1. Jianfeng Luo, David Dornfeld
Effect of Particle Size Distribution in Chemical-Mechanical Polishing: Modeling and Verification
SFR Workshop
November 8, 2000
Jianfeng Luo, David Dornfeld
Berkeley, CA
2001 GOAL: To build an integrated CMP model for basic mechanical and chemical elements by 9/30/2001.
11/8/2000

2. Modeling of Abrasive Geometry and Size
Two Abrasive Geometries
Spherical Shape for Obtuse Abrasives
Conical Shape for Sharp Abrasives
100nm X X
Schematic of Spherical and Conical Abrasive Shapes in the Model
SEM Picture of Slurry Abrasives for Si CMP
(Moon, PhD Thesis, 1999) y
Abrasive Size and Size Distribution
Nano-Scale Size X
Normal Distribution (Xavg , ) and p((Xavg , )
Xavg, Xmax and Standard Deviation 
Xmax
Xavg
Portion of Active Abrasive
Schematic of Abrasive Size Distribution
11/8/2000

3. Role of Abrasive Size in the Architecture of the Integrated CMP Model
Contact Mechanics( Pad Topography/Abrasive Size/Pressure ) ?
Chemical Reaction
Slurry pH Value and so on
a12= F2/Hw
 V = Vol
Abrasive Geometry
Material Removal Rate Function:
MRR= N Vol= C1Hw-3/2 {1-(1-C2P01/3}P01/2V. Correct on both average scale & local single points
Schematic of Wafer-Chemical-Abrasive-Pad Interaction to Model the Volume Removed by A Single Abrasive 1
Surface Damage N
Contact Mechanics( Pad Topography/Abrasive Size/Pressure )
Abrasive Size Distribution
Abrasive Geometry
WIWNU
a22= F2/Hp
Pad Hardness
Xmax-Y=2
Pressure and velocity distribution over wafer-scale
WIDNU n
Schematic of Wafer-Abrasive-Pad Interaction to Model the Number of Active Abrasive Number
Pattern Density
Detailed Fluid Model
11/8/2000

4. MRR As A Function of Particle Size Distribution Before Saturation (Luo & Dornfeld, 2000)
MRR as A Function of Down Pressure and Velocity: MRR= N Vol= C1Hw-3/2 {1-(1-C2P01/3}P01/2V.
MRR=
C3: A Function of Down Pressure, Velocity, Weight Concentration etc.
C4: 0.25(4/3)2/3(1/Hp)Ep2/3/b1P01/3 A Function of Down Pressure, Pad Hardness and Pad Topography.
Function p: The probability of the appearance of abrasive size
Function : Probability density function.
Contribution of Active Particle Number
Contribution of Active Particle Size (Larger than Xavg)
Contribution of Total Number of Particles over the Wafer-Pad Interface
MRR as A Function of Particle Size and
Size Distribution
11/8/2000

5. Particle Size Distribution Measurement
Dynamical Light Scattering
Mean Size (m)
Standard Deviation (m)
AKP50
0.29
AKP30
0.38
AKP15
0.60
AA07
0.88
AA2
2.00
*Bielmann et. al. 1999
11/8/2000

6. Particle Size Dependence on MRR: Experiment VS. Model Predictions
(0.29, )
(0.38, )
(0.60, )
(0.88, )
(2.0, )
C4: 0.25(4/3)2/3(1/Hp)Ep2/3/b1P01/3= 0.015
*Bielmann et. al. 1999
11/8/2000

7. Fraction of Active Particles Based on
Model Prediction
[0.726, 0.737m]
0.1827%
[1.213, 1.231m] %
[1.720, 1.746m] %
[0.49, 0.50m] %
[5.091, 5.169m] %
11/8/2000

8. Relationship between Standard Deviation
and MRR Based on Model Prediction
Number
Dominant
Region
Size
Dominant
Region
11/8/2000

9. 2003 Goals
Develop comprehensive chemical and mechanical model. Perform experimental and metrological validation, by 9/30/2003.
Down Pressure
Wafer
Smaller contact area
Larger contact area H H a
11/8/2000