Abstract - McGill Physicspeter/theses/schirmeisen.pdf · Abstract The metallic adhesion and...

Metallic Adhesion and Tunneling at theAtomic Scale

by

Andr�e Schirmeisen

Center for the Physics of Materials

Department of Physics� McGill University

Montr�eal� Canada

June ��

A thesis submitted to the

Faculty of Graduate Studies and Research

in partial ful�llment of the requirements for the degree of

Doctor of Philosophy

c� Andr�e Schirmeisen� ��

Abstract

The metallic adhesion and tunneling properties of an atomically de�ned junction

were measured and analyzed� The junction consisted of a tip opposing a �at surface in

the scanning probe microscopy �SPM con�guration� Measurements were performed

in ultrahigh vacuum �UHV at �� K� Sub�nN force resolution was achieved on a

sti cantilever beam employing an in�situ di erential interferometer� Tips were pre�

pared from W and Ir wire and imaged with atomic resolution in�situ using �eld ion

microscopy �FIM� Ultrasharp tips with an apex radius of �� A were fabricated

from single crystal W�� wire and engineered with FIM to terminate in only three

atoms� Calculations indicate that for those tips metallic adhesion forces dominate

over van der Waals and capacitive electrostatic forces� The sample was a thin ��

oriented Au �lm� Metallic adhesion forces and the tunneling current were measured

simultaneously for the W�Au system as a function of tip sample separation� In con�

trast to theoretical simulations the system featured exceptional mechanical stability

with adhesive forces of up to nN� In particular no indications of a sudden jump�to�

contact� which is commonly believed to be an inherent property of metallic contacts�

were found� Furthermore� the range over which the metallic adhesion forces act is

four times larger than expected� Experiments with sharp but not atomically de�ned

W tips corroborate those results� The observed long interaction range is discussed in

the framework of various models� Some of the consequences of this new property for

force microscopy applications are pointed out�

i

R�esum�e

L�adh�esion m�etallic et les propriet�es de l�e et tunnel d�une jonction charcteris�ee

a l��echelle atomique on �et�e mesur�ees et analys�ees� La jonction� con�gur�ee comme

un microscope de sonde a balayage �SPM� consiste d�une pointe oppos�ee �a une sur�

face plane� Les exp�eriences ont �et�e conduites sous la ultra�vide �UHV �a �� K�

L�utilisation d�un interfrometre di erentiel in�situ� pour mesur�e les forces sur un can�

tilevier rigide� a permis d�atteindre une r�esolution superieure au nN� Les pointes

furent pr�epar�ees �a partir de �ls de W et Ir� puis mise en image in situ �a l��echelle

atomique �a l�aide d�un microscope a champs ionique� A partir d�un crystal W��

des pointes ultrapointues ont �et�e fabriqu�ees avec un rayon au sommet de �� A�

Elles ont ensuite �et�e taill�ees �a l�aide d�un microscope �a champs ionque� ne laissant

que � atomes �a leur pointes� D�apr�es les calculs e ectu�es sur ces pointes� les forces

d�adh�esion m�etallique dominent comparativement aux forces de van der Waals et aux

forces �electrostatique� L��echantillon utilis�e etait une �ne couche Au�� Les forces

d�adh�esion m�etallique et le courant tunnel� pour le syst�eme W�Au� ont �et�e mesur�es

simultan�ement en fonction de la s�eparation entre l��echantillon et la pointe� A la

di �erence des simulations th�eoriques� le syst�eme a demontr�e une stabilit�e m�echanique

exceptionnelle pour une force d�adh�esion ne d�epassant pas nN� En particulier� au�

cune indication d�un soudain �saut�au�contact�� qui est g�en�eralement regard�e comme

une propri�et�e inherente des contacts m�etalliques� n�a �et�e observ�e� De plus� la distance

sur laquelle la force d�adh�esion m�etallique agit est quatre fois plus grande que pr�evue�

Des exp�eriences faites avec des pointes de W pointues mais non d�e�nies �a l��echelle

atomique� con�rment ces r�esultats� Une discussion de cette longue interaction est

pr�esent�ee en parrall�ele �a de nombreux mod�eles� Quelques cons�equences de cette nou�

velle propri�et�e concernant les applications en microscopie de force sont ainsi mises en

evidence�

ii

Acknowledgements

First of all I would like to thank my supervisor Peter Gr�utter for continuous

support and friendship throughout my entire work in his research group� He possesses

the unique ability to motivate� excite and guide his students in their research� which

makes it so very enjoyable to work in his group� Much advise and help was also

povided by Urs D�urig�

Graham Cross has contributed to the success of this thesis in countless ways� as a

good friend and research partner at the same time� His enthusiasm and good humor

have made our team work a memorable experience�

Thanks go to Phil LeBlanc for evaporating �lms on the cantilevers and Vincent

Tabard�Cossa for help with the scans and the translation� I am also grateful to

the rest of the research group� where everybody contributed to the pleasant working

atmosphere�

Furthermore� I want to use this opportunity to thank my friends in Montr�eal who

have made this stay such a unique experience� In particular there are Pietro �PouPou�

Pucella� Tiago �Diablo� deJesus� Florence� May� Narly� the �new� Wai and all the rest

of the gang� Many thanks go to Camille� the �ying Dutchman� Special mentions go

to Sara�n� Copacabana and the sta at QStix�

I am grateful to Danny for all the love she has given to me�

Financial support from the Hydro Qu�ebec McGill Major scholarship is gratefully

acknowledged�

I am indebted to my family for their ever present help� Only the continuous

support of my parents in many ways have made my stay in Canada and this work in

particular possible�

iii

Contents

Abstract i

R�esum�e ii

Acknowledgments iii

List of Figures vi

� Introduction �

� Experimental Set�up �

� The Probe �

�� Probe Requirements � � � � � � � � � � � � � � � � � � � � � � � � � � � �

�� Macroscopic Tip Shape� Electrochemical Etching � � � � � � � � � � � ��

�� Treatment in UHV � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

�� Annealing � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

�� Field Emission � � � � � � � � � � � � � � � � � � � � � � � � � � ��

�� Self Sputtering � � � � � � � � � � � � � � � � � � � � � � � � � � ��

�� Oxygen Etching � � � � � � � � � � � � � � � � � � � � � � � � � � ��

�� Atomic Scale Engineering� Field Ion Microscopy � � � � � � � � � � � � ��

�� Working Principle � � � � � � � � � � � � � � � � � � � � � � � � � ��

�� Image Interpretation � � � � � � � � � � � � � � � � � � � � � � � ��

�� Electric Field of Nanotips � � � � � � � � � � � � � � � � � � � � ��

�� Experimental Issues � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��

iv

�� Tip Cleanliness � � � � � � � � � � � � � � � � � � � � � � � � � � ��

�� Gold on Tungsten� FIM � � � � � � � � � � � � � � � � � � � � � ��

�� Field Emission Stability � � � � � � � � � � � � � � � � � � � � � ��

�� Background Forces � � � � � � � � � � � � � � � � � � � � � � � � ��

�� Summary � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

� The Sample ��

�� Preparation of Au Sample � � � � � � � � � � � � � � � � � � � � � � � � �

�� Surface Analysis � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

�� Cleaning Procedure � � � � � � � � � � � � � � � � � � � � � � � � �

�� Force versus Tunneling � � � � � � � � � � � � � � � � � � � � � � �

� Adhesion Experiments �

�� Theoretical Predictions � � � � � � � � � � � � � � � � � � � � � � � � � � �

�� Metallic Adhesion � � � � � � � � � � � � � � � � � � � � � � � � � �

�� Mechanical Relaxation E ects � � � � � � � � � � � � � � � � � � �

�� First Experiments � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��

�� Experimental Procedure � � � � � � � � � � � � � � � � � � � � � � � � � ��

�� Preliminary Studies� Unde�ned Tip � � � � � � � � � � � � � � � � � � � ��

� W on Au experiments � � � � � � � � � � � � � � � � � � � � � � � � � � ��

�� Part A � Structural Stability � � � � � � � � � � � � � � � � � � � ��

�� Part B � Scaling Length and Tunneling � � � � � � � � � � � � � ��

�� Summary � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��

Conclusion and Outlook ��

v

List of Figures

�� Schematic representation for the experimental set�up� The combined

FIM�AFM�STM is housed in a UHV chamber with p��mbar

and cooled at �� K� The sample stage can be quickly moved to switch

between FIM and AFM�STM mode using piezoelectric motors� � � � � �

�� Experimental set�up for electrochemical etching� The W tip is dipped

into �� KOH solution� The cathode is made of W wire as well� � � � ��

�� The drop�o method while etching W wire in KOH solution� Etching

products collect at the end of the wire giving rise to preferential etching

at the liquid air interface� necking occurs� The top graph shows the

current during the process� indicating the sudden change in current�

when the drop�o occurs� � � � � � � � � � � � � � � � � � � � � � � � � � ��

�� Etched W tip as viewed through optical microscope� Left �� and

right �� magni�cation �using polarized light to enhance contrast � ��

�� Set�up for etching iridium tips� The hole in the center of the shallow

bath� with the tip placed in it� forces the neck formation� The liquid

container is made of stainless steel and acts as the counter�electrode

at the same time� The voltage is applied in form of pulses �see text� ��

�� Etched iridium tip as viewed through optical microscope� Left ��and right �� magni�cation� � � � � � � � � � � � � � � � � � � � � � �

�� TEM micrograph of an electrochemically etched W tip� A thick amor�

phous oxide layer covers the tip apex�image courtesy of A� Zaluska� � ��

vi

�� Potential diagram governing �eld emission� With no �eld applied�

the workfunction determines the energy an electron at the Fermi edge

needs to escape from the material� The applied �eld� though� lowers

the potential� At a critical distance� the energy needed for the elec�

tron to leave the metal becomes zero and it can tunnel through the

e ective potential barrier� The image potential is a correction due to

the induced charge in the metal caused by the electron� � � � � � � � � ��

�� The Fowler�Nordheim plot as measured for a polycrystalline W tip�

The slope of �� V gives k �R � ��A � from which one can calculate

the tip radius �knowing the �eld reduction factor k� � � � � � � � � � � ��

�� FIM images of a W tip� Graph a shows a typical �� oriented W tip

imaged at �� kV� Subsequently the tip was treated with �eld emission�

extracting currents of �A for � min� Graph b shows the tip apex

right after� imaging at �� kV� indicating rearrangement of the atoms�

In c and d the original apex is recovered� � � � � � � � � � � � � � � � ��

�� Field ion microscopy images of a �� oriented W tip treated with

oxygen etching� Image a shows the tip before� and image b after the

treatment� The larger FIM magni�cation in b indicates an overall

sharpening of the apex� � � � � � � � � � � � � � � � � � � � � � � � � � � ��

�� The imaging process in �eld ion microscopy� The image gas is attracted

towards the tip� ionized and then repelled along the �eld lines� A screen

�� cm away from the tip visualizes the He atoms� � � � � � � � � � � ��

�� Potential diagram for the electron of an image gas atom close to a

metal surface at high �elds typical for FIM� Only at a critical distance

the electron can tunnel from the atomic level of the image gas into the

metal surface� into an empty level just above the Fermi energy� If the

atom is too close� the atomic level is actually below the Fermi energy�

and there is no free state for the tunneling electron� If the atom is too

far from the surface� the tunneling probability is negligibly small� � � �

vii

�� FIM image of a polycrystalline W tip indicating the di erent crystal�

lographic planes� Imaging was done with He at �� kV and �� K� � � ��

�� FIM images of a �� oriented W tip taken at room temperature

using He at �� kV� In between each image the voltage was increased

to �� kV for the �eld evaporation of single atoms� � � � � � � � � � � � ��

�� Potential diagram for the process of �eld evaporation� As described in

the text� the ionic ��eld evaporated state is at higher potential than

the atomic state� unless a strong external �eld is applied� Then� at a

certain distance xcritical� the ionic state has a lower potential energy

and �eld evaporation can occur� � � � � � � � � � � � � � � � � � � � � � ��

�� W�� tip imaged at di erent voltages� demonstrating atomic resolu�

tion FIM at � kV� where the regular image forms only at � kV� � � � � ��

�� W�� tip terminating in one single atom� FIM image taken with He

at �� kV� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��

�� FIM image �left of a �� oriented W tip and the corresponding

projection map �right� indicating the di erent crystallographic poles

�from reference �� The grey circle in the map outlines the area

imaged in the FIM graph� � � � � � � � � � � � � � � � � � � � � � � � � ��

�� FIM image of a polycrystalline W tip �left and the reduced facet

projection map �right of a �� oriented bcc crystal� The grey circle

shows the area seen in the FIM image� � � � � � � � � � � � � � � � � � �

�� FIM image of W�� tip �left and the reduced facet projection map

�right of a �� oriented bcc crystal� � � � � � � � � � � � � � � � � � � �

�� FIM image of polycrystalline Ir tip �left and the reduced facet projec�

tion map �right of a �� oriented fcc crystal� The grey circle outlines

the area image in the FIM graph� � � � � � � � � � � � � � � � � � � � � ��

viii

�� FIM image taken at �� kV of a W�� trimer tip and the two recon�

struction steps� � computer simulated FIM reconstruction �only edge

atoms are visible � the full atom by atom reconstruction from two

di erent viewing angles� Rendering done with POVRAY� � � � � � � � ��

�� High resolution TEM micrograph of a polycrystalline W tip which had

been imaged by FIM before �image courtesy A� Zaluska � � � � � � � ��

�� a FIM image of a W�� tip at �� K� b�d The same tip imaged

after it had been left in vacuum for ��h� counting �� adsorbates� Suc�

cessive �cleaning� of the tip from adatoms reveals the original trimer

structure� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��

�� FIM image of a W�� trimer tip before �left and after �right im�

age� adsorbates carefully �eld evaporated before it was left at room

temperature for a period of six weeks� proving structural stability� � � ��

�� FIM image of a W�� tip at �� K at �� kV �upper left� After

gold had been evaporated onto the tip surface� single Au atoms are

seen� which �eld evaporated at voltages of �� to �� kV� After the

cleaning the original structure is recovered �one W atom lost during

cleaning procedure� � � � � � � � � � � � � � � � � � � � � � � � � � � � ��

�� FIM image of a W�� trimer tip before �left and after �right a �eld

emission current of �� nA was drawn from the tip for �� sec� � � � � �

�� FIM image �left of a W�� tip imaged at �� kV and the correspond�

ing FEM image at �� V negative tip bias� The trimer can be seen

in the FEM� indicating almost atomic resolution in the �eld emission

mode� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��

�� Calculated van der Waals forces for a �� A radius tip �squares and a

�� A radius tip �circles in comparison to forces typically encountered

in the experiments �solid line� � � � � � � � � � � � � � � � � � � � � � � ��

ix

�� Calculated capacitive electrostatic forces for a �� A apex radius tip as

a function of tip sample separation� Curves are calculated for �� V�

�� V and �� V tip bias� � � � � � � � � � � � � � � � � � � � � � � � � � ��

�� Dimensions of cantilever beam with mounted Au sample indicating the

measured spring constants in N�m at various points on the sample� � �

�� STM scans �� A �� nA at �� mV bias of a Au sample at

di erent preparation stages� a Au sample� which was atomically �at

before� exposed to air for several days� Surface contaminations of an

average corrugation height of �� A have built up� b Sample was

sputtered with � keV Ne ions for min� yielding surface with circular

bumps of �� A diameter� c The same surface as in a sputtered and

annealed for � min� showing atomically �at terraces stretching over a

length of �� A� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

�� STM scan �� A �� nA at �� mV of a Au�� surface�

The herringbone reconstruction with a height corrugation of �� A is

resolved� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

�� Schematic of STM constant current operation on a �exible sample� For

a clean metal�metal contact the adhesion forces keep the cantilever in

a constant position �left image� If the tip scans over a non�metallic

contamination layer� much reduced adhesive forces will cause the can�

tilever to move away from the tip� Since the contamination does not

substantially a ect the tunneling current� the feedback� in trying to

maintain the same tunneling current� is extending the piezo to account

for the cantilever movement� � � � � � � � � � � � � � � � � � � � � � � � �

�� Contributions to the total metallic interaction energy from di erent

physical mechanisms� The exchange�correlation energy clearly domi�

nates the adhesion energy� whereas the kinetic energy of the electron

gas gives rise to the repulsive part �from reference ��

x

�� Scaled binding energy versus scaled distance of separation for four

di erent types of binding mechanisms� The curves for molecular� in�

terfacial� chemisorption and bulk interaction are well described by the

Rydberg function �from reference ��

�� Scheme of the approach�retraction cycle� showing the voltage applied

to the piezo tube �z�piezo� the logarithm of tunneling current and the

feedback signal �indicating on or o � i�e� feedback is active�not active� ��

�� Scan of �� A before a and after b one set of �� approach�

retraction cycles� which exhibited hysteretic behaviour� The inset in

b shows a zoom and a linescan of the hill structure with a peak height

of � �A�� atomic steps of Au��

� Approach�retraction cycles of W�� tip �not used in FIM� hence

unde�ned on a Au�� surface� The �rst � cycles of this set are

very reproducible and show no hysteresis or jump�to�contact� Part a

shows three representative curves� In graph b the Rydberg function

was scaled to one of the force�distance curves� with a distance scaling

parameter of � � �� A� � � � � � � � � � � � � � � � � � � � � � � ��

�� c The ��th approach�retraction cycle of the same set as in �gure �

shows a sudden change in behaviour� Graph d shows some curves

indicating the unstable behaviour during �� cycles after this change� � ��

�� MD simulation of a clean Ni tip approaching a Au surface from refer�

ence �� Parts a and b show approach�retraction cycles with di erent

approach depths� The horizontal axis is the tip sample separation of

the undisturbed system �here large tip sample separations are to the

right� opposite to �gure �� zero describes the point of mechanical

contact� Note that substantial hysteresis is seen even upon only light

contact in a indicating structural change of the tip and�or sample� � �

xi

�� Two approach�retraction cycles �averages of �� consecutive runs with

a W�� tip as described in the text� Horizontal axis is the z�piezo

expansion �where zero marks the �� M� tunneling point� the vertical

axis is in arbitrary units� The solid line indicates a Rydberg �t with

� � �� A� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��

�� Force versus tip extension of a Au�Au contact� A big hysteresis indi�

cates permanent changes of the junction� � � � � � � � � � � � � � � � � ��

�� FIM image and computer reconstruction of the eight last tip layers of

the W�� tip before a and after b the approach sets� There are

virtually no changes in the tip structure� in particular the trimer was

mechanically stable� Two foreign adsorbates �bigger spheres in b are

compliant with the restgas contamination� � � � � � � � � � � � � � � � ��

�� Three sets of approach�retraction cycles of a W�� trimer tip on a

Au�� surface� The approach depth was increased from graph a to

c� Zero tip�sample separation is at the �� M� tunneling point� The

solid line represents a scaled and di erentiated Rydberg energy curve�

scaling length �� A� � � � � � � � � � � � � � � � � � � � � � � � � � � � ��

�� Simultaneously acquired force and tunneling data versus tip�sample

separation� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��

�� Scaled adhesion energy versus the scaled distance �stars and the Ry�

dberg function �solid line� The adhesion energy curve was generated

by integrating the force curve from �gure �� over the tip�sample sep�

aration� Scaling parameters were Eadhesion � �� eV and � � �� A� ��

�� Simulation by Jouko Nieminen� An Ir tip approaches a Au�� sur�

face� The force versus distance graph shows hysteretic behaviour be�

tween approach and retraction� � � � � � � � � � � � � � � � � � � � � � ��

�� Sketch of a charged tip facing a sample at distance d� The �eld lines

emerge from the imaginary charge Q within the tip at position A� � � ��

xii

�� Correlation between force and tunneling current using Chen�s model�

The graph shows the square of the force versus the current� where

approximately a linear relationship can be observed for currents above

��nA� The slope of the curve of �f�

�It� �� nN��nA translates to a

convoluted LDOS of tip and sample of �con � �� states�eV�atom� � � ��

�� Visualization of the di erent contributions to tunneling current and

adhesion force of a typical nanotip� The inner cylinder shows the tun�

neling atoms and the outer cylinder indicates the atoms which con�

tribute �� of the total force� � � � � � � � � � � � � � � � � � � � � � � ��

�� Approximations for the DOS of W and Au� The area of the box has

to equal the area underneath the DOS curve for electron conservation� ��

xiii

xiv

Chapter �

Introduction

The study of metallic adhesion on the atomic scale lays the foundation for under�

