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Fabrication of metallic nanostructures with ionsRibas Gomes, Diego

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Fabrication of metallic nanostructures with ions

Theoretical concepts and applications

PhD thesis

to obtain the degree of PhD at the University of Groningen on the authority of the

Rector Magnificus Prof. E. Sterken and in accordance with

the decision by the College of Deans.

This thesis will be defended in public on

Tuesday 9 October 2018 at 11.00 hours

by

Diego Ribas Gomes

born on 28 August 1985

in Ponta Grossa, Brazil

Supervisor

Prof. J. T. M. De Hosson

Co-supervisor

Dr. D. I. Vainchtein

Assessment committee

Prof. H. A. De Raedt

Prof. P. Rudolf

Prof. A. A. Turkin

Fabrication of metallic nanostructures with ions Theoretical concepts and applications

Diego Ribas Gomes

PhD thesis University of Groningen Zernike Institute PhD thesis series 2018-23 ISSN: 1570-1530 ISBN: 978-94-034-0925-2 (Printed version) ISBN: 978-94-034-0924-5 (Electronic version) Print: Ipskamp Printing The research presented in this thesis was performed in the Materials Science group of the Zernike Institute for Advanced Materials at the University of Groningen, the Netherlands. This work was funded by the Coordination for the Improvement of Higher Level Personnel (CAPES) and the Zernike Institute for Advanced Materials. Cover design by Diego Ribas Gomes. Engraving by Matthias Greuter (1620-1647) © Trustees of the British Museum.

CONTENTS

Introduction: flashback and look ahead on nano’s 1

1.1 References ......................................................................................................... 3

Experimental methods 5

2.1 Introduction to electron microscopy ............................................................... 5 2.2 Transmission Electron Microscopy ................................................................ 8 2.3 Illumination system ......................................................................................... 8 2.4 Interaction with specimen .............................................................................. 12 2.5 Quantitative X- Ray Microanalysis ............................................................... 24 2.6 Scanning Electron Microscopy ...................................................................... 26 2.7 Focused Ion Beam .......................................................................................... 28 2.8 Free-standing thin films ................................................................................ 32

2.8.1 Solid bulk films .................................................................................... 33 2.8.2 Nanoporous films ................................................................................ 34

2.9 References ...................................................................................................... 35

Electrochemical fabrication of nanoporous materials 41

3.1 Actuators .......................................................................................................... 41 3.2 Electrochemical nanofabrication .................................................................. 43

3.2.1 Anodized aluminum oxide (AAO) templates ..................................... 43 3.2.2 Templated electrodeposition of metals .............................................. 44

3.3 Experimental results and discussion ............................................................ 45 3.3.1 Commercial membranes ..................................................................... 45 3.3.2 Electrochemical deposition of nanowires .......................................... 46 3.3.3 The goal-structure ............................................................................... 49 3.3.4 Home-made AAO templates ................................................................ 51

3.4 Conclusion ...................................................................................................... 55 3.5 References ...................................................................................................... 56

Radiation Damage 59

4.1 Ion-solid interactions ..................................................................................... 59 4.2 Deep damage ................................................................................................... 65 4.3 Defect formation and diffusion ..................................................................... 69 4.4 Reaction rate theory ...................................................................................... 73 4.5 References ...................................................................................................... 76

Dense solid samples 81

5.1 Initial observations on Au cantilevers ............................................................ 81 5.2 Model of ion induced bending ....................................................................... 84

5.2.1 Point defect kinetics ............................................................................. 84 5.2.2 Analogy to thermoelasticity ................................................................ 87 5.2.3 Accumulation of interstitial clusters .................................................. 92 5.2.4 Gallium build-up ................................................................................. 95 5.2.5 Comparison with experiments ............................................................ 95

5.3 Aluminium cantilevers ................................................................................... 98 5.3.1 Kinetics of interstitial clusters ........................................................... 101 5.3.2 Comparison with experiments .......................................................... 108

5.4 Considerations about the model .................................................................. 110 5.4.1 Temperature increase due to irradiation ........................................... 110 5.4.2 Effects of dynamic composition change ............................................ 112

5.5 Conclusions ................................................................................................... 112 5.6 References ..................................................................................................... 113

Nanoporous specimens 116

6.1 Introduction ................................................................................................... 116 6.2 Experimental considerations ....................................................................... 117 6.3 Ion-induced coarsening ............................................................................... 120 6.4 Model of (IB)² for nanoporous gold ............................................................ 124

6.4.1 Kinetics of coarsening ........................................................................ 127 6.4.2 Young’s modulus of nanoporous Au .................................................129

6.5 Comparison with experiments ..................................................................... 132 6.6 Conclusions ................................................................................................... 142 6.7 References ..................................................................................................... 142

A compendium for bending of nanostructures: summary and outlook

147

7.1 Thesis summary ............................................................................................. 147 7.2 Samenvatting .................................................................................................149 7.3 Outlook ......................................................................................................... 150

7.3.1 Layered systems .................................................................................. 151 7.3.2 Size-dependent coarsening of ion-irradiated np-Au ........................ 155

7.4 Opportunities of Ion Beam Induced Bending or (IB) ² ..............................158 7.5 References...................................................................................................... 161

List of publications (thesis subject and related) 163

Acknowledgements 165

Curriculum Vitae 167

Introduction: flashback and look ahead on nano’s

“What is it that we humans depend on? We depend on our words... Our task

is to communicate experience and ideas to others. We must strive uninterruptedly

to extend the scope of our description, but in such a way that our messages do not

thereby lose their objectives or unambiguous character… We are suspended in

language in such a way that we cannot say what is up and what is down. The

word "reality" is also a word, a word which we must learn to use correctly.” [1]

As much as the clichés might hurt the readers' sensibility, in talking about

miniaturization there seems to be little way to escape mentioning Richard

Feynmann's lecture given at Caltech in 1959, "There is plenty of room at the

bottom" [2]. The revolutionary idea that a given material could be arranged at the

atomic level and give rise to novel properties and applications paved the way to the

rise of a field that still sounds fancy and intriguing 60 years later - the field of

nanoscience. Just a few years after that legendary lecture, Moore laid out his

famous law proposing that the number of components in integrated circuits would

not stop doubling every two years [3]. At the time of this writing, Moore's law has

just started to slow down and that is probably fair enough considering that inside

the laptop where this text is being typed, the processor transistors are mere 22

nanometers apart from each other. As the properties of materials at those very

small scales differ substantially from bulk systems, the exploration of all that "room

at the bottom" has required and continues to require theoretical and experimental

2 Chapter 1

studies that have the potential to revolutionize existing scientific fields and create

new ones.

With the reader's excuse for another paragraph of historical background, the

onset of the theme of this Thesis started before the episodes mentioned above. The

displacement of atoms caused by energetic irradiation - although with neutrons

instead of ions - was a problem for Eugene Wigner who was, during World War II,

in charge of a group tasked with the design and production of the first nuclear

reactors (incidentally, the project to which his group belonged was originally called

"Development of Substitute Materials" but was renamed posteriorly, for concealing

purposes, to the well-known name “Manhattan” – probably better so for the

material scientists!). The build-up of energy in the graphite moderators presented a

danger for certain types of reactors and became known for some time as "Wigner's

disease" [4], [5]. In the best spirit of Paracelsus, we try here to show that sola dosis

facit venenum: only the dose makes the poison, that is, that the displacements

induced by energetic impacts can very well be used to achieve beneficial effects, i.e.

accurate and reproducible bending of nanostructures.

The Thesis is structured as follows. Chapter 2 describes the experimental

techniques and procedures that were used for the synthesis and characterization of

the samples described in the chapters regarding ion-induced bending (Chapters 5

and 6 as explained below). Exploratory studies on nanofabrication using

electrochemical methods are described in Chapter 3. Those were inspired in the

pursuit of a structure with enhanced actuation performance by combining different

approaches described in the literature, i.e. maximization of surface area;

intercalating solid layers in between the high-surface actuation layers to improve

strain in the direction normal to the planes by Poisson effect and facilitating the

transport of charge by using aligned nanowires rather than random ligaments. In

that endeavor, the process of template electrodeposition of metals was explored

along with the fabrication of porous aluminium oxide templates. Due to the

experimental nature of this Chapter, the procedures are described in its text instead

of in Chapter 2.

A compilation of the theory on radiation damage in solids is presented in

Chapter 4 which provides the fundamental base for the approaches used in

Chapters 5 and 6. Those deal with the investigation of ion-induced bending of

dense solid and nanoporous cantilevers, respectively.

Introduction 3

Dense solid bulk Au and Al cantilevers were studied and presented different

bending behaviours under 30 keV Ga+ irradiation. While Au cantilevers bend

continuously towards the inciding ion beam with increasing fluence, Al cantilevers

bend initially away from the beam and reverse direction as irradiation continues. In

both cases, experimental results were succesfully reproduced by a reaction-rate

model based on the diffusion of crystallographic point defects and clusters. In the

case of nanoporous Au, the bending sensitivity to irradiation was greatly enhanced

in comparison to the solid bulk counterparts. The process was described in terms of

ion-induced coarsening of the structure top layers, which generates a volume

contraction responsible for the bending moment.

Chapter 7 wraps up the Thesis with an outlook on ion-induced bending

research. Preliminary experiments with bilayered cantilevers of Au and Pt

suggested a behaviour controlled by the thickness of the irradiated layer and the

stiffness of the underlying material. Deposition of a thin layer of Al2O3 onto solid Al

cantilevers markedly accentuated bending in the direction away from the beam and

increased the fluence at which reversion occurs. Furthermore, the densification of

ion-irradiated nanoporous gold cantilevers was observed to occur by different

means depending on the initial ligament size distribution.

1.1 References

[1] R. G. Newton, The Truth of Science: Physical Theories and Reality. Harvard University

Press, 1997.

[2] R. Feynman, ‘APS meeting lecture’, Caltech Engineering and Science, vol. 23, no. 5, pp.

22–36, 1960.

[3] G. E. Moore, ‘Cramming more components onto integrated circuits, Reprinted from

Electronics, volume 38, number 8, April 19, 1965, pp.114 ff.’, IEEE Solid-State Circuits

Society Newsletter, vol. 11, no. 3, pp. 33–35, Sep. 2006.

[4] E. P. Wigner, ‘Theoretical Physics in the Metallurgical Laboratory of Chicago’, Journal

of Applied Physics, vol. 17, no. 11, pp. 857–863, Nov. 1946.

[5] F. Seitz, ‘Radiation effects in solids’, Physics Today, vol. 5, no. 6, p. 6, 1952.

Experimental methods

“We become what we behold. We shape our tools and then our tools shape us.” [1]

2.1 Introduction to electron microscopy

As it goes without saying, microscopy in the field of materials science is

devoted to linking microstructural observations to properties. However, the actual

linkage between the microstructure studied by microscopy on one hand and the

physical property of a material on the other hand is almost elusive. The reason is

that various physical properties are determined by the collective behavior of

moving defects rather than by the behavior of a single stationary defect. For

instance, there exists a vast but also bewildering amount of electron microscopy

analyses concerned with post-mortem observation of ex-situ deformed materials,

which try to link observed patterns of defects to the mechanical property. However,

in spite of the enormous efforts which have been put in both theoretical and

experimental work since the theoretical concept of a crystal dislocation was

introduced in 1934, a clear physical picture that can predict even one simple stress-

strain curve based on these microscopy observations is still lacking. In fact there

does not exist an easy and unique back transformation from microscopy

observations to properties.

There are at least three reasons which hamper a straightforward correlation

between microscopic structural information and materials properties, both from

fundamental and practical viewpoints. First, in materials we are facing non-

6 Chapter 2

equilibrium effects. Defects determining the physical performance are usually not

in thermodynamic equilibrium and their behavior is very much non-linear. Non-

linearity and non-equilibrium are both tough problems in materials physics and in

fact unsolved. Second, metrological considerations of quantitative electron

microscopy of materials pose very critical questions to the statistical significance of

the electron microscopy observations. In particular, in situations where there is

only a small volume fraction of defects present or where there is a very

inhomogeneous distribution, statistical sampling may be a serious problem. Third,

even when statistical sampling is adequate, still the physical property might be

determined, not by its mean value, say grain size, but by the extremes, e.g. in a

nanostructured metallic material with many nano-grains but still having one

singular big grain, macroscopic yielding is determined by the local plasticity in that

largest grain and not by the many nano-sized grains present! Therefore statistical

averaging of grain-size distributions is not the right thing to do when explaining the

onset of plasticity in metallic systems. As a consequence, do not only magnify to the

highest point-point resolution in TEM - which is quite popular these days- but also

de-magnify so as to clarify and not falsify the essentials in the structure-property

relationship.

Electron microscopy is the interaction between a plane-wave (wave vector is

very large because of picometer wavelength) and an object. The wave-like

characteristics of electrons that are essential for electron microscopy were first

postulated in 1924 by Louis de Broglie (in fact in his PhD thesis [2]! , Nobel Prize in

Physics 1929), with a wavelength far less than visible light. In the same period

Busch revealed that an electromagnetic field might act as a focusing lens on

electrons [3]. Subsequently, the first electron microscope was constructed in 1932

by Ernst Ruska. For his research, he was awarded, much too late of course, in 1986

the Nobel Prize in Physics together with Gerd Binnig and Heinrich Rohrer who

invented the scanning tunneling microscope. The electron microscope opened new

horizons to visualize materials structures far below the resolution reached in light

microscopy. The most attractive point is that the wavelength of electrons are much

smaller than atoms and it is at least theoretically possible to see details well below

the atomic level.

However, currently it is impossible to build transmission electron microscopes

with a resolution limited by the electron wavelength, mainly because of

Experimental methods 7

imperfections of the magnetic lenses. In the middle of the 70's the last century

commercial TEMs became available that were capable of resolving individual

columns of atoms in crystalline materials. High voltage electron microscopes, i.e.

with accelerating voltages between 1 MV and 3 MV have the advantage of shorter

wavelength of the electrons, but also radiation damage increases. After that period

HRTEMs operating with intermediate voltages between 200 kV – 400 kV were

designed offering very high resolution close to that achieved previously at 1 MV.

More recently, developments are seen to reconstruct the exit wave (from a

defocus series) and to improve the directly interpretable resolution to the

information limit. During the last two decades, electron microscopy has witnessed

a number of innovations that enhanced existing approaches and introduced

qualitatively new techniques. One of the most important novel technologies is

aberration correction. Correction of spherical aberration Cs has been demonstrated

by Haider et al [4]. In the years that followed, this hexapole corrector was applied

to various materials science problems [5]–[7]. A quadrupole/octopole corrector

was developed and applied by Dellby et al. [8] for scanning transmission electron

microscopy (STEM) mode. Since then, aberration correction has been used to help

solve various material science problems [9]–[11]. Recently, correction of chromatic

aberration has been demonstrated [12] and successfully applied to improve

resolution in energy-filtered TEM (EFTEM) by a factor of five or so. Furthermore,

there has been significant progress in EELS, resulting in improved energy

resolution (monochromator) and a larger field of view for electron-spectroscopic

[13] and energy-filtered imaging [14]. For a review reference is made to [15].

Elastically scattered electrons generate the basis of the image formation in

HRTEM and they are the predominant fraction of the transmitted electrons for

small sample thickness (<15 nm). In contrast, the thicker the sample the more

electrons become inelastically scattered and this must be prevented as much as

possible, because they contribute mostly to the background intensity of the image.

Therefore, the thinner the specimen (≤15 nm) the better the quality of the HRTEM

images. The inelastic scattered electrons can be removed by inserting an energy

filter in the microscope between specimen and recording device. In the following

section on image formation, only the elastic scattered electrons are considered. The

main technique for detailed examination of the defect structure of nanoligaments

8 Chapter 2

in our work concerns transmission electron microscopy and scanning electron

microscopy.

Here we present a concise review for non-experts, without going into every

detail. This part is based on summaries that were also presented in several reviews

[16], [17] and by former PhDs of our MK group, in particular by Bas Groen, Patricia

Carvalho, Wouter Soer, Zhenguo Chen, Sriram Venkatesan, Stefan Mogck, Mikhail

Dutka and Sergey Punzhin [18]–[25].

2.2 Transmission Electron Microscopy

A schematic picture of a TEM is shown in Figure 2.1a. A transmission electron

microscope consists of an illumination system, specimen stage and imaging system,

analogous to a conventional light microscope. Several textbooks and reviews have

been written on the subject of (high resolution) microscopy, sadly with different

notation conventions. This chapter adopts the notation used in [26], [27] Spence

[28] has presented a more in-depth description of imaging in HRTEM theory.

Williams and Carter [29] have written a very inspirational textbook on general

aspects of electron microscopy. In our work a JEOL 2010F TEM (FEG, 200kV) was

used for atomic structure observations and EDS analysis. For a textbook on theory

behind elastic and inelastic scattering processes in TEM reference is also made to

[30].

2.3 Illumination system

Electrons are generated in an electron gun, accelerated towards the anode and

focused at the specimen with condenser lenses. High resolution TEM requires

planar coherent electron waves, since high-resolution micrographs are formed by

phase contrast. For elemental analysis, it is also important to have the possibility to

focus the electron beam within a diameter (FWHM) of the order of 1 nm to

determine chemical compositions in the nanometer range. Several demands must

be fulfilled: high brightness, small source size and little energy spread of the

electrons.

Experimental methods 9

Figure 2.1 – (a) Cross section of a basic TEM. Simplified ray diagram showing

the two basic operations modes of the TEM. (b) Diffraction pattern mode (c)

Imaging mode. Figures adapted from Refs. [29], [31].

(a)

(b) (c)

10 Chapter 2

The brightness of the beam is an important parameter and is defined as

follows:

I

BA

, (2.1)

i. e. the brightness value B is related to the electron current I emitted from the area

A (which also determines the spatial coherency) into the spatial angle Ω. The

conventional way to generate electrons is to use thermionic emission. Any material

that is heated to a high enough temperature will emit electrons when they have

enough energy to overcome the work function. In practice this can only be done

with high melting materials (such as tungsten) or low work function materials like

LaB6. Richardson’s law describes thermionic emission as a function of the work

function W and temperature T:

2 exp

WJ CT

kT

(2.2)

with the current density J at the tip and C the so-called Richardson-Dushman's

constant depending on the material used for the tip. In electron microscopes

tungsten filaments were most commonly used until the introduction of LaB6. LaB6

sources have the advantages of a lower operating temperature that reduces the

energy spread of the electrons and increases the brightness.

Another way of extracting electrons from a material is to apply a high electric

field to the emitter that enables the electrons to tunnel through the barrier.

Sharpening the tip may enhance the electric field since the electric field at the apex

of the tip is inversely proportional to the radius of the apex:

ER

V

k , (2.3)

with k a correction factor for the tip geometry (usually around 2). The advantage

of this cold field emitter gun (cold FEG) is that the emission process can be to done

at room temperature, reducing the energy spread of the electrons. The small size of

the emitting area and the shape of the electric field results in a very small (virtual)

source size in the order of nanometers with a brightness that is three orders of

magnitude higher than for thermionic sources. It is thus possible to focus the beam

to a very small probe for chemical analysis at an atomistic level or to fan the beam

Experimental methods 11

to produce a beam with high spatial coherence over a large area of the specimen.

The disadvantages of this type of emitter are the need for (expensive) UHV

equipment to keep the surface clean, the need for extra magnetic shielding around

the emitter and the limited lifetime. For electric fields E > 107 V/cm the electron

current density J can be described according the modified Fowler-Nordheim

relation:

6 7 3/2

2

2

1.54 10 6.8 10 ( )exp

( )

v y WJ E

EWt y

, (2.4)

where J is the field-emitted current density in A/m2, E is the applied electric field at

the tip, and W is the work function in eV. The functions v and t of the variable

4 1 23.79 10y E depend weakly on the applied electric field and have been

tabulated in literature [32]. In our FEG-TEM it is therefore possible to focus the

beam to a very small probe for chemical analysis at a sub-nanometer range and

produce a beam with high spatial coherence over a large area of the specimen. The

small (virtual) source size reaches values for the brightness in the order of B = 1011

to 1014 Am-2sr-1 with an energy spread of 0.2–0.5 eV compared with ~ 109 Am-2sr-1

and an energy spread of 0.8–1 eV for thermionic emission.

Some of these disadvantages of cold FEG emitters can be circumvented by

heating the emitter to moderate temperatures (1500C) in the case of a thermally

assisted FEG or by coating the tip with ZrO2 which reduces the work function at

elevated temperatures and keeps the emission stable (Schottky emitter). For

thermal assisted FEGs the work function is often reduced by coating the tip with

ZrO2 which keeps the emission stable (Schottky emitter). This increases the energy

spread of the emitted electrons by about a factor of 2 and some reduction of the

temporal coherency compared with cold FEGs. The Schottky emitter is widely used

in commercial FEG-TEMs, because of the stability, lifetime and high intensity.

Table 2.1 gives an overview of the technical data of the different electron sources.

12 Chapter 2

Table 2.1 – Properties of different electron sources [33]

Parameter Tungsten LaB6 Cold FEG Schottky Heated

FEG

Brightness, A/m2sr (0.3-2)109 (3-20)109 1011-1014 1011-1014 1011-1014

Temperature, K 2500-3000 1400-2000 300 1800 1800

Work function, eV 4.6 2.7 4.6 2.8 4.6

Source size, μm 20-50 10-20 <0.01 <0.01 <0.01

Energy spread, eV 3.0 1.5 0.3 0.8 0.5

Transmission electron microscopes operate generally between 80 kV and

1000 kV meaning that the velocity of the electron includes relativistic effects. This

must be taken into account applying the De Broglie relationship to calculate the

wavelength:

1/2

00 0 2

0

2 12

eEh m eE

m c

(2.5)

For 400 kV electrons = 1.64 pm which is much smaller than the resolution

of any electron microscope because the resolution is limited by aberrations of the

objective lens and not by the wavelength of the electrons. The electron beam is now

focused on the specimen with the condenser lenses and aligned using several

alignment coils. The function of the condenser lens system is to provide a parallel

beam of electrons at the specimen surface. In practice this is not possible and the

beam always possesses a certain kind of convergence when imaging at high

resolution, usually in the range of 1 mrad for LaB6 emitters and 0.1 mrad for FEGs.

2.4 Interaction with specimen

After entering the specimen most of the electrons are scattered elastically by

the nuclei of the atoms in the specimen. Some electrons are inelastically scattered

by the electrons in the specimen. Compared to X-ray or neutron diffraction the

interaction of electrons with the specimen is huge and multiple scattering events

are common. For thick specimens at lower resolutions an incoherent particle model

can describe the interaction of the electrons with the specimen. However, with thin

Experimental methods 13

specimens at high resolution this description fails because the wave character of the

electrons is then predominant. The electrons passing the specimen near the nuclei

are somewhat accelerated towards the nuclei causing small, local, reductions in

wavelength, resulting in a small phase change of the electrons. Information about

the specimen structure is therefore transferred to the phase of the electrons.

After the (plane) electron wave strikes the specimen a part of the electrons

experience a phase shift. The essential part of image formation in TEM is the

transformation of the phase shift stored in the exit wave into amplitude

modulation, and therefore into visible contrast. With the assumption that the

specimen is a pure phase object the phase shift can be described with the image

function:

( )( ) i r

image r e (2.6)

For sufficiently thin objects the phase can be considered as weak ϕ(𝑟) ≪ 1 and

( )image r can be approximated to first order: ( ) 1 ( )image r i r . r is the

projected potential distribution in the materials slice, averaged over the electron

beam direction. The technique of HRTEM has a base in the technique of phase

contrast microscopy, introduced by Zernike [34] for optical microscopy in the

physics department of our own university, the University of Groningen. In 1953 he

received the Nobel Prize in Physics for this invention which made an undisputed

immense impact, in particular into bio- and medical sciences. The principle and

very basic problem in microscopy, both in optical and electron microscopy, is to

derive information about the object we are interested in. The object is defined by

amplitude and phase and to retrieve information about ( )object r from the intensity

of the image2

( )image r is a very complex. Even in an ideal but non-existing

(because of aberrations in any optical system in practice) microscope the intensity

of the image is exactly equal to the intensity of the object function but still phase

information in the intensity is lost.

Zernike had a brilliant and at the same time an utmost simple idea, i.e. most

probably a prerequisite of any Nobel Prize. He realized that if the phase of the

diffracted beam can be shifted over 2 it is as if the image function has the form

exp ( ) 1 ( )image r r and in fact the weak phase object acts as an

14 Chapter 2

amplitude object, i.e. the intensity observed, i.e. I= 2

( ) 1 2 ( )image r r , can be

connected to ( )r . High-resolution TEM imaging is based on the same principles.

Phase-contrast imaging derives contrast from the phase differences among the

different beams scattered by the specimen, causing addition and subtraction of

amplitude from the forward-scattered beam. Components of the phase difference

come from both the scattering processes itself and the electron optics of the

microscope. Just because of a fortunate balance between spherical aberration and

defocus we can perform high-resolution TEM with atomic resolution as will be

shown in the following.

A possibility to visualize the phase contrast in TEM was introduced by

Scherzer. Perfect lenses show no amplitude modulation, but imaging introduces an

extra phase shift between the central beam and the beam further away from the

optical axis of the objective lens (deviation from the ideal Gaussian wave front).

Deviations from the ideal Gaussian wave front in lenses is known as spherical

aberration. For particular frequencies the phase contrast of the exit wave will be

nearly optimally transferred into amplitude contrast. Therefore the observed

contrast in TEM micrographs are mainly controlled by the extra phase shift of the

spherical aberration and the defocus. The influence of the extra phase shift on the

image contrast can be taken into account by multiplying the wavefunction at the

back focal plane with the function describing the extra phase shift as a function of

the distance from the optical axis. The lenses can be conceived cylindrical

symmetric, and will be represented as a function of the distance of the reciprocal

lattice point to the optical axis 1/22 2 U u v , where u and v are the angular

variables in reciprocal space. The extra phase factor ( )U depends on the

spherical aberration and defocus [28]:

2 3 4( ) 0.5 sU fU C U (2.7)

with f the defocus value and sC Cs the spherical aberration coefficient. The

function that multiplies the exit wave is the so-called transfer function ( )U :

( )( ) ( ) i UU E U e . (2.8)

Experimental methods 15

For the final image wave after the objective lens, assuming a weak phase

object:

1( ) ( ) ( ) ( ) ( )image object objectr r U r r

, (2.9)

where and 1 are symbols to represent the Fourier transform and inverse

Fourier transform, respectively. In fact ( )object r is the electron diffractogram in

the back focal plane of the objective lens. As said before because of a fortunate

balance between spherical aberration and defocus, i.e. with the transfer function

( )r in Eq. (2.9) going close to unity, information about the object can be obtained

from the image. After the multiplication of Eq. (2.9) with its complex conjugate and

neglecting the terms of second order and higher the image formation results in:

1( ) 1 2 ( ) [ ( )sin( ( ))]imageI r r E U U . (2.10)

Under ideal imaging conditions the wave aberration must be /2 or

sin( ( ))U = 1 for all spatial frequencies U . Therefore sin( ( ))U is called the

contrast transfer function (CTF). Only the real part is considered since the phase

information from the specimen is converted in intensity information by the phase

shift of the objective lens. In the microscope an aperture is inserted in the back

focal plane of the objective lens, only transmitting beams to a certain angle. This

can be represented by an aperture function A U which is unity for 0U U and

zero outside this radius. When ( )U is negative the atoms in the specimen would

appear as dark spots against a bright background and vice-versa. For ( ) 0U no

contrast results. An ideal behaviour of ( )U would be zero at 0U (very long

distances in the specimen) and 0U U (frequencies beyond the aperture size) and

large and negative for 00 U U .

The contrast of a high-resolution image depends strongly on the microscope

settings and parameters. In practice not all the information in ( )U is visible in the

image. This is caused by electrical instabilities in the microscope causing a spread

of focus because of the chromatic aberration of the objective lens, resulting in

damped higher frequencies. Mechanical instabilities and energy loss due to

16 Chapter 2

inelastic scattering of the electrons by the specimen also contribute to the spread in

defocus. The inelastic scattered electrons contributing to the image can be removed

by inserting an energy filter in the microscope between the objective lens and the

image recording media. Another factor that damps the higher frequencies is the

beam convergence. Since the electron beam has to be focussed on a small spot on

the specimen there is some convergence of the beam present. This also affects the

resolution since the specimen is now illuminated from different angles at the same

time.

These effects which affect the resolution can be represented by multiplying

sin( ( ))U by the damping envelopes E and E which represent the damping by

the convergence and spread in defocus respectively:

2 2 2 412

22 2 2 2 2

( ) exp ,

( ) exp .s

E U U

E U U f C U

(2.11)

The resulting contrast transfer function (CTF) for the microscope we used is

plotted in Figure 2.2 (bottom) with the damping envelopes E and E . For higher

frequencies the CTF is now damped and approaching zero. It becomes clear that

defining a resolution for the HRTEM is not obvious.

Experimental methods 17

0 2 4 6 8 10 12

-1.0

-0.5

0.0

0.5

1.0

E

E

sin((U))

Contr

ast,

a.u

.

Scattering vector, U, nm-1

EEsin((U))

0 2 4 6 8 10 12

-1.0

-0.5

0.0

0.5

1.0

Contr

ast,

a.u

.

