A Multiscale Elastohydrodynamic Contact Model for CMP

Abstract

We present a three-dimensional multiscale elastohydrodynamic lubrication (EHL) contact model for chemical mechanical planarization (CMP) based on satisfying the fundamental mechanical force and moment balance equations appropriate for a rotational CMP tool. We describe surface-surface and fluid-surface interactions in conditions where pad asperities are in direct contact with the wafer and the effective film thickness is comparable in size to the roughness of the bounding surfaces. A hyperelastic material is used for our asperity scale model to account for large deformations of the soft polymer asperities. We iteratively solve the soft elastohydrodynamic contact problem, i.e., the solid-solid contact problem coupled with fluid pressure, until the global force and moment balances are satisfied for given operating conditions. The multiscale model computes contact stress across the wafer surface due to asperity deformation that is, in turn, caused by the externally applied load and interfacial slurry pressures. Finally, a relative measure of material removal rate across the wafer is represented by the computed local asperity contact stress. Flat, concave, and convex rigid wafers are considered. The work of this paper focuses on understanding fundamental mechanical aspects of CMP and presents a methodology to simulate mechanical aspects of the CMP process. © 2003 The Electrochemical Society. All rights reserved.