Presentation V

7/28/2019 Presentation V

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Carne ie Mellon Universit Particle Flow & Tribolo Laborator

A Wafer-Scale CMP Modeling Framework,Extended to Industrial Scale Semiconductor

Manufacturing

Gagan Srivastava, C. Fred Higgs IIICarnegie Mellon University

Particle Flow & Tribology Laboratory

Annual STLE MeetingMay 8, 2013

Detroit, Michigan


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Overview

Introduction and motivation

Recap of PAML-lite Modeling of physical interactions

Representative results

Model Expansions Oscillations

Industrial Applications

Conclusion

2


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Particle Flow & Tribology Laboratory

Core competencies

One of the most difficult areas of tribology relates to

the multi-physics behavior of particulate materials

large or small. They can wear and damage relatively

sliding materials, or they can be used to protect

materials.

Our strength is that we develop:

Experiments Simulations Predictions

Granular flows

Slurry

Powder lubrication


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Carne ie Mellon Universit Particle Flow & Tribolo Laborator4

Motivation

CMP, often results in defective output. To increase the yield and minimize waste,

accurate modeling of CMP is required.

PadWafer

Slurry


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Non-uniform Fluid Pressure

Affects Dishing and Erosion

Dishing only

Erosion only

Dishing and ErosionIdeal CMP

Before CMPCopperCopper seedTantalumSilicon DioxideSilicon

Higgs, et al., International Asia Tribology Conference, 2002

CMP : Feature Scale


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CMP : Wafer Scale

Differential wear across the wafer

Material removal map on a polished wafer

Nolan and Cadien (2012)

Wafer curvature

Variation of mean material removal with

wafer radius of curvature

Tseng et al. (1999)


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History of Chemical Mechanical Polishing Modeling

Empirical Preston (1927), Zhao and Shi ( ), Boning (1990s)

Fluid hydrodynamics based erosion wear

Runnels (1994 ), Sundararajan and Thakurta (1994)

Contact mechanics

Zhao and Chang (2002), Luo and Dornfeld (2001)

EHL / Mixed Lubrication (no wear)

Shan et al. (2000), Higgs et al. (2005), Jin et al. (2005)

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Zhao and Shi(1998)

Empirical Models

9

Boning and associates (1997)

H

VPkMRR =


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Empirical Models

Always include an all-purpose, empirical constant 'K'


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Fluid Hydrodynamics and Erosion Wear Based Models

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Sundararajan et al. (1999)

Runnels and Eyman (1994)Only load carrying capacityNo wear modeling



Fluid Hydrodynamics and Erosion Wear Based Models

Ignored the effect of solid-solid contact between wafer and pad.Unable to capture the effect of using different abrasives and pads


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Contact Mechanics Based Models

Known Particle SizeDistribution

Material Removed Per Particle

Soft Pad Model

Zhao and Chang (2002)

Luo andDornfeld (2001)

Particle Mono-layerModel



Contact Mechanics Based Models

Attempt to modify the Preston's equation by calculating Preston's coefficient(k) based on known parameters. Ignored the effect of the slurry.



EHL / Mixed Lubrication Based Models

1-D EHL Model

Shan et al. (2000) Jin et al. (2005)

2-D Mixed Lubrication Model



EHL / Mixed Lubrication Based Models

Ignored the effect of particles. No wear calculation.



CMP : A Mixed Lubrication

System



(b)

(d)

Other PAML Tribosystems

Artificial hip wear

Disk drive contamination wear

Bearing wear vialubricant debris

(a)

(c)

Teeth wear

Slurry Flows: Particles Augmented Mixed Lubrication (PAML)


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CMP Model: Particle Augmented Mixed Lubrication (PAML)

A deterministic model capturing major physical phenomenon :

Fluid hydrodynamics (3D Navier Stokes Equations)

Contact mechanics (Winkler Elastic Foundation)

Particle dynamics (Eulerian Lagrangian treatment)

Wear (Abrasive wear due to spherical particles)

Addresses asperity scale issues: dishing, erosion



CMP Model: Particle Augmented Mixed Lubrication (PAML)

Computationally very expensive.Could only model very small domains, at a very slow computational speed.