Scattering vector, U, nm-1

E

E

EEsin((U))

Figure 2.2 – Contrast transfer functions and damping envelopes of the JEOL

4000 EX/II (top) and JEOL 2010F (bottom) at optimum defocus of 47 and 58

nm, respectively. The highly coherent electron source used in the 2010F, a FEG,

is apparent from the many oscillations in the CTF of the 2010F.

Several different resolutions can be defined as stated by O’Keefe [35] :

(1) Fringe or lattice resolution: This is related to the highest spatial frequency

present in the image. In thicker crystals second-order or non-linear

interference may cause this. Since the sign of sin((U)) is not known there

18 Chapter 2

is in general no correspondence between the structure and the image. This

resolution is limited by the beam convergence and the spread in defocus.

(2) Information limit resolution: This is related to the highest spatial

frequency that is transferred linearly to the intensity spectrum. These

frequencies may fall in a passband, with blocked lower frequencies. Usually

this resolution is almost equal to the lattice resolution. A definition used is

that the information limit is defined as the frequency where the overall

value of the damping envelopes corresponds to 2e (e.g. the damping is 5%

of the CTF intensity).

(3) Point resolution. This is the definition of the first zero point in the contrast

transfer function, right hand side of the Scherzer band. For higher spatial

frequencies, the image contrast and thus the structure cannot be

unambiguously interpreted. The optimal transmitted phase contrast is

defined as a Scherzer defocus 1/2

4 3 sC and the highest transferred

frequency is equal to 1 4 3/41.5 sC .

In Figure 2.2 the CTFs of the JEOL 4000EX and JEOL 2010F at optimum

defocus are plotted with the damping envelopes. The corresponding electrical-

optical properties are listed in Table 2.2. For the two microscopes with a different

illumination system, it is clearly visible that with the JEOL 2010F a rapid

oscillation of the CTF occurs. These oscillations arise because the spatial coherence

is higher for the 2010 F (spread of defocus and in particular beam convergence is

smaller) than for the 4000 EX/II. Correspondingly, the information limit of the

JEOL 2010F is better than of the 4000EX/II. For the JEOL 2010F the information

limit is a factor 2 higher compared with the point resolution. For microscopes with

higher operating voltages, a FEG will not significantly increase the information

limit, because the higher the voltage the larger the energy spread of the electrons

and the damping envelope is limited by the spread of defocus, instead of beam

convergence. For lower (≤200 kV) voltage TEMs the situation is clearly more

favorable and a FEG thus significantly improves the information limit. With higher

voltage instruments the higher acceleration voltage increases the brightness of the

source and the damping envelope is limited by the spread of defocus. The spherical

aberration of the objective lens can be lowered but generally at the expense of a

decrease in tilt capabilities of the specimen. It is possible to compensate sC by a set

Experimental methods 19

of hexapole lenses as suggested by Scherzer [36] in 1947 but it was only feasible

recently due to the complex technology involved. Haider demonstrated a sC

corrected 200 kV FEG microscope [37] in which sC was set at 0.05 mm to reach an

optimum between contrast and resolution. The point resolution of this microscope

was now equal to the information limit of 0.14 nm. Successful application of this

technology would put the limiting factors of the microscope at the chromatic

aberration and mechanical vibrations that currently limit the resolution around

0.1 nm.

Table 2.2 – Technical data of JEOL 4000EX and JEOL 2010F microscopes

Parameter JEOL 4000EX/II JEOL 2010F

Emission LaB6

(filament)

FEG

(Schottky emitter)

Operating voltage, 0E , kV 400 200

Spherical aberration coefficient, sC , mm 0.97 1.0

Spread of defocus, , nm 7.8 4.0

Beam convergence angle, , mrad 0.8 0.1

Optimum defocus, f , nm –47 –58

Information limit, nm 0.14 0.11

Point resolution, nm 0.165 0.23

For a correct interpretation of the structure the specimen has to be carefully

aligned along a zone axis, which is done with the help of Kikuchi patterns and an

even distribution of the spot intensities in diffraction. The misalignment of the

crystal is in this way reduced to a fraction of a mrad. Beam tilt has a more severe

influence on the image because the tilted beam enters the objective lens at an angle

causing phase changes in the electron wave front. To correct the beam tilt the

voltage centre alignment is used by which the acceleration voltage is varied to find

the centre of magnification that is then placed on-axis. This alignment might not be

correct due to misalignments in the imaging system after the objective lens. For a

better correction of the beam-tilt the coma-free alignment procedure is necessary.

This is done by varying the beam tilt between two values in both directions and

optimizing the values until images with opposite beam tilts are similar. This

20 Chapter 2

procedure is only practically feasible with a computer-controlled microscope

equipped with a CCD camera and is not used here; instead, the voltage centre

alignment is used which could result in some residual beam tilt.

Besides high-resolution transmission electron microscopy ‘conventional’

transmission electron microscopy has been employed in this thesis work trying to

unravel the character of the defects after using Focused Ion Beam methods. Here,

to interpret electron micrographs it is essential to understand the factors that

determine the intensities of Bragg-diffracted beams. Various approaches can be

followed, i.e. ranging from the kinematical theory to the dynamical theory of

electron diffraction. The former is based on the assumptions that only elastic

scattering takes place (hence no absorption) and that an electron can be scattered

only once, whereas the latter also allows for interaction between the diffracted

beams. This interaction is particularly well-defined when the crystal is tilted in such

a way that, besides the direct beam, only one beam is strongly diffracted (i.e. gs

>>0 for the other reflections). As the transmitted wave with amplitude 0 z

propagates through the crystal, its amplitude is depleted by diffraction and the

amplitude zg of the diffracted beam increases, i.e. a dynamical interaction

between 0 z and zg exists. If we assume that sg is parallel to the electron

beam, the interaction can be described by the following pair of coupled differential

equations, known as the Howie-Whelan equations:

2

0

0

is zd i ie

dz

gg

g

g

(2.12)

and

20

0

0

is z

g

d i ie

dz

g

g

, (2.13)

where sg = |sg| and ξ0 and ξg are the extinction distances for the direct and

diffracted waves, respectively. The extinction distance is a characteristic length

scale determined by the atomic number of the material, the lattice parameters and

the wavelength of the electrons, it typically lies between 10 and 100nm. The above

equation shows that the change in 0 z as a function of depth z is the sum of

Experimental methods 21

forward scattering and scattering from the diffracted beam, taking into account a

phase change of π/2 caused by the scattering. Solving the previous 2 equations for

zg gives:

2 2g g g2 2

gg g

sin 11

i ts

s

, (2.14)

where t is the thickness of the crystal. Accordingly, the intensity of the diffracted

beam becomes:

2

2eff

2 2g eff

sin tsI

s

g g , (2.15)

where seff is an effective value of sg defined by 1/22 2 effs s g g

. In fact, by

replacing seff by sg , the intensity according to the kinematical approximation is

found. Absorption can be included in the dynamical theory by adding appropriate

terms to both ξ0 and ξg. Mathematically speaking, absorption is included simply by

allowing the arguments of the sines and cosines to become complex.

Dislocations, dislocation loops or stacking faults give rise to contrast because

they locally distort the lattice and thereby change the diffraction conditions. If the

distortion is given by a displacement field R, i.e.

0

0

exp 2 g

d i ii s z

dz

g

g

g

g R (2.16)

In order for a dislocation to contribute to contrast formation, the dot product

g·R must be nonzero. A screw dislocation in an isotropic elastic medium has a

displacement field parallel to its Burgers vector, and therefore produces no contrast

when g·b = 0. General dislocations have a displacement field with more

components; their image contrast also depends on g·be and g·(bu), where be is

the edge component of the Burgers vector and u is a unit vector along the

dislocation line. In practice however, only very faint contrast occurs when g·b = 0

but g·be 0 and g·(bu) 0. Therefore, the “invisibility criterion” g·b = 0 is used

commonly to determine Burgers vectors of dislocations in elastically isotropic

22 Chapter 2

solids. The determination of a Burgers vector involves finding two reflections g1

and g2 for which the dislocation is invisible, so that b is parallel to g1g2.

The situation where only one beam zg is strongly diffracted is referred to

as a two-beam condition. This type of diffraction is widely used in conventional

TEM of crystalline materials because the contrast is well defined and the Burgers

vectors of the dislocations can be determined as described above. By using the

objective aperture in the microscope, either of the two beams can be selected to

form an image and accordingly, two imaging modes may be distinguished: bright

field (BF) when the direct beam 0 z is used, and dark field (DF) when the

diffracted beam zg is used. Generally, the diffracted beams do not coincide with

the optical axis of the microscope and consequently the DF image will not be of

maximum quality due to spherical aberration. To overcome this problem, the

incident beam is normally tilted in such a way that the desired diffracted beam

passes along the optical axis.

While two-beam conditions produce high contrast of dislocations, the

resolution at which these defects are resolved is not optimal since the lattice planes

around the dislocations are distorted over a relatively large area. To obtain the

maximum resolution, the crystal should be tilted slightly further by such an amount

that the exact Bragg condition is only fulfilled within a small region near the

dislocation. In this way, a high-resolution image is obtained in which the

dislocation shows up as a bright line. This technique is referred to as weak-beam

imaging. The deviation from the exact Bragg condition for perfect crystal is given

by sg as mentioned above and can be determined accurately by the relative position

of the so-called Kikuchi pattern with respect to the diffraction pattern. The origin of

the Kikuchi pattern lies in the elastic re-scattering of inelastic scattered electrons as

further explained in the following section.

The width of a dislocation image is approximately 0.3ξg, i.e. several tens of

nanometers in conventional bright- and dark-field imaging. This width can be

detrimental to the observations of dislocations that are very closely spaced. Since

the effective extinction distance decreases for increasing deviation away from the

Bragg condition, the width of a dislocation image can be reduced to values in the

order of 1 to 5 nm in weak-beam imaging.

Experimental methods 23

At lower magnifications, the average crystal orientation may vary considerably

within the observed area, so that only a small area of the specimen can be set up in

two-beam condition. This is especially relevant in specimens that have been

deformed prior to preparation. In these cases, it is often convenient to orient the

specimen close to a zone axis, so that many reflections are weakly excited,

independently of small changes in orientation. By using the direct beam for

imaging, the dislocation structure can be imaged with good contrast over a

relatively large area. However, the contrast from individual dislocations is generally

smaller than in two-beam condition and not well defined since it results from many

different reflections.

Besides dislocations also dislocation loops appear in this Thesis, generated by

radiation damage. In the past years the nature of small point defect clusters has

been analyzed successfully by means of the black-white contrast figures produced

under dynamical two-beam conditions. In particular, this technique has been

applied to dislocation loops which are so small that their geometrical shapes are

not resolvable under dynamical two-beam conditions or under other strong beam

conditions [38]–[40].

From the black-white contrast the following properties of small loops can in

principle be determined: (a) the Burgers vector, (b) the normal n of the loop plane,

(c) the type of the loop (differentiating between loops of vacancy and interstitial

type). For the assessment of (d), the diameters and (e), the number densities, the

so-called kinematical two-beam conditions were mainly applied. However, there

are a number of experimental difficulties which sometimes complicate the

application of the black-white technique. Cockayne et al [41], [42] have shown that

imaging with a weakly excited beam (weak-beam technique, WB) has considerable

advantages when high resolution is attempted. For instance, Häussermann has

shown that this method, applied to small defect clusters, facilitates the

differentiation between isolated single loops and clusters of loops lying closely

together (multiple loops). These multiple loops are not resolvable under strong-

beam conditions. For a theoretical study of the black-white contrast figures on

electron micrographs produced by small dislocation loops under dynamical two-

beam conditions reference is made to [43].

24 Chapter 2

2.5 Quantitative X- Ray Microanalysis

Quantitative X-ray microanalysis was performed using a JEOL 2010F

analytical transmission electron microscope. Additionally to the operation in the

TEM-mode (parallel incidence of the electron beam) there exists also the possibility

to operate in X-ray energy-dispersive spectrometry (EDS) and nano-beam-

diffraction (NBD) mode. In the NBD-mode the convergences angle α of the beam

incidence is smaller, whereas in the EDS-mode these angles are larger. In the latter

case, the diameter of the electron probe can be reduced to approximately 0.5 nm

(FWHM) and thus enables very localized chemical analysis. The NBD-mode will be

not considered in the present work.

In EDS the inelastic scattered electrons are essential. In general, the highly

accelerated primary electrons are able to remove one of the tightly bound inner-

shell electrons of the atoms in the irradiated sample. This “hole” in the inner-shell

will be filled by an electron from one of the outer-shells of the atom to lower the

energy state of the configuration. After recombination each element emits its

specific characteristic X-rays or an Auger electron. The electron of the incident

beam also interacts with the Coulomb field of the nuclei.

These Coulomb interactions of the electrons with the nuclei lower their

velocity and produce a continuum of Bremsstrahlung in the spectrum. The results

is that the characteristic X-rays of a detected element in the specimen appear as

Gaussian shaped peaks on top of the background of Bremsstrahlung. This

background of the EDS spectrum must be taken into account in quantitative

analysis.

A Si(Li)-detector is mounted between the objective pole pieces with a ultra-

thin window in front of it. This has the advantage that X-rays from light elements

down to boron can be detected. The EDS unit in an analytical TEM has three main

parts: the Si(Li)-detector, the processing electronics and the multi-channel

analyzer (MCA) display. After the X-rays penetrate the Si(Li)-detector a charge

pulse proportional to the X-ray energy will be generated that is converted into a

voltage. This signal is subsequently amplified through the field-effect transistor.

Finally, a digitized signal is stored as a function of energy in the MCA. After manual

subtraction of the background from the X-ray dispersive spectra the quantification

of the concentration iC (i = A,B) of elements A and B can be related to the

Experimental methods 25

intensities iI in the X-ray spectrum by using the Cliff-Lorimer [31] ratio technique

in the thin-film approximation:

A AAB

B B

C Ik

C I . (2.17)

For the quantification, the Cliff-Lorimer factor kAB is not a unique factor and

can only be compared under identical conditions (same: accelerating voltage,

detector configuration, peak-integration, background-subtraction routine). The

ABk factor can be user-defined or theoretical ABk values are stored in the library of

the quantification software package [44]. With modern quantification software, it is

possible nowadays to obtain an almost fully automated quantification of X-ray

spectra using the MCA system. The intensities IA and IB are measured, their

background is subtracted and they are integrated. For the quantification the Kα-

lines are most suitable, since the L- or M-lines are more difficult due to the

overlapping lines in each family. However, highly energetic Kα-lines (for energies >

20 keV non-linear effects in the Si(Li)-detector) should be excluded for

quantification in heavy elements and L- or M-lines must be taken into account

instead. The possible overlapping peaks in X-ray spectra must be carefully

analyzed. Poor counting statistics, because of the thin foil can be a further source of

error in particular for detection of low concentrations. A longer acquisition time

increases the count rates (better statistics), but this may have the drawback of

higher contamination and sample drift during the recording of the spectra. Sample

drift is extremely disadvantageous in experiments where spatial resolution is

essential.

The correction procedure in bulk microanalysis is often performed with the

ZAF correction; Z for the atomic number, A for absorption of X-rays and F for

fluorescence of X-rays within the specimen. For thin electron-transparent

specimen the correction procedure can be simplified, because the A- and F factors

are very small and only generally the Z-correction is necessary. All acquisitions of

the present work were performed using a double-tilt beryllium specimen holder.

The beryllium holder prevents generation of detectable X-rays from parts of the

specimen holder. A cold finger near the specimen (cooled with liquid nitrogen)

reduces hydrocarbon contamination at the surface of the specimen.

26 Chapter 2

2.6 Scanning Electron Microscopy

The Scanning Electron Microscope (SEM) is a type of electron microscope

that study microstructural and morphological features of the sample surface by

scanning it with a high-energy electron beam in a raster scanning pattern. The

electrons interact with the sample matter producing a variety of signals that

contain information about the sample surface topography, composition and other

properties.

The first SEM image was obtained by Max Knoll, who in 1935 obtained an

image of silicon steel showing electron channeling contrast [45]. The first true

scanning electron microscope, i.e. with a high magnification by scanning a very

small raster with a demagnified and finely focused electron beam, was produced by

von Ardenne a couple of years later [46]. The instrument was further developed by

Sir Charles Oatley and his postgraduate student Gary Stewart and was first

marketed in 1965 by the Cambridge Instrument Company as the “Stereoscan”.

The signals produced by an SEM include secondary and back-scattered

electrons (SE&BSE), characteristic X-rays, cathodoluminescence (light), specimen

current and transmitted electrons. SE detector is the most common one in SEM. As

shown by the schematic Figure 2.3, in an FEI /Philips XL-30 FEG-SEM (Field

Emission Gun) of the Applied Physics – Materials Science group electrons are

generated by the field emission gun using a high electrostatic field. They are

accelerated with energies between 1 keV and 30 keV down through the column

towards the specimen. While the magnetic lenses (condenser and objective lenses)

focus the electron beam to a spot with a diameter of approximately 10 nm, the

scanning coils sweep the focused electron beam over the specimen surface. If the

microscope is operated in the backscattered mode, the result is a lateral resolution

on the order of micrometers. The number of back-scattered electrons produced is

proportional to the atomic number of the element bombarded. The result is that

material with a high(er) atomic number produces a brighter image. To capture this

information a detector is required which can either be metal, which is the least

effective, but is versatile and used in environmental scanning electron microscopy

(ESEM); semi-conductor, which is most common or a scintilator/light

pipe/photomultiplier, which are the most efficient.

Experimental methods 27

Figure 2.3 – Schematic view of a Scanning Electron Microscope

The primary electrons current is approximately 10-8 to 10-7A. The large

penetration depth of the high energy electrons will cause the electrons to be

trapped in the material. When studying conducting materials, the electrons will be

transported away from the point of incidence. If the specimen is a non-conducting

material, the excess electrons will cause charging of the surface. The electrostatic

charge on the surface deflects the incoming electrons, giving rise to distortion of

the image. To reduce surface charging effects, a conducting layer of metal, with

typical thicknesses 5-10 nm, can be sputtered onto the surface. This layer will

transport the excess electrons, reducing the negative charging effects. An adverse

effect of the sputtered layer is that it may diminish the resolving power of the

microscope, since topographical information is no longer gained from the surface

of the material, but from the sputtered layer. Charging of the surface is not the only

factor determining the resolution of a scanning electron microscope. The width of

the electron beam is also an important factor for the lateral resolution. A narrow

electron beam results in a high resolution. The spot size however, is a function of

the accelerating voltage

28 Chapter 2

2 2

2 2 2 6

20

1 1

2p c s

i Ed C C

B E

. (2.18)

The broadening of the spot size is the sum of broadening effects due to several

processes. The first contributor is the beam itself, B is the brightness of the

source, i is the beam current and its divergence angle. The second part is the

contribution due to diffraction of the electrons of wavelength by the size of the

final aperture. The last two parts are the broadening caused by chromatic and

spherical aberrations. Where 0E is the electron energy and E is the energy

spread, sC represents the spherical aberration and cC is the chromatic aberration

coefficient. To achieve the smallest spot size, all contributions should be as small as

possible. Decreasing the accelerating voltage will not only cause the wavelength of

the electrons to increase, but also the chromatic aberration increases as well,

resulting in increasing of the spot size and, as a consequence, a decrease in

resolving power of the microscope.

A field emission gun has a very high brightness B , reducing the contribution

in broadening due to the beam itself. The energy spread E in the electron

energies is also small. Together with the fact that the coefficients sC and cC can be

reduced by optimizing the lenses for low-energy electrons, provides the FEG low

voltage scanning electron microscope with very high resolving power.

2.7 Focused Ion Beam

The effects of high-energy particles striking a material are a major concern in

the nuclear materials industry, where reactor housings and the components used

within have to be designed with consideration of the influence of alpha, beta,

gamma and neutron radiation. Such effects can be extremely detrimental to the

operation of a reactor. Amongst them are, for example, the formation of voids

within reactor walls, the embrittlement of affected surfaces, the formation of

secondary phases or the formation of entirely new materials due to nuclear effects

which can lead to the reduction of functionality of critical components.

High-energy particles have a beneficial use, however. The modern focused ion

beam (FIB) instrument has a wide variety of applications in many fields [47], and is

a versatile tool for sample preparation for scanning and transmission electron

Experimental methods 29

microscopy. The FIB operates through either deposition or sputtering of material to

perform topological alterations to a sample. In both cases, ions of a particular

species, usually Ga+, He+, Ne+ or Ar+ are excited to a high energy, typically 30 keV,

and accelerated towards their target. An incident ion imparts a large amount of

energy to the target surface and it results in a series of effects: sputtering of

material i.e. the release of the sample’s surface atoms, ion implantation and

formation of defects along the ion’s trajectory within the material until it reaches a

stopping point.

The sputtering effect is the most common and traditional use for the FIB,

where material can be precisely and quickly removed. However, a high-energy

particle emitted from a FIB entering a material will also transfer its energy to

adjacent particles through inelastic collisions. These particles will do the same to

their own neighbors in a process of so-called “knock-on” effects. Whilst some

particles displaced in this manner will recover to their initial locations in the

atomic lattice, others will remain displaced as interstitial atoms, leaving behind a

vacancy in a defect type called a vacancy-interstitial or Frenkel pair. In this

manner, a single high-energy particle traveling through a material will create a

large amount of defects, and continuous exposure to a beam of high-energy

particles will create a defect-rich layer in a material that is approximately as deep

as the maximum penetration depth of the accelerated ions.

In this Thesis work we have intensively used a Focused Ion Beam integrated

into a dual beam FEG scanning electron microscope. The typical function of an ion

beam apparatus is either the removal or the addition of material - depending on the

nature of ions and their acceleration energy - through bombarding a target with

accelerated ions. Incoming ions typically have much more energy than the bond

energy of the atoms of their target and, upon impact, break a large amount of

atomic bonds as they move into the material. The release of atoms as they break

free from the source material due to this imparted energy is called sputtering, and

the use of this process to selectively change the shape of an object using the ion

beam is called milling.

The dual beam FIB/scanning electron microscope (SEM) microscope (Lyra,

Tescan, CZ) apparatus was used in all ion-beam related experiments. The

apparatus produces a Ga ion beam with an acceleration voltage of 30 keV. The ion

beam’s spot size and ion current can be varied. During all experiments, the spot

30 Chapter 2

size remained unchanged. The ion current operates on factory presets, with settings

for 1, 10, 40, 150, 200, 1000 and 10000 pA. True ion current is measured internally

using a Faraday cup, and it is consistently observed that the true ion current varies

from that of the setting at which that current is produced. The variation can be up

to a factor of two above or below the preset value. While this variation is small on

the absolute scale at low ion current values, it quickly becomes significant as ion

current increases.

The FIB apparatus is equipped with a computer-controlled moving stage that

allows for 360 degree rotation as well as tilt that ranges from –20 to +70 degrees.

Through a combination of rotation and tilt a sample can be observed from any

angle (for schematics see Figure 2.3). There is a 55 degree angle between the

electron and ion emitters, such that a sample being observed from a perpendicular

inclination with the SEM will be 55 degrees tilted away from the normal when

observed with the ion beam and vice-versa. As such, it is customary for a sample to

be tilted 55 degrees once the working area has been found.

The FIB apparatus is capable of masking its ion beam during emission to

allow for a variety of milling types – random and polish. During random milling a

selected area is continuously bombarded with ions with each ion striking a random

point within the area. During polish milling the ion beam removes material a row

of ion “pixels” at a time, which often ensures a far cleaner edge than random

milling.

Figure 2.4 shows a general schematic of the steps involved in the preparation

and irradiation of bending cantilevers. The details for fabrication of the initial free-

standing thin films is described in the next section. The surroundings of the regions

of interest were ion cut and removed, leaving arrays of ~ 5×2 µm2 cantilevers. A

rectangular area that slightly exceeded the cantilever edges was scanned using a

parallel strategy, i.e. the ion beam scanned the selected areas sequentially in lines,

repeating for the necessary number of times until the desired fluence was achieved.

Experimental methods 31

Figure 2.4 – Schematic diagram of cantilevers fabrication and bending: (a)

free-standing film; (b) ion cutting of surrounding areas; (c) linear irradiation

(over the dashed lines) to remove adjacent areas from the line of sight; (d)

cutting of the cantilevers; (e) bending experiment: area scan up to desired

fluence and subsequent SE imaging; (f) y-axis is used for modeling defect

kinetics in the cantilever as a function of depth (chapters 5 and 6), (x, z) is the

larger-scale coordinates describing cantilever curvature.

The experimental fluence was calculated as the average number of ions

over the scanned area according to the formula

22 1

dwell

I abjt t

abe r o

, (2.19)

where j is the averaged flux (ion rate per area considering single charged ions), t is

the irradiation time considering the number of scanning spots in the irradiated

area, I is the ion current, e- is the elementary charge, a and b are the dimensions of

the scanned rectangle, r is the ion beam radius, o is the scanning beam overlap

ratio and dwellt is the dwell time in each scan spot. The values dwellt = 1 µs, r = 50

nm and o = 0.5 were kept fixed while those of I and ab varied between experiments.

After irradiation to a desired fluence, the cantilevers were imaged with the

SEM. Steps of irradiation and SE imaging proceeded until the cantilevers were

32 Chapter 2

almost vertical. The sequential images were measured with ImageJ [48] and the

vertical dimensions of the images were adjusted by a factor of 1/sin(55º) = 1.2208

due to the 55º perspective of the electron beam to the samples normal (Figure

2.5a). The deflections corresponding to each fluence step were finally measured

using Engauge [49] to extract the cantilevers coordinates. Each measurement

corresponds to the average of the coordinates of at least three simultaneously

irradiated cantilevers (Figure 2.5b).

Figure 2.5 – Diagram of the required correction for the cantilevers

displacement due to the relative positions of the electron and ion beams (a); and

example of measurement of displacement from SE images (b).

2.8 Free-standing thin films

In this Thesis, most of the work was done on free-standing metallic films with

sub-micrometer thickness. As counterintuitive as it may appear, the (nano-)

technology to achieve such small thicknesses has been available since ancient times

and artifacts found in Egypt dating to as back as 2690 BC show signs of having

been covered in gold leaves [50], [51]. The method employed to produce such

leaves, i.e. repeatedly beating a stack of intercalated gold and paper or gut layers;

was discussed by Pliny the Elder in the first century and is still in use today. In fact

the precursor alloy films for the synthesis of nanoporous gold (section 2.8.2), are

commercialized mainly for gilding and are still made via that fabrication route.

Experimental methods 33

Present-time students could probably find some useful advice about handling these

leaves in the colorful description of a 12th century Benedictine monk [50] :

"In laying on the gold take glair, which is beaten out of the white of an egg

without water, and with it lightly cover with a brush the place where the gold is to

be laid. Wet the point of the handle of the brush in your mouth, touch a corner of

the leaf that you have cut, and so lift it up and apply it with the greatest speed. Then

smooth it with a brush. At this moment you should guard against drafts and hold

your breath, because if you breathe, you will lose the leaf and find it again only with

difficulty."

The development of the transmission electron microscope stirred new interest

in thin specimen preparation techniques and the fast development of thin film

technologies since then led to breakthroughs in areas as diverse as energy

harvesting and storage, electronic semiconductor devices, corrosion or abrasion

protective coatings and others, making it a significant subfield of Materials Science.

Several techniques exist for the synthesis of thin films and they can be generally

divided in top-bottom and bottom-up approaches. The top-bottom techniques

involve thinning of bulk material, typically by chemical, electrochemical or

mechanical means. The bottom-up approach means building a thin deposit by e.g.

electrodeposition, sputtering or vacuum evaporation, which was the technique of

choice in the present work.

2.8.1 Dense solid bulk films

Thin films of gold, platinum and aluminum were synthetized via physical

vapor deposition using a Temescal FC-2000 electron-beam evaporator. In such a

machine, an electron beam is used to heat and evaporate a solid material source

inside a high vacuum chamber. The evaporated atoms condense on the chamber’s

walls and the deposited thickness can be monitored by means of a quartz crystal

microbalance.

Free-standing films were produced by evaporating the aforementioned metals

on mechanically polished NaCl substrates that were posteriorly dissolved in

distilled water. The pressure in the deposition chamber was kept at 8×10−7 Torr

and an evaporation rate of 0.1 nm s−1 was used for all samples. After dissolving the

34 Chapter 2

rocksalt substrates, the floating films were collected with TEM grids, rinsed with

distilled water and allowed to dry in air. The grids were finally mounted in a home-

designed holder that enables the grid surface to be positioned normally to the

incident ion beam in the Tescan Lyra FIB-SEM dual system.

2.8.2 Nanoporous films

“Separate thou the earth from the fire, the subtle from the gross sweetly with

great indoustry…” [52]

The process of dealloying the less noble component from a metallic alloy does

not lack its own historical curiosities. Andean pre-colombian metalsmiths already

knew the process of depletion gilding, in which the surface of a gold-alloy artifact

would be treated to give it the appearance of being made of pure gold – much for

the disappointment of Spanish looters [53]. What the Andeans did not know (or so

we assume!) was that the dealloyed morphology consisted of an open, bicontinuous

nanoporous gold structure, as shown by Forty [54].