standing the physics of nanometer sized structures� In particular� issues surrounding

nanoscale tribology �nd widespread interest in newly developing �elds such as nan�

otechnology� As we are trying to control materials on the nanometer level and exploit

their atomic dimension properties we are led to answer the following fundamental

question� How do two surfaces interact if they are brought together within the range

of atomic dimensions Naturally� in designing an experiment that allows us to inter�

rogate this issue� we have to employ a technology that allows us to de�ne a contact

with atomic precision� Ever since the invention of the scanning tunneling microscope

�STM �� and the atomic force microscope �AFM �� the �eld of scanning probe

microscopies �SPM has provided an arena to investigate electronic and mechanical

properties of nanometer sized junctions�

Of particular interest are the adhesion forces between two metal surfaces ��

It was recognized that they play a crucial role in understanding imaging mechanisms

in STM �� and AFM �� Moreover� tip�sample forces are critically

important for atomic �� and molecular�scale manipulation �� The in�uence of

the geometric and chemical nature of the metallic probe itself had received special

attention �� However� earlier adhesion studies �� were handicapped

by the inability to analyze the geometric structure and chemical nature of the tip�

This limitation was �nally addressed in this thesis using in situ �eld ion microscopy

�

� CHAPTER �� INTRODUCTION

�FIM �see also references �� Full control over the atomic shape and

chemical nature of the tip was achieved opening up a whole new �eld of questions ��

that can now be answered experimentally� In this thesis special attention is given to

the issue of structural stability of atomic sized junctions� Secondly I will focus on the

range of tip�sample separations over which the metallic adhesion forces interact�

The �rst chapter describes the experimental set�up that provided the necessary

environment to investigate atomic sized contacts� The fabrication and analysis of

a suitable tip is the focus of the following chapter� where tip preparation from the

macroscopic down to the atomic level is described in detail� Single atom control over

those tips is demonstrated� The sample is given special attention in the third chapter�

focusing on the preparation techniques and analysis of atomically �at Au surfaces�

Lastly� several experiments measuring the force interaction of a tungsten tip with

a gold surface are presented� Measurements of tips terminating in only three apex

atoms are contrasted to experiments with tips of less de�ned shape� Furthermore�

I will present simultaneous measurements of force and tunneling current� These

results are discussed on the basis of existing theoretical models and calculations� New

concepts governing the understanding of adhesion force interactions are introduced�

Throughout this thesis the common unit �Angstrom is used� where � �A� �� m

� �� nm�

Chapter �

Experimental Set�up

The experimental set�up was designed and constructed by U� D�urig and A� Stalder

and �nally comissioned by G� Cross and myself� Detailed descriptions of this set�up

can be found in references �� and �� In this chapter I will give a brief review of

the design� since it has important implications for the experiment itself and the later

analysis�

Our goal is to investigate metallic adhesion and tunneling properties of an atom�

ically de�ned metallic contact� Not explicitly stated yet crucially important is the

control parameter� The force and conductivity properties shall be measured as a func�

tion of distance of separation between two surfaces� An atomically de�ned junction

implies that we need to achieve distance control of subatomic precision� The well es�

tablished �eld of scanning probe microscopies �SPM has produced reliable methods

of precision distance control of the tip�sample con�guration� The probe typically is

a tip shaped material which is facing a �at sample� The interaction between tip and

sample can now be used to gain information about the distance of separation of the

two� This information is fed back to a distance control unit� a piezoelectric actuator�

The interaction mechanism used for the feedback control can be manifold� In the

�rst SPM set�up the tunneling current between a biased tip and sample was used�

the scanning tunneling microscope �STM was born �� Not much later researchers

found a way to measure interaction forces with nN precision� The tip was at the

end of a compliant beam� the bending of this beam due to tip�sample forces could

�

� CHAPTER �� EXPERIMENTAL SET�UP

be measured by de�ecting a laser beam from this cantilever� leading to atomic force

microscopy �AFM �� Forces can be of any origin and so a vast �eld of specialized

force microscopies has developed�

A mandatory prerequisite for investigating an atomically de�ned junction is to

perform the experiment in an atomically clean environment� The whole exper�

iment therefore must take place under ultrahigh vacuum conditions �better than

�� mbar�

There are three key considerations for the experimental design� which are treated

consecutively in the following three chapters� The control over the probe� the de�ni�

tion of the sample� and the force measurement between the two�

� Atomic resolution images of tip shaped structures are a well�established proce�

dure since the invention of the �eld ion microscope �FIM �� Kuk and Sil�

verman �� were the �rst to combine a FIM with an STM and investigated the

in�uence of the atomic structure of the tip on the tunneling current� Fink ��

proposed the use of single atom tips for STM investigations� In order to include

a FIM in the experimental set�up� it must be possible to bias the tip at high

positive voltages of several kV� and an imaging device �multichannel plate and

screen has to be placed to �� cm across the tip� In order to achieve good

image contrast and maintain mechanical stability of the tip atoms the tip is

cooled to liquid nitrogen temperature�

� The sample should be atomically �at and clean� For geometric analysis purposes

of the sample an STM is used� This allows one to �nd atomically �at terraces

as the proper site for the tip�sample interaction measurements�

� The interaction force is measured using an AFM� Conventionally the tip is

mounted on a cantilever beam which bends in proportion to the force acting

on the tip� The resulting de�ection is measured typically using a laser beam�

However� using FIM for our tips requires a rather stable tip support and tip

preparation procedures �e�g� high temperature annealing also make it di!cult

to integrate a FIM tip with a cantilever� Therefore the conventional set�up

is altered and instead of the tip the sample is mounted on a cantilever� Im�

portant is also the sti ness of the beam� If the positive force gradient �force

becomes more adhesive with decreasing tip sample separation of the tip sample

interaction is larger than the spring constant of the beam the system becomes

unstable and tip and sample jump to contact� In order to avoid this the beam

compliance must be of the order of �� N�m �typical spring constants in AFM

are well below �� N�m� This means that the cantilever de�ections are rather

small� Forces are of the order of nN yielding beam de�ections of �� A� This

poses a special challenge to design a beam de�ection detection system with

sub��A resolution�

The tip is analyzed with FIM just before the experiment� However� contamination

of the tip apex are imminent even in an UHV environment� Therefore the exchange

between FIM and AFM�STM mode must be quick� This demands that the whole

system is an integrated FIM�AFM�STM� Figure �� shows a schematic drawing of

such a system� which to date is unique in the world�

The focus of the experimental set�up is the tip sample junction in the center of

�gure �� The sample is mounted on a glass cantilever� the de�ection of which is

measured using an in�situ di erential interferometer �� with sub��A resolution� The

metallic tip holder is attached with magnets to a piezo tube acting as the distance

control unit typically used in SPM set�ups� For STM operation a small bias between

tip and sample can be applied and the tunneling current is measured� The current

is converted into a voltage initially using an Keithley I�V converter with a gain of

�� nA � �� V� The input current limit is �� nA� In order to measure the

total occurring current range an I�V converter was built which ampli�es the current

linearly up to � nA� From � nA to �� mA the voltage output is the logarithm of the

current� covering � orders of magnitude�

The sample stage can be removed quickly by means of piezo motors� The tip is

then facing a multichannel plate and a phosphorus screen � cm away� The tip can be

� CHAPTER �� EXPERIMENTAL SET�UP

Figure �� Schematic representation for the experimental set�up� The combinedFIM�AFM�STM is housed in a UHV chamber with p��mbar and cooled at�� K� The sample stage can be quickly moved to switch between FIM and AFM�STMmode using piezoelectric motors�

�

biased with a positive voltage of up to �� kV and the FIM image is formed on the

screen� The imaging gas is ultrapure helium� which is supplied via a heatable glass

leak valve�

The whole system is cooled to �� K using liquid nitrogen� Special care must be

taken that the liquid nitrogen container �boiling noise and the UHV chamber �pump

vibrations is mechanically decoupled from the SPM sample stage with su!cient

thermal contact� This is achieved by hanging the sample stage from a double bellow

construction with a thermal exchange gas as described in reference ��

The whole system is housed in a UHV chamber with a base pressure of better

than �� mbar� An adjacent UHV chamber serves as the preparation stage for

tip and sample� It is used for the annealing and �eld emission treatment of the tip�

The sample can be sputtered and annealed� A third chamber serves as an air�lock�

for a quick exchange of tips and samples from air to UHV�

Another challenge is the decoupling of the UHV chamber from building vibrations�

A commercially available optical table with air dampening at a resonance frequency

of �� Hz proved insu!cient� Alternatively the whole UHV assembly was supported

from four custom made bungee cords �� with an extension under load of �� The

resonance frequency of the bungee�UHV chamber assembly is below � Hz providing

excellent vibration isolation�

No alternative set�up with comparable features has been reported up to date�

However� an intriguing and closely related experiment was conducted by real�time

observation with atomic resolution of a nanometer sized metallic contact in a trans�

mission electron microscope �TEM �� In the TEM studies the dynamic behaviour

of the atoms in the contact can be observed� However� the force properties can not be

measured� Hence those studies pose an almost ideal complement to our experiments�

Chapter �

The Probe

Ironically� in the vast majority of scanning probe applications� the name giving probe

itself is the biggest unknown factor in the measurements� This is a consequence of the

di!culty of determining the probe�s geometric shape and chemical composition in�situ

during those experiments� Yet the in�uence of the probe�s properties on the imaging

mechanisms has been pointed out in numerous publications �� Some

of the few researchers addressing this issue �� used an in�situ �eld ion microscope

�FIM and a scanning tunneling microscope �STM� They found that the atomic

corrugation height during STM operation of a W tip on a Au surface depends on the

precise atomic structure of the probe� Using an in�situ FIM allows atomic resolution

imaging and manipulation of the tip� just before and shortly after the interaction of

probe and sample� The method of FIM allows even to reach the ultimate limit of

making tips terminating in a single atom �� and therefore it is feasible to measure

the interaction of a controlled single atom with a surface�

The cost for using a powerful method like FIM is that extensive e orts have

to be made to prepare suitable tips� In this chapter I will explain in detail how

to make those tips� starting with the macroscopic etching method� continuing with

the treatments in ultrahigh vacuum and the mesoscopic analysis and closing with

the microscopic imaging and manipulation techniques using FIM� Finally� crucial

experimental aspects of using those tips in the intended metallic adhesion studies are

addressed�

�

�� PROBE REQUIREMENTS �

�� Probe Requirements

There are several important requirements the probe has to satisfy for use in FIM

and the subsequent metallic adhesion measurements� One aspect is the chemical

reactivity of the material� High reactivity means it is easy to shape the tip shank by

electrochemical etching but on the other hand also is more likely to contaminate due

to reactions with restgas atoms in the UHV chamber� If the material is very inert�

it can become very di!cult to etch it even when using very aggressive chemicals�

although surface contaminations later are less of a problem� We found it is more

preferable to use a material which is easy to etch and rather assure that excellent

ultrahigh vacuum conditions prevail �base pressure of p � �� mbar�

Secondly� the material has to be very sti in order to withstand the tensile stresses

due to the imaging voltages occurring during FIM� These stresses can reach values of

up to � GPa �� and therefore are comparable to the macroscopic fracture stresses

of polycrystalline metals� Fortunately� due to the very small size of the tip apexes�

there are fewer dislocations present than in macroscopic materials and fracture will

not occur� Nevertheless� it was often observed that polycrystalline materials are less

stable under FIM conditions than their single crystalline counterparts�

Not only can the material fracture under FIM conditions� but also can the tip

atoms evaporate from the crystal due to the high �elds ��eld evaporation typically

at �� GV�m�� V��A� see FIM section later� Although this e ect is desirable

for atomic engineering of the tip� the �eld needed to image the material should be

lower than the evaporation �eld� This excludes soft metals like gold or nickel ��eld

evaporation begins at �� V��A from being imaged with Helium as the image gas

�ionization �eld of �� V��A � It is possible to use an image gas that is easier to ionize

�e�g� neon� with compromises in the ultimate resolution of the FIM�

Lastly� the tips have to be extremely sharp� so that the force signal from the

metallic adhesion is not buried in a background of long�ranged Van der Waals inter�

�Compare also extreme conditions for tips encountered in SPM in general� e�g� forces�� nN�nm�� GPa� electric �elds� � V�nm�� GV�m and current densities� � nA�nm�� GA�m�

�� CHAPTER �� THE PROBE

actions and ultimately single atom sensitivity can be achieved� As will be shown in

the last section of this chapter� this means that the tip apex radii have to be much

smaller than what is typically used in FIM applications� This is the most stringent

condition for the preparation techniques� and the physical properties of those true

nanotips will prove to be unique in several aspects�

The most commonly used material in FIM is tungsten� It can satisfy all of

the above conditions and is readily available in single crystalline form due to its

widespread use� We have also been able to make suitable tips from iridium wire�

as will be demonstrated in the following sections� The use of softer metals like gold

and nickel would also be very desirable from the perspective of metallic adhesion

measurements �see experimental section�

�� Macroscopic Tip Shape� Electrochemical Etch�

ing

In order to produce a tip shaped structure it is most convenient to use a wire of the

desired tip material �diameter �� mm or smaller and to electrochemically etch the

metal until a �ne tip shank is made �a review of etching parameters of commonly

used materials is found in reference �� A typical set�up for the etching process is

depicted in �gure �� A wire of the tip material is dipped into the etching solution�

which contains a counter electrode� A voltage bias �ac or dc� depends on the material�

refer to �� is supplied between the wire and the electrode� the etching reaction takes

place and removes material from the tip shank�

In the particular case of W� the desired tip shape formation is readily achieved

by the etching process itself� The etching solution is �� KOH �NaOH can also be

used� in practice however KOH produced more reliable results and a bias of �� VDC

is applied �tip on positive bias� The reaction governing the material removal is�

W �s " �OH� �� WO�� anode "H��gas� cathode ��

�� MACROSCOPIC TIP SHAPE� ELECTROCHEMICAL ETCHING ��

Figure �� Experimental set�up for electrochemical etching� The W tip is dippedinto �� KOH solution� The cathode is made of W wire as well�

The WO� is dissolved in the solution� producing a very viscous �uid that builds

up around the lower part of the tip shank� This layer inhibits the further etching

around the end of the wire� the etching rate around the air�liquid interface starts to

dominate and the phenomenon of necking is observed �see �gure �� Upon further

etching the neck becomes very thin and eventually the lower part of the wire breaks

o � resulting in a very sharp tip geometry�

Now the etching reaction has to be stopped very quickly in order to prevent

the sharp tip from being etched any further and therefore reducing the overall tip

sharpness �overetching� To this e ect� an electronic device monitors the current

during the etching process� Initially the current will drop roughly linear with time�

re�ecting the reduction in interface area of the wire with the solution� At the breaking

point� the current will drop quickly by a larger amount which is detected electronically

and the device instantly switches o the applied voltage�

For a W wire �� mm in diameter� the current starts at around �� mA� reduces

to �� mA just before the breaking point and drops by an amount of � mA when the

lower part breaks o � The whole etching process takes a few minutes�

The apex diameter of the so�formed tip is determined by the smallest wire diam�

eter just before the breaking� To avoid premature breaking due to the weight of the

supported lower wire part �tensile stresses reach several �� MPa for a �� nm wire

diameter the length of wire dipped into the solution should be as small as possible�


Figure �� The drop�o method while etching W wire in KOH solution� Etchingproducts collect at the end of the wire giving rise to preferential etching at the liquidair interface� necking occurs� The top graph shows the current during the process�indicating the sudden change in current� when the drop�o occurs�

