Modeling of CMP - University of California, San...

© Laboratory for Manufacturing Automation, 2005

University of California at Berkeley

Modeling of CMP

David Dornfeld

CMP researchers: Jihong Choi, Sunghoon Lee, Dr. Hyoungjae Kim, Dr. Dan Echizenya

Department of Mechanical EngineeringUniversity of California Berkeley CA 94720‐1740

http://lma.berkeley.edu

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Overview

• Background on modeling

• Review of work to date

• Some new developments• pattern/feature sensitivity• pad design

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New Book on Modeling Chemical Mechanical Planarization (CMP)“Integrated Modeling of Chemical Mechanical Planarization for Sub-Micron IC Fabrication:

From Particle Scale to Feature, Die and Wafer Scales,” J. Luo and D. A. Dornfeld

For information:

www.springeronline.com/east/3-540-22369-X.

Written by researchers at UC-Berkeley, this monographreviews CMP modeling literature (from Preston to present

day efforts) and develops, with a strong emphasis on mechanical elements of CMP, an integrated model of CMP addressing wafer,die and particle scale mechanisms and features. Special emphasis is on abrasive sizes, distributions and resulting material removal rates and uniformity resulting over all scales.

175 Figures and 14 tables

ISBN 3-540-22369-x Springer-Verlag 2004

Or contact: [email protected]

LMA© Laboratory for Manufacturing Automation, 2005


Chemical Mechanical Planarization

Mechanical Phenomena

Chemical Phenomena

Interfacial and Colloid

Phenomena

CMP Team in FLCCDornfeld, et alDoyle, et alTalbot, et al

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Scale Issues in CMP

From E. Hwang, 2004

Scale/sizenm µm mm

Material Removal

Mechanical particle forcesParticle enhanced chemistry

ChemicalReactions

ActiveAbrasives

Pores,Walls Grooves

Tool mechanics,Load, Speed

critical features dies

Pad

Mechanism

Layoutwafer

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w p :pad rotation

tablepad

slurry feedconditioner

head

w w : wafer rotationOscillationF : down force

Backingfilm

Retainerring

Wafer

Wafer Carrier

Pad

Pore Wall

Abrasive particle

CMP Process Schematic

Electro plated diamond conditioner Typical pad



Bulk Cu CMP Barrier polishing W CMP Oxide CMP Poly-Si CMP

Physical models of material removal mechanism in abrasive scale

Chemical reactions

Bulk Cu slurry Barrier slurry W slurry Oxide slurry Poly-Si slurry

Mechanical material removal mechanism in abrasive scale

Abrasive type, size and concentration

[oxidizer], [complexing agent], [corrosion inhibitor],

pH …

Pad asperity density/shape

Pad mechanical propertiesin abrasive scale

Pad properties in die scale

Slurry supply/ flow patternin wafer scale

Wafer scale pressure NU Models of WIWNU

Models ofWIDNU

Topography

Wafer scale velocity profile

Wafer bending with zone pressures

Better control of WIWNU

Reducing ‘Fang’

Small dishing & erosion

Ultra low-k integration

Smaller WIDNU

Reducing slurry usageUniform pad performance

thru it’s lifetimeLonger pad life time

Reducing scratch defects

Better planarization efficiency

E-CMPPad groove

Pad design

Fabrication

Test

Fabrication technique

Slurry supply/ flow pattern in die scale

Cu CMP

modeldesign goalPad development

PatternMIT model

Dornfeld modelDoyle

An overview of CMP research in FLCC

Talbot

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The 4‐component system

• Hypotheses:– all polishing processes can be described as a 4 component

system;– Understanding the components and their interactions (pair-wise,

triplets, etc) provides a structure to catalog our knowledge (and ignorance)

Lap (rigid)

Workpiece LapGranuleCarrier fluid

Platen Pad }

“Granule”?Deliberately sought a word that covers the range of particles used without implying anything about size, hardness, or removal mechanism: µm to nm size range; from hard (diamond) to soft (rouge);

Source: 86. Evans, J., Paul, E., Dornfeld, D., Lucca, D., Byrne, G., Tricard, M., Klocke, F., Dambon, O., and Mullany, B.,“Material Removal Mechanisms in Lapping and Polishing,” STC “G” Keynote, CIRP Annals, 52, 2, 2003.

