Tribologija tribology

8/13/2019 Tribologija tribology

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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 -R ESOLUTIONFRICTIONAL FORCE MICROSCOPY


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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 -R ESOLUTIONFRICTIONAL FORCE MICROSCOPY

PROEFSCHRIFT

TER VERKRIJGING VAN

DE GRAAD VAN DOCTOR AAN DE UNIVERSITEIT LEIDEN ,OP GEZAG VAN DE RECTOR M AGNIFICUS DR . D.D. B REIMER ,

HOOGLERAAR IN DE FACULTEIT DER W ISKUNDE ENNATUURWETENSCHAPPEN EN DIE DER GENEESKUNDE ,

VOLGENS BESLUIT VAN HET COLLEGE VOOR PROMOTIESTE VERDEDIGEN OP DONDERDAG 13 MAART 2003

TE KLOKKE 14.15 UU R

DOOR

M ARTIN DIENWIEBEL

GEBOREN TE L ICH IN 1971


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Promotor: Prof. dr. J.W.M. FrenkenReferent: Prof. dr. P.H. KesOverige leden: Prof. dr. S.P. Jarvis

dr. R. Bennewitzdr. A. Fasolinodr. ir. C. F. J. FlipseProf. dr. J. M. van Ruitenbeek dr. ir. T. H. Oosterkamp

Cover Design: Hiroko Takei Atomic-scale Friction and Superlubricity studied using High-Resolution FrictionalForce Microscopy

Martin Dienwiebel

ISBN 90-9016598-3A digital version of this thesis can be downloaded fromhttp://www.physics.leidenuniv.nl

The work described in this thesis was performed at the FOM Institute for Atomicand Molecular Physics (AMOLF), Kruislaan 407, 1098 SJ Amsterdam, the Kamer-lingh Onnes Laboratory, Leiden University, Niels Bohrweg 2, 2333 CA Leiden, andthe Tokyo Institute of Technology, Department of Materials Science and Engineering,4259 Nagatuta, Midori-Ku, Yokohama, 226, Japan. The work is part of the researchprogram of the Stichting voor Fundamenteel Onderzoek der Materie (FOM) and was

made possible by nancial support from the Nederlandse Organisatie voor Weten-schappelijk Onderzoek (NWO).


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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),137150 (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 84,1824 (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-DimensionalForce 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-ResolutionFrictional 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 andJ.W.M. Frenken, Why Graphite is a Good Solid Lubricant: an atomistic view (Chapter5), 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. Jarvisand T.H. Oosterkamp, Noncontact atomic force microscopy in liquid environment withquartz tuning fork and carbon nanotube probe , Appl. Surf. Sci. 188 , 440444 (2002).


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Contents

1 Introduction 11

1.1 Nanotribology 12

1.1.1 Single-asperity experiments and continuum mechanics models 131.1.2 Friction Anisotropy 141.1.3 Atomic-scale friction experiments and simple atomistic models 151.1.4 Superlubricity 17

1.2 Scope of this thesis 19

2 The ideal nanotribology experiment 21

2.1 Introduction 222.2 Requirements 23

2.3 Traditional frictional force microscopy 242.4 Design of a novel force probe 25

3 Microfabrication of the Tribolever 33

3.1 Tribolever structure 343.2 Fabrication difculties 343.3 Fabrication process 363.4 Microfabrication results 393.5 Miniaturized Tribolever 423.6 Summary 43

4 Design and performance of a high-resolution frictional force microscope 45

4.1 Detection principle 464.2 The berhead 494.3 Electronics 504.4 Sample movement 524.5 Experimental setup and procedures 54

4.5.1 Calibration 544.5.2 Tip mounting 56

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C O N T E N T S

4.5.3 Setup 574.6 Performance 59

5 Superlubricity of graphite 63

5.1 Introduction 645.1.1 Structure and mechanical properties of graphite 645.1.2 Tribological Properties 645.1.3 Nanotribological properties 66

5.2 Experimental 67

5.3 Results 695.3.1 Lateral force images 695.3.2 Friction versus load 725.3.3 Friction vs. sample rotation 775.3.4 A loose ake 815.3.5 Large-scale images on polycrystalline graphite 815.3.6 TEM analysis of the tip 845.3.7 Friction anisotropy 84

5.4 Discussion 875.5 Conclusions 89

6 Superlubricity in the Tomlinson model 91

6.1 Introduction 926.2 Model 936.3 Results 96

6.3.1 Symmetric contacts 966.3.2 Asymmetric contacts 98

6.4 Discussion 1026.5 Conclusions 105

7 Towards the ideal friction experiment 107

7.1 Introduction 1087.1.1 The need for ultra-high vacuum 1087.1.2 Imaging the contact 108

7.2 Design of a miniaturized FFM for use in combination with HRTEMor SEM 110

7.2.1 FFM/HRTEM berhead 113

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C O N T E N T S

7.2.2 HRTEM-FFM assembly 1147.2.3 HRTEM-FFM sample stage 1157.3 Design of the UHV setup for FFM 116

7.3.1 UHV chamber 1167.3.2 UHV-FFM stage 1197.3.3 Mini-SEM 1197.3.4 Field ion microscope 122

7.4 Summary 122

A Processing steps of the Tribolever fabrication 123A.1 Overview 123A.2 Processing 124

B FFM-TEM observations 129

B.1 Introduction 130B.2 Experimental 130B.3 Nanoscale wear of a gold surface 131B.4 Summary 133

Summary 137

Samenvatting 139

Zusammenfassung 141

Nawoord 143

Curriculum Vitae 145

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C O N T E N T S

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I

Introduction

It is quite difcult 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 issurprising that more understanding of this phenomenon has not come

about. At present time, in fact, it is even impossible to estimate the co-efcient of friction between two substances

