Understanding residual stress in thin films: Analyzing wafer curvature measurements for Ag, Cu, Ni, Fe, Ti, and Cr with a kinetic model

Abstract

An analytical model for the evolution of residual stress in polycrystalline thin films is used to analyze numerous previously reported wafer curvature measurements obtained for a variety of materials and processing conditions. The model, which has been described in previous publications, considers stress-generating mechanisms that occur at the grain boundary as it forms between adjacent grains and stress due to the subsurface grain growth in layers that have already been deposited. Current work extends the model to include different types of microstructural evolutions. A set of parameters for each dataset is obtained by non-linear least square fitting. Model parameters that are not expected to depend on the processing conditions are constrained to have a common value when fitting the multiple datasets for each material. The dependence of the fitting parameters on the material and process conditions is evaluated and compared with the physical mechanisms implemented in the model.