�� MACROSCOPIC TIP SHAPE� ELECTROCHEMICAL ETCHING ��

Figure �� Etched W tip as viewed through optical microscope� Left �� and right�� magni�cation �using polarized light to enhance contrast

If the wire is not dipped in far enough� however� the necking phenomenon will not

occur� The ideal length was determined to be �� mm� measured from the highest

point of the liquid�air interface to the end of submerged wire� After the etching the

wire is rinsed with water and propanol� to remove etchant residues� If inspection in

a �� magni�cation optical microscope �see �gure �� shows a smooth tip surface

ending in a very sharp point reaching the di raction limit� in � out of �� cases the

tip apex has a radius of � to � nm�

Contingent for this success rate is that the wire and the solution are very clean �a

pre�etching step� where the whole W wire is etched for some seconds and subsequently

rinsed with water to remove any dirt particles� highly improves the reliability of the

process and that the etching process is observed �using a �� microscope for any

irregularities�

Much more di!cult is the etching of iridium wire� owing to its poor chemical

reactivity� In the literature �� the use of very toxic etchants �molten salt solutions or

KCN� which is lethal if the developing HCN is accidentally inhaled# is suggested� We

were able to establish a technique employing only weak chemicals but still rendering


Figure �� Set�up for etching iridium tips� The hole in the center of the shallow bath�with the tip placed in it� forces the neck formation� The liquid container is madeof stainless steel and acts as the counter�electrode at the same time� The voltage isapplied in form of pulses �see text�

excellent results� Figure �� shows the slightly altered set�up� The etching solution

was �� HCL in H�O� For iridium the automatic dropping o process does not work�

because the reaction products do not form an inert protective layer� Instead the wire

was immersed in a shallow bath of etchant liquid� which had a small hole in the

center� Due to surface tension the liquid would not drip through the small hole� but

the lower end of the wire can stick out below the bath and act as the dropping o

part� The voltage was applied in a series of pulses� each pulse only lasting �� s with

an amplitude of � V �positive bias on tip� at a pulse frequency of � kHz� During the

time between the pulses� we applied a negative bias of �� V� which helps to remove

etching byproducts�

The total etching time for a �� mm diameter wire is of the order of some min�

utes� until the drop�o is observed� The success rate of this method is very low� but

as it turns out� tips can actually be re�sharpened by simply dipping the tip apex

into the solution and applying the pulses again� The mechanism is not fully under�

stood� Figure �� shows the image of an etched iridium tip under a �� and ��magni�cation optical microscope�

�� TREATMENT IN UHV �

Figure �� Etched iridium tip as viewed through optical microscope� Left �� andright �� magni�cation�

�� Treatment in UHV

�� Annealing

After the electrochemical etching process the tip is put into the UHV environment for

further treatment� The �rst step is to anneal the tip� The tips are typically bonded

to a W wire� through which a current of the order of � to A is passed in order to

reach temperatures of about �� K �orange glow�

For W this has two e ects� First the annealing process helps healing out dislo�

cations at the tip apex� which have been induced by the rather violent breaking o

process during etching� It also smoothes the overall surface structure� Secondly� it

removes residues from the etching process� in particular W oxides� Figure �� shows

a TEM micrograph of a typical W tip before the annealing process� revealing a thick

�� nm amorphous oxide layer at the apex of the tip� WO� readily starts to sub�

limate at �� K �� whereas the melting temperature of the W itself is �� K�

However� surface di usion of the W atoms might already set in at lower temperatures

and blunt the tip� We found that our nanotips with apex radii of � nm are struc�

turally stable for several minutes at the above annealing temperatures� The removal


Figure �� TEM micrograph of an electrochemically etched W tip� A thick amor�phous oxide layer covers the tip apex�image courtesy of A� Zaluska�

of the oxides is not always complete� The process of FIM� though� allows to remove

the last layers of contaminations in a very controlled fashion�

For Ir tips� the pulse etching method prevents the build up of a big amount of

contaminations already� Here the annealing process serves more the e ect of healing

out dislocations and smoothing of the overall apex shape� It has also been possible

to make good FIM images of iridium tips� without the annealing step�

�� Field Emission

If the tip is negatively biased at high enough voltages� the probability that electrons

tunnel from the metal into free space becomes appreciable and �eld emission occurs�

The potential barrier the electrons have to tunnel through is determined by the work

function of the material� As schematically drawn in �gure �� the potential due to

the �eld produced at the material�vacuum interface determines the e ective width

of the barrier �the image potential� caused by the electron�s in�uence on the metal

surface� somewhat softens the barrier shape�

In the case that the apex radius of the tip is much smaller than the distance

�� TREATMENT IN UHV ��

Figure �� Potential diagram governing �eld emission� With no �eld applied� theworkfunction determines the energy an electron at the Fermi edge needs to escapefrom the material� The applied �eld� though� lowers the potential� At a criticaldistance� the energy needed for the electron to leave the metal becomes zero and itcan tunnel through the e ective potential barrier� The image potential is a correctiondue to the induced charge in the metal caused by the electron�


tip ��cathode to anode the �eld E depends on the applied voltage V and the tip

geometry as follows �apex radius R�

E �V

kR��

The �eld reduction factor k equals unity assuming that the tip is a sphere of

radius R opposing an in�nite plane� Since the sphere is connected to the tip shank�

and therefore the �eld lines are not only concentrated on the sphere itself� the �eld is

reduced by a factor k� This factor is � to for typical FIM tips with an apex radius

of the order of �� A� For our ultra�sharp tips� however� k depends strongly on the

exact geometry and can reach values of up to �� to �� This will be discussed in

detail in the following FIM section�

The relationship between the �eld emission current I� the applied �eld E �in V��A

and the material workfunction $ �in eV was derived by Fowler and Nordheim ��

I � �E� � exp �� $��

E ��

Using equation �� to calculate the �eld� and taking the natural logarithm on

both sides we �nd�

lnI

V �� ln

�

�kR�� $

��kR

V��

The slope of plot ln IV � versus ��V therefore allows us to extract the tip radius�

Figure �� shows such a graph for a polycrystalline W tip� Unfortunately� this method

does not work to extract reliable tip radii for our nanotips� since here the k factor

depends strongly on the radius itself� In practice� however� it was found that if �eld

emission currents of �� nA can be extracted from the tip at a bias of about �� V

�with the anode at a distance of about cm� the tip usually features an apex radius

of � nm or less� We therefore have a useful method to determine if a tip is suitable

for FIM� without actually using the FIM�


Figure �� The Fowler�Nordheim plot as measured for a polycrystalline W tip� Theslope of �� V gives k � R � ��A � from which one can calculate the tip radius�knowing the �eld reduction factor k�


It was reported before that �eld emission currents change with time� even though

the voltage is kept constant �� In particular it was found that the emission current

at low values of �� nA decrease with time and eventually reach equilibrium� We found

that the reverse e ect for high �eld emission currents is true� which is not mentioned

in the literature before� After annealing in UHV very often the �eld emission current

is initially lower than desired �� nA only at �� V� We then apply a bias to extract

currents of �A and� while carefully monitoring the current never to exceed this

critical limit� slowly decrease the bias� This treatment repeatedly resulted in a lower

voltage needed to emit �� nA�

Since a contaminant layer presents an additional barrier for the �eld emitted

electrons �and therefore currents are expected to be lower �� we could be observing

a cleaning e ect� Possibly �eld evaporation of oxides is taking place� which is a well�

established e ect during the initial FIM stages of new tips �at the opposite bias

however� It is also known that �eld emission currents of some nA can already

resistively heat the tip apex to several hundred degrees �� By drawing a current

of �A at about � kV from the tip the apex could be heated to temperatures where

tungsten oxide becomes volatile�

A combined study of �eld ion microscopy and high current �eld emission address�

ing this e ect is shown in �gure �� as a small prelude to the FIM section� The atomic

structure of the tip apex is shown in a and then a high current �eld emission �I��A

for � min treatment was applied� In b the image of the tip apex after the �eld emis�

sion shows severe changes� We �nd a random arrangement of atoms as opposed to

the well de�ned structure before� This image was taken at lower �elds� indicating

an overall sharpening of the tip of about �� Images c and d show the subse�

quent recovering steps of the original tip apex �using �eld evaporation� explained in

the FIM section� Hence� the mechanism underlying the sharpening e ect could be

linked to �eld induced surface di usion �possibly activated by heating� where the W

atoms move towards the tip apex and build up a small asperity leading to an overall

increase in sharpness� However� this e ect is too small to explain some of the big


Figure �� FIM images of a W tip� Graph a shows a typical �� oriented W tipimaged at �� kV� Subsequently the tip was treated with �eld emission� extractingcurrents of �A for � min� Graph b shows the tip apex right after� imaging at �� kV�indicating rearrangement of the atoms� In c and d the original apex is recovered�

changes observed during high current �eld emission treatment�

For the sake of completeness� I will also describe two methods commonly encoun�

tered for tip preparation� which we only occasionally used� due to low reproducibility�

�� Self Sputtering

If the tip is �eld emitting electrons� these electrons can ionize gas atoms� which in

return will be accelerated towards the tip and sputter its surface� This sputtering

process has been shown to result in an overall sharpening of the tip �already found

by M�uller in �� owing to the shape of the �eld lines� The impact of the ions�


Figure �� Field ion microscopy images of a �� oriented W tip treated withoxygen etching� Image a shows the tip before� and image b after the treatment�The larger FIM magni�cation in b indicates an overall sharpening of the apex�

however� can induce defects and this rather crude process has not yielded any good

results for nanometer sized tip apexes� In fact one has to consider that if the UHV

pressure is not low enough� restgas atoms could be ionized and destroy the delicate

apex structure of the nanotips�

�� Oxygen Etching

If the tip is heated to �� K� the reaction ofW"Ox � WOx takes place at high rates�

At the same time the products of this reaction sublimate at those temperatures and

material is therefore removed �� Since the reaction has di erent etching rates for

di erent crystallographic planes� an overall sharpening takes place for �� oriented

W tips �this method has also been employed to sharpen polycrystalline W tips ��

Typically this is done at oxygen pressures of � �� mbar� We have successfully

employed this technique once for tip re�sharpening �see �gure �� However� it

could never be reproduced� probably because the temperature� as a rather critical

parameter� has to be better controlled�

�� ATOMIC SCALE ENGINEERING� FIELD ION MICROSCOPY ��

�� Atomic Scale Engineering� Field IonMicroscopy

In this section I will explain the working principle of a �eld ion microscope and

especially focus on the peculiarities of our nanotips� Image interpretation� which is

crucial to the overall analysis of our atomic scale adhesion and contact experiments�

will be covered in the last section�

�� Working Principle

The �eld ion microscope was invented by E�W� M�uller �� in �� and was the �rst

microscope capable of imaging atoms� Initially he used a �eld emission microscope�

realizing though that its inherent lateral resolution is �� A� owing to the lateral

movement of the electrons �� Instead of using electrons� he decided to use atoms as

the imaging medium� These atoms are �eld adsorbed on the tip surface� where they

get ionized and are subsequently repelled towards a phosphorus screen� Since the

lateral motion of atoms can be e ectively reduced by cooling the tip surface� lateral

resolution can be better than � �A�

A schematic ��gure �� visualizes the di erent processes� The tip is in a vacuum

chamber� usually cooled down to liquid nitrogen temperatures� An image gas� most

commonly helium or neon� is introduced in the chamber at partial pressures of � �� mbar� while the tip is biased at a high positive voltage of several kV� The

positively charged tip surface now polarizes the image gas atoms� they are attracted

and eventually physisorbed� In order to be physisorbed� they have to lose their

kinetic energy� which is the sum of the polarization energy and thermal energy� They

thermalize by a random hopping motion� which can take anywhere from � to almost

�� hops� In reality� though� most of the image gas atoms do not come directly from

the surrounding space of the tip apex� It was found that there is a dominant �ux

of already physisorbed image gas atoms from the tip shank towards the apex� and

�In fact� due to the peculiar geometry of our nanotips� this limit can be overcome and �eldemission images with atomic resolution will be shown later� However� this is a special case and haslimited applicability�


Figure �� The imaging process in �eld ion microscopy� The image gas is attractedtowards the tip� ionized and then repelled along the �eld lines� A screen �� cmaway from the tip visualizes the He atoms�

therefore the atoms are already very well thermalized� This� however� puts more

stringent requirements on the cleanliness of the whole tip shank�

Once the image gas atoms are physisorbed� an electron can tunnel to the positively

charged tip and the He is ionized� This is the critical process from which the image

contrast originates� As it turns out� there is a very exact distance of gas atom to tip

surface at which ionization will occur� Figure �� shows a potential diagram of the

electron of the image gas atom close to the surface with a strong �eld� If the atom

is far away� the e ective barrier through which the electron has to tunnel is too wide

and the tunneling probability is close to zero� On the other hand� if the gas atom is

very close to the surface� the atomic energy level of the electron �� eV for He is

below the Fermi energy �usually around eV of the tip material� All the states in

�� ATOMIC SCALE ENGINEERING� FIELD ION MICROSCOPY �

Figure �� Potential diagram for the electron of an image gas atom close to a metalsurface at high �elds typical for FIM� Only at a critical distance the electron cantunnel from the atomic level of the image gas into the metal surface� into an emptylevel just above the Fermi energy� If the atom is too close� the atomic level is actuallybelow the Fermi energy� and there is no free state for the tunneling electron� If theatom is too far from the surface� the tunneling probability is negligibly small�

the tip at that energy level are full� the electron can not tunnel into the tip states�

As soon as the gas atom is ionized it is strongly repelled from the tip along

the direction of the �eld lines� which point towards the phosphorus screen opposite

from the tip� Hence an image of the ionization probability is formed� The lateral

magni�cation then is determined by the opening angle of the �eld lines emerging

from the tip�

� �Z

R��

where Z is the distance from tip to screen �Z�� cm in our set�up� R the tip radius


Figure �� FIM image of a polycrystalline W tip indicating the di erent crystallo�graphic planes� Imaging was done with He at �� kV and �� K�

and is a correction factor �typical values �� to �� which takes into account that

the image gas ions do not exactly follow the �eld lines� Typically there are ��

�� image gas atoms per second originating from each atomic site� amounting to

a total ion current of �� pA for a �� atom tip apex�

A quantitative analysis shows that ionization can only occur at a distance of � �A�

within a very narrow spatial zone of �� A at the best imaging conditions �� This is

called the ionization disk� If one now imagines an ionization layer at a �xed distance

around the tip apex� atoms at step edges will reach farther into this critical zone than

atoms on planes �see �gure �� the dashed line� This is why one sees primarily the

edge atoms of planes in FIM images� and not the atoms in the planes themselves�

A typical FIM micrograph of a polycrystalline W tip� imaged at �� kV with a He

pressure of �� mbar and at a tip temperature of �� K is shown in �gure ��

The image shows atoms arranged in circular structures� representing the edges of

di erent index planes� How the indices are assigned to the rings is discussed in a

later section�

In general there is a voltage at which one observes the best contrast in the FIM

images� the so�called best imaging voltage �BIV� Accordingly there must be a best

�The bright line in the lower left corner of the image is an artifact due to a crack in the multi�channel plate� It might be viewed as a �ngerprint of the originality of our FIM images��


imaging �eld �BIF at the tip surface� which will depend on the image gas properties�

Experimentally it was found that these values are �� V��A for He and �� V��A for

Ne to within a precision of �� We can therefore determine the �eld at the

tip surface from the FIM observation� The link between the voltage and the �eld is

then provided by equation �� From the �eld and the voltage one can calculate the

tip radius� assuming the �eld reduction factor k is known� In fact� for the W tip in

�gure �� the values for the product k � R as determined from the �eld emission

characteristics �slope of the Fowler�Nordheim plot in �gure �� and alternatively

using the best imaging �eld method are in very good agreement �k �R � �� A and

�� A respectively� although these measurements originate from entirely di erent

physical processes�

The other important aspect of the FIM is the lateral resolution� There are three

main factors which limit the resolution� First� the uncertainty principle puts a lower

limit on the lateral momentum of the image gas� if con�ned to a small area %x like

a surface atom %p � �

�x� Furthermore� the statistical Brownian motion of the image

gas due to the �nite tip temperature will limit the lateral precision of the image

mechanism� And lastly� the size of the image gas atoms themselves will pose an

inherent limit to the resolution� The resolution has then the following dependencies

on image gas atom of size � and mass M ��

�

��

��R��

�keME�

��

" ��

��kBTR

keE�

�" ��

��

��

with tip radius R� electric �eld at tip E�� image correction factor � �eld reduction

k and Boltzman constant kB� T is the temperature of the image gas atom at the time

of ionization� i�e� it depends on how well the gas is thermalized�

The three terms in the squareroot �the root originates from the vector addition of

the three independent contributions are terms from the uncertainty principle� Brow�

nian motion and image gas size� respectively� The best resolution can be achieved

with a small tip radius� a low thermal equivalent of image gas atoms� a high ionization


potential so that E� is high and the smallest gas atom size� He is therefore the best

choice� Ne and H� are second best at low temperatures below �� K�

For our nanotips it turns out that the lateral resolution even at room tempera�

ture is below � �A� owing to the extremely small tip radii� This is demonstrated in

�gure �� where good atomic resolution is achieved with a �� oriented W tip at

room temperature� The sequence also shows steps of the atomic manipulation pro�

cedures using �eld evaporation� which will be discussed in the following paragraph�

Consider the potential energy curve of a system containing the tip apex and a

surface atom of the same material �as depicted in �gure �� The same energy curve

for the ionized state �positively charged surface atom on neutral� since metallic� sur�

face should be shifted to higher energies� For large separations the energy di erence

between those two states is the energy required to ionize the atom minus the energy

e$ gained by returning the electron to the tip apex with workfunction $� If now a

strong electric �eld is introduced �straight line in �gure �� the energy of the ionic

state is greatly reduced and at a critical distance xcritical the ionic state is energeti�

cally lower than the adsorbed state� Hence� a thermally activated surface atom with

a vibrational amplitude close to the critical distance can be �eld evaporated� It is

interesting to note that the �eld evaporated atoms can be multiply charged� and in

the case of W it turns out that the evaporation �eld for triply charged W atoms is

the lowest�

If the evaporation �eld is below the image gas ionization �eld� the tip apex would