R. P. Feynman, 1963 [1]

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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 lostnothing of its timeliness. This is not to say that there has been no progress in the eldof 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 illustratedby the evolution of cars. Modern car engines do not need to be driven carefully for therst few thousand kilometers anymore because engine parts are machined better andthe engines are run in at the factory at optimal conditions to reduce initial wear. Alsooil change cycles have become longer over the last decades due to improved lubricantsand additives.Over the centuries the phenomenon of friction has attracted both physicists and en-gineers, as is beautifully illustrated in Duncan Dowsons book History of Tribol-ogy [3], which covers the tribological progress of mankind from early prehistorictoolmaking to the present (1997). The modern history of tribology since the indus-trial revolution is characterized by the fact that technological advances have beenmade mainly empirically in the eld of engineering. On the other hand, in the eldof 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 difcult tomeasure. This has changed since the advent of new experimental techniques, such asthe 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 inatomic-scale surface science this has caused a renaissance of tribology on the nanome-ter scale, or nanotribology . For the physicist, the wealth of phenomena encounteredwhen 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 rediscoveredby Guillaume Amontons [11] and Charles Augustin Coulomb [12], state that the fric-tion force F F is proportional to the normal load F N and independent of the slidingspeed and the contact area of the sliding bodies i.e.,

F F = F N . (1.1)

is a proportionality factor that is commonly known as the coefcient of fric-

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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 areawas recognized much later by Bowden and Tabor [13]. When two macroscopic bodiesare brought into contact, the roughness of their surfaces leads to the creation of a largenumber of microcontacts or asperities. For the case of dry, wearless sliding, Bowdenand Tabor proposed that the friction force is directly proportional to the real area of contact A,

F F = A, (1.2)

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

increases proportional with normal load [14], in which case the classical friction lawis 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-asperitybehavior. Such a prototype asperity can be the tip of an FFM touching a surface or thecontact 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 exible 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 reecting from the cantilever (see also section2.3). In the SFA, two curved, smooth mica sheets are brought into contact in a crossedcylinder geometry. The friction force between the two sheets is measured by detectingthe extension or contraction of springs, connected to one of the two mica surfaces. Inaddition, the contact area and separation can be measured by shining white light acrossthe contact and detecting the fringes of equal chromatic order (FECO) resulting frommultiple beam interference.

Several monographs have been published on nanotribology, of which we would liketo mention particularly the book by Bo Persson [16]. Also several review articles havebeen published, which give a good overview over recent experimental and theoreti-cal progress in nanotribology [1723]. In the following, we will briey review a fewselected 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 withthe normal load, but follows a F F F n N relation,where n < 1. A number of continuum

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mechanics theories exist that describe the elastic deformation of two bodies underload. The rst 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 F 1/ 3 N and the friction forcescales as F 2/ 3 N . The Johnson-Kendall-Roberts model (JKR) [25] also takes adhesiveforces inside the contact into account. The result is, that the friction force is non-zeroalready 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 ingredientsof the Hertz, JKR and DMT models. All above models scale with the normal loadas F 2/ 3 N . 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 tipsliding over diamond [30] and M-D for a silicon tip sliding over NbSe 2 [31]. In SFAexperiments, JKR behavior is commonly observed [32]. Recently, different frictionlaws have been found by Wenning et al. [33] using a molecular dynamics (MD) simu-lation. They observed F F F 0.63 N for amorphous contacts and a linear dependence for

incommensurate and commensurate, crystalline contacts. A F F F 0.85

N dependencewas found for incommensurate, boundary lubricated contacts, but was not regarded tobe 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 frictionanisotropy strictly for the variation of friction with respect to the sliding direction andnot 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 analternating tilt of TGS molecules in two domains of the substrate. Overney et al. [36]and others [3739] observed friction anisotropy on organic bilayer lms, caused bydifferent molecular alignments in the substrate as in the case of TGS. An extreme caseof anisotropy was reported by Sheehan and Lieber [40]. They observed that MoO 3islands on a MoS 2 surface, that were manipulated using the tip of a FFM, could only

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

Figure 1.1: Two simple one-dimensional atomistic models. In the single-atom Tomlinsonmodel (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 V 0 . The sup-

port position is denoted with x m and the position of the atom with x t . 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 rst experiment that revealed atomic resolution of lateral forces was performedby Mate et al. [4] using the tungsten tip of a modied scanning tunnelling micro-scope (STM) sliding over a graphite surface. In this measurement, a saw-tooth patternin 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 laterobserved on many other materials, such as e.g. mica [41], MoS 2 [42], copper [43],

diamond [44, 45], and alkaline-halides (NaF, NaCl, KF, KCl, KBr) [4648].Two simple ball and spring models are often used to analytically model atomic-

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Figure 1.2: The Aubry transition in the Tomlinson model. The lateral force F lat = k ( xt

xm) vs. xm is plotted for < 1 (a), = 1 (b) and > 1. In panel (c) the dashed line showsthe 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 atomor 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 xed periodic potential energy surface(g. 1.1a). In a second version of the Tomlinson model, the single atom is replacedby an innite 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 atomsby springs, and the coupling to other atoms in the top sliding surface (g. 1.1b) isneglected. The simplest version is the one-dimensional static Tomlinson model of apoint-like contact (g. 1.1a). If the potential energy surface of the substrate has a sin-gle Fourier component with amplitude V 0 , we can write the total force as

2a

V 0 sin(2a

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 2V 0/ ka . For a weak surfacepotential and a stiff spring ( < 1) the upper solid slides continuously over the lowersurface and the average friction force is zero [50]. When exceeds unity, multiplesolutions exist to equation 1.3. The atom or the tip of the upper surface is stickingat 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,

