1. Jianfeng Luo and David A. Dornfeld
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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2. 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
Vol
Softened wafer surface
with density w
Wafer
Abrasive particles in Contact area
Abrasive particles in Fluid (All inactive)
Polishing pad
Pad asperity
Active abrasives in Contact area
Inactive abrasives in Contact area
Schematic of Material removal mechanism
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3. 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)
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=
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.
Pad surface
Wafer-Pad Contact under Down Pressure P0
Area in Contact
(Micro-Scale Size) R
An Asperity with spherical tip under Load F
(Johnson, 1987)
Before deformation
After deformation
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4. Plastic Deformation over Wafer-Particle and Pad-Particle Interfaces
Relative Velocity V
Assumption of Spherical Abrasive Particles
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 Pad-Particle Interface: Indentation depth 2 is determined by hardness Hp of pad and indentation force F.
Softened Wafer surface with Hardness Hw
Down Pressure P0 on Wafer Top Surface
Indentation Depth 1 a1 a X
Contact Pressure P
Indentation Force F
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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5. Number n of Abrasives (Both Active and Inactive) Captured in Contact Area
Slurry out
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.
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.
Slurry in
Wafer
Pad L
Slurry in with Concentration G
Slurry out with Concentration G
Abrasives Captured in Contact Area with Number n
Abrasives in Fluid (inactive) with Concentration G
Area in Contact
(Micro-Scale Size)
Constant Volume of An Asperity Before Deformation and After Deformation L
Before deformation
After deformation
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6. Size Distribution of Abrasives and Active Abrasive Number
Down Pressure P0 on Wafer Top Surface 
Portion of Active Abrasives
Portion of Inactive Abrasives
1+ 2
Xavg
Xmax
Xmax- 1- 2 a
Xmax- 1- 2
Xmax
Xmax
Contact Pressure P
Size Distribution of Abrasives
Indentation Force Fmax
Active 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=
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.
Inactive Abrasive
Pad Asperity
Largest Abrasive
Schematic of Wafer-Particles, Pad-Particles and Wafer-Pad Contact
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7. Formulation of Material Removal Rate and Model Verification
MRRmass= N w Vol= C1 (1- [3-C2 P0 1/3 ])P0 1/2V
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.
Most Influential Parameters are: Contact Area, Hardness of Pad and Abrasive Size Distribution.
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.
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. P0
5psi
7psi
9psi
11psi %
0.896
1.092
1.287
1.474
Table 1. Probability of active abrasives
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8. 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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9. Conclusion and Future Work
A model is developed to explain the material removal mechanism in CMP based on assumptions of plastic contact over wafer-abrasive and pad-abrasive 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 :
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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