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A Time Dependency CMP Model for Dishing and Erosion in Copper
Damascene and STI Process
SFR Workshop & ReviewApril 17, 2002
Jianfeng Luo, Runzi (Tiger) Chang and Professor David A. Dornfeld
Berkeley, CA
2002 Goal: To build an integrated CMP model for basic mechanical and chemical elements.
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Motivation
• Need to know what input variables and how they influence the formation of dishing and erosion in copper damascene and STI process.
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Oxide Erosion and Copper Dishing in Copper Damascene Process
ErosionDishing
Source: Hitachi, 2000
Similar phenomena happen in STI process
• Copper line thinning is equal to erosion plus dishing. • Resistance is a function ofline thinning• Dishing worsens the copper line topography
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Si
Cu
Ox
S
SiOx
Pad
∆h
Definition of Input and Output Variables in Damascene Process
Pad
Start point of polishing End point of polishing
∆h0Th
(L/E): A parameter related to the pad material (Young’s modulus E) and pad topography (L)S: Original step height∆h: Step height during polishing∆h0: Initial deformation of pad asperitiesP0: Down pressure applied on dieD: Pattern density of copper lineT: Time of Polishing Ke and C1: Preston’s Coefficients for copper (MRR= KeP0+ C1)Kox and C2: Preston’s Coefficients for oxide (MRR= KoxP0+ C2)
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First Stage of Material Removal: Linear Time Dependency of Step Height Reduction
Si
Cu
Ox
Pad∆h0= (L/E)P0/(1-D) the deformation of pad asperity
∆h
∆h= KeP0/(1-D)T when ∆h> ∆h0. Only higher part of the step is in contact with pad. One single material--copper is removed. Step height is a linear function of time.
Si
Cu
Ox
Pad
∆h= ∆h0
Start point of the first stage End point of the first stage
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Second Stage of Material Removal: Exponent Time Dependency of Step Height Reduction
Si
Cu
Ox
Pad
∆h= ∆h0
∆h= ∆h0 Exp(-(KeE/L)T)when ∆h< ∆h0, where ∆h0= (L/E)P0/(1-D). Both higher and lower part of the step are in contact with pad. Step height is an exponent function of time.
Si
Ox
Pad
∆h
Start point of the second stage End point of the second stage (Dishing is formed before erosion)
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Third Stage of Material Removal (Over-polishing): Exponent Time Dependency of Dishing and Erosion
Si
Ox
Pad
∆h= ∆hc
Dishing ∆h= a/b-[a/b- ∆hc] Exp(-bT)] where a=(-KoxP0-C2+KeP0+C1), b= (E/L)(KoxD+Ke(1-D)) and ∆hc is the initial dishing.
Erosion Er= (KoxP0+C2)T+(KoxED/b[∆hc-a/b][1-Exp(-bT)]Both dishing and erosion are exponent functions of time.
SiOx
Pad ∆h= ∆hc
∆hCu
Er
Start point of the third stage End point of the third stage
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Selected Simulation Results of the Step Height as a Function of Time
-100
0
100
200
300
400
500
600
0 20 40 60 80 100 120 140 160 180 200
Time (Second)
Ste
p H
eig
ht
(nm
)
PD= 0.9
PD= 0.1
First Stage
Second Stage
Third Stage
Ke= 0.278nm/(Sec.kPa)C1= 2.5nm/Sec.
Preston’s Coefficeint for Copper Ke and C1
Kox=0.00199nm/Sec.kPa)C2=
Preson’s Coefficient for Oxide Kox and C2
0.1295kPa.nm-1Pad Coefficient E/L
27.8 Sec.Time Constant for Second Stage KeE/L
261Sec. for PD= 0.940 Sec. for PD= 0.1
Time Constant for Third Stage (E/L)(KoxD+Ke(1-D)).
6 Sec. for PD= 0.176 Sec. for PD= 0.9
Duration of Stage 3
127 Sec. for PD= 0.1121 Sec. for PD= 0.9
Duration of Stage 2
0 Sec. for PD= 0.964 Sec. for PD= 0.1
Duration of Stage 1
12kPaDown Pressure P0
1300nmOriginal Copper Thickness Th
500nmOriginal Step Height S
Final Dishing
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00.10.20.30.40.50.60.70.80.9
11.1
0 20 40 60 80 100 120 140
Polishing Time (Second)
Nor
mal
ized
Rem
aini
ng S
tep
Hei
ght
Experimental (PD= 0.9)
Experimental (PD= 0.85)
Experimental (PD= 0.8)
Experimental (PD= 0.67)
Experimental (PD=0.5)
Experimental (PD=0.2)
Model (PD= 0.9)
Model (PD= 0.85)
Model (PD= 0.8)
Model (PD= 0.67)
Model (PD= 0.5)
Model (PD= 0.2)
Experiment Results VS. Model Predictions of the Time Dependency of Step Height Reduction in
The First and Second Stages
Experimental data from Stavreva et. al., Microelectronic Engineering, Vol. 33, 1997.
Linear Stage
Exponent Stage
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0
500
1000
1500
2000
2500
0 10 20 30 40
Overpolishing (%)
Dis
hing
(nm
)
Experimental Data 1Model Experimental Dta 2ModelExperimental Data 3Model
Experiment Results VS. Model Predictions of the Time Dependency of Dishing in The Third Stage
Experimental data from Pan et. al., IEEE IITC, San Francisco, 1999.
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Discussion
• Dishing and erosion depend on polishing time, pattern density, pad material, topography, and material removal mechanism (Parametersrelated to Preston’s coefficient including abrasive size, slurry chemicals, etc.)
• This model can be integrated with the comprehensive material removal model developed earlier.
• Dishing and erosion depend on processes before CMP such as electroplating, CVD, and copper line thickness before polishing.
• More experimental verification is needed. • Model Limitations
(1) An important parameter: copper line width is not included in the model yet.(2) Model may be invalid when the copper line width is small incomparison with the pad asperity.
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2003 Goals
Develop comprehensive chemical and mechanical model. Perform experimental and metrological validation, by 9/30/2003.