Indenting thin films using an atomic force microscope

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2-7-1997

Indenting thin films using an atomic force

microscope

Cheryl O'Neal

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Indenting Thin Films

Using An Atomic Force Microscope

by

Cheryl Anne-Bell O'Neal

A Thesis Submitted in Partial Fulfillment

of the Requirements for the Degree of

MASTERS OF SCIENCE

III

Mechanical Engineering

Professor

_

Dr. M. Scanlon (Thesis Advisor)

Professor

_

Dr. V. Gupta

Professof

_

Dr.

C.

Nilsen

Professor

_

Dr. c..W. Haines (Department Head)

DEPARTMENT OF MECHANICAL ENGINEERING

COLLEGE OF ENGINEERING

PERMISSION GRANTED:

I, Cheryl Anne-Bell 0 'Neal, hereby grant permission to the Wallace Library of

the Rochester Institute of Technology to reproduce my thesis entitled:

INDENTING THIN FILMS

USING AN ATOMIC FORCE MICROSCOPE

in whole or in part. Any reproduction will not be for commercial use or profit.

February 7, 1997

Abstract

The

feasibility

of_usinga

Scanning

Probe Microscopeto measurenanomechanical

propertiesofthinfilmswas investigated. An Atomic force Microscopewas utilized inan

attempt to perform nanoindentations to measure the hardness and elastic modulus of

several materials. A high modulus cantilever beam was constructed from silicon and a

tungstenbead was adhered to its free end.

Using

this cantilever _assembly three samples

were indented: a bulk aluminum _sample, a 2\im thick aluminum film sputtered onto a

glass _substrate,and a elastomer(rubber band). Subsequentto the

indenting

_process,force

curves were captured in the form of

tip

deflection versus the z-displacement of the

piezoelectric.

Using

transformationequations typical

loading

and_unloading curves were

generated from this data. The

loading

portion ofthe curves were used to generate the

hardness of the materials, while the _unloading portions of the curves were used to

generatethematerial's elastic modulus. Two analysistechniquesarepresentedforuse in

the determination of the elastic modulus in conjunction with the type of _unloading

behaviorexhibited. To assesthe_accuracyofthe methods_used, thevalues ofhardness and

elastic moduli for several materials were calculated and compared to available literature

values determined

by

independent means. The results demonstrate that with the

construction of a stiff cantilever _assembly and with the proper analysis of good force

curves, thepotential of _{obtaining hardness} andelastic moduli forthinfilm_material's, via

Acknowledgments

Ibegin first

by

thanking

Professor Marietta

Scanlon,

_mythesisadvisorand

friend,

forherguidanceinthe_writingofthis thesis.

Secondly,

Iwouldliketo thank_myparents,

Mr. andMrs. Augustus

Bell,

fortheir_manyprayers andcontinued supportthroughout_my

manyendeavors.

Third,

_my aunt Marthaand

"Ma"

O'Neal _{for ensuring}that I didn't go

without nourishment after a

long day

ofresearch work.

Also,

I thank

Yvette,

_{my best}

friend,

for her encouragement andher abilityto never passjudgment overme whether I

succeeded or failed in my pursuit of _many aspirations.

Furthermore,

I would like to

express _{my deepest} gratitudeto _{any friends} or

family

membersthat _{I may have failed}to

acknowledge,fortheirloveandunderstanding.

Finally,

I express an _overwhelming appreciationto _my

husband, Russell,

for his

patience and _{understanding} of the trials and tribulations of a _{struggling engineering}

graduate student. His numerous sacrifices extended farbeyondthe duties ofa

husband,

Tableof Contents

Abstract iii

Acknowledgments iv

ListofTables viii

ListofFigures ix

ListofSymbols xi

1. Introduction 1

2. Literature Review 4

2.1. Traditionalhardnesstesters 4

2.1.1.

Commonly

usedhardnesstesters

-(Brinell, Rockwell,

Vickers,

and

Knoop)

4

2.1.2. Nanoindenter 6

2.1.3. Surface Profiler 18

2.2.

Scanning

Probe

Microscopy

20

2.2.1.

Scanning Tunneling

Microscope,

STM 23

2.2.2. AtomicForce

Microscope,

AFM 24

Tableof Contents

3.1. Materialsselection 34

3.2. Cantilever and

tip

construction 36

3.2.1.

Loading

theAFM

tip

holderand_placingthecantilever

ontothepiezoelectric 37

3.2.2.

Determiriing

the_{spring constant,}kofthecantilever

assembly usinga nondestructive method 41

3.2.3. _{Procedure for placing}a new

tip

onto thecantilever 44

3.3. Samplepreparation 46

3.4. _{Nanoindentation using}anAtomic Force Microscope 46

3.4.1.

Indenting

procedure 47

3.4.2.

Getting

aforcecurve 55

3.4.3.

Plotting

theforcevs. displacementcurve 57

3.4.4. Forcecurveanalysis

-interpreting

dataoutputfrom

theAFM 61

4. Results 71

4.1.

Spring

constant 71

4.2. Bulkaluminum sample 74

4.3. Thin filmaluminum sample 80

Tableof Contents

5. DiscussionofResults 91

5.1. Forcecurves 91

5.2. Hardness 91

5.3. Modulus of

Elasticity

92

6. Conclusion 97

7. RecommendationsforFuture Development 99

ListofTables

Tables _Page

2.1 Comparisonof penetration

depths,

material_thickness,andtheloads

applied

by

severaltraditional testers 6

4.2 Summarizedhardnessdata for abulkaluminumsample 77

4.3 Summarizedelastic modulusforabulkaluminum sample 80

4.4 Summarizedhardness data forathinfilmaluminumsample 83

4.5 Summarizedelasticmodulusforathinfilmaluminum sample 85

4.6 Summarizedhardness data foran elastomer sample 88

4.7 Summarized elastic modulusdata foran elastomer sample 90

5.8 Comparisonof measuredhardnesswith valuesfrom literatureand

conventionalhardnesstest 92

5.9 Comparisonofmeasured elastic modulus with valuesfromliterature 93

ListofFigures

Figure Page

2.1.

Commonly

usedhardnesstesters:

Brinell, Rockwell,

and

Knoop

Hardness Testers 5

2.2. ANanoindenter 7

2.3. Typical

loading

and_{unloading force} curve 7

2.4. Across-section ofanindent 10

2.5. Surface Profiler 18

2.6. Schematicof ageneralized

Scanning

Probe Microscope 22

2.7. SchematicofanAtomicForce Microscope 24

2.8. AnSEMmicrograph of a cantilever

tip

assembly. Siliconcantilever

withintegral

tip

25

2.9. Schematicofbeam-bounce detectiontechniqueusedfor

detecting

cantileverdeflection 26

3.10. Cantilever installation fixture (a 2.5 inch diameteranodized aluminum

block),

and

tip

holder 38

3.11. An SEMmicrograph_showingasilicon cantilever withatungsten

beanaffixedtoits freeend 45

3.12. Digital

Instruments,

Dimension3000 AFM 47

ListofFigures

Figure Page

3.1.

Ideally

_elastic,

ideally

plastic and elasto-plastic

loading

and

unloadingcurves 67

4.2.