PAML lite(Computations: From Days to Minutes)

Objective

To develop an experimentally validated, computationally

efficient framework, without sacrificing major physical

phenomenon in action during CMP Extend the model to industrial scale



Virtual CMP

PAML lite

Fluid Mechanics Contact Mechanics Wear

Film thickness

h = h(r,)

Hydrodynamic

Pressurep = p[h, , ]

Equilibrium

Separation

d = d(r,)

Elastic Contact = (z, F, E)

Material Removal

Rate

MRR = f(,w,,V)

Particle Dynamics

Uniform

Concentration

Size distribution

Active ParticlesNactive=f(G, , )

PAML-lite is a wafer scale model

Particle Indentation

= f(, Hw*, pd)



PAML - lite : Fluid Mechanics

Reynolds Equation in Polar Coordinates (Beschorner et al. 2009)



PAML - lite : Contact Mechanics

Wafer : A flat rigid punch pressedagainst the pad

Pad : Winkler Elastic Foundation

(Johnson, 1983)

o Asperities act as independent springs

o Deformation in the plane of the pad is neglected

oNormal deformation due to tangential shearloading is neglected

PARALLEL SPRINGS

RIGID WALL

WAFER

LOAD

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PAML - lite : Contact Mechanics

Wafer : A flat rigid punch pressedagainst the pad

Pad : Winkler Elastic Foundation

(Johnson, 1983)

o Asperities act as independent springs

o Deformation in the plane of the pad is neglected

oNormal deformation due to tangential shearloading is neglected

PARALLEL SPRINGS

RIGID WALL

WAFER

LOAD

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PAML - lite : Wear

Soft pad model given by Luo and Dornfeld (2003) is implemented

Abrasive wear due to nano-particles getting trapped between a pad

asperity and the wafer

Total wear at an asperity contact depends on:o Number of active particles (Particles participating in the wear event)

o Average wear (Material removed by a particlewith diameter equal to the

average diameter of active particles)

Abrasive particle sizes follow

normal distribution

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Compute

new: ,,

Equilibrium orientation

{,,}, p(r,), (r,)

Calculate Active

Particles

Calculate Average

Wear

Calculate Total Wear

YES

START

Guess ,,0

Film thickness : h (,,0)

Find: fluid pressure

p(r,)

Fz,Mx,

My = 0

NO

Find: contact stress

(r,)

PAML - lite : Model Flowchart



PAML - lite : Model Flowchart

Compute

new: ,,

Equilibrium orientation

{,,}, p(r,), (r,)

Calculate Active

Particles

Calculate Average

Wear

Calculate Total Wear

YES

START

Guess ,,0

Film thickness : h (,,0)

Find: fluid pressure

p(r,)

Fz,Mx,

My = 0

NO

Find: contact stress

(r,)

Reynold's

Equation

Winkler

Foundation

Integrator

Root Finder



Modeling ParametersPad Properties

Model Simulated IC 1000

Hardness 5.0 MPa

Elastic Modulus 300 MPaAsperity Distribution Random Gaussian

Pad Thickness 1.3 mm

Roughness 10 m

Poissons Ratio 0.4

Wafer PropertiesHardness 2.0 GPa

Elastic Modulus 110 GPa

Poissons Ratio 0.16

Slurry Properties

Particle Material SilicaParticle Density 2000 kg / m3

Particle Size Distribution Gaussian

Mean Particle Radius 70 m

Standard Deviation of Particle Radius 15 m

Fluid Density 1000 kg / m3

Fluid Viscosity 0.001 Pa - s


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Y

X

(Osorno, 2005)

Experiments

Results: Interfacial slurry pressure


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Y

X

(Osorno, 2005)

Experiments

Results: Interfacial slurry pressure

Increasing from highlynegative values


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Results: Contact Stress on Pad

max

= 800 KPa

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Results: Evolution of Wafer Wear Over Time

t = 0

t = t1 t = 2t1 t = 3t1

t > 0


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Soft-EHL and Wear Modeling of CMP (wafer-scale)

Application:

CMP

Virtual CMP(Multiphysics fluid structure interaction (FSI)

& Wear)

Wafer-scale mixed

lubrication problem is

being computed in silico.

