either plastic or elastic depending on the hardness of the wafer material and the slurry
particles.
Material Removal by a Single Particle
In the present analysis, it is assumed that the slurry particles are monosized and of
radius 'R'. The overall material removal rate is assumed to be the multiple of the removal
rate by a single particle and the number of particles in contact with the wafer:
(RR) = n (RR)v/Ao (2.23)
where n is the number of slurry particles anchored in the region of the pad that is in
contact with the wafer, and (RR)v is the volumetric removal rate by a single particle. The
overall removal rate, (RR), is typically described in terms of the thickness removed per
unit time; hence the division by the nominal wafer area Ao.
Schematic illustration of single particle abrasion is given in Fig. 2-3. The material
removal is viewed as a sliding-indentation process in which the volumetric removal rate
by a particle is given as
(RR)v = AiV (2.24)
where Ai is the cross-sectional area of the particle immersed in the wafer under pressure
(hashed area in Fig. 2-3a), and V is the relative velocity of the pad to the wafer.
Assuming that the hard particle maintains its spherical shape,
A, = -a(R o)+ R2 arcsin a
R (2.25)
where co is the indentation depth and a the radius of the circular indentation on the wafer
surface by the particle of radius R,
Because co is very small compared to R, a/R is also very small and Equation 2.25
can be linearized about a/R to give