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Often a linear relationship is observed, although non-linear behavior has also been reported. The simplest linear relationship between wear rate, pressure, and velocity is known as Preston’s law and is given by
R (x, y, t) = k (x, y, t) v (x, y, t) p (x, y, t),
where k (x, y, t) is the wear coefficient. If the wafer surface consists of different materials, the wear coefficient is a function of position. It should be noted that in the current model any chemical elects in the CMP process are captured by the wear coefficient. Slurry chemistry, for instance, has a signi4cant impact on the removal rate and hence on the value of k. Finally, the removal rate is directly linked to local changes in wafer shape:

Integration of Preston’s equation yields the evolution of the surface pro4le S (x, y, t) as a function of time. Note that Preston’s law is used in the present formulation of the model, but this is not essential to the model and any wear law in which the removal rate increases monotonously with pressure could be used instead. Qualitatively, the results remain the same.

## What are the different types of Preston Law?

Three types of Preston’s law or Model:
1. Chen, Feng, Chang, Lee, Li, and Baisie's models use kinematic approaches to predict the amount of wear across the pad by employing the Preston equation. In the kinematic approach, a major assumption is that pad wear is determined by the sliding distance on the pad. A related kinematic approach was adopted by Chen to relate the distribution of scratch numbers of diamond grit on a pad to the pad profile. Yeh improved upon Chen's model to consider multiple cuts for a specific portion before the glazed layer is finally removed and the effective Preston's constant is restored. To measure the effectiveness of conditioning, Yeh defines a performance metric called recovered area ratio, which is the ratio between the recovered and total pad areas.
2. Tso and Ho's and Liao's models focus more on the relationship between conditioner parameters and the pad wear rate (MRR). However, Tso and Ho utilize the Preston equation while Liao's model presumes metal cutting theory.
3. On the other hand, Horng's model calculates pad deformation across the pad, which is not accounted for by the other models.

## What is the Example of Preston Law?

At the higher wafer velocity, the slurry film 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 film becomes thinner and more pad asperity is in contact with the wafer surface. In this case, material removal per sliding distance is maximized.
Abrasives in the polishing slurry are trapped between the wafer surface and the polishing pad asperity during the polishing process. This phenomenon enables the abrasion action on the wafer surface caused by the relative motion between the pad and the wafer. Therefore, the more pad asperity in contact with the wafer surface, the more material removal per sliding distance can be expected. In both cases, the wafer travelled the same distance. However, material removal during the identical distance changes depending on how fast the wafer travels the distance. As indicated in the Stribeck curve, the wafer with high velocity will interact less with the pad and the abrasive due to thicker slurry film. This results in lower material removal. The wafer with low velocity, however, will interact more with the pad and the abrasive due to thinner slurry film. This results in higher material removal. This phenomenon is very important to understand the material removal mechanism in dielectric CMP

## What is the principle of Preston law?

The Preston equation states that MRR is proportional to the applied pressure P and the relative velocity V between the wafer and the pad and Kp is a constant, called Preston's coefficient. The material removal rate (MRR) of CMP is explained by the Preston equation, which was developed in the glass polishing application. It simply indicates that the MRR is proportional to the pressure applied on the wafer and the relative velocity of the wafer.

MRP = C * P * V

(Where, C: Preston’s coefficient, P = Pressure, V = Velocity)

## Where is Preston Law used?

The material removal mechanism of dielectric CMP is further well explained by Cook in his paper published in 1990. It was explained that the rate of mass transportation during glass polishing is determined by five factors: the rate of water diffusion into the glass surface, the dissolution of the glass under the applied load, the adsorption rate of the dissolved material onto the abrasive surface, the redeposition of the dissolved material onto the surface of the work piece, and the aqueous corrosion between particle impacts. Water diffuses into siloxane bonding (SiOSi) and the diffusion rate is controlled by multiple process conditions such as pressure or temperature. This hydrated oxide surface is removed by an abrasion process. The indentation process by each abrasive was modelled by Hertzian contact and their contact stress was calculated from the theory of elasticity.

The Preston equation is a very simple equation to explain the major process parameters in predicting the MRR of glass polishing. In the modern CMP process, which is used in advanced semiconductor fabrication, it is almost impossible to predict the accurate MRR from a certain process condition by knowing only pressure and velocity of the wafer being polished. This is because there are quite a few process parameters in addition to pressure and velocity, which can greatly impact on the MRR and mechanism. There are numerous process models that can predict the MRR at given process conditions, but none of them is able to provide a precise MRR because of the complexity of the process