knowledge of critical factors that effect the CMP process and the interactions among
them is critical to select the respective parameters and design an enhanced CMP process,
predicting material removal rate, and surface quality (roughness, defects, etc.). The most
popular material removal equation is the Preston's Equation [54], which was initially
introduced for glass polishing,
MRR= KePV, (2 1)
where MRR is the material removal rate, Ke an all-purpose coefficient, P the down
pressure and V the relative velocity over the wafer-pad inteface. It demonstrates a linear
dependency of material removal rate on the pressure and velocity. Not all experimental
MRR data in CMP, especially in metal CMP, support the linear dependency between
material removal and the product of pressure and velocity.
Modifications to Preston Equation
In order to explain the non-Prestonian behavior of the CMP process, revised
Preston's equations were proposed by several researchers. For example, considering that
the material removal rate does not extrapolate to zero, Maury et al. [74] introduced a
fitting parameter MRRo into Preston's equation
MRR= KePV + MRRo (2.2)
Later, the nonlinear equation
MRR= KePu VO, (2.3)
where ac and P are two fitting parameters, was proposed by Wrschka et al. [75] to get a
better fit for the experimental data.
The major problem with Preston's equation and its revisions are that they are
empirical modeling efforts. Therefore, they do not shed any light on gaining insight into