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surfaces slide over each other in dry contact without wear. This was rst shown in aquasistatic calculation by Hirano and Shinjo [64] for rigid crystals with fcc, bcc andhcp symmetry and different orientations. In a later study they used a F-K model tostudy 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 asuperlubric regime for a small interaction strength P and a high stiffness k of the uppersurface. This is equivalent to the Aubry transition at = 1 in the one-dimensional F-Kand 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 and they noted thatsuperlubricity should appear for any combination of at and clean metals when theinteraction 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 conrmed by Srensen et al. [65] who studied the friction between aat copper asperity and a copper surface in an MD simulation at T = 0. For the caseof a (111) terminated asperity sliding over a Cu(111) surface, atomic-scale stick-slipmotion 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 smallasperities, 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, containing19 19 atoms, superlubricity was observed also for the highest normal loads used inthe simulation. For a (100) terminated asperity that was sliding over a Cu(100) surface,Srensen et al. observed adhesive wear and transfer of Cu atoms from the asperity tothe 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 thatfrictional forces between mica sheets in contact in an SFA experiment were maximalwhen the orientation of the mica sheets matched. Friction forces were a factor 4 lowerwhen the crystallographic directions of mica sheets were misoriented relative to eachother. 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 forceas function of the mist angle between two Ni(100) crystal surfaces using a UHV tri-bometer [67]. They found a lower friction coefcient for 45 and 135 mist anglesthan for other orientations, which was consistent with superlubricity. However, these

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

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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 certaindirections was caused by easy shearing along the preferred slip planes in the bulk.This explanation is consistent with the results found by Srensen [65], who concludedthat superlubricity between fcc metal surfaces should only be expected between (111)surfaces. Recently, Falvo et al. [68, 69] manipulated carbon nanotubes (CNTs) on agraphite surface using the tip of a FFM. They observed that the CNTs changed fromsliding to rolling motion, depending on the lattice mismatch between the tube and thesubstrate. The rolling motion of the CNT in the case of a commensurate contact wasfound to require a higher lateral force than the sliding motion of the CNT in the caseof 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 aselectronic 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 superuidity istherefore 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 newinstrument, with which quantitative measurements of friction processes can be per-formed at the atomic and nanometer scale. As a rst application of our frictional forcemicroscope, we revisited the atomic scale friction of a tungsten tip sliding over agraphite 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 forcemicroscope. We further present the design of a new friction force sensor that enablesone 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

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sensor. This rst 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 analyzedin chapter 6 , where we make use of a static Tomlinson model to describe the frictionbetween 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), ispresented in chapter 7 . A preliminary friction measurement inside a high-resolutionTEM is described briey in appendix B . In addition, chapter 7 introduces the design of the ultra-high vacuum setup, which makes use of the miniaturized FFM. This secondversion of the FFM will be combined with additional microcopy techniques, such aseld ion microscopy (FIM) and scanning electron microscopy (SEM), to allow fullcharacterization and control of the sliding contact.

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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 nanofrictionexperiment should be able to address these questions and demands anumber of technical specications to be met, which are not available

using commercial frictional force microscopes and force sensors. Based on the technical specications we present the design of a novel force

sensor.

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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 eld of nanotribology has produced tremendous insight into energy dis-sipation processes at the atomic scale, friction coefcients 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 consideringwhich FFM experiments need to be carried out, in order to establish the link withmacroscopic friction; in the framework of tribology, the interesting regime is certainlynot that of a single-atom contact, but rather that of contact areas ranging from a fewatoms to a few million atoms. The ideal experiment would be one in which werecord all three components of the force between two extended surfaces in which weknow 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 thesurfaces 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 wouldbe one in which the two surfaces in contact consist of the same material. Certainunlubricated material couples are known to form sliding contacts that provide goodtribological properties, while other combinations lead to high friction coefcients andexcessive wear. The fundamental processes that cause these different behaviors stilllie in the dark. (4) How does the friction force depend on the relative crystallographicorientation of the two surfaces? Single-atom contacts exhibit pronounced atomic-scale

stick-slip sliding motion. When two rigid lattices are sheared with the lattices rotatedout of registry, there should be a signicant cancellation of the individual contributionsto the friction force, leading to superlubricity. Of course, for larger contacts, this naivepicture should break down, as the two lattices are not perfectly rigid, and a network of mist dislocations forms between the two. It is important to nd 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 thefriction 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 orientationsof the two surfaces? (7) How does the friction force depend on temperature? (8) How

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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 frictionforce depend on sliding speed? (10) How and why does a contact age?With quantitative experimental answers to these questions for ideal, fully controlledcontacts, 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 idealinstrument 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 highsensitivity. (2) The force sensing device should be stiff enough to withstand the highforce gradients normal to the contact, which otherwise lead to snap-to-contact. (3)Next, we want full control over the contact area. In traditional FFMs, the contact areais 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, wewant to control the contact area and the loading force independently. This means thatwe need to go beyond the usual hemispherical tip shape. The tip should end in anatomically at 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 crystalsurface with which it is to be brought in contact. (5) To complicate matters further, wewant control over the precise crystallographic orientations of the two surfaces. Thismeans that we have to specify not only the crystallographic orientations of the surfacenormal of the tip and the countersurface, but also their azimuthal orientations. (6) Thesliding 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 thematerials 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.

