A model for wafer scale variation of removal rate in chemical mechanical polishing based on elastic pad deformation

It is well known that within wafer non-uniformity (WIWNU), due to the variation in material, removal rate (MRR) in the whole wafer plays an important role in determining the quality of a wafer planarized by CMP. Various material removal models also suggest that the MRR is strongly influenced by the interface pressure. In the present work, an analytical expression for pressure distribution at the wafer and pad interface is developed. It is observed that depending on the wafer curvature and polishing conditions, the interface pressure may exhibit significant variation. The analytical model predictions are first verified against finite element method (FEM) simulations. The predicted analytical pressure profiles are then utilized in Preston's equation to estimate the MRR, and these MRR predictions are also compared to experimental observations. The analytical results suggest, that for a specified wafer curvature there exists a certain polishing condition (and vice versa) that will enable holding the WIWNU within a specified tolerance band. The proposed model facilitates the design space exploration for such optimal polishing conditions.