And fluid film thickness

J. Coppeta, J. Rogers, L. Racz, C. Duska, D. Bramono, J. Lu, A. Philipossian, and F. Kaufman, Pad Effects on Slurry Transport and Fluid Film Thickness Beneath a Wafer, Proc. of CMP-MIC, Santa Clara, CA, Feb. 1998. 

Because EHD film thickness is determined by the viscosity of the fluid in the contact inlet [46], it is obvious that the viscosity of OMCTS remains at the bulk value down to approximately 0.1 m/s. However, below this speed the discretization of both central and minimum film thicknesses can be observed. The central film thickness begins to deviate from the theory at about 10 nm and the interval of the discretization is approximately 2 nm. If the molecular diameter of OMCTS that is about 1 nm is taken into account, it corresponds to approximately two molecular layers. 

The relationship between film thickness of hexadecane with the addition of cholesteryl LCs and rolling speed under different pressures is shown in Fig. 25 [50], where the straight line is the theoretic film thickness calculated from the Hamrock-Dowson formula based on the bulk viscosity under the pressure of 0.174 GPa. It can be seen that for all lubricants, when speed is high, it is in the EHL regime and a speed index 4> about 0.67 is produced. When the rolling speed decreases and the film thickness falls to about 30 nm, the static adsorption film and ordered fluid film cannot be negligible, and the gradient reduces to less than 0.67 and the transition from EHL to TFL occurs. For pure hexadecane, due to the weak interaction between hexadecane molecules and metal surfaces, the static and ordered films are very thin. EHL... 

Background on Spin Casting. As early as 1958, Emslie, et al. (A) proposed a theoretical treatment of spin casting for nonvolatile Newtonian fluids. This theory predicted that films formed on a flat rotating disc would have radial thickness uniformity. They predicted that the final film thickness would depend on spin speed (w) and viscosity (ij) as well as other variables such as liquid density and initial film thickness. The dependence of thickness on u> and ij was also recognized by many of the other authors reviewed in this paper, and their proposed relationships are compared in Table I. Acrivos, et al. (5) extended the Emslie treatment to the general case of non-Newtonian fluids, a category into which most polymers fall. Acrivos predicted that non-Newtonian fluids would yield films with non-uniform radial thickness. 

While the resulting model is not quantitatively predictive, important observations can be made based on parametric simulation studies. It is proposed that changes in viscosity due to wafer temperature may be as large as 30%, and that such viscosity dependencies can have significant impact on fluid film thickness and transitively on removal rate. The importance of other process parameters, such as wafer curvature, is also indicated by the model. 

A rotated disc in a fluid behaves as a pump which draws fluid towards the disc and throws it out radially, Fig. 5.17. Flow to a rotated disc has the surprising property that, under laminar flow conditions, the film thickness is uniform across the whole of the disc surface, excluding edge eifects, and the film thickness (5) is rigorously calculable using fluid mechanics theory [22]. ft is given by Equation 5.12 where D is the diffusion coefficient in cm2 s-1, v is the kinematic viscosity in cm2 s 1 and a> is the rotation speed in rad s-1 ... 

Since liquid does not completely wet the packing and since film thickness varies with radial position, classical film-flow theory does not explain liquid flow behavior, nor does it predict liquid holdup (30). Electrical resistance measurements have been used for liquid holdup, assuming liquid flows as rivulets in the radial direction with little or no axial and transverse movement. These data can then be empirically fit to film-flow, pore-flow, or droplet-flow models (14,19). The real flow behavior is likely a complex combination of these different flow models, that is, a function of the packing used, the operating parameters, and fluid properties. Incorporating calculations for wetted surface area with the film-flow model allows prediction of liquid holdup within 20% of experimental values (18). 

FIGURE 2.19 The coefficient of friction at (a) 60 RPM and (b) 5 RPM, measured using DELIF technique, show no correlation with instantaneous fluid film thickness. 

MEASUREMENT OF FLUID FILM THICKNESS AND DETECTION OF FILM FAILURE... 

In the same investigation [1] Crook demonstrated another effect in a dynamically lubricated system which has an important influence on the validity of film thickness determinations by electrical resistance. Direct measurement showed that the resistivity of a commercial turbine oil decreased from 10 " ohm-cm at 273 K (32 F> to 10 ohm-cm at 549 R (530 F). It was also demonstrated that the bulk of the metal in the rotating disks acted as such a large heat sink during a run that it took considerable time for the temperature of the system to stabilize, and even then the temperature of the oil film was not exactly known. Both of these influences cast doubt on the reliability of the electrical resistance technique for evaluating fluid film thickness. The usefulness of the resistance method is restricted to special circumstances such as light loads, very slow speeds and simple linear geometry. 

Such being the case, further inferences about the nature of the wear process follow. A disrupted fluid film allows localized contacts at the rubbing surfaces, and it is the mechanistic processes at these contacts that determine the course of lubricated wear. When the wear process is abrasive, it is most likely influenced directly by fluid film thickness and surface roughness, whereas processes such as adhesion, transfer, oxidation, additive reaction and the like are responsive to surface conditions at the contacts as well as to the number of contacts. These are the aspects of lubricated wear that are emphasized in this chapter, from the viewpoint of phenomenology, mechanisms and modeling. 

The problem of wear when the fluid film lubricant is no longer intact is associated with the asperity contact of structured surfaces. The contact behavior of such surfaces was discussed in Chapter 12 wear models governed by asperity contact were described in Chapter 13. Theoretically the laws controlling fluid film thickness can be coupled with asperity contact models to yield quantitative descriptions of the course of wear. In this section we shall deal with those cases in which the function of the lubricant is only to provide a fluid film separating the two rubbing bodies, and the events at the contact, once it is established, are determined by the interaction of mechanical parameters such as load and rubbing speed with the properties of the contacting interface. 

Equivalent Film Thickness Refers to an experimentally determined fluid film thickness for which some assumptions about the structure and properties of the film have been made. The experimental technique used should also be stated when using this term. 

Heat and Mass Transfer The flow pattern, that is to say the fluid particle shape and dimensions, and the film thickness play a dominant role concerning these transport phenomena due to their importance for the determination of the size of the interfadal area. In bubbly and foam flow it can be characterized by the interfacial... 

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