The precursor materials used for the present studies were commercial AuAg

foils (Noris Blattgold GmbH, Schwabach, Germany) with thickness between 100

and 200 nm. The formation of nanoporous gold by free dealloying of these foils was

investigated in our MK group using transmission electron backscatter diffraction

(t-EBSD). This rather recent technique is based on the collection of Kikuchi

patterns formed by transmitted electrons in a SEM and has improved resolution

compared to standard EBSD [55], [56].

The AuAg foils microstructure consists of a matrix of large whirlpool-shaped

grains containing clusters of elongated smaller grains (Figure 2.6). The initial

<001> and <111> fiber texture was found to be enhanced after etching, while the

residual strain measured by the average misorientation inside grains was reduced.

Additionally, the formation of low-angle grain and twin boundaries at the expense

of high-angle grain boundaries hinted to grain boundaries as nucleation points for

the etching process [57].

Experimental methods 35

Figure 2.6 – The [001] inverse pole figure maps of AuAg foil before (left) and

after (right) dealloying. Black lines represent grain boundaries. The arrows

denote locations with a changed grain boundary. From ref. [57]

Ligament and pore sizes of the nanoporous structure can be tuned by

adjusting the dealloying potential during electrochemical etching, as well as by acid

or thermal post-treatments [58]. The free-standing thin films of nanoporous gold

used for ion-induced bending experiments (Chapter 6) were synthetized by free

etching on 65% nitric acid solution. Foils with composition of Au35Ag65 and

Au25Ag75 were dealloyed for times between 15 minutes and 1 day in order to achieve

various ligament and pore sizes. The dealloyed samples were collected from the the

acid solution with gold TEM grids and thoroughly rinsed with distilled water before

drying in air. Thermal post-treatments for further coarsening were performed at up

to 400ºC under Ar atmosphere. The characteristic size of the nanoporous

structures was measured using the rotationally averaged FFT method [59] using

either SEM micrographs or bright field TEM images.

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Experimental methods 37

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38 Chapter 2

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vol. 47, no. 1, pp. 282–297, Nov. 1992.

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aberration-corrected 200kV transmission electron microscope’, Ultramicroscopy, vol.

75, no. 1, pp. 53–60, Oct. 1998.

[38] M. Wilkens and M. Rühle, ‘Black–white contrast figures from small dislocation loops. I.

Analytical first order perturbation solution’, physica status solidi (b), vol. 49, no. 2, pp.

749–760, 1972.

[39] F. Häussermann, M. Rühle, and M. Wilkens, ‘Black-white contrast figures from small

dislocation loops II. Application of the first order solution to small loops in ion-

irradiated tungsten foils’, physica status solidi (b), vol. 50, no. 2, pp. 445–457, 1973.

[40] F. Häussermann, K. H. Katerbau, M. Rühle, and M. Wilkens, ‘Calculations and

observations of the weak-beam contrast of small lattice defects’, Journal of Microscopy,

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[41] D. J. H. Cockayne, ‘A Theoretical Analysis of the Weak-beam Method of Electron

Microscopy’, Zeitschrift für Naturforschung A, vol. 27, no. 3, pp. 452–460, 1972.

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Experimental and Applied Physics, vol. 20, no. 168, pp. 1265–1270, Dec. 1969.

[43] P. B. Hirsch, Electron Microscopy of Thin Crystals. R. E. Krieger Publishing Company,

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[44] EDAX Phoenix software, TEM Quant Materials. Mahwah (NJ): EDAX Inc., 2000.

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Zeitschrift für technische Physik, vol. 16, pp. 467–475, 1935.

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553–572, Sep. 1938.

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‘engauge-digitizer: Version 9.2 Bug fix release’, Zenodo.

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Applied Metalworking, vol. 1, no. 1, pp. 50–58, Jul. 1978.

Experimental methods 39

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166, Dec. 1979.

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Electrochemical fabrication of nanoporous materials

This chapter describes exploratory efforts aimed at the fabrication of high

surface area actuators by means of electrochemical methods. A structure was

idealized which consisted of stacked layers of 1. aligned nanowires and 2. solid

metal, inspired by reports of improved performance in literature. The aligned

nanowire arrays would be produced by potentiostatic electrodeposition of metals

into the nanopores of an aluminium oxide template that could be selectively

dissolved. As preliminary results indicated that commercial membranes did not

match that purpose, the focus shifted to the production of adequate home-made

templates. Although the idealized structure could not be obtained, this chapter

describes some potentially interesting observations made along the way.

3.1 Actuators

A specific problem in the design of any machine (micromachines included) is

that of moving and controlling its mobile parts. The component with that function

could well be called a "mover" but the technical community surely looks smarter

calling it an "actuator". In fact, if an external stimulus (say potential difference) is

not needed we call the system ‘a sensor’; when an external source is still applied we

call it an ‘actuator’. In several cases, nanoporous materials systems may respond

both as actuator and sensor [1]–[3].

42 Chapter 3

Leaving aside pneumatic or hydraulic actuators and focusing now on

microsized elements, the most common type of actuators are piezoelectric

materials. The piezoelectric effect consists in the generation of charge as result of a

mechanical strain and vice-versa. It has numerous applications from day-to-day

devices such as cigarette lighters and wristwatches to scientific uses where ultrafine

motion is required such as in the alignment of optical assemblies or in scanning

probe microscopy. Since the typical piezoactuator delivers ~0.2% strain at a

relatively high potential of 150V [4], an alternative that delivered comparable or

higher strains at lower potentials would be desirable for the use in miniaturized

devices such as MEMS. One recent development that showed particular aptitude to

accomplish that goal was the use of nanoporous metallic materials as actuators.

Contrary to piezoelectric materials where the charge-strain relation stems from the

occurence of electric dipole moments, dimensional change in metallic nanofoams is

achieved by the redistribution of charge at its surfaces. Since the surface-to-volume

ratio in these materials is extremely high, a change in the interatomic distance at

the surface (due to, for example, adsorption of charged species) is enough to

produce macroscopic displacements.

In our research group, previous research successfully increased the strain of

nanoporous metallic actuators at the time by roughly two orders of magnitude [5].

By means of a clever manipulation of the precursor alloy microstructure via cold-

rolling, a nanoporous material with dual lenght scale was synthesized in which

actuation was amplified by buckling of partially delaminated grains. Another

example of optimization of the actuation strain by manipulating its architecture

instead of relying in intrinsic material properties was demonstrated in ref. [6]. In

that study, an increase of 20% in relation to monolithic np-Au was achieved by

fabricating multilayer solid/nanoporous composites. Since the actuating

nanoporous layers were laterally confined by the solid layers, strain was increased

in the normal direction by the Poisson effect. Yet another strategy in tailoring

nanoporous actuators architecture involves facilitating ion transportation, as high

strains require short charging rates [7]. A semiordered hierarchical nanoporous

structure with µm-sized tubes consisting of nm-sized ligaments was shown to

produce remarkable strains that were attributed to the fast ion transfer kinectics.

Inspired by these concepts, work has been put into the pursuit of a structure

that would combine (1) the high surface to volume ratio of actuating nanoporous

Electrochemical nanofabrication 43

metals, (2) the concept of intercalated solid layers improving the actuation strain

and mechanical robustness and (3) linear (non-tortuous) channels that allow easy

diffusion of charge-transporters. The following sections present some of the

exploratory efforts made into the fabrication of such a structure by means of

electrodeposition of metals in anodized aluminium oxide templates.

3.2 Electrochemical nanofabrication

3.2.1 Anodized aluminum oxide (AAO) templates

Pure aluminium metal is a relatively recent tool in mankind box, having been

first isolated less than two centuries ago by Danish scientist Hans Christian Ørsted.

A “symbol of the future” during the nineteenth century, the metal was showcased in

world fairs at the time and Napoleon III of France would serve his honoured guests

in aluminium plates and utensils, while the less noble guests had to manage with

gold and silver [8]. As the processes of mass-production of aluminium evolved and

its price dropped, it quickly found uses in a widespread range of day-to-day

applications. Besides the metal high abundancy and low density which made it an

important part of modern aerospace, transportation and building industries;

aluminium alloys presents good resistance to corrosion thanks to a naturally

forming passive oxide layer. The ability to electrochemically oxidize aluminium

parts to form thicker layers of protective oxide was called “anodization” and was

applied in industrial scales already in the 1920s to improve the corrosion resistance

of seaplane parts.

Depending on the solubility of the formed oxide in the anodization electrolyte,

the resulting coating may be either of barrier or porous type (Figure 3.1). The

porous-type anodization received considerable attention over the last century due

to the fact that the high porosity provided excellent base for decorative coloration

in consumer products. Additionally, while the thickness of barrier-type oxides is

controlled by the anodization potential, porous-type oxide thickness can be

controlled by the anodization type as it is linearly proportional to the total charge.

It wasn’t until 1995, however, that it became a hot topic in nanotechnology with the

discovery that a tunable self-ordered nanoporous structure could be obtained by

44 Chapter 3

performing two-step anodization under the right electrolytes and parameter ranges

[9], [10]. These ordered nanoporous films were the starting point of the efforts

described below for the production of an actuating metallic nanowire structure. A

detailed review on the various aspects of the AAO production is given in ref. [11].

Figure 3.1 – The two types of anodized aluminium oxide: barrier-type (a)

and porous-type (b). Adapted from [11].

3.2.2 Templated electrodeposition of metals

In general, electrodeposition consists in the reduction of metallic species

present in a given electrolyte on the surface of a conductive substrate by means of

an applied electric current [12]. When using an open-through AAO membrane as

template for electrodeposition, one of its sides is typically covered by a conductive

film that acts as the working electrode while the other side is exposed to the

electrolyte so that electrodeposition takes place inside the pores. Four typical stages

can be defined, as depicted in Figure 3.2 [13], [14]. When a potential is applied

(stage I), the current density increases sharply and decreases with time as the

diffusion layer increases from zero to the thickness of the membrane, according to

the so-called Cotrell equation for diffusion-controlled redox reactions. As the pore

filling (stage II) proceeds, the current density stays relatively constant. When the

wires reach the top surface of the membrane (stage III), the increase in electrode

area leads to an increase in current and finally a continuous film is formed (stage

IV) and its thickness continues to grow at constant current.

Electrochemical nanofabrication 45

Figure 3.2 – Typical stages of metal electrodeposition in AAO templates (a) and

associated behavior of current density in time for the potentiostatic case (b).

Adapted from ref. [13] and [15].

3.3 Experimental results and discussion

3.3.1 Commercial membranes

The first attempts at producing nanowire arrays made use of commercial

Anodisc Whatman AAO filter membranes (Figure 3.3). These are available as 13

mm diameter discs with approximately 65 µm thickness. Two pore sizes were

selected for the preliminary experiments, i.e. 20 and 100 nm. The original

justification was that smaller pores would be advantageous considering the highest

specific surface of the final deposited structures while the bigger pore size was

46 Chapter 3

selected for comparison. These membranes quickly proved unfit, however, due to

the fact that only a small fraction of their thickness is composed by pores with the

nominal sizes. As the membranes are intended for filtration, most of their thickness

is composed by ~200 nm pores making them useful only for testing purposes.

Figure 3.3 – Commercial AAO membranes. SEM micrographs of the top surface

and cross-section of 100-nm membrane (a-b); top-view of 20-nm membrane

(c). The different pore sizes are visible through broken regions in (a) and (c).

The scale bar is 1 µm in all images.

3.3.2 Electrochemical deposition of nanowires

The electrode design for deposition inside the pores of the membranes was

inspired by the protocol provided in reference [16]. A layer of gold was evaporated

Electrochemical nanofabrication 47

onto the the filtering side of the membranes and on one side of small glass slides

(Figure 3.4a-b). The coated membranes were attached to the glass slides and kept

in place using small strips of adhesive tape. A copper tape was connected to the

coated region of the glass slide for electrical contact (Figure 3.4c) and the whole

part except for the membrane was covered with nail polish for insulation

(Figure 3.4d, after successful electrodeposition of copper).

Figure 3.4 – Preparation of working electrodes for templated metal deposition.

AAO membranes and glass slides are coated with a thin layer of gold (a-b);

membranes are assembled onto the slides and secured with conductive copper

tape (c); electrode is covered with nail polish leaving only the middle part of the

membranes exposed (d).

Electrochemical deposition of copper, nickel and magnesium into the

templates was performed using a Metronohm Autolab potentiostat and a three-

electrode setup consisting of the aforementioned working electrodes, a platinum

counter-electrode and a Ag/AgCl reference electrode. The deposition baths and

potential were selected from refs. [17], [18] and are listed in Table 3.1.

48 Chapter 3

Table 3.1 – Electrodeposition parameters

NW metal Deposition bath Deposition conditions (DC)

Cu 0.4 M CuSO4 +

0.2 M H3BO3 in water

0.15 V

Ni 0.1 M NiSO4 +

0.2 M H3BO3 in water

1 V

Mg 0.4M (PhMgCl)2-AlCl3 in THF 40 mA cm-2

Figure 3.5 shows an example of a successfully fabricated solid-nanowire-solid

structure, after dissolution of the AAO template by immersion in 1 M NaOH at

room temperature. The nanowires were composed of pure copper as confirmed by

EDS. These structures were robust and easy to handle and the bottom Au layer was

intentionally damaged to allow observation of the middle layer. Figure 3.5a shows a

wide view of the damaged Au layer with the exposed inner nanowire array. The

spherical particles that can be seen on top of the nanowires are an indication of the

early stages of the overfill of the pores before a continuous film is formed on the

surface of the AAO template [19]. Nanowires that remained attached to the top

layer can be seen in the bottom-right corner of Figure 3.5b.

These preliminary results indicated the feasibility of fabricating mechanically

stable, high-surface structures with a relatively uncomplicated setup. It should be

noted, however, that although the deposition of nanowires was shown to be

achievable, the I-V behavior of these cathodes during deposition was not

satisfactorily reproducible. This issue was attributed mainly to the difficulty in

assuring a good contact between the glass slides and the membranes due to the

fragility of the latter; and the imperfect covering of the membranes pores by the

evaporated gold layer. This probably caused the electrolyte to leak in between the

slide and the membrane leading to deposition in that space. Consequently,

incomplete or inconsistent pore filling (Figure 3.6b, described ahead) and general

deviations from the expected characteristic stages were often observed. The

difficulty to achieve reproducible behavior has been mentioned in the literature and

attributed to the current distribution through the cell [14], the statistical nature of

nucleation at the ealier deposition stages as well as to the blocking of pores by

residual air and formed hydrogen bubbles [15].

Electrochemical nanofabrication 49

Figure 3.5 – SEM micrographs of electrodeposited Cu nanowire array. The top

layer was intentionally damaged to allow for observation of the inner nanowire

layer (a-b). A bundle of broken nanowires lay upon the dense array of

nanowires oriented parallel to the viewing direction (c), with zoomed-in details

(d-e). Various views of the exposed nanowires (f-h).

3.3.3 The goal-structure

Bearing in mind the objective of a multilayered structure consisting of

multiple layers of solid and nanowire-arrays, a rather practical problem appears.

While the length of the nanowire-array layer is defined by the thickness of the AAO

template, control of the solid layers thicknesses is not so straightforward.

Copper electrodeposition was performed in an electrode like the one described

in the previous section, but using two stacked membranes instead of a single one.

The resulting structure after dissolution of the template can be seen in Figure 3.6.

50 Chapter 3

Due to inhomogeneous pore filling of the bottom membrane, filling of the space in

between membranes and of the top membrane pores was incomplete and therefore

all these layers are visible in Figure 3.6b. The solid layer that was formed in the

space between the membranes had approximately 3 µm thickness but a method to

tune it isn’t immediately obvious (Figure 3.6a).

Figure 3.6 – SEM micrographs of multilayered structure after deposition in two

stacked templates. The solid layer in between the membranes formed a solid

layer with thickness of aproximately 3 µm (a). Top view shows inconsistent

filling of the pores (b).

Since the fabrication of our own membranes seemed unavoidable considering

the large pores and thickness from the commercial ones, the strategy to tackle the

Electrochemical nanofabrication 51

problem of controlling the thickness of the solid layers was inspired by an approach

to AAO fabrication named “pulse anodization” [20]. When anodization is

performed at different potential regimes, the chemical composition of the formed

oxide layers can be tailored allowing for selective dissolution. If a supporting

material is infiltrated in some areas of the AAO multilayers prior to dissolution, a

template could be achieved for electrodeposition of the aimed solid/nanowire-

arrays with tunable thicknesses (Figure 3.7). Not only this process would allow for

the control of the solid layers thickness, but the possibility to fabricate thin

nanowire templates would be highly desirable. The reduction in aspect ratio of the

nanowires would likely benefit both mechanical stability and pore filling uniformity

during electrodeposition.

Figure 3.7 – SEM micrograph of multilayered AAO structure after etching of

the most soluble layers. From ref. [20].

3.3.4 Home-made AAO templates

For the anodization studies, high purity (99.999%) aluminium sheets with a

thickness of ~300 µm were used as the starting material. Pieces of ~20x20 mm

52 Chapter 3

were cut and annealed at 500 ºC for 3 h under Ar atmosphere. Anodization was

performed in a double-wall cell for temperature control and the sample was

exposed to the electrolyte through a 1.5 cm² circular opening in the bottom of the

cell. A platinum sheet was used as counter-electrode and the potential bias was

applied using a Keithley 2601 sourcemeter.

The “two-step anodization” process described in the seminal papers by

Masuda [9], [10] takes advantage from the fact that the growth of the porous oxide

leaves a textured pattern of concaves in the underlying aluminium substrate. If the

first grown oxide layer is removed and a second anodization step is performed,

pores nucleate preferentiably on those concaves and the resulting oxide layer

exhibit orderly arranged nanopores (Figure 3.8).

Figure 3.8 – Two-step anodization in oxalic acid. SEM micrographs of oxide

layer formed after first step anodization in 0.3M oxalic acid at 40V for 24h at

room temperature (a); patterned aluminium substrate after dissolution of the

oxide (b); oxide layer after second step anodization under same conditions for

75 min. The scale bars are 2 µm in all images.

The geometric parameters of the AAO such as pore diameter and interpore

distance are determined by the temperature and concentration of the electrolyte,

but mainly by the applied voltage. Among the most common electrolytes, sulfuric

and oxalic were chosen aiming at the smallest sizes as their optimal self-ordering

potential is reported to be 25-27 V and 40 V respectively [21], [22].

While the process of anodization may sound straightforward, it was found that

a great deal of experience is required before high quality templates can be obtained.

Electrochemical nanofabrication 53

Important practical details are often omitted from the reported methods, making

reproducibility difficult. For instance, while uniform AAO films with long-range

ordering were successfully grown in oxalic acid, films grown in sulfuric acid were

highly defective, with extensive cracking and signs of partial dissolution (Figure

3.9). The reasons for this are not clear but they are probably related to the higher

solubility of the aluminum oxide in sulfuric acid and the need to quickly rinse the

electrolyte once anodization is complete.

Figure 3.9 – AAO membrane grown in 0.3 M sulfuric acid at 25 V for 2h at 0ºC.

The damage was visible to the naked eye (a). Although the ordered nanopore

structure could be discerned (b), extensive damage was observed over its

surface (c) with signs of partial dissolution (d) and interpore cracking (e).

The process of pulse anodization involves combining two self-ordering

potential regimes i.e. mild and hard anodization (MA and HA). These regimes

differ in their typical current-time behaviours in that HA processes present a sharp

initial increase in current followed by an exponential decrease while MA processes

are characterized by a steady-state current throughout anodization [23]. Since the

54 Chapter 3

dependence of interpore distance on potential differs for each regime, the

production of oxide layers with continuous pores requires the HA potential and

pulse durations to be carefully tuned. Attempts to use that process in oxalic instead

of sulfuric acid were reported to fail because the HA pulse forms a barrier layer

(Figure 3.1b) that is too thick and prevents current recovery in a reasonably short

time [20]. Yet another attempt was made to produce such layered structures, based

on the principle of producing oxides with different composition to allow selective

dissolution as described in the last section.

The production of through-hole membranes for applications such as filtering

or the present case of nanowire synthesis requires detachment of the oxide layer

from the aluminum substrate and the opening of the barrier layer. This is usually

accomplished by dissolving the aluminium substrate and posteriorly etching the

barrier layer. The process brings complications as the top layer must be protected

against dissolution and it is hard to avoid the increase in pore size due to

infiltration of the etchant. Dealing with the problem of reliably detaching and

opening the AAO membranes, a method was proposed which consists in

performing an additional anodization step in concentrated sulfuric acid [24]. As the

alumina formed under this electrolyte incorporates a larger amount of sulphur, it

can be selectively dissolved leaving a free-standing through-hole membrane and

allowing further use of the already patterned aluminium substrate. In the present

case, that approach was tried as an alternative to pulse anodization with the

advantage that the voltage could be kept constant and therefore no tuning would be

required to guarantee continuous pores. Figure 3.10 shows the structure produced

under 15 V at 0ºC using 2.4 M and 12 M sulfuric acid for 34 and 5 minutes

respectively. The potential is quite far from the 25 V reported in the literature but it

was the one that gave best results for single layer anodization. The method of two-

layered anodization failed nonetheless, with extensive interpore cracks in the upper

layer that probably resulted from the very high concentration of sulfuric acid.

Electrochemical nanofabrication 55

Figure 3.10 – SEM micrographs of AAO layered structure after anodization in

2.4 M and 12 M H2SO4 under 15 V at 0ºC. The scale bars are 1 µm in both

images.

3.4 Conclusion

“(…) Let your workings remain a mystery. Just show people the results.” [25] The fabrication of Cu, Ni and Mg nanowire/bulk layered structures was

performed by electrodeposition in commercial membranes. These structures with

high specific-area were mechanically robust and relatively easy to handle. Their use

into useful structures for e.g. actuation would benefit from optimized templates

and electrode designs to allow for uniform pore filling during electrodeposition.

AAO membranes were successfully grown using oxalic acid and mild

anodization conditions. Although the production of highly ordered pores with

~60nm diameter is relatively easy to accomplish, reproduction of the reported

process in sulfuric acid to achieve smaller pores was not satisfactory. Furthermore,

the use of these membranes as a template for electrodeposition involves additional

steps that can make the whole process rather cumbersome.

56 Chapter 3

The attempts to produce dettached open-through membranes revealed that

frequent examination under the microscope would be required after every couple of

minutes of etching to avoid pore dilation or even the complete dissolution of the

oxide. The fabrication of such membranes likely requires stringent controls of bath

composition and temperature as well as in-situ monitoring of current density

evolution for acceptable reproductibility.

3.5 References

[1] E. Detsi, Z. G. Chen, W. P. Vellinga, P. R. Onck, and J. T. M. De Hosson, “Actuating and

sensing properties of nanoporous gold”, J Nanosci Nanotechnol, vol. 12, nr. 6, pp.

4951–4955, jun. 2012.

[2] E. Detsi and J. T. M. De Hosson, “Nanoporous Metals: New Avenues for Energy

Conversion and Storage”, Nano World Magazine, apr. 2017.

[3] J. Fu, E. Detsi, and J. T. M. De Hosson, “Recent advances in nanoporous materials for

renewable energy resources conversion into fuels”, Surface and Coatings Technology,

vol. 347, pp. 320–336, aug. 2018.

[4] E. Detsi, S. H. Tolbert, S. Punzhin, and J. T. M. D. Hosson, “Metallic muscles and

beyond: nanofoams at work”, J Mater Sci, vol. 51, nr. 1, pp. 615–634, aug. 2015.

[5] E. Detsi, S. Punzhin, J. Rao, P. R. Onck, and J. T. M. De Hosson, “Enhanced Strain in

Functional Nanoporous Gold with a Dual Microscopic Length Scale Structure”, ACS

Nano, vol. 6, nr. 5, pp. 3734–3744, mei 2012.

[6] S.-M. Zhang and H.-J. Jin, “Multilayer-structured gold/nanoporous gold composite for

high performance linear actuation”, Applied Physics Letters, vol. 104, nr. 10, p. 101905,

mrt. 2014.

[7] C. Cheng, L. Lührs, T. Krekeler, M. Ritter, and J. Weissmüller, “Semiordered

Hierarchical Metallic Network for Fast and Large Charge-Induced Strain”, Nano Lett.,

vol. 17, nr. 8, pp. 4774–4780, aug. 2017.

[8] S. Venetski, “‘Silver’ from clay”, Metallurgist, vol. 13, nr. 7, pp. 451–453, jul. 1969.

[9] H. Masuda and K. Fukuda, “Ordered metal nanohole arrays made by a two-step

replication of honeycomb structures of anodic alumina”, Science, vol. 268, nr. 5216, pp.

1466–1468, jun. 1995.

[10] H. Masuda and M. Satoh, “Fabrication of Gold Nanodot Array Using Anodic Porous

Alumina as an Evaporation Mask”, Jpn. J. Appl. Phys., vol. 35, nr. 1B, p. L126, jan.

1996.

Electrochemical nanofabrication 57

[11] W. Lee and S.-J. Park, “Porous Anodic Aluminum Oxide: Anodization and Templated

Synthesis of Functional Nanostructures”, Chem. Rev., vol. 114, nr. 15, pp. 7487–7556,

aug. 2014.

[12] Y. D. Gamburg and G. Zangari, Theory and Practice of Metal Electrodeposition. New

York: Springer-Verlag, 2011.

[13] D. A. Bograchev, V. M. Volgin, and A. D. Davydov, “Simple model of mass transfer in

template synthesis of metal ordered nanowire arrays”, Electrochimica Acta, vol. 96, pp.

1–7, apr. 2013.

[14] P. L. Taberna, S. Mitra, P. Poizot, P. Simon, and J.-M. Tarascon, “High rate capabilities

Fe3O4-based Cu nano-architectured electrodes for lithium-ion battery applications”,

Nature Materials, vol. 5, nr. 7, pp. 567–573, jul. 2006.

[15] K. S. Napolskii e.a., “Tuning the microstructure and functional properties of metal

nanowire arrays via deposition potential”, Electrochimica Acta, vol. 56, nr. 5, pp. 2378–

2384, feb. 2011.

[16] A. W. Maijenburg, E. J. B. Rodijk, M. G. Maas, and J. E. ten Elshof, “Preparation and

Use of Photocatalytically Active Segmented Ag|ZnO and Coaxial

TiO&lt;sub&gt;2&lt;/sub&gt;-Ag Nanowires Made by Templated Electrodeposition”,

Journal of Visualized Experiments, nr. 87, mei 2014.

[17] W. J. Stępniowski and M. Salerno, Fabrication of nanowires and nanotubes by anodic

alumina template-assisted electrodeposition. One Central Press: Manchester, UK,

2014.

[18] W. Gu, J. T. Lee, N. Nitta, and G. Yushin, “Electrodeposition of Nanostructured

Magnesium Coatings”, Nanomaterials and Nanotechnology, p. 1, 2014.

[19] M. P. Proenca, C. T. Sousa, J. Ventura, M. Vazquez, and J. P. Araujo, “Distinguishing

nanowire and nanotube formation by the deposition current transients”, Nanoscale Res

Lett, vol. 7, nr. 1, p. 280, mei 2012.

[20] W. Lee, K. Schwirn, M. Steinhart, E. Pippel, R. Scholz, and U. Gösele, “Structural

engineering of nanoporous anodic aluminium oxide by pulse anodization of

aluminium”, Nat Nano, vol. 3, nr. 4, pp. 234–239, apr. 2008.

[21] K. Nielsch, J. Choi, K. Schwirn, R. B. Wehrspohn, and U. Gösele, “Self-ordering

Regimes of Porous Alumina:  The 10 Porosity Rule”, Nano Lett., vol. 2, nr. 7, pp. 677–

680, jul. 2002.

[22] R. B. Wehrspohn, Red., Ordered Porous Nanostructures and Applications. Springer

US, 2005.

[23] W. Lee, R. Ji, U. Gösele, and K. Nielsch, “Fast fabrication of long-range ordered porous

alumina membranes by hard anodization”, Nat Mater, vol. 5, nr. 9, pp. 741–747, sep.

2006.

58 Chapter 3

[24] T. Yanagishita and H. Masuda, “High-Throughput Fabrication Process for Highly

Ordered Through-Hole Porous Alumina Membranes Using Two-Layer Anodization”,

Electrochimica Acta, vol. 184, pp. 80–85, dec. 2015.

[25] Laozi and S. Mitchell, Tao Te Ching: A New English Version. HarperCollins, 2000.

Radiation Damage

4.1 Ion-solid interactions

Several macroscopic properties of materials are strongly affected by changes

in composition and the structure of the sub-surface layer of about 1 micrometer

thickness. Among these properties are the electronic characteristics of semi-

conductor devices and the corrosion resistance, the mechanical hardness and

friction and lubrication properties of metals. There are even indications for an

influence on the fatigue lifetime.

Since the advent of semiconductors the process of ion implantation has been

increasingly adopted as an effective way of notifying near-surface properties of

materials. With ion implantation, impurity atoms penetrate into a material at high

velocities. Normally, ion energies between 10 and 200 keV are used. At these

energies heavy ions penetrate to a depth of 10 to 100 nm. After injection of ions, the

surface layer often is not in thermodynamic equilibrium. This is extremely

important, because it allows us to bypass the normal chemical solubility rules to

achieve impurity levels far above those obtainable by conventional treatments.

