University of California at Berkeley
Modeling of CMP
David Dornfeld
CMP researchers: Jihong Choi, Sunghoon Lee, Dr.
Hyoungjae Kim, Dr. Dan Echizenya
Department of Mechanical Engineering
University of California
Berkeley CA 94720-1740
http://lma.berkeley.edu
 Laboratory for Manufacturing Automation, 2005
University of California at Berkeley
Overview
• Background on modeling
• Review of work to date
• Some new developments
• pattern/feature sensitivity
• pad design
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LMA
University of California at Berkeley
New Book on Modeling Chemical Mechanical Planarization (CMP)
“Integrated Modeling of Chemical Mechanical Planarization for Sub-Micron IC Fabrication:
From Particle Scale to Feature, Die and Wafer Scales,” J. Luo and D. A. Dornfeld
Written by researchers at UC-Berkeley, this monograph
reviews CMP modeling literature (from Preston to present
day efforts) and develops, with a strong emphasis on
mechanical elements of CMP, an integrated model of
CMP addressing wafer,die and particle scale mechanisms
and features. Special emphasis is on abrasive sizes,
distributions and resulting material removal rates and
uniformity resulting over all scales.
175 Figures and 14 tables
ISBN 3-540-22369-x Springer-Verlag 2004
For information:
www.springeronline.com/east/3-540-22369-X.
Or contact: dornfeld@berkeley.edu
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Chemical Mechanical Planarization
CMP Team in FLCC
Dornfeld, et al
Doyle, et al
Talbot, et al
Chemical
Phenomena
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Mechanical
Phenomena
Interfacial and
Colloid
Phenomena
LMA
University of California at Berkeley
Scale Issues in CMP
Mechanical particle forces
Particle enhanced chemistry
Material
Removal
Active
Abrasives
Pores,
Walls
Tool mechanics,
Load, Speed
Chemical
Reactions
critical features
nm
mm
µm
5
Mechanism
wafer
dies
From E. Hwang, 2004
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Pad
Grooves
Layout
Scale/size
LMA
University of California at Berkeley
CMP Process Schematic
F : down force
Oscillation
conditioner
w w : wafer rotation
slurry feed
Retainer
ring
Backing
film
head
Wafer Carrier
Wafer
table
pad
w p :pad rotation
Electro plated diamond
conditioner
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Pore
Wall
Pad
Abrasive particle
Typical pad
6
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An overview of CMP research in FLCC
Cu CMP
[oxidizer],
[complexing agent],
[corrosion inhibitor],
pH …
Bulk Cu CMP
Barrier polishing
W CMP
Oxide CMP
Poly-Si CMP
Bulk Cu slurry
Barrier slurry
W slurry
Oxide slurry
Poly-Si slurry
Abrasive type,
size and concentration
Doyle
Chemical reactions
Dornfeld model
Talbot
Pad asperity density/shape
Mechanical material removal mechanism in abrasive scale
Physical models of material removal mechanism in abrasive scale
Pattern
Topography
Pad mechanical properties
in abrasive scale
MIT model
Pad properties in die scale
Models of
WIDNU
Slurry supply/ flow pattern
in die scale
Wafer scale pressure NU
Wafer scale velocity profile
Pad design
Models of
WIWNU
Small dishing & erosion
Reducing scratch defects
Reducing ‘Fang’
Reducing slurry usage
Uniform pad performance
thru it’s lifetime
Longer pad life time
Wafer bending with zone pressures
Slurry supply/ flow pattern
in wafer scale
Pad groove
Better planarization efficiency
Better control of WIWNU
Smaller WIDNU
model
design goal
Ultra low-k integration
Fabrication
technique
Fabrication
Test
E-CMP
Pad development
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The 4-component system
• Hypotheses:
– all polishing processes can be described as a 4 component
system;
– Understanding the components and their interactions (pair-wise,
triplets, etc) provides a structure to catalog our knowledge (and
ignorance)
“Granule”?
Lap (rigid)
Deliberately sought a word that
covers the range of particles
used without implying anything
about size, hardness, or removal
Workpiece Carrier fluid Granule
Lap mechanism: mm to nm size
range; from hard (diamond) to
Platen
soft (rouge);
Pad
}
Source: 86. Evans, J., Paul, E., Dornfeld, D., Lucca, D., Byrne, G., Tricard, M., Klocke, F., Dambon, O., and Mullany, B.,
“Material Removal Mechanisms in Lapping and Polishing,” STC “G” Keynote, CIRP Annals, 52, 2, 2003.
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Six possible pair-wise interactions
•
•
•
•
•
•
Fluid-workpiece
Workpiece-pad
Workpiece-granule
Granule-pad
pad-fluid
Fluid-granule
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Three-way interactions (triplets)
•
•
•
•
Workpiece-fluid-granule
Workpiece-fluid-pad
Workpiece-granule-pad
Fluid-pad-granule
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Stribeck Curve and Characteristics of slurry
film thickness
Polishing pad
Direct contact
Film thickness
Slurry
Wafer
Direct
contact
Semi-direct
contact
Hydroplane
sliding
Elastohydrodynamic Hydrodynamic
lubrication
lubrication
Semi-direct contact
Boundary
lubrication
Hydroplane sliding
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Hersey number(=
ViscosityVelocity
)
Pressure
Stribeck curve
11
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University of California at Berkeley
Gap effects on “mechanics”
Eroded surface by
chemical reaction
--- softening
Silicon wafer
Delaminated by brushing
‘Small’ gap
Abrasive particle
Polishing pad
Pad-based removal
Silicon wafer
‘Big’ gap
Abrasive particles
Slurry-based removal
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Polishing pad
12
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Idealized CMP
‘Softened’ surface by
chemical reaction
Silicon wafer
Abrasive particle
Polishing pad
Pad asperity
Mechanical Aspects of the Material Removal Mechanism in
Chemical Mechanical Polishing (CMP)
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Interactions between Input Variables
Four Interactions: Wafer-Pad Interaction; Pad-Abrasive Interaction;
Wafer-Slurry Chemical Interaction; Wafer-Abrasive Interaction
Velocity V
Vol
Chemically
Influenced Wafer
Surface
Abrasive particles
in Fluid (All
inactive)
Wafer
Abrasive
particles on
Polishing pad
Pad asperity
Contact
area with
number N
Active abrasives
on Contact area
Source: J. Luo and D. Dornfeld, IEEE Trans: Semiconductor Manufacturing, 2001
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Framework Connecting Input Parameters with Material
Removal Rate
Basic Equation of Material Removal: MRR= N  Vol
N
Slurry Abrasive
Weight
Concentration C
Average Abrasive
Size Xavg

