Here A, is the real contact area between the wafer surface and the pad asperities as
it was described in previous section. p, is the number density of the particles in the slurry
(i.e., number of particles per unit slurry volume), that can be calculated from the solid
loading Ca (wt%) of the slurry particles as
3 Cap,
P, (2.38)
4 7R3 pa
where pa and ps are the densities of the particle and the slurry solution, respectively.
Substitute of Eqs. 2.38 into 2.37 gives
3 Cap9
n = A, (2.39)
2 7R2pa
By combining Eqs. 2.39 and 2.18, the number of particles anchored on the pad asperities
becomes
3 Ca s 0 pAA
n- 2C -CR (2.40)
2C 7R2 pa a E
Now that (RR), and n are given in terms of various processing variables and material
properties, the overall material removal rate in a CMP process can be estimated from Eqs.
2.32, 5.27 and 2.40 for the two different cases described above:
Removal Rate: Indentation depth smaller than surface layer thickness (i.e., co t),