Transcript Introduction

1
Material Removal Mechanism in
Chemical Mechanical Polishing (CMP):
Theory and Modeling
SFR Workshop
November 8, 1999
Jianfeng Luo and David A. Dornfeld
Berkeley, CA
This work aims to develop a comprehensive model to explain the
fundamental mechanism of material removal in chemical
mechanical polishing
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Basic Idea of the CMP Model
Basic Equation of Material Removal: MRR= NwVol
where N is the number of active abrasives, w the density of wafer and
Vol the mean volume of material removed by a single active abrasive
per unit time.
Velocity
Softened wafer
surface
Vol
Wafer
with density w
Abrasive particles
in Fluid (All
inactive)
Abrasive
particles in
Polishing pad
Pad asperity
Contact
area
Active abrasives
in Contact area Inactive abrasives
in Contact area
Schematic of Material removal mechanism
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Wafer-Pad Contact Model: Real Contact Area A and
Real Contact Pressure P
Modeling of Pad and Wafer Surface ( A simplification from G-W Contact Model)
Pad Surface:
i. Uniform distribution of Asperity with Density DSUM
ii. Spherical Asperity Tip with Radius R
iii. Equal Height of Asperities ( All asperities are in contact with wafer)
Pad surface
Wafer Surface: Smooth in comparison with Pad Surface
Conclusions Based on Contact Mechanics
(Johnson, 1987):
i. Apparent Contact Area A0= 0.25 D2
ii. Real Contact Area A= bA0=
2
3
 3R P0 
 DSUM A0
 
*
 4DSUM E 
iii. Real Contact Pressure P= P0A0/A= (1/b1) E*2/3P01/3
where P0 is the down pressure, D the
diameter of wafer, E* the effective Young’s modulus,
b contact area ratio, and b1 a constant value
introduced for simplification.
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Wafer-Pad
Contact under
Down Pressure
P0
R
Before
deformation
An Asperity with
spherical tip
under Load F
(Johnson, 1987)
Area in Contact
(Micro-Scale
Size)
After
deformation
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Plastic Deformation over Wafer-Particle and PadParticle Interfaces
Relative Velocity V
Assumption of Spherical Abrasive
Particles
Softened Wafer
surface with
Hardness
Down Pressure P0 on Wafer Top Surface
Hw
 Indentation Force F on Abrasive Particles
is determined by contact pressure P and
abrasive size X.
 Deformation over Wafer-Particle
Interface is sliding-plastic deformation:
Radius a1 of the projected circle of the
indentation and indentation depth 1 can be
determined according to F and hardness of
Wafer Hw
• Mean Volume Vol removed by a single
particle in unit time is determined by a1, 1 and
relative velocity V.
 Static-Plastic Deformation over PadParticle Interface: Indentation depth 2 is
determined by hardness Hp of pad and
indentation force F.
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Indentation
Depth 1
a1
a
X
Indentation
Force F
Contact
Pressure P
Indentation
Depth 2
Pad Asperity with
Hardness Hp
Schematic of Wafer-Particle, Pad-Particle
and Wafer-Pad Contact
A Gap X- 1 -2 is introduced between the
wafer and pad where the abrasive sits. The
gap determines the chance for other
abrasives to be involved in material removal.
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Number n of Abrasives (Both Active and Inactive)
Captured in Contact Area
Total Number nallof Abrasives in
Wafer and Pad Interface is
determined by G, the
concentration of abrasives in the
slurry, A0 , the area of wafer
surface and L, the height of the
asperity after deformation
 Number nf of Abrasives in Fluid
is determined by G, A0 L and Vola
where Vola is the volume of all
asperities, if the concentration of
abrasives in fluid kept as G.
Vola is a constant independent of
down pressure.
Wafer
Pad
Abrasives Captured in
Contact Area with Number
Abrasives in Fluid
(inactive) with
n
Concentration
Number n of abrasives Captured
in the Contact Area is determined
by G and Vola n is dependent on
the roughness of pad but
independent of down pressure.
Constant Volume
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Area in Contact
(Micro-Scale
Size)
of An Asperity Before
Deformation and After
Deformation
Before
deformation
G
After
deformation
L
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Size Distribution of Abrasives and Active
Abrasive Number

