Hydrodynamic characteristics of the thin fluid film in chemical-mechanical polishing

This paper presents results of an analytical study involving the kinematics and pressure distribution developed in the wafer-pad interface during a chemical-mechanical polishing (CMP) process. The mathematic modeling of the kinematics and dynamics of the interface is simplified by the use of the circumferential average technique yielding equations that are readily solved. The analytical results are in reasonably good agreement with those reported by previous authors using the direct numerical simulation of the Navier-Stokes equations. Furthermore, the present analysis clearly demonstrates the physical significance in the CMP process contributed by a variety of the operating parameters including rotation speed, offset of rotational axis, wafer curvature, slurry viscosity, and thickness of fluid film between the wafer and pad.