Xavg
Vol
g Fraction of
Active Abrasives
X avg-a
Fraction of Active Abrasive:
1-((g-Xavg)/ ) where g is
the minimum size of active
abrasives
Proportion of
Active Abrasives
Pad Topography
& Pad Material
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Abrasive Size
Distribution 
15
Force F & Velocity
Active Abrasive
Size Xavg-a
Wafer Hardness
Hw / Slurry
Chemicals &
Wafer Materials
Down
Pressure P0
LMA
University of California at Berkeley
Experimental Verification of Pressure Dependence
of Material Removal Rate (MRR)
MRR= N Vol= K1 {1-(1K2P01/3)}P01/2.
Ke1 (K1=84148, K2=
0.137)
Advantage over
Preston’s Eq. MRR=
KePV+ MRR0:
What input variables
and how they influence
Ke is predicable
Ke2(K1=8989, K2=
0.3698)
SiO2 CMP Experimental Data
from Zhao and Shi,
Proceedings of VMIC, 1999
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University of California at Berkeley
Abrasive Size Distribution Dependence of MRR:
Particle Size Distribution [1]
Five Different Kinds of Abrasive (Alumina) Size Distributions for Tungsten CMP
Abrasive Size X (Log Scale)
1.
Bielmann et. al., Electrochem. Letter, 1999
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Normalized Material Removal Rate
University of California at Berkeley
Relationship between Standard Deviation
and MRR Based on Model Prediction
2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
Xavg= 0.29um
Xavg=0.38um
Xavg=0.60um
Xavg=0.88um
Xavg=2um
Size influenced
Std dev influenced
0
0.05
0.1
0.15
0.2
0.25
0.3
Standard Deviation (10-6m)
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University of California at Berkeley
Pattern-Density Dependency Model
pad
pad
MRR
oxide
oxide
Up Area
K/density
Time
K
Down Area
0
InterLevel Dielectric Case (single material)
Source: MIT
Same Pattern Density
Different Orientations
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Framework of a CMP Topography Evolution Model
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Dishing and Erosion in Copper Damascene Process
Trench
SiN
SiO2
Via
(a)
(b)
(c)
(d)
Fabrication steps in dual damascene process (a)
deposition of SiN, SiO2 and etching trenches and vias in
SiO2 (b) deposition of barrier layer (c) copper fill (d) CMP
and deposition of SiN (courtesy of Serdar Aksu)
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LMA
University of California at Berkeley
Definition of Feature-Scale Topography
S
Hcu
H
Oxide
Erosion e
Copper
Thinning
Wox
Wcu
Hox=
Hox0
H=
Copper
Dishing
d=S
Hox
(a)
(b)
(a) Feature scale topography before dielectric material is
exposed and (b) feature scale topography after dielectric
material is exposed
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University of California at Berkeley
Models of Polishing Pad
E
E
E

