Electrical Properties, Tunability and Applications of ... Properties, Tunability and Applications of...

Electrical Properties, Tunability

and Applications of

Superconducting Metal-Mixed

Polymers

Andrew Peter Stephenson

A thesis submitted for the degree of Doctor of Philosophy at

The University of Queensland in July 2010 The School of Mathematics and

Physics

ii

c© Andrew Peter Stephenson, 2010.

Typeset in LATEX 2ε.

iii

Declaration by author

This thesis is composed of my original work, and contains no material previously published

or written by another person except where due reference has been made in the text. I have

clearly stated the contribution by others to jointly-authored works that I have included in

my thesis.

I have clearly stated the contribution of others to my thesis as a whole, including statis-

tical assistance, survey design, data analysis, significant technical procedures, professional

editorial advice, and any other original research work used or reported in my thesis. The

content of my thesis is the result of work I have carried out since the commencement of my

research higher degree candidature and does not include a substantial part of work that has

been submitted to qualify for the award of any other degree or diploma in any university or

other tertiary institution. I have clearly stated which parts of my thesis, if any, have been

submitted to qualify for another award.

I acknowledge that an electronic copy of my thesis must be lodged with the University

Library and, subject to the General Award Rules of The University of Queensland, imme-

diately made available for research and study in accordance with the Copyright Act 1968.

I acknowledge that copyright of all material contained in my thesis resides with the

copyright holder(s) of that material.

Statement of Contributions to Jointly Authored Works Contained in the Thesis

Chapters 3 – 5 of this thesis are each based on separate, submitted or published, bodies

of work. The manuscripts which they are based were written as a collaborative effort by

Adam Micolich, Ben Powell, Paul Meredith and this author. However, in all three cases the

original manuscript was written by this author and the content contained in chapters 3–5 of

this thesis have been rewritten and is the sole responsibility of this author.

Chapter 3 is based on a manuscript entitled Preparation of metal mixed plastic super-

conductors: Electrical properties of tin-antimony thin films on plastic substrates that was

published in the Journal of Applied Physics. All work contained in the publication was

produced by this author with the exception of the data shown in Fig. 3.2, which was taken

iv

by Ujjual Divakar and the fabrication of the samples from which the data shown in Fig. 3.11

was taken, which were made by Adam Micolich.

Chapter 4 is based on a manuscript entitled Competition between Superconductivity and

Weak Localization in Metal-Mixed Ion-Implanted Polymers that was published in Physical

Review B. All the work contained in the submitted manuscript was produced by this author

with the exception of the sample from which the data shown in Figs. 4.9 and 4.10 was taken,

which was fabricated by Adam Micolich.

Chapter 5 is based on a manuscript entitled A tunable metal-organic resistance ther-

mometer that was published in ChemPhysChem. All the work contained in the submitted

manuscript was produced by this author.

Statement of Contributions by Others to the Thesis as a Whole

The work contained in this thesis would not have been possible without the guidance and

support given by Ben Powell, Paul Meredith, Adam Micolich and Ujjual Divakar.

Statement of Parts of the Thesis Submitted to Qualify for the Award of Another

Degree

None

Published Works by the Author Incorporated into the Thesis

• Andrew P. Stephenson, Ujjual Divakar, Adam P. Micolich, Paul Meredith, and Ben

J. Powell Preparation of metal mixed plastic superconductors: Electrical properties of

tin-antimony thin films on plastic substrates. Journal of Applied Physics 105, 093909

(2009)

• Andrew P. Stephenson, Adam P. Micolich, Ujjual Divakar, Paul Meredith, and Ben J.

Powell Competition between Superconductivity and Weak Localization in Metal-Mixed

Ion-Implanted Polymers. Physical Review B 81, 144520 (2010)

• Andrew P. Stephenson, Adam P. Micolich, Paul Meredith, and Ben J. Powell A tunable

metal-organic resistance thermometer. ChemPhysChem 12, 116-121 (2011)

v

Additional Published Works by the Author Relevant to the Thesis but not Form-

ing Part of it

None.

Acknowledgements

There are many people I would like to thank, for without them this project would have been

a lot harder and less enjoyable.

Firstly I must thank my supervisors Ben Powell, Paul Meredith, Adam Micolich and

Ujjual Divakar. Your guidance has been invaluable and without your help I would not have

been able to complete this research. The knowledge and insight you have imparted on me

has increased my ability to be a scientist immensely.

A special thanks must go to those I’ve shared an office with Andrew Sykes, Dave Barry,

Michael Garrett, Tim Vaughan and Glenn Evenbly. Together we shared many laughs and

in doing so you’ve provided me with an enjoyable atmosphere to work in.

On more than one occasion I’ve encountered a problem and I need to thank all those

who have help me over the years, especially Anthony Jacko, Chris Foster, Alex Stilgoe, Paul

Schwenn, Bernie Mostert, Elvis Shoko and Eden Scriven.

In addition, I would like to that Chris, Sam, Geoff, Vince, Aggie and Kim for you have

made this period in my life something I will look back on fondly.

Finally I would like to thank my family Peter, Gabrielle, Lynnford, Heather, Anna,

Margaret, Donald, Evan, Cassarndra, Siobhan, Ethan, Tia, Lauchlan and Charlotte. Your

love and support has been unwavering and without you all I would not be where I am today.

vii

viii Acknowledgements

Abstract

We investigate the newly discovered, superconducting metal-mixed polymers made by em-

bedding a surface layer of metal (a tin-antimony alloy) into a plastic substrate (polyetherether-

ketone - PEEK). Focusing initially on pre-implanted systems, we show that while the sub-

strate morphology does affect the distribution of metal deposited on the surface, the mor-

phology has no affect on the film’s electrical properties. We find that the metal content can

be characterised via the film’s optical absorption, which along with the conductivity, scales

with thickness. By conducting low temperature resistivity measurements we observe that

the superconducting critical temperature, Tc, remains at that of bulk Sn but the transition

broadens with decreasing film thickness.

Studying N-implanted metal-mixed polymers, we find that the implant temperature can

influence the electrical properties of these systems, as higher implant temperatures result in

greater disorder, which in turn causes higher residual resistances and broader superconduct-

ing transitions. We observe peaks in the magnetoresistance of superconducting/insulating

systems, which we attribute to the competition between superconductivity and weak locali-

sation in a granular network.

We determine that the substrate morphology does not influence the electrical properties

of implanted systems. We investigate the role sputtering plays by implanting heavier ions

(Sn) and show that this technique can be used to overcome the issue of inhomogeneity

inherent with using thinner initial films. We study the effect the fabrication parameters of

implant dose, beam energy and film thickness have on Sn-implanted metal-mixed polymers

and find that with only minor changes in the fabrication conditions, it is possible to tune the

conductivities of these materials between a zero-resistance superconducting state, through a

metal-insulator transition, to a severely insulating state (Rs > 1010 Ω/). We find that the

electrical properties can be further controlled by annealing the samples, and that it is possible

to induce optical changes at temperatures approaching the glass transition temperature of

PEEK. We demonstrate that metal-mixed polymers are suitable for use in resistance-based

temperature sensors by comparing their performance directly against commercially available

products and find that the metal-mixed polymers perform at least as well as the commercial

models and, indeed, pass the highest industry standards.

ix

x Abstract

Keywords

Superconductivity, ion-implantation, conducting polymers, metal-mixing, soft electronics,

thermometers.

Australian and New Zealand Standard Research Classifications (ANZSRC)

Contents

Acknowledgements vii

Abstract ix

List of Figures xv

List of Tables xix

List of Abbreviations xxi

1 Introduction & Background 1

1.1 Metals and Insulators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.1.1 Band Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.1.2 Disorder and Localisation . . . . . . . . . . . . . . . . . . . . . . . . 7

1.2 Superconductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

1.2.1 When something other than opposites attract . . . . . . . . . . . . . 11

1.2.2 The Meissner Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

1.2.3 Which type are you? . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

1.2.4 Granular Superconductors and the Josephson Effect . . . . . . . . . . 17

1.3 Conducting Polymers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

1.3.1 The Key to Conducting Polymers: The Delocalised π-System . . . . . 21

1.3.2 Generating Charge Carriers . . . . . . . . . . . . . . . . . . . . . . . 24

1.4 Ion Implantation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

1.4.1 Implanting Polymers . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

1.4.2 Metal-Mixing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

1.5 Motivation and Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

1.5.1 Soft Electronics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

1.5.2 Thermometers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

1.6 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

xi

xii Contents

2 Methods and Techniques 43

2.1 Base Materials and Sample Preparation . . . . . . . . . . . . . . . . . . . . . 43

2.1.1 Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

2.1.2 Sample Preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

2.2 Electrical Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

2.2.1 Four-Terminal Van Der Pauw Measurements . . . . . . . . . . . . . . 48

2.2.2 Four-Terminal Hall Bar Measurements . . . . . . . . . . . . . . . . . 57

2.3 Equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

2.3.1 Cryostat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

2.3.2 Spectrometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

2.3.3 Atomic Force Microscopy . . . . . . . . . . . . . . . . . . . . . . . . . 63

3 Effects of Substrate Morphology 65

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

3.2 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

3.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

3.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

4 The Competition Between Superconductivity and Weak Localisation in

Metal-Mixed Systems 79

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

4.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

4.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

4.3.1 The Effect of Implantation Temperature . . . . . . . . . . . . . . . . 81

4.3.2 Crossing Over to the Insulating Side . . . . . . . . . . . . . . . . . . 83

4.3.3 Weak Localisation in Unimplanted Films with Metallic Conductivity 92

4.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

5 Metal-Mixed Polymers: Effects of Heavy-Element Implantation and Ap-

plications 99

5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

Contents xiii

5.2 Sample Preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

5.3 Effect of Substrate Morphology on Metal-Mixed Polymers . . . . . . . . . . 101

5.4 Tunability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

5.5 Applications - Thermometers . . . . . . . . . . . . . . . . . . . . . . . . . . 111

5.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

6 Conclusions 123

6.1 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

A Additional Thin Film Data 127

A.1 IV Sweeps of SnSb Thin Films . . . . . . . . . . . . . . . . . . . . . . . . . . 127

A.2 Absorption Spectra of Thin Films . . . . . . . . . . . . . . . . . . . . . . . . 131

B Magnetoresistance of Organics Charge Transfer Salts 135

C Sheet Resistance of Metal-Mixed Polymers 139

References 141

xiv Contents

List of Figures

1.1 Milk carton with inbuilt soft electronics . . . . . . . . . . . . . . . . . . . . . 2

1.2 A diagram illustrating atomic orbitals in a lattice hybridising to form bands. 5

1.3 Paths taken by backscattered electrons in the classical and quantum regimes. 9

1.4 Diagram illustrating the phonon mediated process behind Cooper pair formation 13

1.5 The Meissner effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

1.6 Type II superconductor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

1.7 The wavefunction of an electron near a barrier . . . . . . . . . . . . . . . . . 18

1.8 The two structures of polyacetylene . . . . . . . . . . . . . . . . . . . . . . . 20

1.9 The formation of an extended π-orbital through hybridisation . . . . . . . . 21

1.10 Energy level diagram of conjugated polymers of varying lengths. . . . . . . . 23

1.11 Energy level diagram illustrating the Jahn-Teller effect . . . . . . . . . . . . 24

1.12 Charge transport in chlorine doped polyacetylene . . . . . . . . . . . . . . . 26

1.13 Bipolaron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

1.14 The crystal lattice of silicon viewed from different angles . . . . . . . . . . . 30

1.15 Schematic of metal-mixing polymers . . . . . . . . . . . . . . . . . . . . . . 32

1.16 STEM image showing the surface region of SnSb metal-mixed PEEK . . . . 33

1.17 Superconducting transition of SnSb metal-mixed PEEK . . . . . . . . . . . . 35

1.18 Types of platinum resistance thermometers . . . . . . . . . . . . . . . . . . . 41

2.1 Polyetheretherketone (PEEK) . . . . . . . . . . . . . . . . . . . . . . . . . . 44

2.2 Diagram of MEVVA ion implanter . . . . . . . . . . . . . . . . . . . . . . . 46

2.3 Diagram of MEVVA ion source . . . . . . . . . . . . . . . . . . . . . . . . . 46

2.4 Sample layout for four-terminal measurements made in a Hall configuration . 49

2.5 Sample layout for four-terminal measurements made in a van der Pauw con-

figuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

2.6 Method for making 4T measurements in a van der Pauw setup . . . . . . . . 50

2.7 Diagram of a semi-infinte plane with 4 contacts . . . . . . . . . . . . . . . . 51

2.8 Hall effect measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

2.9 Layout of a four-terminal Hall bar electrical measurement. . . . . . . . . . . 58

xv

xvi List of Figures

2.10 Schematic diagram of an Oxford Instruments OptistatDN cryostat . . . . . . 61

2.11 Sample attached to cryostat probe . . . . . . . . . . . . . . . . . . . . . . . . 62

3.1 IV sweeps of thin SnSb films on PEEK substrates . . . . . . . . . . . . . . . 67

3.2 AFM images of the surface of uncoated PEEK and of PEEK with SnSb films

at various thicknesses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

3.3 Absorption spectra of PEEK coated with SnSb films at various thicknesses . 69

3.4 Relationship between absorbance and nominal film thickness of SnSn films on

PEEK substrates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

3.5 Sheet conductance, G‖, as a function of nominal thickness for SnSb films on

PEEK at various temperatures . . . . . . . . . . . . . . . . . . . . . . . . . 71

3.6 Sheet conductance, G‖, as a function of absorbance for SnSb films on PEEK

at varying temperatures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

3.7 Comparison between G‖ and G⊥ for all films at varying temperatures . . . . 73

3.8 Comparison between G‖ and G⊥ for the thinnest films (≤ 12 nm) at varying

temperatures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

3.9 Temperature dependence of the resistance for SnSb films on PEEK substrates

at various thicknesses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

3.10 Gradient of R(T ) as a function of absorption . . . . . . . . . . . . . . . . . . 77

3.11 Superconducting transition of SnSn films of varying thickness on PEEK sub-

strates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

4.1 Superconducting transition of metal-mixed polymers with a pre-implant film

thickness of 200 A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

4.2 Angular dependence of the criticial field for the 20 nm sample implanted at

77 K . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

4.3 Temperature dependence of R2T measured in orthogonal directions of a metal-

mixed polymer with a pre-implant film thickness of 10 nm implanted at 300 K 85

4.4 Two-terminal magnetoresistance along orthogonal directions of 10 nm metal-

mixed samples implanted at 77 and 300 K . . . . . . . . . . . . . . . . . . . 87

List of Figures xvii

4.5 An Arrhenius plot of the high resistance direction of the 10 nm, Sn+,++ metal-

mixed polymers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

4.6 Resistance versus lnT for the high resistance direction of the 10 nm, Sn+,++

metal-mixed polymers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

4.7 Resistance field dependence in orthogonal directions along on a PEEK sample

with a 10 nm SnSb film implanted with a N+ ion-beam . . . . . . . . . . . . 91

4.8 Height of magnetoresistance peak as a function of temperature for a metal-

mixed polymer implanted with an N+ ion-beam . . . . . . . . . . . . . . . . 93

4.9 Magnetoresistance of a unimplanted 20 nm film on a PEEK substrate . . . . 94

4.10 (a) Location of magnetoresistance peak, and (b) peak height, as a function of

temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

5.1 Comparing Rs between orientations as a function of temperature for metallic

metal-mixed polymers implanted with Sn+,++ ions at low doses . . . . . . . 102

5.2 Comparing Rs between orientations as a function of temperature for insulating

metal-mixed polymers implanted with Sn+,++ ions at low energies and high

doses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

5.3 Comparing Rs between orientations as a function of temperature for insulating

metal-mixed polymers implanted with Sn+,++ ions at high energies and high

doses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

5.4 Temperature dependence of Rs for Sn+,++ implanted metal-mixed polymers . 107

5.5 Absorption spectra of Sn+,++ implanted metal-mixed plastics at varying: (a)

film thickness, (b) beam energy, and (c) implant dose . . . . . . . . . . . . . 109

5.6 A diagram illustrating how large scale production of metal-mixed polymers

could be achieved . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

5.7 Calibration curve of a PT100 resistive sample . . . . . . . . . . . . . . . . . 113

5.8 Calibration curve of sample A . . . . . . . . . . . . . . . . . . . . . . . . . . 114

5.9 Calibration curve of samples B and C . . . . . . . . . . . . . . . . . . . . . . 116

5.10 Temperature measured by RTD’s based on a PT100 sample and three metal-

mixed polymers between the melting and boiling points of water. . . . . . . 117

xviii List of Figures

5.11 Residual plots comparing the performance of the four thermometers (PT100

and sample A – C) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118

5.12 Proof of concept data showing the performance sample A in a ‘real-world’ test 120

A.1 IV sweeps of 5 and 6 nm SnSb films on PEEK substrates at 300 K. . . . . . 127

A.2 IV sweeps of 7 – 9 nm SnSb films on PEEK substrates at 300 K. . . . . . . . 128

A.3 IV sweeps of 10 – 14 nm SnSb films on PEEK substrates at 300 K. . . . . . 129

A.4 IV sweeps of a 16 – 20 nm SnSb films on PEEK substrates at 300 K. . . . . 130

A.5 IV sweeps of a 30 nm SnSb films on PEEK substrates at 300 K. . . . . . . . 131

A.6 Absorption spectra of SnSb films on PEEK substrates at various nominal

thicknesses. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131

A.7 Absorption spectra of SnSb films on PEEK substrates at nominal thicknesses

between 5 and 10nm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132

A.8 Absorption spectra of SnSb films on PEEK substrates at nominal thicknesses

between 12 and 30nm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133

B.1 Magnetoresistance of κ-(BEDT-TTF)2Cu(NCs)2 at temperatures below 5 K 135

B.2 Magnetoresistance of κ-(ET)2Cu(NCs)2 at temperatures between 5− 10 K . 136

B.3 Temperature dependence of themagnetoresistance peak of κ-(ET)2Cu(NCs)2

at temperatures below 10 K . . . . . . . . . . . . . . . . . . . . . . . . . . . 136

B.4 Interlayer resistance of κ-(ET)2Cu(N(CN)2)Br . . . . . . . . . . . . . . . . . 137

List of Tables

5.1 Comparing the Arrhenius parameters between orientations for insulating Sn+,++

metal-mixed polymers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

5.2 Residual values between comparisons of temperature readings given by a

PT100 sample and three metal-mixed polymers . . . . . . . . . . . . . . . . 119

C.1 Comparing Rs of Sn+,++ metal-mixed polymers at T = 100 K . . . . . . . . 139

xix

xx List of Tables

List of Abbreviations

Common Acronyms

2T, 4T . . . . . Two-, four-terminal.