The evolution of wear,

fluid pressure and

contact stress is known.


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Soft-EHL and Wear Modeling of CMP (wafer-scale)

Application:

CMP

Virtual CMP(Multiphysics fluid structure interaction (FSI)

& Wear)

Wafer-scale mixed

lubrication problem is

being computed in silico.

The evolution of wear,

fluid pressure and

contact stress is known.


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Results: Material Removal Rate

Terrell and

Higgs (2007)

MRR vs Normal Load

The model has excellent predictions for lower loads ( < 15 PSI), but then requires

improved accuracy for higher loads.39

Experiments


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PAML liteExtending to Industrial Scale Manufacturing

1. Oscillating wafer carrier

2. Multi-wafer carrier

Breadth of Application

O ill ti H d


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Oscillating Head

The wafer carrier oscillates to-and-fro with respect to the pad center

commons.wikikmedia.org

P t i St d PAML lit ( O ill ti W f )


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Parametric Study: PAML-lite (non-Oscillating Wafer)

Hydrodynamic pressure and wafer wear with varying separation

Increased separation

Increased average pressure

Increased separationReduced wear

Parametric St d PAML lite (non Oscillating Wafer)


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Parametric Study: PAML-lite (non-Oscillating Wafer)

The eccentricity (separation between the wafer and the pad axis of rotationclearly affects the polishing behavior)

Oscillating Head


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Oscillating Head



Oscillating Head


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Oscillating Head



GnP Poli 300 Polisher

Oscillating Head


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Oscillating Head


GnP Poli 300 Polisher

PAML-lite

Oscillating Head: Comparison with stationary head


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Oscillating Head: Comparison with stationary head

Variation in MRR with increasing applied load

0 2 4 6 8 10 12 14 16 18 200

50

100

150

200

250

300

350

400MRR vs Load for Carrier Oscillation

Non-oscillating

Oscillating

Load (PSI)

MRR(nm/min

)

Oscillation

Amplitude: 0.15 mFrequency: 40 Hz

Oscillating Head: Effect of oscillations


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Oscillating Head: Effect of oscillations

Variation in MRR with oscillation parameters

0 0.05 0.1 0.15 0.2 0.250

50

100

150

200

250

300

350

MRR vs Oscillation Amplitude

Amplitude (m)

MRR(nm/min

)

0 20 40 60 80 1000

50

100

150

200

250

300

350

MRR vs Oscillation Angular Frequency

Frequency (Hz)

MRR(nm/min

)

Load : 6 PSIAngular Frequency : 60 Hz

Load : 6 PSIAmplitude : 0.2 m


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Multi-wafer carriers

At the industrial scale, it is

expensive to polish one wafer at

a time

Larger carriers are designed to

hold multiple wafers to reducepower and slurry usage

We observe motion at three

places: velocity of the pad (P),

velocity of the carrier (C) and

the velocity of the wafer (W)


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Multi-wafer carriers: Pad and the Carrier

Carrier on Pad

(Equilibrium Animation)

Individual Wafer Wear Animation

Individual Wafers on Pad Animation


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Multi-wafer carriers: Effect of Parameters

Normalized MRR vs Load(for multiple wafers)


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Conclusions

A new multiphysics framework, PAML lite was introduced that

coupled fluid mechanics, contact mechanics and abrasive wear

Wafer-scale phenomena are modeled Wafer scale defects can

be monitored

The flexibility of the model allows expansion to realistic polishing

systems Oscillating carrier and multi-wafer carrier

The expanded model can be used to monitor effects of untouched

parameters, to enhance efficiency


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THANK YOU

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APPENDIX

Presentation V

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