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Figure 2.1: Model of a rectangular AFM cantilever. The motion of the cantilever is detected bymeasuring the position of a light beam that is reected 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 deection of an atomic forcemicroscope (AFM) cantilever. One of the most successful and widely used techniquesis optical beam deection, developed by Meyer and Amer [72]. In this method, anoptical beam is reected from the rear side of a cantilever onto a split photodiode (g.2.1). Using a four-quadrant photodiode, vertical motion (normal to the surface) andtorsional motion of the cantilever can be simultaneously detected. The image obtainedby monitoring the vertical deection 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.Navely, this dual force measurement is trivial to implement but great difculty comes

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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]. Thespring 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 andtorsional directions can be calculated using classical mechanics textbook equations,

k z = Ew

4t 3

L3 (2.1)

k x = Et

4w3

L3 (2.2)

k = Gwt 3

3 La2 . (2.3)Here, E and G are the Youngs 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 usedV-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 signicant couplingbetween the normal and torsional responses of AFM cantilevers, making it difcult todistinguish buckling from bending [75]. Small misalignments of the system produce

large errors in the FFM measurements. A true calibration of the cantilevers responsein the lateral direction is rarely performed and usually does not take into account thedependence of the force signals on the location of the beam spot on the cantilever, andon the precise tip position on the cantilever [74]. For cantilevers that are relatively stiff in the lateral direction, the exibility 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 highvalues of the proportional and integral gain of the feedback loop inuence the mea-sured lateral force to a great extent [76]. As we see, these traditional force probes failto meet several of the essential requirements that we formulated above. Our efforts tobuild a new experimental setup therefore started by nding or constructing a suitableforce probe.

2.4 Design of a novel force probe

In the last 10 years, serious efforts have been made to produce force probes withbetter 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 touse cantilevers with a small width and a large thickness. This would result in reduced

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Figure 2.2: Two examples of complex structures that have been designed for lateral forcedetection. (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 deection. 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 Stoweet al. [79]. Using a cantilever that was oriented perpendicular to the surface, they couldachieve a lateral force resolution of 5.6 attonewtons (5 .6 1018 N/ Hz). The lateralspring constant of this cantilever ( k lateral = 6.5 106 N/m, k normal > 1000N/m) wasso low that the cantilever would snap into contact 60nm away from the surface, whenit would have been mounted parallel to the sample surface. In a geometry, where thecantilever is mounted parallel to the surface, the width of a cantilever is limited bythe size of the tip and optical detection of the cantilevers deection is not feasiblebecause the cantilevers endpoint is very close to the sample unless the spot size of thelight beam is smaller than the height of the cantilver. Piezoresistive detection, however,

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

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than optical detection.A more practical approach is to modify commercial cantilevers using focusedion beam (FIB) methods [80]. It has been demonstrated, that by cutting a hinge into arectangular cantilever, the lateral spring constant in the x-direction could be reducedby roughly an order of magnitude to 118N/m. However, the normal spring constantwas reduced as well, to 16 .4N/m.

By cutting a more complex H-shape into a rectangular cantilever, a lateral springconstant 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 byone, so that reproducible results are difcult to obtain. In addition, modifying a singlecantilever 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 theX-, Y-, and Z-direction.In spite of the improvements, none of the above designs provides low and symmetricspring 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 shouldof course be symmetric in the X- and Y-directions. Ideally, one would like to placefour equal springs around the scanning tip of the cantilever as depicted in gure 2.3a.

This cannot be achieved by using four straight rectangular beams as the springs,as this structure would be completely inexible. Therefore we introduced a 90 bendin each beam to provide the required exibility in the lateral plane (g. 2.3b). Aswe discussed above, it is not trivial to measure the displacement of the cantileverin the plane parallel to the sample surface by optical means. Therefore we placed adetection pyramid at the center of the cantilever. Using this pyramid as a set of fourmirrors, we can detect the displacement of the pyramid with the use of four glass-berinterferometers, which are placed symmetrically around the pyramid, under an anglewith the plane of the sample surface. This is the basic design of our new force probe(gure 2.4) that we called the Tribolever 1

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 nite element

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

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Figure 2.3: Design of a cantilever that is symmetric in two lateral directions (X and Y). Theidea 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 ratiolegs, 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 = 450 m and height t = 10 m(for comparison with the thickness of simple beam cantilevers we will denote theheight with t ). We used the following material properties for silicon: Youngs modulus, E = 1.69 1011 N/m 2, Poissons ratio s = 0.333 and density = 2330kg/m 3 . For ourideal experiment the lateral spring constants should be signicantly lower than thenormal spring constants, which means that the width of the legs should stay well belowthe cross-over point in gure 2.5a , which for 10 m-high legs, is 7 .4 m. The smallestwidth that can be achieved by our microfabrication methods is about 1 m (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 widthwas kept constant at 5 m. The microfabrication process allows a maximum height of about 20 25 m, which would lead to a normal spring constant in the order of a fewhundreds to one thousand N/m.

Table 2.6 shows a comparison of our calculated results to those of a traditionalAFM diving board cantilever. The Tribolever data in this table were calculated forthe actual dimensions of our prototype sensor of w = 1.4 m and t = 10.6 m Si legs,

which will be discussed later. The torsional spring constant ( ) for AFM cantileversgoverns the lateral response for a traditional FFM, as discussed earlier.

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Figure 2.4: Model of the Tribolever used in the nite 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 reecting from the pyramids 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 bers that are guiding light on the pyramid

and collecting the reected 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 k x = k y for Tribolevers are signicantly lowerthan those for simple beams. It is important to note that although the lateral springconstant ( k y), which causes buckling of AFM cantilevers, is small compared to ,this component of the lateral force is extremely difcult to extract from the verti-cal response and is therefore usually not measured in traditional AFMs. In additionto making the spring constants ideal for frictional force microscopy, the Triboleverdesign 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 %. Thisis due to the torque introduced by the scanning tip. Besides the leg geometry, otherconsiderations have played an important role in the overall design. For example, at thefront side of the central detection block (gure 2.4b) the tip is sticking out. In order toallow 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 rst step towards the ideal nanotribology ex-

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Figure 2.5: (a) Spring constants of the Tribolever as function of the width of the legs for a xed height of 10 m, calculated using nite 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 t for the lateral spring constant and the solid line is a linear t 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 E e f f = 9.33 1012 N/m230


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Figure 2.5: continued obtained from the cubic t differs signicantly from the value of E for silicon from literature, which demonstrates that the response of the Tribolever differs signi-

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

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

the legs for a xed width of 5 m.

