Determining local residual stresses from high resolution wafer geometry measurements

Multiple thin film deposition steps are central to most semiconductor device fabrication processes. The residual stresses in these thin films can induce both in-plane and out-of-plane distortions to the wafer. These residual stresses can vary spatially across the wafer, and the residual stress distributions can change between lithography steps. This can result in noncorrectable overlay errors in the lithography processes. In order to develop strategies for minimizing overlay errors due to residual stress-induced distortion, there is a critical need for techniques that allow the distributions of residual stresses in deposited thin films to be characterized with high spatial resolution. In this paper, the application of established analytical methods for extracting local residual stress from wafer geometry measurements (shape) is investigated. Three-dimensional finite-element models were used to generate simulated wafer shapes resulting from nonuniform residual stress distributions in thin-films. The results of these finite element simulations were used to assess the effectiveness of established analytical techniques. Furthermore, the results demonstrated that local mean curvature of the wafer shape is a simple metric that can be used to qualitatively describe local residual stress variation across the wafer. The simulations also demonstrated that when residual stresses varied over scales of tens of millimeters that high spatial resolution (<1 mm) shape measurements were required in order to accurately predict local residual stress.