ATOMIC-SCALE FRICTION - Interface...

A T O M I C - S C A L E F R I C T I O NA N D S U P E R L U B R I C I T Y

STUDIED USING HIGH-RESOLUTIONFRICTIONAL FORCE MICROSCOPY

A T O M I C - S C A L E F R I C T I O NA N D S U P E R L U B R I C I T YSTUDIED USING HIGH-RESOLUTIONFRICTIONAL FORCE MICROSCOPY

PROEFSCHRIFT

TER VERKRIJGING VAN

DE GRAAD VAN DOCTOR AAN DE UNIVERSITEIT LEIDEN,

OP GEZAG VAN DE RECTOR MAGNIFICUS DR. D.D. BREIMER,

HOOGLERAAR IN DE FACULTEIT DER WISKUNDE EN

NATUURWETENSCHAPPEN EN DIE DER GENEESKUNDE,

VOLGENS BESLUIT VAN HET COLLEGE VOOR PROMOTIES

TE VERDEDIGEN OP DONDERDAG 13 MAART 2003

TE KLOKKE 14.15 UUR

DOOR

MARTIN DIENWIEBEL

GEBOREN TE LICH IN 1971

Promotor: Prof. dr. J.W.M. Frenken

Referent: Prof. dr. P.H. Kes

Overige leden: Prof. dr. S.P. Jarvis

dr. R. Bennewitz

dr. A. Fasolino

dr. ir. C. F. J. Flipse

Prof. dr. J. M. van Ruitenbeek

dr. ir. T. H. Oosterkamp

Cover Design: Hiroko Takei

Atomic-scale Friction and Superlubricity studied using High-Resolution Frictional

Force Microscopy

Martin Dienwiebel

ISBN 90-9016598-3

A digital version of this thesis can be downloaded from

http://www.physics.leidenuniv.nl

The work described in this thesis was performed at the FOM Institute for Atomic

and Molecular Physics (AMOLF), Kruislaan 407, 1098 SJ Amsterdam, the Kamer-

lingh Onnes Laboratory, Leiden University, Niels Bohrweg 2, 2333 CA Leiden, and

the Tokyo Institute of Technology, Department of Materials Science and Engineering,

4259 Nagatuta, Midori-Ku, Yokohama, 226, Japan. The work is part of the research

program of the Stichting voor Fundamenteel Onderzoek der Materie (FOM) and was

made possible by financial support from the Nederlandse Organisatie voor Weten-

schappelijk Onderzoek (NWO).

This thesis is partly based on the following articles:

J.W.M. Frenken, M. Dienwiebel,J.A. Heimberg, T. Zijlstra, E. van der Drift, D.J. Spaan-

derman and E. de Kuyper, Towards the Ideal Nano-Friction Experiment, (Chapter 2),

In: Fundamentals of Tribology and Bridging the Gap between the Macro- and Mi-

cro/Nanoscales (B. Bhushan, ed.)( Nato Science Series Vol. 10, Kluwer Academic,

Dordrecht),137–150 (2001).

T. Zijlstra, J.A. Heimberg, E. van der Drift, D. Glastra van Loon, M. Dienwiebel,

L.E.M. de Groot and J.W.M. Frenken, Fabrication of a novel scanning probe device

for quantitative nanotribology, (Chapter 3), Sensors and Actuators A: Physical 84,

18–24 (2000).

M. Dienwiebel, J.A. Heimberg, T. Zijlstra, E. van der Drift, D.J. Spaanderman, E. de-

Kuyper and J.W.M. Frenken, A Novel Frictional Force Microscope with 3-Dimensional

Force Detection, (Chapter 4), In: Nanotribology: Critical Assessment and future Re-

search needs (S.M Hsu and Z.C. Ying, eds.)(Kluwer Academic, Boston) (2002).

M. Dienwiebel, J.A. Heimberg, T. Zijlstra, E. van der Drift, D.J. Spaanderman, E. de-

Kuyper, L. Crama, D. Glastra van Loon and J.W.M. Frenken, A High-Resolution

Frictional Force Microscope with Quantitative 3-Dimensional Sensitivity and Track-

ing,(Chapter 4), submitted to Rev. Sci. Instrum.

M. Dienwiebel, N. Pradeep, G.S. Verhoeven, J.A. Heimberg, H.W. Zandbergen and

J.W.M. Frenken, Why Graphite is a Good Solid Lubricant: an atomistic view (Chapter

5), submitted to Science.

M. Dienwiebel, N. Pradeep, G.S. Verhoeven, H.W. Zandbergen and J.W.M. Frenken,

Superlubricity of graphite (Chapter 5), submitted to Phys. Rev. B.

G.S. Verhoeven, M. Dienwiebel, and J.W.M. Frenken, A Tomlinson model for super-

lubricity of graphite (Chapter 6), submitted to Phys. Rev. B.

Other publications:

M. Kageshima, H. Jensenius, M. Dienwiebel, Y. Nakayama, H. Tokumoto, S.P. Jarvis

and T.H. Oosterkamp, Noncontact atomic force microscopy in liquid environment with

quartz tuning fork and carbon nanotube probe, Appl. Surf. Sci. 188, 440–444 (2002).

Contents

1 Introduction 111.1 Nanotribology 12

1.1.1 Single-asperity experiments and continuum mechanics models 13

1.1.2 Friction Anisotropy 14

1.1.3 Atomic-scale friction experiments and simple atomistic models 15

1.1.4 Superlubricity 17

1.2 Scope of this thesis 19

2 The “ideal” nanotribology experiment 212.1 Introduction 22

2.2 Requirements 23

2.3 Traditional frictional force microscopy 24

2.4 Design of a novel force probe 25

3 Microfabrication of the Tribolever 333.1 Tribolever structure 34

3.2 Fabrication difficulties 34

3.3 Fabrication process 36

3.4 Microfabrication results 39

3.5 Miniaturized Tribolever 42

3.6 Summary 43

4 Design and performance of a high-resolution frictional force microscope 454.1 Detection principle 46

4.2 The fiberhead 49

4.3 Electronics 50

4.4 Sample movement 52

4.5 Experimental setup and procedures 54

4.5.1 Calibration 54

4.5.2 Tip mounting 56

7

C O N T E N T S

4.5.3 Setup 57

4.6 Performance 59

5 Superlubricity of graphite 635.1 Introduction 64

5.1.1 Structure and mechanical properties of graphite 64

5.1.2 Tribological Properties 64

5.1.3 Nanotribological properties 66

5.2 Experimental 67

5.3 Results 69

5.3.1 Lateral force images 69

5.3.2 Friction versus load 72

5.3.3 Friction vs. sample rotation 77

5.3.4 A ‘loose’ flake 81

5.3.5 Large-scale images on polycrystalline graphite 81

5.3.6 TEM analysis of the tip 84

5.3.7 Friction anisotropy 84

5.4 Discussion 87

5.5 Conclusions 89

6 Superlubricity in the Tomlinson model 916.1 Introduction 92

6.2 Model 93

6.3 Results 96

6.3.1 Symmetric contacts 96

6.3.2 Asymmetric contacts 98

6.4 Discussion 102

6.5 Conclusions 105

7 Towards the ideal friction experiment 1077.1 Introduction 108

7.1.1 The need for ultra-high vacuum 108

7.1.2 “Imaging the contact” 108

7.2 Design of a miniaturized FFM for use in combination with HRTEM

or SEM 110

7.2.1 FFM/HRTEM fiberhead 113

8

C O N T E N T S

7.2.2 HRTEM-FFM assembly 114

7.2.3 HRTEM-FFM sample stage 115

7.3 Design of the UHV setup for FFM 116

7.3.1 UHV chamber 116

7.3.2 UHV-FFM stage 119

7.3.3 Mini-SEM 119

7.3.4 Field ion microscope 122

7.4 Summary 122

A Processing steps of the Tribolever fabrication 123A.1 Overview 123

A.2 Processing 124

B FFM-TEM observations 129B.1 Introduction 130

B.2 Experimental 130

B.3 Nanoscale wear of a gold surface 131

B.4 Summary 133

Summary 137

Samenvatting 139

Zusammenfassung 141

Nawoord 143

Curriculum Vitae 145

9

C O N T E N T S

10

I

Introduction

· · ·

“It is quite difficult to do quantitative experiments in friction, and

the laws of friction are still not analyzed very well, in spite of the enor-

mous engineering value of an accurate analysis. [...] At any rate, this

friction law is another of those semiempirical laws that are not thor-

oughly understood, and in view of all the work that has been done it is

surprising that more understanding of this phenomenon has not come

about. At present time, in fact, it is even impossible to estimate the co-

efficient of friction between two substances”

R. P. Feynman, 1963 [1]

11

1. I N T R O D U C T I O N

Exactly forty years after Richard Feynman wrote his famous “Lectures on Phy-

sics”, the comment he made about our fundamental understanding of friction has lost

nothing of its timeliness. This is not to say that there has been no progress in the field

of tribology and engineering. The name “Tribology” refers to the science and technol-

ogy of friction, lubrication and wear [2]. In every day life, this progress is illustrated

by the evolution of cars. Modern car engines do not need to be driven carefully for the

first few thousand kilometers anymore because engine parts are machined better and

the engines are run in at the factory at optimal conditions to reduce initial wear. Also

oil change cycles have become longer over the last decades due to improved lubricants

and additives.

Over the centuries the phenomenon of friction has attracted both physicists and en-

gineers, as is beautifully illustrated in Duncan Dowson’s book “History of Tribol-

ogy” [3], which covers the tribological progress of mankind from early prehistoric

toolmaking to the present (1997). The modern history of tribology since the indus-

trial revolution is characterized by the fact that technological advances have been

made mainly empirically in the field of engineering. On the other hand, in the field

of physics, for a long time friction research has lived a shadowy existence because the

processes that cause friction were considered to be too complex, thus too difficult to

measure. This has changed since the advent of new experimental techniques, such as

the frictional force microscope (FFM) [4], the surface forces apparatus (SFA) [5, 6],

and the quartz crystal microbalance (QCM) [7, 8]. Together with a fast progress in

atomic-scale surface science this has caused a renaissance of tribology on the nanome-

ter scale, or nanotribology. For the physicist, the wealth of phenomena encountered

when two surfaces slide over each other is no longer perceived to make friction inac-

cessible, and is now experienced as a great motivation.

1.1 Nanotribology

The classical friction laws, discovered by Leonardo da Vinci [9, 10] and rediscovered

by Guillaume Amontons [11] and Charles Augustin Coulomb [12], state that the fric-

tion force FF is proportional to the normal load FN and independent of the sliding

speed and the contact area of the sliding bodies i.e.,

FF = µFN . (1.1)

µ is a proportionality factor that is commonly known as the “coefficient of fric-

12

1.1 N A N O T R I B O L O G Y

tion”. That the true contact area is a very small percentage of the apparent contact area

was recognized much later by Bowden and Tabor [13]. When two macroscopic bodies

are brought into contact, the roughness of their surfaces leads to the creation of a large

number of microcontacts or asperities. For the case of dry, wearless sliding, Bowden

and Tabor proposed that the friction force is directly proportional to the real area of

contact A,

FF = τA, (1.2)

where τ is the shear strength of the contact. For randomly rough surfaces, A

increases proportional with normal load [14], in which case the classical friction law

is recovered from equation 1.2.

The nanotribology approach to the fundamental processes of friction is to cre-

ate and investigate a single model asperity, with the idea that the behavior on a macro-

scopic scale naturally emerges from the statistical combination of the single-asperity

behavior. Such a prototype asperity can be the tip of an FFM touching a surface or the

contact formed in an SFA. The FFM is a variation of the well-known atomic force mi-

croscope [15], which makes use of a sharp tip, that is attached to a flexible cantilever.

The cantilever twists, when a lateral force acts on the tip. The degree of twisting is usu-

ally measured with a light beam that is reflecting from the cantilever (see also section

2.3). In the SFA, two curved, smooth mica sheets are brought into contact in a crossed

cylinder geometry. The friction force between the two sheets is measured by detecting

the extension or contraction of springs, connected to one of the two mica surfaces. In

addition, the contact area and separation can be measured by shining white light across

the contact and detecting the fringes of equal chromatic order (FECO) resulting from

multiple beam interference.

Several monographs have been published on nanotribology, of which we would like

to mention particularly the book by Bo Persson [16]. Also several review articles have

been published, which give a good overview over recent experimental and theoreti-

cal progress in nanotribology [17–23]. In the following, we will briefly review a few

selected studies to illustrate interesting new phenomena found in nanometer scale fric-

tion experiments.

1.1.1 Single-asperity experiments and continuum mechanics models

For a single asperity experiment, the friction force usually does not scale linearly with

the normal load, but follows a FF ∝ FnN relation,where n < 1. A number of continuum

13


mechanics theories exist that describe the elastic deformation of two bodies under

load. The first contact theory, which was formulated in 1881 by Heinrich Hertz [24],

describes the contact area of two elastic spheres with radii R1 and R2. In the Hertz ap-

proximation the contact area scales with the normal load as F1/3N and the friction force

scales as F2/3N . The Johnson-Kendall-Roberts model (JKR) [25] also takes adhesive

forces inside the contact into account. The result is, that the friction force is non-zero

already at zero normal load. The Derjaguin-Muller-Toporov (DMT) model [26, 27]

includes not only adhesive forces but also attractive forces between those regions of

the two surfaces that are close to but outside of the contact. The Maugis-Dugdale (M-

D) theory [28] is a generalization of the above theories and includes the ingredients

of the Hertz, JKR and DMT models. All above models scale with the normal load

as F2/3N . In FFM experiments, nearly all types of behavior have been observed exper-

imentally; JKR for a Pt tip sliding over mica [29], DMT for a tungsten carbide tip

sliding over diamond [30] and M-D for a silicon tip sliding over NbSe2 [31]. In SFA

experiments, JKR behavior is commonly observed [32]. Recently, different friction

laws have been found by Wenning et al. [33] using a molecular dynamics (MD) simu-

lation. They observed FF ∝ F0.63N for amorphous contacts and a linear dependence for

incommensurate and commensurate, crystalline contacts. A FF ∝ F0.85N dependence

was found for incommensurate, boundary lubricated contacts, but was not regarded to

be universal.

1.1.2 Friction Anisotropy

Another interesting phenomenon, observed in single asperity experiments, is that of

“friction anisotropy”, where the friction depends on the sliding direction of the asper-

ity over the substrate lattice. Some authors use this term also for changes in friction

as a function of commensurability [34]. In this thesis, we will use the term friction

anisotropy strictly for the variation of friction with respect to the sliding direction and

not for a variation in the friction as function of commensurability (see section 1.1.4).

Bluhm et al. [35] observed that the frictional contrast on a triglycine sulfate (TGS)

surface depends on the sliding direction. The variation in friction was caused by an

alternating tilt of TGS molecules in two domains of the substrate. Overney et al. [36]

and others [37–39] observed friction anisotropy on organic bilayer films, caused by

different molecular alignments in the substrate as in the case of TGS. An extreme case

of anisotropy was reported by Sheehan and Lieber [40]. They observed that MoO3

islands on a MoS2 surface, that were manipulated using the tip of a FFM, could only

14


Figure 1.1: Two simple one-dimensional atomistic models. In the single-atom Tomlinson

model (a) an atom or a point-like tip, that is connected to a moving support by a spring with

stiffness k, is pulled through a periodic potential with periodicity a and corrugation V0. The sup-

port position is denoted with xm and the position of the atom with xt . In the Frenkel-Kontorova

model (b), the moving top solid is modelled by atoms that are connected by springs with stiffness

k. The springs are separated by a distance p and the periodicity of the potential is denoted with

q.

be moved along low-index directions of the substrate.

1.1.3 Atomic-scale friction experiments and simple atomistic models

The first experiment that revealed atomic resolution of lateral forces was performed

by Mate et al. [4] using the tungsten tip of a modified scanning tunnelling micro-

scope (STM) sliding over a graphite surface. In this measurement, a saw-tooth pattern

in the lateral force with the lattice periodicity of the graphite surface was observed,

which could be explained by a stick-slip motion of the tip. Stick-slip motion was later

observed on many other materials, such as e.g. mica [41], MoS2 [42], copper [43],

diamond [44, 45], and alkaline-halides (NaF, NaCl, KF, KCl, KBr) [46–48].

Two simple ball and spring models are often used to analytically model atomic-

15


Figure 1.2: The Aubry transition in the Tomlinson model. The lateral force Flat = k(xt −xm) vs. xm is plotted for λ < 1 (a), λ = 1 (b) and λ > 1. In panel (c) the dashed line shows

the inaccessible solution of equation 1.3, the solid lines show the physically meaningful paths

probed by an atom sliding from left to right and from right to left. The area in between the two

solid lines corresponds to the dissipated energy in one cycle (left-right plus right-left).

scale friction between two crystalline bodies. In the Tomlinson model [49], one atom

or a point-like tip is coupled by a spring to a moving support. This represents the slid-

ing top solid. The bottom solid is treated as a fixed periodic potential energy surface

(fig. 1.1a). In a second version of the Tomlinson model, the single atom is replaced

by an infinite number of atoms, each connected by a separate spring to the support.

In the Frenkel-Kontorova (F-K) model the atoms are coupled to their neighbor atoms

by springs, and the coupling to other atoms in the top sliding surface (fig. 1.1b) is

neglected. The simplest version is the one-dimensional static Tomlinson model of a

point-like contact (fig. 1.1a). If the potential energy surface of the substrate has a sin-

gle Fourier component with amplitude V0, we can write the total force as

2πa

V0 sin(2πa

xt) = k(xt − xm) (1.3)

where a is the periodicity of the potential energy surface and k is the stiffness

of the spring. xt and xm denote the tip and the support positions.

The relative strength of the spring with respect to the potential amplitude is

often characterized by a dimensionless parameter λ ≡ 2πV0/ka. For a weak surface

potential and a stiff spring (λ < 1) the upper solid slides continuously over the lower

surface and the average friction force is zero [50]. When λ exceeds unity, multiple

solutions exist to equation 1.3. The atom or the tip of the upper surface is sticking

at a metastable minimum position until the spring force is large enough to make the

atom rapidly slip to the next (meta)stable minimum. This leads to the stick-slip mo-

tion, which is commonly observed in FFM experiments and stick-slip motion, in turn,

16


implies energy dissipation. The transition to the onset of friction at λ = 1, due to the

breaking of analyticity, is called an Aubry transition [51]. Note, that this approach

implies the instantaneous, complete, and irretrievable dissipation involved in each slip

event. The Aubry transition is also observed in the one-dimensional F-K model [51,52]

but static friction and the transition depend strongly on the ratio p/q of the lattice con-

stants of the top and bottom solid.

Consoli et al. showed, in the framework of an incommensurate dynamic F-K model

[53], that the onset of friction also depends on the velocity of the sliding chain of

atoms.

In the kinetic Tomlinson model, also the momentum and the damping are con-

sidered, leading to the following equation of motion

mxt − γxt − k(xt − xm)+2πa

V0 sin(2πa

xt) = 0, (1.4)

where m is the effective mass of the sliding object and γ a phenomenological damping

factor. The values of m,k and γ determine the motion of the system immediately after

each slip event. When the system is not overdamped or critically damped (γ =√

2km),

each slip event will be followed by a damped oscillation. This situation even can result

in jumps over multiple lattice spacings if the spring is soft [54].

Gnecco et al. [55] have introduced a static Tomlinson model that includes the thermal

energy of the tip. This model predicts that the friction force increases logarithmically

with sliding velocity. The model also predicts a critical velocity vc at which the fric-

tion force becomes velocity independent [23]. The logarithmical dependence of the

friction force has been observed experimentally on the atomic scale for a silicon tip

sliding on NaCl [55].

In order to model lateral force maps measured with FFMs, Gyalog et al. [56] have

used a two-dimensional Tomlinson model. Similar models have been used later by

others [57–60] to explain lateral force maps. Depending on the employed spring con-

stants, the atom in general will not only move in the pulling direction but also in the

perpendicular direction, leading to “zig-zag” stick-slip motion, which has been ob-

served experimentally, e.g. by Fujisawa et al. [61, 62] using a 2D-FFM.

1.1.4 Superlubricity

The term superlubricity was introduced in 1993 by Hirano and Shinjo [63]. It de-

scribes the effect that friction can vanish almost completely even when two crystalline

17


surfaces slide over each other in dry contact without wear. This was first shown in a

quasistatic calculation by Hirano and Shinjo [64] for rigid crystals with fcc, bcc and

hcp symmetry and different orientations. In a later study they used a F-K model to

study the transition from kinetic friction to superlubricity in one and two dimensions.

In the one-dimensional case they found an Aubry transition from static friction to a

superlubric regime for a small interaction strength P and a high stiffness k of the upper

surface. This is equivalent to the Aubry transition at λ = 1 in the one-dimensional F-K

and Tomlinson model. In the two-dimensional case they observed that the superlu-

bric regime can be reached for a much wider range of values of λ and they noted that

superlubricity should appear for any combination of flat and clean metals when the

interaction potential is weak. They concluded that a way to tune the interaction poten-

tial experimentally, is to change the commensurability between the two surfaces.

This notion was confirmed by Sørensen et al. [65] who studied the friction between a

flat copper asperity and a copper surface in an MD simulation at T = 0. For the case

of a (111) terminated asperity sliding over a Cu(111) surface, atomic-scale stick-slip

motion was observed, when the two lattices were in perfect registry. When the asper-

ity was rotated 16.1 out of registry, the friction force vanished. However, for small

asperities, containing 5×5 atoms, an Aubry transition was observed at a positive nor-

mal load and a small friction force was observed. For larger asperities, containing

19×19 atoms, superlubricity was observed also for the highest normal loads used in

the simulation. For a (100) terminated asperity that was sliding over a Cu(100) surface,

Sørensen et al. observed adhesive wear and transfer of Cu atoms from the asperity to

the substrate. The wear was caused by slip along the 111-planes inside the asperity,

leading to the creation of a dislocation network.

In search of experimental evidence for superlubricity, Hirano et al. [34] showed that

frictional forces between mica sheets in contact in an SFA experiment were maximal

when the orientation of the mica sheets matched. Friction forces were a factor 4 lower

when the crystallographic directions of mica sheets were misoriented relative to each

other. In a consecutive experiment, Hirano et al. [66] claimed the observation of su-

perlubricity between a tungsten tip and a Si(001) in a scanning tunnelling microscope

(STM) experiment (see also section 5.4). Ko and Gellman measured the friction force

as function of the misfit angle between two Ni(100) crystal surfaces using a UHV tri-

bometer [67]. They found a lower friction coefficient for 45 and 135 misfit angles

than for other orientations, which was consistent with superlubricity. However, these

orientational variations were still observed even after adsorption of up to 20 mono-

18

1.2 S C O P E O F T H I S T H E S I S

layers of ethanol or sulfur. Therefore they concluded that the low friction in certain

directions was caused by easy shearing along the preferred slip planes in the bulk.

This explanation is consistent with the results found by Sørensen [65], who concluded

that superlubricity between fcc metal surfaces should only be expected between (111)

surfaces. Recently, Falvo et al. [68, 69] manipulated carbon nanotubes (CNTs) on a

graphite surface using the tip of a FFM. They observed that the CNTs changed from

sliding to rolling motion, depending on the lattice mismatch between the tube and the

substrate. The rolling motion of the CNT in the case of a commensurate contact was

found to require a higher lateral force than the sliding motion of the CNT in the case

of an incommensurate contact.

Finally, we note that the concept of superlubricity only takes into account en-

ergy dissipation due to excitation of phonons. Other dissipative processes, such as

“electronic friction” or “quantum friction” [70], will not depend on the degree of

commensurability. Therefore even in the case of complete, phononic superlubricity,

the total friction force will not be identical to zero. The similarity of the term “su-

perlubricity” with similar terms such as “superconductivity” and “superfluidity” is

therefore misleading. Nonetheless, under appropriate conditions, superlubricity might

cause a reduction of the friction force by two orders of magnitude or more.

