Contact Model for a Pad Asperity and a Wafer Surface in the Presence of Abrasive Particles for Chemical Mechanical Polis
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Contact Model for a Pad Asperity and a Wafer Surface in the Presence of Abrasive Particles for Chemical Mechanical Polishing Dincer Bozkaya, and Sinan Muftu Northeastern University, Boston, MA, 02115 ABSTRACT A contact model for a single spherical (pad) asperity and a flat (wafer) surface, with an interface filled with spherical (abrasive) particles is introduced. Finite element method is used to determine the deformation characteristics of a single spherical abrasive indenting a hyper-elastic pad material. The asperities in Greenwood and Tripp (GT) model, which is widely used for the contact of rough spheres, are replaced with the spherical particles. Relations are developed to predict pad-to-particle-to-wafer contact in two distinct regimes, where a) pad and the wafer are separated by the particle; and b) all three bodies come in contact simultaneously. The results of the model show that the abrasive particles in the (pad) asperity-wafer interface causes the contact to be distributed over an area larger than that predicted by the Hertz model, while the maximum contact pressure becomes relatively lower. The fraction of the load carried by pad-to-wafer and pad-to-abrasive-to-wafer varies along the contact interface of the pad asperity and wafer. INTRODUCTION Some studies have shown that the majority of the material removal in chemical mechanical planarization (CMP) is achieved by the abrasion of the particles trapped between the pad asperities and the wafer [1]. Accurate characterization of the particle contact, as a function of pad elastic modulus E, particle size/distribution, and applied pressure is necessary for developing material removal rate (MRR) models. The applied pressure is carried partially by pad-to-wafer (direct) contact, and partially by pad-to-abrasive-to-wafer (particle) contact. The fraction of the applied pressure carried by particle contact is an important factor affecting the MRR. Hertz contact has been used to model the contact of an asperity of a rough pad with a wafer, neglecting the particles [1-3]. Smooth pad models were also constructed [4-5]. Luo and Dornfeld calculated the distribution of the applied load between particle and direct contact, by assuming that that the particles indent the pad plastically [2]. The direct contact load was also found by modeling the pad as an elastic beam supported by particles [5]. Qin et al. assumed the contact pressure to be constant in the pad asperity-wafer contact interface, and used the particle cross-section area to find the particle contact force [3]. Bastawros et al. utilized a finite element model of a single particle for the distribution of the total load to particle and direct contact [6]. The objective of this study was to determine the effect of the particles on the contact of a single pad-asperity with a wafer; and to investigate the effects of particle concentration and size distribution. Greenwood and Tripp (GT) model [7], which is widely used for the contact of rough spheres, forms the basis of the current model. Greenwood an
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