1

E2
(a)
(b)
Linear Elastic and
Linear
ViscoElastic Models
E1
2
(d)
(c)
Separated Models of
Pad Bulk and Asperities
Kd
Kf
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University of California at Berkeley
Three Stages of Wafer-Pad Contact
S=S0
H=Hcu0+Hox0
Df
Hcu0
1
Hox0
Only upper part of
step is in contact
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H=
Hstage1
S1=Df1
2
Erosion
e
3
Two different
Both upper and
bottom parts of step materials are
removed
is in contact
simultaneously
LMA
24
Dishing
d
University of California at Berkeley
Simulation Results of Step Height
Evolution for Different Pattern Density
500
400
350
300
400
350
250
200
300
200
150
100
100
50
50
0
20
40
60
100 120 140
80
Polishing Time t (second)
160
180
0
200
Planarization time (sec)
0
20
40
60
80
100
120
140
Polishing Time t (second)
160
180
Planarization time (sec)
Linear Elastic Pad
Linear Viscoelastic Pad
Wcu = 100 microns
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0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
250
150
0
PDi=
PDi=
PDi=
PDi=
PDi=
PDi=
PDi=
PDi=
PDi=
450
Step Height S (nm)
450
Step Height S (nm)
500
PDi= 0.1
PDi= 0.2
PDi= 0.3
PDi= 0.4
PDi= 0.5
PDi= 0.6
PDi= 0.7
PDi= 0.8
PDi= 0.9
25
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200
University of California at Berkeley
Copper Dishing as a Function of Pattern Density
using commercial pads
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Copper Dishing as a Function of Selectivity
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Effect of Pattern Density - Planarization
Length (PL)
High-density region
Global step
Low-density region
ILD
Metal lines
Planarization Length
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University of California at Berkeley
Modeling of pattern density effects in CMP
Effective pattern density
Planarization length
(window size) effect
on “Up area”
a=320um
< Test pattern >
a=640um
a=1280um
< Post CMP film
thickness prediction at
die-scale >
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< Effective density map >
29
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Die scale modeling of topography evolution during CMP
Contact wear model
Initial pressure distribution
MRR model
Topography evolution
Iteration
with time
step
Contact wear model
New pressure distribution
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University of California at Berkeley
Feature level interaction between pad asperities and pattern topography
PAD
Z(x,y)
Z_pad
Reference height (z=0)
Z ( x , y )  Z _ pad
F ( x, y)  Kp 
 (asperity _ density)  (PDF ( z  dz)  PDF ( z))  (Z ( x, y)  z)
0
F _ tent 
 F ( x, y)dxdy
die
No
No
dz
F_tent > F_die ?
Yes
Z(x,y)
++Z_pad
z
F_tent < F_die ?
Yes
--Z_pad
Z_pad
Z_pad
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University of California at Berkeley
Chip level interaction between pad and pattern topography
k2
k1
r
PL
k1k 2
Kpad 
 k2
k1  k 2
MIT model : approximation of contact wear model
w
4(1   2 )qr
w(r ) 
E
40um
Pattern
40um
40um x 40um cell
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

