SCALING OF THE ADHESION BETWEEN PARTICLES AND …euvlsymposium.lbl.gov/pdf/2005/pres/55 3-MA-43 Kumar.pdfGautam Kumar, Shanna Smith, Florence Eschbach, Arun Ramamoorthy, Michael Salib,

School of Chemical Engineering

SCALING OF THE ADHESION BETWEEN PARTICLES AND SURFACES FROM MICRON-SCALE TO THE NANOMETER

SCALE FOR PHOTOMASK CLEANING APPLICATIONS

Gautam Kumar, Shanna Smith, Florence Eschbach, Arun Ramamoorthy, Michael Salib, Sean Eichenlaub,

and Stephen Beaudoin

Purdue UniversitySchool of Chemical Engineering

Forney Hall of Chemical Engineering480 Stadium Mall Dr.

West Lafayette, Indiana 47907-2100Phone: (765) [email protected]


Rationale• Mask cleaning processes can be more

quickly optimized if the magnitude of particle-mask adhesion forces known

• Mask layers and contaminants offering most difficult cleaning challenge can be identified

• Effects of solution properties on contaminant adhesion can be evaluated

• Range of adhesion forces for given contaminant/mask layer can be determined


Particle Characteristics

5 μm

5 μm

Alumina Particle

• Ideal geometries • Can model contact area using classic

approaches• Contact mechanics (JKR, DMT…)• DLVO

• Uniform microscopic morphology• Empirical, semi-empirical

approaches

• Unusual geometry• Random microscopic morphology• Compression/deformation of

surface asperities• Chemical heterogeneities• Settling (tilting, shifting)• Statistical information

The Academic System The Real World

Polystyrene Latex Sphere (PSL sphere)


Macroscopic Adhesion Model: DLVO Theory

EDLvdWA FFF +=

Total Adhesion Force

van der Waals Force

Electrostatic Double Layer Force

)h,a,d,A(fFvdW =

)h,d,,,(fFEDL κζε=

)I(f)pH,I(f

==

κζ

A = System Hamaker constantd = Particle diametera = Contact radiush = Particle-surface separation distanceε = Medium dielectric constantζ = Zeta potentialκ = Reciprocal double-layer thicknessI = Medium ionic strength

d

FA

Particle

2aSurface


Electrostatic Double Layer (EDL) Force

Stern LayerDiffuse Layer

Ions in Bulk Solution

Negative Co-Ion

Positive Counter-Ion

Zeta Potential, ζ+

-

-

+

+

+

+

-

-

-

-

Surface

Diffuse Double Layerψ

Distance

ψsζ

Shear Plane

Outer Helmholtz Plane

Pot

entia

l

( )⎥⎥⎦

⎤

⎢⎢⎣

⎡−

+⋅

−⋅

+= −

−

−h

sp

sph

hsp

EDL eeed

F κκ

κ

ψψψψκψψεε

222

220 2

14

ψ approximated by ζ


van der Waals (vdW) Force

-q

+q

lElectrons

Surface

μ = ql (instantaneous dipole moment)

Lithium atom

Surface

Electric field lines

Surfaceμ1μ2

Induced dipole moment

FvdW = FKeesom + FDebye + FLondon

permanent-permanentinduced-permanent induced-induced


Distribution of Forces

Freq

uenc

y

Adhesion Force

Particles Mounted on AFM Cantilevers

Al2O3 Particle

PSL Particle

cantileverSample

Sample holder and translation

stage

Mounted particle

AFM Schematic

AFM Force Curvea

bc

de

Def

lect

ion d

ab

ec Adhesion

Force

Position

Particle Adhesion Measurements


Surface Roughness and Adhesion5 μm PSL spheres in contact with

a silicon substrate in 0.03 M KNO3

Removal Force = Adhesion Force

0

40

80

120

160

200

1 2 3 4 5 6 7 8 9pH

Transition Region

Modified vdW for a smooth silicon surface

Rem

oval

For

ce (n

N)

