Busnaina [83]. Tseng and Wang attributed the normal stress at the particle-wafer contact
to the elastic indentation of the particle into the wafer surface, which is similar to that
proposed by Cook and calculated the normal stress over the wafer-particle interface as
F
n (2.8)
where F is the force acting on the spherical particles, which is proportional to the pressure
P. The radius of particle-wafer contact, re is given by
r3 3d 1 2 1 v '2
r 8 F+ Er- (2.9)
8 E E'
where d is the diameter of particles, v and v' the Poisson's ratios of wafer surface and the
particle and E and E' the elastic modulii of the wafer and particles, respectively. The
shear stress due to the slurry flow can be approximated as
t =CeIVPA, (2.10)
where |t is the dynamic viscosity of the slurry and Ao the area of wafer surface
respectively. Substitution of equations (2 8) and (2 10) into (2 7) yields
MRR=KeP5/6V1/2 (211)
where Ke is the parameter to account for material properties, slurry abrasive
concentration and chemical processes. This model demonstrated a nonlinear relationship
between the material removal and the product of pressure and velocity. Tseng's model
attempted to connect the elastic indentation to the erosion rate, whereas Cook's and Liu's
models connect it to the mechanical abrasion. While the down pressure dependency (P5/6)
is quite close to linear dependency, the velocity dependency (V2) however, is quite
nonlinear. This is because the contribution of velocity has been attributed to the slurry