Wafer Velocity

It was shown that the friction force applied on the wafer was directly proportional to the downforce. In a dry pad condition without any slurry, the friction on the wafer was relatively constant with the wafer velocity. However, in the presence of polishing slurry on the pad, the friction force decreased with the wafer velocity (Figure 1.3). This phenomenon can be well explained by the Stribeck curve from tribology (Figure 1.4). 

The Stribeck curve shows that the friction force applied on the moving surface decreases with the relative velocity of the moving object in the presence of lubrication. This is because the thickness of the lubrication film between two objects increases with the relative velocity. In the presence of the abrasive slurry, the friction between the wafer and the pad decreased with the wafer velocity. It is believed that this is caused by increased slurry thickness between the wafer and the pad from higher wafer velocity. 

In the dry pad condition, however, the friction force remained constant with the wafer velocity since there is no lubrication fihn under the wafer surface. This can be illustrated in terms of interaction with pad and abrasives (Figure 1.5). In the condition of high downforce or low wafer velocity, the wafer moves on the pad with thinner slurry film. This can cause increased interaction between the wafer surface and the abrasives supported by the polishing pad. In the condition of low downforce or high wafer velocity, wafCT behavior can be the opposite. Wafer can slide on the pad with thicker slurry film. This can result in less interaction between the wafer and the abrasives. 

In order to understand the kinetics of the material removal mechanism in CMP, the amount of material removal per sliding distance needs to be measured and understood (Figure 1.6). By using the same test set-up shown previously, the amount of oxide removal per sliding distance was measured with different wafer velocity and down-force. The amount of oxide removal per sliding distance was at the maximum at the lower wafer velocity. As the wafer velocity increased, material removal per sliding distance decreased. This phenomenon can explain how material removal is made in different vertical positions of the wafer. 

At the higher wafer velocity, the slurry him between the wafer surface and the polishing pad becomes thicker and there is less chance of the polishing pad asperity being in contact with the wafer surface. This means there will be fewer abrasives in contact with the wafer surface and, thus, the material removal per sliding distance is minimized. At the lower wafer velocity, the slurry him becomes thinner and more pad asperity is in contact with the wafer surface. In this case, material removal per sliding distance is maximized. 

Pa (10 10 ° Torr)) condition such that the volatile species travels at a relatively high velocity to the substrate wafer. The growth rate is 0.01-0.3 ///min which starts to be competitive with CVD deposition rates. 

In 1999, Luo and Domfeld [110] proposed that there are two typical contact modes in the CMP process, i.e., the hydro-dynamical contact mode and the solid-solid contact mode [110]. When the down pressure applied on the wafer surface is small and the relative velocity of the wafer is large, a thin fluid film with micro-scale thickness will be formed between the wafer and pad surface. The size of the abrasive particles is much smaller than the thickness of the slurry film, and therefore a lot of abrasive particles are inactive. Almost all material removals are due to three-body abrasion. When the down pressure applied on the wafer surface is large and the relative velocity of the wafer is small, the wafer and pad asperity contact each other and both two-body and three-body abrasion occurs, as is described as solid-solid contact mode in Fig. 44 [110]. In the two-body abrasion, the abrasive particles embedded in the pad asperities move to remove materials. Almost all effective material removals happen due to these abrasions. However, the abrasives not embedded in the pad are either inactive or act in three-body abrasion. Compared with the two-body abrasion happening in the wafer-pad contact area, the material removed by three-body abrasion is negligible. 

In all of the above discussions, the focus has been entirely on the local condition, such as the pressure exposed on the wafer and relative velocity between pad and wafer. A model is to be proposed to describe the entire available re-... 

More modern systems (diffractometers) follow the same principles but the diffracted X-rays are detected with a solid state detector, as described earlier. Typically, the X-ray source is static and the sample and detector are rotated, with the detector moving at twice the angular velocity of the sample to maintain the equivalent angle. Such instruments typically make use of relatively large samples compressed into the window of a 35 mm sample holder. However, where the sample size is restricted, as is common with archaeological applications, a smaller sample (a few mg) can be attached to a silica wafer. In all cases the sample needs to be hnely ground to ensure a uniform diffracted beam. 

