Thin film/substrate systems featuring arbitrary film thickness and misfit strain distributions. Part II: Experimental validation of the non-local stress/curvature relations
The classical Stoney formula relating local equibiaxial film stress to local equibiaxial substrate curvature is not well equipped to handle realistic cases where the film misfit strain, the plate system curvature, and the film thickness and resulting film stress vary with in-plane position. In Part I of this work we have extended the Stoney formula to cover arbitrarily non-uniform film thickness for a thin film/substrate system subject to non-uniform, isotropic misfit strains. The film stresses are found to depend non-locally on system curvatures. In Part II we have designed a demanding experiment whose purpose is to validate the new analysis for the case of radially symmetric deformations. To achieve this, a circular film island with sharp edges and a radially variable, but known, thickness is deposited on the wafer center. The plate system's curvatures and the film stress distribution are independently measured by using white beam and monochromatic X-ray microdiffraction (μXRD) measurements, respectively. The measured stress field (from monochromatic μXRD) is compared to the predictions of various stress/curvature analyses, all of which have the white beam μXRD measurements as input. The results reveal the shortcomings of the "local" Stoney approach and validate the accuracy of the new "non-local" relation, most notably near the film island edges where stress concentrations dominate.
© 2006 Elsevier Ltd. Received 20 July 2006; received in revised form 10 October 2006. Available online 20 October 2006. The Advanced Light Source is supported by the Director, Office of Science, Office of Basic Energy Sciences, Materials Sciences Division of the U.S. Department of Energy under Contract No. DE-AC03-76SF0098 at Lawrence Berkeley National Laboratory.