1.2 Scope of this thesis

The objective of this thesis is to describe the development and performance of a new

instrument, with which quantitative measurements of friction processes can be per-

formed at the atomic and nanometer scale. As a first application of our frictional force

microscope, we revisited the atomic scale friction of a tungsten tip sliding over a

graphite surface. To our surprise, the results show a strong signature of superlubricity,

which sheds new light on the extremely low friction forces found on graphite surfaces.

The outline of this thesis is as follows. In chapter 2, we formulate a list of require-

ments that serves as a roadmap for the development of a dedicated frictional force

microscope. We further present the design of a new friction force sensor that enables

one to simultaneously measure forces in three directions with very high sensitivity.

Chapter 3 describes the microfabrication of this novel force sensor. The complete fab-

rication “recipe” of the sensor is provided in appendix A. In chapter 4, we present

the design and performance of the complete FFM, that makes use of the special force

19


sensor. This first version of the microscope operates in ambient conditions. In chapter

5 we present friction measurements on the atomic scale between two graphite sur-

faces. We show that the ultra-low friction forces found using the ambient version of

our FFM is caused by superlubricity. The data, shown in chapter 5 is further analyzed

in chapter 6, where we make use of a static Tomlinson model to describe the friction

between a thin sheet of graphite and a graphite substrate. A miniaturized version of

the FFM, that can be operated inside a transmission electron microscope (TEM), is

presented in chapter 7. A preliminary friction measurement inside a high-resolution

TEM is described briefly in appendix B. In addition, chapter 7 introduces the design of

the ultra-high vacuum setup, which makes use of the miniaturized FFM. This second

version of the FFM will be combined with additional microcopy techniques, such as

field ion microscopy (FIM) and scanning electron microscopy (SEM), to allow full

characterization and control of the sliding contact.

20

II

The “ideal” nanotribology experiment

· · ·

In this chapter, we present a list of fundamental questions that

are at present of importance in nanotribology. The “ideal” nanofriction

experiment should be able to address these questions and demands a

number of technical specifications to be met, which are not available

using commercial frictional force microscopes and force sensors. Based

on the technical specifications we present the design of a novel force

sensor.

21

2. T H E “ I D E A L ” N A N O T R I B O L O G Y E X P E R I M E N T

2.1 Introduction

Although the field of nanotribology has produced tremendous insight into energy dis-

sipation processes at the atomic scale, friction coefficients measured in nanotribolog-

ical experiments and macroscopic “tribo-testing” differ often by orders of magnitude.

Because of this, the usefulness of atomic-scale frictional force microscopy (FFM) ex-

periments is currently being debated [71]. Therefore, we should begin by considering

which FFM experiments need to be carried out, in order to establish the link with

macroscopic friction; in the framework of tribology, the interesting regime is certainly

not that of a single-atom contact, but rather that of contact areas ranging from a few

atoms to a few million atoms. The “ideal” experiment would be one in which we

record all three components of the force between two extended surfaces in which we

know and control ‘where all the atoms are’.

Some of the fundamental questions that can be addressed with such an exper-

iment are: (1) How does the friction force build up when the distance between the

surfaces is decreased? At which distance do we experience the ‘onset’ of friction?

(2) How does the friction force depend on the contact area? (3) How does the fric-

tion force depend on the materials? Of course, the simplest model experiment would

be one in which the two surfaces in contact consist of the same material. Certain

unlubricated material couples are known to form sliding contacts that provide good

tribological properties, while other combinations lead to high friction coefficients and

excessive wear. The fundamental processes that cause these different behaviors still

lie in the dark. (4) How does the friction force depend on the relative crystallographic

orientation of the two surfaces? Single-atom contacts exhibit pronounced atomic-scale

stick-slip sliding motion. When two rigid lattices are sheared with the lattices rotated

out of registry, there should be a significant cancellation of the individual contributions

to the friction force, leading to superlubricity. Of course, for larger contacts, this naive

picture should break down, as the two lattices are not perfectly rigid, and a network of

misfit dislocations forms between the two. It is important to find out whether superlu-

bricity exists, how it develops when the contact is made larger than just a few atoms,

and how it disappears when the contact area is increased further. (5) How does the

friction force in a multi-atom contact depend on contact pressure? (6) How does the

friction force depend on the sliding direction with respect to the crystal orientations

of the two surfaces? (7) How does the friction force depend on temperature? (8) How

22

2.2 R E Q U I R E M E N T S

does a (model) lubricant change the friction force? (9) How and why does the friction

force depend on sliding speed? (10) How and why does a contact age?

With quantitative experimental answers to these questions for ideal, fully controlled

contacts, very detailed comparisons can be made with microscopic theories and com-

puter simulations, in search for the energy dissipation mechanisms relevant on differ-

ent length scales.

2.2 Requirements

Based on the above ideas we can directly formulate the requirements that our ideal

instrument must meet: (1) First, we want to measure the lateral force in the sliding di-

rection as well as the component perpendicular to this direction with equal, and high

sensitivity. (2) The force sensing device should be stiff enough to withstand the high

force gradients normal to the contact, which otherwise lead to snap-to-contact. (3)Next, we want full control over the contact area. In traditional FFM’s, the contact area

is determined by the initial radius of the tip and the deformations caused by the forces

between the two surfaces (loading and adhesion forces). In our ideal experiment, we

want to control the contact area and the loading force independently. This means that

we need to go beyond the usual hemispherical tip shape. The tip should end in an

atomically flat plane, i.e. a crystal facet, with a controllable radius. Here, it is of ut-

most importance that the two surfaces are well characterized and clean. (4) The facet,

formed by the end face of the tip, has to be oriented precisely parallel to the crystal

surface with which it is to be brought in contact. (5) To complicate matters further, we

want control over the precise crystallographic orientations of the two surfaces. This

means that we have to specify not only the crystallographic orientations of the surface

normal of the tip and the countersurface, but also their azimuthal orientations. (6) The

sliding direction has to be adjustable, independently of the azimuthal orientations of

tip and countersurface. (7) Of course, we want to have full freedom in the choice of the

materials of the two surfaces. (8) Measurements should be possible as a function of

temperature. (9) Finally, the instrument should allow us to add controlled overlayers

(model lubricants) on each of the two surfaces.

23


Figure 2.1: Model of a rectangular AFM cantilever. The motion of the cantilever is detected by

measuring the position of a light beam that is reflected from the back side of the cantilever. Us-

ing a four-quadrant photodetector, normal motion and torsional motion can be simultaneously

monitored.

2.3 Traditional frictional force microscopy

Different techniques have been developed to detect the deflection of an atomic force

microscope (AFM) cantilever. One of the most successful and widely used techniques

is optical beam deflection, developed by Meyer and Amer [72]. In this method, an

optical beam is reflected from the rear side of a cantilever onto a split photodiode (fig.

2.1). Using a four-quadrant photodiode, vertical motion (normal to the surface) and

torsional motion of the cantilever can be simultaneously detected. The image obtained

by monitoring the vertical deflection is commonly called the topographic “AFM” im-

age, while the image obtained by tracking the torsional motion of the cantilever has

come to be known as the “FFM” image.

Naıvely, this dual force measurement is trivial to implement but great difficulty comes

24

2.4 D E S I G N O F A N O V E L F O R C E P R O B E

in performing quantitative measurements and in analyzing the data [57, 73, 74]. The

spring constants of AFM cantilevers are commonly deduced from their dimensions.

For the simplest case of a rectangular cantilever the spring constants in the x, z and

torsional directions can be calculated using classical mechanics textbook equations,

kz =Ew4

t3

L3 (2.1)

kx =Et4

w3

L3 (2.2)

kτ =Gwt3

3La2 . (2.3)

Here, E and G are the Young’s and the shear moduli, w, t and L are the width, thick-

ness, and length of the cantilever and a is the tip height, respectively. For widely used

V-shaped cantilevers the relations for the spring constants are more complicated [73].

The ratio between the torsional and normal spring constants can be on the order of

100, resulting in a relatively small frictional force signal. There is significant coupling

between the normal and torsional responses of AFM cantilevers, making it difficult to

distinguish buckling from bending [75]. Small misalignments of the system produce

large errors in the FFM measurements. A true calibration of the cantilever’s response

in the lateral direction is rarely performed and usually does not take into account the

dependence of the force signals on the location of the beam spot on the cantilever, and

on the precise tip position on the cantilever [74]. For cantilevers that are relatively stiff

in the lateral direction, the flexibility of the tip, typically several tens of N/m, adds ex-

tra uncertainty to the total response of the system. Furthermore it is known, that high

values of the proportional and integral gain of the feedback loop influence the mea-

sured lateral force to a great extent [76]. As we see, these traditional force probes fail

to meet several of the essential requirements that we formulated above. Our efforts to

build a new experimental setup therefore started by finding or constructing a suitable

force probe.

2.4 Design of a novel force probe

In the last 10 years, serious efforts have been made to produce force probes with

better lateral sensitivity. Using rectangular cantilevers as a starting point, a simple

way to improve the lateral sensitivity would be, to turn them simply by 90 and to

use cantilevers with a small width and a large thickness. This would result in reduced

25


Figure 2.2: Two examples of complex structures that have been designed for lateral force

detection. (a) shows a meandering structure that was designed to have low spring constants in

the x-, y- and z-directions. Reprinted from [77] c© 1992, with permission from Elsevier Science.

(b) shows a cantilever that consist of a combination of rectangular beams for lateral force

detection and a V-shaped cantilever for normal force detection. Piezoresistive readout is used

to monitor the cantilevers’ deflection. Reprinted with permission from T. Kenny [78]. c© 1998,

American Institute of Physics.

spring constants in one lateral direction and a high spring constant in the z direction

(equations 2.1 and 2.2). This approach was has been pushed to the extreme by Stowe

et al. [79]. Using a cantilever that was oriented perpendicular to the surface, they could

achieve a lateral force resolution of 5.6 attonewtons (5.6 · 10−18 N/√

Hz). The lateral

spring constant of this cantilever (klateral = 6.5 · 10−6 N/m, knormal > 1000N/m) was

so low that the cantilever would snap into contact 60nm away from the surface, when

it would have been mounted parallel to the sample surface. In a geometry, where the

cantilever is mounted parallel to the surface, the width of a cantilever is limited by

the size of the tip and optical detection of the cantilever’s deflection is not feasible

because the cantilever’s endpoint is very close to the sample unless the spot size of the

light beam is smaller than the height of the cantilver. Piezoresistive detection, however,

would be possible (figure 2.2) but is usually about an order of magnitude less sensitive

26


than optical detection.

A more practical approach is to modify commercial cantilevers using focused

ion beam (FIB) methods [80]. It has been demonstrated, that by cutting a hinge into a

rectangular cantilever, the lateral spring constant in the x-direction could be reduced

by roughly an order of magnitude to 118N/m. However, the normal spring constant

was reduced as well, to 16.4N/m.

By cutting a more complex H-shape into a rectangular cantilever, a lateral spring

constant of 20N/m was obtained with a normal stiffness of 126N/m [80]. The draw-

back of the FIB method is, that it can be used only to modify single cantilevers one by

one, so that reproducible results are difficult to obtain. In addition, modifying a single

cantilever is extremely time consuming. Cantilevers with more complex geometries,

that were optimized to measure lateral forces with higher sensitivity, have been fabri-

cated using lithography and micromachining techniques [77,78,81,82]. For example,

Buser et al. have designed a meandering cantilever with low spring constants in the

X-, Y-, and Z-direction.

In spite of the improvements, none of the above designs provides low and symmetric

spring constants in both lateral directions x and y, in combination with a normal stiff-

ness in z.

To obtain symmetric spring constants, the geometry of the force probe should

of course be symmetric in the X- and Y-directions. Ideally, one would like to place

four equal springs around the scanning tip of the cantilever as depicted in figure 2.3a.

This cannot be achieved by using four straight rectangular beams as the springs,

as this structure would be completely inflexible. Therefore we introduced a 90 bend

in each beam to provide the required flexibility in the lateral plane (fig. 2.3b). As

we discussed above, it is not trivial to measure the displacement of the cantilever

in the plane parallel to the sample surface by optical means. Therefore we placed a

detection pyramid at the center of the cantilever. Using this pyramid as a set of four

mirrors, we can detect the displacement of the pyramid with the use of four glass-fiber

interferometers, which are placed symmetrically around the pyramid, under an angle

with the plane of the sample surface. This is the basic design of our new force probe

(figure 2.4) that we called the Tribolever1

In order to test the principle of our new design and to choose suitable dimen-

sions of the four legs for a sensor made out of silicon, we have used finite element

1. Tribolever R© is a registered trademark of Interface Physics Group, Leiden University.

27


Figure 2.3: Design of a cantilever that is symmetric in two lateral directions (X and Y). The

idea is to place four equal springs around a central scanning tip (a). Using rectangular legs

with a 90 bend we precisely create such a symmetric geometry. By choosing high aspect ratio

legs, we can create a device with low lateral spring constants but with high normal and torsional

spring constants (b).

analysis (FEA) [83].

Figure 2.5a shows the calculated spring constants as a function of the width of

the four legs. For the FEA we used legs with lenght L = 450µm and height t = 10µm

(for comparison with the thickness of simple beam cantilevers we will denote the

height with t). We used the following material properties for silicon: Young’s modulus,

E = 1.69 · 1011 N/m2, Poisson’s ratio s = 0.333 and density ρ = 2330kg/m3. For our

“ideal” experiment the lateral spring constants should be significantly lower than the

normal spring constants, which means that the width of the legs should stay well below

the cross-over point in figure 2.5a , which for 10µm-high legs, is 7.4µm. The smallest

width that can be achieved by our microfabrication methods is about 1µm (for details

see chapter 3). This forms a lower limit for the lateral spring constants of 0.3N/m.

Figure 2.5b shows a FEA calculation as a function of the thickness, while the width

was kept constant at 5µm. The microfabrication process allows a maximum height of

about 20−25µm, which would lead to a normal spring constant in the order of a few

hundreds to one thousand N/m.

Table 2.6 shows a comparison of our calculated results to those of a traditional

AFM “diving board” cantilever. The Tribolever data in this table were calculated for

the actual dimensions of our prototype sensor of w = 1.4µm and t = 10.6µm Si legs,

which will be discussed later. The torsional spring constant (κτ) for AFM cantilevers

governs the lateral response for a traditional FFM, as discussed earlier.

28


Figure 2.4: Model of the Tribolever used in the finite element analysis. Lateral and normal

forces acting on the scanning tip are measured via the displacement of the central pyramid,

which is detected by four laser interferometers reflecting from the pyramid’s faces. The leg

geometry has been optimized to be sensitive for lateral forces while providing relatively high

normal and torsional stiffness. Panel (a) shows the back side of the Tribolever with the detection

pyramid pointing up. Also shown are the four glass fibers that are guiding light on the pyramid

and collecting the reflected light. Panel (b) shows a zoom-in at the central part of the front side

with a scanning tip pointing up.

Calculated lateral spring constants kx = ky for Tribolevers are significantly lower

than those for simple beams. It is important to note that although the lateral spring

constant (ky), which causes buckling of AFM cantilevers, is small compared to κτ,

this component of the lateral force is extremely difficult to extract from the verti-

cal response and is therefore usually not measured in traditional AFMs. In addition

to making the spring constants ideal for frictional force microscopy, the Tribolever

design also minimizes the coupling between the three orthogonal directions. The cou-

pling of the the lateral response on vertical motion is in the order of 10−5 %. This

is due to the torque introduced by the scanning tip. Besides the leg geometry, other

considerations have played an important role in the overall design. For example, at the

front side of the central detection block (figure 2.4b) the tip is sticking out. In order to

allow measurements for a range of tip materials (requirement 7), the tip should be a

completely separate entity, to be placed at the center of the Tribolever.

The design of the Tribolever forms the first step towards the “ideal” nanotribology ex-

29


Figure 2.5: (a) Spring constants of the Tribolever as function of the width of the legs for a

fixed height of 10µm, calculated using finite element analysis: the open circles show the values

for the lateral spring constants and square points are for the Z spring constant. The dashed

line represents a cubic fit for the lateral spring constant and the solid line is a linear fit for

the Z spring constant, according to equations 2.1 and 2.2 for the spring constants of a simple

rectagular beam. However, the value for the effective Youngs modulus Ee f f = 9.33 ·1012 N/m2

30


Figure 2.5: continued obtained from the cubic fit differs significantly from the value of E for

silicon from literature, which demonstrates that the response of the Tribolever differs signifi-

cantly from that of a simple beam and emphasizes the importance of the finite element analysis

prior to the microfabrication. (b) Spring constants of the Tribolever as function of the height of

the legs for a fixed width of 5µm.

Dimensions [µm] Length, L Width, w Thickness, t Tip Height, a

simple beam cantilever 450 47 2.1 15

Tribolever 351 1.4 10.6 50

Spring constants [N/m] kx ky kz κτ

simple beam cantilever 4.03 101.1 0.2 71.6

Tribolever 1.48 1.48 25.8 136

Tribolever (hole joints) 0.93 0.93 25.8 136

Figure 2.6: Comparison between the mechanical characteristics of a traditional AFM can-

tilever and a Tribolever with and without hole joints. Torsional spring constants are for torques

along the x-axis. All dimensions are in µm. See schematic figures for definitions of ‘simple beam’

and ‘Tribolever’ dimensions. Values of silicon constants used in the calculation are Young’s

modulus, E=1.69 ·1011 N/m2, Poisson’s ratio, s=0.333, and density, ρ = 2330kg/m3.

periment. During the following chapters, we will stay enroute towards the “ideal” ex-

periment. A discussion of the silicon microfabrication of the Tribolever will be given

in chapter 3. In chapter 4 we will then describe the technical details, the operation and

performance of our ambient-condition friction force microscope that makes use of the

Tribolever. Chapter 7 introduces the design of a new ultra-high vacuum setup that will

meet all requirements that we formulated at the beginning of this chapter.

31


32

III

Microfabrication of the Tribolever

· · ·

This chapter describes the fabrication process of the Tribolever.

Because of the complexity of the structure of the Tribolever device, a

special etching scheme needed to be developed, that combines different

etching techniques. The etching process development and the fabrica-

tion of a prototype were performed at the Delft Institute of Microelec-

tronics and Submicron Technology (DIMES) [84].

The chapter is organized as follows. First, we will discuss problems in

the fabrication and describe in short the process that solves these prob-

lems. Then results of the fabrication of a first prototype are presented.

Finally, we will turn our attention to the fabrication process of a smaller,

second generation device.

33

3. M I C R O F A B R I C A T I O N O F T H E T R I B O L E V E R

Figure 3.1: Schematic drawing of the Tribolever device. The prototype chip (10mm×8mm)

includes two force sensors, each with its own set of kinematic mounts.

3.1 Tribolever structure

The aim of the microfabrication described in this chapter was to produce an all-silicon

force sensor, with a shape and dimensions according to those discussed in chapter 2

(figs. 2.4 and 2.6). Furthermore, the sensor was produced with a central hole, such that

tips can be placed in the sensor relatively easily. Finally, the microfabrication also in-

cludes provisions for reliable and reproducible mounting of the sensors in the friction

force microscope.

The first prototype sensors have been realized on 10×8×0.525mm3 chips that each

include two Tribolevers and a set of kinematic mount structures to ensure that the chip

can be mounted in the FFM with high reproducibility (figure 3.1). The dimensions of

the prototype chip were too large for the final UHV version of the microscope, since it

inhibited the combination of the FFM with high-resolution electron microscopy (chap-

ter 7). Therefore in a second fabrication run the layout of the chip was changed such

that its dimensions could be greatly reduced (5×2×0.525mm3).

3.2 Fabrication difficulties

Before describing the actual fabrication process, we briefly list some of the fabrication

difficulties, arising from the special shape of our force sensor. At the front side two

34

3.2 F A B R I C A T I O N D I F F I C U L T I E S

Figure 3.2: Processing scheme of the central Tribolever part: (a) pattern overview, (b)

anisotropic etch of the leg and cross pattern, (c) all-sided thermal oxidation, (d) optical fiber

window etch (KOH), (e) mechanism of self aligned pyramid formation. Figures (a-d) are shown

front side up; (e) front side down.

35


anisotropic dry etching steps are required; one to define the leg geometry and one to

create the tip hole, with etching depths of about 15µm and 100µm respectively. This

implies that the patterning step for the legs has to be done after the etching of the hole

structure or vice versa, giving rise to severe step coverage problems in the resist spin

coating.

A second problem is introduced by the convex structure of the pyramid at the rear

side of the cantilever. Its facets are not easily obtained from a KOH etch along 〈111〉planes because of underetching at the corners [85]. Sacrificial corner compensation

structures to retard the underetching may help [86]. However, with the pyramid height

comparable to the lateral dimension (see above), this approach has serious limitations

for the resulting facet area and the shape of the central detection body.

A third problem is that the pyramid is deeply embedded in the wafer as seen from

the rear side. This can be understood as follows. The tip must extend out from the

cantilever structure in order to interact with a sample. Hence, the front side of the can-

tilever has to be flush with one face of the 525µm thick silicon wafer. With the central

detection body approximately 100µm high, the top of the pyramid is recessed about

400µm with respect to the rear side of the wafer. Therefore, a wide, recessed window

is needed on the rear side to allow room for the detection fibers to access the pyramid

faces. As a consequence, fabrication of the pyramidal structure at the rear side would

have to be done at a depth of about 400µm, which would further complicate the pro-

cessing involved.

In the following, we will show how a procedure of anisotropic dry etching of spe-

cific geometries at the front side, followed by a protective thermal oxidation and a

subsequent wet crystallographic etch at the rear side solves all of the problems listed

above.

3.3 Fabrication process

In this section we qualitatively describe the fabrication process. For a more complete

overview of the entire process, we refer to appendix A.

Starting with a Si (100) substrate, the first step is to create alignment marker patterns

at the front and the rear side by anisotropic dry etching, 2µm deep , with a 200nm ther-

mal oxide serving as the mask. The mutual alignment of front and backside marker

patterns is performed by IR detection through the wafer. All lithographic steps are

36

3.3 F A B R I C A T I O N P R O C E S S

done with photoresist (HPR) in a mask aligner (K. Suss MA 56). Oxide patterning is

done by anisotropic reactive ion etching (RIE) in a CHF3/O2 plasma (25:1) in a paral-

lel plate reactor (Leybold Z401). Typical plasma conditions are 10µbar gas pressure,

50sccm1 gas flow and 0.16W/cm2 rf power with rf bias voltage of −330V, giving an

oxide etch rate of 20− 25nm/min. All anisotropic dry etching in Si is achieved in a

high density plasma setup (Alcatel DECR200) with a SF6/O2 gas mixture (7.5:1), at

a substrate temperature of −95C. Plasma process conditions are 2.3µbar pressure,

25.5sccm gas flow, 750W microwave power (at 2.45GHz) and −10V substrate bias.

Si etch rates are in the order of 1µm/min, with a typical slope angle of 90± 3. All

dry etch processes are monitored with in situ laser interferometry.