AFM . . . . . . . Atomic force microscopy.

BEC . . . . . . . Bose-Einstein condensate.

PEEK . . . . . . Polyetheretherketone.

RT . . . . . . . . . Room temperature.

SnSb . . . . . . . Tin-antimony alloy.

XPS . . . . . . . X-ray photoelectron spectroscopy.

Common Symbols

Tc . . . . . . . . . . Superconducting critical temperature.

Bc . . . . . . . . . Superconducting critical field.

T+c . . . . . . . . . Temperature just above critical temperature.

∆Tc, ∆Bc . . Transition widths.

∆ . . . . . . . . . . Energy gap.

xxi

xxii List of Abbreviations

There are two mistakes one can make along the road to truth...

not going all the way, and not starting.

Buddha 1Introduction & Background

To say modern society is dependent upon electronics is an understatement. With silicon chips

in everything from home computers to cars, from phones to farming machinery, electronic

devices have made their way into every avenue of our lives. With advances in nanotech-

nology and organic-based electronics opening new avenues for electronics, ambitious ideas

like Gundlach’s milk container with interactive labels shown in Fig. 1.1, which may have

once seemed like science fiction, are now thought of products that will be on store shelves in

the not too distant future. However, the attitude of pursuing these technological advances

without caution is now changing.

We live in an age of growing environmental consciousness, where we try to limit our

impact on the earth by using renewable resources. This includes using energy more efficiently

and reducing the amount of minerals mined from the ground. Now although humanity has

devised many ways in which to be more environmentally friendly, these advances have been

held up due to the significant costs involved in development and implementation.[2]

The phenomenon that allows currents to flow without loss, superconductivity, the build-

ing blocks of low-cost organic-based plastics, polymers, and a tool widely used to make semi-

conductors, ion beams, are three fellows rarely seen in another’s company. Yet this thesis is

the study of exactly that, or to be more precise, the study of the electrical and supercon-

ducting properties of a newly created material manufactured by ion-irradiating polymers, a

process called metal-mixing.

Given that metal-mixed polymers are a fairly recent discovery, the need to have a high

1

2 Introduction & Background

Figure 1.1: A disposable milk container with inbuilt interactive labels run low level organic-basedelectronics monitoring product quality and displaying that information for the consumer. Image takenfrom Ref. [1].

understanding of one specilised area is replaced by a more general and far broader under-

standing of the three aspects of this research: electronic charge transport, polymers and

ion-implantation. As these three facets are quite different, rather than giving a single intro-

duction encompassing all three, it is best if each are introduced individually.

To achieve this, the beginning chapter of this thesis is broken into sections: the first giving

a brief overview of metals and insulators; the following three sections are introductions to

superconductivity, conducting polymers and ion-beams respectively; section 5 gives details

1.1 Metals and Insulators 3

of the motivation behind this research; while the final section gives an outline of the thesis.

1.1 Metals and Insulators

This research is focused on the electrical properties of a new type of material. As such a

thorough understanding of how different materials are characterised and their charge trans-

port properties is essential. This chapter will give an introduction of the mechanisms behind

charge transport and define the terminology used throughout this thesis.

There are many ways to characterise the electrical properties of materials. The simplest

is to measure how much a material opposes the flow of an electrical current. This quantity

is known as resistance and denoted R. However, merely characterising materials by their

resistance or its inverse, conductance (S ), is not sufficient to differentiate one material from

another as an appropriately small poor-conductor can have an equal resistance to a suffi-

ciently large good-conductor. Thus the property of resistivity, ρ, (units of Ωm) is a more

intrinsic value as it is not influenced by geometry. The relation between the resistance and

resistivity is given by

R = ρA

l, (1.1)

where A is the cross sectional area the current is passing through and l is the distance the

current is flowing. Now it should be noted that resistivity and its inverse conductivity, σ, are

also not fundamental parameters of a material. This is because different materials can have

the same resistivities and the same material can have different resistivities depending on

how they were made. Furthermore, it is not possible to explain all the behaviour exhibited

by semiconductors using resistivity. When characterising a material’s electrical properties it

is best to determine the charge carrier density, n, and mobility, µ. These are fundamental

properties that theory can use to explain the electronic properties of materials. However, in

many cases, including this project, it is perfectly adequate to characterise materials in terms

of their resistance and resistivity, and their respective inverses.

Materials are generally classed into one of two categories depending on how their re-

sistance changes with temperature. Metals are materials whose resistance decreases with


decreasing temperature, whereas an insulator’s resistance increases with decreasing temper-

ature. In order to explain the mechanisms behind this we must first have an understanding

of band structure.

1.1.1 Band Structure

In single atoms, electrons have quantised momentum states. If one considers an array of

atoms, like that found in a crystal lattice, the states of neighbouring atoms overlap, as

illustrated in Fig. 1.2(a). If there are interactions between states (which there typically is)

an avoided crossing situation occurs [Fig. 1.2(b)] resulting in the formation of delocalised

orbitals called bands [Fig. 1.2(c)]. These bands are the pathway that allows electrons to

move throughout the lattice. These bands are separated in energy-momentum space and the

difference in energies between neighbouring bands is referred to as a band gap and is denoted

∆.

Within each band there are many states. Electrons occupy these states much like they do

in single atoms. At zero temperature, states fill each band starting from those with lowest

energy and, as a result of the Pauli exclusion principle, each state has two electrons with

opposite spins. The highest occupied energy level is called the Fermi level, or Fermi surface

in three dimensions, whose energy is the Fermi energy, εF . The Fermi energy is given by

εF =(~kF )2

2m(1.2)

where kF is the Fermi wavevector.[3] For a spherical Fermi surface kF is given by

kF = (3πn)1/3 (1.3)

where n is the number of occupied states per unit volume and is equal to

n =1

4π3r3s

(1.4)

where rs is the radius of a sphere containing one electron.[3] Combining Eqns. 1.3 and 1.4


Ylabel

D

Ylabel

Xlabel

(c)

(a)

(b)

Ylabel

Xlabel

Xlabel

Figure 1.2: A diagram illustrating atomic orbitals in a lattice hybridising to form bands with abandgap ∆. Note that this is a representation in momentum space, ~k and not real space.


one finds that

kF =

(9π

4

)1/3

× 1

rs=

1.92

rs. (1.5)

At finite temperatures, electrons can be thermally excited to other levels. As such, only

electrons within ∼ kBT of the Fermi energy may participate in thermal excitations, and only

if there are unoccupied states in the same energy range. Therefore, a material’s electronic

properties are predominantly determined by the electrons close to the Fermi surface.[3, 4]

What is a Metal?

The difference between metals and insulators is the energy gap between the highest occupied

and lowest unoccupied energy levels.[3] If the states within a band are partially filled, then

there exist unoccupied states arbitrarily close to the Fermi surface. Charge can move freely

to these excited states and, therefore, around the lattice resulting in a large conductivity. It

is these systems, with partially filled bands, that are metals.

In metals, the conduction electrons’ motion can be impeded by either interacting with

other electrons or being perturbed by the crystal lattice through vibrations. These lattice

vibrations a termed phonons. The rates of both these interactions are thermally driven. As

such, when the temperature rises, these interactions increase and the resistivity goes up.

The expression for the resistivity of a metal as a function of temperature is [3]

ρ(T ) = ρ0 + αeeT2 + βphT

5, (1.6)

where ρ0 is the resistivity at zero temperature and results from electrons scattering off

impurities,[5] αee is the coefficient for electron-electron interactions[6] and βph is the coeffi-

cient for electron-phonon interactions.[7] Of the two, βph is typically much larger than αee,

and unless the system is at extremely low temperatures the electron-electron interactions

can be considered negligible and ignored.[7] At zero temperature the interaction terms of

Eqn. 1.6 go to zero and the resistance is simply ρ0.[8] However, for systems with impuri-

ties localisation effects (which will be discussed below) dominate the transport properties of

metals.[7]


What is an Insulator?

Unlike metals, insulators have no partially filled bands.[3] As such there is an energy gap

(∆) between the highest occupied, and lowest unoccupied, energy levels.[3] Therefore extra

energy is required to excite the electrons and allow charge to move. At finite temperatures

the probability of electrons being thermally excited across a gap ∆ is of order [3]

e−∆/2kBT (1.7)

where kB is Boltzmann’s constant.[4] Once excited, electrons move freely in what is termed

the conduction band, and the hole left behind moves in the valence band. Due to this energy

gap the number of charge carriers in insulators is much lower than in metals, resulting in

higher resistivities.

From Eqn. 1.7 we can see that the probability of electrons being excited to the conduction

band increases with temperature. Now although thermally driven electron and phonon

scattering occurs in insulators as well as metals, its negative contribution to the conductivity

is dwarfed by the positive effect thermally activating charge carriers has. As such, the

resistivity of insulators decreases with increasing temperature. The typical relationship

between conductivity and temperature for insulators is given by [3]

σ(T ) = A× e−∆/kBT . (1.8)

1.1.2 Disorder and Localisation

With the exception of dopants in semiconductors, impurities generally have a negative effect

on a system’s conductivity. Disorder-site scattering is most evident at low temperatures,

when thermal effects are minimal. Therefore it primarily affects metals as its contribution

to an insulator’s resistance at low temperatures is negligible. The temperature independent

term, ρ0, in Eqn. 1.6 results from disorder and a pure metal would have zero resistance at

zero temperature.[8, 9] However, disorder can impact a metal’s electrical properties beyond

simply scattering charge carriers.


From Eqns. 1.6 and 1.8 we see that at zero temperature the DC conductivity, σ(0), is

finite for metals and zero for insulators. The cross over between these two regimes of movable

and immovable charge can be driven by disorder-induced localisation.[10, 11]

Electron localisation is a quantum phenomenon that, naturally, only occurs at low

temperatures.[12] It was proposed by Phillip Anderson in 1958 and was born out of a

model he developed to explain an absence of spin diffusion observed in phosphorous-doped

silicon.[13, 14] Anderson realised that scattering from randomly distributed dopants, in oth-

erwise pure Si, was causing electrons to become localised and thus unable to transmit spin,

or charge.[14]

To understand the mechanism behind localisation, imagine an electron being scattered

off an impurity such that it travels a path bringing it back to that same impurity. The

simplest example is where there exist only two paths – each the time reversed path of the

other. Classically we think of the electron taking only one of the two paths, as depicted in

Fig. 1.3(a). The probability of this occurring is simply the sum of each path’s amplitude

squared, Pcl = |A1|2 + |A2|2 = 2|A|2. However, due to the electron’s wave-nature in the

quantum regime, the electron does not simply take one path, but rather both at the same

time, depicted in Fig. 1.3(b). The probability of this occurring is the square of the summed

amplitudes, PQ = |A1+A2|2 = 4|A|2, which is twice that of the classical case (i.e. PQ = 2Pcl).

Thus the rate at which disorder backscatters electrons increases by a factor of two at low

temperatures.

The electron’s quantum nature at low temperatures allows other phenomena to occur,

namely interference effects. Backscattered electrons, which form closed paths have the ability

to interfere with themselves at low temperatures. If these closed paths contain no other

scattering events, then both paths will start and end in phase. This phase coherence of

time-reversed paths allows electrons to destructively interfere with themselves. If this occurs

then the electrons are no longer free to move and become localised. This reduction in charge

mobility decreases the conductivity. It is these time-reversed trajectories that are the key to

localisation.[7]

The electron localisation described here can be overcome by an external magnetic field.[12]

Ampere’s law describes how charges moving in closed loops relate to magnetic fields. As


Classical

or

PqPcl

Quantum

Figure 1.3: Paths taken by backscattered electrons. In the classical regime (left) electrons arethought of as particles, which take one of two paths. However, in the quantum regime (right) the elec-tron’s wave-nature means it travels both paths at the same time. This leads to interesting phenomena,such as the probability of electrons being backscattered increasing by a factor of 2.

the time-reversed paths are being traversed in opposite directions, an external field will have

opposite effects on the two paths.[15] The effect of the field is to induce a phase shift, of op-

posite sign, to each path. Therefore, electrons localised through self-destructive interference

will be delocalised via a perpendicularly applied field, resulting in an increase in conductivity.

A key signature of localisation is therefore a negative (slope in the) magnetoresistance.[12]

When characterising disordered systems it is useful to define a parameter, γ, which can

indicate the strength of disorder. Here we shall define

γ =1

πkF `, (1.9)

where ` is the electron’s mean free path. In Eqn. 1.5 it was shown that kF is roughly the same

order of magnitude as the electron’s mean spacing, rs. In metals rs is typically ∼ 1 A,[3] as

such kF is roughly the inverse of the lattice spacing.

It is possible to predict the effect localisation has on the conductivity. This was first

demonstrated in 1979 using perturbation theory.[10] Doing so, the conductivity is written as

σ = σ0 + δσ, (1.10)

which is the sum of the zeroth-order DC conductivity, σ0 = e2neτ/m in the Drude regime


where τ is the relaxation time of the electron between scattering events,[4] and a localisation-

induced correction, δσ. In a weakly disordered (γ 1), weakly localised regime (|δσ| σ0)

the temperature dependence of δσ varies greatly between systems of 1, 2 and 3 dimensions.

For a detailed account, please refer to Chapter 12 of Advanced Solid State Physics by Philip

Phillips.[7] The corrections for the three cases are:

δσ

σ0

≡ −γd

T−η/2 D = 1

η~2

ln( ~kBT

) D = 2

~2T η/2 D = 3

(1.11)

where η is the power of the term in Eqn. 1.6 responsible for the greatest scattering. For

D ≤ 2, δσ diverges as T → 0, indicating that there is a minimum temperature for which

Eqn. 1.11 is valid as δσ/σ0 must be less than unity. In the D = 3 case, the weak localisation

correction vanishes as T → 0, indicative of how very unlikely an electron has of returning

to the same site in a weakly disordered, 3D system. In strongly disordered systems (γ ' 1),

where perturbation theory breaks down, it is possible to gain insight using scaling theory.[10]

However, the behaviour predicted here has been experimentally verified [16, 17]

In 1979 Abrahams et al. predicted using scaling theory that in the absence of an ex-

ternal field, arbitrarily weak impurity scattering in any 2D system will cause the resistance

to increase (logarithmically in the weakly localised, and exponentially in the strongly lo-

calised regime) to an infinite value at zero temperature.[10] Since then this issue has been

a topic of great debate in low-dimensional condensed matter physics,[11, 18, 19] with con-

siderable attention focused on the interesting interplay between interactions, disorder and

dimensionality in determining the electronic ground state. [6, 20] In the two decades since

Abrahams’ prediction there has been mounting evidence in support of a non-metallic ground

state in 2D,[16, 17] to the point where the logarithmic signature of localisation in 2D has

become a useful tool to investigate electron scattering in all three dimensions.[21] However,

it should be noted that occasionally there have been indications from theory[22, 23] and

experiment[24–26] that this view might not be entirely correct.[18, 27]

1.2 Superconductors 11

1.2 Superconductors

In the century since the phenomenon was first discovered,[28] superconductivity has had a

dynamic history. With intermittent periods of rapid discovery and comparatively tedious

study. It took twenty years for the mechanism behind the zero resistance state, the Meiss-

ner effect, to be discovered.[29] Another quarter of a century past before Bardeen, Cooper

and Schrieffer formulated their microscopic theory explaining superconductivity.[30] Three

decades later the, then understood, world of superconductivity was rocked by the discovery

of cuprates,[31] resulting in the fastest Nobel Prize in history. However, despite the large

interest, a theory explaining cuprates is still highly sought after. This project studies a

newly discovered superconducting system, as such an understanding of superconductivity is

required. This section will detail the mechanisms behind superconductivity and give a brief

overview of the theory behind it.

It is now known that superconductivity is a quantum phenomena, resulting from a phase

transition to a macroscopic occupation of the lowest energy state, otherwise referred to as

the ground state.[7] However, it initially took scientists quite a while to realise this. In 1925

Albert Einstein predicated that it was possible for a system of bosons (particles with integer

spin) to all occupy a single collective ground state at sufficiently low temperatures.[32] It

was later realised that superfluid 4He was a Bose-Einstein Condensate (BEC). The first real

progress in understanding superconductivity came when Ogg suggested that their may be a

link between BECs and superconductivity.[33] This theory, which required electrons to form

bound pairs, was given support when it was shown that a charged superfluid would display

the Meissner effect and have zero resistance.[34, 35] However, there were two problems with

this theory: how do electrons overcome Coulomb repulsion to form bound pairs?; and how do

electrons, which are fermions (have half integer spin), overcome the Pauli exclusion principle,

to form a condensate?

1.2.1 When something other than opposites attract

The first evidence to suggest that electrons could form bound pairs came in 1950 when Frolich

showed that phonons could lead to a weak attractive force.[36] A few years later Leon Cooper


showed that at sufficiently low temperatures it was possible for two electrons interacting

above a Fermi sea to form bound pairs as long as any attractive force between electrons

existed.[37] These pairs are phonon mediated and formed between electrons with opposite

spin and momentum. The integer spin of the Cooper pair avoided the Pauli exclusion

principle and the newly created ‘psuedo-boson’ was able to condense into a coherent ground

state, much like a BEC.

To understand the electron’s attraction let us consider an electron traveling through a

crystal lattice with spin ↑ and momentum ~k, as shown in Fig. 1.4(a). The electron at-

tracts the nearest ions as it moves through the lattice causing a small region of net positive

charge [Fig. 1.4(b)], which then attracts a second electron with spin ↓ and momentum −~k

[Fig. 1.4(c)]. These two electrons, which are spatially separated have formed a pair in

momentum-space. The average separation between paired electrons is called the coherence

length, ξ.[38] The convenience of this phonon mediated process is that ξ is typically much

larger than the lattice spacing, thereby avoiding Coulomb repulsion between the two elec-

trons. This process is only possible at low temperatures and the maximum temperature at

which pair formation can occur is called critical temperature and is denoted Tc.

The supercurrent, Is, is not the movement of individual electrons, as it is for conventional

conductivity, but rather the motion of the Cooper pair’s centre of mass. BCS theory shows

that electrons are not confined to pairing one at a time, and are in fact able to form pairs

with many electrons simultaneously.[39] Thus allowing Cooper pairs to form and move freely,

thereby giving superconductors their most well known feature – zero resistance. However,

although this is probably the most well known and useful trait of a superconductor, especially

from an applications perspective, it is not its defining feature.