�eld evaporate before it is even imaged� For W the evaporation �eld is �� V��A �hence

larger than Eion�� V��A for imaging with He and the �eld evaporation process

can be visually observed� The sequence in �gure �� represents FIM images taken at

the BIV of �� kV� with careful evaporation steps in between at V�� kV� achieving

controlled evaporation of single atoms� In fact� this process can be used as another

means of calibrating the �eld on the tip apex� Since we know that the �eld to

evaporate W is �� V��A �� for Ir the value is �� V��A we can again calculate the

factor k � R from equation �� and therefore relate voltage and �eld� Since before


Figure �� FIM images of a �� oriented W tip taken at room temperature usingHe at �� kV� In between each image the voltage was increased to �� kV for the �eldevaporation of single atoms�


Figure �� Potential diagram for the process of �eld evaporation� As describedin the text� the ionic ��eld evaporated state is at higher potential than the atomicstate� unless a strong external �eld is applied� Then� at a certain distance xcritical�the ionic state has a lower potential energy and �eld evaporation can occur�

the judgement of a �best imaging condition� is somewhat arbitrary� this calibration

should be more reliable�

We consistently were observing very faint FIM images� with atomic resolution� at

voltages typically �

�of the BIV �see �gure �� This had not been reported before�

probably due to the extremely small intensity of the image� which could only be

visualized with long integration times of a CCD camera� Hydrogen gas is not very

well pumped by turbomolecular pumps owing to its small mass and is therefore one

of the main constituents of the rest gas in UHV� Its ionization energy is roughly half

of that of helium� This image is therefore attributed to �eld ionized hydrogen atoms�

In fact� this is a very useful side e ect� because it allows one to image the tip surface

at very low voltages� that for example contaminant atoms with small evaporation

�elds can be seen before they evaporate�

The �eld above atoms at step edges or protruding atoms is slightly increased over

the �eld above in�plane atoms� an enhancement due to the geometry� This is why


Figure �� W�� tip imaged at di erent voltages� demonstrating atomic resolutionFIM at � kV� where the regular image forms only at � kV�


Figure �� W�� tip terminating in one single atom� FIM image taken with Heat �� kV�

those atoms have a brighter intensity in FIM �seen in �gure �� bright atoms at

the corners of the �� plane� Moreover� they inherently have less binding partners

and are more loosely bound to the tip surface� They are therefore the most likely to

evaporate next� which can be very nicely observed in the FIM sequence of �gure ��

Since protruding and edge atoms are preferentially evaporated� �eld evaporation is a

self regulating process and will always render a more smooth surface�

However� �eld evaporation is still a statistical process depending on the vibrational

amplitude of the atoms� Tips at room temperature are therefore much less stable

under high �eld imaging and evaporation conditions than cooled tips� and all of the

following experiments in this thesis where conducted at low temperatures� Another

example of the control achievable with FIM and nanotips is shown in �gure ��

where careful �eld evaporation lead to a tip apex terminating in one single atom�

�� Image Interpretation

Experiments on an atomically de�ned junction assumes the knowledge of the exact

atomic structure of the tip� FIM imaging only provides insight into the relative

position of certain atoms on the tip apex� and a detailed analysis and interpretation

of images is necessary to extract information about the tip apex radius and the exact


Figure �� FIM image �left of a �� oriented W tip and the corresponding projec�tion map �right� indicating the di erent crystallographic poles �from reference ��The grey circle in the map outlines the area imaged in the FIM graph�

position of all the atoms�

The FIM image of a �eld evaporated surface � typically exhibits an arrangement of

rings or polygons� the so�called decoration �e�g� see �gure �� Each ring represents

the edge atoms of a full plane� where the in�plane atoms themselves usually are not

visible in the FIM image� Concentric rings around the same center belong to the

same atomic plane� Therefore the tip surface can be thought of as a series of circular

planes on top of each other� each smaller concentric ring in the FIM representing one

step up towards the end of the tip� the smallest ring indicating the topmost plane�

The planes are indexed by their crystallographic orientation� The key to the full

interpretation of the FIM image is now to assign the correct crystallographic index to

the rings� To this e ect� one uses a stereographic projection map of the investigated

crystal structure� Figure �� shows such a map for a �� oriented bcc crystal

in direct correlation to a W�� FIM image� where the shaded area indicates the

�A �eld evaporated surface is not in thermal equilibrium� However� the surface diusion of Watoms even at room temperature is so small� that the atomic structure has been observed to bestable over several days at zero �eld�


overlap of the map with the FIM graph� The dots show the position of the di erent

planes and therefore represent the centers of the concentric rings in the FIM image�

The size of the dots indicates the dominance of the plane� i�e� it gives a relative size

estimate of the rings for the di erent facets�

In order to assign the right crystallographic index to each ring� it is most useful

to start with symmetry considerations� In the bcc crystal structure the �� facet

has a threefold symmetry with �� and also with �� which distinguishes it from

all other low index planes �see �gure �� The symmetry of the other planes �e�g�

�� is twofold with �� as well as with �� and the relative facet size taken

from the stereographic map then allows an unambiguous classi�cation of the rest of

the planes�

For our nanotips� the image often does not show very many planes due to the

extremely high magni�cation� and the interpretation proves more di!cult� On the

other hand� higher index planes are not visible and a reduced facet projection map can

be used� allowing a full assessment of the tip structure� while eliminating ambiguities�

An example is shown in �gure �� where the tip structure of a polycrystalline W tip

�and therefore a priori unknown crystallographic orientation � is fully analyzed using

the customized facet projection map� The equivalent analysis for a �� oriented W

tip is shown in �gure ��

For tips with a fcc crystal structure the same general rules apply� but one has to

use a somewhat di erent facet projection map� As an example for a fcc material�

the FIM image of an iridium tip and its corresponding reduced projection map are

shown in �gure �� again demonstrating the index plane classi�cation scheme�

The detailed atom by atom reconstruction of the tip apex is not as straightfor�

ward� First� each plane must be identi�ed and reconstructed with the help of plane

indexes� the number of atoms inferred from the ring size and �nally the FIM image

of this model must be calculated� This is very time consuming and only possible

with suitable computer simulations �or delicate ping pong ball constructions�� An

�In fact� due to the fabrication process� most crystallites in a polycrystalline W wire are mainly�� oriented which can be observed in this example as well�

�� ATOMIC SCALE ENGINEERING� FIELD ION MICROSCOPY �

Figure �� FIM image of a polycrystalline W tip �left and the reduced facet pro�jection map �right of a �� oriented bcc crystal� The grey circle shows the areaseen in the FIM image�

Figure �� FIM image of W�� tip �left and the reduced facet projection map�right of a �� oriented bcc crystal�


Figure �� FIM image of polycrystalline Ir tip �left and the reduced facet projectionmap �right of a �� oriented fcc crystal� The grey circle outlines the area image inthe FIM graph�

example of a �� oriented W nanotip can be found in reference �� A computer

rendered view of a so reconstructed tip with the corresponding FIM image is shown

in �gure �� This will serve as a reference for the tip structures typically encoun�

tered in our experiments�

One of the most important parameters of the investigated tips� which is con�

sistently used in the later experimental analysis� is the apex radius� Although the

detailed structure of the tip is described by a polyeder� with a surface terminated by a

set of di erently oriented planes� one can approximate the tip apex with a halfsphere�

The radius of this halfsphere is the tip apex radius �as used in the previous sections

and can be determined from the location of the crystallographic poles in the FIM

graphs�

The radius R of a sphere de�ned by the angle � between two crystallographic

poles and their respective distance on the FIM image is given by�

�Rendering done with the freeware POVRAY� www�povray�org��with �a �

�b � ab cos�


Figure �� FIM image taken at �� kV of a W�� trimer tip and the two re�construction steps� � computer simulated FIM reconstruction �only edge atoms arevisible � the full atom by atom reconstruction from two di erent viewing angles�Rendering done with POVRAY�


R �ns

�� cos ��

Here s is the plane separation with respect to the reference pole �e�g� �� for a

�� oriented tip and n is the number of rings �and therefore steps visible between

the two poles� The step height s for cubic crystals with lattice constant a is�

s �a

ph� " k� " l�

��

For a bcc lattice � � if h " k " l is an even number and �� otherwise� For

fcc � �� if h�k and l have the same parity and � �� if they have mixed par�

ity� For the polycrystalline W tip in �gure �� we calculate R��A �counting

�ve steps between the �� reference pole and the �� pole� or� alternatively�

taking � steps from �� reference to the �� facet� For the W�� tip from �g�

ure �� the radius ranges from R��A �� over R��A ��

to R��A �� Hence� the uncertainty in the determination of the local

radius of curvature is about �� due to using di erent poles as the reference and

target facet�

�� Electric Field of Nanotips

If one of the most important parameters is the tip radius� why not simply deter�

mine this apex radius from a �eld emission experiment� from the slope of a Fowler�

Nordheim plot as in �gure �� All we need to know then is the previously introduced

�eld reduction factor k� Modeling the tip as a paraboloid of revolution� k can be cal�

culated from the the tip to screen distance Z and the tip radius R ��

k ��

�lnZ

R��

The value of k is around for a �� A radius tip� which agrees with experimental

observations� For our nanotips with an apex radius of � �A� k is expected to be around


Figure �� High resolution TEM micrograph of a polycrystalline W tip which hadbeen imaged by FIM before �image courtesy A� Zaluska

�� Using our ability to determine the apex radius directly via FIM analysis and at

the same time knowing the �eld needed to ionize the image gas� we can calculate this

factor k �equation �� For tips with an apex radius around ��A� k reaches values

as high as �� This is about four times the expected value� For tips with an apex

radius of ��A� we �nd that k has a value of ��

It seems that especially for ultrasharp tips equation �� grossly underestimates

the correct �eld reduction factor� The �eld strength expected from such a small tip

radius is overcompensated by the� in comparison� huge tip base� To get an idea of the

actual geometry of the tip� �gure �� shows a high resolution TEM �transmission

electron microscope micrograph of a polycrystalline W tip with a �� A apex radius�

after it was imaged by FIM at �� kV� In passing we note the absence of an oxide

layer �as seen in �gure �� thus proving the cleanliness of the whole tip apex even

of the areas which are not directly observed and manipulated in FIM�

Atlan et al�� have modeled ultrasharp tips as a big base �with the geometry of

a hyperboloid of radius �� A with a �� A wide and �� A high pyramid on top

of the support &teton tip&� The base �eld is determined by the large radius� and the

pyramid only gives rise to a �eld enhancement factor of � to �� In the spirit of this


idea we could therefore model our tips as a hyperboloidal support structure of radius

R�� A �from �gure �� with a pyramidal apex of height and width of the order

of �� A� The �eld enhancement factor of such a large pyramidal structure should

be between � and � only �compare �build�up� tip in reference �� The k factor of

a �� A hyperboloidal tip base after equation �� is k�� and with this small �eld

enhancement factor we would predict imaging voltages of �� to �� kV� which are

reasonable� but lack useful precision�

In conclusion� the relationship between applied voltage and the �eld at the tip

surface is highly non�trivial for our nanotips� and satisfying values for the tip apex

radius can so far only be obtained from the detailed FIM analysis�

�� Experimental Issues

Although we now have established a way of fabricating and analyzing the probe

structure with atomic precision� there are several issues which have to be discussed

with respect to the adhesion experiments� Is the tip structure� although not in

thermal equilibrium� actually stable for the time period between FIM imaging and

adhesion measurements We will be investigating a W tip on Au surface junction

in the following adhesion experiments� How much contamination is expected on the

rather reactive W surface during this time An issue of crucial importance is also

whether or not we can actually see Au atoms picked up from the surface in the

following FIM� an aspect related to the wetting behaviour of Au and W�

For a careful� yet not prohibitively slow approach of the tip towards the investi�

gated surface� �eld emission is often used to get a rough idea about the tip sample

distance� How does the �eld emission current a ect the tip stability And lastly� we

want to estimate how much background forces we expect from Van der Waals and

electrostatic interactions� to quantify their in�uence on the metallic adhesion force

measurements�

�� EXPERIMENTAL ISSUES ��

�� Tip Cleanliness

The high �eld gradients encountered during FIM prevent any contamination atoms

from being adsorbed on the tip surface� Unless there is an overwhelming amount of

�dirt� transported due to image gas �ux �see section �Working Principle� from the

tip shank� the surface stays atomically clean during imaging� If the FIM analysis is

�nished� however� contaminations due to surface di usion and restgas atom adsorp�

tion can be appreciable� The time frame that lies between the FIM analysis and the

actual adhesion force experiment is of the order of �� to �� min�

Although the base pressure of the vacuum chamber is � � �� mbar� the base

vacuum during FIM can be worse� since the main turbomolecular pump is shut o

from the chamber in order to sustain a He gas pressure of � � �� mbar� One

obvious precaution to prevent contamination is therefore to pump out the image gas

before the FIM voltage is turned down� This also makes sure that there remains no

physisorbed image gas layer on the tip surface�

Figure �� shows a FIM image of a W�� tip at �� K before and after it was

left in vacuum for a period of �� hours� We count �� adsorbed atoms� which gives us

a rate of �� contaminant atoms per hour� This experiment also proves that a �eld

evaporated surface� ending in a three atom con�guration� actually is stable to surface

di usion over at least a period of �� hours� In fact� even at room temperature such

a tip was found to be stable over a period of six weeks ��gure ��

�� Gold on Tungsten� FIM

During adhesion measurements of a tungsten tip in contact with a Au sample� the

question is whether the Au will �stick� to the W surface �wetting behaviour� which

is theoretically expected for metallic systems �� In order to see if gold atoms were

transferred to the tip� we image the tip after the adhesion experiment but we have

to be sure we do not �eld evaporate the Au atoms before we image the W surface�

This issue was addressed by thermally evaporating Au �pressure during evaporation

better than � �� mbar onto the tip apex� Figure �� shows a W�� tip before


Figure �� a FIM image of a W�� tip at �� K� b�d The same tip imaged afterit had been left in vacuum for ��h� counting �� adsorbates� Successive �cleaning� ofthe tip from adatoms reveals the original trimer structure�

Figure �� FIM image of a W�� trimer tip before �left and after �right image�adsorbates carefully �eld evaporated before it was left at room temperature for aperiod of six weeks� proving structural stability�


Figure �� FIM image of a W�� tip at �� K at �� kV �upper left� Aftergold had been evaporated onto the tip surface� single Au atoms are seen� which �eldevaporated at voltages of �� to �� kV� After the cleaning the original structure isrecovered �one W atom lost during cleaning procedure�

and after the Au evaporation� It is also indicated at which voltage the individual

gold atoms were evaporated �BIV was �� kV with the He BIF of �� V��A and thus

can give us an idea of the adsorption energies of Au on W�

Previous studies �� reported that the adsorbtion energy of a Au atom on W��

is �� eV and that the Au is �eld evaporated at �elds of �� V��A� These

values actually are �� smaller than what we measured� which could be related to

the somewhat arbitrary determination of the best imaging voltage�

One interesting feature of the Au evaporation sequences is� that during the �eld

evaporation there is a tendency of the Au atoms to move towards and then onto the

�� plane �� This is expected� since the �eld induced surface di usion is directed

�In fact there was so much Au evaporated onto the tip shank as well� that even at low temper�atures Au would constantly diuse towards the tip apex and could neither be cleaned o by �eldevaporation nor annealing�


towards the higher �elds� From an atomical engineering point of view� this e ect

could be used to place single atoms of a certain metal directly on top of a W��

tip� However� the structural stability of such a fabricated composed single atom tip

has yet to be investigated�

�� Field Emission Stability

As mentioned before one interesting issue is how much current the tips can sustain�

First� the approach mechanism �� is using a �eld emission current of �� nA to

estimate the tip sample distance� Secondly� we typically encounter tunneling cur�

rents of � nA in our experiments� In fact� during the approaches tip towards sample�

currents can reach some �A� but here the power dissipation can occur in tip and sam�

ple and the situation is somewhat di erent� Typically W�� oriented tips showed

no changes in the atomic arrangement of the tip apex if a current of up to �� nA

was drawn for several minutes from them� Currents of �� nA� though� start to in�

duce more severe changes� as shown in �gure �� This is contrary to observations

by Fink �� who stated that trimer tips where structurally stable for currents up

to �A� We observed consistently that those currents completely change the atomic

structure �e�g� see �gure ��

Small Excursion� Atomic Resolution FEM

Instead of only analyzing the current during �eld emission� one can also use a phospho�

rus screen to look at the lateral distribution of the current� �eld emission microscopy

�FEM� However� atomic resolution can usually not be achieved with this technique

due to the uncertainty principle and the temperature dependent lateral momentum of

the electrons �� The lateral con�nement necessary to have an electron come from

one atomic site� produces an uncertainty in lateral momentum owing to Heisenberg�s

theorem� The lateral resolution is given by �m�electron mass� e�electron charge�

V�applied voltage�

�� EXPERIMENTAL ISSUES �

Figure �� FIM image of a W�� trimer tip before �left and after �right a �eldemission current of �� nA was drawn from the tip for �� sec�

uncertainty � �Rk��

�

meV

��

��

For a conventional tip with an apex radius of �� A imaged at �� kV the lateral

resolution is then uncertainty � � �A� More importantly though� the temperature of the

electron gas as determined by Fermi energy� gives rise to a random lateral velocity of

the emitted electrons which limits the resolution for FEM to�

thermal � �� k

�R

k$��

��

��

This means that thermal � �� A for conventional tips�

However� these numbers depend on the apex radius of the tip� Calculating the

di raction and temperature limits for our nanotips with an apex radius of �� A we

