A Fast, Experimentally validated, Particle Augmented Mixed Lubrication Framework to Predict CMP
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A Fast, Experimentally validated, Particle Augmented Mixed Lubrication Framework to Predict CMP Gagan Srivastava and C . Fred Higgs III Mechanical Engineering. Carnegie Mellon University, 5000 Forbes Ave, Pittsburgh PA 15213 ABSTRACT Fabrication of integrated circuits is a multi-step process that involves chemical mechanical polishing (CMP) for planarizing the deposited layers. Although dependent on the consumables and machine operating conditions, most CMP researchers assume that the polishing occurs in the mixedlubrication regime, where the applied load on the wafer is supported by the hydrodynamic slurry pressure and the contact stress generated during the pad-wafer contact. The particle augmented mixed lubrication (PAML) approach has been employed by Terrell and Higgs (2009) as a high-fidelity asperity-scale mixed-lubrication CMP model. The current work introduces a more computationally efficient wafer-scale PAML model, called PAML-lite, which employs a two-dimensional average flow Reynold's Equation incorporating spatial dependence of entrainment velocities to model the hydrodynamic pressure. The contact mechanics are modeled using a Winkler elastic foundation in cylindrical polar coordinates. The resulting slurry hydrodynamic pressure distribution and contact stress are used to determine the equilibrium configuration of the system in the form of a nominal clearance and rolling and pitch angles. Local and wafer scale material removal rate (MRR) is predicted by assuming a uniform distribution of particle sizes. The prediction of PAML-lite were then benchmarked against experimental results. Upon verification, parametric studies were conducted to understand the effect of some unexplored CMP parameters. INTRODUCTION Although CMP is a common practice in the semiconductor manufacturing industry, the physics behind the process is not completely understood due to the complex nature of the slurry flow and interaction between the wafer, pad and abrasive particles. Several models have been proposed to explain the wear action in the CMP process, ignoring one or more of the physical phenomena involved. The majority of approaches in the literature are set up at the wafer scale and do not predict the presence of dishing, erosion and micro-scratching, defects at feature scale. Identifying a modeling approach they called PAML (Particle Augmented Mixed Lubrication), Terrell et al. [1] presented an asperity scale model that can overcome the shortcomings of wafer scale models. However, due to the high computational costs of the model, even with a small domain, the model is still computationally very expensive. The present study, like PAML, integrates the effect of slurry fluid flow and mechanics of wafer and pad contact. and includes abrasive wear of particles for the process of polishing. The model is presented here as a wafer scale analysis, intended to capture the wafer scale defects such as inter-die polishing differences. However, with sufficient computing resources, it can easily be scaled to a much higher resolution to capt
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