After stripping the oxide used for the marker step, the actual processing for the Tri-

bolever follows as depicted in figure 3.2. The wafer is thermally oxidized (1.3µm

oxide thickness) and after lithography of the leg pattern and central cross patterns,

these patterns are etched anisotropically in the oxide with a CHF3 plasma. The two

patterns are etched with different depths, the cross pattern down to the silicon and the

leg pattern somewhere halfway through the oxide thickness (figure 3.2b). The idea

is to transfer one pattern after the other into the Si substrate. In this way, the resist

step coverage problem at the front side (legs, central cross) is reduced to spin coating

of about one micron topography in the oxide mask layer. The cross pattern is etched

first, about 85µm deep into the Si. Next the leg pattern is opened down to the silicon

(with CHF3 plasma) and the silicon etching (of leg and cross patterns) is continued for

15µm. Resulting depths of cross and leg patterns are approximately 100µm and 15µm

respectively. The pattern quality is superior due to the extreme oxide mask selectivity

of about 1000 : 1 in the silicon etching process. This is because the ion energy can

be tuned independently from the reactive species in the high density plasma [87]. The

most decisive element in the overall fabrication process is the cross-shaped pattern in

the middle at the front side, rotated 45 with respect to the central square block. The

center of the cross forms the hole for the scanning tip. In addition, the cross is used

to realize the 〈111〉 faceted pyramid, which is central to the detection system (figure

3.2c-e). After thermal oxidation of the freshly etched surfaces of both the leg and cross

patterns (figure 3.2c), the wide recessed window at the rear side of the cantilever is

made using a crystallographic wet KOH-etch through the wafer (figure 3.2d). As the

etching front from the rear side reaches the oxidized cross (figure 3.3a), the 〈111〉facets are exposed while the corners are protected by the oxidized sidewalls (figure

1. 1sccm = 1.69 ·10−3 Pa m3/s

37


Figure 3.3: Optical (a-c) and scanning electron micrographs (d) of the KOH etching process:

(a) At t = 3h22 the etching front passes halfway through the oxidized cross and part of the

pyramid becomes visible; (b) at t = 4h the etching front reaches the leg pattern; (c) at t = 4h08

the KOH etching is completed. A thin oxide layer still connects the pyramid, the legs and the

wafer; (d) SEM image of the pyramid after KOH etching, with the oxide sidewalls still present.

3.3b-d).

The pyramid with a central hole for a tip is made in a self-aligned way and in

one wet etch step. In this way, complicated fabrication on the bottom of the optical

fiber window to realize a pyramid structure by convex KOH etching is avoided. The

area of the 〈111〉 facets can be precisely tuned by the etch depth difference between the

cross and leg pattern. Finally, after a final all-sided oxide strip, the Tribolever structure

38

3.4 M I C R O F A B R I C A T I O N R E S U L T S

Figure 3.4: First prototype of the Tribolever integrated in a silicon wafer: (a) central part of

the device showing the pyramid side; (b) Tribolever with a tungsten tip glued in the central hole;

(c) zoom-in on the tungsten tip, which was mounted without damage to the tip; (d) cross-section

of the device showing (1) the optical fiber window, (2) two of the three elements of the kinematic

mount.

is released and the sidewall passivation layer removed.

3.4 Microfabrication results

The first generation of the Tribolever integrated in a Si(100) wafer is shown in figure

3.4. The Tribolever (fig. 3.4a) includes the four 〈111〉 facets, the high aspect ratio legs

with a width of 1.4µm, a height of 10.6µm, a length of 351µm and a cross-shaped

hole for the scanning tip.

39


Figure 3.4b shows a Tribolever from the front side with a metal tip fitted in the

central cross. The tip shown is an electrochemically etched tungsten wire, of 50µm di-

ameter, which extends approximatly 50−60µm out of the front side. It was positioned

into the Tribolever using micromanipulators and attached with wax (wax was used in

this first test, in the FFM experiments the tip was attached using silver epoxy). Figure

3.4d shows a part of the Tribolever environment embedded in the Si wafer. The big

window around the Tribolever (indicated by arrow 1) is for proper access of the optic

fibers as discussed earlier. The other KOH-etched windows (2) serve as a kinematic

mount for a highly reproducible fit of the Tribolever chip in the FFM setup. These ad-

ditional recesses complicate the overall process scheme and require all oxide patterns

to be buried in an all-sided CVD nitride layer (300nm) before opening one pattern

after the other. The nitride serves as a mask for intermediate local thermal oxidation

of Si structures existing already, to protect them against deterioration in subsequent

etching steps.

Reduced lateral spring constants of the four legs are crucial for proper operation and

essential to these spring constants are the widths of the legs. We explored several tech-

niques to tune a given Tribolever to the right operation regime. One successful method

is to thermally oxidize the total device and stripping the oxide selectively in a buffered

HF solution in an iterative approach until the required leg thinning has been obtained

(fig. 3.5a). In this way, we can reduce the leg width from 10µm to 1−3µm, but some

width variation due to rounding of corners has been observed. Another option is to

define precise hole joints in the crucial corners of the leg construction, either with a

focused ion beam (FIB) or by lithographic means (Table 2.6). Results of both methods

are depicted in figure 3.5c-d.

The lateral accuracy of the FIB treatment (FEI 200) is around 100nm. Prelimi-

nary FIB experiments show that a single ion milling step is highly reproducible within

one cantilever structure, but is not homogeneous over the full leg height and requires

additional trimming.

Calibration (see chapter 4) of the Tribolevers shows that the spring constants kx and

ky of the prototype are 1.67N/m, close to the calculated value of 1.48N/m. The slight

difference might be due to roundings and increased thickness at the bends of the legs.

The measured kz = 10.32N/m is significantly different from the calculated value of

25.8N/m. This is due to the fact that the Tribolever is positioned in the center of the

large fiber window, which is only 10.6µm thick (like the leg height) and acts as an

additional spring.

40

3.4 M I C R O F A B R I C A T I O N R E S U L T S

Figure 3.5: Tuning of the Tribolever to proper operation regime of the spring constants: (a)

leg thinned by thermal oxidation and stripping of the oxide in HF; (b and c) hole joints created

by focused ion beam milling; (d) hole joint by integral patterning, the inset shows the top view.

41


Figure 3.6: SEM image of the miniaturized Tribolever showing: (a) the chip, including the

Tribolever structure, the cross-shaped fiber window and the kinematic mounts; (b) a close-up

view of the Tribolever through the fiber window.

3.5 Miniaturized Tribolever

As mentioned before, we need a smaller device than the prototype device, for com-

bining our FFM with scanning electron microscopy (SEM) as well as transmission

electron microscopy (TEM). For the case of TEM, the dimensions of the Tribolever

are simply too large to place the FFM inside the TEM column. For the case of SEM,

the quality of the SEM images depends on the dimensions of the Tribolever. The

resolution of SEM critically depends on the working distance, which is the distance

between the objective lens of the SEM and the object that is to be imaged (the tip of

the Tribolever). Hence, by reducing one side of the Tribolever we will be able to also

reduce the working distance and obtain high-resolution images with the SEM.

The new layout contains only one Tribolever per device, which allows a bisection of

the long side of the device. A major problem in further reducing the dimensions, is

the size of the large window for the glass fibers, which would form a predetermined

breaking point of the device. Since a reduction of the size of the fiber window is not

possible, we rotated the fiber window by 45 and with it the Tribolever. In addition,

we changed the window geometry to a cross. It is not possible to rotate the pyramid

and the kinematic mounts on the wafer, so we rotated the pattern of the device except

the Tribolever pattern on the wafer. The result of the second processing run, using the

new layout, is shown in figure 3.6. The dimensions of the miniaturized version could

be reduced to 5×2mm, thus making the device fit in the typical gap between the pole

shoes of a high-resolution TEM column, and reducing the minimum working distance

42

3.6 S U M M A R Y

for SEM to 1mm.

3.6 Summary

We presented the fabrication process of a novel all-silicon force sensor, the Tribolever.

Difficulties in the microfabrication could be solved using deep reactive ion etching

from one side of a silicon wafer and wet etching from the opposite side of the wafer.

The first prototype device was shown to meet the requirements formulated in chapter 2

and to have properties close to the predictions that were obtained from finite element

analysis prior to the fabrication. In addition, we presented the microfabrication of

a miniaturized second generation Tribolever that can be used in combination with

transmission electron microscopy and scanning electron microscopy.

43


44

IV

Design and performance of a high-resolution frictional

force microscope

· · ·

In this chapter, the construction and initial tests of a prototype

version of the friction force microscope is described. Our main objec-

tive was to develop an instrument which achieves high-resolution force

detection in three directions with the Tribolever (chapter 3). In order to

allow for quick modifications, the prototype operates in ambient condi-

tions. Some of the requirements for the “ideal” nanotribology experi-

ment (chapter 2) are therefore not yet included. However, consideration

of these requirements and future additions played an important role in

some of the design decisions for this prototype.

45

4. D E S I G N A N D P E R F O R M A N C E O F A H I G H - R E S F F M

4.1 Detection principle

As mentioned already in chapter 2, the detection system of the Tribolever motion is

formed by four fiber optic interferometers. In an optical glass fiber, light is partially

reflected at the endface of the fiber, while most of the light is leaving the fiber. By

means of an external mirror, a fraction of that light can be made to reenter the fiber.

This leads to a phase difference between the two backward travelling coherent waves,

which depends on the distance between the endface and the external mirror. With

a fiber coupler (the analog to a beam splitter) the backwards travelling light can be

coupled out and detected with a photodiode. The interferometer’s output is given by

I = I0

[1+Acos

(2π

2Dλ

)], (4.1)

where I is the output current, A is the relative interference amplitude, D is the

fiber-sample distance, and λ is the wavelength of the laser (780nm in our case). The

offset I0 and the amplitude A are both determined by the reflectivities of the two in-

terfaces responsible for the interference signal. Taking a refractive index of n1 = 1.5

for a well-cleaved quartz glass fiber and n2 = 1 for air, the maximum reflectance of

the endface is ( n1−n2n1+n2

)2 = 4%. For the pyramid surface a maximum reflectance in the

order of 60% is expected. The 〈111〉 facets of the pyramid are at a well-defined angle,

θ = 54.74, with respect to the (100) surface plane of the wafer.

If each of the four glassfibers is adjusted such, that the light intensity increases

when the fiber-pyramid distance decreases (equation 4.1), the three-dimensional dis-

placement with respect to the fixed fibers can be extracted from the normalized sum

and differences of the signals coming from the four interferometers [44].

These linear combinations need to be weighted by the appropriate geometrical

projection (figure 4.1):

X =X2 −X1

2sinθ(4.2)

Y =Y2 −Y1

2sinθ(4.3)

Z =X1 +X2 +Y1 +Y2

4cosθ(4.4)

The design of our interferometers follows closely those discussed in the litera-

ture [88, 89], with attention given to the stability of the laser diode’s output intensity

46

4.1 D E T E C T I O N P R I N C I P L E

Figure 4.1: Schematic drawing depicting two of the four glass fibers. If the pyramid moves

laterally (panel a), the distance X1 between the left glass fiber and the pyramid increases and

the distance X2 between the right glass fiber and the pyramid decreases or vice versa. If the

pyramid moves normal to the sample surface, both distances either decrease or increase. This

allows one to extract the displacements of the pyramid in the X- and Z-directions. Similarly, from

the other fiber pair one obtains the displacements in the Y- and Z-directions. The displacements

are extracted from the distance changes, according to equation 4.1.

and wavelength [90]. One unique aspect of our design is that each opposing pair of

interferometers is driven by a single laser diode so that the influence of fluctuations in

laser intensity and wavelength is greatly reduced, while the remaining variations can

be divided out by use of a reference signal. A schematic of one such pair (e.g. the X

pair) is seen in Figure 4.2.

Light coming from the laser diode is first divided over two branches using a

bidirectional 2×2 fiber coupler. The two branches are denoted with X1 and X2, re-

spectively. A second 2×2 coupler in each arm completes the interferometer, by cou-

pling out the backwards travelling reflected light into the photodiode detector. The

same coupler couples out 50% of the primary light into the reference signal detector.

We see no evidence for optical cross-talk between the two fiber pairs. Such coupling

was not expected, as little diffuse reflection occurs at the pyramid faces. As a result,

we see no change in one pair, even when the other pair is optically disconnected. In

order for the 125µm diameter fibers to be positioned close to the pyramid faces, they

must be tapered to a maximum endface diameter of 80µm. Methods developed for

making sharp near-field scanning microscopy tips cannot be used in our application

because they stretch the core and decrease its diameter as it is melted. This would in-

troduce spurious backreflections into our interferometer. We have used both sharpened

fibers with cleaved endfaces [91] and fibers chemically etched using the liquid layer

47


Figure 4.2: Components of one interferometer pair. The interferometer can be divided in three

distinct sections: the laser system, the fiber system and the detection system. The laser system

consists of the laser diode with integrated Faraday isolator and the controlling power supplies.

The fiber system consists of couplers, connectors, adapters and the fiber itself. The detection

system consists of photodiodes and supporting electronics.

48

4.2 T H E F I B E R H E A D

protection procedure [92]. In this method a sharp glass tip is etched at the interface of

the etching liquid (40% hydrofluoric acid) and a protective immiscible organic fluid.

The process is self-terminated when the tip is formed. The cone angle of the tips can

be varied from 8 to 41 depending on the protection fluid [93]. To create a flat end-

face and to remove the part of the fiber core that was reduced in diameter by the HF

etch, the fiber tips were first embedded in wax and then mechanically polished using

12, 3 , 1, and 0.3µm aluminium oxide polishing paper for the final polishing step [94].

The former method results in slightly stronger interference signals (presumably due

to the better endface quality by a cleave with respect to a polished endface). The latter

method routinely produces endface diameters on the order of 30µm, which allows for

more flexibility when positioning all four fibers.

4.2 The fiberhead

Two versions of the the fiberhead were constructed. In the first version, the fibers

were fixed with respect to each other. Once glued into place, the four fibers could be

positioned together with respect to the pyramid using an x-y table formed by a sys-

tem of flexure hinges and micrometer screws. This design had the disadvantage that

the positioning of the fibers relied on a precise glueing step of the glass fibers, since

misalignments of a single fiber could not be corrected afterwards. In addition, the me-

chanical path between the fibers and the Tribolever in this design was approximately

35cm, which caused high thermal drift between the fibers and the Tribolever. The

variation in the distance between each endface and the pyramid was in the order of

15−30nm/hour even though the temperature was kept constant within 0.2 C.

Because of these disadvantages, we constructed a second, much smaller fiber-

head that allowed to individually mount and position each fiber. The improved second

version of the fiberhead is shown in figure 4.3. The fiberhead was machined by spark-

erosion from a single block of low-thermal-expansion metal (Invar). The distance of

the endface of each fiber with respect to the pyramid face is adjusted by miniature in-

ertial piezomotors ( Nanomotors R© [95]), which can be driven either in discrete steps

over a maximum distance of approximately 4 mm or be adjusted continuously with

sub-A resolution over a range of 400 nm. The first mode allows one to retract the glass

49


Figure 4.3: Schematic drawing of the fiber positioning head cut open for illustration (a) and

solid model (b). (1) Tribolever, (2) Tribolever support plate, (3) Nanomotor R©, (4) flexure hinge

and, (5) adjustment screws.

fibers to a safe distance during an exchange of sensors, the latter is used to calibrate the

interferometer signals and to position the fibers at the distance of maximum sensitivity.

Additionally, the continuous mode can be used to compensate possible drift between

the fibers and the pyramid due to residual thermal expansion of the microscope (see

electronics section). The Nanomotors are mounted in miniature flexure hinge springs,

which are part of the fiber head. These springs allow the adjustment of each fiber axis

in a plane parallel to the pyramid plane.

Different types of the Tribolever device (see chapter 3) can be clamped onto exchange-

able support plates by means of two stiff leaf springs. Three ruby spheres, glued on

the Tribolever support plate, make each Tribolever “click” in with its kinematic mount,

with a reproducibility of better than 10µm, which is a fraction of the fiber endface.

4.3 Electronics

The system electronics can be split into two main components: data acquisition and

sample motion (see fig. 4.4). As discussed in section 4.1, the signal coming from each

interferometer consists of a sinusoidal interference component plus an offset, which

50

4.3 E L E C T R O N I C S

Figure 4.4: Block diagram of the microscope’s electronics (again shown only for the X pair).

From the X1 and X2 signals coming from the interferometer, an adjustable fraction of the ref-

erence signal is subtracted before the first amplification. The result is divided by the reference

signal. This procedure allows the maximum amplification of the signal while introducing the

lowest noise level. In the addition and subtraction electronics, the outputs from the X1 and X2

dividers are combined according to equations 4.1-4 in order to obtain voltages that correspond

to the true displacement of the Tribolever (X and Z). These voltages are then fed into a commer-

cial scan electronics system, which acquires the measured data and controls the sample motion

(scanning and feedback).

51


is due to the difference in reflection amplitudes. In our detection electronics, we first

subtract a fraction of the reference signal and amplify only the interference compo-

nent. The amplified signal is then divided by the reference signal to reduce the effect

of fluctuations in laser diode intensity. The four resulting signals are then added and

subtracted according to equations 4.1-4 to produce the three-dimensional Tribolever

displacement information. All signals are then used as input for an RHK STM200 [96]

system with added input capabilities so that the full, three-dimensional motion of the

tip can be monitored in real time.

Although we have used materials with low thermal expansion coefficients for

the fiber head components, the fiber-pyramid distance drifts slowly due to temperature

variations in our non-climatized laboratory, which is typically 5 C during a day. Us-

ing home-built electronics we apply slow voltage ramps to the Nanomotors, to keep

the fiber-pyramid distance constant for several hours without additional temperature

stabilization of the microscope’s chamber.

4.4 Sample movement

The sample, with maximum lateral dimensions of 10 × 10mm2, sits on a piezo scan

tube [97], which rests inside a set of nested inertial piezo motors that allow for four-

dimensional motion of the sample with respect to the tip: X, Y, Z and rotation (Φ).

The scan piezo tube is directly coupled to the Z coarse approach motor. The Z

motor is located in the center of a X-Y-Φ motor. The Z and XY motors are similar

to those discussed in the literature [98]. The nested design is new, therefore it will be

described in more detail. The X-Y-Φ motor consists of a sapphire disk of 100mm di-

ameter, which is clamped between three pairs of piezo stacks using CuBe leaf springs

(Figure 4.5) .

Each of the stacks contains 3 shear piezoplates. (see figure 4.6). Two plates are

used for the X and Y motion [99], the third one (7×7 mm) is oriented tangetially for

the Φ motion .

The sapphire disk slides on a thin polished Al2O3 plate, which is glued on the

piezo stack (figure 4.6). For the electrical connections of the piezo plates copper beryl-

lium foil [100] is used, which is glued on the shear plates using two-component silver

epoxy glue [101]. Special care is taken regarding the amount of glue used and the

52

4.4 S A M P L E M O V E M E N T

Figure 4.5: The sample stage. (a) perspective drawing of the X-Y-Φ motor showing: (1) CuBe

leaf springs; (2) motor house; (3) v-grooves of the kinematic mount for the fiberhead; (4) sap-

phire disk; (5) z coarse approach motor; (6) upper piezo support plate. (b) cut open view of

the z-motor showing (7) sapphire hexagon; (8) z-motor house; (9) shear piezos; (10) CuBe leaf

spring; (11) ruby ball.

53


Figure 4.6: Exploded view of one piezo stack. Figure (a) shows a side view of the stack.

Figure (b) shows a top view of the piezo stack parts:(1) polished Al2O3-plate (2) Y-electrode

(CuBe-foil) (3) Y-shear piezo plate (4) Ground electrode (5) X-shear piezo (6) X-electrode (7)

Al2O3-plate (insulation) (8) Φ-electrode (9) Φ-shear piezo.

mixing of the two components of the glue. Non-ideal mixing of the epoxy can lead

to elasticity in the stack, which degrades the motor’s performance or can even cause

failure of the motor. Therefore, the amount of the two components of the epoxy is

weighed with highest care using a micro balance with a resolution of 0.01 mg. A thin

layer of glue is then applied on both piezo electrodes as well as on the electrodes us-

ing an optical microscope at 63× magnification. A hole in the center of the electrodes

provides room for excess glue (fig. 4.6). The two piezos are afterwards clamped in a

special holder and the glue is annealed at 150 C for one hour.

We use commercial electronics from Omicron to drive the piezos with a sawtooth-

shape waveform at a frequency of 1kHz [102]. We reach a maximum speed of 600

µm/s in X- and Y-direction, and 0.5/s for rotation. The smallest step size in the Z-

direction is approximately 30nm, in the X- and Y-directions it is 45nm.

4.5 Experimental setup and procedures

4.5.1 Calibration

One of the extreme advantages of the Tribolever is that it allows easy, yet very precise

calibration. We routinely calibrate each Tribolever prior to its first use. By exciting

the Tribolever acoustically with a loudspeaker, which is placed close to the fiberhead,

frequencies of the resonances in the X-, Y- and Z-directions can be measured. Small

Sodalime glass beads [103] are placed on the central cross of the pyramid before a tip

is mounted inside the central cross. The diameters of the beads are determined using

54

4.5 E X P E R I M E N T A L S E T U P A N D P R O C E D U R E S

Figure 4.7: Calibration data for one Tribolever using the added mass method. Plots of the

added mass versus frequency of the resonance peak (a) for the X-direction, (b) for the Y-

direction, and (c) for the Z-direction. (d) Typical resonance spectrum of the microscope and

the Tribolever without added mass in the X-direction (solid line) and in the Y-direction (dashed

line).

a scanning electron microscope (SEM) prior to the calibration. The masses are then

calculated from the diameter, and are ranging from 1.57µg to 9.01µg. By measuring

the resonance frequencies as a function of the added mass, extremely accurate values

of the Tribolever’s lateral and vertical spring constants are determined [104].

Figure 4.7 is an example of one such calibration run. This calibration procedure

has no effect on the Tribolever because the sphere is held in place by gravity on the

central cross of the Tribolever (i.e. no glue is needed). Calibration of the lateral (tor-

sional) spring constant on traditional AFM cantilevers is more time consuming, more

complex, and significantly less accurate [105].

Measured lateral spring constants in this example (figure 4.7) are kX =(1.67±0.03)N/m

and kY = (1.67± 0.04) N/m. These two spring constants are virtually identical and

they are close to the value of 1.48N/m calculated from the dimensions of the legs

55


of the Tribolever using finite element analysis. The measured vertical spring constant

for the Tribolever is kZ = (10.3± 0.1) N/m as compared to the calculated value of

25.8N/m. The large deviation is due to the additional flexibility of a thin diaphragm

(2mm×2mm×10.6µm), which supports the Tribolever on the silicon chip. This dia-

phragm is the result of a wet etch step that forms a wide, recessed window to allow

room for the detection fiber’s access to the pyramid. In the new design of the Tri-

bolever device the geometry of the window was changed to overcome this problem

(Chapter 3) .

We also used the resonance spectra of the Tribolever to estimate the noise levels

of the optical detection and the electronics. With a spectrum analyzer, we measured

the thermally excited X- and Y- resonances of a Tribolever with lateral spring con-

stants of 5.75N/m. The amplitude of the resonant motion can be calculated by the

equipartition theorem 12 kxx2

rms = 12 kBT , where xrms is the root mean-square thermal

motion amplitude, kB is the Boltzmann constant and T is the temperature. If the elec-

tronic instrument noise is much smaller than the thermal motion of the sensor, the root

mean square voltage noise Vrms at the resonance frequency is given by the relation

αVrms = xrms =√

kBT/kx [106]. α is a known calibration factor that relates the output

voltage to the displacement of the Tribolever. We compared the measured Vrms with

the calculated value of Vrms at the thermal limit. We found that the detected noise in

the frequency range of the lateral resonances (9.38 kHz) is a factor of 1.9 (X1) to 4.8

(Y2) higher than the thermal noise. In a FFM measurement, the noise levels are cer-

tainly different. Typical signal frequencies are lower (below 2−3kHz) and the tip is in

contact with a surface. However, the measured noise levels provide a good indication

that the detection is operating close to the thermal limit, which is confirmed by test

measurements on a graphite sample (see next section).

The differences in the noise levels between X and Y might be due to specific details

of the interferometer branches (especially the quality of connectors and of the endface

of each fiber). We assume that the signal to noise ratio can be further improved by

coating the fiber endfaces with a metal layer to increase the reflectance of the fiber/air

interface (see section 4.1).

4.5.2 Tip mounting

After the calibration is performed, a specimen has to be mounted in the center of the

Tribolever that provides the counter surface that will slide over the sample surface.