�nd uncertainty � �� A and thermal � �� A� leading to an e ective resolution limit

of � � �� A� For a W�� tip ending in a three atom con�guration ��trimer�

the interatomic distance between those three atoms is trimer � �� A� We therefore

expect to just about reach atomic resolution FEM for the trimer nanotips� This is

evidenced in �gure �� which shows the FIM image of a W�� trimer tip imaged


Figure �� FIM image �left of a W�� tip imaged at �� kV and the correspondingFEM image at �� V negative tip bias� The trimer can be seen in the FEM� indicatingalmost atomic resolution in the �eld emission mode�

at �� kV and the corresponding FEM image at �� V� just revealing the three atom

structure� Atomic resolution in FEM was predicted before �� to be only possible

for a certain geometric arrangement of the tip apex ��teton� tip�

�� Background Forces

For bi�metallic contacts expect force contributions from three physical mechanisms�

The metallic adhesion forces due to the electron wavefunction overlap� the van der

Waals forces and electrostatic forces between two charged surfaces� We are interested

in measuring the metallic adhesion forces� The expected contributions from the other

two mechanisms we calculate here� and eventually show that for our nanotips these

forces can be neglected�

Van der Waals Forces

Van der Waals forces originate from time dependent perturbation of the polarization

of molecules� For two molecules the dependence on the distance d of the interaction

energy is proportional to ��d� For two surfaces this changes� in particular the energy

per unit area W of one surface interacting with an in�nite plane is ��


W ��A

��d��

The Hamaker constant A has a value of around �� J for metals� We can now

calculate the van der Waals energy of the fully reconstructed nanotip from �gure ��

by adding the contributions of each �� plane with their respective surface area at

the speci�c distance� The force then is calculated from the derivative of the energy

with respect to the tip sample distance� The results are shown in �gure �� For tip

sample separations smaller than � �A deviations from equation �� due to screening

e ects �� occur� which in general reduce the interaction energy and in particular

get rid of the unphysical singularity at d�� As we can see the van der Waals forces

are typically at a least one order of magnitude smaller than what we measure in our

adhesion experiments�

For comparison we also calculated the van der Waals forces of a �ctitious tip� that

could actually produce the force values we observe in our experiments �see �gure ��

the solid curve representing our adhesion measurements� The apex radius of this tip

would have to be R�� A to get a comparable contribution� more than an order of

magnitude larger than what we typically encounter with our nanotips�

Electrostatic Forces

The potential energy stored in a capacitor of capacitance C at potential V is�

Wcapacitor ��

�CV � ��

In a �rst crude approximation we model the tip as many capacitors in parallel�

each tip layer represented by a parallel plate capacitor of capacitance C � �Ad�

Summing up each layer contribution to the total energy and di erentiating gives us

an estimate of the electrostatic forces� The results in �gure �� suggest that at our

voltage bias of V�� mV electrostatic forces are vanishingly small� However� due


Figure �� Calculated van der Waals forces for a �� A radius tip �squares anda �� A radius tip �circles in comparison to forces typically encountered in theexperiments �solid line�


Figure �� Calculated capacitive electrostatic forces for a �� A apex radius tip asa function of tip sample separation� Curves are calculated for �� V� �� V and �� Vtip bias�

to the square dependence of the energy on the voltage bias� forces increase strongly

with voltage and can reach values of several nN at around V�

For a tip with a larger apex radius we can use the Derjaquin approximation

�distance of separation d is smaller than the tip radius R to calculate the electrostatic

force Fel between a sphere and a �at surface ��

Fel � � ��RV�

d��

At the bias of V�� mV the tip apex radius has to be of the order of �� A to

contribute forces of nN�

� CHAPTER �� THE PROBE

�� Summary

In this chapter I was describing the di erent aspects of fabrication and analysis of

an atomically de�ned tip for metallic adhesion experiments� We required a tip which

is sharp �apex radius of some nm� atomically stable and well�de�ned� As a brief

summary the following steps were employed to reach this goal�

� Tips are electrochemically etched fromW and Ir wire using the drop�o method�

If done carefully this yields nm sized tip apexes and no further sharpening is

necessary�

� The tips are treated in a UHV environment� Annealing serves to remove con�

taminants and also helps stabilizing the tip structure� Field emission at high

currents improves overall sharpness and stability� At low currents it is used to

analyze the tip radius�

� The �eld ion microscope allows to image tips with atomic resolution� It also

serves to engineer the tip apex atom by atom� Image interpretation of FIM

graphs is not straightforward since not all atoms are imaged� However full

information about the exact atomic structure can be obtained by using image

projection maps� which are the link between the position of the crystallographic

facets and the FIM image� Important for quantitative analysis of FIM exper�

iments is the knowledge of the electric �eld at the tip apex� For nanotips

the relation between �eld and applied voltage is inconsistent with conventional

theory�

� Before using those tips for adhesion experiments several issues have to be re�

solved� The contamination rate of tips in UHV is �� atoms per hour� Au

atoms �possible contamination from the sample can be readily imaged without

altering their positions� Tips are mechanically stable when drawing electron

currents from them which are typically encountered during tunneling and �eld

�� SUMMARY �

emission� Van der Waals and capacitive electrostatic force contributions are

negligible for nanotips�

Chapter �

The Sample

The sample used for the adhesion experiments must be an atomically �at surface

which is free of contaminants� A material commonly used in SPM due to its inertness

and the relative ease of preparing atomically �at terraces is Au�� The following

sections will describe the preparation and the analysis of the Au surface�

�� Preparation of Au Sample

The Au�� surface was prepared using standard techniques �� A thin layer of

Au with thickness �� A was thermally evaporated in vacuum onto a heated mica

substrate� A small piece was then cut from the mica �about �� mm and glued

with a small drop of Torr Seal onto a thin glass beam �� mm wide� mm long and

�� m thick� On the opposite side a small Au coated glass square was glued as

well� acting as the re�ective part for the beam de�ection measurement� One end of

this beam was sti'y clamped to a holder� The so�constructed cantilevers typically

have a resonance frequency of �� Hz� The spring constant is measured ex�situ with

a sti micro�balance� It is necessary to measure the spring constant exactly at the

location where the tip approaches the sample� since it scales to one over the third

power with the distance between contact and pivot point� As an example �gure ��

shows the schematic of a cantilever beam with a Au sample� indicating the measured

spring constants at various points on the sample� The pivot point is at the very left

end of the cantilever beam�

�

�� SURFACE ANALYSIS �

Figure �� Dimensions of cantilever beam with mounted Au sample indicating themeasured spring constants in N�m at various points on the sample�

�� Surface Analysis

�� Cleaning Procedure

In order to clean the Au surface from foreign contaminations� the sample was sput�

tered in UHV with a beam of Ne ions �� mA accelerated to � kV for �� min� The

resulting surface is clean but the surface corrugations are of the order of some nm�

To obtain atomically �at terraces the Au sample was annealed in UHV at a tempera�

ture of �� K� Typically after annealing for �� min the rough surface healed out and

atomically �at terraces �� A in size were obtained�

Figure �� shows STM scans of a Au�� surface at those di erent stages� Fig�

ure ��a shows a scan of a highly contaminated Au sample which was exposed to

air for several days �the surface had been cleaned and annealed before several times�

The contaminations are removed by the sputtering procedure� yielding a clean but

rough surface in b� Finally the sample was annealed and the subsequent STM scan

in c shows atomically �at terraces� We �nd single atomic steps of �� A at the ter�

races edges� In fact this can be used to measure the expansion to voltage coe!cient

of the piezo tube�

The surface typically features elongated �ngerlike islands and also holes� These

structures were attributed �� to anisotropic self�di usion of surface atoms on a

reconstructed Au surface�

The structure of bulk Au�� is fcc� At the surface the crystal symmetry is broken

� CHAPTER �� THE SAMPLE

Figure �� STM scans �� A �� nA at �� mV bias of a Au sample atdi erent preparation stages� a Au sample� which was atomically �at before� exposedto air for several days� Surface contaminations of an average corrugation height of�� A have built up� b Sample was sputtered with � keV Ne ions for min� yieldingsurface with circular bumps of �� A diameter� c The same surface as in a sputteredand annealed for � min� showing atomically �at terraces stretching over a length of�� A�

and the surface reconstructs� In the case of Au�� the well�known herringbone

reconstruction occurs� It stems from the e ect that on top of a line of �� bulk atoms

one �nds �� surface atoms� which slightly bulge out� This surface corrugation forms

dislocation lines along the �� axis� with a alternating separation of �� A and �� A�

Even more strikingly there is a long range elastic interaction between the dislocation

lines which arranges them in a herringbone like structure� The corrugation height of

the dislocation lines is �� A� This surface reconstruction is clearly seen in �gure ��

and therefore proves the sub��A stability of the Au sample� despite being mounted

on a low resonance frequency cantilever beam�

The Au surface is sputtered and annealed shortly before �� hours each adhesion

experiment�

�� Force versus Tunneling

The Au surface might be clean right after the sputtering and annealing procedure�

but we have to ask for the surface contamination rate even in UHV� E�g� in a similar

UHV system �� a carbon contamination rate of �� monolayers per day� as measured

�� SURFACE ANALYSIS

Figure �� STM scan �� A �� nA at �� mV of a Au�� surface� Theherringbone reconstruction with a height corrugation of �� A is resolved�


by Auger analysis� on a polycrystalline Ir sample was reported�

Under ambient conditions it was found that �� a surface contamination layer

forms within some hours� However� STM scans of the surface still show perfect

atomic terraces� where AFM scans reveal that a thick adsorption layer has formed�

It was suggested that STM is not sensitive to the contaminant layer in this case�

This prohibits us from drawing conclusions about the Au surface cleanliness only

from STM scans� However it seems that the interaction force is severely a ected by

this additional barrier�

This discrepancy between STM and AFM can be understood along the following

terms �� The tunneling current is in lowest order approximation proportional to

the product of the density of states �DOS of tip and sample at the Fermi energy EF �

A non�metallic contamination layer typically provides no substantial contribution to

the density of states� The electrons from the probing tip can tunnel through the

layer providing it is thin enough� Therefore in this particular case a thin contami�

nation layer might be invisible to STM� On the other hand the interaction force is

an integrated value over all electron states� Non�metallic adsorbate atoms exhibit

a much reduced electron density� The metallic adhesion forces are reduced and the

interaction forces might even turn repulsive�

This chemical sensitivity was demonstrated by scanning a slightly contaminated

surface in constant current STM mode while measuring simultaneously the force

gradient �� Contrast was seen for carbon molecules on polycrystalline Ir and oxides

on an aluminum sample�

Figure �� demonstrates the e ect of the sudden change in force if the sample is

mounted on a �exible cantilever beam� While scanning the clean surface in constant

current STM mode the metallic adhesion forces are constant and therefore give rise

to a constant de�ection of the cantilever towards the tip� If now the tip reaches

a contaminated area the force is reduced or even goes repulsive and the cantilever

de�ection changes away from the tip� Since tunneling properties are not changed

by the additional layer yet the feedback is trying to keep the current constant� the

�� SURFACE ANALYSIS �

Figure �� Schematic of STM constant current operation on a �exible sample� Fora clean metal�metal contact the adhesion forces keep the cantilever in a constantposition �left image� If the tip scans over a non�metallic contamination layer� muchreduced adhesive forces will cause the cantilever to move away from the tip� Sincethe contamination does not substantially a ect the tunneling current� the feedback�in trying to maintain the same tunneling current� is extending the piezo to accountfor the cantilever movement�

piezo tube is expanded to account for the change in sample position� Measuring the

piezo extension during the scan therefore should show the presence of a non�metallic

contamination layer� Inherently� this can not be distinguished from a hole in the

surface� yet the absence of any holes or contaminations on an atomically �at terrace

would indicate a clean surface� Hence chemical sensitivity can be reached even during

STM operation without directly measuring the force by simply mounting the sample

on a su!ciently �exible cantilever�

For a closer analysis we need to correlate the force and the tunneling current�

Metallic adhesion forces for the W�Au system are �� nN at a �� M� tunneling

resistance as will be shown later� The spring constant of the cantilever beam used in

�gure �� was � N�m� Already the reduction of the adhesive forces by nN due to a

contamination layer would result in a sample de�ection of � �A� With the demonstrated

sub��A sensitivity of the scan in �gure �� we would easily detect such a change� This

is a strong indication of the absence of any non�metallic surface contaminations on


the Au terraces� However� the �nal proof of a chemically clean Au surface should be

provided by an in�situ Auger electron analysis� The implementation of such a device

into the preparation chamber is under way�

Chapter �

Adhesion Experiments

We now have the tools to examine the adhesion forces and tunneling current of an

atomically de�ned junction� The tip material is W� a very rigid metal� approaching

a comparably soft gold surface� The mechanical properties of such a junction are of

great interest and have been treated in much detail elsewhere ��

One focus of the experiments will be the range over which the forces interact�

which are due to the electron wavefunction overlap of tip and sample� Closely related

is the issue of stability of such a junction� If forces are large and act over a short range

only� then we expect large force gradients� which give rise to a mechanical instability

of the atomic tip sample junction�

This chapter starts with the description of the theoretical models governing metal�

lic adhesion and mechanical properties� After highlighting some experimental work

done so far� it continues with the description of our adhesion experiments� which are

analyzed in light of the theoretical discussion�

�� Theoretical Predictions

�� Metallic Adhesion

In an adhesion experiment two metals are brought together and the force of the ad�

hesive bonding is measured� The energy needed to separate the two surfaces from

a distance d to in�nity �normalized by twice the surface area is the adhesion en�

�

�� CHAPTER �� ADHESION EXPERIMENTS

ergy Eadh� Even though a surface has a boundary de�ned by the position of the

surface atoms the electron wave functions can reach far out into the vacuum� Hence

interaction due to the overlap of the wavefunctions will occur�

Ever present dispersive van der Waals forces will also give rise to an adhesion of

the two metals� However� they are su!ciently small if the interaction area is very

small as is the case for nanotips �see discussion in section �The Probe � Experimental

Issues��

It was calculated� that such an adhesion energy versus distance curve should have

the following shape ��gure �� Coming from in�nite separations and approaching

the two surfaces now to within some �A� the adhesive forces increase �� Fur�

ther approach of the two interfaces will yield an extremum in the energy distance

curve� indicating the maximum adhesive bonding energy� Eventually the repulsive

interaction due to the kinetic energy of the electron gas starts to dominate� The

contributions of the di erent terms in the adhesion energy calculations are plotted in

�gure �� showing that the exchange�correlation energy of the electron gas plays the

dominant role for the adhesion forces�

The particular characteristics of this adhesion energy versus distance curve should

depend on the speci�c material properties� such as e�g� the electron density� band

structure and crystallographic orientation� However� it was found that those energy

curves could be scaled to �t one single curve� the universal binding energy relation ��

which is analytically described by the Rydberg function f�x�

f�x � �� " x � exp��x ��

Here x is a measure of the distance between the two surfaces of a bimetallic

contact� For �tting f�x to the energy distance curve of various materials� x is the

true distance divided by the material dependent scaling length ��

x � �d� dm��

�� THEORETICAL PREDICTIONS ��

Figure �� Contributions to the total metallic interaction energy from di erent phys�ical mechanisms� The exchange�correlation energy clearly dominates the adhesionenergy� whereas the kinetic energy of the electron gas gives rise to the repulsive part�from reference ��


with d as the distance of separation of the two surfaces and dm the distance at

which the adhesion energy has its maximum �taken from the energy distance curve�

The energy axis is scaled by the maximum adhesion energy Emax�

f�x �E

Emax

��

� has been associated with the Thomas�Fermi screening length ��

�TF ��

�

��

��

��

n��

�� in atomic units with � a�u�� m which is a direct function of the electron

density n �in a�u�� in the metal� This describes how well the metal can screen an

additional charge placed in it� If the electron density is high �TF is small and the

extra charge can be screened well� i�e� the additional electrostatic potential of the

charge is reduced to ��e within a distance of �TF away from the charge� The screening

length therefore sets the scale over which electronic forces can act� For the link to the

metallic contact we imagine an in�nite bulk material being cut into two half�spaces�

The disturbance due to the creation of the surfaces is an e ective foreign charge and

can be better screened by metals with a higher electron density�

An example of a theoretically calculated and then scaled adhesion energy curve

is shown in �gure �� for an Al�Zn interface �� open circles� Even more stun�

ningly� this scaling also works for the molecular interaction energy �shown for H��

in �gure �� chemisorbed molecules on surfaces �here oxygen and bulk cohesion�

Especially for the molecular interaction energy the term �electron screening length�

is ill�de�ned and one resorts to another de�nition of the scaling length� � is speci�ed

by requiring that the second derivative of the adhesion energy at dm is equal to ��

This results in�

� �

�Em

��E�d

�d�

��

d dm

��

��

�� THEORETICAL PREDICTIONS ��

Figure �� Scaled binding energy versus scaled distance of separation for four di er�ent types of binding mechanisms� The curves for molecular� interfacial� chemisorptionand bulk interaction are well described by the Rydberg function �from reference ��

The physical interpretation of a such de�ned � is less obvious� however it gives

good results for all four cases in �gure �� According to this scaling rule� we could now

analytically predict the binding energy distance relationship of all metallic contacts�

where we would only need the maximum adhesion energy and the scaling length as

our inputs�

One has to keep in mind that the examples all are calculated curves from dif�

ferent theoretical models� Those calculations generally neglect the band structure

of the surfaces� No direct experimental veri�cation has been done so far� owing to

the di!culties in designing an experiment that measures directly the forces of two

atomically de�ned metallic surfaces� In fact� the plausibility arguments given in ref�

erence �� to explain the universal scaling rely on the approximation that the total

charge density between the two surfaces is a simple superposition of the solid�vacuum

electron distributions�

The scaling lengths � for the metals investigated in this thesis are expected to be

around �� A �� More accurately than using the Thomas�Fermi equation �� they

were calculated from theoretical surface energies � �� and the experimental elastic


constants C�

�� for strain along the surface normal ��

� �

��s

C �

��

��

Here s is the interplanar separation along the surface normal�

In uence of Tip Shape

Before we can apply these results to our tip�sample set�up� we have to ask what the

in�uence of the peculiar shape of our nanotips might be� A study concerned with

the e ect of the tip shape was done by the same authors who proposed the universal

binding curve �� Using a so�called equivalent crystal theory �� they calculate the

energy versus distance curves for several same metal contacts �including tungsten

for a highly idealized tip sample geometry� The tip is modeled as a semi�in�nite

slab on which one atom is placed� a single atom tip� The surface is a same material

semi�in�nite slab� For the simulated fcc and bcc metals the shape of all the curves

comply to the Rydberg function format� The peak adhesion energy of the single

atom contact� however� was sensitively dependent on tip geometry and material� In

general the single atom tip is more reactive than just a double �at surfaces geometry�

