Bhattacharya, A.

Breward, C.J.W.

Evans, J.

Gratton, M.

Nicholas, M.

Please, C.

Schwendeman, D.

Surles, M.

Witelski, T.

English

Mathematics in Industry Information Service Eprints Archive

LJB - MPI 2005
Lubrication Layer Perturbations in
Chemical-Mechanical Polishing
Dr. Len Borucki
CTO, Araca, Inc.
LJB - MPI 2005
Outline
• A quick tutorial on chemical-mechanical polishing (CMP).
• Elastohydrodynamic lubrication with a pure lubricant.
• Questions posed by the presence of slurry particles.
LJB - MPI 2005
Quick CMP Tutorial
LJB - MPI 2005
Wafer Planarization in Integrated Circuit Fabrication
•Integrated circuits are made by deposition and modification of numerous material layers.
•Photolithography, the main method of creating patterns, works best on flat surfaces.
•Chemical-Mechanical Polishing (CMP) is currently the leading method for planarizing surfaces.
Schematic of an integrated circuit
produced without CMP
Schematic of an integrated circuit
produced with CMP
Peter Wolters
LJB - MPI 2005
Generic Rotary Polishing Tool
Platen
Polishing Pad
Slurry
Stream,
Puddle
Wafer
Wafer CarrierConditioner
AMAT Reflexion
Commercial tool
Bench top polisher
Struers. Photo by Rob Hight
Georgia Tech.
A rotating tool with a
diamond-covered face
maintains pad surface
roughness, counteracting
abrasive wear, removing
debris, exposing new
pad surface.
The wafer is held
upside down by a
rotating carrier.
The wafer surface
reacts with chemicals
in the slurry and is
abraded by slurry
particles. The pad
also experiences
abrasive wear.
LJB - MPI 2005
Polishing Pads
The most commonly
used pad, IC-1000TM,
(Rohm and Haas) is
a closed cell
polyurethane foam
with a mean void
diameter of about
30 microns. Voids
occupy about 35%
of the volume and
are not interconnected
except at the surface.
The pad is shown
here next to a scaled
drawing of a 100 µm
wide, 2 µm deep
trench. The pad
surface roughness
is large compared
with typical wafer
features.
Wafer Topography
Letitia Molina, Motorola
LJB - MPI 2005
C.Elmufdi et al., 2004 CAMP Symposium.
Polishing pads are soft compared with most of the materials they polish.
Copper: 110 GPa Silicon Dioxide: 43-77 GPa
The pad elastic modulus generally decreases with increasing temperature
and water content. A wide range is possible: ~100-550 MPa.
LJB - MPI 2005
Polishing Pad Surfaces
Kojima and
Nishiguchi,
2003 CMP-
MIC.
The pad surface is not static, but evolves under conditioning and abrasive wear.
Freshly conditioned After polishing without conditioning
Scott Lawing,
Rohm and Haas
ECS 2003
This shows that
there is pad/wafer
contact. The wear
rate varies with
the abrasive type.
Spherical particles
produce less wear,
irregular particles
more wear.
LJB - MPI 2005
Slurry Particles
Slurry particles are very much smaller than pad asperities. Typical mean diameters for
spherical colloidal particles range from a few tens to a few hundreds of nanometers.
Solid loadings vary from ~0.3% to ~30% by weight. Slurry viscosity is similar to water.
S. Lawing, ECS 2003
We’ll assume spherical colloidal particles
LJB - MPI 2005
Polishing Mechanisms (SiO2)
Hypothesized
mechanism for
SiO2 removal
by ceria. Most
removed silica is
found on the slurry
particles and
in colloidal
suspension.
(W. America,
CAMP 2003).
Particle surface
chemistry matters
Polishing pad
Wafer (held upside down by carrier)
Chemically-softened layer with surface charge.
Reactive fluid and charged slurry particles
(Particle size greatly exaggerated)
Pressure p
Relative sliding velocity V
Chemical
reaction/softening
and mechanical
removal.
- - - - - - - - - - - - - - - - - - - -
+
+
+ +
+
+
+ + + +
+
+ + + +
+
+
LJB - MPI 2005
Pad
Wafer
Pad asperities
and fluid
thickness –
tens of microns
.
..
.
. .
.... . .
.
Slurry particles
tens-hundreds
of nm.
Nominal pressure p=7 - 49 kPa (1-7 PSI)
Relative sliding speed ~1 m/sec
Summary of Scales and Numerical Values

1 GPa
E 100-500 MPa
E
LJB - MPI 2005
Elastohydrodynamic Lubrication (EHL)
LJB - MPI 2005
Dry Contact
Hertzian Theory
o Undeformed asperity tips are
spherical.
o Contact area is circular.
o Pressure is elliptic.
2/12
0 ))/(1( arpp =
 RaA == 2
+
+
K.L. Johnson, Contact Mechanics