1.2.2 The Meissner Effect

In 1933 Walther Meissner and Robert Ochsenfeld observed that the field strength outside

a sample increased as it became superconducting. It was soon realised that what they

were indirectly observing was the sample becoming a perfect diamagnet1 and expelling the

1Diamagnetism is the property of an object to produce a magnetic field apposing an external magneticfield.


(a) kp

(b)

kd(c)

Figure 1.4: A Diagram illustrating the phonon mediated process forming Cooper pairs: (a) anelectron with momentum and spin ~k↑ moving through a crystal attracts ions; (b) resulting in a smallregion of net positive charge; (c) which attracts a second electron with opposite momentum and spin,− ~k↓.

penetrating field.[29] The Meissner effect is simple to illustrate: above Tc, magnetic flux flows

through a bulk sample in its normal state, as shown in Fig. 1.5(a); and as the temperature

is lowered past Tc the flux is expelled and forced around the superconducting sample, as

shown in Fig. 1.5(b).

It is the Meissner effect, and not zero resistance, that is superconductivity’s defining

ability, and which all others stem from. This is best illustrated using Maxwell’s equations[40]

which describe electromagnetism:

∇ · ~E =n

ε0(1.12)

∇ · ~B = 0 (1.13)

∇× ~E = −∂~B

∂t(1.14)

∇× ~B = µ0~J + µ0ε0

∂ ~E

∂t(1.15)


(b)(a)

Figure 1.5: The Meissner effect: (a) above Tc a magnetic field permiates through a non-superconducting sample; (b) below Tc the Meissner effect forces the magnetic flux around the nowsuperconducting sample.

where ~E and ~B are the electric and magnetic field, ε0 and µ0 are the permittivity and

permeability of free space, n is the total charge density and ~J is the total current density.

Given Ohm’s law, ~E = ρ ~J ,[3] we see that if ρ → 0 (i.e. a perfect conductor) while ~J

remains constant, ~E must also go to zero. This results in the right hand side of Eqn. 1.14

equalling zero, which in turn implies that ∂ ~B/∂t = 0 not ~B = 0. As the magnetic flux in a

superonductor must change to zero as the temperature is lowered through Tc the ability to

be a perfect conductor is not a superconductor’s defining ability. However, if we set ~B = 0

(i.e. a perfect diamagnet) then by default ∂ ~B/∂t = 0 and as a result ρ = 0. Thus perfect

diamagnetism, which induces zero resistivity, is a superconductors defining ability.

As magnetic fields destroy Cooper pairs it is easy to see why superconductivity and

magnetism are thought of as antagonistic phenomena. The field strength required to destroy

all Cooper pairs is called the critical field and is denoted Hc. A current that produces a field

of Hc also destroys superconductivity and is called the critical current, denoted Ic.

In 1935, just two years after the Meissner effect was discovered, the London brothers,

Fritz and Heinz, published the first accurate description of superconductivity, which utilised


two equations:[41]

∂~Is∂t

=nse

2

m~E (1.16)

and

∇× ~Is = −nse2

mc~B (1.17)

where ns is the density of superconducting electrons, e and m are the charge and mass of

the electron respectively and c is the speed of light. The first equation describes perfect

conductivity, as any electric field causes a supercurrent to flow. The second equation, when

combined with Eqn. 1.15 gives [42]

∇2 ~B =1

λ2~B (1.18)

where

λ =

√mc2

4πnse2. (1.19)

This implies that a magnetic field is exponentially screened from the interior of a supercon-

ducting sample (i.e. the Meissner effect) according to the equation

B(x) = B0e−x/λ (1.20)

where λ is the characteristic length scale the field penetrates and is called the London pene-

tration depth.[43] The penetration depth, λ, and coherence length, ξ, are two key parameters

for describing superconductivity. At first glance it might appear that superconductivity can

only exist when ξ > λ, but this is not necessarily the case. Abrikosov showed in 1957 that

it was possible for superconductivity to exist when λ > ξ.[44] This indicated that there are

two types of superconductors.

1.2.3 Which type are you?

Superconductors are divided into two groups according to the ratio of the coherence length

and penetration depth [42]

κ =λ

ξ. (1.21)


When κ <√

2, the magnetic flux is completely expelled and conventional superconductivity

persists. However, when κ >√

2, it is energetically favourable to allow fields to penetrate

a superconducting sample by channeling flux through non-superconducting regions, called

vorticies.[44] Type I superconductors are when κ <√

2 and type II when κ >√

2.[45, 46] A

diagram of a magnetic field flowing through a type II superconductor is shown in Fig. 1.6.

SC Vorticies

Figure 1.6: In a type II superconductor magnetic flux is channeled through non-superconductingregions called vortices.

Bulk metals are typically type I superconductors.[4] Two dimensional (2D) and quasi-

2D systems, such as cuprates[47] and organic charge transfer salts,[48, 49] are examples of

type II superconductors. In the case of thin metallic films it generally takes less energy to

allow the formation of vorticies than to expel the field entirely. Therefore it is possible for

type I superconductors to behave like type II superconductors.[50, 51] A point of difference

between the two types is that type I superconductors have one critical field, whereas type

II superconductors have two: a lower critical field, Hc1, which separates a type I and type

II (Meissner and vortex) phases; and an upper critical field, Hc2, which separates the vortex

and normal phases.[42]

It is possible to determine the dimensionality of a superconductor via the dependence of

the critical field on the angle at which the field is applied to the superconductor. For bulk

(3D) superconductors, λ is always much smaller that the distance the field has to penetrate.

As such, Hc is independant of the direction the external field is applied. However, for 2D

and quasi-2D superconductors, the distance the field has to penetrate in order for flux to


flow through the superconductor depends greatly on the relative angle between the applied

field and the plane of the superconductor. For example, if an external field is applied

perpendicular to a superconductor’s plane, a vortex state can form relatively easily due to

the short distance the field has to penetrate. If however, the field is applied parallel to the

superconducting plane, the distance flux has to penetrate is much larger than λ, thereby

making it much harder for a vortex state to form. For 2D superconductors, the angular

dependence of the critical field is of the form:[52]

∣∣∣∣Bc(θ) sin θ

B⊥c

∣∣∣∣+

(Bc(θ) cos θ

B‖c

)2

= 1, (1.22)

where θ is the angle of the magnetic field relative to the film, and B⊥c and B‖c are the critical

fields obtained when the magnetic field is perpendicular (θ = 90) and parallel to the plane

of the superconductor (θ = 0), respectively.

1.2.4 Granular Superconductors and the Josephson Effect

Along with cuprates and organic charge transfer salts, one of the most popular areas of

superconducting science is granular systems.[53, 54] Granular superconductors consist of

superconducting islands surrounded by a sea of either metallic or insulating material, which

provide a ‘weak link’ between granules.[42] This weak link allows Cooper pairs to tunnel/form

between granules, a feat once said to be impossible.[55]

The probability of two electrons tunneling through a barrier is the square of the proba-

bility of one electron tunneling. Since the one electron case is already very unlikely it was

thought that supercurrents could not flow through barriers. However, in 1962 a 22 year old

graduate student called Brian Josephson realised that individual electrons need not tunnel

as long as Cooper pairs did.[56] The mechanism behind tunneling supercurrents is best de-

scribed using the electron’s wave-nature, as opposed to the particle-like behaviour utilised

in Fig. 1.4.

Consider a superconducting electron at an interface between an insulator which separates

two superconductors. For a sufficiently thin barrier, at sufficiently low temperatures, the


wavefunction of the electron will continue through the barrier to the other superconductor

(shown schematically in Fig. 1.7). The same can be said for a similar electron on the

other side of the barrier. As the electron’s wavefunctions overlap they can interact across

the barrier and from Cooper pairs. Therefore, supercurrents can flow through the barrier

without the need for actual electrons to tunnel.

IS S

Y

k

Figure 1.7: The wavefunction of an electron near an insulating barrier (I) separating two super-conductors (S).

Josephson predicted that a zero-voltage supercurrent could exist between the two super-

conductors equal to

Is = Ic sin ∆ϕ, (1.23)

where Ic is the maximum supercurrent the junction can support and ∆ϕ is the phase differ-

ence between the superconducting electrons’ wavefunction (or Ginzburg-Landau wavefunc-

tion) in the two superconductors. Josephson also predicted that if a potential difference, V ,

between the electrodes could be maintained ∆ϕ would vary with time according to

d(∆ϕ)

dt=

2eV

~, (1.24)

resulting in an AC supercurrent with amplitude Ic and frequency ν = 2eV/~.[57, 58]

Initially, Josephson’s idea was met with a lot of criticism from many physicists, none


more vocal than the father of superconducting theory John Bardeen.[55] However, within

a year of when Josephson’s predictions were first published the DC and AC supercurrents

were both experimentally verified.[59, 60] Josephson went on to win the 1973 Nobel Prize in

physics for this discovery.

It was later realised that this result was far more general than the specific problem

Josephson had solved – quantum mechanic tunneling of electrons through an insulating

barrier.[56] The Josephson effect can explain any system where superconductors are weakly

linked, provided the barrier is thinner than the coherence length of the Cooper pair.[42]

This includes thin metal barriers made superconducting by the proximity effect and short,

narrow constrictions within continuous superconductors capable of carrying supercurrents

greater than the constriction’s critical current. Superconducting quantum interference de-

vices (SQUIDs) utilise all three of these types of Josephson junctions : S-I-S, S-N -S and

S-c-S, where S, I,N and c denote superconductor, insulator, normal metal and constric-

tion respectively.[58] Granular superconductors are, in essence, a large array of Josephson

junctions.

Given their structure, it is not surprising that granular superconductors suffer effects

arising from disorder[20, 61] and reduced dimensionality.[62] These effects produce many

intriguing phenomena and help contribute to the popularity of granular superconductors.

However, superconductivity in disordered and reduced dimensional systems are keenly stud-

ied in their own right.[63] The 2D superconductor-insulator transition has been studied in

a variety of ultrathin films with differing compositions (e.g., elemental metals, alloys, etc.)

and morphologies (e.g., amorphous, crystalline, granular, etc.). [50] Disorder in these films

is heavily dependent upon morphology, producing many sample-specific behaviors such as

quasi-reentrant transitions [64, 65] and anomalous magnetoresistance peaks.[66–68] These

behaviors are much more common in granular systems. However, what is important for this

work is that it has been shown that superconductivity should survive well into the localised

phase outlined in § 1.1.2. [69] From an experimental perspective, superconducting, metallic

and insulating ground states have been observed in ultrathin metal films, [70] with transi-

tions between these states induced by tuning the film thickness [71] or applying a magnetic

field. [66]


1.3 Conducting Polymers

Strictly speaking metal-mixed polymers are conducting organic based materials, however

they are very different systems to conventional conducting polymers. Nonetheless an under-

standing of the electrical nature of organic materials is required to best understand the work

of this thesis, even if for no other reason that to appreciate the competition metal-mixed

polymers face in becoming commercially viable.[72] In this section the nature of conventional

conducting polymers will be discussed.

The first polymer to attain metal-like conductivities was discovered by Heeger, MacDi-

armid and Shirakawa in 1977.[73, 74] This breakthrough was achieved by chemically doping

a polyene2 and earned its discoverers the Nobel prize in Chemistry in 2000.[75–77] Their

method involved exposing thin films of the semiconducting polymer, polyacetylene (CH)x,

to bromine, chlorine or iodine vapour at room temperature for a few minutes. This process

resulted in a dramatic decrease in the bulk resistivity (up to 12 orders of magnitude).[73]

Furthermore, the resistivity was found to decrease with temperature, thereby showing the

polymers were truly metallic and not just less insulating semiconductors.[78] This qualitative

change was the case whether the polyacetylene was a cis-isomer or trans-isomer (see Fig.

1.8).[73]

H

C

C

H

C

C

H

C

H

C C

C

H

H H H

Cis-isomer

C

C

C

C

C

C

H

H H H

H H

Trans-isomer

Figure 1.8: The two structures of polyacetylene first used to make conducting polymers

Since the initial discovery an immense amount of work has been done synthesising other

conducting polymers for electronic applications. This includes creating metallic polymers,

like halogenated polyaniline, but the dominant focus for over a decade has been to produce

2A polyene is an even number of CH groups, covalently bonded to form a linear carbon chain with one πelectron per carbon atom.

1.3 Conducting Polymers 21

semiconducting polymers.[2] Devices based on semiconducting polymers, such as organic

light emitting diodes (OLED),[79] organic photovoltaics (OPV),[80, 81] organic field effect

transistors (OFET)[82] and many other organic electronics, otherwise known as soft elec-

tronics, have well and truly got a foothold in a wide range of commercial applications.[2]

To date the industry of soft electronics is primarily based on one thing: the conducting

polymer.[83]

1.3.1 The Key to Conducting Polymers: The Delocalised π-System

Conducting polymers3 share one common feature, a conjugated carbon-based backbone,

which typically makes the molecule quite rigid.[83] In a conjugated polymer each carbon

in the chain shares four bonds. In most cases, two of these are σ-bonds with adjacent

carbons and one σ-bond is with the nearest hydrogen atom, leaving one p-orbital, which lies

perpendicular to the σ-bonded sp2-system of the carbon backbone.[75, 77] The remaining

p-orbitals hybridise forming an extended, delocalised, π-orbital along the entire molecule,

demonstrated in Fig. 1.9.[84] It is this delocalised π-orbital, brought about by the presence

of the conjugated carbon-based backbone, which is the key to conducting polymers.[84] This

extended π-system is the highway with which the molecules move their charge. Without it

they would be insulators just like their unconjugated polymeric counterparts.

Figure 1.9: A diagram demonstrating p-orbitals of adjacent atoms in a polymer hybridising to forman extended, delocalised π-orbital.

For reasons that will be touched on in a moment, in practice the structure of conjugated

3In organic electronics the term conducting polymer is use to refer to both metallic and semiconductingpolymers


molecules such as polyacetylene cause them to dimerise. This results in the π-orbital be-

ing split into two (π and π∗) bands.[75] Compared to the σ-bonds forming the molecule’s

backbone, π-bonds are significantly weaker.[84] As such, the lowest electronic excitations of

conjugated molecules are the π−π∗-transitions. Due to the nature of the extended π-system

being dependent upon the polymer’s structure, the charge mobility can be greatly affected

by the morphology of the carbon chain.[83] For example, although in their original discovery

Heeger, MacDiarmid and Shirakawa found that both iodinated cis-(CH)x and trans-(CH)x

were metallic, cis-(CH)x had a conductivity ten times higher than trans-(CH)x.[73]

There is more to conducting polymers than just the intramolecular charge transfer. On

any practical scale, bulk samples/devices won’t have single molecules spanning the entirety

of any of its dimension. Thus it is essential that the charge can hop easily between chains.

Intermolecular conductivity is usually much lower than its intramolecular counterpart and

as such the conductivity of a polymer is always lower that that of the single chains that it

is comprised of. This charge hopping is facilitated by π bonding between molecules and is

greatly affected by the order of the bulk sample.[84] In general, crystalline polymers have

higher conductivities as the total energy required for hopping is less than that of amorphous

polymers.[85, 86]

Let us now try to understand the electronic properties of conducting polymers in the

formalism outlined in § 1.1. For insulators to conduct, charge was excited from the fully

occupied valence band to the unoccupied conduction band. In a similar picture, for molecules

to conduct electrons must be excited from the highest occupied molecular orbital (HOMO)

to the lowest unoccupied molecular orbital (LUMO). The simplest system is ethylene with

only two levels: the π level (HOMO), where the two carbons have parallel p-orbitals; and

the π∗ level (LUMO), where they are antiparallel.[83] The next simplest system is butadiene,

where there are 4 carbons (2 double bonds) and 4 molecular orbitals. Increasing the number

of carbon atoms in the conjugated molecule increases the number of energy levels and, as a

result, decreases the energy gap between them.[83] This includes the gap between the HOMO

and LUMO. Thus a conjugated molecule can be considered in a molecular orbital regime as

a series of π and π∗ orbitals. For a finite molecule the orbitals are always discreet, but a

polymer’s molecular orbitals are so numerous that they are indistinguishable.[83] An energy


level diagram for ethlyene, butadien, octatetraene and polyacteylene is shown in Fig. 1.10.

One might expect that for polyactylene the π-electrons will form a half filled band resulting

in the polymer being metallic, but this turns out not to be the case thanks to the Jahn-Teller

effect.

(HOMO)

Energy(LUMO)

(LUMO)

(LUMO)

(LUMO)

(HOMO)

(HOMO)

(HOMO)

Figure 1.10: Energy level diagram of conjugated polymers of varying lengths.

The Jahn-Teller Effect

In 1934 Hermann Jahn and Edward Teller showed that if a chain, consisting of three or

more atoms, has a degenerate groundstate, it is energetically favourable for the chain to

undergo a geometrical distortion.[87] To explain, consider a chain of equidistant atoms that

each have one valence electron, thereby making a degenerate ground state [the 3 atom case

is illustrated in Fig. 1.11(left)]. If however, the chain were to have alternating longer and

shorter bonds, the previously half filled degenerate state would split, resulting in a fully

occupied single state of lower energy [illustrated in Fig. 1.11(right)]. This effect causes

any non-linear molecule with a partially filled degenerate state to undergo a distortion that

breaks symmetry, thereby splitting the degenerate state. This phenomenon is also sometimes


referred to as the Jahn-Teller distortion or, when working with organic systems, the Renner-

Teller effect.[88] It is for this reason that a band gap persists and polyactylene remains a

semiconductor even though the π and π∗ states are indistinguishable.

Total energyTotal energy −2∆

−∆

∆

0δ

−δ

−∆

∆

−2∆−2δ

Figure 1.11: An energy level diagram illustrating that systems comprised of alternating longer andshorter bonds (right) are lower in energy that those spaced equidistant apart (left). This phenomenon,which breaks the 2 fold degenerate ground state, is called the Jahn-Teller effect.

1.3.2 Generating Charge Carriers

Although we have discussed how polymers move charge we still have to explain how they

actually generate the charge carriers in the first place. After all it is no good having a high

carrier mobility if it is wasted by a low carrier density. The extended π-system is diffuse

in nature and readily allows the removal or introduction of electrons into the polymer.[83]

Introducing charge carriers has been done to conventional semiconductors like silicon and

germanium since the 1950’s. In essence it is the same process for conducting polymers. So

much so, the term doping has been borrowed from semiconductor physics, with p-type and

n-type referring to the removal and introduction of electrons respectively.[76] However, the

processes of doping for inorganic semiconductors and conducting polymers are very distinct.