Clearly the modified surface layer will differ from the bulk in chemical and physical

properties.

Numerous examples of the beneficial effects of ion implantation can be found

in the literature. Semi-conductors can be doped in a highly controllable fashion by

ion implantation, and the benefits of ion implantation for the corrosion resistance

of metals have been indicated by several investigators [1]–[4].

60 Chapter 4

The influence of ion implantation is twofold. The first effect is a change in

chemical composition, the second a change in crystal structure. In most cases these

aspects cannot be separated. The changes in structure may be influenced by the

presence of the implanted foreign atoms. For instance, these foreign atoms may

adhere to defect structures and form stable configurations. The two effects may be

separated to a certain extent by applying self-ion implantation into ultra-pure

material.

If an energetic ion penetrates into a metal, it loses its energy by two

mechanisms. The first mechanism, electronic stopping' is due to the interaction of

the incident ion with the electrons of the crystal. The collisions may be elastic or

inelastic, but no permanent damage remains in metals, because the electronic

structure quickly recovers. The energy transferred to the electrons is largely

dissipated as heat. At an energy of about 100 keV, the contribution of electronic

stopping is about 10%. The second mechanism, nuclear stopping, is due to

collisions with lattice atoms. If the incident ion approaches a lattice atom to within

the Thomas-Fermi screening distance, it experiences a strong repulsive force. Since

the energies used in this work are too low to produce nuclear reactions the nuclear

collisions are always elastic.

If sufficient energy is transferred to a lattice alone, it is displaced from its site

to become a self-interstitial. The vacant lattice site is called a vacancy and the

combination of the interstitial and the vacancy a Frenkel pair. The energy needed

for the formation of a Frenkel pair in copper is about 29 eV. After implantation of a

self-ion of 100 keV, one expects about 1000 Frenkel pairs to be formed. The region

where these Frenkel pairs are produced is called the damage cascade. The change

of structure (damage) due to self-implantation is the result of the loss of energy of

the incident ions by nuclear collisions only.

To make the description a bit more quantitative the following remarks are

made: as said above the distribution of implanted ions with depth in a target is

determined by the energy loss processes which slow down the ion on its way

through the target. Generally it is considered that the ion loses energy by two

independent processes, namely nuclear and electronic collisions. In nuclear

collisions kinetic energy is transferred to the target atoms. These collisions are

elastic and result in relatively large angular deflections of the ion. Electronic

collisions are inelastic and they involve energy transfer to the electrons of the target

Radiation Damage 61

atoms. Contrary to the nuclear collisions, these electronic collisions result in

negligible angular deflection of the ions.

Ever since the discovery of energetic particle emission by radioactive

materials the interest in how these particles were slowed down in solids has driven

the steady development of stopping theories. The present understanding of

stopping mechanisms is mainly due to the work of Bohr [5], [6], Bethe [7], Firsov

[8], Lindhard, Scharff and Schlott [9].

If we assume that nuclear and electronic losses are independent processes the

energy loss per distance can be written as

( ) ( )n e

dEN S E S E

dx , (4.1)

dE is the energy loss, dx is the travelled distance by ion, N is the target density, nS

is the cross-section for nuclear stopping and eS is the electronic stopping power.

The nuclear scattering process, with conservation of energy and momentum,

is depicted in Figure 4.1.

Figure 4.1 – Scattering between particles of mass M1 and M2, impact parameter

p and scattering angles 1 , 2 in the laboratory system.

In the non-relativistic case, the kinetic energy transferred to the target atom is

given by

1 2

21 2

( ) (1 cos )( )

m mT E E

m m

, (4.2)

62 Chapter 4

where E is the energy before scattering, is the deflection angle in the center of

mass system (in which the total momentum of the system is zero). is a function

of the impact parameter p and of the interatomic potential V r . In a head-on

collision (p = 0) equals and from Eq. (4.2) it can be seen that the maximum

amount of energy is now transferred.

In our consideration of the electronic stopping power we restrict ourselves to

the energy range far below 1 MeV, which is of practical interest for ion

implantation. The LSS theory, named after Lindhard, Scharff and Schiott [9], was

the first to focus on this low energy region were the ion velocity is less than the

velocity of the target electrons at the Fermi level (i.e. less than about 25 keV/amu).

Here it is assumed that electrons form a free electron gas and from this it is derived

that the stopping is proportional to the ion velocity (or the square root of the

energy):

elS ion velocity k E . (4.3)

Figure 4.2 gives the nuclear and electronic stopping powers calculated from

the LSS-theory for the case of aluminum and nitrogen implanted in copper [10]. It

also gives the ion range R as obtained by integrating the nuclear and electronic

stopping powers using

0 0

1

0 0

= ( ) (E)

E E

n e

dxR dE N S E S dE

dE

. (4.4)

A major advance in electronic stopping calculations has been achieved by

Brandt and Kitagawa [11]. In their approach the effective charge of the ion is

calculated by assuming all electrons to be stripped which have velocities less than

the relative velocity between the ion and the Fermi velocity of the target electrons.

This revises the Bohr concept which stated that all electrons with a velocity less

than the absolute ion velocity would be stripped. Their approach is incorporated in

the TRIM simulation program of Biersack and coworkers [12].

Radiation Damage 63

Figure 4.2 – a) Stopping powers for Al and N in amorphous copper as

calculated by LSS-theory. b) Projected ranges of Al and N in amorphous copper

as calculated by LSS theory [10].

The LSS-theory as discussed so far, is widely applied for calculating ion range

distributions. On doing this one should bear in mind that this theory assumes the

target to be structureless (i.e. amorphous). In reality however, most of the metal

targets to be implanted are polycrystalline and, moreover, they very often have a

pronounced texture. Particularly the semiconductor targets implanted for device

applications have an extremely high perfection in crystallinity.

This crystallinity has been found to lead to discrepancies in the ion

distribution, especially in the deeper tail, as compared to the distribution calculated

from Eq. (4.4). In 1960 Davies [13] reported long ranges for heavy ions implanted

in polycrystalline aluminum and tungsten. At about the same time it was shown

[14] that the sputtering yield for ions bombarding single crystals depends markedly

on the crystal orientation (Figure 4.3).

64 Chapter 4

<100> <110>

<111> random

Figure 4.3 – XTEM micrographs of copper crystals with <100>, <110>, <111>

and random surface orientation perpendicularly implanted with 170 keV

aluminum ions to a dose of 1016 Al/cm2 at room temperature (scale: width of

sub-figure is 1 micrometer) [15].

As a result channeling contributions were investigated and described

theoretically by the continuum model of Lindhard [16] where the actual periodic

Radiation Damage 65

potential of the atomic axes or planes is replaced by a potential averaged over a

direction parallel to these axes or planes. As the incidence angle to a row becomes

larger than some critical angle, the ion trajectory no longer can remain channeled.

These axial critical angles as calculated by Lindhard appear to correspond well with

experimental values [17].

The relative amount of ions being channeled is very sensitive to the precise

orientation of the ion beam. Nevertheless it may also happen that ions that start in

a random direction, get scattered into open channels. This is especially so for heavy

ions at low energies because of their large critical angles. Furthermore, the relative

amount of channeled ions depends on the ion dose because of the accumulation of

radiation damage and the eventual destruction of the channels by amorphization

If the ion profile ( )N x is assumed to be Gaussian it can be expressed in terms

of the average projected range pR (in cm), the spread

pR (in cm) and the

implanted dose D (in ions/cm2) as

2

2( ) exp

2( )2 .

p

pp

x RDN x

RR

(4.5)

in ions/cm3. The projected range pR is defined as the range projected onto

the incidence direction of the ion beam. For ions which terminate at substitutional

lattice positions the atomic concentration is obtained from ( )N x through dividing

by the atomic density of the target. For interstitially implanted ions the atomic

density is increased with ( )N x . In deriving Eq. (4.5) the erosion of the target by

sputtering and the reflection of incident ions is not taken into account.

4.2 Deep damage

In this work it is anticipated that after ion implantation in metals damage is

created not only in the region of the damage cascades, but in a much deeper region

as well. The range in which the damage cascades are expected coincides

approximately with the range in which the incident ions lose their energy.

Figure 4.4 shows the XTEM micrographs of copper (110) single crystals

implanted with copper ions along the <110> axis with ion energies of 170 and 700

66 Chapter 4

keV. The LSS-projected ranges for these implants are pR = 0.04 µm and

pR = 0.16

µm respectively. The insets show the vacancy profiles as calculated by the

simulation code MARLOWE. The extension of the tail of these profiles is in good

agreement with experimental damage ranges. There is a clear dependence of the

damage range on the ion energy.

Figure 4.4 – XTEM micrographs of copper (110) crystals implanted with 170

keV and 700 keV copper ions at a dose of 1016 Cu/cm2. The insets give the

vacancy depth distribution as calculated by MARLOWE [15].

For the 170 keV implant the damage extends to 0.7 µm and for the 700 keV

implant this is about 1.4 µm. This observation confirms the square root dependence

of the damage range on the ion energy which is expected if this damage range is

Radiation Damage 67

determined by the range of channeled ions. It should be noted that the dependence

of the LSS projected ranges on the ion energy is about linear for these implants.

The maximum ion ranges can again be calculated by using the electronic stopping

constant k = 1.05 eV/nm as obtained from SRIM [12], which gives maxR (170 keV) =

0.8 µm and maxR (700 keV) = 1.6 µm, in reasonable agreement with the damage

ranges in Figure 4.4.

But in actual fact, different damage regions can be observed: a region

coinciding with the range of the incident ions, and a region containing less damage

extending far beyond the first region. Other authors have also reported a damage

range extending beyond the range of the incident ions [18]–[21]. It has been

suggested that the deep damage may be due to mobile defects, i.e. this damage is

due to migration and aggregation of self-interstitial atoms escaping from the

damage cascades.

Deep damage due to the clustering of interstitials escaping from the damage

cascades at pre-existing trapping centers have been studied in [22], [23]. The

results described gave a strong indication that preexisting trapping centers do not

play a ro1e in the formation of the deep damage. The main problem is the

formation of nucleation seeds by clustering of interstitials. Once the seeds are

present they are expected to grow to larger clusters by further capture of

interstitials, because the capture radius is large and there are enough free

interstitials available. Large clusters are expected to collapse to dislocation 1oops

(see below for a theoretical analysis).

The growth of dislocation loops has been studied, solving rate equations, by

many authors (see e.g. [24]). In these calculations, however, the problem of

nucleation has not been treated: a fixed cluster density has been assumed as an

initial condition of the calculation. The results are usually compared with the

results of in-situ high voltage electron microscopy irradiation experiments. If the

cluster seed formations were due to the aggregation of migrating interstitials, there

should be a sufficient probability for the formation of clusters in the region where

the deep damage has been found.

In general deep damage does not depend on the implantation dose-rate, and

therefore we conclude that these cluster seeds are formed by interstitials created by

one incident ion only. A calculation of the diffusion of interstitials during the time

68 Chapter 4

interval between two ions incidents within an appropriate distance from each

other, leads to the same conclusion.

As has been observed in FIM studies [25] and confirmed in simulation studies

[26] a primary damage cascade consists of one or several depleted zones containing

clusters of vacancies and a concentration of (di)vacancies. This network of vacancy

type of damage may collapse partly to form vacancy clusters or dislocation loops

(see below). The interstitial atoms are formed for the major part in a region

separated by some length of nm from the depleted zone [27]. The most elementary

theory to estimate the number of Frenkel pairs is that of Kinchin and Pease [28].

Assuming an amorphous so1id, two body hard-sphere collisions, a sharp

displacement threshold energy Ed and no inelastic losses, they obtain for the

number of Frenkel pairs created by one incident ion with energy E :

2

d

d

EN

E . (4.6)

Robinson and Torrens have modified this theory, using a more realistic

interatomic potential and a crystalline structure. In addition, these authors

replaced the total kinetic energy of the incident ions by E - Ein, where Ein represents

the inelastic energy loss to the electrons.

The Kinchin-Pease formula may then be rewritten as [29]

2

ind

d

E EN

E

, (4.7)

where is called the displacement efficiency, which depends on the scattering law

assumed. With 0.85 , and / 0.28inE E [30] and a displacement threshold

energy of 29 eV [31] the number of Frenkel pairs produced by one incident ion of

100 keV in copper is about 1000.

In the evaluation of the experimental results (see Chapters 5 and 6) it should

be kept in mind that during implantation the atomic collisions in the near surface

region may lead to ejection, or sputtering, of target atoms from the surface. This

process can be quantified by the sputtering yield S , defined as the number of

ejected target atoms per incident ion, which can take values from less than one to

ten.

Radiation Damage 69

Sigmund [32] has developed a rigorous theoretical treatment where

sputtering arises from discrete nuclear energy loss processes. In this so called

linear cascade region the intersection of the collision cascade with the surface

determines the magnitude of the sputtering yield S , which, for normal incidence

on elemental targets, can be approximated by

( )S n

yield

surface atomic binding

S E

E . (4.8)

Sputtering yields calculated with Eq. (4.8) have often shown remarkable

agreement with experimental values, when the binding energy is taken equal to the

sublimation energy of the target material. This agreement even appears to hold

when the underlying assumptions of this linear cascade theory are violated (e.g. for

heavy ions at high energies producing very dense collision cascades or spikes).

It is found that, except for glancing angles, the sputtering yield is about

inversely proportional to the cosine of the angle between the incident ion beam and

the surface normal [33]. Sputtering in particular puts a practical upp

er limit to the concentration which can be obtained during high dose implantation.

This is a serious drawback to the general claim that ion implantation, being a non-

equilibrium process, is able to produce new metastable compounds. Also, the

angular dependence of the sputtering yield makes it difficult to achieve uniformity

in retained dose over a target of complex shape. Furthermore, during high dose

implantations, sputtering may lead to very profound topography on crystalline

surfaces by the formation of facetted pits and regular pyramidal features [34]. The

development of these features depends on the crystallographic orientation of the

surface with respect to the ion beam. In addition, surface irregularities and

contaminations initially present can also give rise to topography changes due to

local differences in sputter yield.

4.3 Defect formation and diffusion

Except at very low temperatures interstitials are highly mobile. A part will

migrate into the collapsed depleted zones and recombine. The number of defects

lost in this way may be estimated from the recovery of radiation damage after stage

I (where interstitials become mobile), as measured by resistivity measurements.

70 Chapter 4

Although the interpretation is difficult it is assumed that 70 to 90% of the

interstitials will be lost by recombination after diffusion. Most remaining

interstitials are assumed to be lost at sinks, such as the surface and dislocations. A

few, however may aggregate to form small clusters with a high binding energy.

These clusters form sinks for interstitials created by subsequent incident ions. We

expect that the deep damage consists of these interstitial clusters.

It has been suggested that clusters of interstitials of considerable size, even

containing up to 13 interstitials, are mobile as single interstitials by regrouping

[35]. If this is true the deep damage cannot be explained without the assumption of

pre-existing trapping centers. This assumption is unlikely, however, in our rather

pure materials. This does not imply that larger clusters do not regroup, but we

assume that in such a process the center of mass of the clusters will not move

appreciably.

In the rate-equations as we will explain later it is assumed that single, di- and

tri-interstitials are highly mobile, but that the center of mass of larger clusters is

only s1owly mobile or immobile. The clusters will grow by capturing mobile

(clusters of) interstitials. Clusters containing 7 to 13 interstitials will convert to

stable Frank sessile loops [35]–[38]. All diameters from 5 to 50 nm change to a

perfect loop, because with larger diameters it is energetically favorable to form a

loop with a perfect Burgers vector (see below), but without a stacking fault. The

energy due to the stacking fault increases with the loop area, whereas the energy

due to the dislocation line increases mainly with the circumference of the loop. An

absolute maximum in the damage may be reached if the loops overlap and a

dislocation entanglement occurs. Such an entanglement has been observed in semi-

conductors [39], [40] but not in pure metals after (self-)implantation [41].

Upon annealing, small clusters may become mobile and aggregate to larger

clusters or loops. At greater depth, where the concentration of damage is low, these

clusters may escape without fusing.

The binding energy of a di-interstitial has been estimated to be about 1 eV in

FCC metals and the binding energy of an interstitial to a di-interstitial is estimated

at 1.5 eV [38]. This value increases further with the number of interstitials. The

formation energy of a single interstitial is 2.5 to 4 eV [37], [42]. These binding

energies are sufficiently high that dissociation never occurs. Already at lower

temperatures than those where dissociation could occur, all defects of interstitial

Radiation Damage 71

type have been removed by annihilation by thermally created vacancies. For copper

a complete recovery of the deep damage was observed at 750 K. At this temperature

the concentration of thermally created vacancies increases sharply.

In the following we will analyze the competition between point defect clusters

(vacancy and interstitial type) and dislocation loops as will be a subject of

evaluation in Chapter 5. If we create a vacancy in the interior of a spherical solid

and ‘spread’ the atom which is taken out over the surface leading to an increase of

the rigid volume (conserved) of R :

2 34

43

a aR R r , (4.9)

or

3 2/3aR r R . (4.10)

The formation energy of a vacancy, i.e. the difference in surface energy of

the solid with and without the cavity follows

24 (1 2 /3 )v

f a aU r r R . (4.11)

Neglecting terms in 2

R and since ar R , the vacancy formation energy

for n vacancies of volume a can be written as

2/3

2 2/34 6sphere nv vf f a a fU U r n n n U . (4.12)

The binding energy is expressed as

1/31binding

nv vfU nU n , (4.13)

i.e. for a divacancy 2 1.6v vf fU U

and 2 0.4v vb fU U

.

Let’s turn now to the conversion a spherical point defect cluster to a

dislocation loop. Suppose the n vacancies are formed on a flat circular disk of

thickness of a single vacancy ( 2 1/3a an r ) and radius r:

2 2/32 2disc

f aU r n . (4.14)

72 Chapter 4

From Eqs. (4.12) and (4.14) it is clear that a sphere has the lowest surface area

and therefore the lowest formation energy. However, when the sphere collapses to

a disc it releases a large amount of surface energy (for metals of the order of 1 J/m2)

but it will lose upon strain energy; in fact the surface energy has to be converted to

strain energy of a dislocation loop.

Roughly speaking the elastic strain energy per unit of length of a dislocation

goes with the product of the shear modulus and the magnitude of the Burgers

vector b squared, i.e.

2 1/3 22 2loop

fU r b n b . (4.15)

Comparing Eq. (4.15) with Eq. (4.14) indicates that when r exceeds a critical

value cr a dislocation loop becomes always favorable:

2

c

br

. (4.16)

Typical values for metals leads to 2 4 nmcr and therefore one does not

expect stable discs at larger cr . Also a dislocation loop is energetically more

favorable than a spherical point defect cluster for large enough values of n :

2 1/6

2/3 1/6 1/3

2

6

disloopf

spheref

U b

U n

. (4.17)

It is quite obvious from the above that we ignore in the analysis the

crystallography. In fact it is an elastic continuum–rigid solid approach. The

collapse of a disc does not mean that the crystallographic planes join in the correct

manner (e.g. the threefold ABC {111) planes stacking in FCC Au leads to the

generation of a stacking fault on {111} condensed vacancy planes) and unfaulting

reactions may occur depending in the diameter of the dislocation loop, residual

stress etc, bound by a partial dislocation 1/3 111 . In fact for unfaulting another

partial dislocation 1/6 112 should be nucleated so as to produce, together with

the bounding partial, a perfect dislocation loop as assumed in Eq. (4.17):

1/3 111 1/6 112 1/2 110 . (4.18)

Radiation Damage 73

These unfaulting reactions in FCC Au are favorable, getting rid of the stacking

fault energy of about 20 mJ/m2, above a critical radius of about 5 nm.

So, the general conclusion which will hold is: upon ion radiation at moderate

energies, say below 1 MeV, point defects clusters are produced. For metals,

spherical clusters will collapse to either faulted or unfaulted dislocations loops

depending on the size and specific stacking fault energy. Spherical voids/clusters

and disks are not stable at RT irradiation according to predictions based on linear

elastic continuum mechanics.

4.4 Reaction rate theory

During irradiation, vacancies and interstitials are formed as Frenkel pairs.

These vacancies and interstitials may diffuse, combine, or be lost at sinks. The

theoretical descriptions of radiation damage by so-called rate theory has been

around since the seventies and were used to calculate swelling and irradiation

creep phenomena in nuclear reactor materials. The first approaches condensed to

[43], [44]

2vv v v v i v

dCK k D C C C

dt , (4.19)

2ii i i i i v

dCK k D C C C

dt , (4.20)

where is the rate constant for bulk recombination of interstitials and vacancies,

vK and iK are their production rates, 2,i vk is the total sink strength and

,i vD

represents diffusion coefficients of interstitials and vacancies .

The reactions describing the main processes occurring during and after

irradiation can be specified in a bit more detail as listed in Table 4.1 [45]

74 Chapter 4

Table 4.1 – Rate Equations

Pirr i+v Production of vacancies and (self)interstitials

Ptherm v Production of thermal vacancies at sinks

ki+lv Kki,lv (k-l)i , k>1;

0, k=l;

(l-k)v, k<1

Recombination of vacancy and interstitial clusters

ki+li Kki,li (k+l)i Clustering of interstitials

kv+lv Kkv,lv (k+l)v Clustering of vacancies

kv Kd,kv (k-1)v+v Vacancy dissociation from vacancy cluster

ki+s Ks,ki s Loss of interstitial clusters at sinks

kv+s Ks,kv s Loss of vacancy clusters at sinks

The symbol v denotes a vacancy, i an interstitial, s an unsaturable sink, and k,l

are natural numbers. The parameter Pirr is the production rate for Frenkel pairs

due to the irradiation. The different K’s denote the rate-constants for

recombination, cluster merging, etc. Dissociation of interstitial clusters is not

expected, because the binding energy is too high.

With these reactions we can describe the change with time in the cluster

concentrations by a set of differential rate equations. For clusters containing n

vacancies this change is given by

, ,

, s,nv ( )

nvnv nv ki nv ki nv kv nv kv nv

k k

eqd nv nv nv nv s

dCD C K C C K C C

dt

K C K C C C

(4.21)

The terms represents subsequently diffusion, recombination, clustering,

dissociation and loss at sinks, respectively.

The interstitial cluster concentration is given by

, , s,ni

ni ni ni kv ni kv ni ki ni ki ni sk k

dCD C K C C K C C K C

dt . (4.22)

The subsequent terms reflect diffusion, recombination, clustering, and loss at

sinks, respectively. Compared to Eq. (4.21) here the dissociation term ,d ni niK C is

Radiation Damage 75

absent, in contrast to ,d nv nvK C , because dissociation of interstitial cluster will not

appear due to the high binding energy.

In both equations k,l and n denote natural numbers. For monovacancies and

mono-interstitials (n=1) the production term Pirr must be added. If only the effect

of a single incident ion is considered, the production can also be introduced via the

initial conditions. The production of thermal vacancies is included as an

equilibrium concentration eqC in the term describing the loss of vacancies at sinks.

If these rate equations could be solved simultaneously for all possible cluster

sizes one could calculate the nucleation and growth of these clusters. However,

because the computation time is limited, the number of rate-equations cannot be

very large. In the present work we have restricted the number of equations to only

those that are absolutely necessary to yield an estimate for the nucleation of stable

interstitial clusters (see Chapter 5).

In order to check the model by a calculation one must know the values of the

parameters involved. However, the values of most parameters are not known

directly from measurements. The diffusion constant D is

0

mE

kTD D e

, (4.23)

with mE being the migration energy, k the Boltzmann constant and T the

temperature. The pre-exponential- constant 0D depends on the migration entropy,

on the jump frequency and on the geometry. For mono-interstitials we used

estimates of Young [38] 0 12.5 2 110i oD a s and mE =0.117 eV, with 0a the nearest

neighbor distance. For the migration energy, interstitials become mobile at a

temperature of about 40 K (end of stage I). In early publications it has been

assumed that di-vacancies become mobile at RT (stage III) and vacancies at about

500 K (stage IV) [46]. In more recent work it has been reported that vacancies

become mobile in stage III ( 0.72 eVmvE ), and that in most FCC there is no

evidence for highly mobile di-vacancies in this stage [47].

Either way, the migration of all vacancy defects (v,2v,3v,..) at RT is many

orders of magnitude slower than the interstitial migration and it can be neglected

on the time-scale of the interstitial cluster formation. We therefore used the value

nvD = 0 (n=1,2,3..). On the basis of Huang scattering experiments it has been

76 Chapter 4

concluded that, di-interstitials are more mobile than mono-interstitials in copper

[48]. Since the vacancy mobility is set equal to zero in the calculation, no vacancy

clustering and neither dissociation will occur. We treat the vacancy clusters as sinks

for interstitials, neglecting saturation.

As will be explained in Chapter 5 in our experiments irradiation is done with a

focused ion beam of Ga+ ions, and therefore it is not a self-implantation

methodology. As a consequence the rate Eqs. (4.21) and (4.22) have to include also

the contributions of Ga, i.e.

, s,v

(1 )

( )

vv v i iGa i i v iGa iGa v

eqd v v v v s

dcD c K c c D c c D c c

dt

K c K c c c

(4.24)

where the last term depends on the relative concentration of sinks, i.e. dislocations,

grain-boundary, cavities, interstitial loops densities etc.

, s,(1 )ii i v iGa i i v i i i i i s

dcD c K c c D c c K c c K c

dt (4.25)

vc and ic are the fractional concentrations of vacancies and interstitials,

respectively.

4.5 References

[1] J. R. Morris, R. A. Collins, and G. Dearnaley, “The influence of ion implantation on the

thermal oxidation of copper”, J. Phys. F: Met. Phys., vol. 8, nr. 6, p. 1333, 1978.

[2] L. G. Svendsen, “A comparison of the corrosion protection of copper by ion

implantation of Al and Cr”, Corrosion Science, vol. 20, nr. 1, pp. 63–68, jan. 1980.

[3] G. Dearnaley and P. D. Goode, “Techniques and equipment for non-semiconductor

applications of ion implantation”, Nuclear Instruments and Methods in Physics

Research, vol. 189, nr. 1, pp. 117–132, okt. 1981.

[4] F. H. Stott, Z. Peide, W. A. Grant, and R. P. M. Procter, “The oxidation of chromium-

and nickel-implanted nickel at high temperatures”, Corrosion Science, vol. 22, nr. 4, pp.

305–320, jan. 1982.

[5] N. Bohr, “II. On the theory of the decrease of velocity of moving electrified particles on

passing through matter”, The London, Edinburgh, and Dublin Philosophical Magazine

and Journal of Science, vol. 25, nr. 145, pp. 10–31, jan. 1913.

Radiation Damage 77

[6] N. Bohr and J. Lindhard, “Kgl. Dan. Vidensk. Selsk.”, Mat.-Fys. Medd., vol. 18, nr. 8,

1948.

[7] H. Bethe, “Bremsformel für elektronen relativistischer geschwindigkeit”, Zeitschrift für

Physik, vol. 76, nr. 5–6, pp. 293–299, 1932.

[8] O. B. Firsov, “A qualitative interpretation of the mean electron excitation energy in

atomic collisions”, Zhur. Eksptl’. i Teoret. Fiz., vol. 36, 1959.

[9] J. Lindhard, M. Scharff, and H. E. Schiott, “K. danske Vidensk”, Selsk., Math.-fys.

Meddr, vol. 33, nr. 1, 1963.

[10] E. Gerritsen, “Surface modification of metals by ion implantation”, University of

Groningen, 1990.

[11] W. Brandt and M. Kitagawa, “Effective stopping-power charges of swift ions in

condensed matter”, Phys. Rev. B, vol. 25, nr. 9, pp. 5631–5637, mei 1982.

[12] J. F. Ziegler, M. D. Ziegler, and J. P. Biersack, “SRIM – The stopping and range of ions

in matter (2010)”, Nuclear Instruments and Methods in Physics Research Section B:

Beam Interactions with Materials and Atoms, vol. 268, nr. 11–12, pp. 1818–1823, jun.

2010.

[13] J. A. Davies, J. D. McIntyre, R. L. Cushing, and M. Lounsbury, “The range of alkali

metal ions of kiloelectron volt energies in aluminum”, Can. J. Chem., vol. 38, nr. 9, pp.

1535–1546, sep. 1960.

[14] P. K. Rol, J. M. Fluit, and J. Kistemaker, “Theoretical aspects of cathode sputtering in

the energy range of 5–25 keV”, Physica, vol. 26, nr. 11, pp. 1009–1011, nov. 1960.

[15] E. Gerritsen and J. T. M. D. Hosson, “Cross Section Transmission Electron Microscopy

(XTEM) on Inert Gas Implanted Metals”, in Fundamental Aspects of Inert Gases in

Solids, Springer, Boston, MA, 1991, pp. 143–152.

[16] J. Lindhard, “Influence of Crystal Lattice on Motion of energetic charged particle”, Kgl.

Danske Vidensk. Selskab. Mat. Fys. Medd, vol. 34, nr. 14, 1965.

[17] D. S. Gemmell, “Channeling and related effects in the motion of charged particles

through crystals”, Rev. Mod. Phys., vol. 46, nr. 1, pp. 129–227, jan. 1974.