Dimensions [ m] Length, L Width, w Thickness, t Tip Height, asimple beam cantilever 450 47 2.1 15

Tribolever 351 1.4 10.6 50

Spring constants [N/m] k x k y k z simple beam cantilever 4.03 101.1 0.2 71.6

Tribolever 1.48 1.48 25.8 136Tribolever (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 m. See schematic gures for denitions of simple beam

and Tribolever dimensions. Values of silicon constants used in the calculation are Youngs

modulus, E= 1.69 1011 N/m2 , Poissons ratio, s=0.333, and density, = 2330 kg/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 givenin chapter 3. In chapter 4 we will then describe the technical details, the operation andperformance of our ambient-condition friction force microscope that makes use of theTribolever. Chapter 7 introduces the design of a new ultra-high vacuum setup that willmeet all requirements that we formulated at the beginning of this chapter.

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

lems. Then results of the fabrication of a rst prototype are presented.Finally, we will turn our attention to the fabrication process of a smaller,second generation device.

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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 ( 10 mm8 mm)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(gs. 2.4 and 2.6). Furthermore, the sensor was produced with a central hole, such thattips 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 frictionforce microscope.The rst prototype sensors have been realized on 10 8 0.525mm 3 chips that eachinclude two Tribolevers and a set of kinematic mount structures to ensure that the chipcan be mounted in the FFM with high reproducibility (gure 3.1). The dimensions of the prototype chip were too large for the nal UHV version of the microscope, since itinhibited 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 suchthat its dimensions could be greatly reduced (5 2 0.525mm 3).

3.2 Fabrication difculties

Before describing the actual fabrication process, we briey list some of the fabricationdifculties, arising from the special shape of our force sensor. At the front side two

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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 ber

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

front side up; (e) front side down.

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anisotropic dry etching steps are required; one to dene the leg geometry and one tocreate the tip hole, with etching depths of about 15 m and 100 m respectively. Thisimplies that the patterning step for the legs has to be done after the etching of the holestructure or vice versa, giving rise to severe step coverage problems in the resist spincoating.A second problem is introduced by the convex structure of the pyramid at the rearside of the cantilever. Its facets are not easily obtained from a KOH etch along 111planes because of underetching at the corners [85]. Sacricial corner compensationstructures to retard the underetching may help [86]. However, with the pyramid heightcomparable to the lateral dimension (see above), this approach has serious limitationsfor 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 fromthe rear side. This can be understood as follows. The tip must extend out from thecantilever structure in order to interact with a sample. Hence, the front side of the can-tilever has to be ush with one face of the 525 m thick silicon wafer. With the centraldetection body approximately 100 m high, the top of the pyramid is recessed about400 m 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 bers to access the pyramidfaces. As a consequence, fabrication of the pyramidal structure at the rear side wouldhave to be done at a depth of about 400 m, which would further complicate the pro-cessing involved.In the following, we will show how a procedure of anisotropic dry etching of spe-cic geometries at the front side, followed by a protective thermal oxidation and asubsequent wet crystallographic etch at the rear side solves all of the problems listedabove.

3.3 Fabrication process

In this section we qualitatively describe the fabrication process. For a more completeoverview of the entire process, we refer to appendix A.Starting with a Si (100) substrate, the rst step is to create alignment marker patternsat the front and the rear side by anisotropic dry etching, 2 m 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

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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. S uss MA 56). Oxide patterning isdone by anisotropic reactive ion etching (RIE) in a CHF 3 /O2 plasma (25:1) in a paral-lel plate reactor (Leybold Z401). Typical plasma conditions are 10 bar gas pressure,50sccm 1 gas ow and 0 .16W/cm 2 rf power with rf bias voltage of 330V, giving anoxide etch rate of 20 25nm/min. All anisotropic dry etching in Si is achieved in ahigh density plasma setup (Alcatel DECR200) with a SF 6 /O2 gas mixture (7.5:1), ata substrate temperature of 95 C. Plasma process conditions are 2 .3 bar pressure,25.5sccm gas ow, 750W microwave power (at 2 .45GHz) and 10V substrate bias.Si etch rates are in the order of 1 m/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 gure 3.2. The wafer is thermally oxidized (1 .3 moxide thickness) and after lithography of the leg pattern and central cross patterns,these patterns are etched anisotropically in the oxide with a CHF 3 plasma. The twopatterns are etched with different depths, the cross pattern down to the silicon and theleg pattern somewhere halfway through the oxide thickness (gure 3.2b). The ideais 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 coatingof about one micron topography in the oxide mask layer. The cross pattern is etchedrst, about 85 m deep into the Si. Next the leg pattern is opened down to the silicon(with CHF 3 plasma) and the silicon etching (of leg and cross patterns) is continued for15 m. Resulting depths of cross and leg patterns are approximately 100 m and 15 mrespectively. The pattern quality is superior due to the extreme oxide mask selectivityof about 1000 : 1 in the silicon etching process. This is because the ion energy canbe tuned independently from the reactive species in the high density plasma [87]. Themost decisive element in the overall fabrication process is the cross-shaped pattern inthe middle at the front side, rotated 45 with respect to the central square block. Thecenter of the cross forms the hole for the scanning tip. In addition, the cross is usedto realize the 111 faceted pyramid, which is central to the detection system (gure3.2c-e). After thermal oxidation of the freshly etched surfaces of both the leg and crosspatterns (gure 3.2c), the wide recessed window at the rear side of the cantilever ismade using a crystallographic wet KOH-etch through the wafer (gure 3.2d). As theetching front from the rear side reaches the oxidized cross (gure 3.3a), the 111facets are exposed while the corners are protected by the oxidized sidewalls (gure

