Fluid Layer Interactions

Contact area, and the surface area occupied by single abrasive particle Note that the indentation depth, 5, is exaggerated, (c) Calculation of the contact radius, from the indentation depth. 

In the presence of a lubricating liquid (i.e., the polish slurry) two solid bodies in relative sliding motion will interact in one of 

A wafer scale CMP process will fall into one of the three categories listed above. In the first case, the load is supported almost entirely via pad wafer contact. In the second case the load is supported partially by pad-wafer contact and partially by hydrodynamic pressure on the slurry between the wafer and pad. In the final case, the load is supported entirely by a continuous fluid layer of slurry between the wafer and pad. As discussed by Preston (Section 4.1), polish rate is proportional to pressure. Because each of these modes is likely to distribute pressure differently, the ability of a CMP process to remove material and to planarize will be affected by which mode a given CMP process operates within. 

In the extreme case where the load is supported entirely by solid-solid contact, frictional wear will be at a maximum. However, the transport of slurry under the wafer will be poor, resulting in a limited amount of chemical activity and little lubrication effect. Under such conditions elevated temperatures would be expected and mechanical abrasion would dominate. As a consequence, the polished surface is likely to be severely damaged. 

The existence of a fluid layer is beneficial for two reasons. First the fluid layer will act as a lubricating agent and conduct heat away from the surface. Second, slurry transport is expected to be more efficient with a fluid layer. It is expected that CMP does indeed involve a fluid layer that is either continuous or partial. It is not clear, however, if the fluid layer is partial or continuous. In the remainder of this section, we discuss the results of a tribological analysis by Runnels and Eyman, while in Section 4.4.2 we shall discuss the implications of partial or continuous fluid layers on the mode of abrasion. 

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Dickinson, E. (1999b). Adsorbed protein layers at fluid interfaces interactions, structure and surface rheology. Colloids and Surfaces B Biointerfaces, 15, 161-176. 

Monolayers of micro- and nanoparticles at fluid/liquid interfaces can be described in a similar way as surfactants or polymers, easily studied via surface pressure/area isotherms. Such studies provide information on the properties of particles (dimensions, interfacial contact angles), the structure of interfacial layers, interactions between the particles as well as about relaxation processes within the layers. Such type of information is important for understanding how the particles stabilize (or destabilize) emulsions and foams. The performed analysis shows that for an adequate description of II-A dependencies for nanoparticle monolayers the significant difference in size of particles and solvent molecules has be taken into account. The corresponding equations can be obtained by using a thermodynamic model developed for two-dimensional solutions. The obtained equations provide a satisfactory agreement with experimental data of surface pressure isotherms in a wide range of particle sizes between 75 pm and 7.5 nm. Moreover, the model can predict the area per particle and per solvent molecule close to real values. Similar equations were applied also to protein monolayers at liquid interfaces. 

The last term in the momentum equation, i.e., Eq. (9.78). represents the affect of the buoyancy forces on the mean momentum balance. However, these buoyancy forces also affect the variation of e and e in the flow. To illustrate how the buoyancy forces can effect e and e, consider again the simple mixing length model discussed in Chapter 5. Lumps or eddies of fluid are assumed to move across the flow through a transverse distance, lm, while retaining their initial velocity and temperature. They then interact with the local fluid layer giving rise to the fluctuations in velocity and temperature that occur in turbulent flow. 

The tear film is a dynamic fluid layer with lipid, aqueous, and mucin components that interact with each other... 

The Landau free energy surfaces provide clear evidence of the existence of a contact layer with different structural properties compared to the pore interior, thereby supporting the experimental observation. The nature of the contact layer phase depends on the strength of the fluid-wall potential. For purely repulsive or mildly attractive pore-walls, the contact layer phase exists only as a metastable phase. As the strength of the fluid-wall attraction is increased, the contact layer phase becomes thermodynamically stable. Like the direction of shift in the freezing temperature, the structure of the contact layer phase also depends on the strength of the fluid wall interaction (i.e., whether the contact layer freezes before or after the rest of the inner layers). 

A systematic study of the influence of the strength of the fluid-wall interaction parameter a revealed that, for a < 0.5, the intermediate phase B remains metastable for all temperatures. For the range 0.5 < a < 1.2. phase B becomes thermodynamically stable with the contact layer freezing at a temperature below that of the inner layers and for Q > 1.6, phase B becomes thermodynamically stable with the contact layer freezing at a temperature above that of the the inner layers [9]. 

Salamacha and coworkers304 306 have carried out a series of studies on Lennard-Jones fluids confined to nanoscopic slit pores made from parallel planes of face centred cubic crystals. Grand canonical and canonical ensemble MC simulations have been used to determine the structure and phase behaviour as the width of the pore and the strength of the fluid-wall interactions were varied. The pore widths were small accommodating 2 to 5 layers of fluid molecules.304,305 The strength of the fluid-wall interaction is linked to the degree of corrugation of the surface, and it is found that the structure of the... 

Figure 15. Collapse of simulation data for the effective viscosity versus shear rate as a glass transition is approached by decreasing temperature (circles), increasing normal pressure at fixed number of fluid layers (triangles), or decreasing film thickness at fixed pressure with two different sets of interaction potentials (squares and crosses). The dashed fine has a slope of 0.69. With permission from Ref. 212. Microstructure and Microtribiology of Polymer Surfaces, American Chemical Society, 2000.

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