Contact Model for a Pad Asperity and a Wafer Surface in the Presence of Abrasive Particles for Chemical Mechanical Polishing

Abstract

ABSTRACTA contact model for a single spherical (pad) asperity and a flat (wafer) surface, with an interface filled with spherical (abrasive) particles is introduced. Finite element method is used to determine the deformation characteristics of a single spherical abrasive indenting a hyper-elastic pad material. The asperities in Greenwood and Tripp (GT) model, which is widely used for the contact of rough spheres, are replaced with the spherical particles. Relations are developed to predict pad-to-particle-to-wafer contact in two distinct regimes, where a) pad and the wafer are separated by the particle; and b) all three bodies come in contact simultaneously. The results of the model show that the abrasive particles in the (pad) asperity-wafer interface causes the contact to be distributed over an area larger than that predicted by the Hertz model, while the maximum contact pressure becomes relatively lower. The fraction of the load carried by pad-to-wafer and pad-to-abrasive-to-wafer varies along the contact interface of the pad asperity and wafer.