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Six possible pair-wise interactions

• Fluid-workpiece• Workpiece-pad• Workpiece-granule• Granule-pad• pad-fluid• Fluid-granule

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Three-way interactions (triplets)

• Workpiece-fluid-granule• Workpiece-fluid-pad• Workpiece-granule-pad• Fluid-pad-granule

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Stribeck Curve and Characteristics of slurry film thickness

Fric

tion

c oef

ficie

ntFi

lm th

ickn

ess

PressureVelocityViscosity ⋅

Hersey number(= )

Hydrodynamiclubrication

Elasto-hydrodynamic

lubrication

Boundarylubrication

Directcontact

Semi-directcontact

Hydroplanesliding

Stribeck curve

Polishing pad

Wafer Slurry

Direct contact

Semi-direct contact

Hydroplane sliding

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Gap effects on “mechanics”

Pad-based removal

Slurry-based removal

‘Small’ gap

‘Big’ gap

Silicon wafer

Polishing padAbrasive particle

Delaminated by brushing

Eroded surface by chemical reaction--- softening

Silicon wafer

Polishing pad

Abrasive particles

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Idealized CMP

Silicon wafer

Polishing pad

Abrasive particle

‘Softened’ surface by chemical reaction

Pad asperity

Mechanical Aspects of the Material Removal Mechanism in Chemical Mechanical Polishing (CMP)

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Interactions between Input VariablesFour Interactions:Wafer‐Pad Interaction; Pad‐Abrasive Interaction; Wafer‐Slurry Chemical Interaction; Wafer‐Abrasive Interaction

Polishing pad

Abrasive particles in Fluid (All inactive) Pad asperity

Active abrasiveson Contact area

VolChemically Influenced Wafer Surface

Wafer

Abrasive particles on Contact area with number N

Source: J. Luo and D. Dornfeld, IEEE Trans: Semiconductor Manufacturing, 2001

Velocity V

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Framework Connecting Input Parameters with Material Removal Rate

Slurry Abrasive WeightConcentration C Fraction of Active Abrasive:

1‐φ((g‐Xavg)/σ) where g is the minimum size of active abrasives

Force F & Velocity

Wafer Hardness Hw / Slurry Chemicals & Wafer Materials

Vol

Active Abrasive Size Xavg‐a

Basic Equation of Material Removal: MRR= N × Vol

Average Abrasive Size Xavg

Proportion of Active Abrasives

N

Pad Topography& Pad Material

Abrasive SizeDistribution φ

Down Pressure P0

gXavgφ Fraction of

Active Abrasives X avg‐a

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Ke1 (K1=84148, K2= 0.137)

Experimental Verification of Pressure Dependence of Material Removal Rate (MRR)

Advantage over Preston’s Eq. MRR= KePV+ MRR0:

What input variables and how they influence Ke is predicable

MRR= N Vol= K1 {1‐φ(1‐K2P0

1/3)}P01/2.

Ke2(K1=8989, K2= 0.3698)

SiO2 CMP Experimental Data from Zhao and Shi, Proceedings of VMIC, 1999

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Abrasive Size Distribution Dependence of MRR:Particle Size Distribution [1]

Five Different Kinds of Abrasive (Alumina) Size Distributions for Tungsten CMP

1. Bielmann et. al., Electrochem. Letter, 1999

Abrasive Size X (Log Scale)

(%) Frequency

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00.20.40.60.8

11.21.41.61.8

2

0 0.05 0.1 0.15 0.2 0.25 0.3

Standard Deviation (10-6m)

Nor

mal

ized

Mat

eria

l Rem

oval

Rat

e �

Xavg= 0.29umXavg=0.38umXavg=0.60umXavg=0.88umXavg=2um

Relationship between Standard Deviation and MRR Based on Model Prediction

Std dev influenced

Size influenced

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Pattern-Density Dependency Model

InterLevel Dielectric Case (single material)

K

K/densityUp Area

0Down Area

Time

pad

oxide

pad

oxide

Same Pattern Density

Different Orientations

Source: MIT

MRR

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Framework of a CMP Topography Evolution Model



Dishing and Erosion in Copper Damascene Process

Via

Trench

SiO2SiN

(a) (b)

(c) (d)