In most cases this specimen will be a sharp tip as it is used in scanning probe ex-

56

4.5 E X P E R I M E N T A L S E T U P A N D P R O C E D U R E S

periments, but we also used small coated balls to create a “ball-on-flat” geometry. It

would be also possible to create other interesting geometries, like e.g attaching a small

flat or bent crystal to the Tribolever and perform experiments similar to surface forces

apparatus (SFA) experiments.

In our first tests of the microscope, we use a sharp tungsten tip. The tip is electrochem-

ically etched with NaOH from a 50µm thick tungsten wire. After the tip is formed,

the wire has to be shortened to a length of about 200µm using a scalpel. Then the

tip is carefully picked up and transferred to the arm of a homebuilt micromanipulator,

which is constructed from a three-axis stage [107]. The arm consists of a 1mm thick

wire, which is etched to a sharp point at the end. The scanning tip is held at the arm of

the micromanipulator by adhesion. Therefore, the material of the arm has to be chosen

such that it provides sufficient adhesion force to allow the tip to be manipulated but a

sufficiently low adhesion force such that the tip cannot be released inside the center

cross of the Tribolever. For the case of tungsten tips, tungsten was found to work well

as arm material.

When the tip is hanging downwards with the sharp end, the tip is lowererd from the

pyramid side through the center of the cross of the Tribolever and then released from

the micromanipulator. Then, the Tribolever is carefully turned around, such that the

tip is pointing up. The tip is held in place at that point again by adhesion forces, so

that it can be carefully adjusted before it is finally glued to the pyramid. The micro-

manipulator arm is used again to bring a small amount of silver epoxy to the sides of

the tip. After this procedure the epoxy is annealed.

4.5.3 Setup

After the sample holder is mounted on the scan piezo tube, the fiberhead is placed

on the sample stage. Three stainless steel balls, which are connected to the matching

plate of the fiberhead rest in the V-grooves of the sample stage (figure 4.5, item 3).

The complete microscope assembly is shown in figure 4.8. The microscope is built

up inside a small chamber [108], which damps acoustical noise. In addition, the at-

mosphere inside the chamber can be controlled by flowing e.g. dry nitrogen through

it. The relative humidity is monitored using a humidity/temperature meter [109] with

an accuracy of ±2%. If we flow dry nitrogen through the chamber, we can achieve a

relative humidity below 1%. The microscope chamber is mounted on an optical table,

which is resting on a vibration isolation frame [110].

57


Figure 4.8: (a) Perspective drawing of the microscope assembly. (b) Side view with (1) Fiber

positioning head, (2) X-Y-Φ motor, (3) z-coarse approach motor, (4) kinematic mount between

the motor/sample stage and the fiber positioning head.

58

4.6 P E R F O R M A N C E

4.6 Performance

For a first testing of the instrument and the complex data acquisition we used a ca-

libration sample with a regular structure of known dimensions [111]. The employed

sample is a glass substrate that has parallel aluminium ridges with a period of 278±1

nm and a height exceeding 30nm.

Figures 4.9(a)-4.9(c) show topography and friction images that were recorded

simultaneously at a constant normal load of 0.85nN. The topography image shows

parallel ridges although some piezo creep and hysteresis is observed. The height of

the ridges is 33nm. The lateral force images show high frictional forces on top of the

aluminium stripes both in X- and Y-direction plus an additional lateral force, where

the tip ran against the stripes. A plot of a scan line in the forward and one in the

backward direction of image 4.10b shows a typical friction loop (fig. 4.10d).

To estimate the force resolution of our microscope we used a highly oriented

pyrolytic graphite (HOPG) sample. Figures 4.10(a-e) show forward and backward

friction maps in X- and Y-direction of a 3nm×3nm wide area measured at a normal

load of 35.8nN. Here, the X-axis of the piezo was aligned with the X-axis of the Tri-

bolever. However, the measurement was performed in a scan direction, which was not

aligned along either the X- or the Y-direction of the Tribolever, and atomic scale varia-

tions in the friction force could be observed in two directions. The friction loops show

a “sawtooth”-like signal, measured in the X-direction of the Tribolever (fig. 4.10c) and

a “square-wave”-like signal for the Y-direction (fig. 4.10f). From these signals it can

be deduced that the tip follows a “zig-zag” trajectory on the graphite lattice [112]. It is

important to note that the lateral forces measured with our new microscope are much

lower than in previous studies (e.g. [4]). From the noise in the X- and Y-channels dur-

ing the friction measurements, we estimate that the lateral force resolution (rms) in the

measurement is 15pN in the X-direction and 41pN in the Y-direction. The topography

image (not shown) does not show any structure (the corrugation amplitude of 0.21A

rms is due to noise), although the feedback system had been set for constant normal

force. This implies that the topography and friction signals are completely decoupled.

59


Figure 4.9: Simultaneously measured topography and lateral force images of a TDG01 cali-

bration sample. (a) Topography (feedback) image. The grey scale corresponds to a height range

of 39.8nm; (b) lateral force image in the X-direction. The grey scale corresponds to 115nN; (c)

lateral force image in the Y-direction. The grey scale corresponds to 258nN; (d) Friction loop

formed by a forward (solid) and backward (dashed) scan line measured in the X-direction. The

image size is 1.5µm×1.5µm and the constant normal force is FN = 0.85nN.

60

4.6 P E R F O R M A N C E

Figure 4.10: Lateral force maps for a W-tip on HOPG moving in the X-direction. Lateral

forces in the X-direction: (a) Forward scan. The grey scale corresponds to 1.4nN; (b) Backward

scan; grey scale: 1.5nN; (c) friction loop.

61


Figure 4.10: continued (e) Lateral forces in the perpendicular Y-direction: (d) Forward scan;

grey scale: 222pN; Backward scan; grey scale: 243pN; (f) friction loop. All images were mea-

sured simultaneously with FN =35.8nN; Image size 3nm×3nm

62

V

Superlubricity of graphite

· · ·

Graphite is known to be a good solid lubricant. The low-friction

behavior is traditionally ascribed to the low resistance to shear. In this

chapter we show that the ultra-low friction found in friction force mi-

croscopy experiments on graphite is caused by superlubricity and we

speculate about the significance of this for the lubricating properties of

graphite.

63

5. S U P E R L U B R I C I T Y O F G R A P H I T E

5.1 Introduction

Graphite is one of the four allotropic forms of carbon found in nature; the other three

forms are amorphous carbon, diamond, and most recently discovered, fullerenes. The

word graphite is derived from the greek word γραϕειν (“graphein”: to write).

Graphite is found in natural form in lenses or layers as lump or crystalline flake, de-

pending on the geological origin. Synthetic or pyrolytic graphite is produced by ther-

mal decomposition of a hydrocarbon gas over a hot substrate. The world production

of graphite in 2001 was estimated to be 873000t with China accounting for 52% of

the overall production [113].

5.1.1 Structure and mechanical properties of graphite

A ball and stick model of the crystal structure of graphite is depicted in figure 5.1. It

can be viewed as a layered structure with three-fold symmetry. The elastic properties

are highly anisotropic, being very different in the direction of the basal planes and

perpendicular to the planes, which makes graphite flexible but not elastic. The in-

plane Young’s modulus of pyrolytic graphite is 1.02TPa [114]. This is more than two

times higher than the Young’s modulus of typical metals (e.g. tungsten has a Young’s

modulus of 411GPa). Perpendicular to the basal planes, the elastic modulus is only

36.5GPa.

5.1.2 Tribological Properties

Graphite is undoubtedly the most common solid lubricant. Mainly used as flaky pow-

der, it is applied for this purpose where liquid lubricants cannot be used, especially

in high-temperature applications. It is further used as friction-reducing additive in oils

and solid materials ranging from cast-irons to plastics. Graphite is also used as bush-

ings, brushes in electrical motors, and for face seals.

It is not surprising that the research on the tribological properties of graphite has a

long history and it is well established that the friction coefficient for many materials

against graphite in ambient conditions is in the range of 0.08− 0.18 (see e.g. [115]).

In 1928 Bragg argued, based on crystal x-ray structure determinations, why graphite

possesses a low friction coefficient [116]:

64

5.1 I N T R O D U C T I O N

Figure 5.1: Ball and stick model of the graphite structure. Graphite possesses a layered struc-

ture with AB stacking. The cell parameters are a = 0.2464nm, c = 0.6711nm. The nearest

neighbor distance between carbon atoms is 0.1423nm.

“Graphite is a flaky substance; when beaten in a mortar it breaks up con-

tinually into thinner and thinner flakes, but it does not become a powder.

[...] Two neighbours in any one layer are drawn together more closely

than two carbon atoms in diamond. But the great distance between layer

and layer is naturally associated with weakness in their mutual attrac-

tion. It is just this peculiarity that makes graphite so perfect a lubricant.”

20 years later, the intuitive idea of “easy shear” was shown to be incomplete and

unsatisfactory. Finch [117] pointed out, that the cleavage by simultaneous rupture of

bonds in a plane requires very high energy, which is supported by the fact that graphite

does not shear readily, unless a high compression is superimposed [115]. Savage and

others [118–120] found that the friction coefficient for graphite in vacuum was much

higher (0.8) and that the wear was very heavy. The high friction was still observed

after admission of hydrogen or nitrogen. After admission of a few ppm of oxygen

65


or certain organic vapors, low friction and wear was restored. It has been shown that

when metal is sliding on graphite in air, graphite is transferred to the metal surface,

while in vacuum metal is transferred to the graphite surface [121]. Moreover it has

been shown, that a metal oxide layer tends to fix the transferred graphite to the metal,

leading to a smooth transfer film [122]. These observations strongly suggest that the

low friction is only obtained when graphite slides over graphite.

5.1.3 Nanotribological properties

The first atomic-scale friction experiment was performed by Mate et al. [4] using a

tungsten tip sliding over a highly ordered pyrolytic graphite (HOPG) surface. They

found friction coefficients between 0.005 and 0.015. Unlike FFM experiments on

other materials, where usually a power law behavior is found, the dependence of the

friction force as a function of the load was found to be almost linear. Similar friction

coefficients and friction versus load behavior were observed also in subsequent FFM

experiments with a variety of tip materials. Table 5.1 gives an (incomplete) overview.

Tip material Normal force range [nN] Friction coefficient Ref.

Tungsten 0–2000 0.005–0.015 [4]

Amorphous carbon 0–40 0.008±0.005 [123]

Si3N4 N/A 0.006 [124]

Si3N4 30–350 0.001–0.01 [125]

Si3N4 −30–20 0.004±0.001 [126]

Table 5.1: Comparison of the friction coefficient of HOPG found in previous FFM experi-

ments.

FFM experiments also revealed that the scanning tip in FFM experiments on

graphite performs a so-called “stick-slip” movement, where the tip jumps discontin-

uously over single lattice spacings. Fujisawa et al. [61] have shown, using a two-

dimensional FFM, that lateral force images can be explained by two-dimensional, i.e.

“zig-zag” atomic-scale stick-slip movement. A simple classical mechanics model [49]

(see also chapters 1 and 6), the so-called Tomlinson model, where a single-atom tip is

moved along in a sinusoidal potential, reproduced the experimental lateral force maps

of the graphite surface quite well [58, 60]. However, the normal forces that were used

in the simulations had to be chosen one to two orders of magnitude lower than in the

experiments [127].

66

5.2 E X P E R I M E N T A L

5.2 Experimental

We performed measurements on HOPG samples with two different grades. Initial

measurements have been performed on grade ZYH, which has a nominal grain size in

the range of 30–40nm and a mosaic spread of 3.5 ± 1.5 according to the supplier.

However, on our particular sample we found only larger grains. Later measurements

were done on grade ZYA, which possesses a lateral grain size of up to 10mm and a

mosaic spread of 0.4 ±0.1. The samples were cut to a size of 2mm×2mm. There-

fore, the grade ZYA sample consisted probably of a single graphite crystal, while

the grade ZYH sample was polycrystalline. The HOPG was freshly cleaved using

Scotch tape and then mounted in the FFM inside a small chamber, which was con-

tinuously flushed with dry nitrogen. The measurements were typically performed at

humidities of 1–10±1% RH. We used a calibrated Tribolever with lateral spring con-

stants of kTriboleverx,y = 5.75±0.15N/m and a normal spring constant of 26±1N/m. A

tungsten tip was glued into the Tribolever using silver epoxy [101], such that it ex-

tended about 50 to 60µm out of the device. The scanning speed in the experiments

was v = 30nm/s. All force maps were recorded in the form of two-dimensional “im-

ages” with 512×512pixels.

We performed two different types of measurements. In the case of “lateral force

imaging”, the external normal load FN was set to a constant value using the feedback

loop of the scan electronics. Zero normal load was defined as the load at which the

Tribolever was not bent in the normal direction. When the tip was scanned over the

surface, we recorded the lateral forces in the two perpendicular directions defined by

the X- and the Y-axes of the Tribolever, both during the forward and during the re-

verse scan lines. Other than with a conventional AFM cantilever, with the Tribolever

it is possible to choose any sliding direction in the measurement. The lateral force was

defined as the lateral spring constant times the lateral displacement of the Tribolever

pyramid with respect to the FFM base: FlatX ,Y = kX ,Y ∆xTribolever

X ,Y . In general, the X di-

rection of the Tribolever and the fast scanning direction (which is the “X direction”

in a lateral force image) will be rotated with respect to each other. Therefore in the

following we denote X and Y as the directions of the Tribolever axes and x and y as

the scan axes of the lateral force image. By changing the sliding direction, also the

angle between the x direction and the lattice orientation changes.

One forward scan line and the subsequent reverse scan line together form a

67


Figure 5.2: Lateral force image of a tungsten tip on HOPG at FN =−3.2nN. The tip is sliding

in the x direction, which is aligned with one symmetry direction of the surface. Lateral forces

in the X direction (a) Forward scan. Grey scale: 1.7nN, (b) Backward scan. Grey scale: 1.9nN.

Lateral forces in the Y direction (c) Forward scan. Grey scale: 93pN, (d) Backward scan. Grey

scale: 102pN. Image size 3nm ×3nm.

68

5.3 R E S U L T S

closed hysteresis loop, that is often referred to as the “friction loop”. An example

of such a friction loop is shown in figure 5.3a. The area that is enclosed inside the

friction loop corresponds to the dissipated energy during the back and forth sliding. We

calculated the average friction force in the X and in the Y direction of the Tribolever

by taking the difference of the mean value of the lateral force in the forward direction

and in the reverse direction:

FFX ,Y ≡

( 〈Flatf wd〉−〈Flat

rev 〉2

). (5.1)

Here, we also define the friction force against the sliding direction as a positive

quantity. The mean value of the lateral force 〈Flat〉 was only obtained from those parts

of the friction loop where the lateral force had fully developed, e.g for x> 0.7nm in

the forward scan line and for x< 2.3nm in the reverse line.

To obtain the friction force in the sliding direction, we computed the appropriate

vector addition of the friction forces in the X- and the Y-direction:

FF = FFX cosζ+FF

Y sinζ, (5.2)

where ζ denotes the angle between the X direction of the Tribolever and the sliding

direction of the tip (x).

The second type of measurement that we performed is referred to in the litera-

ture to as “friction force spectroscopy” [128]. Here, we initially set the normal force

FN to a positive value and lowered it during scanning until the tip lost contact with

the surface. From a single line, one (FN ,FFX ,FF

Y ) data point was obtained using equa-

tion 5.1, for each value of FN . Together, the scan lines resulted in a friction spectrum

FF (FN).

5.3 Results

5.3.1 Lateral force images

Figure 5.2 shows typical lateral force images measured simultaneously in the X-

direction of the Tribolever (a,b) and in the direction perpendicular to that (c,d) on

the polycrystalline HOPG surface. The x- and X-directions were aligned. Not shown

is the topography image (Z), which does not reveal any surface features. The rms

roughness of 0.27A, measured from the topography image is caused only by the noise

69


Figure 5.3: Comparison between an experimental friction loops and a force loop calculated

using a Tomlinson model for a single-atom tip (for details see chapter 6). The calculation was

performed using a potential energy amplitude of V0 = 0.08eV and lateral spring constants

kx = ky = 2.65N/m.

in the measurement. As has been shown in several experiments [4, 61, 62, 123], the

lateral force in the sliding direction exhibits typical sawtooth waveform, which can be

explained by atomic-scale stick-slip motion. Depending on the sliding direction, the

lateral force image in the perpendicular direction shows different patterns. If the slid-

ing direction is parallel to one of the six symmetry directions of the HOPG surface,

the lateral force measured perpendicular to the sliding direction shows a horizontal

stripe pattern (Fig. 5.2 c,d). If the tip is scanned under a different angle, the patterns

in the X- and the Y-images change. A second example is shown in Figure 4.10, where

the Y-image exhibits a checkerboard-like pattern. There, the tip performs a “zig-zag”

stick-slip movement over the graphite lattice, and the forces in the sliding direction

cannot be regarded independently from those in the perpendicular direction.

Figure 5.3 shows a comparison between a friction force loop, that was obtained

from one forward and one reverse scan line of figure 5.2 and a friction loop, obtained

from a Tomlinson model calculation (chapter 6). The comparison shows good qualita-

tive agreement between the experimental and the calculated friction loops, suggesting

that our measurements can be understood using a two-dimensional Tomlinson model.

However, to obtain quantitative agreement between the force magnitudes in the

calculated and experimental force loops, we had to use a lateral spring constant in the

70

5.3 R E S U L T S

calculation which differed from the known kTribolever.

This suggests that also the elastic compliance of the contact contributes to the

total spring constant. The effective spring constant can be obtained directly from the

slope those parts of the measured force loops where the contact sticks [31, 129]. To

understand this, one can view the measurement system as a set of springs in series.

The effective spring constant is constituted of

dFlatX

dx=[(

kTriboleverx

)−1+(kcontact

x

)−1]−1

, (5.3)

where kTriboleverx is the known spring constant of the Tribolever and kcontact

x is called

“contact stiffness” [31]. This contact stiffness can be separated further in

kcontactx =

[(kadd

x

)−1+(kinter f ace

x

)−1]−1

, (5.4)

where kinter f acex = ∂2V/∂x2 =

(2πa

)2V0 is the spring formed by the local curvature in

the wells of the potential energy landscape of the substrate as experienced by the tip,

and kaddx is the spring formed by additional elastic compliances such as the elastic

compliance of the tip and that of the sample. Since we cannot distinguish between the

compliances introduced by the tip and those introduced by the surface, we will take

these together.

From equation 5.3 we find a contact stiffness in figure 5.3a of 2.3±0.3N/m. Be-

cause the curvature of a corrugated potential energy landscape acts also in the Tomlin-

son model as a spring that contributes to the contact stiffness, also the calculated fric-

tion loop possesses an effective stiffness that differs from kTribolever, but since kaddx = ∞

in the model, we simply have kcontactx = kinter f ace

x =(

2πa

)2V0 in the model calculation.

From the force at which the slip events take place, we obtain the amplitude of the

potential to be 0.08eV. For the potential corrugation of V0 = 0.08eV, the ‘potential

spring constant’ is kinter f acex = 15.9N/m. This kinter f ace

x also contributes to the experi-

mentally found contact stiffness, so that we can now estimate the additional stiffness

to be kaddx = 2.7 N/m. We find indeed good agreement between the experimental force

loops and the calculated one, if we use 2.7N/m in the calculation. The precise origin

of the additional elastic compliance cannot be determined from these measurements.

A clear difference between the simulated friction loop and the experimental one,

is that the positions where the slip occurs in the experimental data display variations

71


in the order of 25 % of the lattice spacing. In the parts of the friction loop where the tip

is sticking, the lateral force fluctuations are much too small to account for these vari-

ations. This is clearly seen also in all lateral force force images, which “look” noisy,

despite good lateral force resolution. We believe that these fluctuations, which can be

seen also in other FFM experiments with comparable effective spring constants and

normal loads (e.g. [55]), are thermally induced. Using a modified Tomlinson model

that included a term representing the effect of random thermal fluctuations, Sang et

al. [130] recently studied thermal effects on atomic friction. With an effective spring

constant of ke f f = 0.86N/m to fit the data from Gnecco et al. [55], they found that

the distribution function of the maximum lateral force in the friction trace, which is

equivalent to the slip position, had a full width at half maximum (FWHM) of approx-

imately 17 %.

In order to evaluate thermal fluctuations in our experiment, we simulated them in the

Tomlinson model calculations using a simple Monte-Carlo approach. At every time

step ∆t, where ∆t is ∆xt/v, we calculated the transition rate Γ, which is an inverse

measure of the time needed before a thermally induced jump over the energy barrier

takes place,

Γ = f0 exp

(−∆V (xt)

kBT

), (5.5)

where f0 is the eigen frequency of the Tribolever, ∆V (xt) is the remaining energy

barrier with respect to the momentary tip position, kB is the Boltzmann constant and

T is the temperature. The “probability” Γ∆t for a thermally induced jump over the

barrier was then compared with a number R ∈ [0,1] obtained from a random number

generator and, if R was lower than Γ∆t, a jump at position xt was induced.

Figure 5.4 shows the normalized distribution for 15000 simulated slip events

using kx,y = 2.68N/m, V0 = 0.08eV, v = 30nm/s and an effective mass of the Tri-

bolever of 10µg. The distribution possesses a FWHM of 33pm, which is 13.5% of the

graphite unit cell. In addition, the jumps occurred on average 38pm before the static

case, recover in the Tomlinson model at T = 0.

5.3.2 Friction versus load

Figures 5.5a-f show three lateral force maps and friction loops measured in the for-

ward X-direction at different normal loads. Again, the x-direction was aligned with

the X-direction of the Tribolever. Figures 5.5g-i display the average waveform of the

lateral force variations over one lattice period. Already at a negative load of −3.4nN,

72

5.3 R E S U L T S

Figure 5.4: Normalized distribution of the slip position at temperature T = 293K. The origin

of the x-axis lies at the slip position of xt without thermal fluctuations. The calculation was

performed using V0 = 0.08eV and kx,y = 2.65N/m.

variations in the lateral force with lattice periodicity are faintly visible. However, these

variations do not have a “sawtooth” shape, typical for stick-slip motion but a “cycloid”

shape (fig. 5.5g). At this normal force, the area enclosed inside one friction loop (fig.

5.5d) is very small. In other words, the energy dissipated during one sliding cycle is

nearly negligible. Correspondingly, the average friction force obtained from the com-

plete lateral force map, according to the procedure described in section 5.2 (eq. 5.1)

is as low as 1.8+16−1.8 pN. At a higher normal load of 11.6nN, the variations in the lat-

eral force increased, and the lattice can be seen more clearly in the force map, but

the average friction force did not increase significantly, as can be seen from the force

loop in figure 5.5e. This is surprising, because increasing the normal load by about

15nN is usually expected to lead to an increased contact area and thus, to an increase

in the friction force. Note, that the waveform of the lateral force variations changed

and appears “sawtooth” shaped (fig. 5.5h). At a still higher normal load of 41nN we

73


Figure 5.5: Lateral force images in the forward X direction (a-c) and force loops (d-f) for

different normal loads; (a) FN = −3.4nN, (b) FN = 11.6nN, (c) FN = 42.6nN; Image size

3nm×3nm. Graphs (g-i) show the typical waveform obtained from the forward scan lines shown

in (d-f) by averaging over three lattice spacings.

observed clearly “sawtooth” shaped lateral force variations (fig. 5.5i) and an increase

in the average friction force to 62±19pN, (fig 5.5f).

Complete friction versus load curves were obtained from friction force spec-

troscopy measurements (see sect. 5.2 for precise procedure). Figure 5.6a shows an

example for a contact that behaved similarly to the one shown in figure 5.5. The nor-

mal force was reduced from 45nN until the tip lost contact with the surface at −24nN,

74

5.3 R E S U L T S

Figure 5.6: Friction force versus normal load curves for two different contacts. Notice that in

both curves the friction force varies little, but the average friction force in (b) is about a factor

of 16 higher than in (a).

at which point the tip was fully retracted by the feedback electronics. The data in fig-

ure 5.6a are representative for a large number of measurements. In the normal force

range from −24 to approximately +30nN the friction force stays almost constant at

a very low value of 28± 16pN. The frictional behavior as a function of normal load

obtained from the friction force spectroscopy experiment shown in figure 5.6a is in

agreement with the friction forces obtained from individual lateral force images at

different, constant normal loads. As in figure 5.5, we see very low energy dissipation

up to about FN = 40nN. For normal loads above 40nN we observe a slight increase.

