Statistical Characterization of the Chemical-Mechanical Polishing Process

A Presentation at the XVI

Oklahoma State University Research Week

Prahalada K Rao

School of Industrial Engineering and Management

Experiments

Math.

Reality

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Introduction: Why CMP Conventional semiconductor

manufacturing processes (CVD) have flaws.

Notably planarity concerns. Notice the “bird beak” structure in the adjoining figure (Zantye, 2004).

CMP is the only known method to achieve both local and global planarity and thus facilitate miniaturization.

The basic principle: Use a chemical reaction to soften material and then mechanically polish off this layer.

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The Advantages and Challenges1. Excellent Planarization.

2. Indifference to wafer surface.

3. Reduce defects.

Zantye, 2004

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Resources

Strasborough CMP M/cRetaining

Ring

Wafer Carrier

PolishingPad

LapMaster Lapping M/c

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Challenges in CMP Complexity of CMP Process

Key Process Input Variables

KPIV’s

State Variables Key Process Output Variables

KPOV’s

Machine

Down Force, Back Pressure, Platen Velocity, Wafer Carrier Velocity, Slurry Flow, Vibration, etc.

Stress Distribution, Velocity Distribution

Endpoint Control (Remaining Thickness Control)

Polishing pad

Stiffness (or Hardness), Macrostructure, Microstructure, Porosity, Topography, Pattern, etc.

Condition, Wet Hardness, Degradation, Temperature Distribution

Material Removal Rate (Å/min)

Slurry

Oxidizers, pH, pH Stabilizer, Complexing Agents, Dispersants, Selectivity ratio, Temperature

pH drifts, Concentration, Temperature Rise, Slurry Thickness

Planarity : Within Wafer Non-uniformity (WIWNU), Wafer to Wafer Non-uniformity, Within Die Non-uniformity (WIDNU)

Abrasive Particles

Size, Shape, Hardness, Chemistry, Density, Oversized Particles

Size Distribution, Aggregation, Agglomeration, Concentration, Debris

Defects & Contamination : Dishing, Erosion, Micro-scratch, Pits, etc.

Wafer

Size, Curvature, Properties of Coating (E, ν, H), Initial Coating Thickness, Coating Thickness Variation, Pattern Geometry

Direct Contact, Semi- Contact, Hydroplaning

Surface Finish : Roughness, Waviness, Form Accuracy

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Method of Analysis

The material in these slides is presented using the Theory of Constraints approach.

The data used for this research is primarily sourced from US patent 6564116 B2.The objective of the research can be briefly summarized as follows.

1. Part 1- Classification: To understand the behavior of key process input variables (KPIV’s).

2. Part 2 – Correlation : To illuminate the effect of the KPIV’s on key process output variables (KPOV’s) namely MRR and Within-wafer-non uniformity (WIWNU) .

3. Part 3 – Effect-Cause-effect : Contribute to the physical understanding of the process.

Experiments

Math.

Reality

Correlate

Exploit

Classify

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Design of Experiment and ANOVA - US patent 6564116 B2.

(Wang et al, 2001)

Part 1: Classification.

The main factors that affect the MRR and WIWNU are classified – What’s happening?

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Part 1: Classification for MRR

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1

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Ab

solu

te C

oef

fici

ent

PlatenSpeed (rpm)

AB DownForce

(psi)

SolidContent(wt%)

BD DE CD BackPressure

(psi)

Time (sec)

BC BE

Effect Name

Pareto Chart of coeffecients of Mean Effecting Factors

This chart tells us which of the factors or their interactions thereofare most significant in the regression equation

A:Solid Content

B:Down force

C:Back Pressure

D:Platen Speed

E:Polishing Time

MostSignificant

Least Significant

•Platen Speed, Down Forceand Solid Content are theKPIV’s that affect MRR most.•Back Pressure and Time arerelatively benign KPIV’s.

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Part 1: Classification for MRR – how the variables behave

Y-hat (Mean MRR affecting factors) Marginal Means Plot

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5

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25

30

5 10 15 20 25 4 5 6 7 8 0 1 2 3 3.5 20 30 40 50 60 40 45 50 55 60

Effect Levels

Solid Content (wt%)

Down Force (psi)

Back Pressure (psi)

Platen Speed (rpm)

Time (sec)

A:Solid Content

B: DownForce

C:Back Pressure

D:RPM

E:Polishing Time (Secs)

Non-LinearEffect Observed

MonotonicallyIncreasing

Non-Linear Effect Observed

MonotonicallyIncreasing

Non-LinearEffect Observed

MRR

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Part 1: Classification for WIWNU

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120

140

Abs

olu

te C

oe

ffic

ient

ABE BCE ABC DE PlatenSpeed (rpm)

BackPressure

(psi)

AD Time (sec)

SolidContent(wt%)

Down Force(psi)

Effect Name

Y-hat Pareto of Coeffs for WIWNU

Series1

Most significant

Least Significant

A: Solid Content B: Down Force C: Back Pressure D: RPM E: Time

•Platen Speed and Back Pressureare KPIV’s that affect WIWNU most.• Solid Content and Down Force arerelatively benign.•Interaction effects are more significantthan the KPIV’s (knobs) themselves.