Modified vdW for a rough silicon surface


Geometry and Adhesion

-5.E-09

-4.E-09

-3.E-09

-2.E-09

-1.E-09

0.E+00

1.E-09

2.E-09

3.E-09

0E+00 2E-09 4E-09 6E-09 8E-09 1E-08Separation Distance (m)

Interaction Forces Ideal Surfaces

van der WaalsElectrostaticCombined DLVO

(a)

(b)

(c)

particle

surface

double layer

Dominant interaction region

Inte

ract

ion

Forc

e (N

)

-5.E-09

-4.E-09

-3.E-09

-2.E-09

-1.E-09

0.E+00

1.E-09

2.E-09

3.E-09


Interaction Forces Ideal Surfaces


(a)

(b)

(c)

particle

surface

double layer

dominant interaction region

Inte

ract

ion

Forc

e (N

)

-2.E-08

-1.E-08

-5.E -09

0.E+00

5.E -09

1.E-08


Inte

ract

ion

Forc

e (N

)

Interaction Forces Irregular Particles


(a)

(b)

(c)

-2.E-08

-1.E-08

-5.E -09

0.E+00

5.E -09

1.E-08


Inte

ract

ion

Forc

e (N

)

Interaction Forces Irregular Particles


(a)

(b)

(c)


Alumina Interactions with SiO2

0

10

20

30

40

50

60

70

80A

lum

ina

Adh

esio

n Fo

rce

(nN

)vdW Model Predictions

Model Predictions

Experimental Measurements

pH (Constant Ionic Strength 0.01 M)2 4 6 8

Electrostatic interactions do affect the adhesion force, which varies with pHLarge area between particle and wafer out of contactSmall contact area


How to Describe?

5 μm

van der Waals

Combination of ideal shapes ( )

( ) ( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛+

+−

+= −

−

−h

sp

sph

sph

ee

edF κκ

κ

ψψψψψψκεε

222

220 2

14

( ) ( )( )22

21212

02

cosh2sinh2

ψψκψψκ

εεκ−−= h

hF r

+

sphere-plate

plate-plate

sphere-sphere++

Hamaker Constant, A12

( ) ( ) ( ){ }3212

212

212

21211212

zzyyxx

dVdVCdU−+−+−

−=ρρ

Point-by-point additivity

2112

6hRAF =

21

21

6 RRRR

hAF

+−

=+

+3

12

12 hAFπ

=+

ψκψ 22 =∇

Tknze

Br

i ioi

εεκ

0

22∑=

( ) ( )( )22

21212

02

cosh2sinh2

ψψκψψκ

εεκ−−= h

hF r

Approximate Solutions Approximate Solutions

Computational Solutions Computational Solutions

Poisson-Boltzmann EquationElectrostatics


Combined vdW, ES Interaction Models

Compression/DeformationCompression/Deformation

SEM(Geometry)

vdW + EDL ModelvdW + EDL Model

AFM(Topographic Data)

Generate MathematicalSurface RepresentationsGenerate Mathematical

Surface Representations

Contact SurfacesContact Surfaces

Load

(mN

)

force/depth profile

AFM Force MeasurementsAFM Force Measurements

3-D Reconstruction

ζ (mV) pH

IEP

Surface Potential

Removal Force StatisticsRemoval Force Statistics

Applied LoadApplied Load


Geometric Models


FFT Roughness Model

AFM scan of actual Cu surface FFT model Cu surface

F(x)

2πx

• Fourier transform of surface profile

• Reconstruction of surfaces generated with random phase angles

FFT with random phase


Validation: PSL Adhesion to Evolving Surfaces Only vdW forces needed to describe adhesion

Rough Silicon Surface

Average Measured Value 127 nN

Average Measured Value

10 nN

Range of Observed

Values

Smooth Silicon Surface

Range of Observed

Values

Removal Force = Adhesion Force

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

1 21 41 61 81 101 121 141 161 181 201Removal Force (nN)

