The extensive application of chemical mechanical polishing ͑CMP͒ in the semiconductor industry requires an understanding of the fundamental mechanisms involved. This paper integrates a group of mechanical models to give a framework for CMP modeling: a mixed three-dimensional ͑3D͒ soft elastohydrodynamic lubrication ͑EHL͒ model with asperity contact considered. The soft-pad mechanics, asperity-contact analysis, and slurry film description are three major components of this framework. Based on the results of a thin-layer contact analysis, the Winkler foundation model is selected to evaluate the pad deformation in bulk. By applying the macro-micro approach, the macroscopic view of the average fluid film thickness ͑average clearance͒ is related to microasperity contact. When CMP is implemented in a mixed lubrication regime, the soft polishing pad usually undergoes a displacement of the same scale as the slurry film, which may change the lubrication boundary considerably. Considering this effect, a modified Reynolds equation is derived, and a stronger coupling is found in the global force and moment balances. Finally, an effective iterative scheme is proposed and modeling results examined.Chemical mechanical polishing ͑CMP͒ is currently used to achieve global planarization over a long length/thickness scale and is being widely applied in the semiconductor industry. During a CMP process, a rotating wafer is pressed face down onto a moving, resilient thin polishing pad, while a polishing slurry containing abrasive particles and chemical reagents flows between the wafer and pad. The extensive utilization of CMP in integrated circuit ͑IC͒ manufacturing requires deep understanding of the CMP mechanisms.Nanz and Camilletti 1 presented a critical review of the CMP models developed prior to 1995 for pad bending, nonplanarity of a wafer, the effect of pad asperities, and slurry flow. Whereas various working conditions may weigh differently due to the factors mentioned previously, it is axiomatic that the contact between the polishing pad and the wafer is determined by the clearance between them. Bhushan et al. 2 pointed out that three contact scenarios, namely, direct contact, nondirect contact, and semidirect contact, may appear at the pad-wafer interface in CMP. Chekina et al. 3 developed an analytical solution for wafer surface evolution in a steady state on the basis of elastic contact mechanics. Zhao and Chang 4 developed an abrasive wear model for CMP on the basis of elastic-plastic microcontact mechanics. They first estimated a relationship among the real area of contact, the number of particles participating in wafer material removal, and the particle indentation depth into the wafer surface, and then derived a closed-form formula to address the material removal rate ͑MRR͒. Runnels and Eyman presented a nondirect-contact model for CMP based on a waferscale slurry flow analysis. 5 Supposing the wafer is completely separated from the polishing pad by the flowing slurry, the slightly tilted wafer with a curvature allows a...

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In many engineering fields surface topography is of crucial importance solving problems of friction and other problems of tribology. A review of mathematical approaches for description of topography of engineering surfaces is presented. Firstly, we give a brief introduction to some of statistical parameters used for description of surface roughness. It is argued that although some of these parameters may be quite useful for specific engineering problems, a set of finite numbers of parameters cannot describe contact properties of rough surfaces. Then we discuss various models of surface roughness based on Gaussian models of the asperity heights. The results of application of various modern tests of normality for checking whether the distribution of the asperity heights is Gaussian, are presented. Further fractal models of roughness are discussed. Using fractal parametric-homogeneous (PH) surfaces, it is demonstrated that tribological properties of a rough surface cannot be characterized just by the fractal dimension of the surface. It is also shown that models based solely on the power-spectral density function (PSDF) are quite similar to fractal models and these models do not reflect tribological properties of surfaces. In particular, it is demonstrated that different profiles may have the same PSDF.