To our surprise, a smaller number of measurements produced entirely different fric-

tion versus load curves. An example is shown in figure 5.6b. The curve was measured

under similar conditions as the one in figure 5.5a. Now, the friction force between −11

and +24nN normal load is on average 453± 16pN, which is a factor 16 higher than

in the measurement shown in 5.6a. The friction force remained at a high and almost

constant level until the tip lost contact at FN = −16nN. In these high-friction mea-

surements, the typical increase in friction between loads of 0 and 25 nN was as low

as 0.05–0.4%. Each friction versus load measurement on the polycrystalline HOPG

surface resulted in a curve of one of the two types shown in figure 5.5, but with dif-

ferent precise values of the average friction force. The measured friction force curves

switched back and forth between the two types (figs. 5.5a and b) randomly in intervals

75


ranging from days to several weeks. Subsequent measurements that were performed

within a short period of several hours were highly reproducible. The switching in the

average friction force could not be attributed to changes in the ambient conditions

such as the humidity inside the FFM chamber, since we did not observe systematic

changes in friction when we varied the humidity from 9 to 42%RH during one experi-

ment. Also, no systematic differences were found between the friction force on freshly

cleaved HOPG and HOPG surfaces that had been exposed to ambient conditions for

several days.

These results raise several important questions. First, why does the friction force

remain almost unchanged over a wide range of normal forces? For other substrates,

FFM measurements usually show a substantial dependence, which, for modest loads,

can be attributed to the elastic variation in the contact area with the load (e.g. [74]).

Secondly, what is the nature of the difference between the two completely different

friction versus load curves? Thirdly, what is responsible for the switching between the

two different states of the contact? Trivial tip changes can be ruled out directly, since

all experiments were performed using the same tip. Finally, what is the mechanism,

that allows the tip to slide with near-zero friction, even at a normal load as high as

30nN? It has been pointed out by Tomanek et al. [50] that it is possible to obtain fric-

tionless sliding in the framework of the Tomlinson model when a single-atom tip is

moving over the surface without instabilities, i.e. without the familiar stick-slip mo-

tion. This can occur when the tip is moving through a potential energy landscape with

a corrugation amplitude that is small with respect to the stiffness of the measurement

system (see chapter 1). However, in our case, this would require a spectacularly low

potential corrugation and an unrealistically high yield strength of the tip to remain a

single-atom contact at a normal load of 30nN.

One single mechanism that could provide a natural answer to all four questions

is that of superlubricity, which was introduced already in chapter 1. Superlubricity

has been proposed to cause two parallel surfaces to slide over each other without

energy dissipation when they are in incommensurate contact [63, 64]. Although this

phenomenon has been proposed already in 1990, it has found little attention, in spite

of the promise that it can dramatically reduce friction in dry, unlubricated contacts,

which would make it highly relevant for a wide variety of applications, such as e.g.

nanoelectromechanical systems (NEMS).

76

5.3 R E S U L T S

In the light of superlubricity, the difference between the high- and low-friction force

loops can be the result of a difference in commensurability, the high friction corre-

sponding to a fully commensurate contact and the low friction to an incommensurate

contact. The large variation in commensurability strongly suggests that the sliding has

been taking place between two graphite surfaces, one being the HOPG substrate, and

the other being a small piece of graphite, i.e. a graphite flake, that is attached to the

tungsten tip. A flake introduces a flat surface parallel to the graphite substrate from

which it originates, a geometry needed for superlubricity to occur. Depending on the

degree of commensurability between the lattice of the substrate and that of the flake,

the friction would be high, as in figure 5.6b, when the flake and the substrate are in reg-

istry, or close to zero, as in figure 5.6a, when they are out of registry. The presence of a

flake would also explain the almost complete absence of a dependence of the friction

on the normal load. Load-independent friction has also been observed in FFM ex-

periments on thermally oxidized MoS2, and it was proposed that MoO3 nanocrystals,

that grew during the oxidation process on the MoS2 surface [131], acted as a spacer

between the tip and the sample, such that the contact area remained unchanged upon

loading. In the present case, the contact area would be completely determined by the

flake size, which would be independent of the loading force. Hence, the friction would

only increase slightly with normal load as the result of the increase in contact pres-

sure. Finally, the seemingly random selection of either low or high friction states can

be explained easily by the slow drift of the FFM or the irreproducibility of the mount-

ing procedure of the HOPG sample holder after cleaving. This results in a change of

the measurement location from one grain of the ZYH-quality polycrystalline HOPG

substrate to the next, differently oriented grain. We will return to this point in section

5.3.5.

5.3.3 Friction vs. sample rotation

In order to obtain further evidence for our interpretation, we rotated the graphite sam-

ple in small steps with respect to the tip, using the Φ-motor of our FFM. Because the

Φ-motor does not rotate perfectly concentrically around the tip, the tip did not stay on

the same area of the sample during rotation. Therefore, we used a single crystalline

HOPG sample (ZYA-grade) to make sure that the lattice orientation of the sample

would not change because the tip would land on a different grain after a few rotational

steps. For each orientation, we performed a complete friction force spectroscopy mea-

surement for loading forces between +25nN and pull-off (−22nN). We recorded the

77


Figure 5.7: Lateral force images (forward direction) and friction loops measured in the X-

direction at 60 (a), 72 (b) and 38 (c) rotation angle Φ. Normal force (a) and (c) FN = 18nN;

(e) FN = 30.1nN; grey scale (a) 590pN (c) 270pN (e) 265pN; Image size 3nm ×3nm.78

5.3 R E S U L T S

lateral forces in the X- and the Y-direction and calculated the average friction force in

the sliding direction of the tip according to equations 5.1 and 5.2.

Figure 5.7 shows lateral force maps and force loops measured in the X-direction

for different rotational orientations. Note that the X- and x-direction are not aligned

here, because the scan piezo rotates together with the sample. A typical force loop is

shown in figure 5.7b, which was measured at a normal force of 18nN. The lateral force

in Fig. 5.7b displays clearly resolved atomic-scale stick-slip sliding and the average

friction force parallel to the sliding direction is 203.3±20pN. Figures 5.7c,d and e,f

show FFM measurements measured with the graphite substrate rotated +12 and −22

degrees around an axis normal to the surface, and parallel to the tip. The rotation by

12 has caused the average friction force to reduce by more than one order of mag-

nitude, to 15± 15pN. Rotating 22 away from the first measurement in the opposite

direction also has caused a reduction to 8+16−8 pN, which is equal to zero friction within

the detection limit of our instrument. This variation of the friction force with angle

was completely reversible. Notice that the ultra-low lateral forces in figures 5.7c-f still

exhibit regular variations with the periodicity of the graphite substrate.

Figure 5.8 displays the average friction forces measured over a 100 range of

substrate rotation angles. We recognize two narrow angular regions with high friction,

separated by a wide angular interval with nearly zero friction. The distance between

the two friction peaks is 61±2, which corresponds well with the 60 symmetry of in-

dividual atomic layers in the graphite lattice. This result corresponds precisely with the

expectation within the scenario of superlubricity. After every 60 rotation, the lattices

of the substrate and the graphite flake align and the friction is high. For intermediate

angles, the lattices are incommensurate and the friction force is close to zero.

The maximum friction forces of the two peaks were found to differ by 103pN. This

possibly reflects the fact that due the AB stacking, graphite does not really possess

a 60 symmetry but rather a 120 symmetry, which should have an influence in case

the flake is more than one layer thick. Unfortunately, we could not measure a third

peak in the present experiment, so that we have not been able to test this hypothesis

experimentally.

We can use the peak width in figure 5.8 to estimate the flake diameter. As an illus-

tration, a single-atom tip should show high friction for all orientations, while an in-

finitely large contact would be completely superlubric, except for infinitely narrow

79


Figure 5.8: Average friction force versus rotation angle Φ of the graphite sample around an

axis normal to the sample surface. Two narrow peaks of high friction were observed at 0 and 61

degrees, respectively. Between these peaks a wide angular range with ultra-low friction close

the detection limit of the instrument was found. The first peak has a maximum friction force of

306±40 pN, and the second peak has a maximum of 203±20 pN. The curve through the data

points shows results from a Tomlinson model for a symmetric 96-atom flake (see chapter 6).

angular ranges around perfect registry, if we assume that no energy can be dissipated

via elastic deformations within the contact. For finite-size contacts, the cancellation of

lateral forces, which causes superlubricity, can be considered complete when the mis-

match between the two lattices adds up to one lattice spacing over the diameter of the

contact. The mismatch condition provides us with the estimate that tan(∆Φ) = 1/D,

where ∆Φ is the full width at half maximum of the friction peak, and D is the flake

diameter, expressed in lattice spacings. From the widths of the two peaks in figure

5.8, of 5.4±1.0 for the first peak and 6.5±0.8 for the second, we estimate that the

flake diameter is between 7 and 12 lattice spacings. How good this estimate is, will

be demonstrated in chapter 6, where we compare the experimental data with a series

of results obtained from a modified Tomlinson model calculation in which we moved

various rigid graphite flakes, connected to the Tribolever springs, in a rigid hexagonal

potential, reflecting the periodicity of the graphite surface. The solid curve in figure

80

5.3 R E S U L T S

5.8 is the calculation for a symmetric 96-atom flake (diameter of 11 atomic spacings).

It provides an excellent fit to the experimental friction data.

We have to mention here that reproducible measurements, such as those in fig-

ure 5.8, in which the same relative orientations always led to the same friction loops,

were rare, the fixed-flake situation occurring as the exception, rather than the rule.

More often, results were obtained of the type described in the next section.

5.3.4 A ‘loose’ flake

Figure 5.9 shows two lateral force maps, measured in the X-direction, before (a) and

after (b) a deliberate, modest misalignment by less than 2 of an initially aligned

contact. While the friction force in figure 5.9a is as high as 550± 21pN (see also

fig. 5.9c), the friction force in the upper part of figure 5.9b is reduced to 27± 16pN

(see also fig. 5.9d). In the course of a few scan lines, the friction force gradually

restores back to about 431± 17 pN (fig. 5.9e) and at the last scanline of figure 5.9b

the friction is as high as in figure 5.9a. We interpret these events as the effect of the

torque exerted by the surface on a nearly aligned flake, which was attached to the

tungsten tip sufficiently loosely to rotate back into registry. During the restoration of

the high friction force the lateral force exhibited irregular sharp peaks, which might

have been caused by the dynamic process of reorientation of the flake.

5.3.5 Large-scale images on polycrystalline graphite

The effect of a change in commensurability between a flake and the surface was also

observed on the polycrystalline graphite sample. In section 5.3.2 we already ascribed

the switching from low friction to high friction and vice versa to the different orien-

tations of neighboring grains on the polycrystalline substrate. Figure 5.10a is a large-

scale topographic image of the polycrystalline grade ZYH sample. The image shows

a grain boundary that runs across the surface. The height and lateral dimensions of the

boundary are similar to those for grain boundaries on HOPG that have been observed

in STM experiments [132]. Figure 5.10c shows the lateral force image in the forward

direction of the same area. The grain in the upper right corner of the image exhibits a

significantly lower friction force, than the grain in the lower left corner. This can be

also seen from the friction loop shown in 5.10d, measured in the x-direction, where

the friction force on the left grain was found to be 319±30pN and on the right grain

222± 29pN. However, the friction force in the Y-direction changed by only 10%.

81


Figure 5.9: Lateral force images (a,b) and friction force loops (c–e) before and after a modest

rotation ∆Φ of less than 2 of an initially aligned contact. The three pairs of markers at the

sides of the images indicate the positions where the three force loops were taken. The lateral

force in (c–e) in the forward scan direction is shown in black and in the backward direction in

grey; Normal force (a) FN = 23nN; (b) FN = −0.9nN; Image size 3nm ×3nm.

82

5.3 R E S U L T S

Figure 5.10: Topography image (a) and lateral force map in the forward x-direction (c), show-

ing a grain boundary running across the polycrystalline HOPG surface. Graph (b) shows a

cross section along the line indicated by the markers in (a). Graph (d) shows a force loop along

the line indicated by the markers in (c); normal Force FN = 5.1nN; Image size 500nm ×500nm.

Also from atomic-scale measurements (3nm×3nm) we found a change in the friction

force in the sliding direction from 326±33pN on the left grain to 221±18pN on the

right grain. The height line (5.10b) taken from the topographic image shows also a

change in the slope by 0.7 between the two grains. Ruan et al. [133] have proposed

a ’ratchet mechanism’, in which the local friction coefficient in microscale measure-

ments should scale with the slope θ of the sample as µ = µ0(1+ tan2 θ

). Therefore

83


it might be possible that the change in friction between the two grains was slope in-

duced. However, using this equation to compute the change in the friction coefficient

due to the change in slope we find ∆µ = 0.05%. Thus, the small change in slope cannot

explain the observed large change in the friction. Again we conclude that the change

in the friction from one grain to another is the effect of a change in commensurability

between a flake and the substrate.

5.3.6 TEM analysis of the tip

We have used high-resolution transmission electron microscopy (TEM) to image the

tungsten tip after our friction experiments. For this purpose, we glued the pyramid of

the force sensor onto a holder that fitted inside the TEM holder (the pyramid had to

be broken out of the Tribolever chip). The TEM analysis showed that the tungsten tip

had a radius of about 80 nm and was covered with a smooth amorphous layer of 7 nm

thick tungsten oxide (fig. 5.11a). Unfortunately, thorough TEM inspection of the tip

was not possible due to rapid removal of the amorphous layer by the electron beam.

Before the tip was modified by the electron beam, which occurred within minutes,

it was not possible to properly correct for astigmatism. This is seen in figure 5.11b,

which displays the tip after approximately 5 minutes. The amorphous layer has been

almost completely removed by the electron irradiation. In the same image we find

several locations that look like layered structures similar to graphite sheets. At a first

glance, one might be tempted to identify these as graphite flakes. However, at that

point of the TEM experiment the tip was already strongly modified by the electron

beam and, in addition, it is possible that these features merely appeared like layered

structures due to astigmatism. Therefore, the present TEM analysis cannot provide

clear evidence for the presence or the absence of either a multilayer flake or a single

layer of graphite.

5.3.7 Friction anisotropy

The measurements of the friction force versus sample rotation, presented in section

5.3.3, were taken for a single sliding direction with respect to the substrate. Miura et.

al found for the sliding of a 1mm×1mm large MoS2 flake on a MoS2 surface [134],

as well as for a 1mm ×1mm large graphite flake on HOPG [135], a variation in the

friction force between 0 and 2nN as a function of sliding direction. Before we discuss

friction anisotropy in our experiment, we first clarify the terminology. Often friction

anisotropy refers to the variation in friction as a function of the sliding direction [136],

84

5.3 R E S U L T S

Figure 5.11: High-Resolution TEM micrographs of the tungsten tip initially (a) and about 5

minutes after the tip was first exposed to the electron beam (b). The circles in (b) show areas

in which layered structures were observed. A zoom-in into one of these regions is shown in the

inset.

85


Figure 5.12: Friction as function of the sliding angle ζ for a commensurate contact (Φ = 0).

The open circles denote the friction FFX measured in the X-direction of the Tribolever, the open

squares the friction FFY in the Y-direction. The closed circles show the friction FF in the sliding

direction calculated from these components, according to equation 5.2. The dashed lines are a

cosine and a sine fit to the friction components in the X- and the Y-direction. The dotted line

shows calculated friction forces, obtained using a Tomlinson model (see chapter 6).

whereas other authors use this term also for changes in friction as a function of com-

mensurability [34] (superlubricity) or for both phenomena [134]. To avoid misunder-

standings, we will use the term friction anisotropy strictly for the variation of friction

with respect to the sliding direction. In the measurements of figures 5.7, 5.8 and 5.9,

where we recorded the friction force as a function of the rotation angle Φ of the sam-

ple, the sliding direction did not change with respect to the substrate lattice because

the scan piezo rotated together with the sample. This is why we can directly rule out

anisotropy as a cause for the observed peaks. However, if a graphite/graphite contact

does exhibit high friction anisotropy, the dependence of the friction force on the de-

gree of incommensurability might change dramatically with sliding direction. In order

to investigate this, we measured the friction force for a number of sample rotation an-

gles Φ as a function of the sliding direction ζ. We invariably observed that the friction

86

5.4 D I S C U S S I O N

force FF varied between high and low simultaneously, for all sliding directions ζ.

The friction anisotropy was very modest (at most 25%) and did not interfere with the

commensurability effect. As an example, figure 5.12 shows the friction force in the

X-direction and in the Y-direction as a function of sliding angle for a commensurate

contact, with high friction. Whereas the friction forces in the X- and Y-directions of

the sensor strongly varied as a function of the sliding angle, the total friction force

in the sliding direction remained nearly constant. The difference between our results

and those in Refs. [134, 135] might be explained by the fact that in Refs. [134, 135]

the friction versus sliding direction was measured using a traditional AFM cantilever

with different sensitivities in the X- and Y-directions. It might be possible that only

the friction component along one direction was measured rather than the full friction

force in the sliding direction. We will show in chapter 6 that in the framework of the

Tomlinson model, for a graphite flake on a graphite substrate, a modest anisotropy is

to be expected for all sample rotation angles Φ.

5.4 Discussion

All measurements presented in this chapter were consistent with friction between a

graphite flake and the graphite substrate. In fact, the notion that graphite flakes adhere

frequently to the tip of scanning probe microscopes has originated already many years

ago in order to explain ’unusual’ contrast in scanning tunnelling microscopy images

(e.g [137,138]). Although we have not been able to directly observe the presence of a

graphite flake with TEM, our friction measurements provide firm evidence that a flake

caused the observed superlubricity.

A few earlier experiments provided indications of superlubricity. Hirano et al. [34]

found a modest reduction in friction between two mica sheets from 8 · 10−4 N to

2 · 10−4 N, caused by rotating the two sheets with respect to each other. In a modi-

fied scanning tunnelling microscope (STM) experiment [66] the same authors claimed

the observation of superlubricity between a tungsten tip and a Si(001) sample. How-

ever, the evidence provided in the paper is rather incomplete. No normal force was

measured or controlled, and the tip was actually only in tunnelling range from the

substrate. The friction force was measured only for two relative orientations. No typ-

ical friction loops were shown. Ko et al. [67] showed that variations in the friction

coefficient caused by the rotation of two (100) metal surfaces with respect to each

87


other do not necessarily have to be the result of a change in lattice mismatch (see also

chapter 1).

Beyond showing the existence of superlubricity between graphite surfaces on the

nanometer scale, which might explain the ultra-low friction coefficients as well as

the large variations found in previous FFM experiments on graphite (table 5.1), our

observation might also have important implications for understanding the macroscopic

lubrication properties of solid lamellar lubricants.

Indications that also in a macroscopic sliding contact of lamellar solids rotated

flakes are created, come from Transmission Electron Microscopy (TEM) observations

by Martin et al. [139] on MoS2. In contrast to our single-contact FFM experiment,

macroscopic-scale friction involves multiple micro-contacts with different sizes and

orientations. Based on our observations, one may speculate that in the case of macro-

scopic lubrication by graphite a large fraction of the graphite-graphite contacts will be

in the superlubric state, while only a small fraction will be in registry. This should lead

to a tremendous reduction in the average friction force, experienced in the ensemble

of micro-contacts, and thus might explain the excellent lubrication by graphite and

similar, layered materials, such as MoS2 and Ti3SiC2. It was shown by Liu et al. [140]

that under sliding conditions, a graphitized tribolayer is formed on top of of diamond-

like coatings (DLC), which leads to a decrease of the friction coefficient after run-in.

Therefore, probably also the excellent lubrication properties of DLC films might be

caused by superlubric graphitic contacts.

We suppose that for sufficiently large contacts superlubricity might break down, as the

two lattices are not perfectly rigid, and a network of misfit dislocations should form

between the two [141]. Therefore, to give an estimate to what percentage superlubric-

ity contributes to the good lubrication properties of solid lubricants, more experiments

are needed to find out at which contact size and normal load superlubricity breaks

down and to find out, how many of the “loose” flakes, which might form the majority

species in a real tribological contact, twist back into registry. Indications that superlu-

bricity breaks down at higher contact pressures might be found in figure 5.6a, where

we observed a slight increase in the friction above 40nN normal load.

Other graphitic systems have been found that show remarkable tribological proper-

ties, which might also be attributed to the phenomenon of superlubricity. TEM obser-

vations [142] imply that nested carbon nanotubes (CNT) possess very low inter-wall

friction. In most cases, the inner and outer tubes in a multiwall CNT form an in-

88

5.5 C O N C L U S I O N S

commensurate graphitic system, similar to a rotated flake that slides over a graphite

surface. Falvo et al. found that carbon nanotubes slide over HOPG when they are out

of registry but rotate when they are in registry with the underlying surface [68, 69].

5.5 Conclusions

By measuring atomic-scale friction as a function of the rotational angle between a

tungsten tip and a graphite surface we have shown that the origin of the ultra-low fric-

tion of graphite in friction force experiments lies in the incommensurability between

between a flake that is attached to the tip and the graphite surface. The observation of

two narrow peaks in the friction force that are separated by 60 provided clear exper-

imental evidence of superlubricity. The width of the two peaks allowed us to estimate

the contact diameter to be 7 to 12 lattice spacings. The occurrence of superlubricity in

layered materials might explain on why these materials are good solid lubricants.

89


90

VI

Superlubricity in the Tomlinson model

· · ·

In this chapter, the friction between a finite nanometer-sized

graphite flake and a graphite surface is analyzed in the framework of

a modified Tomlinson model with finite contact size. The calculation

shows that the orientation dependence of the friction provides informa-

tion on the contact size and demonstrates the effect of the shape of the

flake.

91

6. S U P E R L U B R I C I T Y I N T H E T O M L I N S O N M O D E L

6.1 Introduction

In the previous chapter we reported atomic-scale measurements, which demonstrated

that the friction between two graphite surfaces depends strongly on the commensura-

bility between the two lattices.

Atomic-scale friction in the absence of wear, plastic deformation, and impurities

has been studied theoretically using simple ball-and-spring models (see chapter 1)

such as the Tomlinson model [49, 143], the Frenkel-Kontorova [53, 144] model, or

a combination of these models, known as the FKT (Frenkel-Kontorova-Tomlinson)-

model [145]. A recent, extensive overview of the field of computer simulations and

modelling of friction, lubrication and wear by Robbins and Muser has been published

in Ref. [146].

Lateral force maps, obtained from FFM experiments, have been explained qual-

itatively using a two-dimensional Tomlinson model. Most of these models have in-

volved either point-like tips or infinite surfaces [58, 60, 127, 147, 148]. However, it is

likely that in the experiments the contact consisted of a large, but finite number of

atoms, performing a collective, atomic-scale slip-stick motion. This is confirmed by

the fact that the normal force in the model, needed to obtain quantitative agreement

with experimental friction force maps, is usually substantially lower than observed

experimentally [58].

Lateral forces in finite, nanometer-sized contacts recently have received atten-

tion in a few theoretical studies. Molecular dynamics and total-energy minimization

calculations (“T = 0”) of a flat Cu(111) tip consisting of 25 to 361 atoms sliding over

a Cu(111) surface have been performed by Sørensen et al. [65]. For matching surfaces

a collective atomic-scale slip-stick motion was found. For misaligned surfaces, the av-

erage friction force vanished. When the friction force did not vanish, this was found

to be due to local pinning at the corners of the contact, a finite-size effect that disap-

peared when the contact area was increased sufficiently. Similar results were found

by Tamura et al. [149] who studied talc(001) surfaces in an MD simulation and He

et al. [150]. Recently, Buldum et al. [151] performed total-energy minimization and

molecular dynamics calculations to study the motion of carbon nanotubes (CNT) on

a graphite surface. They found sharp, unique energy minima for different types of

CNT’s as a function of the orientation of the tube axis with respect to the surface lat-

tice. These energy minima were separated by 60. They marked the transition from

sliding to rolling, when the CNT’s were subjected to a lateral force.