Down Pressure P0 on Wafer Top Surface
Portion of Active
Abrasives
60
50
Portion of Inactive
Abrasives
40
30
1+ 2
20
10
0
-8
-6
-4
-2
0
2
Xavg
4
6
8
Xmax
Xmax- 1- 2
Xmax- 1- 2
Xmax
Xmax
Size Distribution of Abrasives
Indentation
Force Fmax
Inactive Abrasive
Only abrasives larger than the gap
Xmax- 1- 2 introduced by the indentation of
largest abrasives can be involved in material
removal. So active abrasive number N=
  xmax  xavg   xmax  xavg  1   2  
  
 
n 


 

  
where n is the number of abrasives in contact
area and  the standard deviation if normal
distribution is assumed. N is a function of
size distribution and hardness of wafer
and pad.
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a
Contact
Pressure P
Active Abrasive
Pad Largest Abrasive
Asperity
Schematic of Wafer-Particles, PadParticles and Wafer-Pad Contact
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Formulation of Material Removal Rate and Model
Verification
MRRmass= N w Vol= C1 (1- [3-C2 P0 1/3 ])P0 1/2V
Experimental Results VS. Predictions
where C1 is a value reflecting the effect of slurry chemicals,
slurry abrasives, wafer size, wafer density, wafer
hardness, pad roughness and pad materials,
C2 is a value reflecting the effect of slurry abrasives (size
distribution), wafer and pad hardness and pad roughness.
•
Model Verification:
Proof 1. Two
sets of Oxide CMP experimental MRR
results, Fig. 1, under different down
pressures are used to verify the pressure
dependence in the MRR formulation.
Lines 9 and 10 in Figure 1 show the
prediction. The pressure dependence is
correct for both oxide CMP and metal
CMP. Table 1 shows the probability of
active abrasives for data set 1 calculated
using the experimental data.
P0
5psi
7psi
9psi
11psi
%
0.896 1.092 1.287
1.474
Table 1. Probability of active abrasives
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Experimental Data
(Slurry 1)
Experimental Data
(Slurry 2)
900
800
700
MRR (nm/min)
Most Influential Parameters are: Contact Area,
Hardness of Pad and Abrasive Size Distribution.
1000
Line 3
Line 1
600
Line 7
Line 5
Line 9
500
400
Line 10
Threshold
pressures
300
Line 2
200
Line 6
100
0
-100 0
-200
1
Line 4
2 Linear3( )
4
5
6
7
8
9
10
11
12
Line
8 (Experimental
Linear
Data (Slurry 2))
Down Pressure P 0 (psi)
Fig. 1 Oxide CMP
•
Proof 2. Estimation of MRR by estimating input
parameters in the MRR formulation. The same order of MRR
with that of experimental MRR can be obtained. The same
range (0.5%~ 1.7%)of active abrasive probability as shown in
Table 1 can be obtained by substituting typical abrasive size
and pad hardness value into the formulation.
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Progress vs Milestones
Process Modeling
Year 1
• Develop experimental database for CMP modeling
and sensitivity analysis. (Done)
Year 2
• Develop integrated CMP model and evaluate
planarization efficiency predictions. (On-going)
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Conclusion and Future Work
Conclusion:
•
•
•
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A model is developed to explain the material removal mechanism in CMP
based on assumptions of plastic contact over wafer-abrasive and padabrasive interfaces, the normal distribution of abrasive size and the periodic
roughness of the pad surface.
Compared with previous work at modeling (e.g., Preston’s equation) the
model integrates pressure and velocity as well as wafer hardness, pad
hardness, pad roughness and abrasive size to predict the material removal
rate.
The model may provide a quantitative tool for consumable design
Better process control may be realized using the proposed model
Future work in 2000- 2002:
•
•
•
•
Further experimental verification of the model.
Investigation of influence of CMP process variables based on the model
including: pad hardness, contact area ratio, and abrasive size distribution.
Modeling of Step Reduction Mechanism of Patterned Wafer.
Comprehensive Study of WIWNU.
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