1. 1sccm = 1.69 103 Pa m 3 /s

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Figure 3.3: Optical (a-c) and scanning electron micrographs (d) of the KOH etching process:(a) At t = 3h 22 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 = 4h08the 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 opticalber window to realize a pyramid structure by convex KOH etching is avoided. Thearea of the 111 facets can be precisely tuned by the etch depth difference between the

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

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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 ber window, (2) two of the three elements of the kinematic

mount.

is released and the sidewall passivation layer removed.

3.4 Microfabrication results

The rst generation of the Tribolever integrated in a Si(100) wafer is shown in gure3.4. The Tribolever (g. 3.4a) includes the four 111 facets, the high aspect ratio legswith a width of 1 .4 m, a height of 10 .6 m, a length of 351 m and a cross-shapedhole for the scanning tip.

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Figure 3.4b shows a Tribolever from the front side with a metal tip tted in thecentral cross. The tip shown is an electrochemically etched tungsten wire, of 50 m di-ameter, which extends approximatly 50 60 m out of the front side. It was positionedinto the Tribolever using micromanipulators and attached with wax (wax was used inthis rst test, in the FFM experiments the tip was attached using silver epoxy). Figure3.4d shows a part of the Tribolever environment embedded in the Si wafer. The bigwindow around the Tribolever (indicated by arrow 1) is for proper access of the opticbers as discussed earlier. The other KOH-etched windows (2) serve as a kinematicmount for a highly reproducible t of the Tribolever chip in the FFM setup. These ad-ditional recesses complicate the overall process scheme and require all oxide patternsto be buried in an all-sided CVD nitride layer (300nm) before opening one patternafter the other. The nitride serves as a mask for intermediate local thermal oxidationof Si structures existing already, to protect them against deterioration in subsequentetching steps.Reduced lateral spring constants of the four legs are crucial for proper operation andessential 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 bufferedHF solution in an iterative approach until the required leg thinning has been obtained(g. 3.5a). In this way, we can reduce the leg width from 10 m to 1 3 m, but somewidth variation due to rounding of corners has been observed. Another option is todene precise hole joints in the crucial corners of the leg construction, either with afocused ion beam (FIB) or by lithographic means (Table 2.6). Results of both methodsare depicted in gure 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 withinone cantilever structure, but is not homogeneous over the full leg height and requiresadditional trimming.Calibration (see chapter 4) of the Tribolevers shows that the spring constants k x andk y of the prototype are 1 .67N/m, close to the calculated value of 1 .48N/m. The slightdifference might be due to roundings and increased thickness at the bends of the legs.The measured k z = 10.32N/m is signicantly different from the calculated value of 25.8N/m. This is due to the fact that the Tribolever is positioned in the center of thelarge ber window, which is only 10 .6 m thick (like the leg height) and acts as an

additional spring.

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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.

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Figure 3.6: SEM image of the miniaturized Tribolever showing: (a) the chip, including theTribolever structure, the cross-shaped ber window and the kinematic mounts; (b) a close-up

view of the Tribolever through the ber 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 transmissionelectron microscopy (TEM). For the case of TEM, the dimensions of the Triboleverare 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. Theresolution of SEM critically depends on the working distance, which is the distancebetween 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 alsoreduce 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, isthe size of the large window for the glass bers, which would form a predeterminedbreaking point of the device. Since a reduction of the size of the ber window is notpossible, we rotated the ber 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 pyramidand the kinematic mounts on the wafer, so we rotated the pattern of the device exceptthe Tribolever pattern on the wafer. The result of the second processing run, using thenew layout, is shown in gure 3.6. The dimensions of the miniaturized version could

be reduced to 5 2mm, thus making the device t in the typical gap between the poleshoes of a high-resolution TEM column, and reducing the minimum working distance

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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.Difculties in the microfabrication could be solved using deep reactive ion etchingfrom one side of a silicon wafer and wet etching from the opposite side of the wafer.The rst prototype device was shown to meet the requirements formulated in chapter 2and to have properties close to the predictions that were obtained from nite elementanalysis prior to the fabrication. In addition, we presented the microfabrication of a miniaturized second generation Tribolever that can be used in combination withtransmission electron microscopy and scanning electron microscopy.

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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 toallow for quick modications, 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 insome of the design decisions for this prototype.

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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 isformed by four ber optic interferometers. In an optical glass ber, light is partiallyreected at the endface of the ber, while most of the light is leaving the ber. Bymeans of an external mirror, a fraction of that light can be made to reenter the ber.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. Witha ber coupler (the analog to a beam splitter) the backwards travelling light can becoupled out and detected with a photodiode. The interferometers output is given by

I = I 0 1 + Acos 22 D

, (4.1)

where I is the output current, A is the relative interference amplitude, D is theber-sample distance, and is the wavelength of the laser (780nm in our case). Theoffset I 0 and the amplitude A are both determined by the reectivities of the two in-terfaces responsible for the interference signal. Taking a refractive index of n1 = 1.5

for a well-cleaved quartz glass ber and n2 = 1 for air, the maximum reectance of the endface is ( n1n2n1+ n2 )

2 = 4%. For the pyramid surface a maximum reectance in theorder of 60% is expected. The 111 facets of the pyramid are at a well-dened angle, = 54.74, with respect to the (100 ) surface plane of the wafer.