Another study �� indicated similar results using the same method for a bi�metallic

contact all combinations of Ni� Au� Pd� Cu and a more re�ned tip model�

A very detailed analysis calculating the LDOS of tip and sample in a W�W tip�

sample contact �� especially concentrates on the d�band properties of tungsten with

a tight�binding type calculation� The tip was modeled as a pyramid on a support

base� The electronic DOS structure of the tip exhibits pronounced peaks due to the

particular tip shape� However� the binding energy versus distance curve� being an

integrated value over all electron states� is not sensitive to those peaks� It scales

well with the universal binding relation proposed before� In particular all of the

above simulations indicate that most of the interaction happens over a distance range

of about � �A� i�e� the distance scaling length consistently is around �� A� It is

�� THEORETICAL PREDICTIONS �

therefore concluded that only the terminating tip apex atoms play the dominant role

for metallic adhesion ��

�� Mechanical Relaxation Eects

So far we have neglected the relaxation of the tip and sample atoms� in fact� all

of the above calculations had �xed atom positions� Taking a di erent step� molec�

ular dynamics simulations can help to gain insight into the dynamic behaviour of

the metallic junction� Rather than using atom�atom potentials and integrating the

equations of motion� the embedded atom method �� models more adequately the

metallic material as an ionic matrix �embedded� in an electron gas� The electron

density dependent energy function then gives rise to the e ective potentials which

govern the motion of the ion cores� The case for a Nickel tip approaching a Au surface

was simulated �� see also �gure �� later and showed the phenomenon of a sudden

avalanche �jump�to�contact of the Au surface towards the tip at a distance where

strong adhesion occurs� The rapid increase of the strong adhesion with decreasing

separation yields very high force gradients� These gradients can lead to high tensile

stress in tip and surface and might induce this atomic scale jump�to�contact�

Experimental veri�cation of this phenomenon was not found �� however� the

experimental conditions were more than ambiguous �uncharacterized tip on Au in dry

nitrogen gas atmosphere� It was concluded that the metallic adhesion interaction

was buried in a background of strong van der Waals forces� Therefore the comparably

smaller metallic adhesion forces could not be resolved�

Upon retraction the Au sticks to the Ni tip� pulling a small wire which eventu�

ally breaks o � Restructuring of this wire complying to the tensile stress happens

in discrete steps� which are apparent in the force versus distance curves� The simu�

lation therefore indicates that metallic contacts should exhibit a sudden instability

upon approach and a distinct hysteresis between approach and retraction �for later

discussions we point out that there is no hysteresis if the tip had been retracted prior

to the jump�to�contact�


For comparison with our W on Au experiments we note that Ni and W have

similar mechanical and electronic properties with respect to Au� both materials being

mechanically much more sti than Au �Young�s modulus �� GPa for Ni and �� GPa

fo W versus �� GPa for Au and having comparable ionization enthalpies and work

functions� We should therefore expect to encounter the main qualitative features�

jump�to�contact and hysteresis� predicted in this simulation�

�� First Experiments

The �rst experiments concerned with metallic adhesion were performed by Ohmae ��

who used a modi�ed FIM set�up� where it was possible to carefully approach a gold

surface towards a W�tip� Although force resolution was only around �N and vacuum

pressures around �� mbar strong metallic adhesion of W on Au could be con�rmed�

Other preliminary experiments with better force resolution using an AFM set�up but

no tip characterization and under ambient conditions �� indicated hysteretic

behaviour even under light load conditions�

Pioneering experiments in an SPM set�up under UHV conditions on a clean surface

with nN sensitivity revealed a more complex behaviour �� in fact� not the force

but the force gradient was measured� For an Ir tip �shape and structure unknown�

prepared by contacting tip and sample approaching a polycrystalline Ir surface the

authors found that the force measurement scaled rather accurately with predictions of

the universal adhesion energy relation� Most of the short range interaction took place

within � �A� the contact was seemingly stable� exhibiting only little hysteresis between

approach and retraction before reaching point contact� The simultaneously acquired

tunneling current showed a sudden increase upon further approach� indicating that

point contact with the resistance of a single atom contact R�� k� was reached�

However� using di erent sample materials the theory consistent behaviour was

jeopardized� For Au and Al as sample materials substantial force gradients were

found to prevail already at much larger tip sample separations than expected� even

at a point where the tunneling junction conductivity was below �� This indi�

�� EXPERIMENTAL PROCEDURE ��

cates that appreciable adhesive forces already are present at a point where the electron

wavefunction overlap does not yet give rise to electron tunneling� Furthermore� the

tunneling conductivity upon close approach does not exhibit the sudden change from

tunneling to point contact behaviour� In fact� the conductivity is at all points sub�

stantially smaller than for the Ir�Ir contact� It was stated that a possible transfer of

Al�Au to the Ir tip apex could be related to the dramatic change in behaviour�

In order answer the questions about the exact tip structure and composition the

design of a new UHV system was initiated by U� D�urig� which combined the very force

sensitive SPM type set�up with an in�situ �eld ion microscope for the tip analysis�

Furthermore the force is measured directly with an interferometer� getting rid of

ambiguities inherent to measuring the force gradient only� An atomically de�ned�

clean metallic contact can now be investigated� addressing the above contradictions

between theory and experiment�

�� Experimental Procedure

A typical experimental run takes a couple of hours� All the steps are performed in

the main STM�AFM�FIM chamber at a constant base pressure of � � �� mbar

and a temperature of �� K� The experimental steps comprise �rst the fabrication�

characterization and imaging of the initial W or Ir tip using FIM� Typically the tips

have been imaged before to ascertain that the contamination rate via di usion of

adsorbates is negligible� Then the sample stage is placed quickly opposite to the tip�

It is important to record the exact position of the tip on the cantilever beam� since

this determines the sample spring constant and therefore the force calibration�

Secondly� the tip is approached towards the sample �cleaned beforehand following

the procedures outlined in section �sample preparation� using an automated approach

mechanism� This consists of a piezo step motor� which can approach the tip about

��m towards the sample in one step� The tip itself is mounted on a piezo tube�

which can extend�retract over a range of ��m� Initially fully retracted the piezo

tube extends at a rate of �� nm�s� while a nanosecond switch detects a possible


tunneling signal of � pA� At the instant a signal is detected the feedback for tunneling

is switched on� yanking the tip back to account for piezo creep� and slowly bringing

it back to the tunneling point �typically � nA at �� mV bias� which will act as the

reference position further on�

Questions have been raised whether this system actually assures that the tip never

comes too close to the sample� therefore contacting before the actual experiment� An

alternative approach method employing �eld emission and a customized slow ap�

proach control have been discussed in reference �� However� an atomically de�ned

W�� tip was shown to be una ected by the conventional approach mechanism �as

described later in �W on Au Experiments��

Once the tip is in tunneling mode� it is necessary to wait a minimum time of

� min in order for the system to equilibrate the piezo creep �� The actual approach�

retraction cycle starts by switching o the tunneling feedback and retracting the tip by

a set amount �� to �� A� Then the piezo tube extends linearly with time at a speed

of �� A�sec to the desired point �see also �gure �� while the force and tunneling

signal are recorded every �� ms� Subsequently the tip is again retracted to the initial

retraction point� After the tip has been brought back to the tunneling point� the

tunneling feedback is switched on again for � sec to re�establish the reference point�

This cycle is typically repeated �� times� further on referred to as one set�

The �nal step is to analyze the tip structure with FIM after the approach ex�

periment� After quickly retracting the tip and removing the sample stage� care has

to be taken that the FIM procedure itself does not induce any tip changes� It is

crucial not to increase the FIM voltage too quickly� in order not to remove possible�

loosely bound atoms from the apex� An important help is using a digital camera

with long integration times� to catch even very faint signals� In fact� �rst low inten�

sity images can be taken at about half the best imaging voltage employing the ever

present H restgas as the image gas �as described in the section �The Probe�� The

FIM procedure should then be able to reveal any changes in the atomic structure or

ad�atoms picked up from the sample� In a preliminary study �section �The Probe� it

�� EXPERIMENTAL PROCEDURE ��

Figure �� Scheme of the approach�retraction cycle� showing the voltage applied tothe piezo tube �z�piezo� the logarithm of tunneling current and the feedback signal�indicating on or o � i�e� feedback is active�not active�

was ascertained that Au atoms on the W tip can indeed be imaged at regular imaging

�elds�

Experimentally the tip excursion %z is the control parameter� Hence the true tip

sample separation must be calculated from the tip excursion and the cantilever beam

movement� The true tip sample separation is�

%s � %z � %F

ccb� ��

with ccb as the spring constant of the cantilever �as calibrated before� usually � to

�� N�m� While the absolute tip�sample separation is still unknown� one can de�ne

zero tip sample separation arbitrarily as the point of the force cross�over� This is a

convenient choice because at z � � we have %s � %z �no correction due to cantilever

beam de�ection and it also marks the point of maximum adhesion energy� A second

order correction to %s is due to the compliance of the gold� This would shift the

adhesion force values towards smaller tip sample distances �some �� A and change

the slope of the force curve slightly� However� this correction is negligible �less than

�� A as a result of detailed experimental investigations of the junction contact


mechanics �see reference ��

�� Preliminary Studies� Unde�ned Tip

The unique feature of the new system is the ability to analyze and engineer the probe

itself with atomic precision using the FIM� It is instructive to do some experiments

�rst� where this capability is intentionally not used in order to contrast to the intended

well�de�ned experiments�

One procedure to get a �good� tip especially for STM applications is to contact the

tip with the surface� possibly applying some voltage pulses as well� Far from being a

reproducible method� it is nonetheless commonly used for tip preparation� for lack of

a better method� Upon this violent approach of tip and sample� material transport

will occur between the two� the mechanically more stable probe �usually W or an Ir

compound being eventually covered with a layer of the sample material�

Polycrystalline W on Au

In trying to gain some insight into this rather statistical process� we have prepared

a polycrystalline W tip with standard methods� not using FIM� the tip was elec�

trochemically etched� annealed and treated with �eld emission� The surface was

Au�� prepared as described in the sample preparation section� The tip was ap�

proached to a typical tunneling contact �It�� nA at Ut�� mV and the Au surface

was imaged in STM mode� Several changes in contrast occurred� indicating changes

in the atomic con�guration of the tip apex� Once stable imaging conditions were

achieved �clear observation of atomic steps� as in �gure �� the tip was used for

approach experiments�

We note that this is a standard STM tip� and no information about the tip apex

is known� The repeated annealing of the tip probably cleaned the tip of any residual

oxides from the etching process� The �eld emission indicated that the tip is fairly

sharp� with an apex radius of the order of some �� A� However we know from the

FIM analysis of similar prepared W tips that the �rst apex layers of the tip are

�� PRELIMINARY STUDIES� UNDEFINED TIP ��

usually far from well structured� and uncertainty about the exact chemical nature

of the very tip atoms remains� Scanning of the Au surface could also have led to

material transfer from the surface to the tip�

Using the procedure described before� the tip was used for several sets of ��

approach�retraction cycles� The force signal of one of those sets is shown in �gure �

and �� It is noted that prior to this set� one set indicated intimate contact between

tip and sample with strong adhesive forces of �� nN� making it likely that indeed

material transfer from surface to tip or vice versa had occurred� The position of the

tip on the surface after this contact was changed as well� Part a is a graph of three

representative force versus tip�sample separation curves of the �rst � cycles� all of

which were reproducible� The �� M� tunneling point of the tip is as at zero on the

horizontal axis�

Starting from the large tip sample distances� the tip approaches the surface and

the adhesive forces are measured from the �� M� tunneling contact on� After further

approaching they reach a maximum of �� nN and eventually decrease steeply� Upon

retraction of the tip the force describes exactly the same curve again� showing no

hysteresis� Therefore the tip sample junction is stable throughout the whole approach

retraction cycle� even at the point of maximum adhesive forces�

During the following cycle in graph c � something di erent happens� while the

approach is consistent with the reproducible behaviour from before� at the point of

maximum extension an instability occurs� resembling a jump�to�contact� Suddenly

large adhesive forces of about � nN are observed and upon retraction of the tip

from the surface we see sudden changes in the force channel� which never reaches

zero again� The next graph d shows four approach�retraction cycles� representative

of the subsequent �� cycles after the sudden change occurred� The force distance

curves now are not reproducible anymore� exhibiting usually large hysteresis and

jump�to�contact behaviour�

�To avoid confusion it should be noted that the horizontal axis in graph c� now is the z piezoextension rather than the tip�sample separation� Since the tip and�or sample changes are unknownduring this cycle� a true tip to surface distance can not be reconciled�


Figure �� Scan of �� A before a and after b one set of �� approach�retraction cycles� which exhibited hysteretic behaviour� The inset in b shows azoom and a linescan of the hill structure with a peak height of � �A�� atomic stepsof Au��


Figure �� Approach�retraction cycles of W�� tip �not used in FIM� hence unde��ned on a Au�� surface� The �rst � cycles of this set are very reproducible andshow no hysteresis or jump�to�contact� Part a shows three representative curves� Ingraph b the Rydberg function was scaled to one of the force�distance curves� with adistance scaling parameter of � � �� A�


Figure �� c The ��th approach�retraction cycle of the same set as in �gure �shows a sudden change in behaviour� Graph d shows some curves indicating theunstable behaviour during �� cycles after this change�

�� PRELIMINARY STUDIES� UNDEFINED TIP �

Figure �� MD simulation of a clean Ni tip approaching a Au surface from refer�ence �� Parts a and b show approach�retraction cycles with di erent approachdepths� The horizontal axis is the tip sample separation of the undisturbed system�here large tip sample separations are to the right� opposite to �gure �� zero de�scribes the point of mechanical contact� Note that substantial hysteresis is seen evenupon only light contact in a indicating structural change of the tip and�or sample�

Clearly the properties of the metallic junction have changed� tip and�or surface are

structurally less stable than before the contact� The tip had then be positioned over

a di erent� not damaged part of the surface� However� stable force�distance curves

could now only be observed in the negative force gradient regime �i�e� before the

adhesion peak approaching no more than � �A from the tunneling point� Farther

approaches now always resulted in a jump�to�contact� positive force gradients could

not be observed anymore� Hence we are led to conclude that the tip had permanently

changed�

To demonstrate the changes the surface had su ered we scanned the surface in

STM mode before and after a similar set of approach cycles in �gure �� The surface

has substantially changed� showing that a hill�like structure was formed where the

approaches had taken place� In an experiment on a Ag surface �� it was found

before that hillocks are formed during small load but clean metal�metal contacts�

Even a small contamination layer adsorbed on the tip or sample would passivate the

contact and indentations are seen�

The mechanical behaviour should be compared to the MD simulations in �gure ��


from �� Here the Ni�Au system exhibits non�hysteretic behaviour only in the regime

of small negative force gradients �i�e� long before the maximum adhesion force is

reached� This is in strong contradiction to our observation�

Experimentally� at a point of � �A in �gure �� extension over the reference point

tip�sample separation the instability occurs� It is instructive to look at the values of

the force gradient� If the negative force gradient is larger than the e ective spring

constant of the system it will become unstable� In �gure �� force gradients reach

values of �� N�m just before the point of instability� On the other hand �gure � a

indicates that maximum positive force gradients are of the order of �� N�m� However�

the absolute values of the occurring forces are of comparable magnitude �compare also

graph b� the actual jump�to�contact� It seems that the metallic adhesion forces do

not change with distance as rapidly as anticipated�

This is closely related to the concept of the distance scaling length discussed

before� According to Rose et al� �� all metallic adhesion energy curves should be

scaled to the Rydberg function� The integrated Rydberg function is shown together

with one of the force�distance curves in �gure � b� In fact� the Rydberg function

can nicely describe the shape of the measured curve� However� the distance scaling

length is �� A� Expected are values about four times smaller �� A� Another

interesting value is the total adhesion energy� which can be found from integrating

the force curve over the distance in graph b� The value is �� eV for this reversible�

stable contact�

What physical mechanism could give rise to this discrepancy A close analysis

is hampered by the fact that the exact tip structure and chemical composition are

unknown� The di erent scaling length could be an artifact from contamination layers

on the tip apex� The sudden instability possibly cleaned o this layer and fabricated a

purely metallic junction� exhibiting afterwards the expected unstable jump�to�contact

instabilities� However this is very unlikely� since strong adhesive forces indicated

intimate tip sample contact already prior to the approach cycles� In any case� a

conclusive discussion can only be continued if the tip properties are unambiguously


known�

Graph c in �gure �� should also be compared to the MD simulations in �gure ��

b� In light of the simulation we identify the point of sudden change in force with

the jump�to�contact phenomenon and hence a small adhesive neck is formed between

tip and surface� Retraction of the tip loads this junction with a strong tensile stress�

which is relieved in several sudden jumps or steps� It is implied �� that during

these jumps the neck is restructured� from a shorter and thicker contact to a longer but

thinner wire� which eventually will break �not evidenced in �gure �� c since the tip

was not retracted far enough� This behaviour compares well to the MD calculations

in �gure �� Experimentally this has also been seen before for Au�Au contacts ��

In fact� the size of the jumps should yield values for the energies involved in the stress

relieving mechanisms� As a �rst number� the overall hysteresis indicates dissipative

energy losses of over �� eV compared to �� eV in the simulation�

W�� on Au

A similar experimental set of approach cycles was performed again with a tungsten

tip on Au� However� two parameters were changed� First the tip was prepared from

single crystalline� �� oriented� W wire� As before the �eld emission characteristics