Double-sided electrolytic contacts are favorable for this method of diffusion length measurement because they are transparent and the required SCRs are easily induced by application of a reverse bias. Therefore homogeneously doped wafers need no additional preparation, such as evaporation of metal contacts or diffusion doping, to produce a p-n junction. Furthermore, a record low value of surface recombination velocity has been measured for silicon surfaces in contact with an HF electrolyte at OCP [Yal], Note that this OCP value cannot be further decreased by a forward bias at the frontside, because any potential other than OCP has been found to increase the surface recombination velocity, as shown in Fig. 3.2. Note that contaminations in the HF electrolyte, such as Cu, may significantly increase the surface recombination velocity. This effect has been used to detect trace levels (20 ppt) of Cu in HF [Re5j. 

CMP processes for oxide planarization (ILD and STI) rely on slurry chemistry to hydrolyze and soften the Si02 surface. Mechanical abrasion then controls the actual material removal. Thus, the key process output control variables (i.e., removal rate and nonuniformity) are strong functions of the mechanical properties of the system, namely, the down force and the relative velocity between the pad and the wafer. Metal CMP processes such as copper CMP rely more on chemical oxidation and dissolution of the metal than mechanical abrasion to remove the metal overburden. Consequently, careful control of the chemistry of the CMP process is more important for these CMP processes than it is for oxide CMP. Thus, CMP tools and processes optimized for ILD may not be optimal for metal CMP and vice versa. 

Orbital motion offers the capability of achieving high relative velocities without sacrificing tool footprint. This point is especially important as the semiconductor industry prepares to make the transition to 300-mm wafers. Several CMP tool concepts have been developed based on orbital motion. Some orbit the carrier while rotating the platen [13]. Others orbit the polishing pad while rotating the carrier [14]. Another design involves orbital (as well as arbitrary nonrotational) motion on a fixed polish pad [15]. 

In addition to controlling the standard process parameters such as down force and the relative velocity, it is also important to have random access capability to route wafers through a CMP tool to optimize both performance and throughput. Low-down-force processes and special CMP pads are likely to be necessary to reduce copper dishing just as they improve oxide planarization. Furthermore, a balance between high relative velocity to reduce copper dishing and moderate relative velocity to minimize the sheering of small oxide feature may be necessary. 

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 ... 

Sources of Wafer-Scale Nonuniformity a. Relative Velocity Mismatch Across the Wafer... 

The Preston relationship provides a pointwise dependency of removal rate based on the relative velocity and pressure within some region of the wafer. A straightforward application of Preston s model is to study the... 

Let the angular rotation of the wafer and table be CO2 id co (in radians per minute) respectively. Preston has obtained the relative velocity between pad and point Q on the wafer as... 

Runnels and Eyman [41] report a tribological analysis of CMP in which a fluid-flow-induced stress distribution across the entire wafer surface is examined. Fundamentally, the model seeks to determine if hydroplaning of the wafer occurs by consideration of the fluid film between wafer and pad, in this case on a wafer scale. The thickness of the (slurry) fluid film is a key parameter, and depends on wafer curvature, slurry viscosity, and rotation speed. The traditional Preston equation R = KPV, where R is removal rate, P is pressure, and V is relative velocity, is modified to R = k ar, where a and T are the magnitudes of normal and shear stress, respectively. Fluid mechanic calculations are undertaken to determine contributions to these stresses based on how the slurry flows macroscopically, and how pressure is distributed across the entire wafer. Navier-Stokes equations for incompressible Newtonian flow (constant viscosity) are solved on a three-dimensional mesh ... 

It is now possible to model the wafer-level performance for most CMP processes. These models cover only some of the important tool or process design issues, such as relative velocities and pressure dependencies additional work is needed to predict the results for other parameters such as slurry composition or particle size, temperature dependencies, pad properties, and other effects. Die-level modeling has been used effectively to identify... 

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