Computer-controlled lapping system for granite surface plates

Abstract

This paper describes a two-dimensional, multiscale, material removal model for chemical–mechanical planarization that includes: (i) asperity deformation; (ii) bulk pad deformation; (iii) wafer compliance; (iv) carrier film deformation; (v) slurry flow; (vi) material removal by abrasive particles in the slurry. A finite element method is used to establish the relationship between the contact stress and the deformation of an idealized asperity made of a hyperelastic material. The total local stress due to the multitude of asperities is computed using the Greenwood–Williamson approach. The wafer deformation, bulk pad deformation, and slurry film thickness are then evaluated from the estimated contact stresses and hydrodynamic fluid pressures. The material removal rate on the wafer is computed as a function of position on the wafer. The wafer scale material removal rate results show large changes in rate near the wafer’s edges, as often seen in practice, with very uniform removal across most of the wafer surface. The computational algorithm used to calculate the contact stresses, slurry fluid pressures, material removal rates, and the global force and moment balances is summarized.