Wafer-scale models slurry flow

The flow of a slurry in a CMP process has been investigated. This wafer-scale model provides the three dimensional flow field of the slurry, the spatial distribution of the local shear rate imposed on the wafer surface, and the streamline patterns which reflect the transport characteristics of the slurry. 

The present study is a wafer-scale modeling which provides the three dimensional flow field of the slurry in the gap between the wafer and the pad which are assumed to be parallel to one another. 

Runnels and Eyman [41] report a tribological analysis of CMP in which a fluid-flow-induced stress distribution across the entire wafer surface is examined. Fundamentally, the model seeks to determine if hydroplaning of the wafer occurs by consideration of the fluid film between wafer and pad, in this case on a wafer scale. The thickness of the (slurry) fluid film is a key parameter, and depends on wafer curvature, slurry viscosity, and rotation speed. The traditional Preston equation R = KPV, where R is removal rate, P is pressure, and V is relative velocity, is modified to R = k ar, where a and T are the magnitudes of normal and shear stress, respectively. Fluid mechanic calculations are undertaken to determine contributions to these stresses based on how the slurry flows macroscopically, and how pressure is distributed across the entire wafer. Navier-Stokes equations for incompressible Newtonian flow (constant viscosity) are solved on a three-dimensional mesh ... 

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