Pad viscoelasticity

The viscoelasticity of a polishing pad has been shown to play an important role in the CMP process [59]. Fu and Chandra [55] in a viscoelastic pad deformation model showed that MRR decay for an unconditioned pad is strongly influenced by the viscoelasticity of the pad. Guo et al. [60] investigated the effects of pad viscoelasticity on dishing and erosion without considering pad roughness (asperity height distribution). 

Viscoelastic solid dampers generally consist of solid elastomeric pads (viscoelastic material)... 

The model was fit to experimental planarization data with good success. Divergence from experimental results was explained by viscoelastic deformation of pad asperities. Incomplete elastic recovery reduces penetration of the trench and improves selectivity. This may be due to velocity effects (i.e., the interaction times are below the relaxation time for the material). 

Guo Y, Chandra A, Bastawros A. Anal5dical dishing and step height reduction model for CMP with a viscoelastic pad. Electrochem Soc 2004 151(9) G583-G589. 

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. 

Pad Elastic and Shear Modulus Units of (MPa) or (psi). These moduli determine the mechanical stability and flexibility of pads during polishing under the load and rotational constraints. The pad s viscoelastic behavior is important in determining the planarization effectiveness and in the feature size effect observed during CMP. 

Pad Hardness Hardness, measured in relative units based on the type and mode of the indentation, is generally a measure of the ability of the pad to maintain its shape, and thus it is linked to elastic and viscoelastic properties. Harder pads are expected to provide better planarity. Softer pads, on the other hand, may provide better (defect-free) surfaces. Whereas it is difficult to measure the hardness of the pads, the viscoelastic behaviors can be measured to provide the necessary information. 

Figure 4.13 shows the deformation behavior of a viscoelastic material. In response to a stress at time tj, the material deforms exponentially with time. When the stress is removed (or lowered, as is the case when the pad passes from a high region to a low region), the viscoelastic material rebounds with an exponential time dependence. However, the strain in the viscoelastic material does not necessarily completely relax upon unloading. Viscoelastic behavior is described mathematically by ... 

As mentioned above, polishing pads show both elastic and viscoelastic behavior. Figure 4.14 shows the time-dependent behav-... 

Figure 4.14 Two hypothetical pads exhibiting both elastic and viscoelastic behavior. Pad A shows less deformation than pad B, and is thoefore less compliant and likely to be more effective at planarizing.

Figure 4.15 Two hypothetical pads exibiting both elasdc and viscoelastic behavior. Even though pad C shows greater long-term deformation, in the time important for planarization, pad C deforms less and therefore should planarize better.

Note that in the current model, the viscoelasticity of the pad will still affect the planarity. An asperity with a high G will rebound sluggishly as it passes over the trench and thus will make... 

The deformation behavior of two pads are shown in Figure 4.14. Which pad shows greater elastic behavior Which pad shows viscoelastic behavior A CMP process is required to planarize a surface with a maximum step height of 5000 A. If the velocity of the pad is 50 cm/sec, which pad will polish faster inside a 5 pm wide trench A 10 pm wide trench A 15 pm wide trench What is the maximum width of a low region that may be planarized by each pad (Note assume that the pad relaxation and deformation behaviors (curves) are similar and symmetric.)... 

Contact during and after CMP is between a wafer and a polymer as a pad or brush thus the nature of the contact is predominantly elastic. As we saw in Section 2.1, the ratio of the elastic modulus E and the hardness H determines the extent of the plasticity in the contact region as well as the surface topography. For metals, E/H is typically 100 or greater, whereas for many of the softer polymers (low P s), E/H is only about 10. Thus the contact between metals and polymers is almost completely elastic except against very rough surfaces. Another factor that affects the friction of polymers is the strong time dependence of their mechanical properties most polymers are viscoelastic and also show a marked increase of flow stress with strain rate. 

This analytical solution review is tractable only for very limited assumptions, such as homogeneity and linearly elastic behavior (not to mention excluding variations that are time- or temperature-dependent). The first deviation that must be examined is the elastic linearity assumption for polishing pads. Polymers, in general, show behavior that lies between that of an elastic solid and a viscous fluid. The term viscoelastic has been applied to this behavior. 

We need to understand the force-bearing characteristics of the asperity-rich pad surface. The scale of this perspective shrinks another order of magnitude from that used to examine the pad s pore structures. As seen in Figure 6.16, the wafer compression action on the polymer material is likely to show a viscoelastic response (the compression span of the traveling wafer is sufficiently long for the polymer material to respond viscoelastically). The asperities in contact with the wafer surface will then suffer a viscoelastic modification. The nature of this modification will be defined by the forces at work on the asperity profiles. 

Generally, polymer of polyurethane type is used for pads. Uniform surface roughness and porosity of pad influence the characteristics of WIWNU (within-wafer non-uniformity), WTWNU (wafer-to-wafer non-uniformity), and LTLNU (lot-to-lot non-uniformity). For this reason, chemical technology durability, hydrophilic, and viscoelastic features differ according to each required CMP process condition. Table 1.4 shows currently used pads types and the CMP process to which they are applied. 

Injury is caused by energy transfer to the body by an impacting object. It occurs when sufficient force is concentrated on the chest or abdomen by striking a blunt object, such as a vehicle instrument panel or side interior, or being struck by a baseball or blunt ballistic mass. The risk of injury is influenced by the object s shape, stiffness, point of contact, and orientation. It can be reduced by energy absorbing padding or crushable materials, which allow the surfaces in contact to deform, extend the duration of impact, and reduce loads. The torso is viscoelastic, so reaction force increases with the speed of body deformation. 

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