Numerical analysis of hydrodynamic process of circular-translational-moving polishing (CTMP)

Abstract

By keeping a pad moving relative to a wafer along a circular path without rotation, we developed a polishing technique called circular-translational-moving polishing (CTMP), which permits multidirectional polishing of the work piece and thus bears the advantage of isotropic polishing and a potential increase of material removal rate (MRR) on the wafer. To illuminate the mechanisms of CTMP and determine the optimum process variables in a CTMP process, a three-dimensional hydrodynamic lubrication model for CTMP with a smooth and rigid pad under a quasi-stable state is established in a polar coordinate system. The model equations are further calculated numerically by the finite difference method. The instantaneous distribution of fluid pressure is obtained, which shows that a negative pressure exists. The reason for negative pressure in CTMP and its effect on polishing is discussed. Moreover, the nominal clearance of the fluid film, roll, and pitch angles under different working conditions are obtained in terms of the applied load, moments, and polishing velocity. The obtained numerical analysis can be used as guidance for choosing operation parameters in a practical CTMP application.

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