92

6.2 M O D E L

Here, we explore whether a simple modified Tomlinson model, adapted for a fi-

nite, multi-atom tip, can reproduce the observed superlubricity of graphite. In addition,

we use the model to estimate the size of the graphite/graphite contact in the measure-

ments of chapter 5 and to study the effect of the shape of the flake. In graphite, the

van der Waals forces between sheets are weak when compared to the covalent bond-

ing between atoms within the sheet. This makes graphite (and other lamellar materials

such as mica and MoS2) very well suited to be modelled with the Tomlinson model,

because the strong bonds within the sheets will make them slide with respect to each

other, almost without internal deformation. However, by completely neglecting elas-

ticity of the flake, we should not expect the model to fail for large contact sizes, as

will be discussed in section 6.4.

6.2 Model

The graphite flake is modelled as a rigid, finite lattice, composed of hexagonal carbon

rings as shown in figure 5.1. The flake is coupled to a support by springs in the X- and

Y-directions. Via these springs, the support pulls the flake through a periodic potential.

The interaction between a single carbon atom and the graphite surface is ap-

proximated by the interaction potential used in [35]:

Vint(x,y,z) = −V0(z) [2cos(a1x)cos(a2y)+ cos(2a2y)] (6.1)

with a1 = 2π/(0.246nm) and a2 = 2π/(0.426nm), determined by the periodicity of

the unit cell. Equation 6.1 represents the first order fourier expansion of the interaction

between a single atom or a point-like tip and the first layer of a graphite surface,

assuming pairwise Lennard-Jones potentials [152]. The corrugation of the potential

energy surface V0(z) depends on the separation z between the flake and the surface.

Because the relative positions of the atoms in the flake are fixed, the flake-

surface interaction potential is simply obtained by the summation over N atomic con-

tributions. The flake can now be treated as a point-like object moving through an

effective interaction potential:

V f lakeint (xt ,yt ,zt) =

N

∑i=1

Vint (xt + xi,yt + yi,zt) . (6.2)

The FFM is operated in contact mode at a range of normal loads of up to +40nN

(chapter 5). Therefore, the system, including the normal force FN can be described by a

93


Figure 6.1: Illustration of the modified Tomlinson model used in our calculations. A rigid flake

consisting of N atoms (here N=24) is connected by an X-spring and a Y-spring to the support

of the microscope. The support is moved with constant velocity vm in the X-direction.

total potential V (xt ,yt ,zt) =V f lakeint (xt ,yt ,zt)−FNzt . The equilibrium height zmin

t (xt ,yt)is given by the minimum of V (xt ,yt ,zt) with respect to zt . Combining these potential

energy values for all positions (xt ,yt), we obtain an effective flake-surface potential

V f lakeint (xt ,yt) [50]. The total potential energy including the elastic energy stored in the

springs is given by

V (rt ,rm) = V f lakeint (rt)+

12

k(rt −rm)2, (6.3)

where rt is the (xt ,yt) position of the center of mass (CM) of the tip, rm the (xm,ym)position of the microscope support and k = kx = ky is the spring constant in the X-

and in the Y-direction. The support is displaced in the pulling direction with steps of

0.001nm (the basic length unit in the calculation). After each step, the position of

the flake is allowed to relax towards the nearest local energy minimum. The system

is assumed to be in equilibrium at each step of the simulation, since typical FFM

94

6.2 M O D E L

scanning velocities are much smaller than the sound velocities of the materials. In the

simple Tomlinson approximation, phonons generated during the slip are assumed to

carry the excess energy away. Since phonon frequencies are much higher than typical

scanning frequencies, this relaxation is therefore assumed to occur very quickly (in

reality, one should expect a variety of sizeable deviations from the Tomlinson model

since the relaxation time is not infinitely short [153]).

The energy is minimized by an iterative procedure that moves the contact one

length unit in the direction of steepest decrease in potential energy per iteration. In-

stabilities in the total energy surface as a function of support (xm,ym) coordinates can

cause atomic scale stick-slip motion, where the contact non-adiabatically (discontin-

uously) “jumps” to a new position. The potential energy built up in the springs is

removed during the energy minimization step, resulting in a non-zero average force

along the pulling direction. After the contact is relaxed the force at the support is given

by

F = −k (rt −rm) . (6.4)

Scanning motion of the support in the pulling direction (defined here as X-direction)

occurs in steps of 0.001nm. The CM position of the flake initially coincides with

the origin of the support. Then the support is scanned 3nm in the pulling direction.

The system is now considered initialized. The support is then scanned backwards and

forwards, again over 3nm. Static friction is defined as the force required in the X-

direction to cause the first slip event. Kinetic friction is defined as the average force

in the X-direction after that first event. The area in a closed friction loop equals the

energy dissipated (removed during the energy minimization steps during the entire

loop). Note that the slope of the force loop of 4.64N/m is lower than the stiffness

of the spring of 5.75N/m (fig. 6.3a): within the framework of the model a lateral

”interface” stiffness kinter f ace exists, that is caused by the curvature ∂2V f lakeint /∂x2 of

the periodic potential energy surface at the sticking positions of the tip. This interface

stiffness and the cantilever springs act in series to produce the effective stiffness that

is observed in the simulated friction loops (see chapter 5).

After every forward plus backward line in the X-direction, the support steps

0.006nm in the Y-direction perpendicular to the scan direction. In this way the support

covers a distance of 3nm, and a two-dimensional lateral force image is generated. The

orientation angle Φ of the flake with respect to the substrate is set prior to calculating

the effective interaction potential for the contact. The angle under which the flake is

pulled through the interaction potential is set independently. The friction force for a

95


Figure 6.2: Symmetric flakes used in the calculations consisting of (a) 6, (b) 24, (c) 54, (d) 96,

and (e) 150 atoms.

certain misfit angle of the contact and/or sliding direction of the support is defined

here as the average of all kinetic friction values for all different Y-coordinates within

one lateral force map, and also averaging over forward and backward lines.

6.3 Results

6.3.1 Symmetric contacts

Figure 6.2 displays symmetric flakes of various sizes that were considered in the cal-

culation. The friction force (as defined in section 6.2) is maximal if the misfit angle

Φ is zero, i.e. the lattices form a commensurate structure, as is illustrated for the 96-

atom flake in figure 6.3. The friction force then increases linearly with the number

of atoms N in the contact. In order to compare different flake sizes for a fixed total

interaction between the contact and the surface, the potential amplitude per atom V0

was lowered with increasing contact size such that V0N = 0.52eV. In this way the total

96

6.3 R E S U L T S

Figure 6.3: Calculated friction loops for a 96-atom flake in registry (a) and 30 out of registry

(b).

interaction energy was chosen such that the calculated friction force with the flake and

substrate in registry (260pN for 0.52 eV) was the same for all flakes, and comparable

to the value measured experimentally. Figure 6.3 shows that when the 96-atom flake

is misoriented by 30 the lateral force displays a continuous, sine-like variation, with

an average value close to zero. Figure 6.4a displays the computed friction force as a

function of Φ for the five flakes shown in figure 6.2. Like in the experiment, we find

angular regions with high friction around 0 and 60. At intermediate angles, we cal-

culated near-zero friction, except for the 6-atom flake, for which the friction drops to

51.7pN. Clearly, the calculations predict superlubricity.

As already discussed in chapter 5, the angular width of the friction maxima should

depend on the contact size and we estimated that

tan(∆Φ) = 1/D, (6.5)

where ∆Φ is the full width at half maximum (FWHM) of the friction peak, and

D is the flake diameter, expressed in lattice spacings. This relation is shown in figure

6.4b, where the FWHM is plotted as a function of contact diameter, using the in-plane

graphite nearest neighbor distance of 0.142nm as lattice spacing. The agreement be-

tween the estimate of equation 6.5 and the peak widths calculated for the five flakes is

excellent. For a symmetric flake of 96 atoms we find a FWHM of 5.5, very similar to

the experimental observations.

97


Different peak heights at 0 and 60 misfit angle, as found in the experiment, can-

not be expected in our calculation, since the simple potential that we used to model

the graphite surface and the flake, has 60 symmetry. This potential only models the

interaction between adjacent graphite layers and ignores the more subtle, long-range

interactions responsible for the AB-stacks in graphite.

In order to investigate the dependence on the pulling direction, calculations have

been performed for a 6-atom, a 96-atom and a 150-atom flake, both in and out registry

with the surface. The variation in the friction force was found to be 24% for both com-

mensurate flakes, and incommensurate flakes. One example of the calculated friction

force as a function of sliding angle is plotted in figure 6.5, together with the measured

friction between 10 and 90. The calculation shows that the force depends modestly

on the sliding direction. A very similar dependence on the pulling direction was found

by Gyalog et al. [147, 148] within a FKT model for two identical infinitely extended

crystal surfaces with a square symmetry. However, in our model the friction force is

lowest 2 left and right of the symmetry directions of the graphite surface and slightly

higher precisely in the symmetry directions. Probably this is caused by the complete

rigidity of the two surfaces and the discretization of the model.

6.3.2 Asymmetric contacts

In spite of the success in fitting the measured friction with the interaction between

a symmetric flake and a graphite substrate, it is unlikely that the real flake in the

experiment has had perfect hexagonal symmetry. Even when the contact has been

defined by a large flake, curved around the metal tip, we would be forced to assume our

tip to have been symmetric, which is again unlikely. In this section, we investigate the

effect of asymmetric flake shapes. Taking the symmetric 96-atom flake that produced

a good fit to the measured data as a starting geometry, we removed rows of carbon

rings at the top and at the bottom (figure 6.6a-b) until a single row of carbon rings was

left (figure 6.6c). This yielded three model flakes with length over width ratios of 1.5,

2.4 and 6.1, respectively.

Figure 6.7 shows the dependence of the friction on the misfit angle. As for the

symmetric flakes, we find regions with high friction that appear every 60, separated

by angular regions that are superlubric. The high friction peaks now possess “shoul-

ders”, which become more prominent the more asymmetric the shape of the flake is.

Due to the stretched shape, the total potential energy surface (PES) becomes “elon-

gated” along the long axis of the rotated flake (figures 6.8b,d,f). For a misaligned flake,

98

6.3 R E S U L T S

Figure 6.4: (a) Friction as function of the misfit angle for different symmetric flakes ranging

from 6 to 150 atoms; (b) Width of the friction peaks (FWHM) versus flake diameter (circles).

The solid line is the peak width according to equation 6.5.

99


Figure 6.5: Comparison between calculated (solid line) and measured (circles) dependence

of friction on the sliding direction, for a 150-atom flake, in registry with the substrate.

this causes the CM of the tip to follow different types of pathways in the forward scan

than in the backward scan. In addition, the changes in the PES cause the force buildup

in the X- and Y-springs of the Tribolever to differ left and right of the friction peaks in

figure 6.7, which results in asymmetric shoulders. This introduces a 90 mirror sym-

metry instead of the 60 symmetry of the corrugation expected from Vint . Note, that

in figure 6.7 the mirror angles were fixed to 30 and 120 by choosing the pulling

direction to be −60.

Calculated lateral force images in the forward X-direction and potential energy

surfaces for an asymmetric flake consisting of 78 atoms are shown in figure 6.8. The

images were calculated for a sliding angle of 70 and for misfit angles of 120 (a,b),

132 (c,d) and 94 (e,f), in order to resemble measured images shown in figure 5.7.

It is obvious that the lateral force patterns are also affected by the asymmetry in the

potential energy surfaces. The grey areas in figures 6.8b,d and f show positions that

have been visited by the CM of the tip during sliding. In figure 6.8b the CM is pinned

at the potential energy minima of the PES and performs zig-zag stick-slip motion.

In figure 6.8d the PES is elongated such, that the sticking areas are connected and

100

6.3 R E S U L T S

Figure 6.6: Three asymmetric flakes consisting of (a) 78,(b) 56, and (c) 30 atoms.

form channels that run across the image. These “low energy channels” in which the

tip slides continuously are still separated by energy barriers over which the tip has to

jump. Finally, when the flake is rotated 26 away from commensurability, the PES is

shallow enough that the tip continuously slides over the entire surface. Depending on

the flake orientation, the sticking zones are elongated in different directions, which

creates the impression that the lateral force pattern is rotating although the pulling

direction is the same for all three images. This is also observed in the measurements,

(fig. 5.7) although the measurement cannot reproduce all of the fine structure that is

seen in the calculated images, which is probably due to the fact that the lateral forces

are close to the thermal noise of the Tribolever and the noise limit of the instrument.

Comparing our calculations with our experimental results, we conclude that the flake,

that was responsible for the data in figure 5.8, was mildly asymmetric. The calculations

for the 30- and 56-atom flakes do not show similarity with the measured data. The peak

shapes and widths for the 78-atom flake and the measured ones are similar (see fig.

6.9), but at this stage we have not attempted to improve the fit further by optimizing

the shape and size with respect to the present 78-atom model.

101


Figure 6.7: Friction as function of the misfit angle for three different asymmetric flakes with

(a) 78 atoms, V0 = 0.0068eV; (b) 56 atoms, V0 = 0.0093eV; (c) 30 atoms, V0 = 0.017eV; All

calculations were performed for a pulling angle of −60. The dashed lines indicate the angles

with respect to which the pattern should be symmetric.

6.4 Discussion

We have shown that a very simple Tomlinson model for a graphite flake against a

graphite substrate reproduces the measured orientational dependence of the friction

rather well. However, the model lacks several important elements of reality. For ex-

ample, when we increase the number of atoms to infinity in the contact the model

predicts that the peaks of high friction become infinitely narrow. In registry, the cor-

rugation amplitude of the interaction potential is predicted to increase linearly with

the number of atoms in the contact. To move a large, aligned flake consisting of a few

thousand atoms would require a very high force, but in our model, only a tiny bit of

rotation out of registry would cause superlubricity. When we model a disordered tip by

placing atoms randomly, the high friction peaks vanish. This means, that in our model

every misaligned crystalline or amorphous tip that is large enough, is fully superlu-

102

6.4 D I S C U S S I O N

Figure 6.8: Lateral force images (3nm×3nm) and total potential energy surfaces

(1nm×1nm), calculated in the forward X-direction for an asymmetric, 78-atom flake, for misfit

angles of 120 (a,b), 132 (c,d) and 94 (e,f). The grey areas in the contour plots denote po-

sitions that were visited by the center of mass of the flake. The grey scale in the lateral force

images corresponds to (a) 2.2nN, (c,e) 92pN;

103


Figure 6.8: continued Solid and dashed contour lines in the PES denote positive (V > 0), and

negative (V < 0) energy values, respectively. The contour lines are separated by (b) 0.1eV (d)

0.02eV and (f) 2 ·10−3 eV.

Figure 6.9: The data points show the average friction force versus the rotation angle of the

graphite sample (chapter 5). The curve through the data points shows results from the Tomlin-

son simulation for the asymmetric 78-atom flake; The calculation was performed for a sliding

direction of −60; in other words, at Φ = 0 the long axis of the flake is oriented at +60 with

respect to the sliding direction.

104

6.5 C O N C L U S I O N S

bric. Therefore, friction between macroscopic surfaces should almost always be zero

in wearless sliding situations. Yet, macroscopic surfaces that exhibit superlubricity

have not been discovered so far. He et al. [150] have shown in an MD simulation that

third bodies, such as hydrocarbon molecules can cause locking of the two surfaces and

hence destroy superlubricity. Another mechanism that might prevent superlubricity at

larger scales is internal elasticity in the contact [141], which will allow the flake to

lock locally into registry. Our model does not include any elasticity, and is not suited

to estimate the transition to the behavior for larger contacts. It is surprising that the

Tomlinson model works so well to fit the experimental data. This is probably due to the

high in-plane Young’s modulus of graphite in combination with the relatively small

flake size. We speculate that precisely these two ingredients namely the presence of

small, rigid flakes might be the key elements making graphite a good solid lubricant.

6.5 Conclusions

In summary, we have set up a Tomlinson model, describing a rigid N-atom cluster with

the symmetry of a graphite flake that was moved through a two-dimensional sinusoidal

potential representing the graphite surface. The calculated friction force shows high

friction and near-zero friction, depending on the (in)commensurability between the

two lattices. By changing N, we vary the width of the peak in the friction vs. orien-

tation plot, so that we can fit the measured peak width. The calculations revealed that

the shapes of the high-friction peaks depend on the precise shape of the flake.

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106

VII

Towards the ideal friction experiment

· · ·

We present a miniaturized version of the dedicated friction force

microscope introduced in chapter 4 that operates in ultra-high vacuum

(UHV). Because of its small size, the FFM can be combined with other

techniques, to image or otherwise characterize the sliding contact dur-

ing force measurements. In the first part, we discuss how the miniature

FFM has been combined with a high resolution transmission electron

microscope. In the second part, we will introduce the design of a new

UHV setup, in which the miniature FFM is combined with a field ion

microscope to characterize and modify the tip before and after contact

with the surface, and with a scanning electron microscope to observe

the contact during sliding.

107

7. T O W A R D S T H E I D E A L F R I C T I O N E X P E R I M E N T

7.1 Introduction

7.1.1 The need for ultra-high vacuum

In chapter 2 we envisioned the “ideal” friction experiment necessary to bridge the gap

between nanotribology and micro-/macrotribology. We formulated a set of require-

ments, that our instrument needs to fulfil in order to enable this ultimate experiment.

Several of these requirements, such as quantitative three-dimensional force detection

with high sensitivity, rotation of the sample lattice with respect of the tip lattice, and

free choice of the tip and sample materials, have already been met by the FFM that

is described in the chapter 4. Using that FFM, tribological systems can be studied

in a controlled ambient environment (e.g. air or nitrogen with controlled humidity).

However, the ambient FFM cannot be used to study any desired material combination,

since most materials are immediately oxidized or otherwise altered under ambient

conditions. Only in ultrahigh vacuum (UHV) one can produce and maintain atomi-

cally clean, well-characterized crystal surfaces of various materials, such as metals

and semiconductors, and deposit well-defined monolayers of adsorbates that can e.g.

act as model lubricants. A second important requirement that is not met by the ambi-

ent FFM, is to provide full information on the tip size and orientation. Only in special

cases can this information be deduced indirectly from the measurements, as is demon-

strated in chapter 5. Techniques that allow one to image the tip with high, e.g. atomic

resolution use electron or ion beams, and therefore require high vacuum. It is evident

that both requirements involve the new FFM setup to be placed in UHV.

7.1.2 “Imaging the contact”

We can think of two methods to obtain information on the contact with atomic res-

olution. The first method is to “look” at the contact from the side using a high-

resolution transmission electron microscope (HRTEM). The combination of scan-

ning tunnelling microscopy and transmission electron microscopy was recently shown

to be possible and to provide a deep understanding of the relationship between the

structure and electronic properties of nanocontacts [154]. In a similar way, with the

combination of a friction force microscope with a HRTEM, it should be possible to

perform quantitative friction force measurements and at the same time know exactly

how many atoms are contributing to the measured lateral and normal forces. A great

advantage of such a combination will be that it will make it possible to observe atomic

reconfigurations inside the contact in real time while the tip is sliding over the surface

108

7.1 I N T R O D U C T I O N

or while the normal force is changed. One of the difficulties introduced by combining

a FFM with a HRTEM is that the lens geometry of the HRTEM puts severe restrictions

on the dimensions of both the FFM (see section 7.2) and the sample.

We have constructed a miniaturized UHV version of our friction force micro-

scope that can be mounted into a dedicated UHV HRTEM [155] at the Tokyo Institute

of Technology. We will briefly discuss the design of the FFM/HRTEM combination in

section 7.2, since it forms the basis for the new UHV setup. Due to time limitations,

our first attempts to perform a FFM measurement inside the HRTEM had only limited

success. A brief account of the results can be found in appendix B.

The UHV setup, which is under construction in Leiden, uses a second method

to obtain atomic-scale information of the scanning tip, which is to combine the FFM

with field-ion microscopy (FIM), to view and to shape the tip [156–159]. With a com-

bined STM/FIM apparatus, Cross et al. [160] studied the adhesion interaction between

an atomically defined W(111) and a Au(111) surface and demonstrated the power of

combination of these two methods. In a FIM, a sharp tip, usually of a high-melting-

point metal, is imaged by placing it in a high electric field in the presence of a low

density of a noble gas, e.g. He. The field strength is highest where the curvature of the

tip is at its maximum, which is at or near the apex. The highest fields are sufficient to

ionize the noble gas atoms. The ions are accelerated from the ionization position to a

phosphor screen, where they build up a strongly enlarged image of the high-curvature

regions at the tip apex. In this way, high-quality FIM images show the tip apex with

atomic resolution, which allows one to directly identify the crystallographic orienta-

tion of the tip and to count the number of atoms at the perimeter of the outermost

atomic facet, from which one immediately obtains the total number of atoms in that

facet. When the tip is brought into contact with the sample surface with a low load-

ing force, these outermost atoms define the contact area. There are several additional

advantages that the FIM provides. The FIM image shows not only which crystallo-

graphic plane terminates the tip apex, but also in which precise direction the surface

normal is pointing. In our setup, we will be able to tilt the sensor and tip assembly

in two independent directions, so that we can align the surface normal of the tip with

that of the extended counter-surface, in order to make these surfaces really parallel.

The FIM can further be used to ‘shape’ the tip and thereby modify the area of the

outermost atomic facet. This is achieved by increasing the electrical field to the point

109


where the tip atoms are field-desorbed. In this way, the tip apex is stripped away atom

by atom. A beautiful illustration of these methods can be found in [159], where tips

are produced with perfect hexagonal facets of Ir(111) that have sizes of 7, 19, 37, 61,

and 91 Ir atoms. However, unlike in a HRTEM, with the FIM we can only image the

tip prior to the formation of a contact and after the contact is broken again.

In order to also view the contact during sliding, the UHV setup in Leiden will be com-

bined with a third type of microscope. We will use a scanning electron microscope(SEM) to look at the tip and the sample from the side. Although the SEM will not

reach atomic resolution, it will provide the possibility to study e.g. the deformations

in and around the contact, the ageing (growing) of a contact when it is resting on the

surface, or the wear debris formation when the tip is moving under high normal loads.

The SEM column and the FFM have to be mechanically strongly coupled, so that vi-

brations between the SEM and the FFM will not compromise high-resolution SEM

imaging. Using a traditional SEM column, this would imply abandoning a vibration

isolation stage for the FFM. This, in turn, would strongly deteriorate the quality of

FFM measurements. However, if the SEM column is sufficiently small and compat-

ible with UHV, it is possible to mount the complete SEM on the vibration isolation

stage of the FFM. Therefore, we use two dedicated miniature SEM columns, which

operate in UHV. The Mini-SEMs are of a prototype version that was developed at the

Philips Research laboratories in Eindhoven [161].

7.2 Design of a miniaturized FFM for use in combination with HRTEM orSEM

A number of technical specifications have to be met to make our specialized

FFM suitable for operation inside a UHV system with either HRTEM or SEM: (1)Most importantly, the FFM’s dimensions have to be reduced. To image the scanning

tip, the Tribolever together with part of the fiberhead has to be placed in between

the pole shoes of the objective lens (OL) of the HRTEM. In the 200keV JEOL mi-

croscope, the pole shoes are separated by a gap of 2.5mm. (2) The FFM has to be

transferrable from a loading chamber to the sample stage that is connected to a go-

niometer inside the HRTEM. This goniometer is needed to position the tip apex in the

110

7.2 D E S I G N O F A M I N I A T U R I Z E D F F M . . .

Figure 7.1: Drawing of the miniaturized FFM for combination with HRTEM. Panel (a) shows

an overview with: (1) sample holder; (2) sample/FFM stage; (3) nonmagnetic UHV Nanomotor;

(4) scan piezo tube; (5) Inchworm motor; (6) FFM transfer holder; (7) connection rod and tube.