[18] J. A. Borders and J. M. Poate, “Lattice-site location of ion-implanted impurities in

copper and other fcc metals”, Phys. Rev. B, vol. 13, nr. 3, pp. 969–979, feb. 1976.

[19] D. K. Sood and G. Dearnaley, “Ion implanted surface alloys in nickel”, Radiation

Effects, vol. 39, nr. 3–4, pp. 157–162, jan. 1978.

[20] I. Nashiyama, P. P. Pronko, and K. L. Merkle, “Annealing studyof self-ion-irradiated

gold by proton channeling”, Radiation Effects, vol. 29, nr. 2, pp. 95–98, jan. 1976.

[21] P. P. Pronko, “Dechanneling measurements of defect depth profiles and effective cross-

channel distribution of misaligned atoms in ion-irradiated gold”, Nuclear Instruments

and Methods, vol. 132, pp. 249–259, 1976.

78 Chapter 4

[22] R. J. T. Lindgreen, D. O. Boerma, and J. T. M. de Hosson, “A study of shallow and deep

damage in Cu after implantation of 100 keV Cu and Ag ions”, Nuclear Instruments and

Methods in Physics Research, vol. 209–210, pp. 963–967, mei 1983.

[23] R. J. T. Lindgreen, D. O. Boerma, and J. T. M. D. Hosson, “A study of shallow and deep

damage in Cu and Al after self-implantation”, Radiation Effects, vol. 71, nr. 3–4, pp.

289–314, jan. 1983.

[24] M. Kiritani, K. Urban, and N. Yoshida, “Formation of submicroscopic vacancy clusters

and radiation-induced refining in metals by electron-irradiation at high temperatures”,

Radiation Effects, vol. 61, nr. 1–2, pp. 117–126, 1982.

[25] D. N. Seidman, M. I. Current, D. Pramanik, and C.-Y. Wei, “Direct observations of the

primary state of radiation damage of ion-irradiated tungsten and platinum”, Nuclear

Instruments and Methods, vol. 182–183, pp. 477–481, apr. 1981.

[26] J. Mory and Y. Quéré, “Dechanneling by stacking faults and dislocations”, Radiation

Effects, vol. 13, nr. 1–2, pp. 57–66, mrt. 1972.

[27] D. Wieluńska, L. Wieluński, and A. Turos, “The effect of dislocations on the planar

dechanneling. I. Analytical model”, physica status solidi (a), vol. 67, nr. 2, pp. 413–419,

1981.

[28] G. H. Kinchin and R. S. Pease, “The Displacement of Atoms in Solids by Radiation”,

Rep. Prog. Phys., vol. 18, nr. 1, p. 1, 1955.

[29] I. M. Torrens and M. T. Robinson, “Computer Simulation of Atomic Displacement

Cascades in Solids”, in Interatomic Potentials and Simulation of Lattice Defects,

Springer, Boston, MA, 1972, pp. 423–436.

[30] M. T. Robinson and I. M. Torrens, “Computer simulation of atomic-displacement

cascades in solids in the binary-collision approximation”, Phys. Rev. B, vol. 9, nr. 12,

pp. 5008–5024, jun. 1974.

[31] P. Lucasson, “Production of Frenkel defects in metals”, 1975.

[32] P. Sigmund, “Sputtering by ion bombardment theoretical concepts”, in Sputtering by

Particle Bombardment I, Springer, Berlin, Heidelberg, 1981, pp. 9–71.

[33] P. C. Zalm, “Quantitative sputtering”, Surface and Interface Analysis, vol. 11, nr. 1–2,

pp. 1–24, 1988.

[34] G. Carter, I. V. Katardjiev, M. J. Nobes, and J. L. Whitton, “Sputtering-induced surface

topography on F.C.C. metals”, Materials Science and Engineering, vol. 90, pp. 21–32,

jun. 1987.

[35] H. R. Schober and R. Zeller, “Structure and dynamics of multiple interstitials in FCC

metals”, Journal of Nuclear Materials, vol. 69–70, pp. 341–349, feb. 1978.

[36] W. Schilling, “Self-interstitial atoms in metals”, Journal of Nuclear Materials, vol. 69–

70, pp. 465–489, feb. 1978.

Radiation Damage 79

[37] P. H. Dederichs, C. Lehmann, H. R. Schober, A. Scholz, and R. Zeller, “Lattice theory of

point defects”, Journal of Nuclear Materials, vol. 69–70, pp. 176–199, feb. 1978.

[38] F. W. Young, “Interstitial mobility and interactions”, Journal of Nuclear Materials, vol.

69–70, pp. 310–330, feb. 1978.

[39] T. Tokuyama, “Use of Ion Implantation in Device Fabrication at Hitachi CRL”, in Ion

Implantation in Semiconductors 1976, Springer, Boston, MA, 1977, pp. 519–533.

[40] J. Fletcher, J. Narayan, D. H. Lowndes, and T. Y. Tan, Defects in Semiconductors.

North-Holland Publishing Co. New York, 1981.

[41] R. A. Johnson, Physics of Radiation Effects in Crystals. North-Holland, 1986.

[42] M. W. Thompson, Defects and radiation damage in metals. London,: Cambridge U.P.,

1969.

[43] A. D. Brailsford and R. Bullough, “The rate theory of swelling due to void growth in

irradiated metals”, Journal of Nuclear Materials, vol. 44, nr. 2, pp. 121–135, aug. 1972.

[44] A. D. Brailsford and R. Bullough, “The theory of sink strengths”, Phil. Trans. R. Soc.

Lond. A, vol. 302, nr. 1465, pp. 87–137, jul. 1981.

[45] R. J. T. Lindgreen, “Radiation damage in fcc metals”, University of Groningen, 1984.

[46] H. Mehrer and A. Seeger, “Interpretation of Self-Diffusion and Vacancy Properties in

Copper”, physica status solidi (b), vol. 35, nr. 1, pp. 313–328.

[47] R. W. Balluffi, “Vacancy defect mobilities and binding energies obtained from annealing

studies”, Journal of Nuclear Materials, vol. 69–70, pp. 240–263, feb. 1978.

[48] P. Ehrhart and U. Schlagheck, “Investigation of Frenkel defects in electron irradiated

copper by Huang scattering of X-rays. I. Results for single interstitials”, J. Phys. F: Met.

Phys., vol. 4, nr. 10, p. 1575, 1974.

Dense solid samples

5.1 Initial observations on Au cantilevers

The investigations discussed in this Chapter start focusing on gold as a typical

example of face-centered cubic material. Irradiation with Ga+ ions caused upwards

bending (towards the beam) in all observations (Figure 5.1). The curvature along

the cantilevers length remains mostly uniform during the initial stages and

assumes a U-shape as irradiation proceeds (Figure 5.2). This effect was later

observed for all the other investigated systems and it can be explained considering

the change in angle between the incident ion beam and the sample normal along

the cantilever in the course of the experiment. As irradiation progresses, the

deflection of the free-end becomes more pronounced than the supported end. The

irradiation angle affects sputtering rate and implantation range resulting in the

observed non-uniform curvature in the late stages. In the following, only the early

stages in which curvature remains uniform along the cantilever length are

considered.

82 Chapter 5

Figure 5.1 – Ion-beam irradiation of the cantilever (a); the implantation profile

of Ga+ ions is shown schematically. Deflection of Au cantilever (d0 = 144 nm)

after irradiation to a fluence of 1.4×1020 m−2 (b).

The observed deformation requires the introduction of some sort of

gradient along the films’ thickness. An intuitive attempt to explain upwards

bending would be to assume a negative volume change in the subsurface region,

e.g. by the accumulation of vacancies. However, a stationary description is not

appropriate as the defects continue to migrate by thermal diffusion after the

cascade relaxation stage and are subject to recombination and/or annihilation.

Added to that, each irradiation step in these experiments consists of an order of 108

collision events (considering r=50 nm, I=40pA, o=0.5 and tdwell=10µs in Eq. (2.19))

making it necessary to model the time-dependent evolution of the generated point

defects. The obtained defect distributions along the film thickness can then be

translated into a volume change distribution. This linear expansion/contraction

can finally be used in the equations of thermoelastic bending of beams to find the

solution to the problem of cantilever bending induced by ion irradiation.

Dense solid samples 83

Figure 5.2 – Deflection and curvature evolution of Au cantilevers with nominal

initial thickness of 200 nm (a, b) and 89 nm (c–f) irradiated with 30 keV Ga+

with parallel (a–d) and serial (e–f) scan strategies. The labels next to the lines

indicate the fluence in units of Ga ions/m2. The curvature 1/R was calculated

from experimental data using Eq. (5.17). The error bars of the experimental

data are not repeated in the calculated curvature representation.

84 Chapter 5

5.2 Model of ion induced bending

5.2.1 Point defect kinetics

The rates of ion implantation and defect generation as well as the sputtering

yield can be simulated for amorphous targets using SRIM [1]. The depth-dependent

PD generation rate K y and Ga implantation rate GaK y are calculated as

 SRIMK y j K y , (5.1)

  Ga

Ga SRIMK y j K y , (5.2)

where j is the flux of Ga+ ions at the film surface, is the volume per lattice site,

SRIMK y is the distribution of Frenkel pairs over the film depth per incident ion

and Ga

SRIMK y is the probability density to find the incident ion at a depth y after

it spent its kinetic energy in collisions with the target atoms.

According to SRIM simulations, PDs are generated mostly within a range of

about 30 nm during irradiation of Au with 30 keV Ga+ ions (Figure 5.3). The

“monolayer collisions – surface sputtering” option of SRIM was selected with

displacement energy of 44 eV [2].

Figure 5.3 – The production rate of PD and the implantation rate of Ga were

calculated with SRIM for 30 keV Ga ion implanted into amorphous Au target at

normal incidence.

Dense solid samples 85

The impingement of the film with energetic ions results in sputtering of the

film, i.e. movement or receding of the film boundary with the rate

  dy

v j Ydt

, (5.3)

where Y is the sputtering yield (number of sputtered atoms per incident ion).

A set of rate equations for the concentrations of vacancies, self-interstitials, Ga

interstitials and Ga substitutional atoms was defined as follows:

α α ρ Δ1vv i i v iGa iGa v v v v v v

dCK y C D C C D C C Z D C D C

dt , (5.4)

α ρ Δ1   iv Ga i i v i i i i i

dCK y C C D C C Z D C D C

dt , (5.5)

α ρ ΔiGaGa Ga iGa iGa v i iGa iGa iGa iGa

dCK y K y C D C C Z D C D C

dt , (5.6)

α ρ  GaiGa iGa v i iGa iGa Ga

dCD C C Z D C K y C

dt , (5.7)

where concentrations are defined per lattice site, α ,4 /i vR is the

recombination rate constant, , ~i vR a is the radius of spontaneous recombination (

a is the lattice spacing), , ,i v iGaD are the diffusion coefficients (𝐷𝑖,𝑖𝐺𝑎 ≫ 𝐷𝑣), ρ is

the dislocation density and ,i vZ are the efficiencies of dislocations as a sink for

interstitial atoms and vacancies [3]. For simplicity, the diffusion coefficient of self-

interstitials and interstitial Ga atoms are assumed to be the same.

The dislocations’ capture efficiency is estimated for the edge configuration as

1

,

,

2 lni v

i v

LZ

r

, (5.8)

where ,i vr is the capture radius of a PD by a dislocation and L is the mean spacing

between sinks. Dislocations attract interstitial atoms more strongly than vacancies

therefore  i vr r and i vZ Z . PDs can be absorbed also by grain boundaries,

86 Chapter 5

however it is assumed here that the distance between grain boundaries is larger

than the dislocation spacing and the film thickness.

The physical meaning of different terms in the set of equations can be

explained conveniently by using Equation (5.4) as an example:

α i i vD C C : mutual recombination of vacancies and self-interstitial atoms

controlled by thermally-activated diffusion of SIA since in metals 𝐷𝑖,𝑖𝐺𝑎 ≫

𝐷𝑣;

α iGa iGa vD C C : recombination of implanted thermalized Ga with vacancies;

ρv v vZ D C : absorption of vacancies by dislocations;

Δ  v vD C : diffusion of vacancies from the implanted layer to external

surfaces.

The rate theory equations do not deal with damage cascade collapse, i.e.

formation of either faulted or unfaulted loops of PDs. Zero boundary conditions are

used at both external surfaces for PDs Equations (5.4)-(5.6):

, , 0v i iGa

y vt

dC

dy

(5.9)

0

, ,0 

v i iGa

y d

dC

dy

(5.10)

Concentration profiles of vacancies, substitutional Ga atoms and interstitial

atoms are shown in Figure 5.4 for various irradiation doses. The concentration

profiles move inside the film as the material is removed from the surface due to

sputtering. The concentration of vacancies is relatively high, whereas

concentrations of interstitial atoms are very low due to fast diffusion to external

surfaces. It should be noted that distributions of vacancies and Ga atoms in the

subsurface region of the film do not depend on time after a short transient period.

Vacancies are essentially immobile, since at the room temperature in metallic

systems the timescale of vacancy diffusion across the projectile range is (30 nm)²/

vD ~ 105 s.

Dense solid samples 87

Figure 5.4 – Concentration profiles of PD and implanted Ga atoms. Irradiation

time is indicated near curves. The left boundary of the film corresponds to the

irradiated surface and moves to the right (indicated with arrow) because of

sputtering. One second of irradiation time corresponds to a fluence of 3×1019

m−2.

5.2.2 Analogy to thermoelasticity

The implanted ions and point defect distributions result in an inhomogeneous

volume change. Bending is a consequence of the stress originating from the volume

change localized within the layer where implanted ions and point defects are

distributed. The relative volume change Ω V V associated with PDs is given

by the sum

Δω Δω

Ωω ω

v GaPD v GaC y C y (5.11)

88 Chapter 5

where Δωv is the vacancy relaxation volume and ΔωGa

is the excess volume

associated with a substitutional Ga atom. Here the contribution of interstitial

atoms is neglected because under typical conditions the remaining concentrations

of interstitial atoms are very small due to high diffusion mobility at room

temperature. They are accounted for in a second term regarding absorption of

point defects by dislocations bounding prismatic loops, which may result in

dislocation climb. The rate of local volume change due to dislocations is given by

Ω

ρdisli i i i iGa iGa v v v

dZ D C Z D C Z D C

dt . (5.12)

The relaxation volume of vacancies is negative in all metals. The excess

volume associated with substitutional Ga atom depends on the specific film

material, being negative in Au (Table 5.1). It can be deduced from the dependence

of lattice parameter on Ga concentration in solid solutions. The volume change due

to dislocations is always positive even when both interstitials and vacancies are

mobile, because of the dislocation bias to absorption of interstitial atoms [3].

Dense solid samples 89

Table 5.1 – Material parameters used in model calculations for gold

Parameter Value

Flux of Ga+ ions j , m-2s-1 3x1019

Temperature, T , K 300

Atomic volume, ω , m-3 1.7x10-29

Sputtering yield, Y (SRIM) 15.5

Recombination rate constant, α , m-2 3x1020

Diffusion coefficient of vacancies, vD , m2s-² 2.43x10-6exp(-0.89 eV/kBT)

[4]

Diffusion coefficient of interstitials, iD , m2s-1 5x10-6exp(-0.06 eV/kBT)

[5], [6]

Relaxation volume of vacancies, Δωv -0.37 ω [7]

Relaxation volume of interstitial atoms, Δωi ≈ω

Misfit volume of gallium, ΔωGa -0.076 ω [8]

Dislocation density, ρ , m-2 1011

Dislocation capture efficiency for SIA, iZ 3.3

Dislocation capture efficiency for vacancies, vZ 3

The bending that results from the inhomogeneous volume change

Ω Ω ΩPD disl can be evaluated using an analogy with thermoelasticity. It is well

known that thermoelastic stresses due to the linear thermal expansion αT y

result in bending of beams and multilayered materials [9]. In the equations of

thermoelastic bending of the cantilever beams we replace the linear thermal

expansion αT y with the linear expansion/contraction λ Ω y /3y and find

the solution to the problem of cantilever bending induced by ion irradiation. The

strain in the film is given by

ε ε0

1

2xx

dy

R

, (5.13)

90 Chapter 5

ε λ0

0

1  

d

y dyd

, (5.14)

λ3

0

1 12

2

dd

y y dyR d

, (5.15)

where 0d d vt is the cantilever thickness, x is the coordinate in the direction

of the free end, R is the radius of curvature at the neutral plane and ε0 is the axial

strain in the x-direction at the neutral plane. The linear elastic stress in the

cantilever is given by

σ ε λ0

1/

2xx

dE y y

R

, (5.16)

where E is the Young’s modulus. The deflection of the beam towards the ion beam

(Figure 5.2) is related to curvature by

2 /2u x R . (5.17)

It should be noted that the radius of curvature (5.15) depends only on the

inhomogeneous volume change, with no explicit dependence on the elastic

modulus. One may expect that the volume change can generate high stresses

leading to plastic deformation. The bending direction depends on the sign of the

local volume change and the location of the layer with respect to the neutral axis in

which the radiation defects are created.

The local volume change due to vacancies and Ga atoms is negative (Figure

5.5) and results in bending towards the ion beam. Both vacancies and

substitutional Ga atoms contribute to volume change. The contribution of

substitutional Ga atoms, however, is small because of their small misfit volume.

Dense solid samples 91

Figure 5.5 – Depth dependence of volume change due to vacancies and

substitutional Ga atoms after irradiation for 10 s (ion fluence of 3×1020 m−2).

In the model described so far there is no accumulation of radiation damage

except for the subsurface layer. The steady-state profiles of PD and implanted Ga

ions are formed after a short transient period. For this reason the cantilever

curvature depends only on maximum vacancy concentration, the thickness of

damaged layer and the current cantilever thickness. Assuming a triangular profile

of vacancy concentration, it can be easily shown by direct integration of Equation

(5.15) that

Δω

ω3

3 21 1 

3v

vmax

d t hC h

R d t

, (5.18)

where vmaxC is the maximum vacancy concentration, h is the thickness of

damaged layer and 0d t d vt is the cantilever thickness. The use of vmaxC

0.05 and 20h nm in Equation (5.18) reproduce well the time dependence of

curvature derived from the numerical solution. However, contrary to experimental

observations, Equation (5.18) does not contain a dependence of curvature on initial

thickness of the cantilever, i.e. the model predicts that upon reaching the same

92 Chapter 5

thickness cantilevers of different initial thicknesses would exhibit the same

curvature. Another factor is clearly lacking in this description.

5.2.3 Accumulation of interstitial clusters

Mobile interstitial atoms can form clusters which can evolve into dislocation

loops. Redistribution of material between top and bottom layers could occur due to

the migration of self-interstitial atoms and the interstitial clusters formed in

cascades.

Molecular Dynamics simulations carried out to date predict that a significant

fraction of interstitial defects created in cascades is produced in ‘sessile’ and

‘glissile’ clusters [3], [10]. The grouping of SIAs into clusters is significant because

these defects are thermally stable and they can migrate away from their parent

cascades. In the undamaged region (without cascades) the mobile clusters can form

sessile clusters due to collisions with each other and absorption of single SIAs.

Eventually these clusters may grow into dislocation loops. Contribution of one

atom in the sessile clusters to the volume increase of the film is about the relaxation

volume of a SIA, i.e. Δω Δω~i. At the same time, there is no accumulation of

excess volume in the irradiated subsurface region because cascades create new

clusters and destroy existing ones due to cascade overlap and the effect of

radiation-induced mixing [11], [12]. In addition, the ion beam sputters the surface

atoms and thus removes the damaged subsurface layers. The conclusion is that ion

beam irradiation not only creates point defect distributions within the ion

penetration range but also causes mass transfer across the whole thickness of the

cantilever.

Change of material microstructure well below the implantation depth (long-

range effect) was observed in various materials [13], [14]. Early transmission

electron microscope (TEM) studies [15]–[17] on Cu and Au foils bombarded with

1–5 kV Ar ions showed that interstitial clusters (in the configuration of Frank

sessile dislocation loops) are formed below the bombarded surface at a depth

remarkably larger than the calculated random range of Ar ions. The difference

between ion-induced damage depth and theoretically simulated range was

observed to be more prominent in fcc metals compared to bcc-Fe [18]. This fact was

attributed to a higher value of the Peierls force opposing dislocation glide in bcc

structures. Both Rutherford backscattering spectrometry (RBS) channeling spectra

Dense solid samples 93

and cross-sectional TEM characterization of single crystalline nickel and Ni-based

binary alloys irradiated with 3 MV Au ions clearly demonstrated that the range of

radiation-induced defect clusters far exceed the theoretically predicted depth in all

materials after high fluence irradiation [14]. The range of defect distribution

beneath the irradiated surface increased dramatically with increasing ion fluence.

The range of visible damage almost doubled when the irradiation fluence increased

from 2×1017 to 5×1019 m−2. The composition of the material was found to have a

great impact on defect distribution, suggesting very different defect migration

properties. Radiation defects in pure Ni stretched much deeper than in NiCo and

NiFe, indicating a higher defect migration rate in nickel for both high and low dose

irradiation.

It should be noted that according to MD simulation, vacancy clusters

(including mobile ones) may also form during early stages of cascade evolution.

However, small vacancy clusters and vacancy voids are thermally unstable [3]. For

this reason, their effect to bending is expected to be small as compared to

interstitial clusters. To estimate the contribution of PD and interstitial clusters to

cantilever bending, the analysis presented above is used to formulate a description

of radiation damage evolution in a thin film.

Assuming that sessile clusters form homogeneously across the undamaged

region, the volume increase during time interval can be estimated as

Ω0

    dcl i

jnd dt

d h vt

, (5.19)

where dn is the total number of defects generated by a Ga ion and 𝜀 ≪ 1 is the

fraction of interstitial atoms in mobile clusters which go to formation of sessile

clusters. Assuming that weakly depends on the cantilever thickness, we find the

relative volume increase due to mass transfer from the irradiated zone:

Ω 0

0

    lni dcl

n d h

Y d h vt

. (5.20)

The curvature can be calculated as

94 Chapter 5

Ω

Δω

ω

0

0

3

0

0 03

00

1 4

( ) 2

( )2 ln

d vt

cl

h

i d

d vty dy

R d vt

n h d h vt d h

Y d h vtd vt

(5.21)

The lower integration range is limited to the thickness of damaged layer.

There is no accumulation of excess volume in this region because cascades create

new clusters and destroy existing ones due to cascade overlap and the effect of

radiation-induced mixing [11], [12].

Figure 5.6 shows the fluence dependence of the relative volume increase in the

unirradiated region of the cantilever due to formation of sessile clusters. The

volume increase or swelling Ωcl is very high and reaches values of several tens of

percent (compare with Figure 5.5).

Figure 5.6 – Fluence dependence of the relative volume increase (swelling) in

the unirradiated region of the cantilever due to formation of sessile clusters for

cantilevers with three different initial thicknesses.

Dense solid samples 95

5.2.4 Gallium build-up

It is reasonable to assume that the mobile interstitial clusters formed during

cascade evolution are composed from Au and Ga interstitial atoms in the same

proportion as the concentration of Au and Ga in the irradiated zone. This means

that mobile clusters deliver Ga atoms to the zone beyond the implantation range.

Consider the cantilever at a steady state after a transient period of ion beam

irradiation. Assuming a triangular profile of substitutional Ga atoms in the

irradiated zone, from the balance of Ga fluxes:

2

ss d Ga

Ga

jn Cj YjC

, (5.22)

the surface concentration of Ga can be estimated:

1

2

s dGa

jnC Y

. (5.23)

Due to the flux of Ga atoms, the concentration of Ga in the unirradiated zone

increases with time similarly to the volume increase given by Equation (5.20):

0

0

  ln2

s

d GaGa

n C d hC

Y d h vt

. (5.24)

The average Ga concentration is a sum of two contributions from irradiated

and unirradiated zones:

0 0

0 0

1 ln2

s

Ga dGa

d h vthC n d hC

d vt Y h d h vt

. (5.25)

5.2.5 Comparison with experiments

The set of equations formulated above was solved numerically by the method

of lines using the RADAU code [19]. The average curvature in the cantilevers’ free-

end half is plotted against fluence in Figure 5.7. Bending rates were inversely

related to thickness and the gradual increase in slope for each curve is hypothesized

to be an effect of the thickness reduction due to sputtering.

96 Chapter 5

Figure 5.7 – Fluence dependence of the curvature 1/R: comparison of

experimental data with model calculations. The initial thickness of cantilevers is

indicated near the corresponding curves. Dash-dotted curves are given by the

sum of contributions to bending from vacancies and substitutional atoms,

Equation (5.18), and sessile clusters, Equation (5.21), with the parameters ε =

1.4×10–2, nd = 440 and h = 20 nm. The dashed curve is calculated only with

contributions of vacancies and substitutional atoms to volume change,

Equation (5.18) (initial thickness 200 nm).

The red dashed curve in Figure 5.7 was calculated only with contributions of

vacancies and substitutional Ga atoms ΩPD; the black dash-dotted curves are given

by the sum of contributions to bending from vacancies and substitutional atoms

(Equation (5.18)) and sessile clusters (Equation (5.21)). It demonstrates that

bending caused by isolated PD is small as compared to bending due to sessile

clusters. The number of defects dn and the thickness of damaged layer h =20 nm

were estimated with SRIM (Figure 5.3); the parameter = 1.4x10-2 was adjusted to

reproduce the behavior of all three experimental curves. It can be concluded from

Figure 5.7 that Equation (5.21) well agrees with the experimental dependence of

curvature on fluence and initial cantilever thickness. Here, it is also relevant to

mention that the cluster hypothesis of bending is supported by a previous

observation that bending was not removed by annealing at 2000C for 5 hours,

Dense solid samples 97

whereas bending due to isolated PD would anneal completely. No recovery of

bending was also observed in ZnO nanowires annealed at temperatures up to

800oC [20].

Transmission electron micrographs of the 89 nm-thick sample with

progressive irradiation fluences are shown in 5.8. The grain structure is clearly

visible as well as growth twins from the films synthesis by evaporation. These

images provide a qualitative impression of the defect structure evolution with the

typical diffraction contrast associated with small PD clusters[21].

Figure 5.8 – Kinematic bright-field images of 89 nm thick Au film before

irradiation (a) and irradiated with 30 keV Ga+ ions to fluences of 6.7x1019 (b);

1.3x1019 (c) and 2.0x1020 m-2 (d).

The concentration of Ga for different fluences as measured by EDS is shown in

Figure 5.9. The values refer to the average concentration along the film thickness.

The measurements dispersion is attributed to the low concentrations of gallium,

close to the precision [22], but the trend agrees with the model prediction.

98 Chapter 5

Figure 5.9 – Concentration of Ga in the gold film with initial thickness of 144

nm as measured by EDS (circles) and predicted by the model.

5.3 Aluminium cantilevers

The choice of aluminum to further test the model based on the diffusion of

clusters was founded on the fact that it shares gold’s face centered cubic structure,

has a similar lattice constant (4.0495 vs. 4.0782 Å) [23], [24] but considerably

different atomic weights and electronic structures, which translates in distinct

diffusion constants and stacking fault energies. A rather unexpected and surprising

observation was made on these cantilevers. Literature on ion-induced bending

reports that the irradiated structures bend most of the time towards the incident

beam. Yoshida et al. [25] reported bending away from the beam when the ion

accelerating voltage was increased so that the implantation region would fall on the

opposite side of the cantilever’s neutral axis. The aluminium cantilevers under

irradiation with 30 keV Ga+ ions exhibited bending away from the beam at low

doses and a reversal of bending direction as irradiation progressed (Figure 5.10 and

Figure 5.11). This is quite an interesting observation from a fundamental viewpoint

but also for the field of fabrication of nano- and microsized objects.

Dense solid samples 99

Figure 5.10 – Ion-induced bending of aluminum cantilevers (d0=200 nm): a

initial position; b deflection after irradiation fluence of 8.0×1020 m−2 (before

direction reversal took place); and c deflection after fluence of 1.8×1021 m−2

Recent experiments confirmed formation of a dislocation network [26] in Au

nanoparticles and dislocation loops in Al thin films [27] at fluences typical for

focused ion beam (FIB) milling. TEM observation of as-fabricated Al nanopillars

revealed the formation of nm-sized dislocation loops [28]. According to [27], the

dislocation loops formed by a high energy Ga+ ion impact in Al at room

temperature are most likely of the interstitial type.

100 Chapter 5

Figure 5.11 – Deflection (left column) and curvature (right column) of cantilever

of initial thickness a, b 200 nm, c, d 144 nm and e, f 89 nm irradiated to various

fluences indicated in units of m−2. The lines at y=0 represent the initial

condition.

Dense solid samples 101

5.3.1 Kinetics of interstitial clusters

The observed change in bending direction means that the approach described

previously for gold cantilevers isn’t suitable anymore since the volume increase in

the undamaged layers cannot be considered uniform. The dynamical evolution of

clusters needs to be accounted for.

As in the previous model description, a cantilever beam of thickness 0d

irradiated with Ga+ ions is considered. The primary defects produced by

displacement cascades are now isolated PDs and mobile interstitial clusters. For

simplicity, it is assumed that clusters are of the same size m. Doing this has the

major advantage of reducing the number of fitting parameters. Mobile clusters

undergo random walks and form sessile clusters when they collide with each other.