For example, semiconductors are generally doped at very low levels (≤ 1%) whereas polymers

with metal-like conductivities have much higher levels of dopants (typically 20− 40%).[83]

There are many methods in which charge carriers can be generated in conducting poly-

mers. Heeger, MacDiarmid and Shirakawa utilised chemical doping. In this process hy-

drogen atoms where replaced with electron-accepting halogens.[74] This has proven to be

a very successful and easy method for doping. In many cases one must be careful not to

incur unintentional doping as atmospheric oxygen can cause p-type doping during synthesis

and handling of the conducting polymers.[84] Semiconducting polymers, like those used in

organic light emitting devices get charge carriers injected from their contacts.[89] This pro-

cess requires that there be low energetic barriers at each metal-organic interface to ensure

even current flow so that both contacts can inject equal amounts of electrons and holes.[84]

Organic photovoltaics use light to generate electron-hole pairs called excitons.[90] Success-

fully getting high currents from OPVs is generally limited for one of two reasons: firstly

the binding energy of excitons is quite large, making it difficult for successful disassociation;

and secondly the exciton diffusion length is quite small (∼ 10 nm). Field-effect doping is

the underlying principle behind organic field effect transistors. In these systems, charge

carrier density of an intermediate layer between the source and drain can be controlled by

the applied gate voltage.[82]

Electron paramagnetic resonance (EPR) studies have shown that both neutral and heav-

ily doped conducting polymers have no net spin, interpreted as no unpaired electrons, while

moderately doped materials were found to be paramagnetic.[83] Electrical measurements

have shown that of the two, it is the spin-less, heavily doped form that has the higher

conductivity. This is due to the free carriers pairing up once a certain level of doping has

occurred.[83] Although the result is the same for all conducting polymers the methods by

which this is done varies depending on the polymer.[91, 92]

In the case of polyacetylene, a single oxidation, due to say chlorine, creates a cation.

This cation is now free to move along the chain, as depicted in Fig. 1.12(a). A successive

oxidation on the same chain creates the opportunity for radical coupling to occur resulting

in a soliton. Polyacetylene has two degenerate ground states, which allows the cations to

move independently of each other, as shown in Fig. 1.12(b).[77]


Figure 1.12: Charge transport in polyacetylene moderately doped (a) and heavily doped (b) withchlorine. Figure taken from Shirakawa et al [77].

For molecules more complicated than polyacetylene, that only have a single ground state,

the process of charge transfer is slightly different for heavily doped systems.[92] After a single

oxidation a cation is formed and the result is called a polaron. A polaron behaves much the

same as single free carrier in polyacetylene. If a second oxidation removes another electron

a dicationic species is formed called a bipolaron. Contrary to polyacetylene’s independent

charges, the bipolaron unit remains intact and the entire entity propagates along the chain.

Fig. 1.13 illustrates the bipolaron movement in polythiophene.[83]

Conducting polymers, and soft electronics in general, are primarily fabricated using

chemical based methods.[2] This is, in part, due to polymers requiring chemical doping

to become conductive,[93] but also because techniques such as spin coating, which require

solution processing,[94] allow easy large scale fabrication.[2, 95] Metal-mixed polymers are

quite distinct in this regard as they are produced by the physically-based process of ion-

implantation.[96]

1.4 Ion Implantation 27

S

S+

S

S+

S

S

S

Bipolaron Unit

S

S

S+

S

S+

S

S

S

S

S

S+

S

S+

S

Bipolaron Unit

Figure 1.13: Charge transport is facilitated by the doubly charge bipolaron unit in polythiophene.

1.4 Ion Implantation

Ion beams are a tool used in a variety of applications. These range from the exotic ion

drives currently propelling spacecraft around the solar system[97] to the seemingly mun-

dane widespread use in the semiconductor industry.[98, 99] This project is an area that is

completely dependent upon ion beams and as such an explanation of them, their effect on

polymers and their use in metal-mixing is given in this section.

The first demonstration of a focused ion beam was over 120 year ago by the German

scientist Goldstein, and the first reports of ion implantation are of Ernest Rutherford using

radon discharges to fire helium nuclei at aluminum foil in 1906.[100] By the time Niels Bhor4

had developed a mathematical model of ion stopping in 1913,[101] J. J. Thomson had worked

out the basic understanding of ion beams[102] and had realised that surface modification was

resulting from the physical absorption of implanted particles.[103] Yet despite these early

4Niels Bhor was working with Ernest Rutherford at the time.


advances, it took many decades for the investigation of ion beams to gain momentum.

It was not until the dawn of the nuclear age in the 1930’s and 40’s that the understanding

of, and technology behind, ion beams began to develop. The motivation for this progress

came from two, quite separate, sources. Firstly, with the advent of the nuclear reactor,

materials were for the first time being subjected to bombardment from fast moving neu-

trons, which caused the atoms they collide with to recoil with energies up to a few hundred

keV.[104] Thus, a greater understanding of how implantation works was needed. The second

motivating factor resulted in the development of particle accelerators, which were needed to

separate uranium isotopes to build massively destructive weapons.[100]

Soon after, the effects ion implantation has on the electrical properties of materials (pri-

marily silicon and germainium) was realised, and in 1952 Russel Ohl at Bell Labs produced

the first transistor made from ion implanted silicon.[105] However, the popularity ion beams

now have in the semiconductor industry took several decades to develop. Originally it was

much simpler and a lot cheaper to dope semiconductors by thermal diffusion or expatial

growth,[99, 104] and as such doping through ion implantation was not seen as an area to in-

vest resources (whether it be time for research or money for infrastructure).[106] However, as

time passed and Moore’s law took effect, computer power increased and ever more complex

circuitry was required. More processing steps were needed to achieve the required high com-

ponent densities and the limitations of the chemical-based methods became apparent.[106]

Ion implantation was the answer, as it offered a low-temperature method for injecting highly

accurate concentrations of different ions into precisely defined regions, and needed fewer

thermal cycles to do so.[106] With the support of the semiconductor industry, ion implan-

tation technology grew rapidly, and it is now used in a wide range of surface modification

applications such as hardening the tips of razor blades or making replacement hip joints and

heart valves more resistance to corrosion, wear or fragmentation.[106–108]

Although ion implantation is a fairly straightforward process: a plasma is created, the

charged ions are accelerated via a potential field and directed at a target;[99] the results

are not. There are two main types of interactions that occur once an ion penetrates a

target, nuclear and electron stopping. Nuclear stopping is where energy is lost through

ion-atom collisions. It is an elastic process that primarily affects slow moving ions.[104]


Electron stopping is an inelastic process where an implanted ion’s energy is lost through

electron scattering and primarily affects high speed ions.[104, 109] There are of course many

recoil events, resulting in ions being affected by both interactions, and many cascade events,

resulting in the ion’s energy being dispersed over large regions.[106] An implanted ion’s

energy (∼ keV – MeV) is much larger than that of the target material’s bonds (∼ eV), and

as such ions are able to penetrate relatively long distances (∼ hundreds of atomic layers),[110]

typically leaving an amorphous structure in their wake.[111] However, it is possible (at low

to moderate doses) for implanted ion’s to leave surface layers relatively contaminant free,

as they will only undergo atomic-displacing (nuclear) interactions towards the end of their

range.[106] Disorder usually has a negative affect on a material’s conductivity, and as such

it is quite common to anneal semiconductors after ion implantation to restore the crystal

structure.[99, 104, 106, 112] Implant temperature can have a great affect on the damage done

to the lattice. Targets at higher temperatures suffer less disorder as the increased lattice

vibrations are more resistant to the structural distorting effects of the incident ion.[104].

As the implanted ion’s energy is lost through collisions with atoms (either their nuclei

or electrons), a target’s structure can greatly affect the distance implanted ions are able to

penetrate.[104] Ion ranges of amorphous materials, which are fairly isotropic, are essentially

orientation independent. Ion ranges of crystalline materials, on the other hand, can vary

greatly depending on the angle of the incident ion’s trajectory relative to the axes and planes

of the crystal’s lattice.[112] The crystal lattice of silicon, viewed from various orientations,

is shown in Fig. 1.14. Ion’s directly along the ‘open channels’ between adjacent rows of

closely packed atoms, like that depicted in Fig. 1.14(c), are able to penetrate much further

than ions directed at random orientations [depicted in Fig. 1.14(e)] as energy is not lost

displacing atoms from the lattice.[99] Ions travel down these open channels not just because

they are the paths of least resistance (although this does contribute) but because an ion’s

trajectory is actually steered down these channels via a series of glancing collisions with

the atoms in the channel walls.[99] Thus, ions do not have to be perfectly aligned to the

channels (± ∼ 1)[106] in order to travel down them.[112] Channeling can enhance the

penetration of ions up to a factor of 5.[106] Channeling is mainly a factor at lower doses


as the implantation process destroys the crystal order with time.[106] A somewhat counter-

intuitive result of this is that when semiconductors are implanted at higher temperatures

(in an effort to maintain crystallinity) there resulting conductivities are often lower due to

dopants being spread further into the lattice.[104]

Figure 1.14: The crystal lattice of silicon viewed from the: (a) 111 axis, (b) 100 axis, (c) 110 axis,(d) 111 plane, and (e) random. Image taken from Ion Implantation: Basics to Device Fabrication [99].

Ion bombardment can greatly alter a materials mechanical, chemical, electrical or optical

properties.[106] A common result of ion implantation is the hardening due to the surface

being compacted by ion bombardment.[113] As this is a dynamic process, the effect of the ion

beam changes over time with the penetration depths slowly decreasing as target densities

increase.[106] Compacting continues until further ions are unable to penetrate, at which

point they simply ‘bounce’ off. Because of this, implantation doses are self limited. The

term for this self-limiting process is sputtering.[104] Beams with higher energies are more

resistant to sputtering than those with lower energy as the ions are able to penetrate further

into the target.[114]


At low doses, ions implanted into amorphous materials are generally as isotropic as

their source, however as the dose increases implanted ions are likely to be found clustered

together.[104] This is due, in part, to the fact that ions are more likely to trail down the

paths of previously implanted ions than create new ones, but also because there is a tendency,

especially in silicon, for impurities to diffuse and cluster together.[99, 104] This process is

facilitated by lattice vibrations and as a result clustering can be enhanced by annealing.[99,

104]

1.4.1 Implanting Polymers

There are a couple of subtle differences between the implantation of polymers and inorganic

crystals. Crystals, such as silicon, are homogeneous on the scale of the incident ion’s cross

sectional area of impact(∼ 10 nm),[115] whereas molecules within polymers can be as large or

exceed this value.[116] Secondly, the bond strength within polymers differs greatly between

the inter- and intra-molecular forces. Although, neither of these facets greatly affect the path

of incident ions, the result of implantation is the breaking of polymer chains, called chain

scission,[117] hydrogen depletion and the formation of new bonds between chains, called cross

linking, in the implanted region.[118, 119] Cross linked bonds are typically formed between

carbon atoms and as such, this process is referred to as carbonisation or graphitisation.[120]

These changes resulting from implantation can greatly effect the properties of polymers.

In 1982 Stephen Forrest et al. showed that irradiating thin polymer films with an argon

ion beam raised the conductivity by 14 orders of magnitude.[121] This large increase was

attributed to carbonisation of the polymer caused by implantation.[122] Further investiga-

tions of the effects ion beams have on polymers have covered a wide range of polymers and

implant conditions (beam species, energy and dose). There is now a wealth of evidence

showing that ion-irradiation can greatly increase a polymer’s conductivity,[111, 123–125] by

as much as 20 orders of magnitude,[126] but changes extend beyond just the electrical prop-

erties. Studies have shown ion implantation can: increase surface toughness;[113, 127, 128]

improve chemical resistance[113] and adhesion characteristics;[117] alter the optical proper-

ties such as transparency and reflectivity;[126] and even improved performance in biomedical


applications.[129] However, despite the success ion-implantation has had in altering all these

properties, it alone has yet to produce truly metallic polymers.

1.4.2 Metal-Mixing

Although this was shown that using a metal-ion implantation, as apposed to the more com-

monly used inert element beams, could further increase the conductivity, the maximally

implanted ion content was insufficient for metallic conductivity due to self-limiting sput-

tering processes.[96] In recent years it has been shown that when an ion beam is directed

at a polymer with a thin surface layer of metal, the metal is embedded within the sur-

face region of the polymer (shown schematically in Fig. 1.15).[96, 130] This process, termed

metal-mixing, allows inert lower mass ions to be used, which greatly reduces sputtering.

Thus, higher concentrations of metal can be achieved than direct metal-ion implantation,

and in 2006 it was shown that metal-mixing was capable of producing low resistance, metal-

lic samples.[114] Furthermore, as the mixed metal was capable of superconducting, these

systems underwent a superconducting transition to a sample-wide zero-resistance state at

sufficiently low temperatures, as shown in Fig. 1.17.

polymer metal ion

Figure 1.15: Schematic of metal-mixing polymers. The incident ions embed the surface layer ofmetal into the polymer substrate.

Prior to the results reported in this thesis, all published work on metal-mixed poly-

mers have used N+ beams (10 – 50 keV), polyetheretherketone (PEEK) substrates with


tin/antimony alloy (19:1) films ∼ 10 nm thick.[96, 114] In an effort to explain the electrical

properties and understand the effect the intermediate layer of metal has on ion bombard-

ment, these studies have focused on determining the structure and electrical properties of

metal-mixed polymers.

Scanning transmission electron microscopy (STEM) with energy dispersive X-ray (EDX)

analysis, conducted by Tavenner et al., have shown that concentrations of mixed-metal peak

at a surface depth of 20 nm, and are still present at depths up to 80 nm, as shown in

Fig. 1.16.[96] Comparisons before and after implantation show that the physically-based

process of metal-mixing induces three key chemical changes: 1) the number of Sn-Sn bonds

decreases by a factor of 4 while the relative content of C-Sn bonds increases from < 0.1%

to ∼ 5%; 2) resulting from being either sputtered off the surface or mixed deeper than the

85 A-deep region probed by X-ray photoelectron spectroscopy (XPS), the surface content of

Sn decreases, indicated by a decrease in the number Sn-Sn bonds; and 3) the concentration

of graphitic carbon has increased from < 0.1% to ∼ 27%, although this is still lower than

that produced by direct implantion.

Figure 1.16: (left) Scanning transmission electron microscopy (STEM) with (right) energy disper-sive X-ray (EDX) analysis showing the surface regions of SnSb films metal-mixed into PEEK substratesusing a N+ ion beam. Concentrations of metal peak 20 nm below the surface and can still be found atdepths up to 80 nm, which far exceed the initial metal film’s thickness of 10 nm. Image modified fromRef. [114].

As stated earlier, electrical characterisation has shown that metal-mixed polymers can

attain both metallic and superconducting properties.[114] This study by Micolich et al.

examined samples with pre-implant film thickness of 10 nm, implanted with a 50 keV, N+


beam to doses of 1× 1016 (sample A) and 1× 1015 ions/cm2 (sample B). It was found that

the maximum residual resistivity ratio (RRR) defined as ρ(300 K)/ρ(T+c ), where T+

c is a

temperature slightly above Tc, of the two samples was 1.2. This is a low value, indicative of

a highly disordered system.

Closer examination of the superconducting properties revealed that the transition tem-

peratures of the samples A and B (shown in Fig. 1.17) were 2.4 and 1.9 K respectively, which

are suppressed from that of bulk tin (Tc = 3.7 K).[4] The magnetoresistance of sample A,

shown in Fig. 1.17(inset) for T = 1.2 K, exhibited a field-induced transition to a normal

state at Bc = 0.12 T, which is above the critical field of bulk tin (Bc = 30 mT).[4] It was

found that Bc decreases with increasing temperature. The typical critical current of these

samples was Ic ∼ 1 mA. Qualitatively similar results were observed in nominally identical

samples. This behaviour was reproduced after repeated cycles between temperatures below

Tc and room temperature, even after several months of being stored under ambient condi-

tions. During this time the samples did not suffer from surface delamination, indicating that

metal-mixed polymers are very robust systems.

Inspired by these results, Micolich et al. assessed the observed electrical behaviour against

two models describing the structure of metal-mixed polymers: a) a residual surface layer of

metal thin enough to decrease Tc and increase Bc; and b) a granular model consisting of

metallic grains weakly-linked by an ion-beam modified PEEK matrix via the proximity or

Josephson effects.

The first model was supported by observations of Tc being suppressed in quenched-

condensed films by disorder, where higher disorder is indicated by a higher R(T+c ), where

T+c is the temperature slightly above the transitions temperatrue.[131] However, this does

not agree with the data shown in Fig. 1.17 where sample B, which had the higher R(T+c )

also had the higher Tc. Furthermore, the suppression observed in the quenched-condensed

films only occurred in systems whose resistance was around the quantum of resistance of

electron pairs, R(T+c ) ≈ h/4e2 ≈ 6.5 kΩ, which is two orders of magnitude higher than the

metal-mixed polymers.

The proposed granular model is supported by the results obtained Tavenner et al. using

XPS: namely that there was a decrease in the number of Sn-Sn bonds and an increased in


Figure 1.17: Four-terminal resistance, R4T , versus temperature T for two metal-mixed samples withan initial SnSb film thickness of 10 nm. Sample A (left axis) was implanted to a dose of 1016N+/cm2,while sample B (right axis) was implanted to a dose of 1015N+/cm2. A zero-resistance state is reachedat 2.4 and 1.9 K for samples A and B respectively. (inset) R4T versus magnetic field, B, appliedperpendicular to the plane of sample A at T = 1.2 K. A field induced transition to a normal-stateoccurs at Bc = 0.12 T. Image taken from Ref. [114].

the number of Sn-C bonds. Furthermore, it was argued that a granular model could explain

why the sample with the higher implant dose had a lower R(T+c ) and Tc: in the normal state

the resistance is dominated by inter-grain hoping, and that samples with a higher implant

dose should be mixed more thoroughly and contain smaller grains with a smaller inter-grain

separation; and as the grains are smaller, the Tc should be suppressed further than for larger

grains. It was concluded that, although further evidence was required, metal-mixed polymers

are granular in nature.


