CMPプロセスにおける接触応力の動的有限要素法解析

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A dynamic analysis model of CMP process is developed by utilizing a finite element method in the present study. By considering relative motion of a wafer and a polishing pad in a steady-state process, a nonlinear equation of motion is derived based on Arbitrary Lagrangian-Eulerian (ALE) method in the proposed model. Since the dynamic CMP process in the steady-state can be treated as a static problem in an ALE coordinate system, computation time can be reduced significantly and meshing procedure can be simplified as compared with conventional dynamic structural analysis, i.e., time history response analysis. As a result, practical large scale problems can be solved accurately with consideration of the dynamic structural behavior. Two-dimensional structural analysis was carried out by applying the proposed model, and it was verified that the computation time can be reduced significantly as compared with the conventional analysis. Effects of viscosity of the polishing pad on polishing pressure distribution were examined, and it was clarified that stress concentration beneath the leading edge of the wafer greatly depends on the viscosity of the polishing pad, i.e., the consideration of dynamic viscoelastic behavior of the polishing pad is important to predict the polishing pressure distribution. The proposed model was subsequently applied to three-dimensional analysis of CMP process, and reasonable polishing pressure distribution, which was similar to that in the two-dimensional analysis, was derived successfully.

CMPプロセスにおける接触応力の動的有限要素法解析

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