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)
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