1.5 Motivation and Applications

The last twenty years has witnessed an explosion of interest in the electronic properties of

organic materials.[75–77] This interest is motivated by their potential use as soft electronics,

which exploits properties of organic materials, such as low cost and mechanical flexibility,

which are not typically found in traditional inorganic electronic materials. Indeed, flexible

organic displays and electronic devices are now beginning to penetrate the market, and

future soft electronic materials will undoubtedly benefit from lower scaled costs and greater

manufacturing simplicity.[72]

While the main focus of research to date has been obtaining semiconducting and metal-

lic organic materials, there is also a long history of research into superconducting organic

materials.[49] Typically, organic superconductors are salts that form highly ordered crystals.

In these salts, electronic charge is transferred between an organic molecule [e.g., bis(ethylene-

dithio)tetrathiafulvalene (BEDT-TTF), tetramethyl-tetraselenafulvalene (TMTSF) or buck-

minsterfullerene (C60)] and a, usually inorganic, counter-ion.[132] These organic supercon-

ducting crystals are extremely brittle and have low critical temperatures. Thus, there has

been relatively little technological interest in organic superconductors to date. The most

prominent attempt to overcome the unattractive materials properties of organic charge trans-

fer salts are the studies involving microcrystals of β-(BEDT-TTF)2I3 embedded in a poly-

carbonate matrix.[133–136] These composite materials retain many of the polycarbonate’s

desirable materials properties, such as its flexibility, and display some hints of superconduc-

tivity, which includes a partial Meissner effect[133] and drop in resistivity[134, 136] below

∼ 5 K. However, there are no reports of such materials obtaining a zero-resistance state.

Thus far, reports of superconductivity in metal-mixed polymers are restricted to rather

low temperatures (2 − 3 K). However the material’s properties remain intriguing; most

prominently, from a technological perspective, these metal-mixed polymer superconductors

retain the mechanical flexibility of the parent polymer.[114] Further, significant scientific

questions still remain concerning the metallic and superconducting states in these systems.

For example, the origin of the superconductivity has not yet been identified: is there a thin

layer of metal below the surface of the polymer, a percolated network of metallic granules,

1.5 Motivation and Applications 37

or is the polymer-metal hybrid an intrinsically superconducting material?

The electrical properties of these materials are certainly intriguing. While it has been

shown that superconducting metal-mixed polymers, which have a metallic normal state,

can be produced, their residual resistivity ratios indicate that these systems are extremely

disordered.[114] This is not unexpected given the manner in which these materials are pro-

duced. What is unexpected is the supression of both the critical temperature and critical

field compared to unimplanted systems (compare Ref. [114] with the results presented in

chapter 3). This is surprising for a thin film of metal on the surface of a plastic and lends

weight to the possibility of more exotic explanations for the origin of the superconductivity.

If the properties of metal-mixed polymers prove to be tunable, as one naturally sus-

pects they might, then they could serve as simple, cheap, experimental test beds for some

of the most profound questions about superconductivity in reduced dimensions includ-

ing superconductor-insulator transitions,[51, 137] superconducting Kosterlitz-Thouless (KT)

phase transitions,[138] and, the recently discovered, superinsulation.[139] Further, metal-

mixed polymer superconductors may prove to be an excellent system in which to study

percolated[140, 141] and granular superconductivity[142] and the competition between weak

localisation and superconductivity.[140, 143] Finally, control of the substrate and/or implan-

tation process could even allow for the controlled study of disorder in these systems.[48, 144]

So it would seem that studying metal-mixed polymers could answer many questions either

in part (i.e. questions regarding: other areas of superconducting science; the implantation of

polymers; etc.) or in full (i.e. questions regarding metal-mixed polymers). However, there

is more than just purely scientific motives behind this research.

As a technology, plastic electronics combines the mechanical flexibility, robustness and

low-cost of plastics with the diversity and chemical versatility of organic semiconductors,

and has now reached commercial maturity with organic light-emitting devices making a ma-

jor impact in the display market.[2] Other applications such as organic photovoltaics,[145]

transistors,[146] and radio-frequency identification (RFID) tags[147] are also under devel-

opment. Another area where plastic electronics hold considerable promise is in sensing

applications.[148] For example, considering Gundlach’s milk carton (Fig. 1.1) as an example


of pervasive portable plastic electronics,[1] a built-in temperature sensor allows the cus-

tomer to determine whether the milk has been stored at low enough temperature to prevent

spoiling. However, the majority of conducting polymer sensors function chemically, by de-

tecting other molecules, rather than physically, by detecting properties such as temperature

or pressure. To some extent, this is a direct consequence of the fact that since conductive

conjugated polymers were discovered,[73, 74] tailoring of their conductivity has mostly been

approached via chemical rather than physical means.[76] The latter stages of this project

were focused on the development of a plastic resistive temperature sensor fabricated using

a physical process of metal-mixing rather than the more familiar chemical routes to organic

electronic devices.

An overview will now be given of the current state of the commercialisation of soft

electronics as well as an introduction to resistance-based thermometry.

1.5.1 Soft Electronics

To date, the most successful soft electronics are organic light emitting diodes.[149] These low-

power, high-output alternatives are well and truly a match for their inorganic counterparts.

When first commercially introduced a few years ago, OLEDs were only utilised for small,

thin, colour displays. Now companies have produced OLED televisions that are 1 m wide, less

than a centimetre thick and use a fraction of the electricity needed by similarly sized liquid

crystal displays (LCD). The success OLEDs enjoy is due to their high levels of performance

and low production costs.[2] However, it is not necessary to be competitive on both these

aspects as long as the cost per output of the device is.

One might initially guess that organics have an advantage from the outset since polymers

are much cheaper than metals or inorganic semiconductors. However, the primary contrib-

utor to the cost of any electronic device is from fabrication.[2] Since the production process

of inorganic electronic devices commonly involves high temperatures, techniques cannot be

directly carried over to soft electronics. As such, new methods for mass production need to

be developed. In the case of OLEDs red, green and blue pixels can be deposited on a screen

directly using specialised ink jet printers.[150] This revolutionary technique dramatically


brought down both the time and cost of producing displays.

At present, materials used in soft electronics typically have lower charge carrier densi-

ties and mobilities. As such their performance levels are not up to the standards of their

competition. For instance, the world record efficiency for OPVs is 7.4%,[151] approximately

six times lower than inorganic based solar cells.[152] Yet despite this OPVs are rapidly ap-

proaching their debut in the mainstream marketplace - with first generation plastic solar

cells now available for portable power applications, thanks to the large scale, roll-to-roll

production their flexibilty and robustness allows.

Other soft electronics in development are organic thin film transistors (TFTs),[153] which

are ideal for applications requiring low level function such as disposable products. The

biggest obstacle TFTs currently face are operating voltages too large for portable use.[1, 154]

Organic materials are also showing considerable promise is in sensing applications,[148] such

as the “Fido” explosive analyte sensor based upon a fluorescent polymer,[155] or as radio-

frequency identification (RFID) tags.[147]

Turning our attention to metal-mixed polymers, we see that they are well suited for com-

mercialisation for several reasons. In certain applications, the flexibility and durability of

metal-mixed polymers are superior to that of traditional metals. As metal-mixed polymers

are fabricated using techniques and facilities already widely used, and directly transferable

from, the semiconductor industry, development and large scale production will be a far eas-

ier prospect than it was for other soft electronics. As such, low-cost, large-scale production

should be readily attainable. In this thesis it will be demonstrated that the electrical prop-

erties of metal-mixed system are wide-ranging and highly tunable, making them aptly suited

for use as temperature sensors. The later parts of this research will verify how suitable metal-

mixed polymers are for use in thermometers. As such a brief overview of thermometers will

now be given.

1.5.2 Thermometers

When designing products for commercial applications it is always desirable to have a product

that is cheap and easy to manufacture. In the case of thermometers it is also desirable to


have a device that is both accurate and have a quick response time, but usually a trade off

between these traits is conceded. Furthermore, unless the device is intended to be used only

once it is necessary for it to give reproducible measurements.

Thermometers are classed as either primary or secondary thermometers. The difference

between these two categories depends on how directly they measure the temperature. Pri-

mary thermometers can determine the temperature directly from a single measurement. For

example, the temperature of a gas can be determined by measuring the velocity of sound

within that medium via the equation

T =mv2

(γkB)2(1.25)

where m is the mass of the atom/molecule, v is the speed of sound, γ is the adiabatic index

and kB is Boltzman’s constant. A secondary thermometer cannot directly determine the

temperature without being calibrated to a primary thermometer at a minimum of one fixed

temperature. In practice multiple fixed points, usually triple points and critical temperatures

of phase transitions, are employed. All early types of thermometers, which utilised the

expansion of a liquid, are of this secondary type. In 1724 Daniel Gabriel Fahrenheit originally

calibrated his scale to three fixed points; the lowest attainable temperature at the time

(achieved by mixing water, ice and salt) was defined as 0 F, the melting point of water

was 32 F and body temperature was 96 F (later refined to 98.6 F). 18 years later Anders

Celcius founded the centigrade scale (later termed the celcius scale) where there is 100

degrees between the boiling point, 0 C, and melting point, 100 C, of water (these assigned

values were switched three years later). Of the two types, secondary thermometers are more

commonly used today due to their convenience and higher accuracy.

With the possible exception of the alcohol thermometer, the most widely used thermome-

ters are resistance temperature detectors or resistance thermal devices (RTD). An RTD is

a secondary thermometer that utilises the predicable change in a materials resistance at

different temperatures. RTD’s require a power source in order to measure the resistance

across a sample, which in most cases is platinum films (e.g. PT100) but ceramics (e.g. RuO2

or BaTiO3) or polymer films loaded with carbon black (e.g., the polyswitch[156]) or metal


Figure 1.18: Different types of platinum resistance thermometers: (a) film, (b) wound and (c) coil.These were taken from www.wikipedia.org on the 3rd of August 2009.[159]

powder[157] are also common, and state the temperature on an electronic display. Platinum

is primarily used due to its predictable, and near linear, resistance-temperature response.

Furthermore, platinum resistance thermometers (PRTs) have a large temperature range

(PRTs are used in industrial applications up to temperatures of 660 C). However, there

are several drawbacks to using PRTs. At temperatures above 660 C the platinum starts

to get contaminated by impurities from the metal casing. At extremely low temperatures

(∼ 3 K) the measured resistance is mainly a result of the impurities and not the platinum

itself.[158] Trying to prevent contamination of platinum during fabrication increases the cost

and difficulty of the manufacturing process. Furthermore the rarity and price of platinum

greatly increases the production cost.

Platinum resistance thermometers fall into one of two broad groups; wire-wound/coil-

element or film. Film PRTs consist of a substrate with a thin surface layer of platinum

[see Fig. 1.18(a)]. The primary advantage of film type thermometers is their fast response

times and relatively low production costs. The drawbacks result from strain gauge effects

caused by the different rates of thermal expansion between the platinum and substrate. Wire-

wound/coil-element PRT’s measure the resistance of a coil of wire that is supported internally

(wound) by a rod or externally (coil) by a tube, [see Fig. 1.18(b) and (c) respectively]. The

coil design gives greater freedom to the platinum to move/expand, although both are superior

than film PRTs in this respect.

Of platinum resistance samples the most common type is the PT100. The name desig-

nates that the platinum sample has a resistance of 100 Ω at 0 C (hence the name) and a

resistance of 138.5 Ω at 100 C.[158]


1.6 Thesis Outline

The following chapter will give an outline of: the base materials and procedures used to

create metal-mixed polymers; experimental techniques used to measure electrical properties;

and a brief overview of the equipment being used in this research.

Chapter 3 presents a study of the electrical properties of pre-implanted systems, with

a particular focus on determining what effect the substrate morphology has on electrical

anisotropies across devices.

Studies of N+ implanted metal-mixed polymers will be presented in chapter 4, where

the fabrication parameters of pre-implant metal film thickness and implant temperature are

varied. These results give insight into the disordered nature of metal-mixed polymers and

reveals intriguing behaviour near the metallic-insulator transition.

In chapter 5 a systematic study determining the effect varying the: beam energy, implant

dose and film thickness has on the electrical and optical properties is presented. These ex-

periments, which involve the use of a heavy-element beam (tin), reveal what effect sputtering

has on implantation. This chapter also reveals proof-of-concept tests aimed at determining

the suitability of metal-mixed polymers as resistance-based temperature sensor.

Conclusion derived from this work and suggestions for the next direction research into

metal-mixed polymers should go are discussed in chapter 6.

Note that chapters 3, 4 and 5 are based on results either published or submitted.[160–162].

Although these manuscripts were the result of a collaborative effort, the content contained

in chapters 3− 5 has been rewritten and is the sole responsibility of this author.

Research is what I’m doing when I don’t know what I’m doing.

Wernher Von Braun

2Methods and Techniques

Chapter 2 outlines the experimental methods and techniques utilised in this research. The

discussion starts in section 1 detailing the materials used, followed by a description of how

samples were prepared. Section 2 gives a detailed account of how electrical measurements

are made and the theory behind them. This is followed in section 3 by a description of the

main experimental apparatus used.

2.1 Base Materials and Sample Preparation

As stated earlier, this work builds upon previous studies[96, 114] and as such we are, for the

most part, confining ourselves to the same materials and methods of sample preparation.

2.1.1 Materials

Polymer

Polyetheretherketone (PEEK) (shown in Fig. 2.1) is a high performance thermoplastic. Its

mechanic flexibility, high tensile strength, good radiation resistance, low flammability, high

chemical resistance and good adhesion properties allow PEEK to be used in a wide range

of applications, which include forming resins for carbon-fibre composite materials used in

aircraft wings.[163–165] With so many desirable properties, PEEK is a robust polymer well

43

44 Methods and Techniques

suited for ion-implantation and with a melting point of 334 C and a glass transition tem-

perature of Tg = 143 C, PEEK is quite adept at resisting high temperatures,[163] making

it ideal to withstand high beam currents. Due to these properties PEEK has a history of

ion implantation studies.[117, 125, 128, 129, 166–169]

C

O

O

*

O

*n

Figure 2.1: Polyetheretherketone (PEEK), (C19H12O3)n

Metal

Tin, like carbon, is a group IV element and has two crystal structures: body centred tetrago-

nal and face centred cubic. The former is referred to as white tin and has a semi-metal band

structure, the later is called grey tin and is a gapped semiconductor.[4] Of the two, grey tin

is stable at temperatures below 286 K (13 C). The majority of this work will focus on the

electrical properties of metal-mixed polymers well below 13 C and as such maintaining the

metallic form of tin at low temperatures is vital. Impurities, such as antimony, are frequently

used to maintain the metallic structure of tin. The metal utilised in this study was a 95%:5%

tin:antimony (SnSb) alloy.

Other than causing the tin to maintain its metallic state, the antimony does not greatly

alter the alloy’s electrical properties from that of pure tin. Bulk tin is a type I superconductor

with a Tc = 3.7 K and Bc = 0.03 T at 0 K, and has a melting point of 505 K (232 C).[4]

Ion Beams

Two ion-beams were used in this research. The first was a nitrogen beam located at the

Crown Research Organisation in New Zealand. This facility had the ability to implant targets

2.1 Base Materials and Sample Preparation 45

on a temperature controlled mount, giving the first opportunity to study the role substrate

temperature has in affecting the properties of metal-mixed polymers. In an effort to best

replicate previous studies of these systems[96, 114] a 0.37 µA/cm2, 50 keV N+ beam was

used to implant PEEK substrates at two film thicknesses (10 and 20 nm). In addition, the

thermally-coupled mount was either cooled with liquid nitrogen or left at room temperature.

The second ion-beam was used to study the effects heavier ions have on metal-mixing.

This study involved using the ion beam element least likely to ‘contaminate’ the sample,

tin. Samples were implanted using the Metal Vapour Vacuum Arc (MEVVA) ion source,

located at the Australian Nuclear Science and Technology Organisation (ANSTO) in New

South Wales. The tin plasma generated by MEVVA contains both singly ionised, Sn+ (47%),

and double ionised, Sn++ (53%), ions. Thus, we will adopt the convention Sn+,++. When

referring to the beam energy of tin implantated systems, we adopt the convention of simply

referring to that of the singly ionised ions (units electron volts, eV ). Due to the higher

mass and greater average charge of the Sn ions, lower accelerating potentials were used

(5 − 20 kV) in an effort to maintain comparable implant energies across both beams. A

schematic diagram of the MEVVA ion implanter and its ion source are showin in Figs. 2.2

and 2.3 respectively.

2.1.2 Sample Preparation

In each of the following chapters the specific method for sample preparation is stated. How-

ever, a general and more detailed overview will now be given.

Amorphous PEEK was obtained in 300 × 300 × 0.1 mm sheets from the Goodfellow

Corporation. The sheets were manufactured using an extrusion process, which resulted

in parallel striations across the surface. The striations can be seen in an atomic force

microscope (AFM) image shown in Fig. 3.2(a). The PEEK is transparent with a pale amber

discolouration.

For film deposition, sections of PEEK were cut from the sheets approximately 4× 10 cm

in size. To remove surface debris, such as dust or finger grease, the substrates were washed

with ethanol and dried using an absorbent lint-free cloth. Following this, substrates were


Discharge

Ion SourceMagnet

Pump

Vacuum

Power Supply

Extractor

Ion BeamTarget

Trigger Unit

Power Supply

Figure 2.2: Diagram of the Metal Vapour Vacuum Arc (MEVVA) ion implanted used to implantSn ions.

Figure 2.3: Diagram of the Metal Vapour Vacuum Arc (MEVVA) ion source. Image taken fromwww.pag.lbl.gov on the 23rd of January 2010.[170]

2.1 Base Materials and Sample Preparation 47

mounted on a sample shadow mask and placed in a Dynavac vacuum evaporator where

SnSb films were deposited. The shadow mask consisted of two 20× 20 mm windows spaced

10 mm apart. The substrate was positioned directly above the tungsten basket source. Film

thickness was monitored during deposition via a Maxtiek TM-400 quartz crystal thickness

monitor placed adjacent to the substrate. Films were deposited at a maximum rate of 4 As−1.

Two sample geometries were required (square and rectangular), one for each of the two

electrical characterisation techniques (see § 2.2 for details). Square samples remained the

same size as the films deposited using the square shadow mask. Rectangular samples were

produced by cutting the 20 mm squares into strips 3.9 mm wide. To ensure all rectangu-

lar samples were the same size, they were cut using a custom made guillotine. Samples

undergoing metal-mixing were then sent to the organisations stated above for implantation.

Contacts were also deposited via vacuum evaporation. However, the contact composition,

evaporator and method with which wires were attached, was one of two methods depending

on the temperature range the samples were to be studied.

