Mechanics and Physics of Nanoscale...

Prof. K. Komvopoulos

Surface Mechanics & Tribology Laboratory

University of California, Berkeley

FLCC Seminar, October 9, 2006FLCC Seminar, October 9, 2006

Mechanics and Physics of Nanoscale Polishing Mechanics and Physics of Nanoscale Polishing

Professor Professor K.K. KomvopoulosKomvopoulos

Surface Mechanics and Tribology Laboratory (SMTL) Surface Mechanics and Tribology Laboratory (SMTL) Department of Mechanical EngineeringDepartment of Mechanical Engineering

University of CaliforniaUniversity of CaliforniaBerkeley, CA 94720Berkeley, CA 94720




Contact Interfaces

z2

z1

x

x

d

Surface (1)

Surface (2)




Engineering Surfaces Exhibit MultiEngineering Surfaces Exhibit Multi--scale Roughnessscale Roughness




x (nm) y (nm)

z (n

m)

Surface Characterization of a PicoSurface Characterization of a Pico--sliderslider

D: fractal dimensionG: fractal roughness

30% pico slider

250 µm40 µm

∑∑= =

−−−

⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

⎥⎥⎦

⎤

⎢⎢⎣

⎡+⎟⎟

⎠

⎞⎜⎜⎝

⎛−⎟

⎠⎞

⎜⎝⎛+

−⎟⎠⎞

⎜⎝⎛

⎟⎠⎞

⎜⎝⎛=

M

m

n

nnm

n

nmnD

D

Mm

xy

Lyx

MLGLyxz

1 0,

122

,)3(

2/12max

tancos2

coscosln),( φππγφγγ




Basics of the Polishing ProcessBasics of the Polishing Process•• PolishingPolishing = relative motion between a soft surface with embedded hard

particles and the work surface.•• FourFour--component systemcomponent system: :

Work material + fluid + particles + polishing medium•• Main processesMain processes:

▪ deformation▪ two-/three-body abrasion▪ adhesion/smearing▪ fracture/fatigue

• Both bulk modulus and hardness of polishing surface affect penetration of the abrasive particles and texturing (e.g., burr formation).

• Mechanical wear can change the polishing surface and, hence, contact mechanics, fluid transport, temperature rise, etc.

• Shape, size and concentration of particles control polishing uniformity and range of dominant wavelengths on polished surface that determine surface roughness.

• A fluid maintains low friction during polishing to minimize frictional heating and excessive tensile stresses and to enable flushing out of material removed.




Asperity Adhesion and Deformation During PolishingAsperity Adhesion and Deformation During Polishing

AdhesionAdhesion

DeformationDeformation




Particle Plowing During PolishingParticle Plowing During Polishing

RigidRigid



University of California, BerkeleyTypical Wear FeaturesTypical Wear Features

Plowing/ductile Ridge flattening & microfrature

Brittle fracture




Significance of Fluid Lubrication in PolishingSignificance of Fluid Lubrication in Polishing

BoundaryLubrication

MixedLubrication

HydrodynamicLubrication




Normal Contact DeformationNormal Contact Deformation

Displacement (nm)

Load

( µN)

hc hmaxhf

S = dP/dh

loading unloading

hmax hc

2/1

2/1max*2

πAE

dhdPS ==




Example: Nanoindentation of Example: Nanoindentation of SiCSiC5000

0 50 100 150 2000

1000

2000

3000

4000

(a)

AE event 2

AE event 1

Nor

mal

load

(µN

)

Normal displacement (nm)

0.00 0.02 0.04 0.06 0.08 0.10

-2000

-1000

0

1000

2000 Event 1

Am

plitu

de (µ

V)

(b)

Time (ms)




FEM Model for SingleFEM Model for Single--Particle IndentationParticle Indentation

Rigid Spherical Particle

x

y




ElasticElastic--Plastic and FullyPlastic and Fully--Plastic Deformation RegimesPlastic Deformation Regimes