If each of the four glassbers is adjusted such, that the light intensity increaseswhen the ber-pyramid distance decreases (equation 4.1), the three-dimensional dis-placement with respect to the xed bers can be extracted from the normalized sumand differences of the signals coming from the four interferometers [44].

These linear combinations need to be weighted by the appropriate geometricalprojection (gure 4.1):

X = X 2 X 1

2sin (4.2)

Y = Y 2 Y 1

2sin (4.3)

Z = X 1 + X 2 + Y 1 + Y 2

4cos (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 diodes output intensity

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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 bers. If the pyramid moveslaterally (panel a), the distance X1 between the left glass ber and the pyramid increases and

the distance X2 between the right glass ber 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 ber 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 inuence of uctuations inlaser intensity and wavelength is greatly reduced, while the remaining variations canbe divided out by use of a reference signal. A schematic of one such pair (e.g. the Xpair) is seen in Figure 4.2.

Light coming from the laser diode is rst divided over two branches using abidirectional 2 2 ber 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 reected 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 ber pairs. Such couplingwas not expected, as little diffuse reection occurs at the pyramid faces. As a result,we see no change in one pair, even when the other pair is optically disconnected. Inorder for the 125 m diameter bers to be positioned close to the pyramid faces, theymust be tapered to a maximum endface diameter of 80 m. Methods developed formaking sharp near-eld scanning microscopy tips cannot be used in our applicationbecause they stretch the core and decrease its diameter as it is melted. This would in-troduce spurious backreections into our interferometer. We have used both sharpenedbers with cleaved endfaces [91] and bers chemically etched using the liquid layer

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Figure 4.2: Components of one interferometer pair. The interferometer can be divided in threedistinct sections: the laser system, the ber system and the detection system. The laser system

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

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

system consists of photodiodes and supporting electronics.

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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% hydrouoric acid) and a protective immiscible organic uid.The process is self-terminated when the tip is formed. The cone angle of the tips canbe varied from 8 to 41 depending on the protection uid [93]. To create a at end-face and to remove the part of the ber core that was reduced in diameter by the HFetch, the ber tips were rst embedded in wax and then mechanically polished using12, 3 , 1, and 0 .3 m aluminium oxide polishing paper for the nal polishing step [94].The former method results in slightly stronger interference signals (presumably dueto the better endface quality by a cleave with respect to a polished endface). The lattermethod routinely produces endface diameters on the order of 30 m, which allows formore exibility when positioning all four bers.

4.2 The berhead

Two versions of the the berhead were constructed. In the rst version, the bers

were xed with respect to each other. Once glued into place, the four bers could bepositioned together with respect to the pyramid using an x-y table formed by a sys-tem of exure hinges and micrometer screws. This design had the disadvantage thatthe positioning of the bers relied on a precise glueing step of the glass bers, sincemisalignments of a single ber could not be corrected afterwards. In addition, the me-chanical path between the bers and the Tribolever in this design was approximately35cm, which caused high thermal drift between the bers and the Tribolever. Thevariation 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 .2C.

Because of these disadvantages, we constructed a second, much smaller ber-head that allowed to individually mount and position each ber. The improved secondversion of the berhead is shown in gure 4.3. The berhead was machined by spark-erosion from a single block of low-thermal-expansion metal (Invar). The distance of the endface of each ber with respect to the pyramid face is adjusted by miniature in-ertial piezomotors ( Nanomotors R [95]), which can be driven either in discrete stepsover a maximum distance of approximately 4 mm or be adjusted continuously with

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

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Figure 4.3: Schematic drawing of the ber positioning head cut open for illustration (a) and solid model (b). (1) Tribolever, (2) Tribolever support plate, (3) Nanomotor R , (4) exure hinge

and, (5) adjustment screws.

bers to a safe distance during an exchange of sensors, the latter is used to calibrate theinterferometer signals and to position the bers at the distance of maximum sensitivity.Additionally, the continuous mode can be used to compensate possible drift betweenthe bers and the pyramid due to residual thermal expansion of the microscope (seeelectronics section). The Nanomotors are mounted in miniature exure hinge springs,which are part of the ber head. These springs allow the adjustment of each ber axisin 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 onthe Tribolever support plate, make each Tribolever click in with its kinematic mount,with a reproducibility of better than 10 m, which is a fraction of the ber endface.

4.3 Electronics

The system electronics can be split into two main components: data acquisition andsample motion (see g. 4.4). As discussed in section 4.1, the signal coming from eachinterferometer consists of a sinusoidal interference component plus an offset, which

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

Figure 4.4: Block diagram of the microscopes 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 rst amplication. The result is divided by the reference

signal. This procedure allows the maximum amplication 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).

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is due to the difference in reection amplitudes. In our detection electronics, we rstsubtract a fraction of the reference signal and amplify only the interference compo-nent. The amplied signal is then divided by the reference signal to reduce the effectof uctuations in laser diode intensity. The four resulting signals are then added andsubtracted according to equations 4.1-4 to produce the three-dimensional Triboleverdisplacement 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 thetip can be monitored in real time.

Although we have used materials with low thermal expansion coefcients forthe ber head components, the ber-pyramid distance drifts slowly due to temperaturevariations 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 keepthe ber-pyramid distance constant for several hours without additional temperaturestabilization of the microscopes chamber.

4.4 Sample movement

The sample, with maximum lateral dimensions of 10 10mm 2 , sits on a piezo scantube [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 ( ).