Fabrication steps in dual damascene process (a) deposition of SiN, SiO2 and etching trenches and vias in SiO2 (b) deposition of barrier layer (c) copper fill (d) CMP

and deposition of SiN (courtesy of Serdar Aksu)

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Definition of Feature‐Scale Topography

(a) (b)

(a) Feature scale topography before dielectric material is exposed and (b) feature scale topography after dielectric

material is exposed

Wcu

S

H

Wox

Copper Dishing d = S

Oxide Erosion e

H= Hox

Hox=Hox0

Hcu Copper Thinning

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Kd

Kf

(a) (b) (c) (d)

η

E E η E1

η1

E2 η2

E

Models of Polishing Pad

Linear Elastic and Linear ViscoElastic Models

Separated Models of Pad Bulk and Asperities

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Dishing d

3Erosion e

21

Df

S1=Df1

S=S0

H=Hcu0+Hox0 H= Hstage1

Hcu0

Hox0

Three Stages of Wafer‐Pad Contact

Only upper part of step is in contact

Both upper and bottom parts of step is in contact

Two different materials are removed simultaneously

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0 20 40 60 80 100 120 140 160 180 2000

50

100

150

200

250

300

350

400

450

500

Polishing Time t (second)

Ste

p H

eigh

t S (n

m)

PDi= 0.1PDi= 0.2PDi= 0.3PDi= 0.4PDi= 0.5PDi= 0.6PDi= 0.7PDi= 0.8PDi= 0.9

0 20 40 60 80 100 120 140 160 180 2000

50

100

150

200

250

300

350

400

450

500

Polishing Time t (second)

Ste

p H

eigh

t S (n

m)

PDi= 0.1PDi= 0.2PDi= 0.3PDi= 0.4PDi= 0.5PDi= 0.6PDi= 0.7PDi= 0.8PDi= 0.9

Simulation Results of Step Height Evolution for Different Pattern Density

Linear Elastic Pad Linear Viscoelastic Pad

Step heigh

t S (n

m)

Step heigh

t S (n

m)

Planarization time (sec) Planarization time (sec)

Wcu = 100 microns

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Copper Dishing as a Function of Pattern Densityusing commercial pads

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Copper Dishing as a Function of Selectivity

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Effect of Pattern Density - Planarization Length (PL)

ILD

Metal linesPlanarization Length

High-density region

Low-density region

Global step

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Effective pattern density

a=320um

a=640um

a=1280um

< Effective density map >

< Test pattern >

< Post CMP film thickness prediction at

die-scale >

Modeling of pattern density effects in CMP

Planarization length (window size) effect on “Up area”



Initial pressure distribution

Topography evolution

New pressure distribution

Contact wear model

Contact wear model

MRR model

Iteration

with time step

Die scale modeling of topography evolution during CMP

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PAD

Z(x,y)

Reference height (z=0)

Z_pad

Z(x,y)

Z_padz

dz

∫−

−×−+××=padZyxZ

zyxZzPDFdzzPDFdensityasperityKpyxF_),(

0

)),(())()(()_(),(

Feature level interaction between pad asperities and pattern topography

∫=die

dxdyyxFtentF ),(_

F_tent > F_die ? F_tent < F_die ?

++Z_pad --Z_pad

No

Yes

No

Yes

Z_pad

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k1

k2

221

21 kkk

kkKpad ≈+

=

Chip level interaction between pad and pattern topography

rPL

w40um

40umPattern

40um x 40um cell

∑ ∑ ⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛×

=ji

ji

E jiwjiPDjiwPD

,,

),(),(),(

θθπγ π

dPLr

Eqrrw ∫ −

−= 2

0

22

22

sin1)1(4)(

MIT model : approximation of contact wear model



100%

50%

33%

20%

50%33%20%

t=0 sec t=10 sec t=20 sec



Simulation result

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Pattern orientation effect on on copper dishingSiO2

Ti CuSi

Kinetic analysis of sliding direction during process time

pad rpm < wafer rpm

pad rpm = wafer rpm

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• Ra = 12.5µm

• Rz = 96.7µm

• Pore diameter : 30~50 µm

• Peak to Peak : 200~300µm

100µm

45µm

-45µm100µm 300µm 500µm

(SEM, x150)

200~300µm

(White light Interferometer, x200)

