A 3D EHL simulation of CMP: Theoretical framework of modeling

The extensive application of chemical mechanical polishing (CMP) in the semiconductor industry requires an understanding of the fundamental mechanisms involved. This paper integrates a group of mechanical models to give a framework for CMP modeling: a mixed three-dimensional (3D) soft elastohydrodynamic lubrication (EHL) model with asperity contact considered. The soft-pad mechanics, asperity-contact analysis, and slurry film description are three major components of this framework. Based on the results of a thin-layer contact analysis, the Winkler foundation model is selected to evaluate the pad deformation in bulk. By applying the macro-micro approach, the macroscopic view of the average fluid film thickness (average clearance) is related to microasperity contact. When CMP is implemented in a mixed lubrication regime, the soft polishing pad usually undergoes a displacement of the same scale as the slurry film, which may change the lubrication boundary considerably. Considering this effect, a modified Reynolds equation is derived, and a stronger coupling is found in the global force and moment balances. Finally, an effective iterative scheme is proposed and modeling results examined.