Spring

constant calculationfora_scanningprobe_microscopy

cantilever 73

4.3. Forcecalibrationplot capturefromtheAFMforabulkaluminum

sample 75

4.4. AFMforce curve re-plottedin Microsoft Excel forabulk

aluminum sample 76

4.5. Complianceplotforabulkaluminumsample 79

4.6. Forcecalibration plot capturefromtheAFMforathinfilm

aluminum sample 81

4.7. AFM forcecurve re-plottedin Microsoft Excelforathinfilm

aluminum sample 82

4.8. Complianceplotforathinfilmaluminum sample 84

4.9. Forcecalibrationplot capturefromtheAFMforanelastomer

(rubber

band)

sample 81

4.10. AFM forcecurve re-plottedin Microsoft Excel foranelastomer

(rubber

band)

sample 82

Listof Symbols

heff

effective depth

hp

plasticdepth

hs

displacementofthesurface attheperimeterofthecontact

Pmax

maximum appliedload

hmax

maximumdepthofindentation

a radius ofthecontact circle

A projectedcontactarea

S contact stiffness

P Appliedload

h depthofindentation

(displacement)

E*

effective modulusforthesystem

u0

Poisson'

sratioofthematerial

being

indented

E0

Young'smodulus ofthematerial

being

indented

u

Poisson'

s ratio oftheindenter

tip

material

E Young'smodulusoftheindenter

tip

material

P

indentershape constant

C system compliance

Listof Symbols

a_'o initial stress

a thermal-expansioncoefficient

AT globaltemperaturevariation

ho

heightofunloaded structure

K _{proportionality} constant

Ey

iterativeYoung's modulus

F appliedload

r radius ofthecontact area

k _springconstant

H hardness

E Young'smodulus_{(elastic modulus)}

w cantilever width

1 cantileverlength

m effectivemass

mb cantilever mass

M endmass

v resonant

frequency

co angular

frequency

Listof Symbols

p

density

Vj finalresonant

frequency

R radiusofthe tungstensphere

1.

Introduction

For centuries materials have played a_primary role in structural and

load-bearing

applications. Because ofthe

importance

of materials to our _{society, many} metallurgists

and materials scientists have persisted in their _{understanding} and development of the

mechanical properties of structural materials.

Mostly,

this research has been focused in

the area of bulk structural materials (thick films). More _{recently though,} the

advancement of new technologies and an increased interest in the _{down sizing} and

minimization of materialshas stimulated an enormous amount ofresearchand interest in

the area ofthinfilms. This spark ofinterest has in recent years focused the attention of

materials scientists towardthe _{understanding} ofthemicroscopic mechanical behavior of

materials. It is argued whether or notthe approaches proven useful inthe _study ofbulk

structural materials can be used in the _{understanding} ofthe mechanical behavior ofthin

films.

Forexample, inconventional studies ofthemechanicalbehaviorofmaterials it is

common practice to testsamples ofthematerialsinquestion

by

_subjectingthemtoforces

or displacements and_measuring the _{corresponding} response. These _responses,

typically

various states of_stress, such as _{tension, compression,} and _torsion, which in conjunction

with the forces and

displacements,

permitthe calculation ofthe mechanical properties of

the material. This approach

however,

can not _{readily be} used to _study the mechanical

in thickness or less and are mounted/bonded to substrates.

This,

_therefore, makes

submicronindentation inevitable inthe_{understanding}ofthinfilms.

Withthe

increasing

trend toward_{miniaturization,}the measurement of mechanical

properties ofthin films is

becoming

increasingly

important. Examples of such materials

are usedinthefabricationofmicroelectronic _circuitry andmagnetic diskswhich not_only

need to perform their electronic and magnetic

functions,

but must also have various

chemical and mechanical propertiesthatwill allowthemtomaintaintheir

integrity

forthe

life of the product. Because of _this, one must have a better understanding of the

structural capabilities ofthin films. Ifthese materials are to remain operable in their

applications, corrosive and mechanical failures must not occur, thus

they

must provide

adequate resistance to the mechanical and chemical forces that

they

_may incur within

their environment.

Due to this increased interest in thin film characterization there is an

increasing

need for the development of reliable methods for _analyzing the nanomechanical

properties,mainlyhardnessand elasticmodulus,ofthinfilms. The informationpresented

in this thesis is intended to address this need throughthe application of an atomic force

microscope

(AFM)

as a nanoindenter. Although there are _commercially available

nanohardness devices capable of _measuring nanomechanical _properties, these devices

requirethe

imaging

of the indentation subsequentto indenting. Thepurpose of

imaging

method is difficult since thin film indents are _very small (< 1/10 ofthe film

thickness)

making them difficult to locate in order to image.

Thus,

the methods introduced in this

thesis attempts to overcome the need to _optically measure the _geometry of the

2

Literature Review

Before

introducing

the ideaof_using anAFM as a_{nanoindenting}

device,

onemust

first become familiarized with the

terminology

ofindentation. _{The proceeding} section

provides abriefoverview of

traditionally

used hardness testers and their applications in

determining

mechanical properties of various materials. Detailed information on how

theseproperties are determinedare

discussed,

sincethis thesis appliesthesetechniques in

its attemptatnonindentation. As acomparisonbetweenmethods usedtoanalyzebulkvs.

thin film materials, section 2.1.1 introduces indentation methods which are applied to

bulk _{materials, whereas,} section 2.1.2 and 2.1.3 introduce methods used to indent thin

films. What separates these methods ofindentation from the method used inthis thesis

viathe

AFM,

_{is that,}either theapplied loads arefar too great forthin film indentationor

the_geometryoftheindentation mustbe measured(this ideal is discussed ingreaterdetail

insection2.3).

2.1 Traditionalhardnesstesters

2.1.1

Commonly

used hardnesstesters

-(Brinell, Rockwell, Vickers,

and

Knoop)

"Hardness is a measure of the resistance of a metal to permanent

(plastic)

deformation"1. Several methods have been developed to measure the hardness of

materials,

however,

the loads applied

by

these hardness testersare far beyondthat which

Brinell hardnesstester Rockwell hardnesstester _Knoophardness tester

Figure 2.1

Commonly

used hardness testers:

Brinell,

Rockwell, and

Knoop

Hardness

Testers. (Photos

by

Chris

Dilts)

perpendicular indenter _{slowly into} the surface

being

tested. Once the indentation has

been _made, the indenter is withdrawn and an empirical hardness number is either read

from a dial (which is arranged such that soft materials with

deep

indentations give low

hardness_numbers) or calculated based on the cross-sectional area ofthe impression. This

areais calculated based on themeasured diameter or diagonal

(depeding

on the shape of

the

indenter)

of the imposed indent left after indentation.

Thus,

the obtained hardness

numbers are dependent on the applied load and the shape ofthe indentation. Table 2.1

shows a comparison between penetration

depths,

material _thickness, and the standard

loads applied

by

commonly used hardness testers and a thin film

indenting

device,

a

seen in the _{table, loads} for nanoindentation ofthin films are much lower than those for

standardhardnesstesting. Because actual penetrationdepths areindicativeofthematerial

being

indented,

this tableis _only meantto establish a general idea oftheindentation sizes

tobe expected.

