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

Abstract

It is well known that within-wafer nonuniformity (WIWNU) due to the variation in material removal rate (MRR) in chemical mechanical polishing (CMP) significantly affects the yield of good dies. The process control for a batch CMP operation is further complicated by wafer-to-wafer nonuniformity (WTWNU) caused by MRR decay when a number of wafers are polished with the same unconditioned pad. Accordingly, the present work focuses on modeling the WIWNU and WTWNU in CMP processes. Various material removal models suggest that the MRR is strongly influenced by the interface pressure. It is also well known that the viscoelastic properties of the pad play an important role in CMP. In the present work, an analytical expression for pressure distribution (and its associated MRR) at the wafer-pad interface for a viscoelastic pad is developed. It is observed that under constant load, which is typical during main polishing in CMP, the spatial distribution of the interface pressure profile may change with time from edge-slow to edge-fast, depending on the combination of wafer curvature, down pressure, and pad properties. For constant displacement operations, the pressure profile retains its edge-slow or edge-fast characteristics over time. The analytical model predictions of MRR based on viscoelastic pad properties also correlate very well to existing experimental observations of MRR decay when an unconditioned pad is used to polish a number of wafers. Based on these observations, it may be conjectured that the viscoelastic material properties of the pad play a primary role in causing the observed MRR decay. The analytical results obtained in the present work can also provide an estimation of evolution of thickness removal distribution over the entire wafer. This may be used for determining the optimum thickness of the overburden material and its polishing time, and for effective control of CMP processes.