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Part 1: Classification for WIWNU – how the variables behave.

Y-hat Marginal Means Plot for WIWNU

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120

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160

180

5 10 15 20 25 4 5 6 7 8 0 1 2 3 3.5 20 30 40 50 60 40 45 50 55 60

Effect Levels

Solid Content (wt%)

Down Force (psi)

Back Pressure (psi)

Platen Speed (rpm)

Time (sec)A: Solid Content

B: DownForce

C: BackPressure

D: Platenspeed

E: Time

NonLinear

NonLinear

Needs further investigation

NonLinear

MonotonicallyIncreasing

o MRR and WIWNU are governed by different set of factors (variables), some of them acting in opposition in each response.

Part 2: Correlation

Correlate the KPIV’s to the KPOV’s. How is it happening?

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Part 2: Correlation for MRR A: Solid Content (wt%), B: Down Force (psi), C: Back Pressure (psi), D: Platen Speed (RPM), E: Time (Sec) The regression equation for mean MRR obtained

as a results of the statistical analysis can be written as

DECDBEBDBCAB

EDCBAY

64748.227617.146890.094317.258153.090190.5

88934.012327.698457.095601.448162.3047.24ˆ

A: Solid Content

B: DownForce

C: BackPressure

D: Platenspeed

E: Time

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Model Validation for MRR

Scatter Plot of Standardized residuals

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1

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0 20 40 60 80 100 120

Observation

Sta

nd

ard

ized

Resid

uals

Series1

UCL = 1.96

LCL =-1.96

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Explaining Significant Interactions – MRR

Interaction Plot of Solid Content (wt%) vs Down Force (psi) Constants: Back Pressure (psi) = 1.75 Platen Speed (rpm) = 40 Time (sec) = 50

0

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20

25

30

35

40

45

5 7 9 11 13 15 17 19 21 23 25

Solid Content (wt%)

MR

R

4 8

Effect ObservedMRR improves with increasing solid cotent for higher values of Downforce, the opposite effect is observed at relatively low values of Down Force

Posisble explanations.1.There could be a threshold value for Downforce below which MRR falls due to increasing solid solid content

The coagulated slurry particles may possibly be broken down due to higher down pressure,thus releasing more number of abrasive particles in the medium

Down Force

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Interaction Plot of Platen Speed (rpm) vs Time (sec) Constants: Solid Content (wt%) = 15 Down Force (psi) = 6 Back Pressure (psi) = 1.75

0

5

10

15

20

25

30

35

40

20 24 28 32 36 40 44 48 52 56 60

Platen Speed (rpm)

MR

R

40

60

Time

MRR improves with platen speed , this effct is observed to be prominent for lower polishing time values.A significant interaction effect is observed.

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Part 2: Correlation for WIWNUA: Solid Content (wt%), B: Down Force (psi), C: Back Pressure (psi), D: Platen Speed (RPM), E: Time (Sec)

On the basis of a regression model connecting the mean WIWNU with the various factors can be written as…

Notice the three way interactions in the equation, these are not seen in the MRR equation.

A: Solid Content

B: DownForce

C: BackPressure

D: Platenspeed

E: Time

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Model Validation for WIWNUStandardized Residual Plot (first 100 readings)

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0 20 40 60 80 100 120

Reading

Sta

nd

ard

ized

res

idu

als

Standardized Residuals

UCL

LCL

Standardized Residual Plot (100-200 readings)

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0 50 100 150 200 250

Reading

Sta

nd

ard

ized

resid

uals

Standardized Residuals

UCL

LCL

Standardized Residual Plot (200-750 readings)

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0 200 400 600 800

Reading

Sta

nd

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ize

d r

es

idu

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Standardized Residuals

UCL

LCL

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Significant Interaction effects for WIWNU

Interaction Plot of Solid Content (wt%) vs Down Force (psi) Constants: Back Pressure (psi) = 3.5 Platen Speed (rpm) = 20 Time (sec) = 40

-300

-200

-100

0

100

200

300

400

5 7 9 11 13 15 17 19 21 23 25

Solid Content (wt%)