Results discussed in chapter 3 pertain to unimplanted samples at temperatures above

77 K. Gold contacts ∼ 50 nm thick were deposited using the same vacuum deposition

equipment and process used for the metal films (described above). Polyurethane-insulated

copper wires, 0.2 mm in diameter, were attached using conducting silver epoxy (obtained

from RS Components) with a conductivity of σ = 1000 S/cm.

Chapters 4 and 5 focus on N+ and Sn+,++ metal-mixed systems respectively. These

studies involved taking measurements at temperatures as low as 1.5 K. The silver epoxy

used for attaching wires to the unimplanted films is not sufficiently strong to cope with the

different rates of thermal expansion between the wires, contacts, adhesive and sample over

such a large temperature range. Fig. 2.11 shows a photo of a sample whose contacts have

come off. This issue is overcome by using two-layer contacts: a 50 nm base layer of titanium

followed by a 50 nm top layer of gold. This dual layer design ensures that the contacts are

securely bonded to the polymer, via the Ti, and wire, via Au and solder. These contacts

were deposited using an Edwards Auto 500 system at chamber pressures < 5 × 10−6 mbar

and at a maximum rate of 1 nm/s.

In an effort to prevent the plastic from burning, copper wires were attached using indium


solder as it has a relatively low melting point of 156 C. As an extra precaution to ensure

the contact’s safety, samples were mounted on glass slides using double sided tape. After

the wire leads were soldered to the sample, they were secured to the slide with araldite. A

photograph of a completed sample is shown in the inset of Fig. 4.1(a).

2.2 Electrical Measurements

When measuring electrical properties such as resistance, care must be taken to ensure that

the resistance of the measuring equipment, wiring or contacts is not included in that of

the material being studied. This issue is best overcome by using a four-probe measure-

ment. As this project is primarily focused on electrically characterising a new material, the

four-terminal (4T) electrical measurement is the experimental technique most vital to this

research. This section gives a detailed description of how 4T measurements are made, the

theory behind them and how parameters such as conductance, resistivity, carrier mobility

and others mentioned in § 1.1 are determined.

There are several orientations in which to do 4T measurements. The most common

are the Hall bar and van der Pauw (vdP) setups shown in figures 2.4 and 2.5 respectively.

Presented now is an overview of the van der Pauw method, including the theory behind

it, and the method to determine the resistance, resistivity, carrier density and mobility.

Following this will be a shorter overview of 4T Hall bar measurements.

2.2.1 Four-Terminal Van Der Pauw Measurements

Ensuring the correct setup is used is very important when making 4-terminal measurements.

There are two key factors that must be considered when making measurements. The first is

sample geometry. It is desirable to have both the sample and the four contacts as symmetrical

as possible. The most preferable configuration is the cloverleaf setup shown in Fig. 2.5(a).

An acceptable, and far more common, configuration is the square setup shown in Fig. 2.5(b).

The square setup’s popularity is due to its increased durability and ease of manufacture

compared to that of the cloverleaf. The second factor is the relative dimensions of the

2.2 Electrical Measurements 49

Figure 2.4: Two configurations for making four-terminal (4T) conductivity measurements. On theright is a Hall bridge setup and on the left is a Hall bar setup.

1

ca

3

21

4

b

4 3

2

Figure 2.5: Configurations for making 4T conductivity measurements. a) The preferred clover-leaf configuration with contacts as separated as possible. b) The most popular, due to its ease ofmanufacture, is the square configuration. Again the contacts are at the extremities of the sample. c)Configurations with the contacts not at the outer most parts of the sample. This is not recommendedas the van der Pauw equation is not applicable to configurations such as these.

sample, contacts and their spacing. Regardless of the configuration used it is best to ensure

that the contact size, D, and the sample thickness, d, are a lot smaller than the distance

between the contacts, L. Relative errors caused by the contact size are of order D/L. It

should be noted that it is critical that the contacts are positioned at the extremities of the

sample and not like that depicted in Fig. 2.5(c). This is because the theory behind these

techniques assumes that the contacts are points.

To make a 4T measurement the method is as follows. (For convenience) label the contacts

1 through 4 in a anticlockwise direction (see Fig. 2.6), starting from the top left corner. To


make the measurement, a current is driven through one side of the sample while a voltage

is measured along the other. Fig. 2.6(a) shows the current going into contact 1 and out

contact 2 (I12) and the voltage being measured across terminals 4 and 3 (V43). From these

Figure 2.6: Method for 4-terminal conductivity measurements. A current is driven down one sideof the samples while a voltage is measured across the other. A resistance is calculated via Ohm’s lawby dividing the measured voltage by the applied current. It is necessary to determine resistance valuesin both the x (bottom) and y (top) directions. The sample’s resistivity can be calculated by simply sub-stituting these resistance values into the van der Pauw equation. Images taken from www.eeel.nist.govon the 25th of May 2007.[171]

two values a resistance, R, can be calculated using Ohm’s law;

RA =V43

I12

This process is then repeated in the orthogonal direction, shown in Fig. 2.6(b), giving

RB =V14

I23

From these two values, and the thickness of the sample, the resistivity, ρ, can be calculated


using the van der Pauw equation [172],

exp

(−RAπd

ρ

)+ exp

(−RBπd

ρ

)= 1,

where d is the sample thickness. To account for any discrepancies, which usually arise from

non-uniform and antisymmetric samples, values for RA and RB should be averages for all

the permutations in which these measurements can be made for each direction. That is

RA =R12,43 +R21,34 +R43,12 +R34,21

4

and RB =R23,14 +R32,41 +R14,23 +R41,32

4

where Rab,cd =VcdIab

Van der Pauw Equation

To derive the van der Pauw equation, let’s consider a semi-infinite plane with contacts P , Q,

R and S, separated by distances a, b, and c respectively, along its edge (shown in Fig. 2.7).

Lets now input a current, I, into point P and take it out at point Q and determine the

potential difference between points R and S.

P Q R S

b ca

ii io

Figure 2.7: A conducting semi-infinite plane with 4 contacts, labeled P,Q,R and S separated bydistances a, b and c respectively. A current is driven into contact P and taken out at contact Q.

If a current is input into a homogeneous half plane the current will disperse radially. The


current density, J , at any given point a distance, r, from the current source is [173]:

J =−Iπrd

(2.1)

Where d is the thickness of the semi-infinite plane. The same is true for the reverse situation

where the current density radially increases to the extraction point. In both cases this will

result in there being a potential difference between any two points not equidistant to both

the input and output points. The potential difference between points R and S is the sum

of the potential differences induced by the input and output currents. To calculate this

difference let’s start by calculating the difference due to the input at point P .

The electric field, E, resulting from the input is found by substituting Eqn. 2.1 into

Ohm’s law[4]

J = σEin =Einρ

∴ Ein =−ρIπrd

The potential difference between points R and S arising from the input current at P is

(VS − VR)in =

∫ S

R

Eindr

=

∫ a+b+c

a+b

−ρIπrd

dr

=−ρIπd

∫ a+b+c

a+b

dr

r

=ρI

πdln

(a+ b

a+ b+ c

)(2.2)

where a, b and c are the spacing between points P,Q,R and S respectively. Now calculating


the potential difference due to the output at point Q.

(VS − VR)out =

∫ S

R

Eoutdr

=

∫ b+c

b

ρI

πrddr

=ρI

πd

∫ b+c

b

dr

r

=ρI

πdln

(b+ c

b

)(2.3)

The resultant voltage difference between points R and S is found by subtracting Eqn. 2.3

from Eqn. 2.2, which gives

VS − VR =Iρ

πdln

(a+ b)(b+ c)

b(a+ b+ c)

Substituting Ohm’s law we find that when driving a current from P to Q and measuring a

voltage between R and S, that the resistance of the sample is

RPQ,RS =ρ

πdln

(a+ b)(b+ c)

b(a+ b+ c).(2.4)

In the same way it can be shown

RQR,SP =ρ

πdln

(a+ b)(b+ c)

ca(2.5)

Rearranging and adding Eqns. 2.4 and 2.5 gives

b(a+ b+ c) + ca

(a+ b)(b+ c)= exp

(−RPQ,RSπd

ρ

)+ exp

(−RQR,SPπd

ρ

)ba+ b2 + bc+ ca

ab+ ac+ b2 + bc= exp

(−RPQ,RSπd

ρ

)+ exp

(−RQR,SPπd

ρ

)1 = exp

(−RPQ,RSπd

ρ

)+ exp

(−RQR,SPπd

ρ

)

From here Van der Pauw then goes on to show that this is true for any arbitrary shape1

1As long as the contacts are small compared to their spacing and along the circumference


using conformal mapping[172].

Now that it has been shown how a sample’s resistance and resistivity can be determined

using 4T measurements, the discussion will be extended to describe how charge carrier

density and mobility can be obtained. These measurements can only be made in the presence

of an external magnetic field.

Hall Effect

If a conducting sheet has a magnetic field applied perpendicular to the plane of the sheet,

a Lorentz force will act on the charge carriers causing the current to gain an orthogonal

component. This phenomenon is called the Hall effect. In the case of a finite sample this

force, which acts perpendicular to both the current and field, will cause the charge to build up

on one side creating a potential gradient, which is called the Hall voltage, VH . This additional

potential, which the current must overcome, causes a sample’s resistance to increase. It is

this increase in resistance that is the means by which the charge mobility is determined.

Making the Hall measurement is very similar to the resistivity measurements described

previously. The difference now is that instead of the current flowing down the side of the

sample it now travels across it.

Using the same labeling system as before (numbered anticlockwise, 1 – 4), a current is

supplied from contact 1 to contact 3, I13, and while a magnetic field, B, is applied perpen-

dicular to the sample, a (Hall) voltage is measured between contacts 2 and 4, V24. This setup

is shown in Fig 2.8.

The charge carrier mobility, µ, and charge carrier density, n, are given by the expressions:2

µ =d

ρ

VHBI

n =d

µρe

where VH is the Hall voltage and e is the charge of the electron. This technique will also

2Derivations given in §2.2.1


Figure 2.8: The setup for a Hall effect measurement. A magnetic field is applied perpendicularto the sample. A current is driven across the sample (I13) and a voltage measured in a directionorthogonal to both the field and the current (V24). Images taken from www.eeel.nist.gov on the 25thof May 2007.[171]

reveal the sign of the charge carrier. The Lorentz force, F , is given by

F = qv ×B

For a current to flow from contact 1 to contact 3 either positive charge must flow out of 1

and towards 3 or negative charge flows from contact 3 towards 1. In both cases the product,

qv, has the same sign. Thus the Lorentz force always pushes the charge carriers in the same

direction regardless of sign. However, the sign of the measured potential change will not

be the same for both positive and negative charge carriers. So if V24 in the setup shown in

Fig 2.8 is negative then the charge carriers are electrons, if V24 is positive then the carriers

are holes.

To account for any asymmetries or inhomogeneities in the samples, it is best to again

take measurements of all permutations of input current and magnetic field and average the

values.


Mobility

The mobility of a charge carrier is the ratio of the drift velocity, vd, it achieves in a field, E,

to the strength of that field:

vd = µE

If the charge carriers have charge, q, and density, n, then the current density is given by the

Drude model is[4]

J = nqvd (2.6)

∴ J = nqµE

Substituting this into Ohm’s law it can be shown that the current density is:

J = σE

∴ σE = nqµE

σ = nqµ

µ =σ

nq

µ =1

ρnq(2.7)

Substituting Eqn. 2.6 into the Lorentz force we find that

F =JB

q.

Dividing the force exerted on the charge carrier by their charge we see that the effect of a

magnetic field is the equivalent of an apparent (Hall) electric field, EH , which is given by

EH =JB

nq. (2.8)

This shows that EH is proportional to J and B via the proportionality constant, 1/nq,


called the Hall coefficient, RH .[173] The Hall voltage is found by integrating EH along a

path between the contacts where the voltage is being measured that is orthogonal to the

current flow.[173]

VH =

∫EH ds

=

∫JB

nqds

=B

nq

∫J ds

=B

nq

I

d(2.9)

substituing Eqn. 2.7 and rearranging gives

µ =d

ρ

VHBI

.

So by applying an external magnetic field and measuring the change in resistance it is possible

to determine the Hall mobility. For further detail on the derviations in this section please

refer to van der Pauw’s 1958 paper entitled A Method of Measuring the Resistivity and Hall

Coefficient on Lamellae of Arbitrary Shape.[173]

2.2.2 Four-Terminal Hall Bar Measurements

If one is merely interested in the resistance or resistivity, and not the carrier density or charge

mobility, then the van der Pauw configuration is not necessary. The Hall configuration is a

simpler, less rigorous3 way to determine the resistivity of a sample. Using the Hall bar setup

shown in Fig. 2.9 we shall (again for convenience) number the contacts 1 through 4 from left

to right. A source current is driven between contacts 1 and 4, I14, and an output voltage is

measured between contacts 2 and 3, V23. The 4T resistance is obtained directly from Ohm’s

law:

R4T =V23

I14

(2.10)

3Asymmetries in a material’s electrical properties cannot be determined from a single sample using a Hallbar configuration.


.

l

21 d

w

L

I

43

Figure 2.9: Layout of a four-terminal Hall bar electrical measurement.

It was mentioned in § 1.1 that a measured resistance was dependent upon an object’s

dimensions. The issue of geometry can be somewhat overcome by utilising the fact that

resistance increases with length, `, and decreases with width, w, at the same rate. Therefore,

if w and ` are equal (making a square) the resistance will only depend on the thickness, d,

and not on the size of the sample. The resistance of samples measured using this unique

geometry are referred to as a sheet resistance, denoted Rs, and to indicate this special case

Rs has units of Ω/. Note that the square symbol is unitless and is indicative of the sample’s

unique geometry for which Rs is obtained. It is often quite useful to chacterise 2D systems

via their sheet resistance, especially when studying the effect thickness has on thin film

conductors. The relationship between sheet resistance and resistivity is

ρ = Rsd (2.11)

and the relationship between sheet resistance and the four-terminal resistance is

Rs = R4T ×w

`(2.12)

This Thesis

The research within this thesis makes use of both the van der Pauw and Hall bar four-terminal

measurements. The results and values quoted in this thesis will primarily be four-terminal

2.3 Equipment 59

and sheet resistances, however in some case 4T measurements are not needed, or not possible,

and as such two-terminal resistances will also be stated.

2.3 Equipment

Aside from the current sources and voltmeters required for 4T measurements, the most

important apparatus for this research are the cryostats, in which most of the electrical

measurements were made, and an absorption spectrometer. In this section a brief description

of these instruments will be given as well as a short overview of atomic force microscopy

which will be briefly utilised in this work for surface characterisation.

2.3.1 Cryostat

The research detailed in the following chapters looks at metal-mixed polymer with wide

ranging conductivities. As such, this required measurements to be made over a large range of

temperatures as the resistance of insulating systems at the very low temperatures required to

study superconductivity, are immeasurably high. To achieve this large temperature range two

cryostats were used: insulating systems were studied at (relatively) higher temperatures, in

a liquid nitrogen cryostat; the superconducting properties of metallic samples were measured

using a helium cryostat.

Optistat

The Oxford Instruments OptistatDN cryostat is liquid nitrogen (LN2) cooled and capable

of temperatures between 77 and 320 K. The Optistat consists of a central sample access

tube that is surrounded by a LN2 reservoir. The sample tube and reservoir are thermally

isolated from each other and their surroundings via an outer high-vacuum chamber(OVC).

A diagram of the Optistat is shown in Fig. 2.10. Within the OVC is a charcoal sorb which

absorbs remnant gases as the cryostat cools. The sorb is fitted with its own heater, which

is activated at room temperature each time the OCV is evacuated, to expel absorbed gases.

Coolant is gravity fed to the sample space heat exchanger via a capillary tube. The flow


rate is manually controlled via a needle valve located at the top of the cryostat. The sample

space temperature is monitored and controlled via a PT100 resistor and temperature sensor

mounted on the heat exchange. The heater is electronically controlled via a temperature

control unit. Samples are placed in the cryostat on the end of a probe which positions them

at the base of the central access tube just below the heat exchange. This model of cryostat

also has windows around the sample’s position to allow for optical measurements (hence the

name Optistat). The cryostat requires an exchange gas (helium), which must be flushed into

the sample chamber before use.

For these experiments, samples were attached to the probe using masking tape and

oriented such that when positioned in the cryostat they were vertical. Wires running down

the probe’s shaft connect the sample to electronic equipment, such as volt and ammeters,

via a 10-point plug at the probe’s top.

VTI

The second cryostat was a Oxford Instruments Variable Temperature Insert (VTI), which

utilizes helium as the coolant. This system is capable of temperatures between 1.2 and 200 K.

The structure is similar to that of the Optistat only much larger in scale. However, there are

two major differences: 1) the liquid helium reservoir is surrounded by a second, LN2 reservoir,

which significantly decreases helium consumption by acting as a radiative shield; and 2) at

the base of helium reservoir is a superconducting magnet, which lies directly beneath the

sample and can apply a vertical magnetic fields up to 10 tesla. Other differences include a

needle valve controlled electronically via the temperature control unit and a resistance-based

temperature sensor mounted on the heat exchange beneath the sample. The particular VTI

used in these experiments has a secondary resistance-based temperature sensors positioned

above the sample in thermal contact with the wires leading to the sample. This is used for

cross checking the temperature readings of the primary sensor.

At extremely low temperatures adhesives, such as masking tape, no longer work. As

such, samples are tied to the probe using Teflon tape. When in the cryostat, the samples

are orientated horizontally, ensuring any applied field is perpendicular to the plane of the

sample. A photo of a sample tied to the end of the VTI probe is shown in Fig. 2.11.

2.3 Equipment 61

Figure 2.10: Schematic diagram of an Oxford Instruments OptistatDN cryostat. Image taken fromoperators handbook.[174]


Figure 2.11: A sample tied to the VTI’s probe using teflon tape. Notice that the top two contactshave come off, caused by the different rates of thermal expansion between the contacts, sample, wiresand solder. This problem can be overcome using two layered contacts - a 50 nm base layer of Ti followedby a 50 nm top layer of Au.

2.3.2 Spectrometer

It was mentioned previously that as a result of the extrusion process by which its manu-

factured, PEEK as a surface covered in striations. Given this, it is not unreasonable to

expect film deposition to be less than uniform. Furthermore, given the rather different wet-

ting characteristics of PEEK and the quartz used in the thickness monitor, determining the

distribution and thickness of deposited metal films is rather difficult. To combat this, a

second method for characterising metal content was achieved by measuring the optical ab-

sorbance/transparency of these materials. This method was also used to characterise changes

resulting from ion-implantation.

