Chemical mechanical polishing (CMP) has emerged as a commonly used method for achieving global surface planarization of micro-/nano-scale systems during fabrication. During CMP, the wafer to be polished is pressed against a rotating polymeric pad that is flooded with slurry. The motion of the wafer surface against the asperities of the pad and the abrasive nanoscale particles in the slurry causes the surface of the wafer to be polished to an atomically smooth level. Past studies have shown that the wear distribution is a function of the distribution of slurry particles in the wafer/pad interface, and thus it is desirable to model the migration of particles in order to predict the wear of the wafer surface. The current study involves the creation and simulation of a mathematical model which predicts the paths of slurry particles in a Lagrangian reference frame. The model predicts the effects of the various forces on each particle to determine its motion. The model also accounts for interparticle collisions and wafer/particle and pad/particle collisions. It is expected that the particle motion that is predicted from this model will allow for a more accurate correlation of the wafer surface wear distribution.

1.
Zhao
Y.
and
Chang
L.
,
A micro-contact and wear model for chemical-mechanical polishing of silicon wafers
.
Wear
,
2002
.
252
(
3–4
): p.
220
226
.
2.
Seok
J.
,
Sukam
C. P.
,
Kim
A. T.
,
Tichy
J. A.
, and
Cale
T. S.
,
Material removal model for chemical-mechanical polishing considering wafer flexibility and edge effects
.
Wear
,
2004
.
257
(
5–6
): p.
496
508
.
3.
Luo
J. F.
and
Dornfeld
D. A.
,
Material removal mechanism in chemical mechanical polishing: Theory and modeling
.
IEEE Transactions on Semiconductor Manufacturing
,
2001
.
14
(
2
): p.
112
133
.
4.
Sundararajan
S.
,
Thakurta
D. G.
,
Schwendeman
D. W.
,
Murarka
S. P.
, and
Gill
W. N.
,
Two-dimensional waferscale chemical mechanical planarization models based on lubrication theory and mass transport
.
Journal of the Electrochemical Society
,
1999
.
146
(
2
): p.
761
766
.
5.
Runnels
S. R.
and
Eyman
L. M.
,
Tribology analysis of chemical-mechanical polishing
.
Journal of the Electrochemical Society
,
1994
.
141
(
6
): p.
1698
1701
.
6.
Cho
C. H.
,
Park
S. S.
, and
Ahn
Y.
,
Three-dimensional wafer scale hydrodynamic modeling for chemical mechanical polishing
.
Thin Solid Films
,
2001
.
389
(
1–2
): p.
254
260
.
7.
Tichy
J.
,
Levert
J. A.
,
Shan
L.
, and
Danyluk
S.
,
Contact mechanics and lubrication hydrodynamics of chemical mechanical polishing
.
Journal of the Electrochemical Society
,
1999
.
146
(
4
): p.
1523
1528
.
8.
Higgs
C. F.
,
Ng
S. H.
,
Borucki
L.
,
Yoon
I.
, and
Danyluk
S.
,
A mixed-lubrication approach to predicting CMP fluid pressure modeling and experiments
.
Journal of the Electrochemical Society
,
2005
.
152
(
3
): p.
193
198
.
9.
Zhou
C.
,
Shan
L.
,
Hight
J. R.
,
Danyluk
S.
,
Paszkowski
A. J.
, and
Ng
S. H.
,
Influence of colloidal abrasive size on material removal rate and surface finish in SiO2 chemical mechanical polishing
.
Tribology Transactions
,
2002
.
45
(
2
): p.
232
238
.
10.
Lin
S. C.
,
Kuo
T. C.
, and
Chieng
C. C.
,
Particle trajectories around a flying slider
.
Journal of Tribology, Transactions of the ASME
,
1998
.
120
(
1
): p.
69
74
.
11.
Shen
X.
and
Bogy
D. B.
,
Particle flow and contamination in slider air bearings for hard disk drives
.
Journal of Tribology
,
2003
.
125
(
2
): p.
358
363
.
12.
Zettner, CM. and M. Yoda. Direct Visualization of Particle Dynamics in Model CMP Geometries. in Proceedings of Materials Research Society Symposium. 2001.
13.
Terrell, E.J., J.I. Garcia, and C.F. Higgs III, Two-Phase Hydrodynamic Modeling of Particulate Fluids in Sliding Contacts. Proceedings of World Tribology Conference, 2005, 2005.
14.
Shan
L.
,
Levert
J.
,
Meade
L.
,
Tichy
J.
, and
Danyluk
S.
,
Interfacial fluid mechanics and pressure prediction in chemical mechanical polishing
.
Journal of Tribology, Transactions of the ASME
,
2000
.
122
(
3
): p.
539
543
.
15.
Saffman
P. G.
,
Lift on small sphere in slow shear flow
.
Journal of Fluid Mechanics
,
1965
.
22
(Part 2): p.
385
400
.
This content is only available via PDF.
You do not currently have access to this content.