Freq

uenc

y


PSL Interactions with SiO2

0

50

100

150

200

250

300PS

L A

dhes

ion

Forc

e (n

N)

vdW Model Predictions

Model PredictionsExperimental Measurements

2 4 6 8pH (Constant Ionic Strength 0.01 M)

• Electrostatic interactions do not have a significant effect at different pHs• Large contact area between sphere and wafer dominated by vdW


Alumina Interactions with SiO2

0

10

20

30

40

50

60

70

80A

lum

ina

Adh

esio

n Fo

rce

(nN

)vdW Model Predictions

Model Predictions

Experimental Measurements

pH (Constant Ionic Strength 0.01 M)2 4 6 8

Electrostatic interactions do affect the adhesion force, which varies with pHLarge area between particle and wafer out of contactSmall contact area


Nanoscale Adhesion Approach• Measure, model micron-

scale adhesion

• Extract vdW, ES constants

• Measure nano-scale adhesion

• Model adhesion using constants from micron-scale

• Can measure nano-scale adhesion

• Can model roughness and geometry effects

• Can predict nano-scale adhesion


Silicon Dioxide Surface

AFM Image FFT model Regeneration

0 50 100 150 200 250

0

100

200

-20

-10

0

10

20

30


Silicon Nitride Particle: Micron-Scale

FESEM image of a Si3N4 particle mounted on an AFM cantilever

Photomodeler Pro® model for the nitride particle


Silicon Nitride Cantilevers: NanoscaleSharpened silicon nitride probe

Max ROC ~ 40nm

~2 μm~10nm

Region considered in force calculations

Geometry considered in modeling the force between nanoscale cantilevers and substrates


Silicon Nitride Adhesion to Silicon Dioxide in Air

Tip ROC=12nm Tip ROC=36nm


Silicon Nitride Adhesion to Silicon Dioxide in Water



Silicon Nitride Adhesion to Quartz in Air



Silicon Nitride Adhesion to Quartz in Water



Theory and Experiment: Silicon Nitride Adhesion to Silicon Dioxide in Air

0 20 40 60 80 100 120 140

Force (nN)

OTR8

MSCT

Particle

Syst

em

Tip ROC=12nm

Tip ROC=36nm


Theory and Experiment: Silicon Nitride Adhesion to Silicon Dioxide in Water

0 2 4 6 8 10 12 14 16

Force (nN)

OTR8

MSCT

Particle

Syst

em

Tip ROC=10nm

Tip ROC=41nm


Theory and Experiment: Silicon Nitride Adhesion to Quartz in Air

0 20 40 60 80

Force (nN)

OTR8

MSCT

Particle

Syst

em

Tip ROC=14nm

Tip ROC=32nm


0 1 2 3 4 5 6 7 8

Force (nN)

OTR8

MSCT

Particle

Syst

emTheory and Experiment: Silicon Nitride

Adhesion to Quartz in Water

Tip ROC=14nm

Tip ROC=32nm


Conclusions

• Micron- and nano-scale particle adhesion can be described by vdW and electrostatic force models

• Proper accounting for roughness and geometry is required

• Particle adhesion characterized by a distribution of adhesion forces– Reflective of the interaction of two rough surfaces

• Particles with highly nonuniform geometry can be influenced by electrostatic forces even when in contact with a substrate


Acknowledgements• Financial support

– National Science Foundation • CAREER grant (CTS-9984620)

– NSF/SRC ERC for Environmentally-Benign Semiconductor Manufacturing

– State of Indiana 21st Century Fund– Intel– Praxair Microelectronics

• SEZ America• Stefan Myhajlenko

– Arizona State University Center for Solid State Electronics Research

• Ann Gelb– Arizona State University Mathematics

Documents

SCALING OF THE ADHESION BETWEEN PARTICLES AND …euvlsymposium.lbl.gov/pdf/2005/pres/55 3-MA-43 Kumar.pdfGautam Kumar, Shanna Smith, Florence Eschbach, Arun Ramamoorthy, Michael Salib,