2
0
r2
1
sin 2  d
2
PL


 w(i, j )  PD(i, j ) 
PDE   

w(i, j )
i, j 


i, j


LMA
University of California at Berkeley
Simulation result
20%
33%
50%
100%
50%
t=0 sec
t=10 sec
t=20 sec
t=30 sec
t=40 sec
t=50 sec
33%
20%
t=60 sec
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t=70 sec
t=80 sec
LMA
University of California at Berkeley
Pattern orientation effect on on copper dishing
Ti
SiO2
Cu
Si
Kinetic analysis of sliding direction during process time
pad rpm = wafer rpm
pad rpm < wafer rpm
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University of California at Berkeley
Pad Characterization
(SEM, x150)
100µm
(White light Interferometer, x200)
• Ra = 12.5µm
• Rz = 96.7µm
45µm
-45µm
100µm
300µm
500µm
• Pore diameter : 30~50 µm
• Peak to Peak : 200~300µm
200~300µm
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University of California at Berkeley
Pad modeling
Peak to Peak
200~300 µm
Pores
40~60µm
Asperity: Real contact area
10~50 µm
1. Reaction Region (10~15 µm)
2. Transition Region
3. Reservoir Region
Simplified Pad Model
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3 Dimensional analysis
Reaction region
Transition region
Reservoir region
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2D and 3D image of reaction region
2 dimensional image (w/o pressure)
3 dimensional image (w/o pressure)
• Contact area : 10-50µm
• Spherical or conical shape edge
• Ratio of real contact area : 10-15%
• Stress concentration when compressed
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Reaction region – ILD CMP
10 µm
10 – 50 µm
Over polishing
Small asperity
ILD
Reaction region (asperity)
wafer
50 µm
Defects of a conventional pad
• Over polishing on recess area
Large asperity
Rounding
ILD
• Smoothing, not planarization
wafer
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University of California at Berkeley
Reaction region – Cu CMP
Stress concentration
Cu-CMP defects
(due to stress concentration in conventional pad)
Pad asperity
wafer
wafer
Pressure
Fang
Dishing
Erosion
Avg. contact pressure
Nominal pressure
wafer
Position
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Pad degradation
New
In 3minutes
In 5minutes
In 7minutes
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Design rules for a pad
Design rules for a pad
Macro scale
 Stacked layer
(Hard/soft)
 Slurry channel
Micro scale
Nano scale
 Constant contact area
 Compatible features to abrasive
 Constant re-generation of nano
(width:10-50um)
 The ratio of real contact area
scale surface roughness
(13-17%)
 Conditioning-less CMP
 High slurry efficiency
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A pad design based on the rules
Channel
Nano scale features
Hard Layer
50-200µm
50-70µm
(i.e. high stiffness)
Soft Layer
(i.e. low stiffness)
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Expectations
ILD CMP
Pad
Advantages
• Conditioning-less process
• High planarity & good uniformity in ILD CMP
Wafer
• Without stress concentration
• Less defects in Metal CMP
Cu CMP
Pad
Wafer
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University of California at Berkeley
Design of new pads
Type 1 – Without slurry guidance
Type 2 – With slurry guidance
50µm
Slurry flow direction
20µm
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University of California at Berkeley
Simulation result
Type 2
Type 1
• Area : 4.3^-10 m2
• Flow rate : 3.93^-11 kg/sec
• Area : 4.294^-10 m2
• Flow rate : 3.24^-10 kg/sec
8 times more flow rate
On contact area
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Pad fabrication
1. Master
2. Silicone Rubber 3. Silicone Rubber 4. Hard Layer
Casting
Mold
Casting
5. Soft Layer
Casting
6. Demolding
New pad
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University of California at Berkeley
Performance of a new pad – Planarity in ILD CMP
20%
20um/80um
50%
50um/50um
Polishing machine
ILD pattern (MIT mask Version 1.0)
Experiment condition
IC1000/SUBA400
New pad
Pad
60rpm
Wafer
3inch wafer
(12-100% density,1.7µm SiO2)
0.77µm
30rpm
SiO2
D-7000 (Cabot Co.)
1.7µm
Slurry
100ml/min
Pressure
1.6psi
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1.6psi
2.7psi
Si wafer
48
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University of California at Berkeley
Density 20% - under same pressure:1.6psi
Newpad
Pad (1.6psi)
New
0.8
0.8
0.6
0.6
0.4
0.2
0
1000
1100
1200
1300
1400
1500
-0.2
-0.4
Position(um)
New
In 3min
In 7min
In 12min
In 17min
Relative Stepheight(um)
Relative Stepheight (um)
IC1000/SUBA400
(1.6psi)
IC1000/SUBA400
0.4
0.2
0
1000
1100
1200
1300
1500
-0.2
-0.4
Position(um)
New
In 3min
In 15min
• Time : 17minutes
• Time : 40minutes
• Over Polishing : 2200Å
• Over Polishing : 400Å
High removal rate
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1400
In 20min
Good planarity
49
LMA
In 40min
University of California at Berkeley
Density 20% - under different pressure:1.6psi &2.7psi
IC1000/SUBA400 (1.6psi)
New pad (2.7psi)
New Pad (2.7psi)
0.8
0.8
0.6
0.6
0.4
0.2
0
1000
1100
1200
1300
1400
1500
0.4
0.2
0
1000
1100
1200
1300
1400
-0.2
-0.2
-0.4
Relative Step Height(um)
Relative Stepheight (um)
IC1000/SUBA400
Position(um)
New
In 3min
In 7min
In 12min
In 17min
-0.4
Position(um)
New
In 10min
• Time : 17minutes
• Time : 20minutes
• Over Polishing : 2200Å
• Over Polishing : 800Å
In 20min
Good planarity & removal rate
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50
LMA
1500