1.0

1.4

1.8

2.2

2.6

3.0

0.001 0.01 0.1 1

Series5Series2Series8Series7Series3Series1Series6Series4Series9Series10M

ean

cont

act p

ress

ure,

pm/Y

Interference, '/ rδ

E/Y450379270160502211

Inception of yielding

Inception of fully plastic regime

10010-110-210-3

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎠⎞

⎜⎝⎛

⎟⎠⎞

⎜⎝⎛+=

651.0656.0

'ln839.0

rYE

Ypm δ




Elastic and Plastic Regions due to IndentationElastic and Plastic Regions due to IndentationInception of Fully Plastic Deformation and Full UnloadingInception of Fully Plastic Deformation and Full Unloading

Contact edgePlastic region

Elastic region

E/Y = 450

Original surfaceOriginal surface

Contact edge

Plastic regionElastic region

LoadingUnloading

E/Y = 11




(b) δ / R = 0.007(a) δ / R = 0.005

(c) δ / R = 0.04 (d) δ / R = 0.059

E/Y = 11




(a) δ / R = 0.072 (b) δ / R = 0.1

(c) δ / R = 0.2 (d) δ / R = 0.4

E/Y = 450




Lateral displacement (µm)

CO

F

20

0

10

Loading

Unloading

15

5

Con

tact

forc

e (µ

N)

Displacement (nm) 100

Nanomechanical Tests (Single-Particle Nanomachining)

0.0

0.2

0.4

0 1 2 3 4

R= 20 µm, L= 200 µN, V= 0.4 µm/s

R= 100 nm, L= 40µN, V= 0.4 µm/sR = 20 nm




Frictional Heating due to a SingleFrictional Heating due to a Single--Particle Particle SlidingSliding

0

1

2

3

-3 -2 -1 0 1 2 3

x/r

∆T/

(2Q

a κ/π

kV)

Pe=0.05Pe=0.5Pe=2.5Pe=5Pe=10

δmax/R = 0.0075 µ = 0.5




Single-Particle Temperature Distribution

∆T/(2Qaκ/πkV)

0.042

0.046

0.051

0.0560.060

0.23

0.47

0.70 0.941.17

(b) Pe = 5(a) Pe = 0.05

δmax/R = 0.0075 µ = 0.5




SingleSingle--Particle SlidingParticle Sliding – Surface Stress

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

-4 -3 -2 -1 0 1 2 3

x/r0

xx/p

0

Pe=0Pe=48.97

δmax/R = 0.0075

µ= 0.5

Elastic

Thermoelastic (Pe = 49)




Segment 4 Segment 3 Segment 2 Segment 1VV

MultiMulti--Particle/Asperity Surface Temperature RiseParticle/Asperity Surface Temperature Rise

0.0030

0.0035

0.00400.0045

0.030

0.0310.033

0.035

0.037

0.0255

0.0264

0.0272

0.0281

0.029

0.031

0.034

0.037

(a) Pe = 2vr/κ = 0.06, µ = 0.5

0.036

0.073

0.21

0.14

0.27

0.33

0.390.43

0.29

0.14

0.58

0.18

0.27

0.36

0.45 0.55

(b) Pe = 5.58, µ = 0.5 ∆T/(2Qaκ/πkV)




Segment 4 Segment 3 Segment 2 Segment 1

V

(a) Elastic

(b) Thermoelastic Pe = 54

σM (GPa)

0.6

1.20.6

Von Mises Stress Von Mises Stress StressStress

σMmax = 5.69 GPa

0.20.4

0.6

0.3

0.3

0.7

0.7

1.4

2.1

1.4

σMmax = 7.01 GPa

0.7

0.7

1.42.1

2.8

0.6

1.2

1.2 1.8

0.20.4

0.6

0.3

0.6 0.6

0.9

0.3




Normal Contact StressesNormal Contact Stresses

σM(GPa)

