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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.