�� nA at �� V bias point towards a tip apex radius of some �� A�

Secondly the whole experiment took place at room temperature� Since FIM was

not used there is no necessity to cool the system down� In fact it is advantageous to

work at room temperature� because temperature drift is negligible and any boiling

noise from the liquid nitrogen container is absent as well� This allows us to investigate

the surface better before the approach sets�

The tunneling current was � nA at �� mV bias� No tip treatment was performed�

i�e� the surface was not intentionally contacted� In fact all the scans in STM mode

were extremely reproducible and no indications for instabilities were found� Notably

the horizontal and lateral resolution were su!cient to image the well�known herring�

bone reconstruction which forms on atomically �at Au surfaces� As discussed in the


section �The Sample� the high resolution STM scan on the cantilever beam is a strong

indication for a contamination free Au surface�

The tip was then placed in the center of an atomically �at terrace and several

approach�retraction cycles were performed� Figure �� shows two approaches with

di erent piezo expansions� In �gure �� a the tip was approached �� A over the

tunneling point� Approach and retraction coincide and no hysteresis is observed� In

�gure �� b the tip is approached over the point of contact �zero force and a small

hysteresis starts to form between approach and retraction� A reliable force calibration

was not performed� however the qualitative features of the force distance curves are

in agreement with the approaches of the polycrystalline W tip before in �gure � a�

A �t of the Rydberg function to the force curve indicates a distance scaling length of

�� A�

We can therefore conclude that neither temperature nor surface structure or clean�

liness play a role in the observed adhesion properties� The exact tip identity� though�

is still unknown and the in�uence of contaminations or structure can not be estimated

at this point�

Au on Au

Another pre�run was performed using a Au tip� Polycrystalline Au wire had been

electrochemically etched in HCl solution followed by a �eld emission treatment in

UHV� To assure cleanliness of the tip apex� it was sputtered with Ne ions at � keV

for several minutes �similar parameters as used for cleaning the Au sample� After

indenting the tip into the sample several times� the tip was now carefully approached

towards the clean Au surface while the force was measured ��gure �� During

the approach we �nd adhesive forces �unfortunately the noise level forbids to make

any further conclusion about instabilities which turn into repulsive force when the

junction is compressed� In fact mechanical relaxation of the junction is observed�

Upon retraction we observe that the tip stays in contact with the sample� Hence the

junction is shorter than before� because we see even a cross�over to adhesive forces�


Figure �� Two approach�retraction cycles �averages of �� consecutive runs with aW�� tip as described in the text� Horizontal axis is the z�piezo expansion �wherezero marks the �� M� tunneling point� the vertical axis is in arbitrary units� Thesolid line indicates a Rydberg �t with � � �� A�


Figure �� Force versus tip extension of a Au�Au contact� A big hysteresis indicatespermanent changes of the junction�

This means we are pulling the cantilever beam with the tip and the contact �nally

breaks when the tensile load is too strong� A broad hysteresis again indicates dissipa�

tive� permanent changes in the atomic structure of tip and sample� The quantitative

reproducibility of this process is rather poor� owing to the mechanical compliance

of the Au tip� but the qualitative features are observed for a series of subsequent

approaches�

The next step is now to repeat the approach experiments while employing the

FIM for the tip structure analysis� Therefore for the �rst time the metallic adhesion

characteristics of an atomically de�ned junction can be explored�

�� W ON AU EXPERIMENTS ��

� W on Au experiments

�� Part A � Structural Stability

A �� oriented W nanotip was prepared with standard procedures �electrochemical

etching� annealing� �eld emission and subsequently used for FIM� Figure �� a

shows the FIM image and the computer reconstruction� The tip apex terminates in a

�� trimer con�guration� with three �� poles adjacent to it� Further away from

the center we can also recognize parts of the �� planes�

The Au�� sample� mounted on a glass cantilever beam of spring constant

�� N�m� was repeatedly sputtered and annealed� The tip was brought into tunnel�

ing contact using the automatic step mechanism� The tunneling voltage was �� mV

�positive bias on tip and the feedback kept the tunneling current at � nA� Using this

trimer tip� we obtained a remarkably stable tunneling current� In particular� noise

spikes frequently associated with sharp W tips were entirely absent�

Using the tunneling point as a reference position we performed three subsequent

sets of �� approach�retraction cycles� For each cycle the tip was retracted from

the sample by �� A and then ramped towards the surface by an amount of ��

�� and �� A� respectively� After each approach the tip was retracted the same

amount and then tunneling was re�established for a period of � sec� The whole cycle

�approach� retraction and tunneling took about � sec� The force� an average of all

�� cycles� measured during those three sets is shown in �gure ��

After the experiment the tip was immediately retracted and investigated with

FIM� Carefully increasing the imaging voltage and using long integration times for

the CCD camera� we avoided any changes to the tip apex by the imaging process� As

shown in the section �The Probe� we are able to image adsorbates and�or Au atoms

without altering their position� The exact tip structure as before was found� however�

three foreign atoms were observed ��gure �� b in the central area� At voltages

below the best imaging voltage �BIV� a very bright spot was seen on top of one of

the �� planes� Although lacking the possibility for chemical analysis of this atom�


Figure �� FIM image and computer reconstruction of the eight last tip layers of theW�� tip before a and after b the approach sets� There are virtually no changesin the tip structure� in particular the trimer was mechanically stable� Two foreignadsorbates �bigger spheres in b are compliant with the restgas contamination�


Figure �� Three sets of approach�retraction cycles of a W�� trimer tip on aAu�� surface� The approach depth was increased from graph a to c� Zero tip�sample separation is at the �� M� tunneling point� The solid line represents a scaledand di erentiated Rydberg energy curve� scaling length �� A�


the brightness� imaging and �eld evaporation voltage of this atom are congruent with

values from the Au on W study in the section �The Probe�� Hence� we conclude that

one Au atom was picked up during the approach sets� The other two adatoms imaged

at the BIV are regular adsorbates from the restgas� compliant with the previously

determined restgas contamination rate of �� adsorbates per hour�

Before discussing the shape of the force curve� already at this point several im�

portant conclusions can be drawn� The tip shows structural stability down to the

atomic level although it was in intimate contact with the Au surface� as evidenced

by the repulsive forces measured during the approach� Apparently the W nanotip

can withstand adhesive forces of �� nN� In the repulsive force regime� the contact

pressure reaches values of the order of � GPa �maximum loading force divided by the

trimer area� This demonstrates the outstanding mechanical stability of nanometer

sized W asperities� A detailed analysis of the elastic and inelastic properties of this

junction can be found in reference ��

The force versus tip�sample separation curves in �gure �� a and b show the

same qualitative features as in the previous experiment for the �rst approaches in

�gure �� Since this time we used a tip with a smaller apex radius the forces also

are smaller by a factor of � and adhesive forces reach a maximum peak of �� nN� In

graph a the approach reaches this adhesion peak point� in graph b the forces turn

around upon further approach and reach again the equilibrium point of zero force�

Throughout this whole range of strong tip sample interaction no sudden changes

in the forces occur� Approach and retraction are reproducible and no evidence for

hysteretic behaviour is found� This is in contrast to the previous experiment with

the unde�ned W tip in �gures ��

We look at the values of the force gradients� and �nd that the negative gradient

is always well below �� N�m� which is related to the observed stability of the junc�

tion� This is in strong contradiction to theoretical calculations of Ni�Au and W�W

contacts �� with gradients of some �� N�m�

We �t the derivative of the Rydberg function to the force curve to compare to

�� W ON AU EXPERIMENTS �

the theory for the adhesion energy curve from Rose� Ferrante and Smith �� In

accordance with the �t from the unde�ned tip experiment� we again �nd a four times

larger than expected distance scaling length of � �A� This means� that the adhesion

forces contribute substantially already at much larger distances than anticipated from

the theoretical considerations� In fact we observe that already half of the maximum

forces are present at the �� M� tunneling point� A treatment of the force induced

e ects �e�g� mechanical strain must therefore accompany any meaningful STM image

contrast calculation�

The point of zero force� the equilibrium of adhesive and repulsive forces� is only

about �A away from the tunneling point� This di ers from the unde�ned tip exper�

iment in �gure �� where at the �� M� tunneling point the adhesion forces amount

to only �� of the maximum and the point of contact is about � �A away from the

tunneling point� This can not be explained by the di erence in tip apex area of about

a factor of �� which will cause a shift of � �A� It hence indicates a di erent electronic

structure of the tip apex� as a �ngerprint of the di erent shape and chemical identity

of this comparably poorly prepared probe�

The metallic junction is stable even throughout the regime of repulsive force�

beyond the point of contact� Instabilities with strong hysteresis have been observed

for Au�Au contacts by others �� and us ��gure �� Furthermore we have found

before evidence of a cross�over from reproducible to jump�to�contact behaviour for

the unde�ned W tip ��gure �� which for the clean contact of de�ned symmetry is

not seen ��gure �� Hence� the di erence must stem from the precise tip structure

and chemical identity�

The before mentioned smaller force gradients are a direct consequence of the long

scaling length� While leaving the total adhesion energy constant� the weaker increase

of the force with distance results in the absence of a jump�to�contact instability� Long

scaling lengths had been observed before in D�urig�s work �� for the Ir�Au and Ir�Al

systems� and was also mentioned by Pethica �� during ac AFM operations� but have

been disputed due to the absence of tip characterization� Naturally the next question


is where this long scaling length originates from� This question will be treated in

the next section� along with another W on Au experiment featuring much enhanced

signal to noise in the force data and simultaneous tunneling current measurements�

The second observation� possibly connected to the scaling length� is the absence

of the predicted wetting behaviour �� Even indentations at high loading pressures

�graph c in �gure �� do not result in the formation of a metallic neck� which would

manifest itself by strong adhesive forces and restructuring events upon tip retraction

�e�g� �gure �� c� In fact� deep indentation experiments performed by us �� with

a similar tip show that no necking is initiated even if repulsive forces of up to �� nN

are imposed on the system� The sharp W nanotip is literally digging into the soft

Au sample without being severely a ected by this process� Other groups from the

SPM community have reported before �� that wetting of a W tip with Au is indeed

very di!cult to achieve and only possible upon violent ramming of the tip into the

sample or �rst �priming� the tip with contaminants such as Ni� Field evaporation

experiments �as in section �The Probe� and reference �� showed that the binding

energy of Au atoms on W tips is indeed very small �below �� eV� in contrast to

the other period � transition metal elements with Ebind around � to � eV �� and

therefore a Au atom remains at a lower energy state staying in the surface rather

than �sticking� to the tip�

Lastly we mention that the hysteretic behaviour changes slightly with the deeper

approach in �gure �� c� The retraction curve shows higher adhesive forces than

during the approach� indicating that dissipative processes were present� losing on the

average � eV per cycle� The point of contact relative to the tunneling point has

shifted by about � �A towards the surface� This could be due to conformational and

mostly reversible changes of the tip structure� However� it seems more reasonable

that the softer Au sample complied to the strong repulsive forces and an indentation

with small structural changes of the surface geometry took place� Since the force

during approach and retraction meet again at larger tip�sample distances we probably

created a dislocation which heals out as soon as the pressure is relieved ��


�� Part B � Scaling Length and Tunneling

In a similar experiment� using a comparable W�� tip and a Au�� surface� we

simultaneously measured the force interactions and the tunneling current� The spring

constant of the sample cantilever beam was calibrated ex�situ to be ccb � � N�m at

the point where the tip approached the sample�

The tungsten tip was analyzed using FIM� Typical images were taken at �� kV

and featured an apex radius of about � �A� The initial tip shape was engineered to

terminate in a trimer con�guration� As we have seen before� this tip con�guration is

stable when approaching a gold surface�

We performed three sets of �� approach�retraction cycles� each set with a succes�

sively smaller tip sample separation� In �gure �� we show the retraction part of a

single force and current�distance curve taken from the third run� For better presen�

tation a to � Hz band block �lter was used to �lter out external vibrations picked

up during the measurement in the force channel� Nevertheless� all of the following

statements about the force can also be inferred from the non��ltered data�

The shape of the force curve is similar to the ones shown in �gure �� All

force values are negative� i�e� the total forces between tip and sample are attractive

throughout the entire distance range� Starting from small tip sample separations the

forces rapidly increase� show a maximum adhesion peak of nN and then fall o to

zero again�

The tunneling current was measured simultaneously up to values of �� nA� cor�

responding to the saturation limit of the current�voltage converter� Figure �� thus

allows for the �rst time an experimental determination of forces present during imag�

ing� manipulation and spectroscopy by STM� The observed exponential tunneling

decay constant of �� A translates into the expected workfunction of �� eV for the

tungsten gold contact� At larger tip sample separations �%z � �� A the current

surprisingly decays more slowly with the tip sample distance�

In addition to the previously discussed force measurements the observed continuity

of the current as a function of distance is a further indication of the absence of an


Figure �� Simultaneously acquired force and tunneling data versus tip�sampleseparation�

atomic�scale jump to contact� For soft approaches we also see no hysteresis between

approach and retraction in It� showing that the atomic con�guration of the junction

does not undergo any changes�

Large Scaling Length

We want to compare the Rydberg function to the adhesion energy of the tip sample

system to extract the adhesion energy values� To this e ect we integrated the force

curve over the distance axis� In �gure �� we show the resulting energy versus

distance relationship� which as before� is well approximated by the Rydberg function

�solid line with scaling parameters Emax � �� eV and � � �� A�

Force Model �� Electron Density

A major theoretical challenge is to �nd out why we observe such a large scaling length

for our system� At this point we also point out that the �rst described experiment

with the unde�ned tip � polycrystalline W with an apex radius of some �� A� possibly


Figure �� Scaled adhesion energy versus the scaled distance �stars and the Ryd�berg function �solid line� The adhesion energy curve was generated by integratingthe force curve from �gure �� over the tip�sample separation� Scaling parameterswere Eadhesion � �� eV and � � �� A�


covered with Au � exhibited the same long scaling features in section �� D�urig also

found this behaviour for his unde�ned Ir tips on Au�Al samples� Therefore this

phenomenon of large scaling lengths seems to be of a more general nature applicable

to bi�metallic contacts and is not only a peculiarity of W�� nanotips�

In order to understand the physical meaning of the scaling length� we remember

that it was associated with the Thomas�Fermi screening length �� According to

equation �� the screening length is a function of one over the sixth root of the

electron density� Therefore� in a �rst attempt to explain a longer scaling length� we

propose that the electron density of our nanotip could be considerably lower than

the bulk value� Furthermore the Thomas�Fermi approximation is valid for a free

electron gas model� The electronic bandstructure of a spatially very con�ned W tip

was calculated �� to exhibit many more structural features than the bulk material�

The overall electron density can also be substantially reduced due to con�nement

e ects �� Hence the electron depletion of the nanometer�scale tip apex could explain

the long scaling length�

In order to account for the four times larger scaling length� however� the electron

density would have to be reduced by a factor of the order of �� This means that

the tip apex layers would exhibit considerably altered conductivity properties and

a strong in�uence on the tunneling behaviour is expected� At the typical tunneling

point of �� M� the tip would be touching the surface and only repulsive force should

be observed upon approaching� The second argument against the low electron density

model is that the same long scaling length was indeed observed for a much duller tip

��gure � where con�nement e ects should be much less pronounced�

Force Model �� Mechanical Relaxation

The e ects of mechanical relaxation of tip and surface� so far neglected� should also

be considered� The tip and in particular the sample atoms might comply to the

adhesive forces and therefore the tip�sample separation could be much altered from

the rigid�body assumption� However� upon approaching the tip to the surface� the


attractive force would make the atoms relax towards each other and therefore the

true tip�sample separation would be smaller then in the rigid�body assumption� The

measured adhesion curve would seem more steep leading to a smaller scaling length

than measured� Thus the mechanical elastic relaxation has the opposite e ect of what

we are looking for� Additionally� a detailed analysis of the mechanical properties of the

metallic junction shows that elastic relaxations are too small to explain the observed

scaling length discrepancies ��

Force Model �� Nanowires

A very di erent explanation employing MD simulations for an Ir�Au contact was

proposed by Nieminen �� As illustrated in �gure �� the tip approaches the

surface with the force increasing according to the Rydberg model with the predicted

short scaling length of �� A� At the point of large positive force gradients the Ir

contact becomes structurally unstable and exhibits a small jump�to�contact� This

actually does not yield a very large increase in adhesion force since only some atoms

are involved in the process� Rather a small nanowire is formed by the instability and

during the retraction the mechanical properties of this small Ir�Au wire are probed

instead of the metal�metal adhesion� In the simulation the instability is small and

the rupturing of the wire takes place in small� somewhat noisy� steps� Hence this

small wire formation could fake us into believing that we measure metallic adhesion

with a large scaling length�

Inherent to this model is that a hysteresis should be observed between approach

and retraction� which was absent in our measurements� However� one could argue that

the tip touched the surface before �possibly during the initial approach establishing

tunneling contact and therefore is already covered with a layer of Au atoms� Then

this Au layer acts as a precursor for the nano�wire formation and a similar force

curve for approach and retraction might be conceivable� It is still di!cult to explain

in this picture the approach sets� where the approach extends only slightly over the

tunneling point and still exhibits the long scaling length ��gure �� a�


Figure �� Simulation by Jouko Nieminen� An Ir tip approaches a Au�� surface�The force versus distance graph shows hysteretic behaviour between approach andretraction�


Furthermore� no su!cient amounts of these Au atoms were observed in the FIM

analysis after the approach sets� Secondly� the single run sub�nN sensitivity approach

cycles ��gure �� and � show no indications of sudden wire restructuring events�

which are of statistical nature� The high reproducibility of those force curves and

in particular also the tunneling current strongly contradict this model idea� Lastly�

experiments on the particular system Ir on Au �� indicated a long scaling

length� without observing hysteretic e ects�

Force Model �� Image Force

In a very idealized yet instructive model it was shown that long range image forces ��

can be substantial for bi�metallic contacts� This dynamic charge interaction force is

used in reference �� to explain the results from D�urig �� who found the �rst

indications of long range adhesion forces for Ir�Al contacts�

The tip was modeled as an in�nite halfspace of W �not Ir with one adsorbed W

or Al atom as the apex� In the case of the Al atom� it is energetically favorable to

push the electrons of the adsorbate somewhat away to expose the positive ion core�

