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 varia tion in material, removal rate (MRR) in the whole wafer plays an important role in determining the quality of a wafer planarized by CMP. Various mater ial removal models also suggest that the MRR is strongly influenced by the interface pressure. In the present work, an analytical expression for press ure distribution at the wafer and pad interface is developed. It is observe d that depending on the wafer curvature and polishing conditions, the inter face pressure may exhibit significant variation. The analytical model predi ctions are first verified against finite element method (FEM) simulations. The predicted analytical pressure profiles are then utilized in Preston's e quation to estimate the MRR, and these MRR predictions are also compared to experimental observations. The analytical results suggest, that for a spec ified 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 opti mal polishing conditions.