WIW

NU 4

8

Down Force

WIWNU decreases with increasing values of Down Force for a given value of Solid Content.A signifcant interaction effect is observed

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Interaction Plot of Solid Content (wt%) vs Time (sec) Constants: Down Force (psi) = 4 Back Pressure (psi) = 3.5 Platen Speed (rpm) = 20

-250

-200

-150

-100

-50

0

50

100

150

200

250

5 7 9 11 13 15 17 19 21 23 25

Solid Content (wt%)

WIW

NU

40 60

Time

WIWNU increases significantly for lower values of Polishing Time for a given level of solid content, a marginal decrease in WIWNU is seen at higher values of Time.A significant interaction effect is seen

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Interaction Plot of Down Force (psi) vs Back Pressure (psi) Constants: Solid Content (wt%) = 15 Platen Speed (rpm) = 20 Time (sec) = 40

0

50

100

150

200

250

300

4 4.4 4.8 5.2 5.6 6 6.4 6.8 7.2 7.6 8

Down Force (psi)

WIW

NU

0

3.5

Back Pressure

WIWNU decreases with decreasing values of Back Pressure for a given value of Down Force, an oppiste effect is observed for higher values of Back Pressure.A significant Interaction effect is evident.

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Interaction Plot of Down Force (psi) vs Time (sec) Constants: Solid Content (wt%) = 15 Back Pressure (psi) = 3.5 Platen Speed (rpm) = 20

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-50

0

50

100

150

200

4 4.4 4.8 5.2 5.6 6 6.4 6.8 7.2 7.6 8

Down Force (psi)

WIW

NU 40

60

Time

WIWNU decreases at higher values of polishing time,for a given value of Down Force, an opposite effect is observed for lower polishing time levels.A significant interaction effect is observed.

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Logarithmic Regression The data was subjected to a logarithmic regression

procedure. The regression equation is

The equation above is in close conjunction with the Preston’s equation. It is imperative to note that a time domain is considered.

00831.0314.0

379.0652.0314.0 )()(01.1

t

VPCMRR

C: Solid Content.P: Down Force

V:RPMt: Time

γ:Back Pressure

Preston’sEquation

Form

Part 3: Effect- Cause-Effect

Leverage the understanding,optimize towards the goal andstretch the correlation.

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Factor SymbolOptimal Values(From Model)

Optimal ValuesAuthors

Solid Content A 25 25

Down Force B 8 8

Back pressure C 0 0

Platen Speed D 60 60

Polishing time E 40 40

Part 3: Effect-Cause-Effect - MRR

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Effect-Cause-Effect - WIWNU

Factor SymbolOptimal Values(From Model)

Optimal ValuesAuthors

Solid Content A 15 15

Down Force B 4 4

Back pressure C 3.5 3

Platen Speed D 20 30

Polishing time E 40 40

Take a designed experiments approach to characterize the lapping processExtrapolate results to the CMP process.

Statistical and Dynamic Comparison to the Lapping Process

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Motivation and Introduction Can we provide an experimental basis for our

conclusions regarding CMP? A study of a similar process and analysis of the

same would provide an excellent starting point. Lapping is a super finishing process, utilized to

achieve submicron surface roughness. Prominent researchers contend Lapping and CMP are closely related.

Material removal mechanisms have been shown to match.

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KPOV = f (KPIV)

KPIV

KPOV

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8728 A 500 Kistler Accelerometer

Polishing Pads

Lapping Machine

Sensor DAQ system

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How do we decide the KPIV’s and KPOV’s

CustomerRequirement

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Results from DOE (Taguchi L8) analysis.

Cannot just predict roughness given parameters alone.

Y-hat Model S-hat Model

Factor Name Coeff P(2 Tail) Tol Act

ive

Factor Name Low High Exper Factor Name Coeff P(2 Tail) Tol Act

ive

Const 0.31676 0.0000 Const 0.04987 0.0000A A -0.00574 0.5969 1 X A A 10 45 10 A A 0.01171 0.0542 1 XB B -0.00767 0.3404 1 X B B -1 1 -1 B B -0.01720 0.0015 0.991 XC C 0.01758 0.0325 1 X C C -1 1 -1 C C 0.02410 0.0001 1 X

ABC -0.02692 0.0163 0.991 X AB -0.01750 0.0086 0.991 X

BC -0.03417 0.0001 0.991 X Prediction BC -0.01083 0.0212 1 X

Rsq 0.4069 Y-hat 0.305323209 Rsq 0.8837

Adj Rsq 0.3363 S-hat 0.002930919 Adj Rsq 0.8255

Std Error 0.0551 Std Error 0.0159

F 5.7632 99% Prediction Interval F 15.1899

Sig F 0.0004 Sig F 0.0002

Lower Bound 0.29653045Source SS df MS Upper Bound 0.314115967 Source SS df MS

Regression 0.1 5 0.0 Regression 0.0 5 0.0

Error 0.1 42 0.0 Error 0.0 10 0.0Total 0.2 47 Total 0.0 15

BAD!