Pad Characterization

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Asperity: Real contact area10~50 µm

Pores40~60µm

Simplified Pad Model

Peak to Peak200~300 µm

1. Reaction Region (10~15 µm)

2. Transition Region3. Reservoir Region

Pad modeling

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3 Dimensional analysisReaction region

Reservoir region

Transition region

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2D and 3D image of reaction region

• Contact area : 10-50µm

• Ratio of real contact area : 10-15%

• Spherical or conical shape edge

• Stress concentration when compressed

2 dimensional image (w/o pressure) 3 dimensional image (w/o pressure)

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10 – 50 µm

Reaction region (asperity)

Reaction region – ILD CMP

• Over polishing on recess area

• Smoothing, not planarization

Defects of a conventional pad

50 µm

Large asperity

wafer

ILDRounding

10 µm

Small asperity

wafer

ILD

Over polishing

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Reaction region – Cu CMP

wafer

Pressure

Position

Stress concentration

ErosionDishingFang

Cu-CMP defects (due to stress concentration in conventional pad)

Pad asperity

Nominal pressure

Avg. contact pressure

wafer

wafer

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New In 3minutes

In 5minutes In 7minutes

Pad degradation

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• Compatible features to abrasive

• Constant re-generation of nano

scale surface roughness

• Constant contact area

(width:10-50um)

• The ratio of real contact area

(13-17%)

• Conditioning-less CMP

• High slurry efficiency

• Stacked layer

(Hard/soft)

• Slurry channel

Nano scaleMicro scaleMacro scale

Design rules for a pad

Design rules for a pad

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Soft Layer(i.e. low stiffness)

Hard Layer(i.e. high stiffness)

Channel Nano scale features

A pad design based on the rules

50-70µm

50-200µm

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Wafer

Pad

Wafer

Pad

• Conditioning-less process

• High planarity & good uniformity in ILD CMP

• Without stress concentration

• Less defects in Metal CMP

AdvantagesILD CMP

Cu CMP

Expectations

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Design of new padsType 2 – With slurry guidanceType 1 – Without slurry guidance

50µm

Slurry flow direction20µm

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Type 1 Type 2

• Area : 4.294^-10 m2

• Flow rate : 3.24^-10 kg/sec• Area : 4.3^-10 m2

• Flow rate : 3.93^-11 kg/sec8 times more flow rate

On contact area

Simulation result

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Pad fabrication

1. Master 2. Silicone Rubber Casting

3. Silicone Rubber Mold

4. Hard LayerCasting

5. Soft LayerCasting

6. Demolding

New pad

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Performance of a new pad – Planarity in ILD CMP

ILD pattern (MIT mask Version 1.0)

50%50um/50um

20%20um/80um

Si wafer

SiO2

0.77µm

1.7µm

2.7psi1.6psi1.6psiPressure

100ml/min

D-7000 (Cabot Co.)Slurry

30rpm

3inch wafer (12-100% density,1.7µm SiO2)Wafer

60rpm

New padIC1000/SUBA400Pad

Polishing machine

Experiment condition

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Density 20% - under same pressure:1.6psi

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1000 1100 1200 1300 1400 1500

Position(um)

Rel

ativ

e St

ephe

ight

(um

)

New In 3min In 7min In 12min In 17min -0.4

-0.2

0

0.2

0.4

0.6

0.8

1000 1100 1200 1300 1400 1500

Position(um)

Rel

ativ

e St

ephe

ight

(um

)

New In 3min In 15min In 20min In 40min

• Time : 17minutes

• Over Polishing : 2200Å



Good planarityHigh removal rate

IC1000/SUBA400 (1.6psi) New pad (1.6psi)

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-0.4

-0.2

0

0.2

0.4

0.6

0.8

1000 1100 1200 1300 1400 1500

Position(um)

Rel

ativ

e St

ephe

ight

(um

)

New In 3min In 7min In 12min In 17min-0.4

-0.2

0

0.2

0.4

0.6

0.8

1000 1100 1200 1300 1400 1500

Position(um)

Rel

ativ

e St

ep H

eigh

t(um

)

New In 10min In 20min

IC1000/SUBA400 (1.6psi) New pad (2.7psi)





Good planarity & removal rate

Density 20% - under different pressure:1.6psi &2.7psi

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