The subsequent evolution of sessile clusters is not followed. In this study the most

important property of sessile clusters is their volume as a function of depth. The

terms for general capture of PDs by dislocations in e.g. Equations (5.4)-(5.7) are

substituted by individual equations for the diffusion of clusters.

The PD generation rate, Ga implantation rate per second and per lattice site

and sputtering yield are calculated with SRIM using Equations (5.1)-(5.3). The

time-dependent rate equations for concentrations of vacancies vC , self-interstitial

atoms iC , interstitial Ga atoms

iGaC , substitutional Ga atoms GaC , mobile clusters

mC and sessile clusters sC are as follows:

1vv v i i iGa iGa v v

dCK C C D C D C D C

dt , (5.26)

1 1 2i

v Ga m S

i i v i i

dCK C C Km C C

dt

D C C D C

, (5.27)

1iGaGa Ga iGa iGa v iGa iGa

dCK K C D C C D C

dt , (5.28)

1GaiGa iGa v Ga

dCD C C K C

dt , (5.29)

102 Chapter 5

21 2mv m m m m m m

dC KC KC D C D C

dt m

, (5.30)

2S

m m m S

dCD C KC

dt , (5.31)

where concentrations are defined per lattice site, ε is the fraction of clustered

interstitial atoms, dc

d

V

n

is a cluster destruction parameter, β is the probability

to destroy a cluster by a cascade, Vdc is volume of a displacement cascade, nd is the

number of defects of one type produced in a cascade and Di,v,iGa,m are the diffusion

coefficients (Dv < Dm < Di,iGa). The parameter dc

d

KVK

n

is the inverse lifetime

of a cluster due to ballistic and thermal spike effects [3], [11], [12]. Here dK n is

the impingement rate per second per unit volume. It is assumed that if a cascade of

volume Vdc develops in the neighborhood of a cluster, then it destroys a cluster with

the probability β<1. The rate constant for cluster formation is written in the so-

called Smoluchowski approximation [29]

8

m m md D

(5.32)

1 33

24

m

md

, (5.33)

where dm is the effective cluster diameter.

For mobile clusters, we use mixed boundary conditions

m

m y vt

y vt

dCC

dy

(5.34)

0

0

mm y d

y d

dCC

dy

, (5.35)

assuming that the flux of clusters at the external surfaces is proportional to the

concentration of clusters near surfaces, i.e., the surface is not a perfect sink for

Dense solid samples 103

clusters as distinct from PD. A physical interpretation of this assumption is related

to how fast interstitial clusters are transformed to be absorbed by external surfaces.

The volume change originating from clusters is now defined as

2 imS m Sm C C

(5.36)

and the inhomogeneous volume change Ω Ω Ω   PD mS is used to substitute the

linear thermal expansion T y in the equations of thermoelastic bending of

cantilevers in the same way as described in the previous section (Equations (5.13)-

(5.15)).

Material parameters used in these simulations are listed in Table 5.2. The

cluster diffusion coefficient mD and parameters , and were adjusted to

reproduce experimental behavior of the cantilever curvature. In the model the

cluster migration energy is 0.3 eV, i.e., higher than reported by MD simulations for

1D migration [30], [31]. This difference can be understood considering that in our

case mD is the effective coefficient of 3D diffusion which requires cluster

reorientation.

104 Chapter 5

Table 5.2 – Material parameters used in model calculations for aluminium

Parameter Value

Flux of Ga+ ions j , m-2s-1 3x1019

Temperature, T , K 300

Sputtering yield, Y (SRIM) 3.8

Recombination rate constant, , m-2 4.8x1020

Rate constant for cluster formation, m , m-2 7.6x1020

Diffusion coefficient of vacancies, vD , m2s-² 7x10-6exp(-0.62 eV/kBT) [32],

[33]

Diffusion coefficient of interstitials, iD , m2s-1 5x10-6exp(-0.1 eV/kBT)*

Diffusion coefficient of clusters, mD , m2s-1 10-5exp(-0.3 eV/kBT)

Atomic volume, , m-3 1.66x10-29

Relaxation volume of vacancies, Δ v -0.33 ω

Relaxation volume of interstitial atoms, Δ i ≈ω

Misfit volume of gallium, Δ Ga -0.08 ω [35]

Number of atoms in cluster, m 4

Fraction of interstitial atoms produced in

clusters,

3.3

Destruction parameter, 3

Simulations carried out with SRIM (‘monolayer collisions-surface sputtering’

option with displacement energy of 25 eV [36]) predict that PD’s are generated

mostly within a range of about 50 nm during normal incident irradiation of Al film

with 30 keV Ga ions (Figure 5.12). According to recommendations [1] the data for

number of defects produced by an ion were divided by factor of 2, since SRIM

overestimates the number of displaced atoms as compared to more realistic MD

simulations.

* At room temperature simulation results do not depend on the diffusion coefficient of

interstitials at typical migration energies ~ 0.1; see also calculation in [34]

Dense solid samples 105

Figure 5.12 – PD production rate K and Ga implantation rate KGa calculated

with SRIM for 30 keV Ga+ ion implanted into amorphous Al target at normal

incidence. The Ga+ flux is 7×1018 m−2s−1 .

For a cantilever of initial thickness 200 nm, the concentration profiles of

vacancies and substitutional Ga atoms are shown in Figure 5.13. The concentration

profiles move inside the film as the material is removed from the surface due to

sputtering. Concentrations of SIAs and Ga interstitial atoms remain below 10−12

because of fast diffusion to external surfaces. At the simulation temperature, the

timescale of vacancy diffusion is (100 nm)²/Dv ~ 37 s. It should be noted that the

concentration of Ga atoms in the subsurface region of thickness 50 nm do not

depend on time after a short transient period.

Figure 5.13 – Concentration profiles of vacancies (a) and implanted Ga atoms

(b). The initial thickness is 200 nm, the Ga+ flux is 7 × 1018 m−2s−1. The left

boundary of the film is moving to the right (indicated with arrow) because of

sputtering.

106 Chapter 5

Figure 5.14 shows concentration profiles of mobile and sessile clusters. It is

seen that the sessile clusters are destroyed near the film surface exposed to the ion

beam. As the irradiated surface recedes due to sputtering, concentration of sessile

clusters increases in the region beyond the penetration range of ions.

Figure 5.14 – Concentration profiles of mobile (a) and sessile clusters (b). The

initial thickness is 200 nm; the Ga+ flux is 7 × 1018 m−2s−1 .

Accumulation of radiation defects results in a high swelling of material, up to

40% in the maximum (Figure 5.15). Vacancies that escaped recombination with

interstitials are removed from the system because of sputtering. Clustered

interstitial atoms survive in the form of sessile clusters, which evolve into

dislocation loops, giving rise to swelling of the film.

Dense solid samples 107

Figure 5.15 – Swelling Ω as a function of depth. The initial thickness is 200 nm;

the Ga+ flux is 7 × 1018 m−2s−1. The vertical solid lines show the position of the

film left boundary subjected to ion irradiation. The dash-dotted lines show the

center lines of the film (neutral axis).

Mobile interstitial clusters that form during cascade evolution can transport

Ga atoms to the unirradiated region. Assuming that the probability to find Ga

atoms in clusters equals the Ga concentration averaged over the implantation

profile thickness imp

GaC (see Figure 5.13b), the increment of Ga concentration in

this region during small time interval is written as

( ) ( )

1

tr imp mSGa Ga

mS

ddC C

(5.37)

108 Chapter 5

Since the Ga implantation profile practically do not change after a short

transient period, i.e. imp

GaC const , Equation (5.37) is easily integrated. The total

Ga concentration in the film is given by

( ) ( ) ( ) ( ) ln 1imp tr imp imp

Ga Ga Ga Ga Ga mSC C C C C (5.38)

5.3.2 Comparison with experiments

The curvature values in the cantilevers’ free-end half were averaged and

plotted against fluence as shown in Figure 5.16. Up to a fluence of 8×1020 m−2

(114 s) the 200 nm cantilever deflects away from the beam; the curvature is

negative. The reason is that most of the swelling occurs between the irradiated

surface and the neutral axis (Figure 5.15). As the film becomes thinner, the bending

direction changes.

Figure 5.16 – Fluence dependence of the curvature 1/R: comparison of

experimental data (symbols) with model calculations (solid lines). The initial

thickness of cantilevers is indicated near the corresponding graphs. The

negative curvature corresponds to downwards bending. The dot-dashed curve

is calculated only with contributions of vacancies and substitutional Ga atoms

to volume change, Equation (5.11) at ε = 0, when cascades do not produce

mobile clusters.

Dense solid samples 109

The minimum curvature reached by the films with initial thickness 200 and

144 nm is similar, while the film with d0=89 nm showed direction reversal at a

smaller negative curvature. This can be reasoned considering the induced swelling

distribution width relative to film thickness is larger in that case. Figure 5.16 shows

also the fluence dependence of bending with ε = 0, i.e. in a system without

production of clusters. In this case the negative value of curvature is due to the

positive volume misfit of substitutional Ga atoms which dominates vacancy

contribution. It is seen, as in the previous chapter, that distributions of isolated

point defects in the damaged region cannot produce the observed cantilever

curvature.

Figure 5.17 compares EDS measurements of Ga concentration in a 200 nm Al

cantilever with the model calculated depth profile and thickness average. The

model prediction that Ga can be found beyond the implantation peak agrees with

the measured values.

Figure 5.17 – Ga concentration in the Al film. a The depth dependence at fluence

8×1020 m−2. b Fluence dependence of Ga concentration averaged over film

thickness as measured by EDS (symbols) and predicted by the model

imp tr

Ga Ga C C (solid line); the dotted line corresponds to the average Ga

concentration without contribution of Ga transported by clusters. The initial

thickness is 200 nm; the Ga+ flux is 7 × 1018 m−2 s−1.

110 Chapter 5

5.4 Considerations about the model

5.4.1 Temperature increase due to irradiation

The model equations take into account the diffusion-limited reactions

between vacancies, interstitial atoms and dislocations, which are controlled by the

mean temperature of the cantilever. The ion irradiation can be expected to cause a

temperature increase in the cantilever.

d Q

Ga+

0 l

T0

-l0

T

x

T0

Figure 5.18 – Temperature distribution in the irradiated cantilever with heat

exchange at x=-l0.

In order to estimate an upper bound of temperature increase δT we assume

that:

the cantilever tip 0 x l is scanned with the Ga+ beam of average flux j;

all kinetic energy of ions transforms into heat in the film (no energy loss to

sputtering, defect creation etc);

the cantilever side-walls are thermally insulated (no heat loss by radiation

to a surrounding medium);

the heat dissipates through the unirradiated cantilever neck of the length l0

into the holder that is kept at constant temperature T0 (Figure 5.18).

The timescale of heat transfer across the 200 nm cantilever is very small and

estimated as κ2 / ~d 3×10-10 s, where κ = 1.27×10-4 m2s-1 is the thermal diffusivity

Dense solid samples 111

of gold. Therefore, on a larger timescale the production rate of heat per unit time

per unit volume can be considered to be uniform across the thickness of the

irradiated part of the cantilever:

00                  at      0

 /       at         0Ga

l xQ

jE d x l

(5.39)

The temperature distribution satisfies the steady state one-dimensional

equation

2

20 

d Tk Q

dx (5.40)

subject to boundary conditions

0

0  x l

T T

(5.41)

0 x l

dT

dx

(5.42)

where k is the thermal conductivity.

The solution of Equations (5.40) and (5.41) is given by

0 0

0 2

0

                      at  0

/2     at        0

x l l xQlT x T

x l x l x lk

(5.43)

The maximum temperature increase is at the cantilever tip x l

2

021  

2GajE l l

Tdk l

(5.44)

For typical parameters j = 3x1019m-2s-1, GaE = 30 keV,

0l l = 5 μm, d = 100

nm and the thermal conductivity of gold k = 314 Wm-1K-1 the temperature increase

is small δT = 0.17 K. Therefore in the cantilever temperature is assumed to be close

to room temperature.

112 Chapter 5

5.4.2 Effects of dynamic composition change

A more sophisticated Monte Carlo code Trydin [37], based on the sputtering

version of the TRIM program for multicomponent targets, computes range profiles

of implanted ions, composition profiles of the target and sputtering rates for a

dynamically varying target composition. However, while SRIM can be readily

downloaded from the internet, Trydin requires a rather bureaucratic procedure.

The concentration of Ga at the surface reaches values of about 5 at.%. By

running the SRIM simulation with the composite target Au95Ga5 it was found that

the influence of implanted Ga on the PD production rate and the sputtering yield is

in the range of a few percent. For this reason SRIM is considered an adequate tool

for our problem; usage of dynamic Trydin code for calculations of the PD

production rate and the sputtering yield would not change the results essentially.

Moreover the average Ga concentration derived from the model well agree with

experimental measurements (Figures 5.9 and 5.17).

5.5 Conclusions

The study demonstrates the ability to bend small structures with sub-micron

precision in a controlled manner using the focused ion beam. A quantitative

relationship between curvature and fluence has been derived which proved to be

helpful in controlling micro- and nanofabrication of small-sized products. Details

of our findings include:

A series of bending experiments with cantilevers made from Au and Al was

performed and different bending responses were observed. The Au

cantilevers bent always upwards (towards the beam) while the Al

cantilevers bent initially downwards and reversed direction as fluence

increased.

The experimental data are discussed in terms of local volume change due to

mass transfer from the cascade region to the so-called undamaged region.

To this end the model for defect diffusion kinetics in the crystalline thin

films under irradiation with energetic ions has been formulated. An

analogy with thermoelasticity is used to convert the inhomogeneous

volume change along the thickness of a free-standing cantilever into

bending curvature.

Dense solid samples 113

It was found that the bending under ion beam irradiation cannot be

explained just by the generation of isolated PDs and deposition of Ga ions

since their effects are too small. Our experimental findings are consistent

with the mechanism of gliding/diffusion of interstitial clusters, which

eventually form sessile clusters. The amount of material transferred to the

unirradiated zone grows with irradiation fluence and leads to swelling in

regions well beyond the penetration range of Ga ions.

The proposed model predicts that the range of ion-induced microstructural

changes far exceeds the SRIM predicted implantation depth. The

application of FIB to prepare samples causes accumulation of radiation

defects and may lead to contamination of the whole sample thickness with

Ga.

5.6 References

[1] R. E. Stoller, M. B. Toloczko, G. S. Was, A. G. Certain, S. Dwaraknath, and F. A. Garner,

“On the use of SRIM for computing radiation damage exposure”, Nuclear Instruments

and Methods in Physics Research, Section B: Beam Interactions with Materials and

Atoms, vol. 310, pp. 75–80, 2013.

[2] P. Jung, “Average atomic-displacement energies of cubic metals”, Phys. Rev. B, vol. 23,

nr. 2, pp. 664–670, jan. 1981.

[3] G. S. Was, Fundamentals of Radiation Materials Science: Metals and Alloys. Berlin

Heidelberg: Springer-Verlag, 2010.

[4] A. Seeger and H. Mehrer, “Interpretation of Self-Diffusion and Vacancy Properties in

Gold”, phys. stat. sol. (b), vol. 29, nr. 1, pp. 231–243, jan. 1968.

[5] S. M. Foiles, M. I. Baskes, and M. S. Daw, “Embedded-atom-method functions for the

fcc metals Cu, Ag, Au, Ni, Pd, Pt, and their alloys”, Phys. Rev. B, vol. 33, nr. 12, pp.

7983–7991, jun. 1986.

[6] S. M. Foiles, M. I. Baskes, and M. S. Daw, “Erratum: Embedded-atom-method functions

for the fcc metals Cu, Ag, Au, Ni, Pd, Pt, and their alloys”, Phys. Rev. B, vol. 37, nr. 17,

pp. 10378–10378, jun. 1988.

[7] W. Maysenhölder, R. Bauer, and A. Seeger, “Effect of three-body interactions on the

formation entropy of monovacancies in copper, silver and gold”, 1985.

[8] B. Predel, “Au-Ga (Gold-Gallium)”, in Ac-Au – Au-Zr, vol. a, O. Madelung, Red.

Berlin/Heidelberg: Springer-Verlag, 1991, pp. 1–5.

[9] R. B. Hetnarski and M. R. Eslami, Thermal Stresses -- Advanced Theory and

Applications. Springer Netherlands, 2009.

114 Chapter 5

[10] D. J. Bacon, F. Gao, and Y. N. Osetsky, “The primary damage state in fcc, bcc and hcp

metals as seen in molecular dynamics simulations”, Journal of Nuclear Materials, vol.

276, nr. 1, pp. 1–12, jan. 2000.

[11] V. Naundorf, “Diffusion in metals and alloys under irradiation”, Int. J. Mod. Phys. B,

vol. 06, nr. 18, pp. 2925–2986, sep. 1992.

[12] A. A. Turkin, C. Abromeit, and V. Naundorf, “Monte Carlo simulation of cascade-

induced mixing in two-phase systems”, Journal of Nuclear Materials, vol. 233, pp.

979–984, okt. 1996.

[13] D. Kiener, C. Motz, M. Rester, M. Jenko, and G. Dehm, “FIB damage of Cu and possible

consequences for miniaturized mechanical tests”, Materials Science and Engineering:

A, vol. 459, nr. 1, pp. 262–272, jun. 2007.

[14] C. Lu e.a., “Direct Observation of Defect Range and Evolution in Ion-Irradiated Single

Crystalline Ni and Ni Binary Alloys”, Scientific Reports, vol. 6, p. 19994, feb. 2016.

[15] H. Diepers and J. Diehl, “Nachweis und Entstehung von Zwischengitteratom-

Agglomeraten in ionenbestrahlten Kupferfolien”, phys. stat. sol. (b), vol. 16, nr. 2, pp.

K109–K112, jan. 1966.

[16] B. Hertel, J. Diehl, R. Gotthardt, and H. Sultze, “Formation of Interstitial Agglomerates

and Gas Bubbles in Cubic Metals Irradiated with 5 keV Argon Ions”, in Applications of

Ion Beams to Metals, Springer, Boston, MA, 1974, pp. 507–520.

[17] J. T. M. D. Hosson, “On the formation of argon-vacancy clusters in copper irradiated

with 4 to 6 kV argon ions”, physica status solidi (a), vol. 40, nr. 1, pp. 293–301, 1977.

[18] E. Friedland and H. W. Alberts, “Deep radiation damage in metals after ion

implantation”, Nuclear Instruments and Methods in Physics Research Section B: Beam

Interactions with Materials and Atoms, vol. 33, nr. 1, pp. 710–713, jun. 1988.

[19] E. Hairer and G. Wanner, “Solving Ordinary Differential Equations II. Stiff and

Differential-Algebraic Problems”, 1996.

[20] C. Borschel e.a., “Permanent bending and alignment of ZnO nanowires”,

Nanotechnology, vol. 22, nr. 18, p. 185307, 2011.

[21] B. L. Eyre, “Transmission electron microscope studies of point defect clusters in fcc and

bcc metals”, J. Phys. F: Met. Phys., vol. 3, nr. 2, p. 422, 1973.

[22] J. Goldstein e.a., Scanning Electron Microscopy and X-ray Microanalysis: Third

Edition, 3de dr. Springer US, 2003.

[23] W. Witt, “Absolute Präzisionsbestimmung von Gitterkonstanten an Germanium- und

Aluminium-Einkristallen mit Elektroneninterferenzen”, Zeitschrift für Naturforschung

A, vol. 22, nr. 1, pp. 92–95, 1967.

[24] A. Maeland and T. B. Flanagan, “Lattice Spacings of Gold–Palladium Alloys”, Can. J.

Phys., vol. 42, nr. 11, pp. 2364–2366, nov. 1964.

Dense solid samples 115

[25] T. Yoshida, M. Nagao, and S. Kanemaru, “Development of Thin-Film Bending

Technique Induced by Ion-Beam Irradiation”, Applied Physics Express, vol. 2, p.

066501, mei 2009.

[26] F. Hofmann e.a., “3D lattice distortions and defect structures in ion-implanted nano-

crystals”, Scientific Reports, vol. 7, p. 45993, apr. 2017.

[27] H. Idrissi e.a., “Point Defect Clusters and Dislocations in FIB Irradiated Nanocrystalline

Aluminum Films: An Electron Tomography and Aberration-Corrected High-Resolution

ADF-STEM Study”, Microscopy and Microanalysis, vol. 17, nr. 6, pp. 983–990, dec.

2011.

[28] S. Lee, J. Jeong, Y. Kim, S. M. Han, D. Kiener, and S. H. Oh, “FIB-induced dislocations

in Al submicron pillars: Annihilation by thermal annealing and effects on deformation

behavior”, Acta Materialia, vol. 110, pp. 283–294, mei 2016.

[29] M. v. Smoluchowski, “Versuch einer mathematischen Theorie der Koagulationskinetik

kolloider Lösungen”, Zeitschrift für Physikalische Chemie, vol. 92U, nr. 1, pp. 129–168,

1918.

[30] D. J. Bacon and Y. N. Osetsky, “Multiscale modelling of radiation damage in metals:

from defect generation to material properties”, Materials Science and Engineering: A,

vol. 365, nr. 1–2, pp. 46–56, jan. 2004.

[31] D. A. Terentyev, L. Malerba, and M. Hou, “Dimensionality of interstitial cluster motion

in bcc-Fe”, Phys. Rev. B, vol. 75, nr. 10, p. 104108, mrt. 2007.

[32] R. W. Balluffi, “Vacancy defect mobilities and binding energies obtained from annealing

studies”, Journal of Nuclear Materials, vol. 69–70, pp. 240–263, feb. 1978.

[33] J. Burke and T. R. Ramachandran, “Self-diffusion in aluminum at low temperatures”,

Metallurgical and Materials Transactions B, vol. 3, nr. 1, pp. 147–155, 1972.

[34] R. Qiu, H. Lu, B. Ao, L. Huang, T. Tang, and P. Chen, “Energetics of intrinsic point

defects in aluminium via orbital-free density functional theory”, Philosophical

Magazine, vol. 97, nr. 25, pp. 2164–2181, sep. 2017.

[35] B. Predel and D.-W. Stein, “Konstitution und thermodynamische eigenschaften der

Legierungen des systems aluminium-gallium”, Journal of the Less Common Metals,

vol. 17, nr. 4, pp. 377–390, apr. 1969.

[36] ASTM E521-16, “Standard Practice for Investigating the Effects of Neutron Radiation

Damage Using Charged-Particle Irradiation”, ASTM International, West

Conshohocken, PA, 2016.

[37] W. Möller and W. Eckstein, “Tridyn — A TRIM simulation code including dynamic

composition changes”, Nuclear Instruments and Methods in Physics Research Section

B: Beam Interactions with Materials and Atoms, vol. 2, nr. 1, pp. 814–818, mrt. 1984.

Nanoporous specimens

“Thirty spokes share the wheel's hub,

It is the center hole that makes it useful.

Shape clay into a vessel,

It is the space within that makes it useful.

Cut doors and windows for a room,

It is the holes which make it useful.

Therefore profit comes from what is there,

Usefulness from what is not there.” [1]

6.1 Introduction

Nanoporous metals have particularities that make them an especially

interesting case for investigating ion-induced bending. Studies have suggested that

nanoporous structures could be resistant to radiation damage when their

characteristic ligament size and the irradiation flux fall within an optimal window

[2]. The reasoning is that if the ligaments are too small, i.e. smaller than the

displacement cascade produced by each collision event, a cascade would cause the

ligament to break or collapse. If on the other hand the ligaments are too large,

consecutive cascades would result in accumulation of defects as in the bulk case.

The sweet spot would be a compromise between ligament size and irradiation flux

such that the irradiation-induced defects are able to diffuse and be annihilated at

the surfaces before another collision event happens in that vicinity.

Nanoporous specimens 117

Those arguments about diffusion lengths and collision frequency do not

consider, however, other effects that may arise from high specific surface area –

enhanced sputtering for instance. Irradiation of gold nanoparticles and thin films

with 25 keV Ga+ ions have been simulated with Molecular Dynamics and the

sputtering yield was found to be size-dependent with a maximum of roughly three

times that of a bulk surface [3]. This effect can be expected to result in high

amounts of internal redeposition and subsequent reconfiguration or densification

of irradiated nanoporous structures. Another important effect arising from ion

irradiation of nanoporous structures is ion-induced coarsening. This effect has not

received much attention in literature. Radiation-induced coarsening was

mentioned in [4], where the response of nanoporous Au samples to irradiation with

400 keV Ne2+ ions to a fluence of ~1019 m-2 was studied. These irradiation

parameters correspond to a uniform radiation damage of 1 dpa in the entire sample

thickness of 150 nm. In this Chapter, ion-induced coarsening is argued to be the

main factor causing the bending of nanoporous cantilevers.

6.2 Experimental considerations

The experimental procedures to cut the bending cantilevers from the free-

standing film in the present work had to be adapted in order to minimize ion-

induced changes in the nanoporous structure. Initial attempts to use the same

cantilever size as the bulk metal samples (around 5x2 µm²) resulted in a curvature

along the cantilever width, which restrains bending along its length, compromising

its measurement. Besides that, the bending of simultaneously irradiated cantilevers

varied considerably (Figure. 6.1) with some amount of lateral bending and cracking

along grain boundaries.

118 Chapter 6

Figure 6.1 – Preliminary attempts to perform bending experiments in

nanoporous cantilevers. Cracking at grain boundaries is clearly visible (red

arrows) as well as curvature induced along the cantilevers width.

In order to minimize these undesired effects, attempts were made to make the

cantilevers as narrow as possible. The intention was to decrease the probability of

the cantilevers being crossed by a grain boundary and at the same time to reduce

any heterogeneities along the cantilever width that could result in lateral bending

and complicate the analysis. By gradually milling the cantilevers lateral edges, free

standing cantilevers could be achieved. Even though the response to irradiation in

these cantilevers did become more uniform than the micro-sized ones shown in

Figure 6.1 the rate of bending seemed to be unexpectedly low and transmission

electron microscopy images of the cantilevers suggest that they experienced

densification (Figure 6.2).

Nanoporous specimens 119

Figure 6.2 – Scanning electron micrograph of ~150 nm-wide cantilever array

after irradiation (a) and bright-field image of as-cut cantilever showing

densified structure (b).

After some trial-and-error iterations, a succesful ion-cutting procedure for the

nanoporous cantilevers was achieved which involved two steps: first the cutting of

two parallel lines in the film, forming a bridge, and then the release of one end of

this bridge, forming a cantilever. When these parallel lines were cut below a certain

distance (roughly 200 nm) the bridges collapsed by themselves in the middle,

leaving equally sized edges in both sides similar to those seen in specimens

subjected to tensile ductile fracture (Figure 6.3).

Figure 6.3 – Preliminary attempts at producing narrow cantilevers with

collapsed bridges.

120 Chapter 6

The optimal width for the cantilevers to avoid densification and achieve

reproducible bending was found to be of around 300 nm (Figure 6.4).

Figure 6.4 – Bending cantilevers with optimized dimensions.

6.3 Ion-induced coarsening

The nanoporous specimens differed from the bulk counterparts in that the

sensitivity to irradiation was considerably higher, and also the displacement

induced by the cutting step, i.e. the position of the cantilevers in the beginning of

the experiments deviate slightly from the plane of the supporting film. These

observations suggest that the governing mechanism in these samples is different

from the solid case, where bending results from bulk mass transfer due to the

diffusion of crystallographic defects. Ion-induced bending of nanoporous

nanopillars was reported in the past by our group [5] and a beam mechanics

description was provided in terms of a stress profile being generated close to the

surface. That was attributed to an ion-induced distribution of vacancies. In the

present experiments, however, some samples had ligament sizes of the same scale

or smaller than that of the displacement cascades as simulated with SRIM for

normal incident 30 keV Ga+ ions. The implantation range for these parameters is

roughly 25 nm while the characteristic length of ligaments in nanoporous gold

prepared by free dealloying lies usually between 5 to 35 nm [6]. Since the stress

Nanoporous specimens 121

profile cannot be assumed to relate to a continuous distribution of defects, a new

hypothesis is presented based on coarsening of the nanoporous structure.

Nanoporosity formation via dealloying involves, in the example of nanoporous

gold, the concurrent removal of Ag and surface diffusion of Au atoms [7]. The

porous structure is very fine in the early dealloying stages and coarsens as it

progresses [8], [9]. Two mechanisms have been suggested to explain the

phenomenon of coarsening, namely localized plasticity in the ligaments and nodes

leading to network restructuring [10]; and surface mediated solid-state Rayleigh

instabilities leading to ligament pinch-off and bubble formation [11]. Both studies

presented reasonable causes for the observation made with HAADF-STEM

tomography of 1-5 nm voids within ligaments [12]; the first as trapping by the

collapse of neighboring ligaments and the second as the result of Rayleigh

breaking-up of the void phase. The voids and the high number of vacancies

resulting from dealloying are thought to play an important role in the process of

coarsening.

