Determination of residual stress in thin films: a comparative study of X-ray topography versus laser curvature method

Abstract

The residual stress in thin films has been determined by X-ray diffraction and laser scanning methods. The usual procedure is to measure the strain via lattice or physical curvature analysis and then to calculate the stress using continuum mechanics models. X-ray and laser techniques measure different physical quantities. In the former case, the curvature of crystal lattice planes is assessed while in the latter situation the curvature of physical surface of the sample is measured. In principle, these two methods should yield the same results. The current experiments use the latest two-dimensional X-ray double crystal diffraction topography (DCDT) and a laser scanning technique (LST) to determine the quantities of interest for a variety of thin films deposited on Si (1 0 0) wafers. The measurements by the two techniques were performed on the same samples, at the same time, under exactly identical conditions. For specimens where the residual stresses produce large curvatures of both types (lattice curvature and surface curvature), the results for DCDT and LST agree within the experimental error. When small to moderate curvatures are present, the two methods deviate to varying degrees. This deviation is of special significance in determining residual stress in nanometer-thickness films. Nevertheless, DCDT and LST generally yield similar results on differential curvatures, i.e. the stress induced curvature differentials. When proper consideration is taken for the inherent limits of each technique, both DCDT and LST can be used as valid procedures for stress measurement in thin film–substrate systems.