Table 2.1 Comparisonofpenetration

depths,

material_thickness,andtheloads

applied

by

severalhardnesstesters.

Hardness Test Standard Load Penetration Depth Material

Thickness

Brinell 500_kg Specimenthicknessmustbe

1500

kg

_(mm) >10x's thedepthofthe

3000_kg penetration.

Rockwell

A 60

kg

C 150_kg

D 100

kg

B 100_{kg (mm)} C(

F 60

kg

G 150

kg

E 100_kg

Vickers 1 120

kg

typically <0.5mmonthe diagonal

Knoopmicrohardness 10g-₅

kg

generally, 0.01mm-0.1mm

CC

Nanoindenter ~1_nkg 1p.

T(

in incrementsof1 |i) average 180u

2.1.2 Nanoindenter

Another type of hardness tester is the nanoindenter. The nanoindenter differs

from traditional hardness testers in its structure and application. The _{shaft, to} which a

diamond indenter is fixed at one end, is vertically held inplace via delicate leafsprings.

magnet

suspending

springs _~\

laoding

coil

m^WL

capacitance

^?\-displacement

gage

diamond indenter

X-Ymotorized_positioningtable

Figure 2.2 A Nanoindenter.

displacement is monitored capacitively. From the force displacement data a

loading

and

unloadingcurve similarto thatin Figure 2.3 canbe generated,wheretheload is plottedas

ForceCurve

o

unloading curve

loading curve

dP/dh

hplastic hmax

Displacement,h

afunction ofthe depth of

indentation.

_From this curve it is possible to ascertain certain

mechanical properties ofthe material

being

indented. Two such properties that can be

determined are the elastic modulus andthe hardness ofthematerial. Note

however,

this

is only possible if the

tip

shape is well characterized on the scale of indentation5. In

Figure 2.3 the final depth is representative of the total displacement of the indenter

relative to the initial position ofthe surface. Asthe load is employed on the sample via

the _tip, the sample will

initially

deformelastically. With further

loading

the deformation

becomesplastic. _{Upon unloading}theelasticdeformation isrecoveredthus theindenter is

being

pushedbackout ofthe sample

by

the elastic_{restoring forces.} This implies that for

this region ofthe curve there is a constant contact area betweenthe

tip

andthe sample.

Constant contact area implies linear _unloading, which is observed for over most ofthe

unloading region for most metals. As the

tip

continues _{to retract,} the contact area

between

tip

andsampleis lost.

Therefore,

theplastic depth canbe defined asthedepthof

the indenterin contact withthe sample under load. Theplastic deformation isthusfound

by fitting

a linetangent to the _unloading curve at maximumload and _{extrapolating it} to

zero load. The abscissa

(x-intercept)

is the plastic depth. From the plastic depth and

compliance, the hardness and modulus of_{elasticity, respectively,} can be found ifthe

tip

shape is well characterized on the scale ofindentation. This method is based on the

notion that the material will conform to the shape ofthe indenterto some

depth;

and if

Although an indenter of _any shape can be used in _{nanoindentation, the} most

common shapetouse isthe three-faceBerkovich

indenter,

athreesided_pyramid,because

ofits small contact area. _{Since any} three nonparallel planes intersect ata single_point, it

is relatively simple to grind a

tip

on an indenter of a three-face Berkovich indenter

geometry.

Preferably

the three-faced Berkovich is the ideal geometry,

however,

invariably

the

tip

ofthe indenter is dominated

by

asperities which makes it difficult to

maintainits idealgeometry6'7. Becauseof_this,theactualdepthofindentationproduces a

largercontact areathan expectedforanindenterwith anideal shape. To compensatefor

this an effective

depth,

heff

is used to calculate the contact area . The effective depth

indicates the depth ofindentation that would be created

by

an

ideally

shaped indenter

while also_producing the contact area created viathe non-ideal

tip

for a plastic

depth,

hp

Figure 2.4 shows a cross-section of an indent and identifies the parameters used in this

analysis. Thetotaldisplacementat_anytime

during loading

iswrittenas

Kff=K

+

K

(2.1)

where

hs

isthe displacementofthe surface at theperimeter ofthe contact. Atmaximum

load the load and displacement are,

Pmax

and /,_. _{respectively,} andthe radius of the

contact circleisa. The final depth isthe residualhardness impressionwhentheindenter

heff

v

VA

K

Figure 2.4 Across-sectionof anindent.

For a Vickers indenter of ideal pyramidal _geometry

(ideally

_{sharp tip),} the

projected contact areato_{depth relationship is}givenas '

jA=j245heJf

(2.2)

Since the area to _{depth relationship} is equivalent for both the Berkovich and Vickers

pyramids, Equation 2.2 holds for the Berkovich indenter as well. A more detailed

discussion on the Doerner/Nix method used to determine the area function for the

Berkovich

indenter,

whichassumesthat theelastic modulusis independentofindentation

Stiffness

Typically

calibrating the shape ofan

indenter,

such asthe Berkovich pyramid, is

done

by

_optically

imaging

the indent.

However,

imaging

hardness impressions on a

nanometer scale can be

time-consuming

and difficult.

Clearly,

insufficient

imaging

techniques needed to _precisely determine the dent shape and area can result in an

inaccurate depiction ofthe indenter shape and _{therefore, producing incorrect hardness}

measurements. Because of

this,

it is more practical to use a means other than direct

observation

(imaging)

to determine the contact area of small indents. As a _way of

alleviating the problems associated with _calibrating the shape of an

indenter,

the

following

technique was introduced for a typical Berkovich pyramid as well as other

indentershapes .

Once contact between the

tip

and sample have been established, the force

gradient, dP/dh is entirelyequivalentto thecontact stiffness.

dP

dh

Where P and h are the load and the depth of indentation respectively. Ifthe contact

1T1 Q

radius, ais

known,

then themodulus canbe deducedviatherelation '

dP

-I-Where E istheeffective modulusforthesystemdefined

by

E =

1-O0

1-u

(2.5)

Where u0 and

E0

are Young's Modulus and

Poisson'

s ratio of_{the material, respectively,}

ando andEare Young's Modulusand

Poisson'

sratio ofthe

indenter,

respectively.

ElasticModulus

Asmentioned earlierthe elasticmodulus can be determined fromtheslope ofthe

unloading curve.

By

further extending Equation

2.3,

Loubet et al showed that the

slope ofthe _unloading curve could be modeled

by

treating

the indenter as a flat-ended

elastic punch. Thus_{the unloading} slopeisgiven

by

dh

(2.6)

the constant

p

for a cylindrical punch is

2/

Vrr

.

King

later showed that (3 only

Circle p=(i.o)-JL

V7T

Square p=

(1.011)

2

Triangle

p

=

(1.034)

V7I

2

Theorigin ofEquation 2.6comes fromthe

theory

of elastic contact. Whileitwas

1 7

originallyderivedfora conical

indenter,

this_{Equation holds equally}well forcylindrical

and spherical shaped indenters. It has also been speculated that _{Equation 2.6 may be}

appliedto other geometry's as well . It was argued that significant deviations fromthe

behaviorpredicted

by

Equation 2.6 should not occurforindentersof pyramidal shape and

that this Equation works well for at least some indenters that can not be described as

1 8

bodies of revolution. This was demonstrated

by King

who showedthat for flat ended

punches with squared and triangularcross-sections the deviations fromEquation 2.6 are

1.2%and

3.4%,

respectively.

