ISSN 1063-7397, Russian Microelectronics, 2016, Vol. 45, No. 4, pp. 270–277. © Pleiades Publishing, Ltd., 2016.
Original Russian Text © R.V. Goldstein, T.M. Makhviladze, M.E. Sarychev, 2016, published in Mikroelektronika, 2016, Vol. 45, No. 4, pp. 289–297.
Characteristics of the Kinetics of Periodic Structures СМР
for a Nonlinear Pressure Dependence of the Polishing Rate
R. V. Goldstein, T. M. Makhviladze, and M. E. Sarychev
Institute of Physics and Technology, Russian Academy of Sciences
Received October 26, 2015
Abstract—For the kinetics of the chemical mechanical polishing (CMP) of wafers containing periodic
metal–dielectric structures, a model is developed and theoretically investigated with the use of contact
mechanics methods for the nonlinear pressure dependences of the polishing rate. In the steady-state regime,
expressions for the dishing effect, which is characterized by the difference in the depths of the polishing metal
and dielectric strips, are analytically derived and investigated. The specific characteristics of this effect, which
are observed for different kinds of nonlinearities of the polishing rate depending on the pressure and the rel-
ative rotation velocity of the pad and wafer, are analyzed. Particularly, it is shown that, under certain condi-
tions, the steady-state regime may be nonunique (the bistability effect).
The chemical mechanical polishing (CMP) pro-
cess is widely employed for fabricating micro- and
nanoelectronic structures. However, it involves so
many factors that it has not yet been thoroughly investi-
gated and is still being discussed in the literature [1–3].
This fact, in addition to the usefulness of this process,
supports the development of adequate models to solve
the problem of CMP optimization.
Modeling the rate of material removal from the
surface being processed is a key element of the com-
plete description of the CMP process. In , an
approach was proposed that regards the formation and
growth of a passivation layer at the interface between
the metal and slurry as a factor restricting this rate.
Presently, the development of models for the kinetics
of change in the thickness of the layer being polished,
which describe the rate of material removal with the
use of phenomenological expressions  or expres-
sions obtained from rather simplified macroscopic
representations [5, 6], is also considered promising.
One of the practically important problems is to
model the process of polishing the surface of the struc-
tures composed of alternating metal and dielectric ele-
ments, which results in a rather inhomogeneous distri-
bution of the process rate. It was experimentally found
that, due to the difference in the polishing rates of
metal and dielectric, at every instant, a certain peri-
odic distribution of the depths of the holes (dishes)
formed in these materials was observed; this effect was
called dishing .
In , it was shown that the most adequate quanti-
tative description of the kinetics of dishing can be done
only when taking into account the nonlocal effects
that are due to the deformations of the pad and the
geometry of the surface being polished. A step-by-step
approach to modeling the nonlocal effects based on
the contact mechanics methods  was proposed in
. In , for a one-dimensional periodic structure
, the time evolution of the contact pressure,
contact area, and contact profile as functions of the
system geometry and load distribution was evaluated.
In , using model , the dependences of the
steady-state regime of polishing the same structures
on various parameters of the system were numerically
In [9, 11], for the polishing rate V
of each material,
Preston’s phenomenological equation  in the form
(where р is the pressure with which the pad
acts on the surface being processed and is the relative
velocity of their rotation) was used. However, some
investigations [4, 5] showed that the experimental data
are better described by relations that are nonlinear in
terms of р and , especially when the pressure range is
expanded. A particular form of these relations is deter-
mined by the elasticity of the polishing material, com-
position of the slurry, pressure range, and distribution
of the sizes of abrasive particles .
In this paper, a nonlocal model is developed that
describes the kinetics of the dishing effect in periodic
metaldielectric structures with the use of contact
mechanics methods for nonlinear р- and -depen-
dences of the rate V
. Using this model, the depen-