Panel (b) depicts a zoom-in of the fiberhead with: (8) glass fiber with aluminium cladding; (9)

“tip bumper” and sample (in form of a wire); (10) Tribolever.

111


Figure 7.2: Solid model of the fiberhead of the miniaturized FFM in between the two pole

shoes of the TEM, cut open for illustration: (3) non-magnetic UHV Nanomotor; (10) Tribolever;

(11) fiberhead; (12) pole shoe.

field of view of the electron beam and to optimize the position in the direction parallel

to the beam in order to place the tip apex precisely in the focal plane. In addition,

the goniometer is used to tilt the sample stage and to optimize the viewing angle. (3)Because of the construction of this goniometer, the mass of the sample stage, includ-

ing the entire FFM, should not exceed 30 gram. (4) Finally, the FFM has to be UHV

compatible and completely non-magnetic, because the FFM has to operate in the high

magnetic field of the OL.

Figure 7.1 shows the design of the sample stage plus FFM. The FFM assembly

consists of a miniature fiberhead, which is directly glued onto a scan piezo tube (4).

Unlike the ambient version of the FFM, the fiberhead does not remain at a fixed posi-

tion but is scanned together with the tip of the Tribolever. The piezo tube is mounted

on the shaft of a commercial inchworm motor (5) [162], which is used to approach

the tip towards the sample (8). Two rods, that are connected to the inchworm motor

house, guide the FFM into the sample stage (2) and form a stable connection.

112


7.2.1 FFM/HRTEM fiberhead

Figure 7.3: Video microscope image during the alignment procedure of the Nanomotors prior

to glueing.

The fiberhead was made by spark erosion from titanium. The contours of the

fiberhead are defined by the shape of the pole shoes of the OL. At the end, the fiberhead

is reduced to a thickness of 2.5mm in order to to fit between the pole shoes (see

fig. 7.2). Because the Tribolever can easily be damaged while the FFM is mounted

inside the HRTEM, it is covered by a titanium strip, that serves as a “bumper”, in

case the fiberhead were to hit one of the pole shoes. A groove, cut in the bumper

allows the scanning tip to be brought into contact with the sample. Several holes have

been drilled into the fiberhead to reduce its mass to 2.1 gram. As in the fiberhead in

113


chapter 4, we used UHV-compatible Nanomotors to approach and position the four

glass fibers close to the four faces of the pyramid of the Tribolever. Because of the

OL, it was not possible to mount the four Nanomotors completely symmetrically,

at 90 angles. The X1 axis is therefore placed under an angle of 68.5 with respect

to the Y1 axis. This results in slightly lower interferometer signals. Less light can

reenter into the glass fibers if they are not perfectly orthogonal to the faces of the

detection pyramid. Also because of the geometry of the pole shoes, we had to leave

out the flexure hinges, which were used in the ambient version of the microscope

to adjust the Nanomotor positions. Because the positions of the Nanomotors in this

design are fixed, the glass fibers needed to be aligned with respect to the pyramid

before the motors were glued into the fiberhead. To this end, the glass fibers [163] were

first mounted into the Nanomotors and then the motors were positioned with respect

to the fiberhead using a x-y-z positioning stage. The process was monitored using a

video microscope (figure 7.3). Without changing the alignment, the Nanomotors were

then glued into the fiberhead. In the original version of the Nanomotor, the carrier

tube, which holds the fiber, is free to rotate. Such rotation can cause a change in

the alignment of the fiber, because the carrier tube is not exactly in the center of the

Nanomotor. In order to avoid rotation, we constructed, in collaboration with Klocke

Nanotechnik GmbH [164], a special non-magnetic version of the Nanomotor, in which

the rotation of the carrier tube is inhibited. This was achieved by replacing the glass

tube inside the Nanomotor by a glass tube with an oval bore that allows the carrier

tube to run easily in only one rotational orientation.

7.2.2 HRTEM-FFM assembly

After mounting the Nanomotors, the fiberhead was glued [165] onto the scan piezo

tube [166]. Scan piezo and fiberhead were then glued on the shaft of an inchworm

motor via a ceramic plate that matches the inner diameter of the piezo tube and the

outer diameter of the shaft. Like the axis of the original Nanomotors, the shaft of the

inchworm is normally free to rotate. In our case, this rotation is not tolerable, since it

would cause also the rotation of the complete FFM. We attached a precision ceramic

pin to the body of the inchworm, which slides inside a groove of the matching ceramic

plate to completely inhibit rotation of the shaft.

114


7.2.3 HRTEM-FFM sample stage

Like the fiberhead, the sample stage was made from titanium to save weight (7.1g)

and to ensure that the stage is non-magnetic. The stage is attached by three screws to

the goniometer of the HRTEM. The sample holder (fig. 7.1, item 1) fits precisely into

a dovetail-shaped groove on the left side of the stage. The sample holder is designed

such that it can be transferred to the stage via magnetic transfer rods that are part of the

HRTEM’s sample preparation chamber. From the opposite side, the FFM is brought

into the stage using a second transfer rod.

When the FFM approaches the sample stage, two rods, that are connected to the

inchworm house, move into two tubes that are connected to the sample stage (fig. 7.1,

item 7). The tubes are used to guide the FFM into the correct position. When the FFM

is pushed into the end, its position is exactly defined with respect to the stage by a tight

fit of the rods inside the tubes. The FFM is then released from the magnetic transfer

rod by turning the transfer rod. Once the FFM is free from the magnetic transfer rod,

the sample stage can be positioned with respect to the OL, using the goniometer of the

HRTEM.

The FFM makes use of the same interferometer system and electronics that were de-

scribed in chapter 4. Also, calibration of the Tribolever and mounting of a scanning

tip is done by the procedures that were described earlier.

After mounting the FFM inside the HRTEM, we could use electron microscopy

to observe the scanning tip approach and make contact to the sample. We were also

able to measure normal and lateral forces between a gold tip and a gold sample.

However, we have not been able to perform a truly simultaneous FFM and HRTEM

measurement, because the uncladded and tapered parts of the four glass fibers were

charged up by the electron beam (see also appendix B). The charging and discharging

caused a strong periodic disturbance in the interferometer signals. It also caused sud-

den motion of the scanning tip every time when a discharge between the fibers and the

Tribolever occurred. This problem will be solved by coating the tapered parts of the

glass fibers with a conducting material and grounding the fibers, to prevent charging.

Initial results from combined FFM and HRTEM measurements can be found in

appendix B. The version of the FFM, developed for use in combination with HRTEM,

is almost identical to the one described in the next section for use in combination with

115


a SEM.

7.3 Design of the UHV setup for FFM

In the following, we will give a brief overview over the general design of the UHV

system for FFM. This instrument will be a combination of the FFM introduced in the

previous section with a FIM and SEM. The setup is at present being assembled at the

Kamerlingh Onnes Laboratory.

7.3.1 UHV chamber

The new FFM will be placed in a UHV chamber with a base pressure below 1 ·10−8 Pa.

The chamber is pumped by a magnetically levitated turbomolecular pump (5) [167]

and an ionization pump (7) with combined titanium sublimation pump (8) [168]. The

chamber has two dedicated compartments, a sample preparation compartment and the

FFM compartment. In the first compartment, a carrousel will be placed that will house

6 sample holders (fig. 7.4, item 10 and fig. 7.5, item 5). Concentrically around the

carrousel, instruments are placed to prepare and characterize an atomically flat and

clean sample. The structure of the sample will be inspected with low energy electron

diffraction optics (LEED, item 4). The LEED system is combined with Auger electron

spectrometry (AES) [169] to analyze the material composition and cleanliness of the

sample surface. A sputter ion gun (12) [170] allows cleaning the sample. A quadrupole

mass spectrometer (11) [171] is used to monitor the vacuum quality and will be used

to perform thermal desorption spectroscopy (TDS) of lubricant molecules that are

adsorbed at the sample surface. Extra flanges allow expanding the system in the future,

e.g. by a Knudsen evaporation cell. The carrousel will be rotatable by means of a

rotary drive, such that each sample in the carrousel can be positioned in front of every

of these instruments. The samples will be transferred from the carrousel to the FFM

compartment using a wobble stick [172].

The FFM compartment will contain a platform (fig. 7.5, item 4) that is con-

nected to a CF419 flange. On that platform we will mount a spring-suspended stage

(3) with eddy-current vibration damping that will house the FFM as well as the two

Mini-SEM columns (see below). Also the FIM will be in the FFM compartment of the

UHV chamber (1).

116

7.3 D E S I G N O F T H E U H V S E T U P F O R F F M

Figure 7.4: The chamber for the UHV-FFM in a perspective view (a) and a side view (b)

showing: (1) FFM flange (2) FIM flange; (3) window for quartz rod; (4) LEED-AES; (5) turbo

pump;117


Figure 7.4: continued (6) vibration isolation feet; (7) ion pump; (8) titanium sublimation

pump; (9) gate valves; (10) sample carrousel flange; (11) quadrupole mass spectrometer; (12)

sputter ion gun.

Figure 7.5: Schematic drawing of the interior of the UHV chamber showing: (1) retractable

FIM screen assembly; (2) Mini FFM; (3) spring-suspended FFM stage; (4) FFM platform; (5)

sample carrousel.

118


7.3.2 UHV-FFM stage

The FFM will be a slightly adapted version of the HRTEM version, discussed in sec-

tion 7.2. The FFM will be mounted with the tip pointing up (figure 7.6, position 2)

on a goniometer (4,5,10,11) that allows tilting of the FFM to a maximum angle of 13

degrees in order to orient the endface of the scanning tip parallel to the sample sur-

face. The center of the tilt motion has to coincide with the tip apex position. Therefore

the FFM position will be adjustable in two directions by means of flexure hinges. The

goniometer consists of two connected parallel spherical shells (4,11) that are sprin

loaded against sapphire spheres (10). The goniometer will be tiltable in two directions

by two separate inchworm piezomotors (6) [173].

7.3.3 Mini-SEM

The Philips miniature SEM [161] consists of a small electron optics column and a

thermal field emission (Schottky) electron gun. The overall length of the SEM column

including the gun is about 90mm. The electron optics consist of electrostatic lenses

and scan units. Secondary electrons are detected by a scintillator that is located inside

the column. The light from the scintillator plate is guided by a quartz rod to a CF63

viewport and there the signal is amplified by a photomultiplier outside of the UHV

chamber. When the tip of the FFM is making contact to the sample, the separation be-

tween the fiberhead and the sample will be about 50µm. This means that the electrons

have to travel through a narrow gap of 50µm over a distance of 1mm. If the FFM is

tilted with respect to the surface of the sample, this gap will become smaller, there-

fore obstructing the view from the SEM towards the tip apex. By using two electron

columns that aim at the tip from the left and from the right side, we will always be

able to obtain an image of the tip from at least one of the two sides, regardless of the

FFM tilt.

The narrow gap between the sample and the Tribolever has also a negative ef-

fect on the collection efficiency of secondary electrons. This effect can be very severe

(see figure 7.7) when using the internal scintillation detector in the Mini-SEM col-

umn. Because the collection efficiency can be improved when the secondary electron

source is close to the detector we will place a channeltron electron detector [174] in-

side the fiberhead. With this miniature detector (item 14 fig. 7.6d) it will be possible

to collect secondary electrons through the central hole of the Tribolever. Figure 7.7

shows a comparison between SEM images of a test structure that were recorded with

119


Figure 7.6: The FFM stage in front (a) and rear view (b). Cross-section of the rear view (c) and

solid model of the modified fiberhead (d). Not shown are the sample and the second (identical)

SEM. (1) Philips Mini-SEM; (2) fiberhead; (3) coarse approach inchworm motor; (4) upper

goniometer shell; (5) goniometer housing; (6) goniometer inchworm motor; (7) SEM linear

translation stage; (8) SEM inchworm motor; (9) flexure hinge SEM x-y table; (10) sapphire

spheres; (11) lower goniometer shell; (12) goniometer axis; (13) Tribolever; (14) channeltron

detector.

120


Figure 7.7: SEM images of a 50µm long tip sticking out of the Tribolever. The tip makes

contact to a silicon sample. Image (a) was recorded using the internal scintillation detector of

the Mini-SEM. Panel (b) shows the same image, recorded with an external channeltron detector.

Printed with kind permission of M. Krans, Philips Research [161].

the internal detector of the Mini-SEM and with an external channeltron detector. The

test structure constisted of a tungesten tip between two silicon plates with the size

of the Tribolever, forming a 50µm-wide gap. The image taken with the channeltron

detector clearly shows higher contrast inside the gap and it resolves the tungsten tip

much better.

To obtain high resolution images of the tip, the SEM columns have to be aligned

such that the tip is in the focus of the electron optics to within 10µm. This means that

both columns need to be adjustable in two directions with respect to the fiberhead.

This adjustment will be performed by moving flexure hinges ex-situ using microme-

ter screws. Once the columns are optically adjusted, the position of the SEM is fixed

and the micrometer screws removed. After the stage is transferred to UHV, residual

misalignment of the columns can be directly measured using the SEMs themselves. In

this way the columns can be fine adjusted iteratively.

In addition to the ex-situ alignment of the column axis, also the distance be-

tween tip and OL of the columns needs to be adjustable in-situ. This has two reasons.

First, the columns need to be brought to a safe position when the FFM is moved using

the goniometer. Secondly, the working distance should be changeable, depending on

the magnification. Therefore the two columns will be mounted on two linear stages,

which can be moved using inchworm motors [175].

121


7.3.4 Field ion microscope

One side of the field ion microscope is formed by the metal tip that is glued inside

the Tribolever. To ionize the imaging gas atoms, a high voltage in the order of several

kilovolts has to be applied to the tip. In our FFM, we will apply this high voltage to the

entire fiberhead, which therefore has to be electrically insulated from the scan piezo.

In order to obtain atomic resolution FIM images, the metal tip needs to be cooled

below about 90K . We have constructed a liquid nitrogen dewar that cools a copper rod

inside the UHV chamber to 77K. The copper rod will be connected to the fiberhead via

a flexible copper braid (not shown in figure 7.6). The copper braid has to be electrically

insulated from the fiberhead but thermally well connected.

The FIM is completed by a combined dual chevron channel plate and phosphor

screen assembly (fig. 7.5, item 1) [176]. Together, the channel plates provide a gain of

8 · 106 at 2000V applied voltage between the front- and the backside of the channel

plate stack and thus intensify the FIM image. Electrons leaving the channel plates

will be accelerated towards the phosphor screen over a voltage of 2keV. The screen

assembly will be located directly above the sample stage. When no sample holder is

placed in the sample stage, the ions can travel through the empty sample stage and

form an image on the screen. After a FIM experiment, the sample will be placed into

the sample stage. The FIM screen assembly will be mounted on a linear translation

stage, which is supported from a CF150 flange (fig. 7.4, item 2). The linear translation

stage makes it possible to retract the FIM screen while a sample is loaded in the sample

stage.

7.4 Summary

We presented the conceptual design of a new UHV setup, with which the “ideal”

experiment can be performed that that was introduced in chapter 2. The heart of this

setup is formed by a miniaturized version of our friction force microscope. This FFM

is based on a special prototype that was used to perform friction measurements inside

a HRTEM. Together with field ion microscopy and scanning electron microscopy this

instrument will enable friction experiments with completely in-situ characterized and

modified sliding contacts.

122

A

Processing steps of the Tribolever fabrication

· · ·

A.1 Overview

This appendix gives a very detailed guideline for the microfabrication of the tri-

bolever. The processing “recipe” was used during fabrication of the small version

of the tribolever at the Delft Institute of Microelectronics and Submicron Technol-

ogy (DIMES), therefore it is written specificly for the cleanroom facilities available at

DIMES. The processing consists of

- seven lithography steps:

• mask alignment markers at the front side of the wafer.

• markers at the back side.

• space for attaching the chip with clips to the microscope (“clip space”) at the

front side.

• protective crosses for the pyramid at the front side.

• legs at the front side.

• laserwindows (back side).

• kinematic mounts.

- seven plasma etch steps (fluorine etching):• markers front side.

• markers back side.

• clip space (front side).

• crosses (front side).

• legs (front side).

• laser window (back side).

• kinematic mounts.

123

A. P R O C E S S I N G S T E P S . . .

- six deep reactive ion etching steps for pattern transfer (MET system fluo-rine):

• mask front side.

• markers back side.

• clip space (front side).

• crosses (front side).

• legs (front side).


- two KOH wet etch steps:• kinematic mounts.


- two deposition steps (LPCVD Si3N4):• mask for the wet etch of the kinematic mounts.

- three thermal oxidation steps:• thin oxide mask for etching markers (front side and back side).

• thick oxide mask for deep etching.

• thick oxide mask for wet etching

and

sawing of the devices.

A.2 Processing

pattern definition and transfer of markers at the front- and back side;1. thermal oxidation:

• recipe: dry oxide; 8 hours; thickness of the oxide 225nm.

2. lithography of markers at the front side:

• spin coating of the mask using HMDS; 5s @ 500rpm ; 55s @ 2500.

• spin coating of the wafer using HPR; recipe “H”: 5s @ 500rpm ; 55s @

3500; thickness 1.2µm.

• prebake: 30min @ 90 C.

• exposure: ±8s.

• development (Microposit developer): 3 parts H2O : 1 part developer; 55s.

• postbake: 30min @ 120 C.

124

A.2 P R O C E S S I N G

3. etching of the oxide at the front side in CHF3 plasma (Leybold Z401-S or Z401)

(dry development of the marker at the fronside):

• CHF3: 50sccm.

• O2: 1.3sccm.

• pressure: as low as possible.

• rf power: 50W (reverse power must be zero to ensure a plasma impedance

of 50Ω).

• bias voltage: −330±30V.

4. Stripping of resist:

• removal of resist in concentrated HNO3.

• cleaning: DI H2O rinse ; dry with N2.

• cleaning and drying

• removal of teflon contaminants in O2 plasma (125W, 5min)

5. HF dip and DI H2O rinse: 1min in 3% solution.

6. etching of the markers at the front side in the MET system (Alcatel RLE200):

• SF6: 22.5sccm.

• O2: 2.8sccm.

• ICP power: 1000W.

• Potential: 13V.

• chuck temperature: −95 C.

• work pressure: 1.95Pa.

• etch depth: 3µm; 7min.

7. lithography of markers at the back side:

• HMDS; 5s @ 500rpm ; 55s @ 2500.

• HPR; recipe “H”: 5s @ 500rpm ; 55s @ 3500; thickness 1.2µm.

• prebake: 30min @ 90 C.

• exposure: using the back side aligner of ICAT; 10s exposure time.

• development (Microposit developer): 3 parts H2O : 1 part developer; 55s.

• postbake: 30min @ 120 C.

8. etching of the oxide at the front side in CHF3 plasma (procedure analogous to

the front side markers)

9. stripping of resist (procedure analogous to the front side markers).

10. HF dip and DI H2O rinse: 1min in 3% solution.

11. etching of the markers at the back side in the MET system (analogous to front

side markers).

125


12. stripping of the oxide in buffered HF and DI H2O rinse.

pattern definition of the clip space:13. RCA cleaning; standard recipe:

• removal of native oxide (HF).

• solution 1 (removal of organic contaminants): 5 parts H2O, 1 part H2O2,

1 part NH4, T=80 C.

• solution 2 (removal of metallic contaminants): 5 parts H2O, 1 part HCl, 1

part H2O2, T=80 C.

• cleaning and drying.

14. thermal oxidation (recipe “wet oxide”); 5h; oxide thickness 1µm.

15. lithography of the clip space (following the steps analogous to the lithography

of the front side markers).

16. etching of the oxide in fluorine plasma (same parameters).

17. stripping of the resist (analogous to markers front side).

pattern definition of the crosses:18. lithography for patterning the crosses at the front side.

19. etching of the oxide in fluorine plasma; etch depth: 650 nm.20. stripping of the resist.

pattern definition of the legs:21. lithography for patterning the legs at the front side.

22. etching of the oxide in fluorine plasma; etch depth: 250 nm.23. stripping of the resist.

pattern definition of the laser window:24. lithography for patterning the legs at the back side.25. etching of the oxide in fluorine plasma; etch depth: 1.3µm.

26. stripping of the resist.

27. optical inspection of the line width of the legs.

28. measurement of the oxide depth using α-step profilometer.

pattern definition of the kinematic mounts:29. deposition of low stress LPCVD Si3N4; thickness 400nm.

30. lithography for patterning the kinematic mounts at the back side.31. etching of the silicon nitride and the oxide in fluorine plasma; etch depth 1.3µm

(300nm Si3N4 and 1µm SiO2).

32. stripping of the resist.

pattern transfer of the kinematic mounts:

126

A.2 P R O C E S S I N G

33. HF dip and DI water rinse.

34. wet etch in KOH; 35 wt. %; 60 C; depth: 100µm.

pattern transfer of the clip space:35. etching of Si3N4 in fluorine plasma (front side).

36. stripping of teflon contaminants in O2 plasma.

37. HF dip and DI water rinse.

38. deep etch of the clip space in MET system (front side):

• etch depth: 90µm.

pattern transfer of the crosses:39. back etching of the oxide in fluorine plasma (front side) to open up the cross

pattern.

• etch depth: depends on the selectivity SiO2/Si in step 38.

40. deep etch of the crosses in MET system (front side).


pattern transfer of the legs:• etch depth: depends on the selectivity SiO2/Si in step 38/40.

41. back etching of the oxide in fluorine plasma (front side) to open up the leg

pattern.

42. deep etch of the crosses in MET system (front side):


pattern transfer of the laser window:43. deep etch of the laser windows in MET system; etch depth: 350µm.

44. deposition of low stress LPCVD Si3N4 in the fiber window.

backline processing:45. sawing of the devices.

46. removal of sawing foil in acetone and propanol.

pattern transfer of the pyramid:47. RCA clean; standard recipe.

48. passivation of the clamp spaces, crosses, legs, kinematic mounts and the sides

of the devices with thermal oxide:

• 8 hours oxidation; 200nm oxide.

49. etching of the Si3N4 using boiling H3PO4 to open up the fiber window.

50. stripping of teflon contaminants in O2 plasma.

51. wet etch in KOH; 35 wt. %; 60 C; depth: until legs are free.

127


backline processing:52. stripping of oxide in HF (40%) and DI water rinse.

53. cleaning and drying in hot propanol.

128

B

FFM-TEM observations

· · ·

This appendix provides a brief account of a combined FFM and

TEM experiment. The goal was to observe metallic nanocontacts with

atomic resolution, using high-resolution (HR) TEM, and simultaneously

measure the normal and lateral forces acting on the contact with our

miniaturized FFM (chapter 7). Experiments of this type will be neces-

sary to explore the full mechanical behavior of atomic-scale wires and

contacts. This project was carried out in a collaboration with the group

of Prof. K. Takayanagi at the Tokyo Institute of Technology, where a

combined UHV-STM-TEM setup had been constructed already [177].

The measurements reported here, have been carried out with our FFM

mounted inside this TEM setup, during three short research stays in

Japan.