The spectrometer used for this research is a dual beam Varian Cary 5000 UV-vis-NIR

spectrometer, which is capable of measurements between 200 and 3300 nm. Samples were

illuminated by a 1 mm diameter circular aperture, which was positioned in the centre of

the spectrometer’s 2 × 10 mm rectangular beam. Identical apertures were used for both

the sample and reference beam. Spectra were taken at a minimum of five locations across

2.3 Equipment 63

the samples to verify homogeneity. Quoted values and errors are the averages and standard

deviations of these repeated measurements.

2.3.3 Atomic Force Microscopy

Analysing the surface of these systems was made using atomic force microscopy (AFM).[175,

176] The images taken in this research were done on a VEECO Multimode Scaning Probe

Microscope in tapping mode.

Success is the ability to go from one failure to another with no

loss of enthusiasm.

Winston Churchill

3Effects of Substrate Morphology

3.1 Introduction

In order to begin to address the scientific questions outlined in § 1.5, and to move forward

on possible technological and scientific applications, it is vital to have good control of the

materials properties of the system. This control is required in two, quite separate, facets

of preparation: (i) controlling the properties of the metal-polymer system prior to ion-

implantation; and (ii) the ion-implantation process itself. This chapter addresses (i) by

reporting the results of a study focused on the electrical and optical properties of unimplanted

thin films of an SnSb alloy on PEEK. These results will also provide a benchmark against

which to examine properties of metal-mixed polymers.

It will be shown that the electrical properties of tin-antimony thin films are remarkably

robust to variations in the substrate morphology. We demonstrate that the optical absorption

of the films, at a fixed wavelength, provides a reliable and reproducible characterisation of

the relative film thickness. We find that as the film thickness is reduced, the superconducting

transition in the unimplanted thin films is broadened, but the onset of the transition remains

at ∼3.7 K, the transition temperature of bulk Sn.

65

66 Effects of Substrate Morphology

3.2 Method

Tin-antimony (SnSb) metallic thin films on polyetheretherketone (PEEK) were prepared and

contacted in two different ways. Set A were made by evaporating a SnSb alloy (see § 2.1.1

for details) onto a 0.1 mm thick PEEK substrate. The substrate was cleaned with ethanol

prior to deposition. The nominal thickness of the film was determined from a quartz crystal

monitor located adjacent to the substrate during the vacuum deposition process. The metal

was deposited at a maximum rate of 0.4 nm s−1. As an independent means of characterising

film thickness, absorbance spectra were taken of all the thin films using a dual beam Varian

Cary 5000 UV-Vis-NIR spectrometer using the method outlined in § 2.3.2.

The samples were then rewashed in ethanol, and 2 mm wide gold contacts were deposited

using a shadow mask and a similar vacuum evaporation process to that used for depositing

SnSb. Contacts were orientated in a Hall bar configuration, outlined in § 2.2.2. All evapora-

tions were performed with a maximum initial pressure of 10−5 mbar. Wires were attached to

the gold contacts using conducting silver epoxy. Two samples were made for each thickness:

one orientated parallel to the substrate striations and the other perpendicular.

The DC electrical properties of set A were assessed using a 4-terminal measurement

in a Hall bar configuration, as shown in Fig. 2.9. The samples were mounted in a liquid

nitrogen Oxford Instrument Optistat (see § 2.3.1 for details), and current-voltage (IV) sweeps

were made over a range of temperatures between 77 K and 300 K. The current, I14, was

sourced using a Agilent E3640A DC power supply and measured using a Keithley 6485

Picoammeter. The voltage, V23, was measured using a Keithley 2400 Source-Measure unit.

The source current was slowly increased (via the voltage) from 0 V in increments ≤ 10 mV

until a maximum source current of ≈ 20 mA was reached. There was a delay between

when the source current was varied and when the output voltage was measured to ensure

that the system was at equilibrium. IV sweeps were made with delays of 100 and 500 ms,

even though comparisons of varying delays showed that the systems stabilised well within

these times. Fig. 3.1 shows IV sweeps taken of samples with SnSb films 10 nm and 16 nm

thick orientated parallel to the substrate striations at T = 300 K. The strong linear trend,

indicative of Ohmic behaviour, was observed for all samples with a thickness ≥ 8 nm (see

3.2 Method 67

Appendix A.1 for IV sweeps of all samples at T = 300 K). The four-terminal resistance is

equal to the gradient of the data (Ohm’s law). The resistances (or conductances) and errors

quoted in this thesis are the averaged gradients (inverse gradients) and their statistical errors

from a minimum of 5 sweeps. The sheet resistance is determined using Eqn. 2.12.

0 5 10 15 200

0.2

0.4

0.6

0.8

1

Current (mA)

Vol

tage

(V

)

0 5 10 15 200

0.1

0.2

0.3

0.4

0.5

Current (mA)

Vol

tage

(V

)

Figure 3.1: Current-Voltage (IV) sweeps used for determining the four-terminal resistance of SnSbthin films 10 nm (left) and 16 nm (right) thick on PEEK substrates at a temperature of 300 K. Thelinear trend was observed in all metallic samples and indicates the strong Ohmic behaviour of the sampleand contacts. The sample’s resistance is equal to the gradient of the data.

Sample set B, used for determining the superconducting properties, had a different con-

tact arrangement to the Hall bar described above. The samples in this second set were

15 mm square with 5 mm radius circular contacts deposited in the corners giving a quasi

van der Pauw configuration.[172] Copper wires were attached using InAg solder. Low tem-

perature measurements were performed between 1.5 and 200 K in an Oxford Instruments

VTI system (see § 2.3.1 for details). The two-terminal DC electrical resistance of the samples

was measured using a Keithley 2400 Source-Measure unit. The fabrication, and some mea-

surements of sample set B, was carried out by Dr Adam Micolich at the University of New

South Wales. This data is included in this thesis as it gives insight into the superconducting

properties of these systems prior to implantation, and provides an invaluable reference point

in understanding the effects implantation has on metal-mixed systems, which is studied in

chapters 4 and 5.


3.3 Results and Discussion

Figure 3.2: Atomic force microscopy (AFM) images of (a) virgin PEEK surface and PEEK coatedwith SnSb thin films of thickness (b) 7.5 nm, (c) 12 nm and (d) 15 nm. The virgin PEEK surfaceis dominated by periodic striations ∼ 1 µm apart running parallel across the surface with a maximumheight of 80 nm. As the film thickness is increased these striations are gradually filled, and have almostdisappeared entirely once the thickness reaches ∼15 nm.

Figure 3.2(a) shows an atomic force microscopy (AFM) image of the uncoated (virgin)

polymer surface. It is very rough with prominent striations ∼ 1 µm apart and ∼80 nm high

resulting from the extrusion process by which it is manufactured. Recently Myojin and Ikeda

showed that such in-plane line defects can behave significantly differently from point defects

in a thin film superconductor.[144] These striations dominate the morphology of very thin

films, as is evident in Fig. 3.2(b), which shows an AFM image of a 7 nm film. The presence

of these striations raises the question of what impact they have on the superconductivity of

thin films deposited upon them. Do these ridges act like line defects in a 2D film, or will they

cause an asymmetry of the current flow for films whose morphology is dominated by that of

3.3 Results and Discussion 69

the substrate? However, one should note that for films thicker than 10 nm [Fig. 3.2(c) and

(d)] the striations no longer dominate the morphology and instead we see granular structures

characteristic of the metallic film itself.

The crystal monitor is calibrated to give the correct thickness of metal evaporated onto

a quartz substrate. Given the rather different wetting characteristics of PEEK and quartz,

one does not expect the recorded absolute thickness to be an accurate measurement of

the thickness of SnSb deposited on PEEK. As an independent means of characterising the

amount of metal deposited on the film, absorbance spectra were obtained.

400 500 600 700 800

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

λ (nm)

A (

arb.

uni

ts)

8 nm14 nm16 nm

Figure 3.3: The absorbance spectra, A(λ), for SnSb films of varying nominal thickness on PEEKsubstrates between λ = 400 nm and 800 nm. For simplicity, we chose to characterise the film thicknessby the 500nm absorbance value (note this choice is somewhat arbitrary since the spectral shape issmooth above 430 nm).

Figure 3.3 shows optical absorbance spectra, in the range λ = 400 − 800 nm for 8, 14

and 16 nm SnSb films on PEEK. While only three thicknesses are shown in this figure, we

have investigated a greater range and find qualitatively similar results (see Appendix A.2 for

all measured spectra), indicating that the absorbance might be a good alternative measure-

ment of film thickness. To explore this, in Fig. 3.4 we plot the absorbance at λ= 500 nm


versus the nominal thickness, as measured by the quartz crystal monitor. There is a clear

linear relationship between the optical absorbance and the nominal thickness recorded by

the crystal monitor. This data suggests that the optical absorption at a fixed wavelength

is at least as good a measure of the relative thickness of metal on unimplanted films as the

crystal monitor. It will be argued below that the absorbance is, in fact, a more reliable

measurement of the films’ relative thickness than the crystal monitor.

5 10 15 20 25 30

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

Nominal Thickness (nm)

A50

0 (ar

b. u

nits

)

Figure 3.4: The relationship between absorbance at 500 nm, A500, and the nominal thicknessmeasured with a quartz crystal monitor of the metallic films. It is clear that there is a strong linearcorrelation between the absorbance and the thickness.

Figure 3.5 shows the relationship between the sheet conductance measured in the parallel

direction, G‖, and the nominal thickness of the SnSb films (i.e., the thickness measured by

the quartz crystal monitor) at temperatures between 77 and 300 K. As one would expect, the

conductance increases with nominal thickness. The data is very smooth with the exception

of an anomaly at 20 nm, which indicates that this sample’s thickness is similar to that of

the 16 nm sample. For comparison, the relationship between G‖ and optical absorbance at

λ = 500 nm is shown in Fig. 3.6. This data is also smooth but the anomaly at 20 nm in


Fig. 3.5 is now absent. This suggests that the absorbance provides a better characterisation

of the actual thickness of the metal on the plastic substrate than the nominal thickness

recorded by the crystal monitor.

5 10 15 20 25 300

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

Nominal Thickness (nm)

G|| (

S)

77 K175 K300 K

Figure 3.5: Sheet conductance, G‖, versus the nominal thickness of a tin/antimony (SnSb) metalfilm on a plastic (PEEK) substrate. The nominal thickness was taken as the value recorded by a quartzcrystal monitor positioned next to the plastic substrate during metal deposition. Conductance data wasobtained with the current flowing parallel to the striations of the substrate. The conductance of thesamples increases with the amount of metal deposited. Note the anomalously small conductivity of the20 nm sample.

To determine what effect the substrate morphology has on the thin film’s electrical prop-

erties, conductivity measurements were made on samples orientated both parallel and per-

pendicular to the striations. Fig. 3.7 compares the conductivity, G, versus absorbance, Aλ,

between the parallel (solid line) and perpendicular (dashed line) orientations for λ = (a) 500,

(b) 600, (c) 700 and (d) 800 nm at various temperatures between 77 and 300 K. Rather than

directly comparing conductivities between orientations of samples with the same thickness we

will analyse the gradient of the profile. Doing so helps eliminate errors in producing samples

with identical thicknesses. In all cases the difference in gradients between orientations was


0.5 1 1.5 20

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

A500

(arb. units)

G|| (

S)

77 K175 K300 K

Figure 3.6: Sheet conductance, G‖, versus optical absorbance at 500nm, A500, for a SnSb film ona PEEK substrate at temperatures ranging from 77 K to 300 K. Conductance data was taken with thecurrent flowing parallel to the striations of the substrate. The anomaly seen in Fig. 3.5 for the samplewith a nominal thickness of 20 nm is absent. This suggests that the absorbance is a more reliablecalibration of the amount of metal evaporated onto the PEEK substrate compared to the quartz crystalmonitor. Further, the absolute values are not meaningful, as they correspond to the thickness of SnSbon quartz rather than PEEK. The same conclusion can be reached by studying data for variation of theconductance perpendicular to the striations with nominal thickness (not shown) and absorbance (Fig.3.7).

always smaller than the statistical error in the gradient. However, it was shown in Fig. 3.2

that only the thinnest films’ morphology was dominated by that of the substrate, therefore,

the result shown in Fig. 3.7, which included samples with nominal thicknesses up to 30 nm,

is not surprising. This analysis was repeated considering only the thinnest films (nominal

thicknesses ≤ 12 nm) and is shown in Fig 3.8. Although the difference in gradient between

the two orientations appears bigger, their values are still within one standard error. This is

further indication that the striations have no measurable effect on the electrical properties of

the SnSb films. This suggests that, in spite of the striations, the film is reasonably uniformly

deposited on the surface of the PEEK, i.e., the metallic film is continuous and conformal.

This is not particularly surprising given that the striations are much wider than they are


high, and that on the scale of the film thickness (or especially the deposited atoms) the

substrate would appear relatively flat. Meaning from the film’s point of view, the PEEK’s

surface more closely resembles smooth rolling hills than it does a steep mountain range.

0.8 1.2 1.60

0.1

0.2

0.3

0.4

A500

(Arb. Units)

G (

S)

(a)

300 K

77 K

ParallelPerpendicular

0.8 1.2 1.6 2A

600 (Arb. Units)

(b)

300 K

77 K


0.8 1.2 1.6 20

0.1

0.2

0.3

0.4

A700

(Arb. Units)

G (

S)

(c)

300 K

77 K


0.8 1.2 1.6 2A

800 (Arb. Units)

(d)

300 K

77 K


Figure 3.7: Sheet conductivity as a function of absorption at: (a) λ = 500 nm, (b) λ = 600 nm,(c) λ = 700 nm and (d) λ = 800 nm, for films with nominal thickness ranging between 8 and 30 nm andat temperatures between 77 and 300 K. An appreciable difference in conductivity-thickness/absorbancerelation was not observed at any temperature of wavelength at which measurements were taken.

Extrapolating the data in Figs. 3.7 and 3.8 indicates that the conductance goes to zero at


0.6 0.7 0.8 0.90

0.02

0.04

0.06

0.08

0.1

0.12

A500

(Arb. Units)

G (

S)

(a)

300 K

77 K


0.7 0.8 0.9 1A

600 (Arb. Units)

(b)

300 K

77 K


0.7 0.8 0.9 1 1.10

0.02

0.04

0.06

0.08

0.1

0.12

A700

(Arb. Units)

G (

S)

(c)

300 K

77 K


0.7 0.8 0.9 1 1.1A

800 (Arb. Units)

(d)

300 K

77 K


Figure 3.8: Sheet conductivity as a function of absorption at: (a)λ = 500 nm, (b)λ = 600 nm,(c)λ = 700 nm and (d)λ = 800 nm, for films with nominal thickness ≤ 12 nm. Again, the differencein gradients between the two orientations is within the error in the slope. This is particularly surprisingfor the thinnest films where the striations dictate the morphology of the metal. We therefore concludethat the striations do not have a significant effect on conductance of the films in the metallic state.


an absorbance corresponding to a nominal thickness of approximately 7 nm for both current

orientations. Measurements were made on films with nominal thicknesses of 5, 6 and 7 nm,

but these samples were insulating with a resistance several orders of magnitude higher than

those of the 8 nm samples. The common thickness value for zero conductance is further

evidence that the morphology of the substrate does not affect the electrical properties of the

thin metal film.

However, although we have shown that the striations do not strongly affect the deposition

of metal on PEEK, this data does not inform us about their effect on the implantation process

and metal-mixed systems. This topic will be discussed in chapters 4 and 5.

The temperature dependence of the resistance for samples with metal layers ≥ 8 nm

for temperatures ranging between 77 K and 300 K is shown in Fig. 3.9. The resistance

monotonically increases with temperature, indicating that these samples are metallic. The

consistency of the data indicates that the quality of these samples is quite high, despite the

relatively basic production process. It is interesting to note that the gradient of the resistivity

increases as the nominal thickness approaches 7 nm, as shown in Fig. 3.10. This is rather

puzzling, as generally one expects that systems with higher disorder have shallower/lesser

gradients than those with higher purity due to the temperature independent term in Eqn. 1.6

being larger.[9]

We now turn to a study of the superconducting properties of thin SnSb films on PEEK

substrates, which involved sample set B. This is important for benchmarking the supercon-

ducting properties of the metal-mixed samples.[114] Current-voltage sweeps were obtained

at temperatures down to 1.5 K. Figure 3.11 shows the temperature dependence of the two

terminal resistance between 1.5 and 10.5 K for samples ranging in thickness between 12.5 nm

and 40 nm, the former having the highest residual resistivity, in agreement with the trend

observed for sample set A. Although it is dificult to determine the width of the superconduct-

ing transition of these samples (i.e. the entire transition happens between 3.7 K and 4.0 K

for the 40 nm sample), the transitions are observed to significantly broadened as the film

thickness decreases. Also, the onset of Tc, defined as the temperature where the resistance

is half it’s normal state value [i.e. R(Tc) = 0.5R(T+c )], is not suppressed, with all transi-

tions occuring around the Tc of bulk Sn (3.7 K). This is in marked contrast to metal-mixed


0

20

40

60

80

R|| (

Ω)

(a)

100 150 200 250 3000

10

20

30

40

T (K)

R⊥ (

Ω)

A500

(b)

0.61

0.65

0.66

0.81

0.90

1.12

1.15

1.21

1.74

Figure 3.9: Temperature dependence of (a) R|| and (b) R⊥ for SnSb films on PEEK substratesat various thicknesses. It is evident that the resistance of the samples increases with temperature,indicating that the thin films are metallic.

polymer superconductors, shown in Fig. 1.17,[114] where a strong suppression of Tc from

that of bulk Sn is observed.1 This suggests that the physics of the superconducting state is

significantly changed by the metal-mixing process.

1Remember that the small amount of Sb in the alloy stabilises the metallic, white, phase of Sn, but,otherwise, does not significantly affect the superconducting properties.


0

0.05

0.1

0.15

dR||/d

T (

Ω/K

)

(a)

0.6 0.8 1 1.2 1.4 1.6 1.80

0.02

0.04

0.06

0.08

Abs500

(arb. units)

dR⊥/d

T (

Ω)

(b)

0

0.05

0.1

0.15

dR||/d

T (

Ω/K

)

(a)

0.6 0.8 1 1.2 1.4 1.6 1.80

0.02

0.04

0.06

0.08

Abs500

(arb. units)

dR⊥/d

T (

Ω)

(b)

Figure 3.10: The gradient of the data shown in Fig. 3.9. Intriguingly the gradient increases as thefilms get thinner. This is surprising as one would expected thicker films to be less disordered.


