Contact wear models

An example application of the contact wear model to simulation of the polish of an embedded array (assuming no material in the trenches within the array) is shown in Fig. 29. One can also observe the evolution of the pressure distribution, where clear sharp pressure concentrations at the edges of the features can be seen. Such localized pressures work to rapidly round the corners of features undergoing polish. 

Zhao, Y., and Change, L., A Micro-Contact and Wear Model for Chemical-Mechanical Polishing, Wear, Vol. 252, 2002,... 

Chekina et al. [8] have applied contact wear methods to the modeling of surface evolution in both oxide and dual material (tungsten-oxide) CMP to predict erosion and dishing or recess. The formulation uses calculation of... 

The contact wear approach is also applicable to modeling dual material systems such as tungsten polish. The calculated shape evolution is shown in... 

Zhao Y, Chang L. A micro-contact and wear model for chemical-mechanical polishing of silicon wafers. Wear 2002 252 220-226. 

The effect of reiterative feedback, therefore, is a major consideration in the construction of wear models that realistically take into account the influence of changing physical parameters on the course of wear. In some cases these changes are the result of the course of wear itself, such as the decrease of contact pressure as the conjunction area enlarges under constant load. In other cases, the externally imposed magnitude of a parameter such as load or rubbing speed will determine the influence that reiteration of contact will have on the course of wear. 

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. 

The most comprehensive fatigue wear model (2) proposed In the literature was used to predict wear rates to within 30 percent or less of the experimentally measured values (J). The exponent t was determined from notched cylindrical specimens In reverse bending. The number of contacts and the areas were determined from surface profiles of the polymer and the counterface after steady-state wear was attained. The wear data was obtained from a polymer pin sliding on a rotating cylinder. 

The wear model combines the simplified theory of rolhng contact, ADAMS/Rail output and the wear coefficients to predict the wear and hence the change of wheel profile as the vehicle passes over given track layouts. 

The approach used in the model for predicting wear is based on a rail wear index [2]. An energy approach is adopted in the analysis of the relationship between wear rate and contact conditions. This assumes that wear rate ( xg/m rolled/mm contact area) is related to work done at the wheel/rail contact (wear rate = KT A, where T is tractive force and / is slip at the wheel/rail interface, K is a wear coefficient and A is the contact area). 

In the present pqrer, we present a simple rigid body model of a spline coupling and use it to determine normal and tangential displacements in the cont region r en misalignment is imposed. We also consider the overall equilibrium and stability of the coiqrling. These results are then compared to those from a boundary element model Mdiich includes elasticity and stick-slip friction in the contact Wear depth predictions are also made. A locked spline, in which the shaft axial location is controlled by a nut and a shoulder is also examined. 

Following the classical works of Archard (6), and later Ratner and coworkers (12) and Lancaster (9), on modeling of the wear rate for materials and in particular polymer, several researchers have tried to present new wear models. These models are mainly based upon the notion that irrespective of the contact deformational mode, the wear rate must be dependent and hence proportional to some combination of bulk mechanical properties, operational parameters, and the initial counterface conditions. These models have essentially tried to empirically fit some experimental data and hence they can be applied to the very specific systems where they have been derived from. Works by Lewis (19), Kar and Bahadur (20), Rhee (21), and Wang and co-workers (22) may be cited here, and a list of these wear models are listed in Table 1 together with the models proposed by Archard (6), Ratner and co-workers (12), and Hollander and Lancaster (15). 

The CMP process is regarded as a combination of chemical effect, mechanical effect, and hydrodynamic effect [110-116]. Based on contact mechanics, hydrodynamics theories and abrasive wear mechanisms, a great deal of models on material removal mechanisms in CMP have been proposed [110,111,117-121]. Although there is still a lack of a model that is able to describe the entire available CMP process, during which erosion and abrasive wear are agreed to be two basic effects. 

DePalma and Tillman investigated self-assembled monolayer films from three silanes, tridecafluorooctyltrichlorosilane, undecyltrichlorosilane, and octadecyl-trichlorosilane, on silicon, a popular model substrate for such studies with great relevance to potential semiconductor coating applications. They characterized the films by ellipsometry and contact angle measurements (data for trideca-fluorooctyltrichlorosilane are included in Table 1), but more usefully from an applicational viewpoint, they carried out friction and wear measurements with a pin-on-disk device where the silicon wafer substrate, coated with monolayer, is moved under a spherical glass slider. Optical microscopy was used to assess wear. Table 2 summarizes DePalma and Tillman s data and their comparison with the classical self-assembled monolayer friction studies of Levine and Zisman [18]. 

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