129

B. F F M - T E M O B S E R V A T I O N S

B.1 Introduction

Nanometer-sized asperities behave qualitatively differently from contacts of larger

dimensions. The relative influence of local atomic rearrangements under either nor-

mal or shear forces on the total energy of the contact can be dramatic, leading to a

wealth of new phenomena, such as atomic-scale stepwise changes in contact length,

the existence of stable, atomic wires [154,178,179], the preference for shell structures,

the occurrence of helical structures [180], etc. Although the initial motivation for in-

vestigations of atomic-scale contacts was dominated by the special, e.g. quantized

electrical conductance [181] properties of these contacts, nowadays the atomic-scale

and mechanical aspects receive a lot of attention. Knowledge of the forces acting on

nanocontacts are of great importance for the fundamental understanding of dry fric-

tion of metals. Mechanical properties in the direction normal to the surface of atomic-

sized metallic contacts have been studied experimentally using scanning tunnelling

microscopy (STM) and related techniques [182–184] and recently in an AFM-TEM

combination experiment [185] and a mechanically controllable break-junction [186]

experiment using a quartz-crystal tuning fork as the force sensor. For a single-atom

gold wire, the breaking force was found to be in the order of 1.5nN [184]. For the

understanding of friction, the forces that are generated when a nanocontact is sheared

in the lateral direction are of special interest. For this purpose, the combination of

our FFM and HRTEM should be ideal, because measured forces can directly be re-

lated to structural changes inside a nanocontact. At present, several research groups

in Japan, Sweden and Finland are attempting to study nanotribological phenomena

using AFM-TEM combination setups. The observations reported here were made for

contacts between a gold tip and a gold foil.

B.2 Experimental

The experiments described here were carried out with the miniature, TEM-compatible

FFM, presented in chapter 7. The FFM, together with its electronics and control

system were transported to the Tokyo Institute of Technology, where the FFM was

mounted in one of the UHV-TEM setups [155]. The sample stage of the FFM (see

fig. 7.1, item 2) was attached the goniometer of the TEM. The fiberhead (fig. 7.1b)

130

B.3 N A N O S C A L E W E A R O F A G O L D S U R F A C E

was positioned on one of the magnetic transfer arms. The glass fibers were threaded

through a CF63 blind flange, in which they were glued with torr seal epoxy [187] to

obtain a UHV-tight seal. The sample (see next section) was introduced via a separate

load-lock system.

Unfortunately, we have not been able to obtain truly simultaneous high-resolution

measurements with the TEM and the FFM because of a technical problem that could

not be solved in the short remainder of the research visit. When running the FFM and

TEM simultaneously, we found that the glass fibers of the FFM electrically charged

inside the electron beam. Each fiber was covered with an aluminium cladding, but in

order to fit inside the fiber window of the Tribolever each fiber had been tapered over

the last 10mm. Precisely over this length, the cladding was absent and the fibers could

charge up. The problem occurred each time when the fiber discharged, which caused

the Tribolever and the fibers to move abruptly with respect to each other. The move-

ment also caused a strong periodic disturbance in the force signals. Therefore, it was

not possible to measure forces with the electron beam switched on. The frequency and

intensity of this disturbance increased with higher electron beam current and with the

size of the electron beam. By withdrawing the glass fibers slightly from the pyramid

and using low beam currents, we managed to reduce the motion of the tip and could

observe the tip to interact with the gold sample while it was scanned. In principle, it

is possible to still measure the two components of the force in the plane of the TEM

image from the displacements of the tip in the image, but the charges on the FFM also

affected the TEM image and caused the image to shift when the FFM was moved.

Therefore, the actual tip position was difficult to determine. In the remainder of the

appendix we show one example of the observation of plastic deformation of asperities

on a gold surface on the atomic-scale.

B.3 Nanoscale wear of a gold surface

The scanning tip was electrochemically etched from a 60µm thick gold wire using

CaCl2 and then glued into the Tribolever. The sample was prepared from a 30µm

thick gold foil. To obtain lattice resolution, the foil was thinned below 50nm using

double-beam argon ion milling. The foil was then spot welded to a CuBe leaf spring.

By moving a small rod at the goniometer against the leaf spring, the sample

could be adjusted in height in order to make contact to the tip. Figure B.1 shows a

131


Figure B.1: Low resolution TEM image showing the thinned gold foil in the upper part and

the apex of the scanning tip in the lower part.

low-resolution image of the tip approaching the sample. The pressure inside the TEM

column was 1.9 ·10−6 Pa. During imaging of the tip, an amorphous hydrocarbon layer

was growing on the tip due to deposition of cracked hydrocarbon molecules from

the residual gas. The tip radius grew hereby from initially approximately 250nm to

950nm during a few hours observation.

Figure B.2 displays the gold sample on the top part of the image at a magni-

fication of 400,000. The lighter gray (thinner) areas of the surface exhibited lattice

resolution. At the bottom part, the surface of the tip is visible. Figures B.2b,c shows

the tip in contact and directly after the contact was broken again. Upon approach, the

tip jumped into contact at a distance of about 3.5nm. After the tip snapped out of

contact the asperity was left behind plastically deformed by about 2.4nm in the z-

132

B.4 S U M M A R Y

direction. Before the tip had jumped into contact, we observed already that a few atom

rows were pushed upwards along the side of the gold asperity, probably due to a much

smaller hydrocarbon asperity on the tip, not visible in the video.

A second example of rearrangements before full physical contact is established,

is shown in figure B.3. The tip was scanned at a close distance from the sample with

a speed of 8nm/s. Due to the scanning motion the tip was only faintly visible in the

images. When scanning the tip, we observed also that the entire field of view moved

slightly, even when tip and surface were completely out of contact, probably due to the

charging of the FFM, which caused a deflection of the electron beam. In figures B.3a-f

we observed several pyramidal shaped asperities on the gold sample to be swept over

the surface from the right to the left by the scanning motion of the tip. We observed

that the transport of material occurred mostly by gliding along the 111-planes. The

close-packed 111-planes are the preferred slip planes in fcc metals and the slip di-

rections are the 〈110〉 direction, which leads to four slip planes and 12 slip directions.

The critical shear stress is lowest between these planes. This has also been observed

in an MD simulation, where a Cu(100) tip was sheared over a Cu(100) surface [65]. In

a right to left scan, material was transported to the left, in a left to right scan, material

was transported back to the right. In the observation of figure B.3, more atoms were

moved to the left than to the right causing a net flux to the left. In between Figures

B.3e and f the tip was moved closer to the gold surface, causing the tip to cut deeply

into the surface. Thereby a new, larger asperity was created, that was pushed back to

the right.

B.4 Summary

The observations described in the appendix demonstrate that a combination of a three-

dimensionally sensitive force probe is possible without compromising the capabilities

of either technique. The combined instrument will be ideal for a range of investigations

of mechanical and structural properties of nanoscale structures, such as nanocontacts

and breaking wires. Due to a charging problem in the current version of the FFM we

have not been able yet to explore the full potential of simultaneous FFM and TEM

measurements.

133


Figure B.2: A tip covered by a hydrocarbon layer touching a gold asperity of 4nm radius.

Panel (a) shows the tip shortly before snap-into-contact; (b) depicts the contours (solid line)

of the scanning tip and the asperity (c) during contact; (d) contour as hollow line; (e) directly

after breaking the contact; (f) contour as dashed line; Magnification 400,000×.

134

B.4 S U M M A R Y

Figure B.3: Grabbed frames from a video showing a gold surface (upper part of images),

while a gold tip (faintly visible) is scanned against it from below. The dashed line indicates the

approximate position of the tip surface. The arrow indicates the position of the asperity that was

modified by the scanning tip. The numbers indicate the time scale of the observation in minutes.

Magnification 400,000×.

135


136

Summary

· · ·

This thesis deals with the development and application of new experimental tech-

niques for nanotribology, the science of friction and wear on the atomic scale. Chapter

1 provided a brief overview over this relatively new subject within the field of inter-

face physics.

In chapter 2, we introduced a list of fundamental questions, which we considered to

be of importance in order to create a link between atomic-scale friction experiments

and experiments on the micro- and macroscale and to compare experiments with the-

oretical calculations and computer simulations. The “ideal” nanofriction experiment

should be able to address these questions. The corresponding requirements on the

“ideal” nanofriction could be only met by introducing a new friction force sensor.

This device was first modelled and optimized using finite element analysis. In chapter

3, we described the fabrication process of this novel all-silicon force sensor, the Tri-

bolever. Difficulties in the microfabrication could be solved using deep reactive ion

etching from one side of a silicon wafer and wet etching from the opposite side of the

wafer. The first prototype device was shown to meet the design specifications obtained

from the finite element analysis prior to the fabrication. In addition, we showed the re-

sults from the microfabrication of a miniaturized second generation Tribolever, which

can be used in combination with transmission electron microscopy and scanning elec-

tron microscopy. The design and performance of a frictional force microscope, which

makes use of the Tribolever, is presented in chapter 4. Using four glass-fiber interfer-

ometers, which are positioned close to the central detection body of the Tribolever, its

motion can be simultaneously tracked in 3 directions. The positioning and manipula-

tion of the glass fibers with respect to the Tribolever is performed by a special fiber

positioning head, which we constructed by spark erosion from a single block of invar.

For the manipulation of the glass fibers we made use of miniature piezo Nanomotors.

As a first test application of the ambient frictional force microscope, we chose to study

atomic-scale friction on graphite surfaces. To our great surprise, although this system

has been studied intensively, the experiment revealed new phenomena. By measur-

137

S U M M A R Y

ing the friction as a function of the rotational angle between a tungsten tip and a

graphite surface we have shown in chapter 5 that the origin of the ultra-low friction of

graphite in friction force experiments lies in the incommensurability between between

a graphite flake that is attached to the tip and the graphite surface. The observation of

two narrow peaks in the friction force that are separated by 60 of ultra-low friction

provided clear experimental evidence of superlubricity: the nearly complete disap-

pearance of the friction force. The width of the two peaks allowed us to estimate the

contact diameter to be 7 to 12 lattice spacings. To verify this assumption, we have

set up a Tomlinson model, describing a rigid N-atom cluster with the symmetry of

a graphite flake that was moved through a two-dimensional sinusoidal potential rep-

resenting the graphite surface (chapter 6. The calculated friction force shows high

friction and near-zero friction, depending on the (in)commensurability between the

two lattices. By changing N, we indeed varied the width of the peak in the friction

vs. orientation plot, so that we could fit the measured peak width. The calculations

revealed that the shape of the high-friction peaks depend on the precise shape of the

flake.

In chapter 7, we then presented the conceptual design of a new UHV setup, with which

the “ideal” experiment can be performed, which was introduced in chapter 2. The heart

of this setup is formed by a miniaturized version of our ambient version of the fric-

tional force microscope. This FFM is based on a special prototype that was used to

perform friction measurements inside a HRTEM. Together with field ion microscopy

and scanning electron microscopy, this instrument will enable friction experiments

with completely in-situ characterized and modified sliding contacts.

In the two appendices, we listed the detailed etching recipe for the Tribolever and gave

a brief account of the first attempts of simultaneous FFM-HRTEM experiments at the

Tokyo Institute of Technology.

138

Samenvatting

· · ·

Wrijving is de welbekende kracht, die altijd optreedt als voorwerpen in contact komen

en over elkaar bewegen. Deze kracht probeert men sinds millennia te beheersen. Vaak

willen we wrijving reduceren, omdat wrijvingskrachten energie verlies en slijtage

veroorzaken, maar soms is ook een zo groot mogelijke wrijvingskracht gewenst. Dit

wordt bijvoordeeld geıllustreed door een skilanglaufer, die in de klassieke stijl ‘loopt’.

De langlaufer verwacht van een goede ski, dat deze zo lang mogelijk vooruit glij-

dt, maar om de langlaufer zich goed te kunnen laten afzetten, mag dezelfde ski niet

achteruit glijden. Zo’n combinatie van hoge en lage wrijvingseigenschappen bestaat

in veel technische systemen en ingenieurs hebben door empirische studies veel ken-

nis opgedaan over hoe de wrijvingseigenschappen beınvloed kunnen worden. Het is

eigenlijk verbazingwekkend dat ondanks de technische ontwikkeling en de uitgebreide

toepassingen er nog maar weinig bekend is over de fundamentele processen die aan

wrijving ten grondslag liggen.

In de jaren 80 van de laatste eeuw wordt de rasterkrachtmicroscoop ofwel AFM door

drie fysici uitgevonden. In dit apparaat wordt een extreem scherpe naald in contact ge-

bracht met het oppervlak van een preparaat. Het naaldje is verbonden met een veertje

waarvan uitwijking nauwkeurig gemeten kan worden met behulp van een laserbundel.

Omdat de uitwijking van de veer een maat is voor de kracht tussen de naald en het

oppervlak, kunnen kleine krachten in de orde van een nanoNewton1 en kleiner geme-

ten worden. Met een variant van de AFM, de wrijvingskrachtmicroscoop ofwel FFM,

kan ook de wrijving gemeten worden als de naald over de atomaire landschap van

het oppervlak glijdt. Door de komst van met name de FFM heeft het onderzoek naar

de oorzaken van wrijving een tweede lente ervaren. Deze nieuwe onderzoeksrichting

staat nu bekend onder de naam “Nanotribologie”.

In dit proefschrift staat de ontwikkeling beschreven van een bijzondere rasterkracht-

microscoop, die gebruik maakt van een nieuwe, speciaal voor dit doel geontwikkelde

krachtsensor, waarmee (wrijvings)krachten vanaf 2/100 nanoNewton niet alleen in

1. Een nanoNewton is ongeveer 1/10.000.000.000 van de kracht die nodig is om een kilogram te tillen.

139

S A M E N V A T T I N G

een richting, zoals met conventionele krachtsensoren, maar in drie ruimtelijke richtin-

gen tegelijk gemeten kunnen worden. Met deze nieuwe microscoop hebben we de

wrijvingseigenschappen van grafiet onderzocht. Grafiet is een bekend droog smeer-

middel en bezit een gelaagde structuur. De koolstof-atomen in een grafietlaag vormen

een soort heuvellandschap, dat op een eierdoos lijkt. Twee over elkaar glijdende lagen

ondervinden uiteraard weerstand als de heuvels van de ene laag precies in de dalen

van de andere laag passen. Als de twee lagen echter tegen elkaar verdraaid worden,

dan valt de wrijving weg. Dit effect wordt “superlubriciteit”, ofwel supersmering ge-

noemd. Met een simpel model konden wij het gemeten superlubriciteits effect ook

met behulp van de computer berekenen en de resultaten daarvan stemden heel goed

overeen met wat er in de meting waargenomen was. In een spuitbus met grafiet smeer-

middel zijn de grafietlaagjes zeker ook tegen elkaar verdraaid. Daarom zou het goed

kunnen, dat de goede smeringseigenschappen van grafiet tot stand komen door de door

ons gevonden superlubriciteit. De resultaten aan grafiet konden worden verkregen met

de microscoop en het preparaat blootgesteld aan de lucht. De meeste materiaalcom-

binaties kunnen helaas niet onder dergelijke omstandigheden worden bestudeerd. Da-

room wordt in dit proefschrift ook de ontwikkeling van de wrijvingskrachtmicroscoop

gepresenteerd, die in ultrahoog vacuum gaat werken. Door combinatie met andere mi-

croscopie soorten zoals veldionenmicroscopie en rasterelektronenmicroscopie zal hi-

ermee in de toekomst een volledige karaterisering van wrijvingssystemen op atomaire

schaal mogelijk worden.

140

Zusammenfassung

· · ·

Reibung ist eine physikalische Kraft, die allgegenwartig ist, wenn sich Gegenstande

bewegen. Diese Kraft versucht der Mensch seit Jahrtausenden zu beherrschen. Oft

versuchen wir dabei Reibung zu minimieren, da Reibungskrafte Energieverlust und

Verschleiß verursachen, aber haufig ist auch eine hohe Reibungskraft erwunscht. Dies

lasst sich zum Beispiel an einem klassischen Skilanglaufer gut illustrieren. Der Lang-

laufer erwartet von einem guten Ski, dass er moglichst lange gleitet, zum anderen

will er mit dem gleichen Ski gut beschleunigen, wobei der Ski nicht ruckwarts gleiten

sollte. Eine solche Kombination von hohen und niedrigen Reibungseigenschaften fin-

det sich in vielen technischen Systemen und Ingenieure haben durch empirische Stu-

dien umfangreiche Kenntnisse erlangt, wie dies technisch erreicht werden kann. Er-

staunlicherweise sind jedoch die fundamentellen Prozesse, die fur hohe oder niedrige

Reibung verantwortlich sind, noch weitgehend unbekannt. In den 80er Jahren des

letzten Jahrhunderts wurde das Rasterkraftmikroskop (atomic force microscope oder

AFM) von drei Physikern erfunden. Ein AFM besitzt eine kleine, sehr spitze Nadel,

die mit einem Federbalken verbunden ist. Kommt diese Nadel nun in Kontakt mit der

Oberflache einer Probe, dann verbiegt sich der Federbalken. Dessen Verbiegung kann

mit Hilfe eines Lasers sehr genau gemessen werden. Da die Verbiegung ein Maß fur

die Kraft zwischen Nadel und Probe ist, lassen sich kleinste Krafte im Nanonewton-

bereich2 nachweisen. Mit einer Variante des Rasterkraftmikroskops, dem Reibungs-

kraftmikroskop (frictional force microscope, FFM), konnen zusatzlich Reibungskrafte

gemessen werden, welche die Nadel erfahrt, wenn sie uber die atomare Hugelland-

schaft einer Probe gleitet. Vor allem durch die Entwicklung des FFM hat die Forschung

nach den Ursachen von Reibung einen zweiten Fruhling erfahren und ein neues For-

schungsgebiet aus der Taufe gehoben, “Nanotribologie” genannt.

Im Rahmen dieser Dissertation wurde ein spezielles Rasterkraftmikroskop ent-

wickelt, welches einen neuen, speziell fur Reibungsmessungen entwickelten Kraftsen-

sor verwendet, mit dem sich (Reibungs-)Krafte großer als 2/100 Nanonewton nicht

2. Ein Nanonewton ist etwa 1/10.000.000.000 der Kraft, die benotigt wird, um ein Kilogramm zu heben.

141

Z U S A M M E N F A S S U N G

nur in einer Richtung, wie bei einem konventionellen Rasterkraftmikroskop, son-

dern in drei Raumrichtungen gleichzeitig messen lassen konnen. Mit diesem neuen

Mikroskop wurden die Reibungseigenschaften von Graphit untersucht. Graphit ist ein

bekanntes Schmiermittel, welches eine Schichtstruktur besitzt. Unsere Messungen er-

gaben uberraschend, dass wenn man einzelne Graphitschichten gegeneinander ver-

dreht, die Reibung zwischen diesen Lagen nahezu verschwindet. Dieser Effekt, der

“Superlubricity”, wortlich ubersetzt etwa “Superschmierung”, genannt wird, konnte

damit erstmals auf atomarer Ebene deutlich nachgewiesen worden. Anschaulich kann

man sich Graphitschichten wie ubereinander gestapelte Eierkartons vorstellen, wobei

die Struktur des Eierkartons die atomare Struktur reprasentiert. Legt man die Eier-

kartons passend aufeinander, lassen sie sich nur schwer gegeneinander verschieben,

verdreht man sie aber gegeneinander, lassen sie sich wesentlich leichter gegeneinan-

der verschieben. Der gemessene ”Superlubricity-Effekt” konnte zudem mit Hilfe eines

einfachen Modells im Computer berechnet werden. In einer Dose Grafitspray sind

die Graphitschichten sicherlich auch gegeneinander verdreht, daher ist zu vermuten,

dass die die von uns gefundene Superlubrizitat fur die guten Schmiereigenschaften

mit verantwortlich ist. Graphit gehort zu den wenigen Materialien, die an Luft oder

in einer Stickstoffatmosphare untersucht werden konnen. Daher wurde zudem eine

miniaturisierte Weiterentwicklung unseres Mikroskops prasentiert, welches im Ultra-

hochvakuum operieren wird. Durch die Kombination von Rasterkraftmikroskopie mit

anderen Mikroskopietechniken (Rasterelektronenmikroskopie und Feldionenmikros-

kopie) wird in Zukunft eine vollstandige Charakterisierung eines Reibungssystem auf

atomarer Ebene moglich.

142

Nawoord

· · ·

Hoewel het nu al vijf jaar geleden is dat ik naar Nederland ben gekomen, lijkt de

tijd voorbij gevlogen. Gedurende deze tijd hebben een groot aantal personen op vier

verschillende locaties bijgedragen aan het tot stand komen van dit proefschrift. Toen

ik op AMOLF begon, was Jenny Heimberg al onderweg richting het ideale wrijv-

ingsexperiment en ik heb in het begin veel van haar geleerd. Voor de opbouw van

de microscoop was de technische ondersteuning op AMOLF onmisbaar: Dirk Jan

Spaanderman met wie ik prettig samengewerkt heb tijdens het ontwikkelen van de

triboscoop (in de werkplaats ook ‘troublescope’ genoemd) en verder Dick Glastra van

Loon, Wim Basingerhorn, Martijn Witlox, Wim Brouwer, Hans Zeijlemaker, Jan Ver-

hoeven en Rene Koper. Onmisbaar waren ook Emile van der Drift en Tony Zijstra van

DIMES in Delft, die voor het etsen van sensoren verantwoordelijk waren en met wie

ik twee leuke maanden in de cleanroom heb mogen samenwerken.

I would like to mention also the great support from Dr. Yukihito Kondo and Dr. Nouari

Kebaili at the ERATO project in Akishima, as well as Takehiko Shinzawa, Dr. Yoshi-

fumi Ohshima and Prof. Hiroyuki Hirayama at the Tokyo Institute of Technology, and

the great hospitality of my host, Prof. Kunio Takayanagi.

Terug in Nederland konden de experimenten weer op gang komen door de hulp van in-

strumentmakers en elektronici in Leiden: Arjen Geluk, Bert Crama, Raymond Koehler

en Ewie de Kuyper. Zeer van belang waren de discussies met en de waardevolle kri-

tiek van mijn kamer- en lotgenoot Bas Hendriksen en de goede sfeer gecreeerd door

alle collegas in de groep Grensvlakfysica. Ook de korte samenwerking aan quartz

stemvorken met Tjerk Oosterkamp, Matthijs Suijlen, Henriette Jensenius, Masami

Kageshima en Suzi Jarvis had veel ‘stemming’. Vlak voor het einde leverde de samen-

werking met de terugkerende Gertjan Verhoeven nog vele interessante resultaten op.

Ik wil mijn ouders bedanken voor hun continue steun en belangstelling tijdens mijn

studie en de promotie bedanken. Vooral mijn vriendin Hiroko wil ik bedanken voor

haar steun en liefde in de laatste twee jaren.

143

N A W O O R D

144

Curriculum Vitae

· · ·

M A R T I N D I E N W I E B E L

Op 9 december 1971 ben ik geboren in Lich in Duits-

land. Na het behalen van het eindexamen (“Abitur”) aan

het Helene-Lange Gymasium in Dortmund en het verrichten

van militaire dienst aan de Heeresfliegerwaffenschule in

Buckeburg, ben ik in oktober 1992 met de studie natuurkunde

begonnen aan de Universitat Dortmund. Na het behalen van

het “Vordiplom” zette ik mijn natuurkundestudie voort aan de

Rheinische-Friedrich-Wilhelms Universitat Bonn. In 1996 be-

gon ik mijn afstudeeronderzoek onder supervisie van Prof. dr.

Peter Zeppenfeld in de group van Prof. dr. George Comsa aan het Institut fur Grenz-

flachenforschung und Vakuumphysik van het Forschungzentrum Julich GmbH. Mijn

onderzoek betrof de groei en de structuur van edelgas lagen op koper eenkristallen,

die ik met behulp van lage-temperatuur rastertunnelmicroscopie bestudeerde. Daarna

begon ik een promotieonderzoek in de groep van Prof. dr. Joost W.M. Frenken, toen

nog aan het FOM-Instituut voor Atoom en Molecuulfysica (AMOLF) in Amsterdam.

In 1999 en 2000 bezocht ik voor drie korte onderzoeksverblijven het Tokyo Institute

of Technology in Japan met het doel om wrijvingskrachtmicrosopie te combineren

met transmissie elektronenmicroscopie. Aansluitend zette ik mijn promotieonderzoek

voort aan het Kamerlingh Onnes Laboratorium van de Universiteit Leiden, waar de

groep intussen naartoe verhuisd was. Het onderzoek dat ik tijdens mijn promotietijd

verrichte, staat grotendeels beschreven in dit proefschrift.

145

C U R R I C U L U M V I T A E

146

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