Surface abrasion model

The hrst mechanism specihcally for tungsten CMP was proposed by Kaufman et al. [67]. They thought, first, chemical action dissolves W and forms a very thin passivating him which stops growth as soon as it reaches a thickness of one or a few moleculars later. Second, the him is removed locally by the mechanical action of abrasive particles, which contact with the protrude parts of the wafer surface, and then cause material loss. In recent years, most of the analysis and models for metal CMP are built based on the Kaufman model [68,69]. However, the model is not involved in microscopic structure analysis for the polished surface, but focuses on interpreting macroscopic phenomena happening during CMP [18]. 

Luo and Domfeld [110] introduced a fitting parameter H , a d5mamical" hardness value of the wafer surface to show the chemical effect and mechanical effect on the interface in their model. It reflects the influences of chemicals on the mechanical material removal. It is found that the nonlinear down pressure dependence of material removal rate is related to a probability density function of the abrasive size and the elastic deformation of the pad. 

Figure 26.61 shows the abrasion of an OESBR tread compound as function of load for different slip angles on a sharp Alumina 60 surface. Because of the wide range of abrasion rates for different slip angles the abrasion data were plotted on a log scale. It is seen that at the small slip angle the dependence on load is small and becomes more pronounced as the slip angle is increased. This is expected from the bmsh model. At small slip angle the side force is independent of the load and hence it is expected that the abrasion behave in a similar way. 

Having calculated the force for a particular event the slip is calculated using the bush model and hence the energy dissipation is obtained. Using the factors of the abrasion equation, determined with the LAT 100 on an alumina surface the abrasion loss for each event is calculated. The forces are different for a driven and a nondriven axle and accordingly different abrasion rates will result. 

Arena et al. (1983) investigated the coal attrition in a mixture with sand under hot but inert conditions. As they increased the sand particle size while keeping its mass in the bed constant, they observed an increase in the coal attrition rate. They interpreted their results by assuming that the abrasion energy is shared out on the entire material surface. On the same basis Ray et al. (1987a) developed their attrition rate distribution model for abrasion in a fluidized bed. 

Modeling ofBubble-Induced Attrition. Merrick and Highley (1974) have modeled bubble-induced attrition as a comminution process. According to Rittinger s law of size reduction by abrasion (cfi, Perry, 1973), the rate of creation of new surface area AS Al is proportional to the rate of energy input Ah. At... 

As mentioned, the erosion of a solid surface depends on the collisional force, angle of incidence, and material properties of both surface and particles. Although abrasive erosion rates cannot be precisely predicted at this stage, some quantitative account of erosion modes which relates various impact parameters and properties is useful. In the following, a simple model for the ductile and brittle modes of erosion by dust or granular materials suspended in a gas medium moving at a moderate speed is discussed in light of the Hertzian contact theory [Soo, 1977]. 

We have also conducted adhesion measurements between real CMP abrasive particles (not model particles) and various surfaces as well as particle hardness and elastic modulus measurements, using colloidal AFM and nanoindentation AFM, respectively, in an attempt to correlate CMP defectivity with mechanical and adhesion properties of CMP abrasives [77,78]. For example, in a carefully designed experiment, we have been able to demonstrate that softer particles, indeed, result in fewer scratches [78]. 

The removal rate depends on how many abrasive particles on the pad are pressed against the surface. The pad has been modeled [70-72] as a Langmuir... 

We now describe an approach for estimating the reaction temperature. Viewed at a microscopic level, this is a very complex stochastic thermal problem involving the frictional interaction of a relatively smooth surface with a rough one in the presence of a cooling lubricant that contains abrasive particles. Rather than treat this problem fully, we try to capture the most important features while neglecting other potentially interesting ones. The end result will be a simple estimate of the reaction temperature that can be used in a compact model. 

Bastaninejad M, Ahmadi G. Modeling the effects of abrasive size distribution, adhesion, and surface plastic deformation on chemical-mechanical polishing. J Electrochem Soc 2005 152(9) G720-G730. 

This model implicitly assumes that, at least to some extent, the pad makes contact with the wafer surface (i.e., the pad directly presses the abrasive against the surface) and exerts pressure directly to the surface. The abrasive then moves across the surface as a Hertzian indenter. As discussed in Chapter 4 however, it is also possible that a continuous fluid layer exists between the wafer and the pad. The pad compresses the fluid layer, which in turn exerts hydrodynamic pressure on the surface. The existence of a hydrodynamic fluid layer is an important distinction because the wear mechanisms are different for fluid-based wear as opposed to Hertzian indenter-based wear (see Chapter 4). 

In this chapter, we shall first propose a model to explain the removal and planarization mechanisms of copper CMP. Next, we discuss surface layer formation during copper CMP, which is important for planarization, followed by copper dissolution during CMP, which is iii5)ortant to maintain high removal rates. Next a comparison of copper CMP to the Preston equation is made, followed by a discussion of the abrasion mode during copper CMP. Lastly, we investigate the dishing and erosion behavior of copper CMP. 

We utilize the Kaufman model as a basis for understanding the removal mechanism in the CMP of copper. Specifically, we hypothesis that a CU2O film forms on the copper and that just as with tungsten, the surface film prevents the removal of the low-lying copper. However, we believe that the dominant mechanism for removal in the case of copper CMP is abrasion of material from the surface by the mechanical action, rather than direct dissolution of material at the metal surface. 

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