On a Particle-Augmented Mixed Lubrication Approach to Predicting CMP
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On a Particle-Augmented Mixed Lubrication Approach to Predicting CMP C. Fred Higgs, Elon J. Terrell, Michael Kuo, Joseph Bonivel, and Sarah Biltz Mechanical Engineering, Carnegie Mellon University, 5000 Forbes Ave, Mechanical Engineering Dept, Pittsburgh, PA, 15213-3890 Abstract Chemical mechanical polishing (CMP) is a process commonly used to planarize or polish thin film surfaces to enable stacking of additional levels to enhance lithographic patterning of wafers. It is used to make surfaces atomically smooth and is also an interim step in integrated circuit (IC) manufacturing. CMP is an example of a tribological regime called Particle-Augmented Mixed Lubrication (PAML) as named by the authors. PAML occurs when two surfaces in relative motion under load are partially separated by an intervening fluid-particle mixture. The load is supported by both asperities and fluid, and the interface is further complicated by the addition of nanoparticles. PAML involves four core components that must be modeled integrallyófluid mechanics, particle dynamics, contact mechanics, and material removal (wear). This work introduces the fundamental tenets of PAML, and describes how it is an effective first principle multi-physics approach to modeling CMP. By inputting the artificial random topographies for the pad and wafer with their actual mechanical properties, the PAML modeling simulation results predict the instantaneous material removal as the wear volume caused by particle-induced wear. These discrete instantaneous material removal events lead to the cumulative wear seen during CMP over a short time. Although only a small fraction of the time of the actual CMP process, tests of 120µs show that the cumulative material removal occurring over the entire simulation is approximately 0.012 µm3. This work suggests that a generalized multi-physics modeling simulation of the CMP process is plausible.
Introduction In chemical mechanical polishing (CMP), most wear or material removal rate (MRR) models have focused on the three-body wear problem [1-4] within a single tribological regime, such as dry lubrication. Three-body wear means that there are two interacting surfaces separated by fluid and a third-body, which usually is a collection of particles. Some models have focused on the fluid mechanics coupled with the chemistry effects [57]. There are some models that have analyzed the integrated solid/contact and fluid mechanics problem [8-16]. For example, Lin et al. developed a model that integrated a solid/fluid mechanics approach considering particle-induced wear [11]. However, their approach did not consider the discrete particle dynamics which is appropriate for low solid fraction slurries. Because most studies seem to focus on one or two aspects of CMP, it is believed that a particle-augmented mixed lubrication (PAML) wear approach is necessary for fully capturing the physical phenomena behind the CMP process. The PAML approach to CMP employs at least four main components integrallyó (i) contact mechanics, (ii) fluid me
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