IUVSTA 15th International Vacuum Congress (IVC-15), AVS 48th International Symposium (AVS-48), 11th International Conference on Solid Surfaces (ICSS-11)
    Tribology Wednesday Sessions
       Session TR+SS-WeM

Paper TR+SS-WeM2
A Multi-Scale Elasto-hydrodynamic Contact Model of Chemical Mechanical Planarization

Wednesday, October 31, 2001, 8:40 am, Room 132

Session: Fundamentals of Tribology & Adhesion
Presenter: A. Kim, Rensselaer Polytechnic Institute
Authors: A. Kim, Rensselaer Polytechnic Institute
J. Tichy, Rensselaer Polytechnic Institute
T.S. Cale, Rensselaer Polytechnic Institute
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We present a physically based multi-scale finite element model to help better understand the CMP process. We extend a model that is presented in Ref. 1. This extended "soft" elasto-hydrodynamic contact model captures the fundamental mechanical and tribological aspects of the CMP process and requires few ad hoc assumptions or adjustable parameters. Recent experimental results show that fluid suction pressures exist,@footnote 2@ and the friction coefficient decreases as the Hersey number (i.e., viscosity*velocity/ pressure) increases.@footnote 3@ These results indicate that there exist mixed direct solid-solid contact and partial fluid lubrication, i.e., elasto-hydrodynmic lubrication. The theoretical results presented in this work support elasto-hydrodynamic contact (abrasion) at the pad-wafer interface. The constitutive equation for the soft polymer pad material must be some form of large strain nonlinear elasticity such as hyperelasticity as the strains of a well-deformed asperity are of order one. A physically based asperity-scale hyperelastic model, which includes a frictional effect, is presented to calculate local stresses at asperity tips. These local stresses are directly related to widely accepted material removal models. In most CMP tools, the external downward force is applied to the wafer-carrier head through a ball joint, which in principle cannot transmit a moment. In order to obtain closure of the analysis, the mean depth into the pad and tilt angle of the wafer are determined by the normal global force applied and momentum balances using the Levenberg-Marquardt method. Finally, we summarize our approach to linking the asperity scale contact analysis to the wafer scale model through a statistical method. @FootnoteText@@footnote 1@J. A. Tichy, J. Levert, L. Shan and S. Danyluk, J. Electrochem. Soc. 146(4), 1523 (1999). @footnote 2@L. Shan, Ph.D. Thesis, Georgia Institute of Technology, 2000. @footnote 3@Y. Moon, Ph. D. Thesis, University of California, Berkeley, CA, 1999.