The scan piezo tube is directly coupled to the Z coarse approach motor. The Zmotor is located in the center of a X-Y- motor. The Z and XY motors are similarto those discussed in the literature [98]. The nested design is new, therefore it will bedescribed in more detail. The X-Y- 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 gure 4.6). Two plates areused for the X and Y motion [99], the third one (7 7 mm) is oriented tangetially forthe motion .

The sapphire disk slides on a thin polished Al 2O3 plate, which is glued on thepiezo stack (gure 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

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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- motor showing: (1) CuBeleaf springs; (2) motor house; (3) v-grooves of the kinematic mount for the berhead; (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.

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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 Al 2O3-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) -electrode (9) -shear piezo.

mixing of the two components of the glue. Non-ideal mixing of the epoxy can leadto elasticity in the stack, which degrades the motors performance or can even causefailure of the motor. Therefore, the amount of the two components of the epoxy isweighed with highest care using a micro balance with a resolution of 0 .01 mg. A thinlayer of glue is then applied on both piezo electrodes as well as on the electrodes us-ing an optical microscope at 63 magnication. A hole in the center of the electrodesprovides room for excess glue (g. 4.6). The two piezos are afterwards clamped in aspecial 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 m/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 precisecalibration. We routinely calibrate each Tribolever prior to its rst use. By excitingthe Tribolever acoustically with a loudspeaker, which is placed close to the berhead,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 tipis mounted inside the central cross. The diameters of the beads are determined using

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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 theadded 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 thencalculated from the diameter, and are ranging from 1 .57 g to 9.01 g. By measuringthe resonance frequencies as a function of the added mass, extremely accurate valuesof the Tribolevers lateral and vertical spring constants are determined [104].

Figure 4.7 is an example of one such calibration run. This calibration procedurehas no effect on the Tribolever because the sphere is held in place by gravity on thecentral 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, morecomplex, and signicantly less accurate [105].Measured lateral spring constants in this example (gure 4.7) are k X = ( 1.670.03) N/mand k Y = ( 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

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of the Tribolever using nite element analysis. The measured vertical spring constantfor the Tribolever is k Z = ( 10.3 0.1) N/m as compared to the calculated value of 25.8N/m. The large deviation is due to the additional exibility of a thin diaphragm(2mm 2mm 10.6 m), 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 allowroom for the detection bers 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 levelsof the optical detection and the electronics. With a spectrum analyzer, we measuredthe 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 theequipartition theorem 12 k x x

2rms = 12 k BT , where xrms is the root mean-square thermal

motion amplitude, k B 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 rootmean square voltage noise V rms at the resonance frequency is given by the relationV rms = xrms =

k BT / k x [106]. is a known calibration factor that relates the output

voltage to the displacement of the Tribolever. We compared the measured V rms withthe calculated value of V rms at the thermal limit. We found that the detected noise inthe 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 incontact with a surface. However, the measured noise levels provide a good indicationthat the detection is operating close to the thermal limit, which is conrmed by testmeasurements on a graphite sample (see next section).The differences in the noise levels between X and Y might be due to specic detailsof the interferometer branches (especially the quality of connectors and of the endfaceof each ber). We assume that the signal to noise ratio can be further improved bycoating the ber endfaces with a metal layer to increase the reectance of the ber/airinterface (see section 4.1).

4.5.2 Tip mounting

After the calibration is performed, a specimen has to be mounted in the center of theTribolever 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-

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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-at geometry. Itwould be also possible to create other interesting geometries, like e.g attaching a smallat or bent crystal to the Tribolever and perform experiments similar to surface forcesapparatus (SFA) experiments.In our rst tests of the microscope, we use a sharp tungsten tip. The tip is electrochem-ically etched with NaOH from a 50 m thick tungsten wire. After the tip is formed,the wire has to be shortened to a length of about 200 m using a scalpel. Then thetip 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 chosensuch that it provides sufcient adhesion force to allow the tip to be manipulated but asufciently low adhesion force such that the tip cannot be released inside the centercross of the Tribolever. For the case of tungsten tips, tungsten was found to work wellas arm material.When the tip is hanging downwards with the sharp end, the tip is lowererd from thepyramid 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 thetip is pointing up. The tip is held in place at that point again by adhesion forces, sothat it can be carefully adjusted before it is nally 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 berhead is placed

on the sample stage. Three stainless steel balls, which are connected to the matchingplate of the berhead rest in the V-grooves of the sample stage (gure 4.5, item 3).The complete microscope assembly is shown in gure 4.8. The microscope is builtup inside a small chamber [108], which damps acoustical noise. In addition, the at-mosphere inside the chamber can be controlled by owing e.g. dry nitrogen throughit. The relative humidity is monitored using a humidity/temperature meter [109] withan accuracy of 2%. If we ow dry nitrogen through the chamber, we can achieve arelative humidity below 1%. The microscope chamber is mounted on an optical table,which is resting on a vibration isolation frame [110].

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Figure 4.8: (a) Perspective drawing of the microscope assembly. (b) Side view with (1) Fiber positioning head, (2) X-Y- motor, (3) z-coarse approach motor, (4) kinematic mount betweenthe motor/sample stage and the ber positioning head.

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4.6 P E R F O R M A N C E

4.6 Performance

For a rst testing of the instrument and the complex data acquisition we used a ca-libration sample with a regular structure of known dimensions [111]. The employedsample is a glass substrate that has parallel aluminium ridges with a period of 278 1nm and a height exceeding 30nm.

Figures 4.9(a)-4.9(c) show topography and friction images that were recordedsimultaneously at a constant normal load of 0.85nN. The topography image showsparallel 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 thealuminium stripes both in X- and Y-direction plus an additional lateral force, wherethe tip ran against the stripes. A plot of a scan

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