Chemical mechanical planarization ͑CMP͒ of copper involves removal of surface asperities with abrasive particles and polishing processes. This leads to copper-containing nanoparticles extruded into the solution. We model the diffusion-limited agglomeration ͑DLA͒ of such nanoparticles which can rapidly grow to large sizes. These large particles are detrimental because they can participate in polishing, causing scratches and surface defects during CMP. The agglomeration is much slower in the reactionlimited agglomeration process. Under realistic conditions the defect generation probability can increase significantly over time scales of ϳ10 to 20 min from DLA, unless prevented by slurry rejuvenation or process modification measures.
A multi-physics model encompassing chemical dissolution and mechanical abrasion effects in CMP is developed. This augments a previously developed multi-scale model accounting for both pad response and slurry behavior evolution. The augmented model is utilized to predict scratch propensity in a CMP process. The pad response delineates the interplay between the local particle level deformation and the cell level bending of the pad. The slurry agglomerates in the diffusion limited agglomeration (DLA) or reaction limited agglomeration (RLA) regime. Various nano-scale slurry properties significantly influence the spatial and temporal modulation of the material removal rate (MRR) and scratch generation characteristics. The model predictions are first validated against experimental observations. A parametric study is then undertaken. Such physically based models can be utilized to optimize slurry and pad designs to control the depth of generated scratches and their frequency of occurrence per unit area.
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