Then the system can take advantage of the strong electrostatic interaction of the ion

core with the electron gas� However� this leads to a substantial charging of the tip

atom� which in return gives rise to a strong image force� In the case of W on W� the

adsorbate is part of the metallic bonding and no charge is expected�

This model can explain D�urig�s long range adhesion energy curves� assuming that

an Al atom terminated the Ir tip� In our case for W on Au we possibly had one

adsorbed Au atom on the tip apex� as mentioned in section �Part A� Structural

Stability�� To comply with the above model� this atom must have been picked up

already during the �rst light approaches in �gure �� a� This is rather unlikely�

since the adsorption energy of Au on W is small �below � eV� compared to Al or

W on a W surface at �� eV� Furthermore it was stated �� that the image charge

behaviour is not expected for a transition metal on transition metal contact� Crucial

for the local charge model is also that the ionization energy of the foreign Al atom


Figure �� Sketch of a charged tip facing a sample at distance d� The �eld linesemerge from the imaginary charge Q within the tip at position A�

on the W tip is substantially smaller than the one of W �Al� Eion� � eV versus W�

Eion� � eV� This is de�nitely not the case for Au� with Eion� �� eV�

Force Model �� Patch Charges

A more general approach concerning the charge build�up in a tip�sample junction was

introduced by Burnham et al� �� Since the workfunction of the tip varies with the

di erent crystallographic poles an e ective surface charge builds up� This so�called

patch charge model �from the patches of charge building up on a polycrystalline

surface originates from the redistribution of surface charge� the total charge remains

zero� For a metallic tip on a �at surface the resulting force �from the tip patch�charge

interacting with its induced image charge in the sample can be calculated as function

of tip sample separation d and the patch charge Q on the tip�

F � � Q�

�� d" A��

The constant A is the virtual position of the e ective charge Q within the tip �see

�gure �� For tips with a large apex radius as considered in reference �� A is

much larger then d and the equation can be simpli�ed�

F � � Q�

�� A�

�� d

A

��

�� W ON AU EXPERIMENTS �

�the o set can not be measured� hence experimentally we see F�d� However for

very sharp tips A and d are of comparable magnitude� In order to produce forces

of nN we calculate that a total surface charge of Q��e must be present� The

workfunction di erence on W between the �� and the �� facet for example is

around �� eV �� Considering that for our tips with apex radius R�� A this

di erence in workfunction occurs over a very small area� a patch charge of �e might

not seem unreasonable�

However� we see exactly the same force distance scaling behaviour with � �

� �A for tips very di erent in size� The patch charge though should be dependent

on the radius of curvature of the tip apex� Secondly we should see a change of force

distance behaviour from F��d� for a small tip to F�d for a large tip� as described

before� Lastly� previous experiments with polycrystalline Ir tip �� on Ir�Al and Au

samples indicated a dependence of the force law on the sample material� not the

tip� In fact we should see an in�uence of patch�charges building up on the rough

polycrystalline Ir surface as well� A detailed study of the in�uence of the tip radius

and crystalline structure on the force distance curves in correlation with theoretical

patch�charge calculation should shed some light into this issue�

So far none of the considered models can give a fully satisfying explanation for

the observed long scaling length� I will continue with the tacit assumption that this

e ect is an inherent property of the W�Au system� and interesting consequences for

various related �elds will be drawn from this property in the following paragraphs�

Consequences of Long Scaling Length

As a consequence of the long distance scaling parameter of � �A the three apex atoms

of the W tip are not the dominant contribution to the total force but also the atoms

from the second� third and fourth layer contribute appreciably� The layer separation

of W in the �� direction �which is parallel to the tip axis is �� A and the tip

radius as analyzed by FIM was R�� A� The arrangement and number of the atoms

per layer can be modeled from the FIM images �� where we �nd � �the trimer� ��


�� and �� atoms in the �rst� second� third and fourth layer respectively� The relative

force contribution of consecutive layers is then �� and �� contribu�

tions from higher layers fall o rapidly at the distance of maximum adhesive force�

This drastically changes the conventional picture for metallic tip sample interactions�

where it is assumed that only the atoms of the �rst layer dominate� With a scaling

parameter of � �A� the �rst three layers account for �� of the total force� each layer

contributing roughly an equal amount� As a consequence for imaging� one would

expect inferior lateral resolution in AFM� as opposed to STM operation� Speci�cally�

atomic resolution imaging in AFM should be much more di!cult to achieve in the

metallic adhesion regime�

The true tip sample separation is conventionally thought of as the distance be�

tween the �rst atomic layer of the tip and the surface atoms of the sample� However�

since the �rst� second and third layer contribute about an equal amount to the total

force� the center of force interaction is at the location of the second layer� Therefore

we expect a shift of about one lattice constant between the force interaction of the

whole tip as opposed to the force contribution of the �rst layer only� This means� for

example� that the �rst layer atoms �in our case the trimer can already experience

repulsive forces� whereas the measured total force interaction is still attractive� In

particular the �rst layer atoms will touch the surface before the point of zero force

is reached� In this context is interesting to note that in the experiment with sud�

den change in adhesion behaviour in �gure �� c the change happened at a position

where the zero force point had not been reached� yet the drastic change indicated that

tip and sample must have touched� This needs to be taken into account in realistic

models of nm scale mechanical contacts in the �eld of tribology�

Since the three apex atoms account for about �� of the total force� we can

calculate a maximum adhesion energy of �� eV�atom for W on Au� which compares

well to Ness� and Gautiers� �� values of �� eV to �� eV for a W�� single atom

tip facing a top or a hollow W�� sample site�


Force and Tunneling

The �rst experiments drawing attention to the connection between adhesion forces

and tunneling were performed by D�urig et al� �� Following a suggestion by Herring

�� Chen �� proposed a model which links force and conductance� The model

relies on the idea that the splitting of eigenstates due to the overlap of the electron

wavefunctions is well described by the Bardeen integral M� which gives rise to the

force�

f � �� jM j�z

��

as well as the tunneling conductance �with � � LDOS � contact area�

G ��

RK

� �tip � �sample jM j� ��

Using the experimental fact that G � exp��z where � �q

�me

��$� V � Chen

�nds for a metallic contact�

f � ��

sG �RK

�tip � �sample��

Here � is a geometric shape factor� with � � �

�for a paraboidal tip and RK � h

e�

the von Klitzing constant�

The proportionality of f andpG could not be observed in our experiments� As

already mentioned before� the tunneling follows an exponential curve with a decay

constant of �

�k� �� A� whereas the force shows a decay constant of � � � �A ��

Therefore we observe f � � G � I� Nevertheless� due to the lack of more sophis�

ticated theories� we will carry on with an analysis of our results in the spirit of

�At this point there is also a discrepancy between theories� According to Chen s model� the forcescaling length should be � �A� whereas the prediction from the universal scaling length theorem is�� A�


Chen�s model and analyze f� versus I� As we will see later� this yields very reasonable

numbers for �tip� We hope this will stimulate further interest in the development of

better theoretical models correlating force and conductance� This will allow a deeper

understanding of the underlying mechanisms�

Figure �� shows a graph of the square of the force f � versus the tunneling current

It from the data in �gure �� In the current regime between �� nA and �� nA�

the graph shows roughly a linear relationship between the squared force and the

tunneling current� even though from the Rydberg �t we found that f � is proportional

to It� However in �gure �� we are only looking at a small part �� A of the

force�tunneling curve� where it is not possible to discriminate between the two power

laws within the noise� Below �� nA we typically observe a much more steep slope

which seems to be due to a less than exponential behaviour of the tunneling current�

It is intriguing to notice is that for atomic resolution imaging with STM on metals�

currents of typically I � �� nA are used�

Using Chen�s model we can extract the convoluted LDOS of tip and sample

�con �p�tip � �sample ��

from the slope in �gure �� which gives us a value of �con � �� states�eV�atom�

The in�uence of the tip shape on the force due to the observed large distance

scaling parameter leads to a modi�cation of �con� Whereas �� of the force originate

from the �rst three layers of the tip� the tunneling current is dominated by contribu�

tions only of the �rst layer atoms �the trimer owing to an exponential decay constant

one quarter the size of that of the force �see �gure ��

For the force we have � atoms in the �rst layer� contributing � force unit each�

In the second layer there are � atoms with �� force units each� and the third layer

has �� atoms at �� each� This adds up to a total force equivalent to �� atoms in

the �rst layer� But there are only � atoms contributing to the tunneling current� A

detailed analysis of Chen�s model shows that the measured DOS of tip and sample

has in fact to be multiplied by the ratio of number of atoms contributing to the force


Figure �� Correlation between force and tunneling current using Chen�s model�The graph shows the square of the force versus the current� where approximately alinear relationship can be observed for currents above ��nA� The slope of the curveof �f�

�It� �� nN��nA translates to a convoluted LDOS of tip and sample of �con �

�� states�eV�atom�

Figure �� Visualization of the di erent contributions to tunneling current andadhesion force of a typical nanotip� The inner cylinder shows the tunneling atomsand the outer cylinder indicates the atoms which contribute �� of the total force�


Figure �� Approximations for the DOS of W and Au� The area of the box has toequal the area underneath the DOS curve for electron conservation�

versus the amount of atoms involved in the tunneling process� We thus calculate an

e ective DOS of tip and sample of�

� � �con�measured � (force atoms

(tunneling atoms� �� states�eV�atom ��

How does this measured DOS compare to theoretical expectations For a �rst

comparison we use a simple model following an idea of Friedel ��see also �gure ��

The total d�band of W ��lled and empty states has a width of Wd � �� eV ��

With �� d�electrons one obtains an average DOS of �� states�eV�atom� We ne�

glect the contribution of the s�electrons which play a minor role for the DOS of

transition metals in general� On the other hand� Au has one s�like electron in a

� eV wide band� therefore �sample � �� states�eV�atom� This gives us a value of

�con � �� states�eV�atom which is in surprisingly good agreement with the above

experimental value�

Clearly� we used a very simpli�ed model for the bandstructures in the above dis�

cussion� Ness and Gautier �� calculated the DOS of W�� and W�� tips�

Transition metals with a bcc structure exhibit a dip in the DOS at a d�band �lling

�� SUMMARY ��

of electrons� which is the case for Cr� Mo and W� The LDOS of surface atoms

usually exhibits a peak at the Fermi energy� which� however� is less pronounced for

densely packed surface orientations like W�� as opposed to W�� which has a

strong surface peak� Furthermore� Ness and Gautier showed that the interaction of

a W�� tip with a W�� sample splits the surface peak into a bonding and anti�

bonding state� the resulting minimum between these peaks leading to a signi�cantly

reduced LDOS at the Fermi energy�

Chen�s model correlates the force to the DOS only at the Fermi energy� which

seems too crude a simpli�cation considering that the the total energy is the integral

over all the states of the DOS� One might argue though that the force is proportional

to the changes in the energy �with respect to tip�sample distance and these changes

are most prominent when peaks in the DOS move across the Fermi energy� This

can be caused by wavefunction overlap resulting in the formation of bonding and

antibonding states� which split farther apart with decreasing tip sample separation�

Therefore the changes of the DOS at the Fermi energy can dominate the forces� and

explain why we see such reasonable agreement of the density of states calculation

with our experiment� It does� however� not explain the surprisingly large force decay

constant ��

� Summary

Previous experiments addressing metallic adhesion indicated behaviour inconsistent

with the standard theory �� The force interaction characteristics of metals

could not in general be described by the universal adhesion energy relation �� In

particular� Ir tips approaching Au�Al samples indicated that the interaction forces act

over a longer range than anticipated� However� the exact tip identity was unknown

leaving ambiguities about the exact junction characteristics�

� A� With a polycrystalline W tip �chemical and structural identity of apex un�

known approaching Au�� we �nd two types of behaviour� We observe strong


forces acting over long distance ranges� where no signs of hysteresis on sub�nN

resolution single approaches are seen� The behaviour suddenly changes to un�

stable� jump�to�contact behaviour� which had been predicted by MD simula�

tions ��

� B� The interaction of a W�� tip �atomic structure unknown with a Au

surface was measured� This time the Au�� surface was just shortly before the

experiment imaged with an STM scan� The location of the approach sets was

chosen to be in the center of a �� A terrace� Approach curves �averages

of �� cycles indicated long ranged forces and non�hysteretic behaviour�

� C� An atomically de�ned W�� trimer tip was employed to approach a Au��

sample� The force�distance curves �averages of �� cycles show stable� repro�

ducible behaviour up to the point of contact� The distance scaling length is

four times larger than theoretically predicted� A small hysteresis develops for

approaches over the point of contact� however� the junction remains stable and

no jump�to�contact is observed� FIM analysis shortly after the approaches in�

dicates no changes to the atomic tip structure�

� D� The current is measured simultaneously with the force of a W�� trimer tip�

Single approach curves with nN resolution prove stable junction characteristics

and show the same long scaling length� The tunneling current data furthermore

provides information about the workfunction and corroborates with the non�

hysteretic force measurements�

The benchmark experiment C shows that the force interaction between an atom�

ically de�ned W tip approaching an atomically �at Au surface acts over a range of

�� A �with distance scaling length �� A and that no sudden instabilities exist�

We �nd that strong adhesive forces exist at typical tunneling distances� Experiment

D provides high resolution force and tunneling data� that underpin the previous ob�

servation� In experiment B we con�rmed the same behaviour for a W�� tip which

had a much larger apex radius and was not atomically de�ned� Furthermore it ruled

�� SUMMARY ��

out that contaminations or structural e ects of the Au�� sample played a role�

With experiment A we found that stable� reproducible and unstable jump�to�contact

behaviour can indeed coexist� The key must lie in the identity of the tip� Pure

apex size e ects can be ruled out� Therefore the exact chemical identity and�or

crystallographic structure of the tip decide between the two types of behaviour�

None of the discussed models can explain the observed long scaling range� We

therefore conclude it is an inherent property of the W��Au�� contact� We

calculate that �� of the force originates from the �rst three layers� each contributing

an equal amount� Therefore the simple model that the force is dominated by the �rst

layer properties only is not generally valid� Secondly� we point out that there is a shift

between the position of the �rst layer of the tip and the center of force interaction

of the whole tip� Thirdly� using Chen�s model to establish a quantitative relation

between force and tunneling current� we extract reasonable values for the DOS of tip

and sample despite the complexity of the electronic structure and geometric shape of

our W�Au system�

Chapter �

Conclusion and Outlook

The goal of this thesis was to investigate the physical properties of an atomically

de�ned� metallic junction� A custom�made UHV system was used to measure si�

multaneously the interaction forces and the tunneling current between a tip and a

surface in the SPM type geometry� The force sensor features a sti spring constant

�t �� N�m in order to ensure junction stability throughout the measurement� how�

ever sub�nN resolution was readily achieved�

Tips were fabricated from polycrystalline W�Ir and single crystalline W�� wire

by means of electrochemical etching� Post�fabrication treatment �annealing and �eld

emission was performed in the UHV environment� The �nal shaping and analysis

was done with atomic resolution in�situ �eld ion microscopy �FIM� In particular the

analysis of ultra�sharp nanotips featuring an apex radius of �� A was discussed�

Several issues concerning the contamination rates of those tips were treated experi�

mentally� Theoretical calculations of the van der Waals and electrostatic forces were

performed� They indicated that for our sharp tips metallic adhesion forces dominate

at tip sample distances from some �� A up to contact�

The Au�� sample was prepared in UHV by sputtering and annealing� This

typically yielded atomically �at terraces of some �� A featuring the well�known

herringbone reconstruction as analyzed by STM�

Experiments with dull W tips �apex radius of some �� A� not atomically en�

gineered by FIM indicated that two types of behaviours can coexist� Upon close

��

��

approach of tip and sample the junction can become unstable and an atomic jump�

to�contact can occur� However it was also observed that the junction remains stable

over several approach�retraction cycles almost up to physical contact� Experiments

with atomically de�ned W tips� featuring an apex radius of � �A and terminating in

three atoms� showed that the stable behaviour prevails for a structurally and chem�

ically well�de�ned contact� It was demonstrated that even when approaching the

tip closer than the point of physical contact �i�e� indenting the surface� the precise

atomic arrangement of the tip apex would survive�

Consistently for well�de�ned contacts we found that the range over which the

metallic adhesion forces act is four times larger than expected from theoretical calcu�

lations �Rydberg scaling length � �A measured versus �� A predicted �� This can

be correlated to the observed stability of the junction� None of the available models

can explain this phenomenon� However� some of the consequences concerning the

imaging mechanisms for STM and AFM due this new material property have been

pointed out�

In order to gain more information about the conduction properties� similar ex�

periments should be performed where the whole occurring current range from nA to

mA can be measured� A corresponding logarithmic current to voltage ampli�er has

already been successfully employed for some preliminary studies� This should give

some more insight into the electronic properties of the tip�sample system�

The next step is to study the adhesion characteristics of di erent metals� Experi�

ments with an unde�ned Ir tip approaching a polycrystalline Ir sample �� indicated

that the force scaling length is around �� A� more consistent with theoretical pre�

dictions �� We have readily prepared Ir tips suitable for FIM� A projected�

enhanced sample preparation chamber will allow the preparation of a corresponding

sample� In particular� a scanning Auger instrument will provide detailed chemical

information about the sample surface�

Simultaneous acquisition of force and tunneling current during scanning have been

proven to yield chemical sensitivity �� With the precise knowledge of the force and

�� CHAPTER � CONCLUSION AND OUTLOOK

current characteristics it should be possible to achieve chemical contrast with high

lateral resolution of the surface�

Realistic ab inito simulations of the tip�sample junction will help to answer the

question for the origin of the observed long scaling length� Corresponding e orts have

been initiated ��

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Abstract - McGill Physicspeter/theses/schirmeisen.pdf · Abstract The metallic adhesion and...

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