The surface instability argument received experimental support by positron

annihilation spectroscopy studies of thermal coarsening [13]. This technique

consists in measuring the time between the injection of positrons in a solid and the

detection of gamma-rays that result from their annihilation with electrons. Since

the local electron density in defects differs from the rest of the crystal, analysis of

the measured lifetimes and their frequencies allows for the characterization of the

number and size of lattice defects such as vacancies, dislocations and voids present

in a sample [14]. In nanoporous gold coarsened at various annealing temperatures,

two positron-lifetime components were identified and assigned to positron

annihilation in: (1) vacancy defects inside the ligaments and (2) larger vacancy

clusters/voids at the ligament-pore interface. The temperature at which the first

component started to decrease, pointing to vacancies annealing, coincided with the

onset of ligament growth. The non-linear variation of the second component with

temperature was interpreted as a signature of the surface instability previously

argued to drive the ligaments’ coarsening, with large voids at the surfaces being

broken down into smaller voids.

Interestingly, thermal coarsening has been shown to be sensitive to the

atmosphere as coarsening was hindered under vacuum or argon when compared to

diatomic nitrogen and oxygen at temperatures up to 400ºC [15]–[17]. The

122 Chapter 6

calculated activation energy for coarsening under vacuum was very close to that of

lattice diffusion in gold, suggesting that surface diffusion is not an active

mechanism in that case. It was proposed that the chemical adsorption of oxygen

and nitrogen (which is generally inactive with gold) causes, as a result of their high

electronegativity, a decrease in the bonding energy of the top-layer gold atoms and

hence facilitates their diffusion as adatoms. A previous study on clusters of

adatoms and vacancies on gold (111) surfaces showed a similar behaviour, where

the area of those features was observed to decay linearly with time under

atmospheric conditions but to be stable under ultrahigh vacuum conditions [18].

Those observations were found to agree well with a model where the mechanism

activating mass flow was the generation of vacancies and adatoms at step edges

instead of the enhancement of free adatoms diffusion. That interpretation was

reinforced by in-situ E-HRTEM studies where nanoporous gold was observed to

coarsen during catalytic CO oxidation [19], [20] by the diffusion of gold atoms at

surface steps.

In nanoporous gold samples subjected to thermal coarsening above 500°C,

grain-boundary cracks were observed as a secondary effect [21]. This was reported

as an observation that was not the focus of the referenced investigation.

Interestingly, coarsening and grain-boundary cracks were also reported to result

from ion irradiation at very low doses , i.e. a single imaging scan with the focused

ion beam [22], and highly strained ligaments were observed across the FIB-induced

cracks. A hint of ion-induced coarsening was also reported in [9], where a

nanoporous gold pillar with diameter of 4 µm was produced by ion milling and

analyzed with X-ray microdiffraction. In the course of the present experiments a

coarsened structure was observed under the scanned lines made amid the

cantilevers cutting steps (Figure 6.5) as well as in the irradiated cantilevers (Figure

6.4).

Nanoporous specimens 123

Figure 6.5 - Coarsened ligaments in the ion-irradiated cutting tracks during the

preparation of nanoporous cantilevers.

An intuitive picture of ion-induced coarsening can be provided based on the

observations above, as follows. In the case of ion-irradiation, one may assume that

a large amount of ligaments will rupture if their sizes are comparable to that of the

displacement cascades. This collapse of ligaments is a pre-requisite for coarsening

according to MD simulations where the decrease of surface area was shown to lag

behind the decrease in topological genus [11]. Additionally, ion-irradiation is

expected to generate point defects that will diffuse and be absorbed preferentially

at the surface steps, leading to either enhanced surface diffusion or direct surface

smoothing via bulk transport [23]. In MD simulations of irradiation of gold

ligaments with 1.5 keV PKA, coarsening was shown to be dose-rate independent,

suggesting that the effect is due to individual cascade effects [4]. Ion-induced

coarsening can then be related to thermal coarsening; assuming (i) direct breakage

of small ligaments by cascades instead of spontaneous collapse by Rayleigh

instabilities and (ii) surface smoothing due to the radiation-induced generation of

point defects instead of thermal activation.

Based on this reasoning, we propose a model that assumes a coarsening

gradient as the main factor generating the bending moment in irradiated

nanoporous cantilevers.

124 Chapter 6

6.4 Model of (IB)² for nanoporous gold

In Chapter 5 we have shown that the mass transfer from the irradiated

cantilever layer to the deeper layers due to transport of interstitial clusters beyond

the Ga penetration range results in cantilever bending. Notwithstanding, ion-

induced bending of nanoporous cantilevers cannot be explained by this

mechanism. The obvious reason is that interstitial clusters cannot escape the

ligament in which they were produced.

To construct a model of nanoporous sample bending under ion irradiation we

use two major experimental observations: (i) nanoporous structure undergo

radiation-induced coarsening and (ii) nanoporous samples are more sensitive to

ion irradiation than solid samples.

The assumption of the model is that ion-induced coarsening (or sintering) of

the nanoporous structure is accompanied with compaction which results in

contraction of the subsurface ligament structure subjected to irradiation. The

nanoporous cantilever is freestanding in the sense it is without constraints against

mechanical deformations; therefore the inhomogeneous volume change causes the

cantilever to bend towards the ion beam. It seems that the ion-induced coarsening

is similar to the effects of annealing on nanoporous gold structures which leads to

coarsening of pores and ligaments [24]–[28]. The underlying mechanism of

thermal coarsening and ligament growth is related to surface diffusion of gold

atoms [11], [28]. The driving force for coarsening is the reduction of total surface

area of ligaments. Evidently, ion beam irradiation enhances atomic mobility in a

similar way as temperature increase. Several mechanisms can control ion-induced

coarsening/sintering:

migration of radiation-induced interstitial atoms to the ligament surface and

surface diffusion of adatoms as controlled by the ligament surface

curvature;

migration of small point defect clusters inside ligaments and to ligament

surfaces.

As discussed in Chapter 5, high mobility of PD clusters of both vacancy and

interstitial types has been confirmed experimentally (for recent results see [29],

[30]) and by means of MD simulations [31]–[33].

Nanoporous specimens 125

In the following our goal is to estimate the relative volume change of the

cantilever material as a function of ligament mean size, ion fluence and depth from

the sample surface. Consider time evolution of a small volume element ( , )V y t

inside the ion-irradiated cantilever, here y is the distance from the cantilever

surface. The volume of all ligaments AuV in the volume ( , )V y t does not change

during irradiation, while volume of pores pV decreases with time due to coarsening

and shrinkage of empty space.

Ion fluence

Ga+

Contraction Contraction

00 pAu VVV pAu VVV

x

y

Figure 6.6 – Schematic view of coarsening and contraction of cantilever

irradiated with ions.

The relative volume change due to coarsening is given by

0 0

( , )( , )

p

Au p

V y ty t

V V

, (6.1)

where 0( , ) ( , ) 0p p pV y t V y t V is the volume decrease from the initial state.

The volume fractions of gold and the porosity are

126 Chapter 6

0

1( , )

1Au Auf y t f

, (6.2)

0( , )

1

p

p

ff y t

, (6.3)

where 0Auf and 0pf are the initial volume fractions.

It is likely that the coarsening is isotropic in all directions, therefore the

relative change in linear dimensions – the linear contraction – is estimated as

1 3

( , ) 1 ( , ) 1y t y t . (6.4)

As in Chapter 5 we use the analogy with the thermoelasticity. Unlike the solid

cantilever the properties of the irradiated nanoporous cantilever such as the linear

contraction and Young’s modulus E depend on position; hence we use formulas of

Ref. [34] describing the thermal stress in an inhomogeneous beam, in which the

linear expansion and Young’s modulus are functions of position y as shown in

Figure 6.6. In equations of thermoelastic bending of the cantilever beam [34] we

replace the linear thermal expansion ( )T y with the linear contraction ( , )y t and

obtain the curvature radius in our problem

0 1

20 2 1

1 T E T E

E E E

M I P I

R I I I

, (6.5)

where

( )

0

( ) ( , ) , 0, 1, 2d t

nEnI t E y t y dy n , (6.6)

( )

0

( ) ( , ) ( , )d t

TP t E y t y t dy , (6.7)

( )

0

( ) ( , ) ( , )d t

TM t E y t y t ydy . (6.8)

Integration is carried out over the cantilever thickness ( )d t which decreases with

time due to ligament sputtering by incident ions and compaction due to coarsening.

Nanoporous specimens 127

0

0

( ) ( , )d

d t d Y jt y t dy

, (6.9)

where Y is the sputtering yield, j is the ion flux and is the atomic volume

(Chapter 5); the upper integration limit d is selected beyond the ion penetration

range in the undamaged region where 0 .

Note that in Eqs. (6.6)-(6.9) the modulus ( , )E y t is the effective Young’s

modulus of the volume element ( , )V y t , which should not be confused with

Young’s modulus of a separate ligament. In our model we use the linear theory of

elasticity. At high ion fluences, when the cantilever deflections is large, one may

expect plastic deformation of ligaments and even microcracking on the far side of

the cantilever.

6.4.1 Kinetics of coarsening

To find the linear contraction ( , )y t we construct below a simple model with

unknown parameters which we will determine from comparison with experimental

data. The total surface area of ligaments S , the characteristic mean ligament size

L and the characteristic mean spacing between ligament (pore size) pL is a

minimal set of variables describing the structure of the volume element under

consideration (Figure 6.6). Parameters defined above are related to gold, pore and

total volumes

AuV ASL , (6.10)

p pV BSL , (6.11)

0 0 0 0 0pAS L BS L V , (6.12)

where A and B are factors associated with the topology of a particular

nanoporous structure. In the following we assume that A and B do not change

essentially with time.

It is natural to assume that (i) the structure with small ligaments coarsens

faster and (ii) the coarsening rate is proportional to the defect production rate

128 Chapter 6

( ) ( )SRIMK y j K y (Chapter 5). Hence the mean ligament size changes with time

according to

1

( )Au

n

dLK y

dt L

, 1n , (6.13)

where n depends on dominating mass transport mechanism, 0Au is a constant.

The solution to this equation can be represented in the form

3

30 ( )

n

n nAu SRIML L n K y

, (6.14)

where is the ion fluence, Au is the dimensionless constant.

In a similar way we construct the equation for the pore size pL

1

( )pP

mp

dLK y

dt L

, (6.15)

where 0p is a constant, the minus sign corresponds to decrease of mean spacing

between ligament. The solution to Eq. (6.15) is given by

3

30 ( )p

m

m mp p SRIML L m K y

, (6.16)

where p is the dimensionless constant.

In the volume element under consideration the volume of solid gold does not

change with time, i.e. SL const , therefore the fluence dependence of the total

area is given by

13

30 00 0 0 ( )

nn

nAu SRIM

S LS S L L n K y

L

. (6.17)

Using Eqs. (6.10),(6.16) and (6.17) we find the pore volume

00

0

( , )( , )

( , )

p

p p

p

L yLV y V

L L y

(6.18)

and the fluence dependence of the relative volume change

Nanoporous specimens 129

00

0

( , )( , ) 1 1

( , )

p

Au

p

L yLy f

L L y

. (6.19)

Using Eq. (6.12) we can obtain the relation between the initial size of pores

0pL and other parameters of the nanoporous structure

00 0

0

1 Aup

Au

fL gL

f

, (6.20)

where g A B

.

6.4.2 Young’s modulus of nanoporous Au

The curvature radius given by Eq. (6.5) depends on Young’s modulus ( , )E y t .

Note that the curvature radius does not change if we substitute ( , ) nAuE y t E for

( , )E y t , where nAuE is Young’s modulus of the undamaged nanoporous material.

This is an important property of the bending phenomenon: it is the relative

modulus (‘relative stiffness’) ( , ) nAuE y t E that contributes to bending rather than

the absolute value of Young’s modulus. Schematically the relative modulus is the

ratio

( , )

nAu

E y t

E

upper layer

bottom layer

E

E, (6.21)

which controls the amount of bending caused by coarsening. A higher modulus of

the upper layer facilitates bending and vice versa: if the upper layer is more

compliant than the bulk the bending is less pronounced.

The Gibson-Ashby scaling relation [35], [36] is used frequently to describe the

dependence of Young’s modulus on density of porous materials, which in our

problems reads

0

( , )1 ( , )

k

kAu

nAu Au

fE yy

E f

, (6.22)

where ~ 2k for the classical Gibson-Ashby relation.

130 Chapter 6

Being designed for low-density cellular (foam) materials, the Gibson-Ashby

relation does not automatically apply to nanoporous gold. The network topology of

a nanoporous structure differs from the cellular architecture of foams. However, in

some materials, this relation is working quite well. Liu and Jin [37] report that in a

Pt-doped nanoporous gold, in which the network connectivity maintained constant,

Young’s modulus varied with relative density according to power-law relation with

an exponent 2.2 0.1k , which agree well with the classical Gibson-Ashby low (

2k ).

It has also been observed that the elastic modulus of nanoporous gold

decreased by more than one order of magnitude in structure coarsening [37], [38]

during which the relative density changed only little. Mathur and Erlebacher [39]

examined Young’s modulus of freestanding, large-grained and stress-free

nanoporous gold films of 100 nm thick over a controlled range of ligament sizes.

Measurements by a buckling-based method [40] have shown a dramatic increase in

the effective Young’s modulus with decreasing ligament size, especially below 10

nm.

All these results indicate that the mechanical response (including the elastic

modulus) of nanoporous metals depends on not only the relative density but also

the topology of the nanoporous structure. The network connectivity [37], [38], [41]

has been suggested as a structural feature that accounts for the anomalous behavior

of Young’s modulus of nanoporous gold. Indeed, strength and stiffness would

decrease if a good number of ligaments in nanoporous metal are ‘broken’ and the

network structure is less connected compared with a foam materials with the same

density (Figure 6.7).

The hypothesis seems to be promising, but then questions arise as to how the

network connectivity parameter can be defined and experimentally measured in

the nanoporous metals, and how it can be correlated to mechanical properties.

Mameka et al [41] proposed a connectivity parameter, which is a ratio between the

diameter of the unit cell of nanoporous structure and the diameter of the closed

rings in a network of load-bearing paths.

Nanoporous specimens 131

Figure 6.7 – Schematic illustration of nanoporous structure with broken or

dangling ligaments (left), and a mechanically equivalent structure obtained by

removing dangling ligaments (right). The density of material with only load-

bearing ligaments is less than the total density (after Ref. [38])

Figure 6.8 shows the influence of coarsening during thermal annealing on the

elastic modulus of the as-dealloyed nanoporous samples [37]. It was found that

Young’s modulus of high density nanoporous samples changed a little when the

structure size was coarsened from 5 nm up to 300 nm during annealing. On the

contrary the elastic modulus of low density samples decreased dramatically after

coarsening. Note a nonmonotonic behavior of Young’s modulus at volume fraction

of gold less than 0.35.

In literature the coarsening of nanoporous structure was proposed to proceed

by the ‘pinch-off’ of some ligaments due to Rayleigh instability [11], [42], [43] and

simultaneous removal (healing) of dangling ligaments by surface diffusion

[11], [44]. Evidently, low density samples with thin ligaments are more prone to

‘pinch-off’ damage caused by annealing which result in decrease of network

connectivity. Increasing ligament size and relative density would decrease the

aspect ratio of ligaments, which decreases the probability of ‘pinch-off’ and

prevents the network connectivity reduction as was observed in [37].

132 Chapter 6

Ligament size, nm

Young m

odulu

s, E

np, G

Pa

Figure 6.8 – Variations of Young’s modulus during coarsening of nanoporous

samples with various initial relative densities, which may increase during

coarsening particularly for low-density samples (after Ref. [37]).

We believe that the influence of ion-induced coarsening on the properties of

nanoporous metals is similar to the thermal coarsening discussed above. Moreover,

the ion irradiation with its sputtering effects is especially efficient to destroy thin

ligaments thereby reducing the connectivity and Young’s modulus. As the sample

become denser with larger ligaments, the radiation-induced coarsening results in a

Young’s modulus increase. In our model the relative modulus is a function of

ligament and pore sizes and initial volume fraction of gold

00 0

0 0

( , )( , )1

( , )

kk

pAuAu Au

nAu Au p

L yf LE yf f

E f L L y

. (6.23)

To model the nonmonotonic dependence on ligament size we will adjust the power

law exponent k for ‘small’ and ‘large’ ligament sizes.

6.5 Comparison with experiments

Figure 6.9 shows the fluence dependence of curvature for nanoporous samples

of different thicknesses and ligament sizes, which are denoted as

Nanoporous specimens 133

‘Thickness/Ligament’. One set of samples was irradiated with 20 keV Ga+ ions; all

other samples were irradiated with 30 keV Ga+ ions. The samples had their

structure tailored by means of varying dealloying times and one was coarsened

thermally. The precursor AuAg alloy foils have thicknesses ranging between 100

and 200 nanometers and therefore coarsening is restricted to that size. In fact, the

sample that was thermally coarsened to the point where the ligament sizes reached

the same scale of the film thickness presented the same bending behaviour as solid

annealed Au samples.

0 1x1019 2x1019 3x1019

0

1

2

3

4

Thickness/Ligament [nm]

128/21

144/47

196/46

196/46 (EGa

= 20 keV)

103/78

89/89 Bulk sample

Curv

atu

re, m

-1

Fluence, m-2

Figure 6.9 – Fluence dependence of curvature for np-samples with different

thicknesses and characteristic lengths.

Figure 6.9 exemplifies the increased bending sensitivity to ion fluence of

nanoporous samples when compared to bulk samples (labelled as 89/89). The

increased sensitivity of the nanoporous samples is evidenced by the fact that the

thickness of the solid cantilever used for comparison was nearly half of the

nanoporous ones.

The four other samples invite a closer look. The argument of ion-induced

ligament collapse and coarsening would predict higher bending rate per fluence for

finer nanoporous structures. However, the finer of the structures produced in this

134 Chapter 6

study, which was dealloyed for 30 minutes (L~25 nm), presented a lower bending

dependence on fluence than the sample dealloyed for 3 hours (L~45 nm). The

reason for such a behavior is the anomalous dependence of Young’s modulus on

ligament size during coarsening of small-sized nanostructures (see below).

0 10 20 30 40 50 60 70

0

5

10

15

20

Ga+ irradiation

C 20 keV

B 30 keV

PD

pro

ductio

n r

ate

KS

RIM

, n

m-1

Depth, nm

Figure 6.10 – The distribution of Frenkel pairs over the sample depth per

incident Ga+ ion at normal incidence. The ‘monolayer collisions – surface

sputtering’ option of SRIM [45] was selected with displacement energy 44 eV

[46].

Depending on the size distribution of ligaments an incident ion can travel

through a ‘surface’ ligament and hit another ligament in a deeper location. On

average in nanoporous materials the ion penetration range is larger than in solids.

To take this into account in our model, which is a mean-field approximation, the

defect generation rate ( )SRIMK y is calculated for an amorphous target of 50%

density of solid gold (Figure 6.10). In reality, nanoporous gold density depends on

fluence and depth y , however for our qualitative model such a refinement is a

second order correction.

The initial fraction of gold in all calculations is 0.3. The initial ligament size

0L was measured in a sample micrograph. To stay in framework of our model the

initial value of 0pL was evaluated using Eq. (6.20) with g 0.45. Other

Nanoporous specimens 135

parameters of the model were adjusted to reproduce the experimental dependence

of curvature radius on fluence: 410Au , 23.0 10p , 2n , 0.5m .

First we show dependence of nanoporous gold geometrical parameters on

fluence of 30 keV Ga+ ions. Figure 6.11 demonstrates that in the near surface region

the volume fraction of gold increases drastically after irradiation to a fluence of

2x1019 m-2 which is a typical maximum fluence in bending experiments with

nanoporous Au

0 20 40 60 80 1000

20

40

60

80

100

Fluence

2x1018 m-2

2x1019 m-2

Au

fra

ctio

n,

%

Depth, nm

a

0 20 40 60 80 1000

20

40

60

80

100b

Fluence

2x1018 m-2

2x1019 m-2

Po

rosity,

%

Depth, nm

Figure 6.11 – Depth dependence of gold volume fraction (a) and porosity (b) at

two values of ion fluences. The initial ligament and pore sizes 0L 46 nm and

0pL = 42 nm.

Figure 6.12a shows depth dependence of ligament size and pore sizes after

radiation-induced coarsening (initial parameters and fluences corresponds with

Figure 6.11). The fluence dependence of the ligament size at a distance of 5 nm

from the surface is presented in Figure 6.12b. This distance can be considered as a

maximum depth which can be seen by SEM in real samples.

136 Chapter 6

0 20 40 60 80 1000

20

40

60

80

100

2x1019 m-2

Siz

e,

nm

Depth, nm

a2x1018 m-2

Ligaments

Pores

0.0 5.0x1018 1.0x1019 1.5x1019 2.0x1019

0

20

40

60

80

100b

Siz

e,

nm

Fluence, m-2

Ligaments

Pores

Figure 6.12 – (a) Depth dependence of ligament size (red) and pore sizes (blue)

at fluences 2x1018 m-2 (dashed curves) and 2x1019 m-2 (solid curves). (b) Fluence

dependence of the ligament size at a depth of 5 nm. Solid and dashed curves

corresponds to ligament and pore sizes respectively.

0.0 5.0x1018 1.0x1019 1.5x1019

40

60

80

100

120

L+

Lp (

FF

T s

ize

), n

m

Fluence, m-2

Figure 6.13 - Evolution of characteristic FFT size with ion irradiation for two

distinct initial average ligament sizes (symbols) Solid curves represents the sum

of ligament and pore sizes calculated with the model.

Figure 6.13 shows the values of the FFT characteristic sizes for samples with

initial average ligament sizes of ~ 27 and ~ 42 nm. The FFT characteristic size is

defined as the position of the first maximum in the dependence of FFT intensity

Nanoporous specimens 137

versus wave vector. For comparison the model predictions for the sum of ligament

and pore sizes are plotted. Examples of the nanoporous structure at different

fluence values are shown in Figure 6.14. Densification can be clearly seen at the last

irradiation step for the sample with smaller ligament size (Figure 6.14c).

Figure 6.14 – Evolution of nanoporous structure under irradiation for samples

with 0L ~ 27 nm (a-c) and 42 nm (d-f) showing unirradiated structure,

intermediate (~7.5×1018 m-2) and final fluences shown in Figure 6.14 In all SEM

micrographs the field of view is 1x1 µm2.

In our experiment it was observed that the bending rate of nanoporous

structures with ligament sizes of ~ 20 nm was lower than the bending rate of

nanoporous structures with 46 nm ligaments. Such a behavior cannot be explained

with the power law exponent 0k in the Gibson-Ashby relation, Eq. (6.23). We

managed to describe bending of nanoporous structures with small ligaments using

the power law exponent 2k . Figure 6.15 shows depth dependence of Young's

modulus (Eq. (6.23)) at a fluence of 1019 m-2 for two types of scaling relation: for the

initial ligament size 20 nm the exponent 2k in Eq. (6.23), for the initial

ligament size 46 nm the exponent 2k . In case of small ligament sizes we

138 Chapter 6

multiplied the right-hand-side of Eq. (6.23) by a factor of 10 in order to emphasize

that undamaged nanoporous material has a higher Young's modulus than the

irradiated subsurface material (as we mentioned above multiplication of the

modulus by a constant does not change the curvature).

0 10 20 30 40 50 60 70

0

2

4

6

8

10

L0 =46 nm k = 2

L0 =20 nm k = -2

Mo

du

lus (

norm

.)

Depth, nm

Figure 6.15 – Depth dependence of Young modulus at a fluence of 1019 m-2 for

two types of scaling relation (6.23).

0.0 5.0x1018 1.0x1019 1.5x1019 2.0x1019

0

2

4

6

8

10

L0 =20 nm k = -2

L0 =46 nm k = 2

a

Mo

du

lus (

no

rm.)

Fluence, m-2

20 30 40 50 60 70 80 900

2

4

6

8

10

L0 =20 nm k = -2

L0 =46 nm k = 2

Mo

du

lus (

no

rm.)

Ligament size, nm

b

Figure 6.16 – Young modulus as a function of fluence (a) and ligament size (b)

at a depth of 20 nm.

Figure 6.16 shows behavior of Young's modulus at a depth of 20 nm. As in

Figure 6.15, in Eq. (6.23) for the initial ligament size 20 nm the exponent 2k ,

whereas for the initial ligament size 46 nm the exponent 2k Figure 6.16b was

plotted as a parametric dependence (20 nm, )K versus (20 nm, )L , where the

Nanoporous specimens 139

parameter is the fluence that changes from 0 to 3x1019 m-2. Note the similarity of

model calculations (Figure 6.16b) with Figure 6.8 which shows a compilation of

experimental data on the effect of annealing on Young's modulus.

In Figs. 6.17-6.19 we compare the curvature radius as predicted by the model

with the curvature found from processing of the experimental data. Figure 6.17

shows that a good agreement with experimental data can be obtained if we use

different power law exponent k for ‘small’ and ‘large’ ligament sizes.

0.0 5.0x1018 1.0x1019 1.5x1019

0

1

2

3

4

Model

L0 = 21 nm k = -2

L0 = 21 nm k = 2

L0 = 46 nm k = 2

Curv

atu

re, m

-1

Fluence, m-2

Figure 6.17 - Fluence dependence of cantilever curvature: influence of initial

ligament size and scaling relation type. Symbols denote experimental data for

the initial ligament size 21 nm (squire) and 46 nm (circles). The blue curve was

calculated with the classical Gibson-Ashby relation (k = 2) for the initial

ligament size 46 nm. The red solid curve was calculated with k = -2 in Eq. (6.23)

for the initial ligament size 21 nm. The dashed curve corresponds to calculations

for the initial size 21 nm with the classical Gibson-Ashby relation (k = 2). Ga+

ion energy is 30 keV.

Figure 6.18 compares the predicted fluence dependence of the cantilever

curvature with experimental data at initial thicknesses 144 and 200 nm. In both

cases the initial ligament size is the same 0L = 46 nm, and the classical Gibson-

Ashby relation (k = 2) was used in calculations.

140 Chapter 6

0.0 5.0x1018 1.0x1019 1.5x1019

0

1

2

3

4 Thickness/Ligament [nm]

144/47

196/46

Model 144/47

Model 196/46

Cu

rva

ture

, m

-1

Fluence, m-2

Figure 6.18 – Influence of initial thickness on the fluence dependence of

curvature. Symbols denote experimental data for the sample thickness 144 nm

(squires) and 200 nm (circles). The model curves are calculated with k = 2 in

Eq. (6.23). The initial ligament size is 46 nm. Ga+ ion energy is 30 keV.

Figure 6.19 shows the fluence dependence of cantilever curvature at Ga+ ion

energies 20 and 30 keV. The model curves reproduce the experimental trend. As it

could be expected the ion beam with lower energy produces lower bending rates,

because of smaller ion penetration range and lower efficiency to create radiation

defects and the consequent structure coarsening.

Nanoporous specimens 141

0 1x1019 2x1019 3x1019

0.0

0.5

1.0

1.5

2.0

2.5

Curv

atu

re, m

-1

Fluence, m-2

20 keV

30 keV

Thickness 200 nm

Ligaments 46 nm

Figure 6.19 – Influence of Ga+ ion energy on the fluence dependence of

curvature. Symbols denote experimental data for the ion energy 20 keV

(squares) and 30 keV (circles). The model curves (solid lines) are calculated

with k = 2 in Eq. (6.23). The initial ligament size is 46 nm.

As an additional test of the model we calculated the thickness decrease of

irradiated nanoporous samples. The total thickness decrease exhibits weak

dependence on ligament size. At the ligament size 46 nm and the fluence

1.5x1019 m-2 the thickness decrease due to sputtering and coarsening is estimated as

sputteringd Y -4 nm (6.24)

0

( , )d

coarseningd y t dy

-7 nm (6.25)

The sum of these values well agree with measurements. However, it should be

noted that experimental measurement of thickness decrease is difficult, because it

is comparable with the ligament size and surface irregularities.

142 Chapter 6

6.6 Conclusions

The stability of nanoporous gold cantilevers with respect to focused ion beam

irradiation was studied and all samples bent toward the 30 kV Ga+ beam. Their

sensitivity to irradiation was observed to be considerably higher than that of solid

samples. A novel message of the model proposed here is that the bending of

nanoporous gold samples under ion irradiation can be explained by coarsening and

sintering of the ligament structure which results in decrease of porosity and

shrinkage of the sample subsurface layer.

An analogy with thermoelasticity was used to convert the inhomogeneous

volume change due to radiation-induced coarsening into the bending curvature of a

free-standing cantilever. The curvature radius depends essentially on the effective

Young's modulus of the damaged nanoporous structure. It turned out that in order

to explain experimental behavior of the cantilevers under irradiation we had to

assume non-monotonic dependence of effective Young's modulus on mean

ligament size: decreasing for small ligament sizes and increasing, of the Gibson-

Ashby type, for larger ligament sizes. The model calculations reproduce

experimental observations on ion-beam-induced bending of nanoporous Au

samples.

The study suggests that nanoporous materials with open-cell porosity are ill-

suited for nuclear applications as structural materials. If on the one hand the high

specific surface area of nanoporous gold facilitates the removal of radiation defects

from the bulk of ligaments; on the other hand it stimulates the radiation-induced

effects of coarsening and sintering, which result in negative swelling, i.e.

dimensional instability.

