Material Removal Model

Yu TK, Yu CC, Orlowski M. A statistical polishing pad model for chemical mechanical polishing. IEEE lEDM Washington DC, Dec 5-8 1993. pp 865-868. Seok J, Sukam CP, Kim AT, Tichy JA, Cale TS. Multiscale material removal modeling of chemical mechanical polishing. Wear 2003 254 307-320. 

A TWO-STEP CHEMICAL MECHANICAL MATERIAL REMOVAL MODEL... 

Chapter 11 is one of the chapters with emphasis on fundamentals and presents an original model for lapping of ceramics the double fracture model. I developed this model with my students over the past fifteen years, trying to provide a more complex material removal model in the case of lapping of ceramics (indentation and scratch). 

Luo and Domfeld (2003) proposed a material removal model that accounts for active slurry particle size (i.e., diameter) effects. This model assumes that only a fraction of the slurry particles is involved in material removal these are defined as active particles. An active particle must fulfill two conditions (1) locating on the contact area between wafer and pad and (2) be large enough. The wafer will contact the largest particles first when a reference pressure is applied. A gap is formed between the pad and wafer surface in the surrounding area of the larger particles only particles larger than this gap can participate in material removal. The particle size distribution affects both the size and number of active particles. 

D. Bozkaya, S. Muftu, A material removal model for CMP based on the contact mechanics of pad, abrasives, and wafer, J. Electrochem. Soc. 156 (2009) H890—H902. 

G. Fu, A. Chandra, Guha, 2000, A Generalized Material Removal Model for the Chemical Mechanical Polish-ing(CMP) Process , Proc. 17th Int. VLSI Multilevel Interconnect Conference 113. 

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. 

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. 

In a typical modeling approach, the material removal rate is modeled as a function of easily controlled process parameters. The most basic model is one that predicts the bulk rate of material removal in a macroscopic fashion. An empirical observation by Preston is widely used, in which the rate of material thickness reduction is proportial to the product of (a) the relative velocity between the wafer and the polish pad and (b) the pressure on the surface of the wafer ... 

Guo, Y., Tang, J., Dornfield, D. (1998). A finite element model for wafer material removal rate and non-uniformity in chemical mechanical polishing process. Proc. 3rd Int. CMP for ULSI Multilevel Interconnect. Conf, Santa Clara, pp. 113-118. 

In the first monolayer of conjugated model material, a model molecular solid or a polymer adsorbate, assume that no chemistry (covalent bonding) occurs, since, in the absence of, for example, mechanical rupturing, the bonds at the surface of the molecular film are completely satisfied. This assumption is supported by the fact that, at least for condensed molecular solids, vapor-deposited films may be re-evaporated (removed) from the surface by gentle heating in UHV. 

Fu G, Chandra A, Guha S, Subhash G. A plasticity-based model of material removal in chemical-mechanical polishing (CMP). IEEE Trans Semicond Manuf 2001 14(4) 406-417. 

Wang C, Sherman P, Chandra A. A stochastic model for the effects of pad surface topography evolution on material removal rate decay in chemical mechanical planarization (CMP). IEEE Trans Semicond Manuf 2005 I8(4) 695-708. 

Fu G, Chandra A. A model for wafer scale variation of material removal rate in chemical mechanical polishing (CMP) based on viscoelastic pad deformation. J Electron Mater 2002 31(10) 1066-1073. 

Experimental evidence strongly suggests that material removal in chemical-mechanical polishing (CMP) processes is a result of one or more chemical steps that alter the wafer surface combined with a mechanical step that removes the altered material. Chemical action by itself also removes material by static etching, but generally at a much lower rate than is observed when mechanical action is also present. Similarly, polishing rates observed when a minimally reactive fluid such as water is used instead of slurry are also low. Both chemical and mechanical processes are therefore involved in material removal at commercially practical rates, and the model we describe reflects this dual nature of the process. 

Runnels assumes the existence of a continuous fluid layer between the pad and the wafer and models planarization using a feature scale fluid-based-wear model. Runnels uses fluid mechanics to model the normal and shear stresses that are developed at the feature scale. Material removal rate is assumed to depend only upon the shear stress, Ot, according to ... 

In all these derivations, the role of the slurry chemicals during the polish process is not apparent. Even under static conditions, some of the chemicals can dissolve the material as in the case of ferric nitrate and copper or even H202/glycine and copper. This effect can, in principle, be easily included in a model description by adding a nonzero, velocity and pressure independent, intercept to the polish rate expression. In practice, it is more complicated since the relation between this nonzero intercept and static dissolution rates is not simple and is unknown due to, among other things, the effects of the polishing pad. In such cases, the role of a threshold pressure, while perhaps obvious when mechanical abrasion is the only mechanism for material removal, is not evident unless the removal rate can be broken neatly into two independent terms, one for the mechanical abrasion and the second for the chemical removal. Such is the case for the... 

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