The inverse ofEquation

2.6,

the stiffness, 1/5 =

dh/

dP is _{the compliance,} C of

thesystem. The complianceistheamountof

flexibility

thesystemhasandis equaltothe

machine _compliance,

Cm

plus the compliance ofthe indenter and the _material, Cindent.

Mx19

showed in his work, that the compliance ofthe nanoindenter itselfcontributes to

the measured displacement at high loads. In other _{words, any yielding} of_{the material,}

yielding, as would be_expected, contributes more with increased loading. Because ofthis

itispreferabletowriteEquation 2.6 intermsofthecompliance

by

_{modeling the}machine

complianceandtheindenter/materialcompliance astwo springs inseries suchthat

dh dh , s dh ,

, s dh

= (m)-\

(indenter)

.

dP dPy ' dPy ' => _dP

t \ an ,. s an

H

+

"^

{indenter)

^

=

c=Cm+Cmdmier (2

7)

then

by

_{combining Equation 2.6}and2.7we get

dh__

1

^~Cm+(3-/I_

C'+

a.n r-*

(2-8)

Furthermore,

this Equation can now be written in terms of the effective depth

by

combining Equations2.2and2.8.

dh 1

C,+

* "

\^iE-K,

^

Rearranging

intheformofastraightline y=_mx+b

, we obtainthe

following

dh 1 1

. u

+c.

(2.10)

dP

pV245 E'

Thus,

showing

that,

ifthe modulus is _{constant, the} measured compliance should _vary

linearly

withrespectto thereciprocaloftheeffectivedepth. Therefore

by

_{plotting dh/dP}

vs.

\jheff

the slope ofthe line will give

1/

p-\/24.5

E'

from which the elastic modulus

ofthe sample canthen be calculated andthe intercept oftheplotyields adirect measure

ofthemachine_compliance, Cm.

Another Method of

Calculating

The Area Function

In_{their studies,} OliverandPharr disagreed withtheNix- _{Doerner assumption}

of

linearity

ofthe _unloading curves for most metals. Through many tests

they

showed

that _unloading curves are _rarely

linear,

even in the initial stages of_unloading and that

unloading data can be better described

by

power laws.

Thus,

they

addressed their

concerns

by introducing

a new technique _{for analyzing indentation} load-displacement

data. Thismethodis thetopicofdiscussion forthis section.

In orderto findthe area functionand themachine _compliance, Oliver and Pharr

suggest that

by

_using a metal oflow

hardness,

like _aluminum, large indentations can be

made and more accurate values for

Cm

are obtainable. This is seen

by

_examining

Equation 2.8 for which the second term approaches zero as the area of indentation

becomes greater. Also for large aluminum

indentations,

the area function for aperfect

Berkovich indenter can be used as an initial guess for the area function with initial

aluminum. These values were then used to compute the contact areas for several

indentations

by

_rewritingEquation 2.10 as

dh

_ _

-Jn

^

=

C=C'"

+

^jg

(2-11)

fromwhich an initial guessatthe area functionwas made

by fitting

A as afunctionof

hp

toan eighth-orderpolynomial

Ah)=^k]

+

cX

+ +cX4+ +

Cshr

VA2)

where the first term describes a perfect Berkovich

indenter;

and

Cj

through

Q

are

constants that

help

in

describing

how the indenter shape deviates from Berkovich

geometrydueto

blunting

atthe tip.

Because the area function influences the values of

Cm

and E* the new area

function was used to repeat the procedure for several iterations until convergence was

achieved. Oliver and Pharr continued on to check the _validity ofthe constant modulus

concept

by

_applying the above method to materials of greater hardnesses for which

Note

however,

Cathcart suggest that thiscorrection forthearea function is not

particularlyimportant for soft metals such as annealed copperor _aluminum,but shouldbe

appliedwhen

indenting

harder_materials,metals and ceramics.

Hardness

As noted _earlier, the hardness of a material is defined as the force divided

by

the

projected area ofthe indentation and can be calculated from the

loading

portion ofthe

load vs. displacement curve. This can be done

by dividing

the indentation load

by

the

indentation contact area at each point _along the

loading

curve. This will permit the

calculation ofthehardness as afunctionoftheindentation depth.

The problem associated with _measuring the hardness of a thin film material via

nanoindentation, is that the substrate _may influence the measurement.

Thus,

it is

23

2.1.3 Surface Profiler

A surface profiler (see Figure

2.5)

is similar to the nanoindenter in that it also

appliesits loadvia a_vertically heldshaft, towhich adiamond

tip

is attached. The sample,

stylus

free standing

structure

substrate

Figure 2.5 Surface Profiler.

a

free-standing

_structure,is fixedatbothends. Asthestylus-type profiler applies various

loadstothe bridgethevertical position ofthe

free-standing

sample undereach

loading

is

recorded.

Using

a mechanical analysis the Young's Modulus for the material and the

effects ofresidual strains, ifany, can be calculated. The procedure is one of iterations

and is as follows.

First,

_using atwo-dimensional finite-element _simulator,

SUPERSAP,

the beam-like structure is modeled. Because SUPERSAP does not provide a direct

throughan artificial use of an elevated

temperature,

but firstthe stresshasto be obtained

througha separate_measuringprocess . Thestressisrelatedtotemperature

by

G0=(aAT)Ey

(2.13)

Within SUPERSAPthisresidual stressisentered

by

_varyingaAr(thethermal-expansion

coefficient and global temperature variation _{respectively)} and _guessing at Young's

Modulus,

Ey

This modulusisthenusedintheEquation

hB-h=

^K

,

(2.14)

E

where

h0

andh aretheheights oftheunloaded andloaded structurerespectively, Fisthe

force created

by

the stylus, and K is a_{proportionality} constant with units ofreciprocal

length.

Re-writing

this Equation inthe

following

form allows forthe calculation ofthe

nextiterativeguessfor

Ey

*.~1

(2-l5)

Where dh/dF is the slope of a plot generated from the beam height versus the stylus

force. Thisprocessisrepeated untilthe_starting

Ey

convergesto the iterative Ey.

Althoughthese

devices,

the nanoindenter andthe surface _profiler, are capable of

measuring mechanical properties of thin

films,

as itbecomes _necessary to measurethe

hardness ofultra thin

films,

such as in the computer

industry

and _{microsystems,} new

techniques areneeded toperformmeasurements at evenshallowerdepths.

Thus,

thishas

prompted others to

develop

methods ofindentation to depths as lowas lnm through the

use of AFM'

s. The

following

sectionis intendedto introducethereaderto theevolution

oftheAFM.

Furthermore,

toassistin establishingthegrounds on whichtheidea's ofthis

thesis were

developed,

adetailed overview onhowtheAFM operatesisalso given.

2.2

Scanning

Probe

Microscopy

Scanning

Probe

Microscopes,

(SPM)

are a

family

ofinstruments withamultitude

of capabilities. SPM'sare

imaging

toolswith vastdynamicranges which spantherealms

of optical andelectron_microscopes, while_provdingtrue three-dimensional images- from

atoms to micron-sized protrusions on the surface of a cell. Some act as profilers with

uncannyresolution and in some cases are capable of_measuring physical properties like

surface conductivity, static charge

distribution,

magnetic fields and elastic moduli.

