While equation 2.35 describes a situation where the deformation reaches into the
bulk wafer beyond the surface layer, deformation of the bulk wafer may not occur if the
bulk wafer material is very hard. This limiting case corresponds to the situation of
infinitely large Bw in equation 2.35 that is reduced to
(RR) =4, R1/2t3/2 (2.36)
3
Equations 2.32, 2.35 and 2.36 indicate that the volumetric removal rate by a single slurry
particle depends on the geometry of the pad and the particle (i.e., 3, C and R), the
material properties (E*, Bw and Be), the thickness of the surface layer (t), and the relative
velocity of the pad (thus the particle) to the wafer (V). It may be interesting to note that
(RR), is independent of the down pressure, P. It is due to the fact that the contact
pressure, Pr, is independent of P. As equation 2.21 indicates, the contact area of the pad
with the wafer (Ar) increases linearly with P. Consequently, the mean contact pressure,
P, which is PAo/Ar, is independent of P. In the following section, the number of particles
in contact with the wafer surface is estimated to determine the overall removal rate.
Estimation of the Overall Removal Rate
When the wafer is pressed against the pad and is in sliding motion relative to the pad, the
particles can be entrapped only in the region where the local distance between the wafer
and the pad asperity is smaller than the particle diameter, 2R. Thus, the number of
particles that can be trapped on the pad asperities is
n = 2R'Areal" Pn
(2.37)