Level Models for the Polishing Process

The most generally satisfactory local-level model for CMP is an asperity contact model such as that described by Yu ef al. [4]. In this model, applied 

The model of Yu et al. [4] is of particular interest as several important aspects have subsequently been experimentally confirmed. The model assumes spherical asperities whose height z and radius P have a Gaussian 

Total eontact area and load L over the overall pad area A are then 

Bhushan et al. [9] independently confirmed the lack of polishing activity due to hydrodynamic lubrication. The depth of the wafer carrier in CMP was adjusted so that samples either projected above the surface of the carrier (the normal case), were essentially coplanar with the carrier, or were recessed below the plane of the carrier. This produced wafer-pad lubrication film thicknesses of controlled dimension. For the case of a wafer recess of 75 um ( 3 X the lubrication film thickness reported in Ref. [7]), removal rate was negligibly small. 

Coppeta et al. [10] made slurry film measurements during using laser-induced fluorescence. By addition of a fluorescent dye to the polishing slurry film thickness was experimentally from the fluorescence intensity of the lubrication film as measured through a transparent substrate. Film thickness measurements were in good agreement with those of Levert et al. [7,8]. This technique can also be used to study slurry transport across the wafer surface, diameter variation in lubrication film thickness, and slurry mixing effects [11]. 

---