Belowisageneralized schematic

illustrating

(Figure

2.6)

thecomponents containedin all

One ofthe first SPMinstruments capable of

directly

_obtaining real-space images

of surfaces with atomic resolution is the _scanning

tunneling

microscope, STM. The

STM,

was developed in 1981

by

Dr. Gerd

Binning

and his colleagueHeinrich Rohrer at

the IBM Zurich Research

Laboratory,

Forschungslabor25 Five years later Binnings and

Afeedbadcsystemtocortrol

theverticle postion ofIhe tip.

Acomputer systemthatdrivesthe

scanner,measuresdataand convertes

fedcfatoanimage.

Avvayof_sensing ttevemclepcdticn

ofthe tip.

Apiezoelectricscanner which mo\esthe_tipover thesampleina raster

pettem.

Asterptip

AnX-Y-Zm_to__d

pcsitioningtable to

bring

thesampleintothe general_vicinityofthe tip.

2.2.1

Scanning Tunneling Microscope,

_STM

STM's are part of a

family

of

instruments,

knownas _scanningprobe microscopes

(SPM),

usedin _studyingthesurface properties of materials atthe atomicto micronlevel.

Because the operation of an STM depends on the use of a _{sharp conducting (or}

semiconducting)

tip

and the induction of an applied bias voltage between the

tip

and sample _surface,

they

can _{only be} used to image surfaces which are constructed of

electrically conductive (or semiconductive)materials.HowdoesanSTMoperate? Asthe

conducting

tip

is brought within _{approximately 1 OA} of the samples surface, electrons fromthe surfacebeganto "tunnel"throughthis _{1 OA gap} and intothe

tip

(thisprocess can

alsotakeplaceintheopposite direction

depending

onthebias ofthevoltage). The

tip

of the STMisthenpassedoverthesample (orvice_{versa) in}ahorizontalplane whichcauses

the currenttovary. Thisvariation, relayed through the piezoelectric, constitutesthe data

set that is representative ofthe topographic image ofthe samples surface. In other

words, the STM senses the number offilled or unfilled electron states near the Fermi

surface, withinan_energyrange determined

by

thebias voltage andratherthan_measuring

the physical

topography

of the samples surface, it measures a surface of constant

tunneling

. It was the invention of this

instrument,

the

STM,

that laid the ground work which ledto

Binning

et al.'s development ofthe atomic force microscope

2.2.2 AtomicForce

Microscope,

AFM

The atomic force microscope,AFM described here is for commercial use in

ambient _air, and is produced

by

Digital Instruments

Inc.,

Santa

Barbara,

CA27'28'29,30 .

Figure 2.7illustratesthemajor components containedinanAFM. Thecantilever and

tip

Laserbeam

photodiodeAandB

\_k

.ft

A-Bvertical deflectionvoltage

\

\

piezo mirrors

mbe

v'oTTs

.VD

converter _;

setpomt

voltage

r \

computer :

v

sample

Figure 2.7 Schematicof anAtomicforceMicroscope.

assembly isattachedto acoarse_positioning system so thatthe

tip

can be moved intothe

2500x

40x

Figure 2.8 An SEMmicrograph of a cantilever

tip

assembly. Silicon cantilevers with

integraltip.

assembly). The sample is attached to a piezoelectric scanner, which guides the sample

under the

tip

in a raster like pattern. In some assemblies the cantilever

tip

_{assembly is}

attached to the piezoelectric, in which case the sample is thenmounted on a flat surface

and the piezo moves the

tip

over the sample. In either case the same end results are

achieved, but the latter will be the type that will be referred to in this discussion. The

sharp tip, which lies at the free end of a microfabricated flexible cantilever, is scanned

across the samples surface in the X-Y plane in a raster like pattern (or the sample is

moved under the _{tip) causing} the cantileverto bend ordeflect. The cantilever deflection

technique called

beam-bounce

_{detection or laser deflection technique (shown in}

Figure

2.9)

which isa _way of_sensingthevertical position ofthe tip. Whilethisinformation is

Laser beam

PSPD detecter

^~\^

trrM

'B*

\

cantilever

mirrors

piezo

tube

sample

Figure 2.9 Schematic of beam-bounce detection technique used for

detecting

cantilever deflection.

fed back to the computer _{system, the} piezo also feeds back signals

informing

the

computer system of its vertical

(Z)

location. In other words the computer system (or

digital signal _processor,

DSP)

controls the Z-position of the piezo based on the

cantilevers deflection error signal. Most AFM's use optical techniques to detect the

laser diode

(light-emitting

diodes or LED's with 5-mW max. peak output at

670nm)

is directed

by

a_prism, at an angle ofabout 10 to the

horizontal,

onto the back ofthe free end ofthe cantilever. The reflected beam is bounced off the vertex ofthe cantilever

through a mirror onto a position-sensitive photodetector (PSPD). A PSPD is a split

photodetector withfour quadrants capable of_{measuring displacements} oflights as small

as 10A. The differential signal from the

top

(T)

and bottom

(B)

photodiodes

[(T-B)/(T+B)]

providestheAFMsignalwhich isa measure ofthecantilever vertical position. This vertical movement can be measured to a _sensitivity of sub-angstroms. This signal

canbeused as inputtoafeedbackcircuittocontrolthevertical positionofthepeizotube

scanner whichtellstheAFMto operateinone of_{two modes,} constant-height or

constant-force. In the constant-height modethe feedbackgains are

low,

so the piezo remains at a

nearly constantdeflection signal (thereforethe _{force is changing)} suchthatthe cantilever

deflection data is collected as the cantileveraccommodates thechanges in

topography

of

the samples surface. In the constant-force mode the gains are

high,

so the piezo height

changes

keeping

thecantileverdeflection nearlyconstant (thereforetheforce isconstant), and the change in piezo height is collected

by

the system. In either case the computer measures the dataoutput from thepiezo and _sensing

device,

andconverts the datainto a

map of

topography

of the materials surface (i.e. generates an image of the samples

surface).

The AFM has two modes of_operation,

tapping

and _contact, both from whichthe

oscillated at its resonant

frequency

with a high amplitude (on the order of

1000A,

(0.1pm)). The cantilever is brought into the _vicinity ofthe sample _causing the

tip

to

touch the sample

during

each oscillation (hencethe term

tapping

mode). The changes in

oscillation, due to the

tip

_contacting the materials _surface, allows the computer to

generateatopographic imageofthesample.

However,

in

tapping

thevertical forceofthe

oscillating cantilever sometimes causes deformation in the surface of a soft or elastic

material, thus the _{resulting images may portray}topographic and elastic properties ofthe

samples surface. In contactmodethetip, which _gentlymakes soft physical contact with

the samples _surface, is dragged across the sample. The soft

tip

contact allows the

cantileverto glide overthe samples surfaceinsuch a_way astoaccommodatethechanges

in_geometry ofthe samplessurface, hence producing atopographic imageofthe samples

surface. It is in this mode that this thesis attempts the analysis of nanomechanical

properties of thin films via a process called nanoindentation.

