applied, employing monochromatic X-ray sources available in the laboratory or either white high-energy synchrotron radiation or the Bremsstrahlung of conventional X-ray tubes, respectively. The methods introduced here assume a biaxial residual stress state within the film. For a triaxial residual stress state with σ₃₃ ≠ 0, a separation of stress and composition gradients is not straightforward, because an a₀(z) gradient cannot be distinguished from the hydrostatic part of the stress tensor.