The above step is repeated for all the pad asperities of various heights that
are in contact with wafer (determined by h) to give overall removal rate by
the following equation:
RR = (1/Ao)J In(r,z) RR,(r,z)drdz
-RR= CpN Area(z) ) w(r)(r,z ddz (3.21)
p, r3 y(r) dr h r
r
where, a(r,z) varies as given in eqs.3.15 and 3.16 depending on particle radius and
asperity height.
The indentation depth, co(r,z) is used to calculate the surface roughness RMS of the
polished wafer according to the following equation:
0)2
RMS = (3.22)
n
where coi is the indentation depth.
The overall removal rate predicted by Eq. 3.21 and surface roughness given by
Eq. 3.22 depend on various parameters that represent the geometry of the pad and the
particle (i.e., 3, o and R), material properties (E*, Bw and Be), thickness (t) of the modified
surface layer on wafer, and the relative velocity of the pad (thus the particle) to the wafer
(V). The PERC II model will be validated with respect to critical CMP parameters in the
next chapter.