However,

before

introducing

the methods used

by

thisthesistoperform nanoindentation viathe

AFM,

the

next sectiondiscusses howothershave attempted_{this task using the}AFM.

2.3

Applying

theAFMas a

Nanoindenting

Device

Colton and

Burnham31

configured anatomic force microscope suchthat it would

measure the force between a cantilever

tip

and a sample surface as afunction ofthe

interface. More precisely,

they

were able to measure the elasto-plastic properties of

materials

(including

elastic modulus and

hardness)

via_{nanoindentation, the} surface forces

associated with tip-surface interaction (Van der Waals

forces),

and the adhesive forces

associatedwithsmall contacts.

The cantileverbeamused

by

Burnhamet. was made oftungstenwire coated

with a thin layer of gold. The _tip, which was made from tungsten _wire, was chosen

because its high elastic modulus would minimize

tip

deformation

during

indentation.

They

approximated the _geometry oftheir

tip

by

_{using scanning} electron micrographs.

For simplicitytheapparatus

they

used was operatedin air under ambient conditions. The

samples indented included: _graphite, an elastomer(arubber

band),

and goldsamples.

In their results it was shownthat the elastomer behaved almost

ideally,

whereas

the graphite exhibited some minimal hysteresis upon unloading. This slight hysteresis

was attestedto the _strong adhesion forces between the

tip

and the graphite.

Using

this

informationand _modeling the

tip

_{using Sneddon's} solution for anindenter of_arbitrary

geometry,the

following

expression was usedto calculatethemodulus of_{elasticity for}the

graphite and elastomer samples , (notethat this solutionwas usedforthe elastomer and

graphite samplesbecausetheir

loading

and_unloadingresponses were

ideally

_elastic),

F=_2Erh/(l

V)

whereFisthe applied

load,

Eisthemodulus of_elasticity, r is the radius ofthe indenter

tip, h is the depth of _penetration, and u is Poisson's ratio for the material. Once

determined,

the modulus for the graphite and the elastomer were compared with

comparable materials(because literaturevaluesforthematerialsused could notbe

found)

likecarbon/industrial_graphite's, and elastomers such asisobuyleneandisoprene. Forthe

gold,whichbehaves likean

ideally

plastic_material, Burnhamet.

al.35

notedthatforsmall

contact areastheapparenthardnesswas showntorise abovethebulkvalue36.

Otherwork inthis area was introduced

by

Bhushan and

Koinkar57

Throughthe

modification of a commercial atomic force microscope (Nanoscope III from Digital

oo

Instruments, Inc.,

Santa

Barbara,

CA)

they

developed a method for _measuring

indentation hardness to depths as low as 1 nm. Previous hardness measurements

documented support indentation depths of 20 nmor more . The indentation technique

used allowed hardness measurements of surface monolayers and ultrathin films in

multilayered structures at _very shallow depths and low loads (in comparison to other

works). The indentationswereperformed on a polished silicon sample

by

_using a

three-sided pyramiddiamond

tip

mountedon agold-plated304 stainless-steel cantileverwith a

stiffness of45 N/m.

By

using anormal loadrange of10-150 uN and

by

_settingthe scan

size to zero,

(allowing

the

tip

to _continuously press into the surface of the sample for

approximately two seconds), indentations on the surface ofthe sample were generated.

thencalculated

by dividing

the indentation load

by

theprojected residual _area, created

by

thediamondtip.

For rough _surfaces, such as magnetic disk surfaces, Bushan et. used a

subtraction technique to _{determine hardness} measurements.

They

overlapped a small

region on the original image (before

indentation)

with the _{corresponding} region on the

indented

image,

such_that, the original image was shifted the required translational shift

until the surface features correlatedto thoseuntouched onthe indented image.

Next,

the

original image was subtracted from the indented image. The indentation was then

measuredfromthesubtractedimage.

More recent developments inthe area ofnanoindentation have been introduced

throughDigital Instruments . Through a supportnote

they

introduce anew software and

hardware package which can be added to _existing Dimension 3000 systems for

nanoindentation. The support note describes basic nanoindentationprocedures _using a

three-sidepyramidal diamond

tip

mountedto a metalfoil cantilever. The spring constants

for the cantilevers are said to range from 100 to 400 N/m. In short their procedure for

indenting

basically

entails

installing

a diamond nanoindentation _tip,

imaging

the sample

to locatean area of

interest,

then _enteringindentationmode and

indenting

_{the surface, the}

latter

being

thenew software addition. Oncetheindentation is completedthe indentation

is imaged in

tapping

mode. This image is then measured in order to establish the

tip

geometry. From these measurements, and through the use of

trigonometry,

the contact

area,A canbe calculated.

Using

Hooke'sLaw: F= kx

forthe cantilever andx isthe cantilever

deflection,

the maximum

force,

Fapplied

during

indentation can be calculated.

Thus,

by

taking

this force and

dividing

it

by

the contact

area, the

hardness,

Hofthe sample canbe determined.

T , 42 4344 .

In each case ' ' _imaging techniques were utilizedto determinethe _geometry of

their indenter. Each uses a three-sided Berkovich type indenter tip, forwhich the actual

geometry ofthe

tip

isnotwelldefined.

Therefore,

to definetheshape ofthe

tip

Burnham

et. al. measured the

tip

_{geometry using scanning} electron _micrographs, whereas

Bhushanet. al. andDigital Instruments chosetoextractthe indentershape via images

obtainedfrom theAFM. Since the indents are_{very small,} bothmethods of measurement

in orderto establishthe tips _geometryprove to be difficult because the small indents are

very hard to locate.

Also,

with the AFM if one is not careful, scanning the samples

surface could causedeformationto theindentation_{thus revealing}afalserepresentation of

the

tip

shape.

This thesis introduces a method of nanoindentation for measuring hardness and

elastic modulus ofthinfilmsamples whichalleviates theproblems associatedwith image

measurements

by

_combiningthe analyticalmethods used

by

Nix , withthe experimental

methods used

by

Burnham et. _al49, Bhushan et. and Digital Instruments51. This is

accomplished

by

_using an indenter

tip

of known geometry. Similar to traditional

hardness testers

(Brinell, Rockwell,

etc.) the geometry chosen was spherical. Based on

are calculated. The proceeding section explains the

theory

behind the methods used to

3

Experimental

In order to use the AFM as a_{nanoindenting}

device,

there are several things that

need to be considered. First a material _{for indentation} must be selected. Next an

appropriate cantilever and

tip

_assemblymustbe constructedand its spring constant must

be determined. It is atthis pointthat the material can be

indented,

a force curve can be

generated, andthemechanical propertiesofhardness andthemodulus of_elasticityofthe

material can be ascertained. The

following

sections are detailed discussions onhowthis

was accomplished.

3.1 Materials selection.

The main concern_regarding material selection isto construct a cantilever and

tip

assembly strongand stiff enoughto _{plastically deform}thesamples surface withoutthe

tip

breaking

or the cantilever bending.

