The effect of preferred orientation on X-ray stress measurement

Based on the boundary conditions for prefer-oriented polycrystals under loading, a new model for the calculation of X-ray elastic constants (XEC) for prefer-oriented materials, the weighted Hill model, is proposed. The model is applied to calculate the X-ray stress measurement curves of some model materials. In order to check the model, the stresses in electroplated and brush-plated copper films are measured. The experimental results have good comparison with the calculated results. This helps to explain the low ψ angle curvature of the stress measurement curve for plasma enhanced chemical vapor deposition (PCVD) TiN films. It is mainly caused by the columnar structure exsisted in the PCVD TiN films. When the stress measurement curve has a linear zone at the high ψ angle, it is suggested to use the slope of the linear zone for the stress calculation.