Stress-warping relation in thin film coated wafers

A misfit strain or stress in a thin layer on the surface of a wafer lets the composite disk warp. When the wafer is thin and large, the Stoney estimation of the film stress as function of the curvature yields large errors. We present a nonlinear analytical model that describes the relationship between warpage and film stress on an anisotropic wafer, and give evidence for its suitability for large thin wafers by a comparison to finite element results. Finally, we show the confidence limit of the Stoney estimation and the benefit by the nonlinear model. For thin coatings, it can be succesfully used even without knowledge of the film properties, which was the main advantage of the Stoney estimation.