Thus,

it is safe to assume that the

tip

must have a

greater modulus of _elasticity than the material

being

indented,

and the cantilever must

have a_reasonablyhigh spring constant. Below is a

listing

ofproposed cantilever and

tip

materials to beused totestabulk aluminum

(2024)

_sample, an aluminum film (2 \xm in

thickness)

depositedonto asilicon waferand a elastomer(arubber

band)

stuckto ametal

substrate via double sided tape. Silicon nitride and silicon are included in this

listing

becausemost cantilever assemblies inuse

today

arefabricated from these materials. The

Cantilevermaterialsinconsideration:

Siliconnitride

Silicon

Tungstenwire

Tip

materialsin consideration:

Siliconnitride

Silicon

Ironbeads

Sphericalglass beads Industrial diamond

Tungstenbeads

Ruby

beads

Dueto thenature ofthematerials chosentobe indented(aluminumand_rubber),it

was decided that a silicon cantilever would suffice as the cantilever material. The

tip

howeverwastobe constructedfroma_{very high}modulus material. Theideal indenter

tip

wouldhavebeenonemade of

diamond,

duetoits large modulus and_{high hardness.}

Also,

due to the nature in which diamonds cleave when

they

are _{struck, obtaining} the ideal

pyramidal shape _geometry would have been oflittle concern.

However,

as discussed

indenter. In _{addition, mounting} and _polishing a diamond ofthe size required would be

extremely difficult.

Thus,

for the purpose ofthis

thesis,

a

tip

of known geometry was

selected. The shape chosen was spherical and the material of choice was tungsten.

Tungsten was chosen because it has the highest modulus of all metals (50 x

106

psi or

345 GPa).

The proceeding sectiondiscusseshowanew cantilever_assembly was constructed

by

placingtungstenbeadsonto an_existingsiliconcantilever.

3.2 Cantileverand

tip

construction

Before a cantilever _assemblycan be constructed, there are several stepsthat must

be taken to prepare the AFM. As mentioned _above, most cantilever assemblies are

constructed of silicon or silicon nitride. Sincethematerialselectedforthecantilever was

silicon this made it possible to utilize an _existing cantilever to which a new

tip

was

attached. This could be accomplished either

by

_removing the old

tip

from the _existing

cantilever and_replacingitwithanew oneor_{simply attaching}anew

tip

in front (closerto

the free end ofthe _cantilever) ofthe oldtip. This last method is suggested since it is a

non-destructive method, it abates the _possibility of

damaging

the cantilever.

However,

one must insure that the new

tip

is largerthan the _existing

tip

so that

during

indentation

the surface_only encountersthe newtip. The

following

sectionsdescribethe construction

3.2.1

Loading

theAFM

tip

holderand_placingthecantilever onto thepiezoelectric.

Beforethecantilever assemble canbeconstructed andthe sample

indented,

the

tip

must be installed onto the piezoelectric. The cantilever installation fixture shown in

Figure 3.1a (ablack 2.5 inchdiameteranodized aluminum

block)

supports the

tip

holder

to which the cantilever

tip

_{assembly is} mounted. Notice that the installation fixture has

three stations. The station positionedat six o'clock in Figure 3.1a is used for standard

AFM _{probing; the} station positioned at two o'clock in Figure 3.1a is used for fluid

imaging

contact

AFM;

and

lastly,

the station positioned at 10 o'clock in Figure 3.1a is

intended foruse in future development oftheAFM. Ofthese three stationsthe one that

will be referenced _to, in the analysis ofthis thesis, will be the station positioned at six

o'clock(the standardAFMstation).

ThestandardAFMstationis distinguished fromtheothers

by

a smallblock inthe

center ofthe gold connector. This block assists the user when _aligning the cantilever

substrate in its correct orientation on the AFM

tip

holder. The

tip

holder is shown in

Figure 3.1b. The

tip

holder is installedontotheinstallation fixture suchthattheAFM

tip

holder's spring clip faces upward, andits sockets (on its reverse _side) matchthe pins of

the AFM installation fixture. Due to the asymmetrical alignment of_{the pins,} the

tip

holder can _only be mounted in one orientation. Once the holder is mounted on the

installation fixturethecantilever with probe

tip

is installed intotheAFM

tip

holder. This

is done

by

pressing down on the back end ofthe _{spring clip} and _{gently sliding it} back.

back end is butted flush against the back end ofthe grooved area and against one side.

andthecantilever _{is pointing in}theoppositedirection. The substrate isplaced suchthat

Figure 3.1 Cantilever installation fixture (a 2.5 inch diameter anodized aluminum

block),

and

tip

holder. (Photo

by

Russell

O'Neal)

thecantilever

tip

is

facing

upward. Thisisevident whenthere is a visible "T" seen onthe

top

of the substrate which representsthe cantilever mountedontothe substrate. Once the

piezoelectric tube is_rigidly mounted nearthe

top

ofthemicroscope. When voltages are

appliedto theXand Yelectrodes onthepiezoelectric _tube, the tube deflects

horizontally

to produce a precise raster-like scan overthe sample surface. Voltages applied to the Z

electrode, onthepiezoelectric_tube, control thevertical height oftheprobe. This voltage

which canbeconverted intoa measure of

length,

tellsus wherethe

tip

is inrelationto the

samples surface.

However,

because the cantilever sometimes deflects when its

tip

encounters certain surface features of the sample, in order to detect the true vertical

position ofthe cantilevers_tip,the systems lasermustbe setsuchthat itis aligned_atop of

the cantilever and

directly

over its tip. This will enable the system to correct for _any

cantilever deflection in its measure of vertical deflection. (The semantics behind this

method is discussed ingreater detail in section 2.2.2 Atomic Force Microscope). Once

thelaseris alignedtheSPM Stage Parametersmustbeadjusted. These controlsandtheir

functions are asfollows :

Sample clearance

-this functioncontrols the height ofthe probe

tip

overthe sample

priorto engagement. (Agoodinitial settingis 1000 p_m).

SPMsafety this functioncontrols the height oftheprobe

tip

over the sample when

the fast approach changes over to the slow approach. (A good _{initial setting is 100}

SPMengage_step

-thisfunctioncontrolsthe _stepsize ofpiezoelectric

during

engage.

(Agoodinitial_settingis 1 pm).

Load/Unload height

-this function controls how high the

tip

will move above the

previously

defined,

or

found,

sample surface

height,

and is used for changing the

cantileverorthesample. (A goodinitial setting is 2000 pm).

Once thelaserhasbeen aligned andSPM Parameters have beenset, the locate

tip

command intheStage menu can be initiated. This command allowsthe optics to locate

the

tip

position (Z

height)

andrecord it inmemory.

Next,

thefocussurface command in

the Stage menu can be initiated. Just as with the locate

tip

command, this command

allowsthe opticstolocatetheposition ofthesamples surface andrecordit in itsmemory.

All ofthe above steps are taken to insure that the system is aware ofthe tip's location

with respect to the sample _surface, inorder to reduce the _possibility ofthe piezoelectric

engaging too fast and _causing the cantilever

tip

to slam into the sample _surface,

thus,

leading

toabroken

tip

or cantilever.

Prior_{to utilizing} thecantilever _assemblyas an

indenter,

the _spring constant, k for

the cantilevermustbe determined. The spring constant is needed for_plotting goodforce

vs. displacementcurves, sincetheappliedindentation forcesaredependenton

k,

suchthat

f

= _{kx. Discussed} here is _{a method} for calculating k _{which was} introduced

Cleveland et. al. , and is of a nondestructive nature. Other destructive methods have

beenintroduced butthesemethodswill notbe discussedhere55,56.