Sensor Based Modeling

DOE doesn't work that well, so what do we do?

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Principal Component Analysis- PCA The following features were extracted from the

sensor based data. 1. Peak to Peak amplitude – P2P2. Energy 3. Variance4. Kurtosis.

A grand matrix consisting of these features was constructed.

This matrix, also called the features matrix is subjected to a PCA, to recognize the most telling features

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The Features Matrix

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Underlying Hypothesis and Results.

Hypothesis

[P] – Parameters Matrix (Time, Pad type, Abrasive)

[F] – Extracted Features

R Sq. %

Adj. R Sq.

%

1 [P]+[F] = [Ra] 47.6 20.3

2 [P] + [F] + [F-1]= [Ra] 45.9 18.0

3 [P] + [F] + [Ra-1] = [Ra] 82.2 75.2

Implicit Conclusions1. Cannot predict the process based on parameters alone2. Process is essentially non-linear3. Need sensor based modeling

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Summary of results from Hypothesis 3

Notice closenessWith CMP

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System Development

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2)(

)/1(2

1

max

2max2

constGeometric

sizeabrasiveMeanD

particlesofNumberN

workpieceandplatethebetweenGapd

sizeabrasiveMaximumD

grainsabrasiveorplateofHardnessH

materialofHardnessH

D

DderfcNdD

HH

HF

m

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p

w

mss

pw

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)'/1(

6

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)/1(2

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3max

3max

2

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KDm

ADNthen

KMP

PsaysLet

ratioworkfluidtoGrainM

densityFluidP

densityGrainP

areaWorkpieceA

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ADN

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DderfcNdD

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int

2

1

3

2

2

2

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3

2

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3

2

2

int

2

2

Based on: Dornfeld et al , ‘An investigation of material removal mechanisms in Lapping’ ,Journal of Manufacturing Science and Engineering, ASME , Vol 122 pp. 413- 2000

From Hanna-Tobiasmachine tool

dynamics model

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Model developmentMeasuring

this

Simulink Model Block Diagram

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Simulation parameters. %------------------------------------------------- %M-File for 'tuning' the model to observed results %------------------------------------------------- m =1 %mass of the system in kg lambda =1.485e7 %hanna tobias stiffness fcn HW =45 %VHN of aluminium beta1 = 350000; %nonlinear constant coeff beta2 = 350000; %nonlinear constant coeff HP =91 %Hardness of Plate - VHN of Silicon Carbide A = (pi*9/4)*2.56/100 %surface area exposed to lapping - 3" dia workpiece Dm = 78e-3 %mean dia of abrasive in mm Dmin = 25e-3 %min dia of abrasives in mm Dmax = 125e-3 %max dia of abrasives in mm Dsigma = (Dmax-Dmin)/2.99 %stdev of the grain size in mm alpha = 0.95; %geometric coeffcient T = alpha*HW/((1+(HW/HP)^2)^0.5) P = 3.2e3 %density of Silicon Carbide Grit kg/m3 Pd = 1000 %density of water kg/m3 M = 0.16 %grain to fluid work ratio K = (1+(P/(Pd*M))) N = 6*A*Dmax/(pi*((Dm)^3)*K) G = N*T dint = 0.001; %initial displacement h =1008050 %Hysteresis damping coefficent w = 10 %Region where energy peaks are observed in the data

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Theory

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Future focus Illuminate the reason for the interactions. Provide a physical model for CMP. Introduce sensor based control techniques.

My Research tool kit.1. Designed Experiments2. Response Surface methodology.3. Regression modeling.4. Theory of Constraints.5. Process Simulation.6. Process Modeling7. Six Sigma Approaches.8. Principal Component Analysis.9. Sensor based monitoring and modeling.

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Acknowledgements

Dr R. Komanduri.http://www.okstate.edu/MAE/maerl/mpmrl.htmlhttp://www2.mae.okstate.edu/Faculty/koman/koman.html

Dr S.T.S. Bukkapatnam.http://www.okstate.edu/ceat/iem/iepeople/bukkapatnam/default.htm

We thank the National Science Foundation (Grant # 0427840) for their generous support of this research.

WenChen Lih – PhD Student, MAE.