Pad Topography, Contact Area and Hydrodynamic Lubrication in Chemical-Mechanical Polishing
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1157-E01-02
Pad Topography, Contact Area and Hydrodynamic Lubrication in Chemical-Mechanical Polishing Leonard J. Borucki1, Ting Sun2, Yun Zhuang1,2, David Slutz3 and Ara Philipossian1,2 1
Araca Incorporated, 6655 N. Canyon Crest Dr., Suite 1205, Tucson, Arizona 85750 USA Dept. of Chemical and Environmental Engineering, U. of Arizona, Tucson, Arizona 85641 USA 3 Morgan Advanced Ceramics, 7331 William Ave, Ste. 900, Allentown, PA 18106 USA 2
ABSTRACT Material removal during CMP occurs by the activation of slurry particles at contact points between pad summits and the wafer. When slurry is present and the wafer is sliding, contacts become lubricated. We present an analysis valid over the full range from static contact to hydroplaning that indicates that CMP usually operates in boundary or mixed lubrication mode at contacts and that the lubrication layer is nanometers thick. The results suggest that the sliding solid contact area is mainly responsible for the friction coefficient while both the solid contact and lubricated areas control the removal rate. INTRODUCTION Because of the difficulty of directly observing material removal at the asperity level in chemical-mechanical polishing (CMP), there are many unanswered questions about the fundamental mechanisms of the process. In particular, the origins of the friction force and the relationship between friction and material removal are still not well understood. In a previous analysis [1], a compact formula from lubrication theory [2] was used to estimate the contribution µvisc to the COF from Newtonian viscous shear at the contacting summits of a pad surface with an exponentially decaying summit height distribution,
µvisc ≈ 0.9 ⋅ (µ0V (1− ν 2 ) / E) 0.36 κ 0.19 λ−0.17 .
(1)
In Eq. (1), µ0 is the (Newtonian) slurry viscosity, V is the relative sliding speed, E is the Young’s modulus of the pad, ν is the Poisson ratio, κ is the mean summit curvature and λ is a measure of € pad surface abruptness. While predictions from this model sometimes agree with observed power law dependences of the COF on velocity, curvature and summit height distribution, the COF from Eq. (1) is in general much smaller than observed experimentally. Here, we examine the causes of friction and removal in CMP at a more basic level. We solve the equations of elastohydrodynamic lubrication directly and include both fluid film cavitation and mixed sliding solid contact and lubrication at contacting summits. This more detailed theory predicts that for typical ranges of pad bulk and surface characteristics, CMP operates in the boundary or mixed lubrication regime with a coefficient of friction in the observed range. In addition, the theory provides some insight into the physics underlying the COF and the removal rate.
THEORY In elastohydrodynamic lubrication theory, the pad is treated as an isotropic elastic solid governed by the linear elasticity equations [3],
∂σ ij /∂x j = 0 , σ ij = λεkk + 2µεij , εij = 1/2(∂ui /∂x j + ∂u j /∂x i ) ,
(2)
where σ ij is the stress tensor, εij is the strain te
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