3.2.2

Determining

the_{springconstant,k of}thecantilever_{assembly using}a

nondestructive methoa .

Most microfabricated cantilevers are either V shaped58,59

or simple beams of

rectangular shape . The

following

spring constant calculation will be based on a

rectangular cross-section cantilever. For an end-loaded cantilever beam of rectangular

cross-section,the _springconstantis given

by

Ef3w

*=

-V

(3.1)

4/

Where k is the _spring constant, E is the elastic _modulus, t is the thickness of the

cantilever, w is the width and / is the length ofthe cantilever . The beam can be

modeled as a _spring of stiffness kwith its effective mass dependent onthe _geometry of

the beam. This effective mass is m*

0.24mb

, where mb is the mass ofthe cantilever

beam. _{When adding} an end mass Mto the

beam,

theresonant

frequency

is given

by

the

V~2ti

~

2n\ M+m*

^

'

rearrangingintheformof _y=_{mx+b the}

following

expressionisobtained

M=

k(2nv)~2

-m*,

(3.3)

Equation 3.3 showsthatifseveral knownmasses are attachedto theend ofthe _cantilever,

andthe new resonancefrequencies are _measured, a plot ofMvs.

(2.tv)~

would yield a

straightlinewitha slope equivalentto

k,

the_spring constant,andthenegative y-intercept

wouldbetheeffective_mass,m*.

In preparation for

determining

the _spring constant, a small sample of tunsten

beads

(masses),

of sizes _ranging from 10 to 30 pm in

diameter,

were dispersed on a

mirror polished substrate. This substrate was placed onto the table ofthe AFM beneath

thepiezoelectric. In

tapping

(non-contact)

mode underthe view menuthe cantilevertune

optionwas selected. Itis herethat the initial resonance

frequency,

_v0was determined

by

selecting auto tune. Under the stage menu the _{first line entry in} the SPM parameters

windowisthesample clearance. Thisvalue,whichdefinestheheightofthecantilever

tip

overthe sample priorto engaging, is normally setat 1000.0pm. This valueis decreased

such that when the focus command is enabled the piezoelectric will

bring

the probe

cantilever and beadsto beviewed simultaneously. Note

however,

this parameter should

be changed _gradually so as not to crash the cantilever into abead orthe substrate while

the

tip

is descending. In this case 60pm was used because the diameter ofthe beads

being

used were 30pm in diameter maximum. This would allow the piezoelectric to

bring

the probe (cantilever

tip)

within 60pm of the substrate and within 30pm ofthe

largest beads when the focus surface command was used. Once the desired focus was

established, the cantilever length and the diameter ofthe bead to be picked _up was

measured.

Knowing

the manufacturers dimensions of the cantilever, a ratio was

established betweenthe screen cantileverlengthandthe actual cantileverlengthsuchthat

this multiplier could be usedto established the diameter ofthe bead with respect to the

actual length ofthe cantilever. The cantileverwas thenmaneuveredsuch that the

tip

was

centeredoverthe

top

ofthebeadwhich was measured.

Using

the_trackball,thecantilever

was then _gradually moved downward

by

the motion of the piezo (while watching the

monitor) suchthatanoticeable deflection inthe cantileverwas detected (this can alsobe

seen

by

_watching to see ifthe

detector,

red

dot,

moves from its center position). This is

anindicationthat thecantileverhasmade contact withthebead.

By letting

thecantilever

setinthispositionfor_{approximately} 30sec. thebead would_staticallyadhereto the

tip

of

the cantilever. To ensure thatthe beadwould adhere the room was kept

dry by

_using a

dehumidifier. Also_{to assist, the} beadswere heated in anoven at200 F for 20 min. and

thenleftto coolintheroomfor 5 min. After

letting

thecantilever set_atop ofthebead for

again a cantilevertune isperformed and a new

frequency,

_v, is determined

by

_performing

auto tune. [Note: ifno change in

frequency

indicated that the bead fell off, therefore

another one was picked _up and another auto tune performed]. Once the new

frequency

was _{recorded, the} bead was blown off _using a delicate burst ofcompressed air. This

procedure was repeated five times with the fifth bead

being

glued on for latter use in

indenting.

Thus,

by

_{using Equation 20} the masses were plotted with respect to their

corresponding frequencies from whichthe slope was equalto the _spring constant ofthe

cantilever.

3.2.3 _{Procedurefor placing}anew

tip

onto thecantilever.

Afterthe _spring constant ofthe cantilever_{assembly has been}

determined,

a bead

canthenbe_permanentlyplacedontotheendofthecantilever.A

drop

of_epoxy

(M-Bond-610 _adhesive) was placed adjacent (but not

touching)

to the bead selected to be

permanently adheredto the cantilever. The cantilever ismaneuvered again suchthatthe

bead andthe cantilever are both in view.

By

_going to the stage menu, selecting the set

reference command and then choosing origin, this will set the location which the

tip

is

now at as the origin (0,0). Now the cantilever is moved over to the _epoxy and _very

slowly the

tip

is dipped into the epoxy, saturating the tip. .

Working

swiftly, but

on_move, thecantilever moves backto the origin

(0,0)

where the bead was located.

Using

the trackball, the

tip

of the cantilever was centered

directly

over the bead and then

gradually moved downward such that a noticeable deflection in the cantilever was

detected Again, this is an indication that the cantilever has made contact with the bead.

By

letting

thecantilever set inthis position for _{approximately} 30 sec. the bead adheres to

the

tip

ofthe cantilever. The cantilever was then left to cure over night _{(the curing} time

can be shortened

by

_placing the cantilever _assembly in an oven at 160C for ~

one

hour,

as specified

by

the manufacturer63). Figure 3.2 shows an SEM micrograph of a silicon

cantileverwithatungstenbeadaffixedto its freeend.

1 60x 1250x

Figure3.2 An SEM micrograph _showing a silicon cantilever with a tungsten bead

3.3 Samplepreparation

The samples used in this experiment were chosen fortheir representative

nature of_exhibiting plastic and elastic behavior. The aluminum was expected to show

plastic behavior while the elastomer was expectedto show elastic. The aluminum thin

filmwas prepare

by

_sputteringa2pmlayerof aluminum ontoaround silicon wafer. The

elastomer (a piece of rubber

band)

was not _{specially prepared,} but it was affixed to a

metal substrate via. double sidedtape.

Also,

testedwas abulk aluminum

(2024)

sample

thatwas mountedin bakelitethenground andpolished.

3.4

Nanoindenting

_usinganAtomic Force Microscope

The process ofnanoindentation used here employsthe same technique as that of

traditionalhardnesstest(as discussed in section

2.1),

that

is,

imposing

ahardened sphere

underaknownload intothesurface of a material.When usinganAFM forthepurpose of

indenting

there arethree_primary stepsinvolved inthe sequence.

First,

intheReal-Time

mode,the sample mustbe indented.

Second,

also in

Real-Time,

a goodforce curve must

be obtained,and

last,

inthe Off-Line modethedata fortheforcecurvemustbe extracted

whichthe

loading

will yieldhardness