Three-body contact scale

Three-body contact scale ( 100 nm) is close to a single abrasive particle size. The three interactive bodies are the wafer, the abrasive particle, and the pad asperity. The wafer and particles are more rigid than the pad asperities, so that the main deformation occurs within the asperity. 

Clean surfaces are known to adhere to each other ill) and the bond formed must be broken for relative motion to occur. host first displacements, waves excepted (12), result in local des-truc-tions of first body surfaces and thus in the formation of wear particles. Figure 2 (13) illustrates what happens to a hard steel surface rubbing against glass after a limited number of short strokes. Scratches are noted, particles are detached bv one mechanism or another, and because of scale factors (fig.3), these particles are trapped at least momentarily in the very confined space of the contact. Wear debris, or wear particles which form rapidly alter the nature of the contact which gradually changes from a two to a three-body contact as in EHD. 

This result, however, cannot be obtained directly by a scaling argument. In a semi-dilute 6 solution, there are two characteristic lengths the correlation length I/c (which represents the distance between three-body contacts and has been chosen here as the tube diameter) and the distance between entanglements 2 (distance between two body contacts) which is the mesh size of the transient network. These two lengths play a role in the viscoelastic properties of semi-dilute 6 solutions. Their relative importance is still a matter of controversy. 

In 1999, Luo and Domfeld [110] proposed that there are two typical contact modes in the CMP process, i.e., the hydro-dynamical contact mode and the solid-solid contact mode [110]. When the down pressure applied on the wafer surface is small and the relative velocity of the wafer is large, a thin fluid film with micro-scale thickness will be formed between the wafer and pad surface. The size of the abrasive particles is much smaller than the thickness of the slurry film, and therefore a lot of abrasive particles are inactive. Almost all material removals are due to three-body abrasion. When the down pressure applied on the wafer surface is large and the relative velocity of the wafer is small, the wafer and pad asperity contact each other and both two-body and three-body abrasion occurs, as is described as solid-solid contact mode in Fig. 44 [110]. In the two-body abrasion, the abrasive particles embedded in the pad asperities move to remove materials. Almost all effective material removals happen due to these abrasions. However, the abrasives not embedded in the pad are either inactive or act in three-body abrasion. Compared with the two-body abrasion happening in the wafer-pad contact area, the material removed by three-body abrasion is negligible. 

A single chain at the compensation point Q has a quasi-ideal behavior. The size R scales like N, and the pair correlation function g r) decreases like 1 r (for r 7 ). However, the three-body repulsive interactions remain effective even at T = 6. Their effect (in three dimensions) is to introduce some correlation between the monomers. The probability of contact between two (or three) monomers is reduced by certain logarithmic factors. These factors could show up in certain measurements which are sensitive to local properties (e.g., specific heat) and possibly in certain optical properties. 

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