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A compendium for bending of nanostructures: summary and outlook

7.1 Thesis summary

In addition to exploratory research in the electrochemical fabrication of

nanoporous materials (see Chapter 3), this Thesis has focused primarily on a novel

understanding of the physical mechanisms responsible for the ion-induced bending

phenomenon in metallic materials. Two distinct mechanisms were found to govern

bending in 1. solid bulk and 2. nanoporous thin cantilevers.

The dense solid bulk case, as explained in Chapters 4 and 5, was shown to

involve the formation and accumulation of a defect structure along the samples

thickness. Since the observed cantilever curvatures were too large to be attributed

to the volume change generated by isolated point defects, we postulated that

bending involves the formation of highly mobile interstitial clusters which diffuse

and combine to form sessile clusters in the regions beyond the ion implantation

zone. This hypothesis was supported by the agreement of a rate-equation model

with the experimental observations of two metals with distinct ion-induced

bending behaviors, namely gold and aluminum.

Gold cantilevers, as most of the materials reported in the literature, bended

towards the incident ion beam in all experiments. The unexpected response of

aluminum cantilevers to irradiation was to bend initially away from the ion beam

148 Chapter 7

and to reverse its direction with increasing fluence. This difference in behavior

stems from the distinct defect kinetics in each material. While in gold the sessile

clusters form a broad distribution over depth that extends all the way to the surface

opposite of the irradiated one; in aluminum this distribution over depth is more

narrow and ‘moves’ along the cantilever thickness as sputtering proceeds. In this

manner, the cantilever bends away from the ion beam when most of the interstitial

clusters distribution falls on the ‘top’ side of its neutral axis. The bending direction

is reversed as the cantilever thickness decreases by sputtering and the clusters

distribution falls mostly on the ‘bottom’ side. The phenomena depend critically on

the sputter rate versus the mobility of the clusters, both of which are material

specific.

The nanoporous case: a similar approach was attempted to explain ion-

induced bending in cantilevers made of nanoporous gold. This revealed a series of

particularities that led to the design of a model description taking into account the

volumetric compaction of the irradiated zone rather than the diffusion of defect

clusters.

To start with, the experimental procedures to fabricate the solid bulk bending

cantilevers was found not to be applicable to the nanoporous thin films for a

number of reasons. Special care had to be taken to avoid some effects that would

have affected the analysis. For one, the cantilevers had to be smaller than their bulk

counterparts to minimize the chance of having a grain boundary from the parent

alloy in the bent area. The ion irradiation produces cracks along the grain

boundaries in the dense solid case, which makes the cantilevers displacement non-

uniform and therefore not suitable for study. If the cantilevers were too small,

however, ion-induced densification in the porous systems occurred and made the

bending behavior deviate towards that of the dense solid case. Secondly, the cutting

steps in the cantilever fabrication procedure had to be adjusted carefully to avoid

excessive displacement of the cantilevers prior to the actual experiment, as the

sensitivity to fluence was much higher than in the dense solid case and the mere

scanning of the ion-beam along its cut edges could already cause considerable

bending. After reaching the optimal preparation method that allowed for

reproducible bending, the experimental results could be satisfactorily described

theoretically by assuming a non-monotonic dependence of the irradiated

structure’s effective Young modulus on mean ligament size.

Summary and outlook 149

7.2 Samenvatting

Dit proefschrift concentreert zich op het verkrijgen van nieuwe inzichten in

de fysische mechanismen van ionen-geïnduceerde buig fenomenen in metallische

materialen. Daarnaast is er ook verkennend onderzoek gedaan naar de

elektrochemische vervaardiging van nano-poreuze materialen (zie Hoofdstuk 3). Er

zijn twee verschillende mechanismen gevonden voor de buiging van: 1. massieve- ,

en 2. nano-poreuze dunne vrijdragende balken.

Zoals beschreven in de Hoofdstukken 4 en 5 blijkt in geval van een massieve

hefboom (een balkje dat aan één kant vastzit), die we cantilever noemen, sprake te

zijn van de vorming en accumulatie van defecten langs de doorsnede. De

waargenomen buiging van de cantilever is te groot om toegeschreven te worden aan

de volumeverandering ten gevolge van geïsoleerde puntdefecten, vacatures en

interstitiëlen. Daarom stellen we voor dat de werking van het buigeffect het gevolg

is van mobiele interstitiële clusters van puntfouten. Deze clusters diffunderen en

combineren om vervolgens stationaire clusters te vormen in de gebieden buiten de

ionen-implantatiezone. Deze hypothese wordt onderbouwd met een

productiesnelheidmodel van defecten en met experimentele waarnemingen aan het

door ionen-geïnduceerde buiggedrag van twee verschillende metalen, te weten

goud en aluminium.

De cantilevers van goud buigen in alle experimenten naar de bundel van

invallende ionen toe. Aluminium laat daarentegen een onverwacht verschijnsel

zien door eerst van de ionenbundel af te buigen, om vervolgens bij toenemende

bestraling om te keren. Dit verschil in gedrag wordt toegeschreven aan de kinetiek

van de defecten in de afzonderlijke materialen. In goud zijn de stationaire clusters

breed verspreid over de diepte, tot aan de zijde tegenovergesteld aan de bestraalde

oppervlakte toe. In aluminium is de distributie in de diepte van de clusters vel

smaller en ‘bewegen’ ze over de diepte van de cantilever als de bestraling langer

voortduurt. De balk buigt van de ionenbundel weg zolang de meeste interstitiële

clusters aan de ‘voorzijde’ van de neutrale as blijven. De buiging gaat vervolgens in

omgekeerde richting wanneer de cantilever door aanhoudend sputteren in dikte

afneemt, waardoor de clusters zich vooral aan de ‘achterzijde’ bevinden. Dit

150 Chapter 7

fenomeen is sterk afhankelijk van de sputtersnelheid en de mobiliteit van de

clusters, en is daardoor materiaalgebonden.

Voor de nano-poreuze objecten is voor een vergelijkbare aanpak gekozen, om

ion-geïnduceerde buiging in cantilevers van nano-poreus goud te verklaren. Dit

heeft geleid tot een reeks van nieuwe waarnemingen waaruit de invloeden van

volumetrische verdichting werden ontdekt in plaats van de diffusie van defecten-

clusters.

Zo bleek de experimentele procedure om massieve cantilevers te maken niet

toepasbaar voor de nano-poreuze dunne lagen om meerdere redenen. Extra

aandacht moest geschonken worden om bepaalde effecten te vermijden, die van

invloed kunnen zijn op de analyse. Het eerste effect is dat de cantilevers kleiner

moeten zijn dan de massieve variant om zo de kans op een korrelgrens van de

oorspronkelijke legering in de buigzone te vermijden. De samentrekking ten

gevolge van ionen-bestraling, zorgt voor scheuren langs de korrelgrenzen waardoor

de cantilevers niet gelijkmatig vervormen en daarom niet geschikt zijn voor

gedetailleerde bestudering. Wanneer de cantilevers echter te klein zijn, vindt een

ionen-geïnduceerde verdichting plaats waardoor het buiggedrag gaat afwijken en

meer op het gedrag van massieve cantilevers lijkt. Ten tweede moet het uitsnijden

van de cantilever aangepast worden om vervorming voorafgaand aan het

daadwerkelijke experiment te voorkomen. Deze dunne cantilevers zijn veel

gevoeliger voor bestraling dan de massieve varianten. Slechts een geringe

blootstelling aan de bewegende ionenbundel langs de snijranden kan al een

aanzienlijke buiging veroorzaken. Na optimalisatie van de preparatiemethode

konden reproduceerbare resultaten worden verkregen, welke op een passende

theoretische manier zijn beschreven. Deze beschrijving is gebaseerd op de aanname

dat er een niet-monotone afhankelijkheid van de effectieve stijfheid van de

bestraalde structuur is op de gemiddelde ligamentgrootte.

7.3 Outlook

A natural continuation of the studies on the ion-induced bending

phenomenon is to investigate the behavior of cantilevers made of more than a

single material. Below some preliminary results on the ion-induced bending

behavior of two layered systems are discussed, which have not been investigated

further but present potentially interesting starting points for future research. The

Summary and outlook 151

methods for fabrication of these systems were the same as described in Chapter 2

for the single component samples.

7.3.1 Layered systems

Au-Pt

The choice of Au and Pt is justified by their lack of oxidation issues (its

possible effects are discussed shortly ahead) and the absence of intermetallic

phases that could introduce complex effects to account for. Figure 7.1 shows the

response to irradiation of films with the same thickness (100 nm) made of pure

metals, i.e. Au and Pt; and of bilayered films composed of the two metals irradiated

from both sides.

The Pt film presented the same bending behavior as the Au film, i.e. toward

the ion beam but at a lower rate. MD studies of irradiation-induced stress in thin Pt

films suggested that the initial stress in the film could change the defect structure

development as much as to result in opposed - tensile or compressive - final stress

states[1]. In the present experiments, the evaporated thin films were not annealed

in order to minimize diffusion and ‘blurring’ of the metal-metal interface. This led

to a higher bending rate of the Au cantilever than observed in annealed samples of

similar thickness in Chapter 5.

152 Chapter 7

Figure 7.1 - Fluence dependence of the curvature 1/R of films made of pure Au

(black); pure Pt (green) and bilayered films with the same total thickness

irradiated on the Au side (red) and Pt side (blue).

The layered systems showed bending rates that fell between those of the pure

metal cases. According to SRIM[2] simulations for irradiation with 30 keV Ga+

ions, the implantation range does not cross the interface for any of the two

irradiated sides (Figure 7.2). The role of the interface in interacting with the

diffusing defects would be an interesting question to investigate. We showed earlier

that the bending response to irradiation is inversely proportional to the film

thickness. Assuming that the interface acts rather as a barrier than as a sink, the

irradiation of the bilayered systems can be seen as the irradiation of a single 50 nm

layer that is restrained by another undamaged layer. With this point of view, the

smaller difference between the bending responses of the Au and Pt layers in

comparison to the pure cases could be understood since the Young’s modulus of Pt

is roughly twice the modulus of Au (168 x 78 GPa [3]) making it a better ‘anchor’

for the bending of the Au layer than vice-versa.

Summary and outlook 153

Figure 7.2 - Ion implantation ranges for both sides of the Au-Pt bilayered

system as calculated by SRIM.

Al-Al2O3

In Chapter 5, the abnormal bending behavior of Al cantilevers under

irradiation was explained in terms of the position of the steady-state distribution of

interstitial clusters relative to the total film thickness. One experimental result

particularly in favor of that hypothesis was that the thinner irradiated samples (89

nm) presented downward bending in a much smaller degree than the thicker

samples before reversing direction and bending towards the beam. That

observation was understood to result from the fact that in the thinner samples the

thickness reduction due to sputtering caused the ‘crossing’ of the distribution to the

bottom side of the cantilever to occur at a smaller fluence than in the samples with

144 and 200 nm thickness.

Since Al is known to form a thin oxide layer on its surface when exposed to air,

the question arises of what would be the influence of that layer in the ion-induced

bending phenomenon. To shine light on that issue, a 10 nm layer of Al2O3 was

evaporated on one side of a 100 nm film of pure Al. The surprising bending

behavior observed after irradiation of those samples on both sides is shown in

Figure 7.3.

154 Chapter 7

Figure 7.3 – Effect of the addition of a 10 nm layer of Al2O3 on both sides of a

100 nm thick Al film on the fluence dependence of curvature 1/R.

While the pure Al cantilevers behaved similarly to the cantilevers with 89 nm

presented in Chapter 5 as expected, those with the added oxide layer showed a

much more pronounced bending in the direction opposed to the beam. More

remarkably, the effect occurred when the cantilever was irradiated on the oxide

side but also when irradiated on the opposite side.

An explanation for the downward bending of Al cantilevers in general and the

increase in magnitude when an extra layer is added on the irradiated (‘top’) surface

is as follows. The 30 keV Ga+ ions can pass through the 10 nm oxide layer and

cause displacements in the underlying metal bulk according to SRIM simulations

(Figure 7.4). While the displacements in the metal will give rise to the formation

and accumulation of clusters as discussed earlier, these are unable to diffuse and

annihilate at the top surface before the oxide layer is sputtered away. This way, the

cantilever bends downward due to the positive volume change induced by the

distribution of clusters being formed in the vicinity of the irradiated surface. When

the oxide layer is removed by the impinging ions, the irradiated surface becomes a

sink causing the defect distribution to move deeper into the cantilever’s thickness

Summary and outlook 155

and the bending direction is reversed. The fact that the bending behavior is similar

when the extra oxide layer is at the non-irradiated side of the cantilever is harder to

interpret. This could mean that annihilation at both surfaces plays a crucial role

from the earliest stages of irradiation – a puzzling question for future investigation.

Figure 7.4 – Trajectories of ~10k 30 keV Ga+ ions and distribution profile of

collision events on a bilayered cantilever of Al2O3 (10 nm) and Al (100 nm).

7.3.2 Size-dependent coarsening of ion-irradiated np-Au

In Chapter 6, the volume contraction of the irradiated surfaces of nanoporous

gold was attributed to ion-induced coarsening. This was hypothesized to result

from the direct fracture of smaller ligaments by the ion beam, followed by surface-

mediated rearranging of the structure. More recent measurements of the irradiated

structures were made using images with higher resolution and an automatic code

AQUAMI [4] which has the advantage of not requiring any subjective interventions

from the user. These revealed a size-dependent behavior where densification

followed from thickening of the ligament diameters only for the sample with finer

ligaments (t0~15 nm); the sample with thicker ligaments densifies rather by the

decrease in ligament length. The normalized probability density function

distributions of the nanoporous samples prior and after irradiation are shown in

Figure 7.5.

156 Chapter 7

Figure 7.5 – Comparison of normalized probability density functions of

nanostructure network parameters of samples with t0~15nm (a-c) and t0~35nm

(d-f) before and after irradiation. The ligament and pore diameters were fitted

to Gaussian distributions while the ligament lengths were fitted to log-normal

distributions.

It has to be emphasized that properties such as plastic yield and ductile

fracture are sensitive to the extremes in the distribution, not to the averaged values

[5]. As can be seen in Figure 7.6, a small volume of these samples can present

variations of ligament diameters in the range of roughly one order of magnitude.

The different responses to ion irradiation between samples is here suggested to be a

consequence of the smaller ligament diameters in the sample with t0~15nm (Figure

7.5a). Making a bridge to the case of thermal coarsening of nanoporous gold,

topology has been shown to be an important driving factor. In MD

simulations, a decrease in the topological genus caused by ligament ‘pinch-off’

(a)

(b)

(c)

(d)

(e)

(f)

Summary and outlook 157

events preceded the increase in ligament diameter [6]. Additionally, studies using a

conserved dynamics phase-field model showed that bicontinuous structures exhibit

an asymptotic behavior of the scaled genus upon coarsening, with samples of

different relative densities reaching the same value of scaled genus [7]. Direct

fracture of fine ligaments by the ion beam followed by surface-mediated

rearrangement provides the most probable explanation for the ion-induced

coarsening of the sample with finer ligaments.

Figure 7.6 – Bright field image of sample with L0~35nm. Red arrows highlight

the dispersion of ligament diameters.

So far ion-induced effects on nanoporous gold have been reported either as

secondary observations or with a focus on the effects on single ligaments or pores

[5], [8]–[11]. The evolution of the nanoporous network in samples with two distinct

initial ligament average sizes is shown here to differ under irradiation with Ga+

ions. Both samples showed an increase in the irradiated surface relative density

associated with an increase in the ligaments width-to-length (t/l) ratio.

Interestingly, the densification rate was higher for the sample with smaller

158 Chapter 7

characteristic sizes (t0~15nm), where the increase in t/l proceeded by simultaneous

increase in diameter and decrease in length. For the sample with to~35 nm, the

change in aspect ratio occurred only by decrease of ligament length with no

observed thickening. A more detailed understanding of the effects of ion irradiation

on nanoporous structures may provide a facile alternative to tune their parameters

over the ion-implantation range with a FIB.

Figure 7.7 – Relationship between relative density and ligament aspect ratio for

samples with t0=15 nm (blue) and t0=35 nm (red).

7.4 Opportunities of Ion Beam Induced Bending or (IB) ²

Throughout the present studies, irradiation was performed by scanning the

whole cantilevers area. This was done in order to obtain uniform curvatures along

the cantilever length for each fluence, allowing for the use of the thermoelasticity

analogy. This does not need to be the case, however, as sharp folding of thin films

achieved by irradiation of lines have been reported before [12], [13]. While this

Thesis focused only on a few materials in an attempt to elucidate the physical

Summary and outlook 159

processes, early reports of the ion-induced phenomenon reported bending of

several classes of materials such as metals, semiconductors and compounds [14]–

[16]. Figure 7.8 shows some examples of 3D structures fabricated by single- and

multi-folding achieved by sequential irradiation strategies. Those publications,

however, concentrated rather in demonstrating the feasibility of producing useful

devices providing rather a qualitative picture than a quantitative one. The ion-

implantation range as calculated with SRIM, for instance, is often taken to result in

a static stress distribution with no regards to defect diffusion and recombination.

Figure 7.8 – Examples of structures fabricated using Ion Beam Induced

Bending: (a) Pt mechanical switch for in-situ testing of nano-electronic circuits

[17]; (b) Ti/Al/Cr microcage for trapping of particles [15]; (c) Si thin film

transistor field emitter array [13]; (d) Al helical optical antennas [16].

Regarding the size limitations for structures fabricated by this method and

restricting the discussion to the bulk metal case, one must consider an interplay

between all parameters that define the depth of the ion-induced volume changes,

(a) (b)

(c) (d)

160 Chapter 7

i.e. film thickness, ion source and energy and defect kinectics. Controlled bending

in both directions (toward and opposed to the ion beam) has been demonstrated

elsewhere by varying beam energy and cantilever thickness and no influence was

observed of the cantilever’s length (in the range of 1 to 2 µm) or width (in the range

from 1 µm up to 20 mm)[14].

The cantilever dimensions need to be considered, however, when they are in a

similar size scale as the film’s grains. Our experiments in strongly textured AuAg

films (Figure 7.9) revealed that the effects of differential sputtering for particular

orientations can be large enough to produce significant variation in thickness in the

cantilevers upon irradiation. This uneven thickness results in non-uniform bending

at higher fluences, compromising the reproducibility of the process. The

orientation effect was not observed in the experiments described in Chapter 5 and

this is attributed to the small grain size of the films produced by evaporation, in the

same scale of the film’s thickness hence 1 to 2 orders of magnitude smaller than the

cantilevers dimensions.

Figure 7.9 – Left: superimposed inverse pole figure and image quality maps

showing typical structure of 1x5 µm² Au15Ag85 cantilevers, with lattice

orientation indicators. Right: SEM image of a set of cantilevers after low dose

irradiation, with visible ion channeling-induced contrast and differential

sputtering.

Yet another aspect that hasn’t yet been studied is the effect of irradiation angle

in bending. The depth of the volume changes that govern bending could be tuned

not only by adjusting the beam energy but also by changing the irradiation angle

relative to the surface. The angular dependence of both penetration range [18] and

Summary and outlook 161

sputtering yield [19] could be explored to e.g. minimize the amount of accumulated

damage in a given structure by decreasing the diffusion path for annihilation of

defects at the surface at the same time as the rate of removal of the top layers is

increased.

To conclude, Ion Beam Induced Bending is not only a promising tool in the

fabrication of micro- and nanosized devices or MEMS components but also a

method of characterization of the physical properties of extremely fine nano-

features that are beyond the capacity of typical physical contact-based techniques

to measure. The open questions exposed earlier in this chapter provide exciting

topics of investigation that will ultimately lead to a deepened understanding of the

details involved in FIB-processing of materials.

7.5 References

[1] W.-L. Chan, ‘Stress evolution in platinum thin films during low-energy ion irradiation’,

Phys. Rev. B, vol. 77, no. 20, 2008.

[2] J. F. Ziegler, M. D. Ziegler, and J. P. Biersack, ‘SRIM – The stopping and range of ions

in matter (2010)’, Nuclear Instruments and Methods in Physics Research Section B:

Beam Interactions with Materials and Atoms, vol. 268, no. 11–12, pp. 1818–1823, Jun.

2010.

[3] G. V. Samsonov, Handbook of the Physicochemical Properties of the Elements.

Springer US, 1968.

[4] J. Stuckner, K. Frei, I. McCue, M. J. Demkowicz, and M. Murayama, ‘AQUAMI: An

open source Python package and GUI for the automatic quantitative analysis of

morphologically complex multiphase materials’, Computational Materials Science, vol.

139, pp. 320–329, Nov. 2017.

[5] N. Badwe, X. Chen, and K. Sieradzki, ‘Mechanical properties of nanoporous gold in

tension’, Acta Materialia, vol. 129, pp. 251–258, May 2017.

[6] J. Erlebacher, ‘Mechanism of Coarsening and Bubble Formation in High-Genus

Nanoporous Metals’, Phys. Rev. Lett., vol. 106, no. 22, 2011.

[7] Y. Kwon, K. Thornton, and P. W. Voorhees, ‘The topology and morphology of

bicontinuous interfaces during coarsening’, EPL (Europhysics Letters), vol. 86, no. 4, p.

46005, May 2009.

[8] Y. Sun and T. J. Balk, ‘A multi-step dealloying method to produce nanoporous gold with

no volume change and minimal cracking’, Scripta Materialia, vol. 58, no. 9, pp. 727–

730, May 2008.

162 Chapter 7

[9] S. V. Petegem et al., ‘On the Microstructure of Nanoporous Gold: An X-ray Diffraction

Study’, Nano Lett., vol. 9, no. 3, pp. 1158–1163, Mar. 2009.

[10] M. Caro et al., ‘Radiation induced effects on mechanical properties of nanoporous gold

foams’, Appl. Phys. Lett., vol. 104, no. 23, p. 233109, 2014.

[11] E. G. Fu et al., ‘Surface effects on the radiation response of nanoporous Au foams’, Appl.

Phys. Lett., vol. 101, no. 19, p. 191607, Nov. 2012.

[12] Z. Liu et al., ‘Spatially oriented plasmonic “nanograter” structures’, Scientific Reports,

vol. 6, p. 28764, 2016.

[13] T. Yoshida, T. Nishi, M. Nagao, T. Shimizu, and S. Kanemaru, ‘Integration of thin film

transistors and vertical thin film field emitter arrays using ion-induced bending’,

Journal of Vacuum Science & Technology B, vol. 29, no. 3, p. 032205, 2011.

[14] T. Yoshida, M. Nagao, and S. Kanemaru, ‘Characteristics of Ion-Induced Bending

Phenomenon’, Japanese Journal of Applied Physics, vol. 49, no. 5, p. 056501, May

2010.

[15] K. Chalapat, N. Chekurov, H. Jiang, J. Li, B. Parviz, and G. S. Paraoanu, ‘Self-Organized

Origami Structures via Ion-Induced Plastic Strain’, Advanced Materials, vol. 25, no. 1,

pp. 91–95, 2013.

[16] Y. Mao et al., ‘Programmable Bidirectional Folding of Metallic Thin Films for 3D Chiral

Optical Antennas’, Advanced Materials, vol. 29, no. 19, p. 1606482, 2017.

[17] S. K. Tripathi, N. Shukla, N. S. Rajput, S. Dhamodaran, and V. N. Kulkarni, ‘Fabrication

of nano-mechanical switch using focused ion beam for complex nano-electronic

circuits’, Micro & Nano Letters, vol. 5, no. 2, pp. 125–130, 2010.

[18] H. Gnaser, Low-Energy Ion Irradiation of Solid Surfaces. Berlin Heidelberg: Springer-

Verlag, 1999.

[19] Q. Wei, K.-D. Li, J. Lian, and L. Wang, ‘Angular dependence of sputtering yield of

amorphous and polycrystalline materials’, J. Phys. D: Appl. Phys., vol. 41, no. 17, p.

172002, 2008.

List of publications (thesis subject

and related)

Journal papers

1. L.T.H. de Jeer, D.R. Gomes, J.E. Nijholt, R. van Bremen, V. Ocelík, J.T.M. De

Hosson, Formation of Nanoporous Gold Studied by Transmission Electron

Backscatter Diffraction, Microscopy and Microanalysis 21 (2015) 1387–1397.

doi:10.1017/S1431927615015329.

2. R. van Bremen, D.R. Gomes, L.T.H. de Jeer, V. Ocelík, J.T.M. De Hosson, On

the optimum resolution of transmission-electron backscattered diffraction (t-

EBSD), Ultramicroscopy 160 (2016) 256–264.

doi:10.1016/j.ultramic.2015.10.025.

3. D.R. Gomes et al., On the mechanism of ion-induced bending of

nanostructures, Applied Surface Science 446 (2018) 151–159.

doi:10.1016/j.apsusc.2018.02.015.

4. D.R. Gomes et al., On the fabrication of micro- and nano-sized objects: the

role of interstitial clusters, Journal of Material Science 53 (2018) 7822–7833.

doi:10.1007/s10853-018-2067-0.

5. D.R. Gomes et al., Ion-induced bending of nanoporous gold thin films: a

modelling approach (2018). Manuscript submitted for publication.

6. D.R. Gomes et al., Size-dependent ion-induced coarsening of nanoporous gold

(2018). Manuscript submitted for publication.

164 List of publications

Conference proceedings

1. D.R. Gomes et al., On the fabrication of functional nanostructures with ions,

7th Latin American Conference on Metastable and Nanostructured Materials

(NANOMAT 2017), Brotas, Brazil.

2. D.R. Gomes et al., The Role of Interstitial Clusters in Ion Beam Induced

Bending, 12th International Conference on Surfaces, Coatings and

Nanostructured Materials (NANOSMAT 2017), Paris, France.

Acknowledgements

First of all I wish to express my gratitude for my promotor Jeff De Hosson for

allowing me to pursue my PhD degree under his aegis, guiding and supporting me

throughout. I will always gratefully remember our weekly meetings which Jeff

coined Tempora Diegonis (whose day and time coincided, by a caprice of fate, with

the official PhD graduation ceremony!) and how delightful it was to discuss the

courses of research, the unexpected results, the ever more frivolous bureaucracy,

the anecdotes involving big names of science and whatnot. It is hard to express the

huge privilege it has been to enjoy your enlightening and stimulating influence!

I am deeply obliged to David Vainchtein, my co-promotor, for the help I

received not only on research-related topics but also on broader life and carreer

matters. More than once during casual conversations your questions and advices

led me to open my eyes about important issues I’ve been neglecting – I value those

guidances dearly!

I am grateful to Anatoliy Turkin, whose knowledge (and patience to discuss

and explain out so many misconceptions I brought to him so confidently!)

definitely brought my understanding of radiation damage in materials to a

heigthened level.

I am also grateful for all the people who were somehow involved in the

achievement of this Thesis. I’m aware that the inelegance of forgetting one name is

hard to avoid. In any case, my special words of appreciation to Paul Bronsveld for

his enthusiasm in teaching the operation of the arc-furnace during my first year

and his continual interest on my research; to Vašek Ocelík for all the trainings,

frequent assistance and fruitful collaboration on the optimum resolution of

transmission-electron backscattered diffraction (t-EBSD) leading to one of my first

co-authored publications; and to Yutao Pei for early discussions on template

electrodeposition. And to all the people who passed by the MK group during these

years as students or visitors – it was great sharing laboratory and lunch-table with

you!

166 Acknowledgements

A special mention goes to the students I had the chance to supervise: Jorrit

Nijholt, Marten Koopmans, Bauke Steensma, Lars Gaastra, Sameer Rodrigues and

Konrad Migacz. My gratitude for your trust and the enjoyable cooperations and my

wishes of success in your lifes!

Last but not least, I am grateful for those who were not directly related to the

work that culminated in this Thesis but whose absence would have made it much

more difficult. My friends Roger de Bortoli with his inspiring easy-going and

sincere attitude and Diego Blaese for exchanging weekend visits and the most

fruitful, insightful ontological discussions. My girlfriend Henrika Lüders for being

there and understanding me so well. Meus amigos Rodrigo de Barros, Daniel

Krzsynski e Frederico Mussi que apesar de estarem separados cada um por umas

tantas centenas de quilômetros, estão sempre perto graças à tecnologia. O humor

doentio de vocês me faz rir alto até nos momentos mais difíceis. Obrigado por

estarem aí, piazada do diabo.

Thanks for all your encouragement!

Curriculum Vitae

Diego Ribas Gomes

28 August 1985 Born in Ponta Grossa, Brazil

Education and Activities

8/2014 – 8/2018 PhD in Applied Physics, Materials Science research group

Zernike Institute for Advanced Materials

University of Groningen

Thesis title: Fabrication of metallic nanostructure with

ions: Theoretical concepts and applications

Supervisor: prof. Jeff Th.M. de Hosson

3/2012 – 3/2014 Master degree in Materials Science and Engineering

Federal University of Santa Catarina

Thesis title: Nanosecond ablation of alumina with an

ytterbium fibre-laser: experimental study, topography

and damage evaluation

Supervisor: Prof. Márcio Celso Fredel

9/2012 – 9/2013 Joint period in the context of the Brazilian-German

Collaborative Research Initiative on Manufacturing

Technology

Institute of Advanced Ceramics/Institute of Laser and

System Technologies

Hamburg University of Technology

Supervisor: dr. Rolf Janssen

2/2003 – 12/2008 Bachelor degree in Materials Engineering

State University of Ponta Grossa