015.631.346.962.578.193.8109.4125.0

75

50

25

0

p (G

Pa)

31.2527.3423.4419.5315.6311.727.813.910

El/Es = 4.0




AsperityAsperity Surface CrackCrack

Layer 1

Layer 2

P

h1

yP

ciF = µP y

x

rθ




Surface CrackSurface Crack

AsperityAsperity

Contact Fatigue ModelContact Fatigue Model




12

3

45 67 7

12

3

45

6

23

8 8

CrackCrack

12

34

1

2

3

4

CrackCrack

5 6 7 8 7 6 5

σM (GPa)

(1) 1.0 (2) 2.0 (3) 3.0 (4) 4.0 (5) 5.0 (6) 6.0 (7) 7.0 (8) 8.0




12

34

56

8 7

1

2

3 4

56

1

2CrackCrack

1

234

1

2

3 4

15 6 7 8

3

CrackCrack

σM (GPa)(1) 1.88 (2) 3.75 (3) 5.63 (4) 7.50 (5) 9.38 (6) 11.3 (7) 13.1 (8) 15.0




εpmax = 0.7353

1

8 7 6 5 4 3 2

1

8 7 6 5 4 3 2εpmax = 0.7437

CrackCrack

CrackCrack

εεpp

(1) 0.08 (2) 0.16 (3) 0.25 (4) 0.33

(5) 0.41 (6) 0.49 (7) 0.57 (8) 0.65




Crack Growth PathCrack Growth Path

Layer 1

Surface

Interface

∆c = h1/16

∆c = h1/4 ∆c = h1/8

Layer 2




Abrasive Wear RateAbrasive Wear Rate

dh/dt = k pa V /π Hw , Hw < 0.8Ha

dh/dt = k pa V (Ha/ Hw)2.5 /5.3 Hw, 0.8Ha < Hw < 1.2Ha

Abrasion coefficient: k ≈ tanθ = 10-3 – 10-1

2-body abrasion: k = 10-2 – 10-1

3-body abrasion: k = 10-2 – 10-3

NanoNano--PolishingPolishing: 10-6 < k < 10-9 — Atomic scale!Modeling?




Friction Coefficient Friction Coefficient µµ = = µµaa + + µµpp + + µµdd

Friction ofFriction ofConical Particles Conical Particles




Friction of Friction of Spherical ParticlesSpherical Particles




Effect of Particle Effect of Particle SharpnessSharpness

Friction ofFriction ofConospherical ParticlesConospherical Particles




Asperity DeformationAsperity DeformationSlipSlip--line Modelline Model

Effect of Roughness




SlipSlip--line Abrasive Wear Model line Abrasive Wear Model -- Wear CoefficientWear Coefficient




Particle Size Effect on Material Removal RateParticle Size Effect on Material Removal Rate




Critical Issues in Nanoscale PolishingCritical Issues in Nanoscale Polishing• Planarization of polishing surface.• Particle charging methods (roller motion, slurry feed, etc.).• Texturing of polishing plate for enhanced slurry movement during charging (burr

formation?).• Scale-dependent surface characterization of charged polishing surface.• Optimization of polishing surface for roughness of <1 nm.• Role of ethylene-glycol in nanoscale polishing lubrication (boundary lubrication?).• In-situ monitoring of the nanoscale polishing process (acoustic emission?).• Modeling of nanoscale polishing process for hard materials.• Knowledge of residual stresses in polished ceramic surface in terms of polishing

process parameters (i.e., particle size/distribution, pressure, speed, fluid viscosity/chemical behavior).

• Removal rate as a function of average size and distribution of diamond particles, pressure, and polishing speed (modeling at the right scale!).

• Causes of metal smearing from soft Sn layer and Fe-Ni magnetic read element.• Sn layer softening due to frictional heating under high-pressure/speed polishing

and/or fluid starved interface.• Dislodging of particles from plastically deformed (softened) Sn layer.• Surface treatment/texturing of polishing surface.

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