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Three-Dimensional Chemical Mechanical Planarization Slurry Flow Model Based on Lubrication Theory

A three-dimensional chemical mechanical planarization slurry flow model based upon lubrication theory is developed, utilizing a generalized Reynolds equation that includes pad porosity and bending. The model is used to calculate slurry film thickness and slurry velocity distributions between the wafer and pad, with the minimum slurry film thickness determining the degree of contact between the wafer and pad. The dependence of the removal rate of copper films as a function of applied pressure and velocity agrees well with model predictions. The minimum slurry film thickness is examined over a range of input variables, namely, applied pressure, wafer-pad velocity, wafer radius and curvature, slurry viscosity, and pad porosity and compressibility.