Chemical mechanical polishing ͑CMP͒ is a key technique for wafer global planarization. Increasing demands for high uniformity and dimensional precision make previously discountable levels of asperity and particle effects significant. However, particle size and pad asperity have not been considered simultaneously in previous literature. This study presents a grain flow model which applies the average lubrication equation with partial hydrodynamic lubrication theory, thereby analyzing slurry flow between wafer and pad and taking into account both grain flow and roughness effects. This model predicts slurry flow film thickness with various convex wafer curvature radii under a variety of the CMP parameters, including applied load, rotation speed, dome height, particle size, and pad roughness. Furthermore, the influence of particle size and pad asperity on removal rate is investigated. The results compare well with experimental data in the literature.Integrated circuit ͑IC͒ gates of 0.13 m and smaller are making it increasingly important to control thickness and planarity. Chemical mechanical polishing ͑CMP͒ is a popular technique to achieve global planarization of wafers for very large and ultralarge-scale integrated circuits. A typical CMP mechanism is shown in Fig. 1. The wafer is held inside a carrier and pressed onto a rotating pad under a user-defined polishing pressure while a powder slurry flows between wafer and pad. Because the CMP mechanism is inadequately understood and because higher levels of CMP performance are desired, significant research is being directed toward improved physically based models of the CMP process.Nanz and Camilletti 1 conducted a survey and compared the physical effects of CMP models up to 1995. Published CMP models are based mainly on contact mechanics, 2-6 slurry hydrodynamics, 7-10 or lubrication theory. 11 Recently, Tichy et al. 12 ͑1999͒ presented a two-dimensional CMP model including both contact mechanics and lubrication hydrodynamics. To account for pad compressibility, porosity, and slurry delivery effects, Thakurta et al. 13 used lubrication theory to describe lubrication regime ͑40-70 m slurry films͒ and contact regime ͑thinner films͒. Luo and Dornfeld 14 proposed a solidsolid contact model of the CMP process based on plastic contact over the wafer-abrasive interface and pad-abrasive interface. The fluid effect is attributed to the number of active abrasives, but the effects of slurry particles under hydrodynamic contact were not investigated. Liang et al. 15 in real-time CMP experiments investigated the wear behavior of polishing wafers and pads by comparing different polishing slurries with different additives. Under optical microscopy, they found that the polishing removal rate of wafers decreases with decreasing slurry particle size. Lu et al. 16 used dualemission laser-induced fluorescence ͑DELIF͒ to measure slurry thickness and friction force between wafer and polishing pad. They demonstrated that slurry thickness and friction force are dominantly dependent on the s...

Chemical mechanical polishing (CMP) is a key technique for wafer global planarization. Many studies have been conducted in recent years to analyse the slurry flow between a pad and a wafer due to its importance in CMP processing. In these studies, however, the grains in the slurry were not considered. Thus this investigation uses a grain flow model to analyse the slurry flow between wafer and pad. The proposed model predicts the film thickness of the slurry flow with various convex wafer curvature radius under a variety of the CMP parameters including load, rotation speed and grain size. The theoretical results compare well with experimental data in the literature. This study elucidates grain flow during CMP processing and further contributes to understanding of the CMP mechanism.

A closed-form average lubrication equation for thin film grain flow with the effects of surface roughness is derived. This equation is based on Haff’s grain flow theory and also the flow factors proposed by Patir and Cheng. The flow factors, derived by the perturbation approach and coordinate transformation, are expressed in terms of surface characteristics (three characteristics for each surface: roughness orientation, Peklenik number and standard derivation) and particle size. Finally, the flow factors under different surface characteristics and particle size are discussed.

In this paper, the average lubrication equation for grain flow is solved using a control volume method to analyze the performance of hydrodynamic journal bearings. The grain particle size effect was investigated. The nondimensional load and friction coefficient are demonstrated in terms of eccentricity ratios under various diameter-to-width ratios. The results demonstrate the performance of powdered lubricated journal bearings, and also accord with the results experimented by Heshmat and Brewe.

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