RR = (1/Ao)J In(r,z) RR,(r,z)drdz (3.9)
where n(r,z) is the number of slurry particles anchored between pad asperity and the
wafer and RR,(r,z) is the volumetric removal rate by a single particle of radius r trapped
by asperity of height z. The overall removal rate, RR is typically described in terms of the
thickness of the wafer surface layer removed per unit time; hence the division by the
nominal wafer area Ao.
Schematic illustration of single particle abrasion is given in Fig. 3-18. The material
removal is viewed as a sliding-indentation process in which the volumetric removal rate
by a single abrasive particle is given by
RR,(r,z)= A,(r,z)V (3.10)
Where A,(r,z) is the cross-sectional area of the particle indented into the wafer
under pressure (hashed area in Fig. 3-18), and Vis the relative velocity between the pad
asperity and the wafer.
I T
Sb Pad
t, Pad t
F. Pad F.
Fig. 3-18 Schematic of single particle abrasion showing the removal of chemically
modified surface layer, (a). co < t; (b). co > t with soft wafer materials.[72]