where pa and ps are the densities of the particle and the slurry solution, respectively and
y(r) the slurry particle size distribution. Substitution of Eq. 3.18 into 3.17 gives
3 Rm Caps Area, (z)
N(z) 2=( (3.19)
2 ap, frv ,(r)dr
From eq. (3.19), the number of trapped particles of radius R is given by,
n(R,z)=N(z)*y(R)= 3 Rm C Area (z) (r) (3.20)
2 ;Tr fJr3 V(r)dr
Estimation of the Overall Removal Rate
The overall material removal rate can be determined by following these steps:
h is calculated using eq. 3.2.
Contact pressure P(z) at a given asperity is calculated along with the real
contact area Areai(z) of that asperity with wafer.
Total number of particles N(z), that are trapped are determined, from which
number of particles of given radii, n(r,z) are derived.
From P(z), removal rate by single abrasive of radius r is calculated which is
multiplied with n(r,z) to give removal rate by that particle size. This process
is repeated to account for all the particles of different radii trapped on that
asperity yielding material removal rate by particles trapped on a given
asperity.
It should be noted that there are 4(z)NAo asperities at a given height which
will each contribute the same material removal.