TLcmp2004 - Tribology Letters, Vol. 17, No. 2, August 2004...

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Surface shape and contact pressure evolution in two component surfaces: application to copper chemical mechanical polishing W.G. Sawyer* Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, Fl 32611,USA Received 10 March 2003; accepted 27 October 2003 Two defects that arise from the polishing process in integrated circuits technology are erosion and dishing. In this manu- script a generic numerical model that is capable of describing these defects from a mechanics perspective is presented. This numerical model formulates evolution of surface shape for an initially flat sample made up of two distinct materials with diFer- ent wear rates under constant average polishing pressure. A two parameter elastic foundation model is used for contact pressure calculations. Qualitatively, the results compare favorably to published experimental data collected for copper chemical mechani- cal polishing. Although entirely mechanical, such modeling may perhaps provide insight into the mechanics of the surface defects and errors encountered during polishing. KEY WORDS: wear, composites, chemical mechanical polishing 1. Introduction As feature sizes continue to decrease in integrated circuits technology, defects arising from the polishing process, such as erosion and dishing, greatly impact ±nal yield. Conventional copper chemical mechanical polishing uses polymeric pads with slurries of ±ne abrasives. The goal is to achieve a planar surface of copper and barrier oxide. Each of the phases has a unique resistance to material removal, and the result- ing non-planar surfaces, shown in ±gure 1, are typical of defects resulting from this process. In this manuscript a generic model for the surface evolution of a two component system under constant polishing load is developed. The approach follows cou- pled evolution approaches that have been successful at predicting shape evolution for 2-dimensional mechani- cal systems such as the scotch-yoke [1,2] and the eccen- trically mounted circular cam [3,4], although it is applied here to a multi-component system under ini- tially uniform contact pressure. The approach changes the surface shape after each cycle using a simple wear model, and uses the new surface shape to calculate tri- bological conditions for the subsequent cycle; these calculations proceed iteratively with both the shape and contact pressure evolving. Over the past decade, eForts have been made to include wear within numerical and ±nite element meth- ods. In the tribology literature, these models use an Archard’s wear model for the incremental wear predic- tions (Archard’s wear model (1957) [5] and Preston’s model (1927) [6], used in CMP, both have removal rate proportional to contact pressure to the ±rst power). These problems are computationally intensive because of the iterative nature of the contact calcula- tions, and researchers often try to extrapolate results to reduce the number of computation cycles. Extrapo- lation errors in such calculations were cursorily addressed by Dickrell et al. [4].
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This note was uploaded on 08/22/2011 for the course EGM 4313 taught by Professor Mei during the Spring '08 term at University of Florida.

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TLcmp2004 - Tribology Letters, Vol. 17, No. 2, August 2004...

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