R
2a
2/1
2/10 )1(
2 
 R
Ep

=
Asperity tip
LJB - MPI 2005
Wafer
EHL Theory
o A thin lubrication layer forms.
o Hydrodynamic pressures deform
asperity tips.
o Positive hydrodynamic pressures in
the lubrication layer support the load.
Asperity
V
Lubricated Contact
Lubrication
Layer
LJB - MPI 2005
EHL Theories
Elastohydrodynamic lubrication has been studied for almost a century. Some early citations
from Szeri, Fluid Film Lubrication, Theory and Design, Cambridge (1998) Ch. 8:
1916 H.M. Martin Assumed rigid bodies. Predicted thinner lubrication layer than observed.
1936 W. Peppler Allowed contacts to deform elastically.
1945 Gatcombe Generalized to pressure-dependent viscosity, µ=µ(p)
1949 A.N. Grubin First satisfactory solution accounting for elastic deformation and µ=µ(p).
Reynolds equation
V
Elasticity theory
http://www.lsbu.ac.uk/water/explan2.html
LJB - MPI 2005
V
Fluid Pressure
Asperity deformation
Hertz theory
From Szeri, Fluid Film Lubrication, Cambridge University Press, 1998
Fluid pressures are approximately
the same as Hertzian pressures
except for a pressure spike near the
trailing edge. Disagreement becomes
more pronounced at lower loads.
The lubrication layer is nearly
uniform in thickness except for
a constriction at the trailing edge
that produces the pressure
spike.
EHL Theory Example (Roller)
V
LJB - MPI 2005
EHL Compact Formulas
Simple formulas are often available for estimating the average lubrication
layer thickness. Some fitting to more complex solutions is involved.
Pad Asperity
hmin hc
22.042.08.064.0)(5.1 = avgc pERVh µ
cavg Npp /=

	
=
d ssc
dzzN )(

s = summit area density

s = summit height PDF.
s =2x108/m2

s Gaussian with =6µm
R=50µm
p=1 kPa
V=1 m/sec
µ=2.5x10-3 Pa-sec
hc=29 nm
about the same as the mean diameter
of some types of slurry particles.
LJB - MPI 2005
Slurry Particles
LJB - MPI 2005
Active Particles
Polish rates are generally low for slurries that do not contain particles. When particles are
added, some are evidently trapped between the wafer and pad asperities and increase the
removal rate by mechanical or chemical means. These are active particles. Experimental
estimates of slurry residence time and utilization suggest that most particles never become
active.
Active
Inactive
Some active particles
also abrade the pad.
LJB - MPI 2005
0
500
1000
1500
2000
2500
0 5 10 15 20 25 30 35
Concentration (wt.%)
M
R
R
 
(
H
/
m
i
n
)
50nm
80nm
140nm
Removal Rate and Solids Loading
Removal rate increases with weight fraction for particles of a given size.
C. Zhou et al., STLE 2002
LJB - MPI 2005
Removal Rate and Particle Size
0
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
0 50 100 150
Abrasive Size (nm)
M
R
R
 
(

/
m
i
n
)
18 kPa, 0.4 m/s
32 kPa, 0.6 m/s
45 kPa, 0.9 m/s
C. Zhou et al., STLE 2002
At a fixed weight fraction, the removal rate has a peak at a size comparable to
a possible lubrication layer thickness.
30 wt% In this figure,
the number of
abrasive particles
decreases as
the size increases.
LJB - MPI 2005
Questions
Slurry particle diameter
Small
particle
Which portion of the particle
distribution becomes active?
If we start out with no particles
in the lubrication layer, then how
fast do they accumulate?
How much does the accumulation of
a few particles affect the probability
of capture of additional particles?
Medium
Large
active?
active
not
active
LJB - MPI 2005
Questions
What happens to the thickness
and shape of the lubrication
layer as the solids loading
increases from zero to typical
upper weight fraction limits?
Are hydrodynamic pressures
the main determinant of the
layer geometry or is there
a point at which particle size
and loading are the main factors?
Can the compact models of
lubrication layer thickness
be generalized to include
slurry particles?
No solids
High solids loading
?
These are the main questions that I would like to address.
LJB - MPI 2005
I have with me …
1. A 2D finite element Reynolds
equation solver.
2. A 2D/3D linear elasticity solver.
3. Some literature.
Fluid pressures from
the Reynolds solver


Lubrication Layer Perturbations in Chemical-Mechanical Polishing

Lubrication Layer Perturbations in Chemical-Mechanical Polishing

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