2 4 6 8 10

500

600

700

800

90012.5 nm

25 nm

30 nm

40 nm

T (K)

R2T

(Ω

)

Figure 3.11: Temperature dependence of the two-terminal resistance, R2T , of SnSb films onPEEK substrates between 1.5 - 10.5 K. The sharp drop in resistance indicates a superconducting phasetransition. The onset critical temperature, Tc, does not seem to depend on the film thickness, but thetransition is significantly broadened. This is in marked contrast to the transition in the metal-mixedmaterials,[114] where Tc is significantly suppressed. The Tc = 3.7 K for bulk Sn is indicated by thedashed vertical line.

3.4 Summary

In order to determine the effect of the implantation process it is necessary to compare

samples before and after implantation. The results discussed in this chapter were of pre-

implanted samples, that is, thin tin-antimony films on PEEK substrates. It was shown

that the electrical properties of SnSb thin films are remarkably robust to variations in the

substrate morphology. It was demonstrated that the optical absorption of the films, at a

fixed wavelength, provides a reliable and reproducible characterisation of the relative film

thickness. We found that as the film thickness is reduced, the superconducting transition in

the unimplanted thin films is broadened, but the onset of the transition remains at ∼3.7 K,

the transition temperature of bulk Sn. This is in marked contrast to the behaviour of metal

mixed films (cf. Fig. 1.17 and results in chapter 4), which suggests that the metal-mixing

process has a significant effect on the physics of the superconducting state beyond that

achieved by reducing the film thickness alone.

If we knew what we were doing, it wouldn’t be called research,

would it?.

Albert Einstein

4The Competition Between Superconductivity

and Weak Localisation in Metal-Mixed

Systems

4.1 Introduction

Now that the electrical and optial properties of pre-implanted metal thin films have been

characterised in chapter 3 we shall move the focus onto implanted systems. In this chapter

we study what affect varying the pre-implant film thickness and implant temperature has

on the electrical and superconducting properties of metal-mixed polymers. It will be shown

that it is possible to drive a superconductor-insulator transition in metal-mixed polymers

via control of these fabrication parameters. We observe peaks in the magnetoresistance

and demonstrate that these features are caused by the interplay between superconductivity

and weak localisation. We compare the magnetoresistance peaks with those seen in unim-

planted films and other organic superconductors, and show that they are distinctly different.

These behaviours are much more common in granular systems, and thus their observation

in systems can give important clues to their morphology.

79

80The Competition Between Superconductivity and Weak Localisation in

Metal-Mixed Systems

4.2 Methods

The samples studied in this chapter are produced and measured using the methods outlined

in § 2.1.2. To briefly summarise, we commenced with cleaned PEEK substrates onto which

a thin film of 19:1 Sn:Sb is deposited by thermal evaporation. For metal-mixed samples, ion-

implantation was then performed using a 0.37 µAcm−2, 50 keV N+ ion-beam that illuminated

a circular area 14 mm in diameter to a dose of 1016 ions/cm2. During implantation, the

samples were mounted on a temperature controlled stage, which was either cooled with LN2

or left at room temperature. Two-layer electrical contacts (50 nm Ti, 50 nm Au) were

deposited, via the shadow-masked evaporation method outlined in § 2.1.2, onto the four

corners of each sample. Following this, the samples were cut into a van der Pauw-cloverleaf

configuration (refer to § 2.2 for details) ensuring that the unimplanted regions did not short

out measurements of the implanted region, which have a relatively lower conductivity. Cu

wires are attached to the contacts using In solder. A photograph of a completed sample

is shown in the inset to Fig. 4.1(a). Low temperature electrical resistance measurements

were carried out using a Keithley 2000 multimeter with the samples mounted in an Oxford

Instruments variable temperature insert system capable of temperatures, T , between 1.2 and

200 K and magnetic fields, B, up to 10 T.

Here we report on five samples – four are metal-mixed and one is not. The four metal-

mixed samples form a (2 × 2) set with two nominal SnSb alloy thicknesses (10 nm and

20 nm) and two sample temperatures during implantation (300 K and 77 K). To avoid

thickness variations from interfering with studies of implant temperature, the samples for

each temperature were cut as pieces from a larger film, coated with a specified thickness of

SnSb in a single evaporation. The fifth sample was an unimplanted SnSb film with nominal

thickness 20 nm. It was produced separately from the set of four metal-mixed samples by

Dr Adam Micolich, and provides an interesting counterpoint to the magnetoresistance data

obtained from the 10 nm thick metal-mixed samples.


4.3 Results and Discussion

Before focusing on the key features of the samples, we first make some general comments

regarding the sample set that we chose to measure. The electronic properties of metal-

mixed polymers can be controlled via a number of the parameters involved in fabrication,

including: substrate composition; pre-implant metal film thickness and composition; beam

energy, current, dose and species; and implantation conditions, such as temperature. An

exhaustive exploration of this very large, multidimensional parameter space is clearly an

onerous task, forcing us to be selective in order to make progress.

In this chapter, we have restricted ourselves to a small sample set focused on two key

parameters. The first is the pre-implant metal thickness because it provides the easiest

control over the conductivity, even though this can be a slightly difficult parameter to control

with precision. [160] The second is the implant temperature, which we believe provides some

control over the disorder of the resulting film, as we will show in the next section. A more

extensive study of the role of the fabrication and ion-implantation parameters in determining

the sample conductivity will be the subject of the following chapter.

4.3.1 The Effect of Implantation Temperature

We start by considering the two 20 nm metal-mixed samples, which exhibit a metallic temper-

ature dependence for temperatures greater than the critical temperature and a clean transi-

tion to a global (i.e., sample-wide) zero resistance state. Comparing the resistance measured

between the four contact pairs along the sides of the sample and the two pairs running diag-

onally (resistances vary from ∼ 170 to 270 Ω for the 300 K sample and from ∼ 140 to 185 Ω

in the 77 K sample) indicates that both samples are relatively isotropic (cf. 10 nm samples

discussed in § 4.3.2). In Fig. 4.1(a) we present the normalised resistance R(T )/R(Tmax),

where Tmax = 202.6 K, measured in a four-terminal configuration for the 20 nm samples

implanted at 77 K (solid blue line) and 300 K (dashed red line). The resistance at Tmax is

24.2 Ω for the 77 K sample and 33.1 Ω for the 300 K sample, which also has the greater

normalised resistance for T > Tc. Additionally, the 300 K sample has the lower Tc and larger

transition width, ∆T , defined as the difference in termperature between when the resistance


Metal-Mixed Systems

2 4 6 8 100

0.2

0.4

0.6

0.8

1(a)

T (K)

R/R

(Tm

ax)

77 K 300 K

−0.5 00

5

10

15

20

25

B (T)

R (

Ω)

(b)

4.0 K

1.5 K

0 0.50

10

20

30

B (T)

R (

Ω)

(c)

4.0 K

1.5 K

2 4 6 8 100

0.2

0.4

0.6

0.8

1(a)

T (K)

R/R

(Tm

ax)

77 K 300 K

−0.5 00

5

10

15

20

25

B (T)

R (

Ω)

(b)

4.0 K

1.5 K

0 0.50

10

20

30

B (T)

R (

Ω)

(c)

4.0 K

1.5 K

Figure 4.1: (a) The normalised four-terminal resistance R(T )/R(Tmax) versus temperature T for20 nm Sn:Sb films implanted at 77 K (solid blue line) and 300 K (dashed red line). The criticaltemperature Tc and transition width ∆T are 3.0 K and 0.63 K for the 77 K sample, and 2.9 K and1.0 K for the 300 K sample. The higher R(T ) for T > Tc, reduced Tc and larger ∆T point to a higherdisorder for the 300 K sample. (Inset) A photograph of a typical ion-implanted sample. Panels (b)and (c) show the resistance R versus applied perpendicular magnetic field B at temperatures T rangingbetween 1.5 and 4.0 K for the 77 K and 300 K samples respectively. At T = 1.5 K, the critical field Bcand transition width ∆B are 0.33 T and 0.19 T for the 77 K sample, and 0.31 T and 0.24 T for the300 K sample. The lower Bc and larger ∆B again confirm the higher disorder in the 300 K sample.

is 90% and 10% its normal state values [i.e. ∆Tc = T (R = 0.9R(T+c ))− T (R = 0.1R(T+

c ))],

almost double that of the 77 K sample, as expected for a sample with a higher normal

resistance and higher disorder. [177–179] Further evidence for the relationship between dis-

order and implant temperature is provided by the magnetic field data presented in panels

(b) and (c) of Fig. 4.1 for samples implanted at 77 K and 300 K respectively. Considering,

for example, the data at T = 1.5 K, the critical field, Bc = B(R = 0.5Rmax), is lower and

the transition width, ∆B = B(R = 0.9Rmax) − B(R = 0.1Rmax), is larger for the 300 K

sample, again pointing to higher disorder in this sample. This dependence of the sample

properties on implant temperature points to an ability to fine-tune the sample properties

via the implant parameter, over and above the tuning provided by the metal thickness. This

provides incredible versatility to metal-mixed polymers as an electronic materials system, as

we will demonstrate systematically in the following chapter.

Focusing on the 20 nm sample deposited at 77 K [Fig. 4.1(b)], the angular dependence

of the sample’s critical field has been measured in order to determine the dimensionality of


0 20 40 60 800.2

0.4

0.6

0.8

1

θ (degrees)

Bc (

T)

Figure 4.2: Angular dependence of Bc for the 20 nm sample implanted at 77 K The angle, θ, ismeasured relative to the normal of the film. The solid line is a fit of Eqn. 1.22 to the experimental data,and the quality of this fit demonstrates that this sample is two-dimensional.

the sample. For a two-dimensional superconductor, the angular dependence of Bc is given

by Eqn. 1.22. Fig. 4.2 shows the measured critical field, Bc, versus angle of the applied field,

θ, with the solid line presenting a fit of Eqn. 1.22 to the data. We obtain Bc as the field

at which the sample resistance is half of that obtained in the normal state. The excellent

fit to the data provided by Eqn. 1.22 indicates that the 20 nm sample implanted at 77 K

is two-dimensional, and since this is the thickest and cleanest of the metal-mixed samples

being studied, it implies that all other samples are also in the 2D limit.

4.3.2 Crossing Over to the Insulating Side

Turning our attention to the 10 nm samples, the most obvious difference is that their resi-

tivities are much higher than the 20 nm samples, commensurate with their reduced metal

thickness. [70] Both of these samples are in the insulating regime (i.e., resistivity increases

with decreasing T ), however an unfortunate side-effect is that the electronic properties of

these samples are significantly more anisotropic. This makes it impossible to sensibly obtain


Metal-Mixed Systems

the 4T resistance as such measurements require homogeneous samples and contacts. There-

fore, all resistance measurements that we report for the 10 nm samples are two-terminal

measurements. Due to the strong anisotropy, the effect of implant temperature on the re-

sistance is not quite as obvious in these samples. The corner to corner room-temperature

resistances vary from ∼ 22 to 135 kΩ for the 300 K sample and from ∼ 13 to 900 kΩ in the

corresponding 77 K sample. The lowest resistance is measured in the 77 K sample, and is

lower by a factor of ∼ 2 than the lowest resistance in the 300 K sample.

In Fig. 4.3 we present the temperature dependence of the two-terminal resistance mea-

surements for two perpendicular edges of the 10 nm samples. For convenience we will

henceforth adopt the convention of referring to the direction with the lower resistance as the

x-direction, Rx, [see Fig. 4.3(a)] and the higher resistance direction as the y-direction, Ry

[see Fig. 4.3(b)]. Considering Fig. 4.3(a) first, the samples are clearly insulating along the

x-direction (increasing R with decreasing T for T > Tc), but both undergo an incomplete

superconducting transition at a temperature of approximately 3.2 K. In either case a sample-

wide zero-resistance state could not be reached within the temperature range available with

our cryostat [R(T = 1.6 K) ∼ 1000 Ω and 100 Ω for the 77 K and 300 K samples respectively],

and it is unclear whether one could be attained by going to lower temperatures. Such incom-

plete superconducting transitions are common in granular metal films on the insulating side

near to the metal-insulator transition. [64, 180–183] Similar quasi-reentrant transitions have

also been observed in granular cuprate samples [184, 185] and organic superconductors. [186]

A rather intriguing feature is that the maximum resistance, Rmax, which one would assume

occurs at T+c for an insulating system, is not only well above the Tc of the sample but also

well above the Tc of bulk tin. This is shown in the inset of Fig. 4.3(a) where Rmax occurs at

T = 4.6 K in the 77 K sample and at T = 5.7 K in the 300 K sample.

In contrast, along the y-direction in these samples [see Fig. 4.3(b)] there is no super-

conducting transition down to T = 1.6 K, or a deviation from a smooth insulating profile.

Comparing between directions for both samples we see that for the 300 K (77 K) sample

the resistance in the x-direction starts ∼ 16 (∼ 40) times higher than that in the x-direction

at T = 200 K and continues to increase as T is reduced, reaching 1.7 MΩ (3.2 MΩ) at

T = 1.6 K.


0

5

10

15

20

25(a)

Rx (

kΩ)

4 5 6 722.5

23

23.5

T(K)

Rx77

K (

kΩ)

27.8

28

28.2

Rx30

0 K (

kΩ)

0 50 100 150 200

0.5

1

1.5

2

2.5

3 (b)

T (K)

Ry (

MΩ

)

77 K 300K

Figure 4.3: The two-terminal resistance, R, versus T measured along the (a) x-direction, and (b)y-direction of the 10 nm sample implanted at 300 K. These two measurements along perpendicularedges of the sample utilise a common contact. In the x-direction a superconducting transition is seenin both samples at Tc = 3.2 K. (inset) It is interesting to note that the samples maximum resistance,which one would expect to occur at T+

c for insulating systems, is well above not only the samples’ Tcbut also bulk tin’s (Tc = 3.7 K).


Metal-Mixed Systems

The anisotropy of both samples is most apparent in their magnetoresistance, shown in

Fig 4.4. In the x-direction a superconducting transition is evident, for both samples, with

the minimum resistance, Rmin, at any fixed T occurring at B = 0. However, in the y-

direction no superconducting transition is visible and Rmin occurs at the maximum field,

Bmax, although there is a local minimum at B = 0 for low T . Such strong anisotropy

is not uncommon in metal-mixed samples in the insulating regime. Unfortunately, insight

into the relative disorder cannot be gained by comparing the x-direction’s field-induced

superconducting transition as we did for the 20 nm samples. For the thicker samples, the

traits of disorder (lower Bc and larger ∆Bc) were common to one sample, whereas for the

10 nm films they give conflicting reports as the 77 K sample has the smaller critical field

(Bc = 0.82 T compared to 0.87 T) and the 300 K sample has the larger transition width

(∆Bc = 0.80 T compared to 0.67 T) at 1.7 K. However, given that a zero-resistance state

was not reached, determining values for parameters is a somewhat subjective process.

One might initially suggest that the observed anisotropy of the sample’s conductivity is

related to the morphology of the substrate. Whereby the striations affect the implantation

process, resulting in a much higher conductivity parallel to these channels. However, in

both cases the lower resistance direction was between contacts oriented orthogonal to the

substrate striations. From this we conclude that the substrate morphology has no effect on

the observed anisotropies of the sample’s conductivity.

We suggest that the observed anisotropy and peculiarly high T (Rmax) in these samples

can be explained with a granular model where some grains are insulating, while others are

superconducting and may be coupled via the Josephson or proximity effects. Anisotropies in

the grain distribution result in there being no percolation path for superconductivity in the

y-direction, whereas in the x-direction a percolation path does exist or is very weakly broken

[consistent with the small, but non-zero, resistance in this direction, Figs. 4.3(a)]. This

model might explain the raising of the peculiarly high temperature of the maximum resistant,

T (Rmax), as thermal contraction brings the granules closer together, and at ∼ 5 K the rate

at which the resistance decreases, due to conducting grains shorting-out, compensates for

the increase in resistance, due to the sample’s inherent insulating behaviour. Although this

does seem unlikely as any contraction effects would be very small. The raised T (Rmax)


Figure 4.4: Two-terminal magnetoresistance of the: 77 K sample in the (a) x- and (b) y-direction;and the 300 K sample in the (c) x- and (d) y-direction. It is evident that the behaviour differs greatlybetween the x- and y-directions due to the high degree of sample anisotropy.

might indicate that metal-mixing has produced a new material comprised of the polymer’s

constituent atoms, the Sn and Sb of the film and the N from the ion beam. However, we

can only speculate as to the validity of this theory at this stage. A natural prediction of

a granular model is that some signatures of the superconducting grains should remain in

the measured resistance along the y-direction, and these signatures are observed, as we will

demonstrate below.

To understand the origin of this insulating behaviour, we fit the data in Fig. 4.3(b) to

two models. Firstly, in Fig. 4.5 we plot the data in Fig. 4.3(b) on a graph of lnσy versus 1/T

and attempt to fit an Arrhenius model [i.e., R ∝ exp(−∆/kBT ), see Eqn. 1.8]. As Fig. 4.5

shows, this model only fits well for low temperatures. However, the most disturbing aspect is


Metal-Mixed Systems

that this fit gives a value for the gap of ∆/kB = 0.6 K and 2 K for the (a) 300 K and (b) 77 K

samples respectively. These values are very small for insulating systems (cf. Si has a bandgap

of 13000 K and grey Sn a gap of 1160 K).[4] Given that measurements are taken (well) above

these temperatures, which should indicate a high carrier density, one would expect to see

lower resistances. Also, since these systems are far removed from the quantum of resistance

(h/e2 = 25.8 kΩ), which separates metals and insulators, the insulating behaviour should be

most apparent. If this were the case then one would expect to see a much larger change in

resistance than what is witnessed here [R(T = 2 K) ≈ 6R(T = 200 K)] given that there was

a 2 order magnitude change in temperature. This behaviour suggests that the values for the

gap are too small to indicate that an opening of an energy gap at the Fermi level in these

two metal-mixed systems is responsible for the insulating behaviour.

0 0.1 0.2 0.3 0.4 0.50.5

1

2

4

1/T (K−1)

ln(σ

y / 1µ

S)

(a)

Fit

0 0.1 0.2 0.3 0.4 0.5

0.5

1

2

1/T (K−1)

ln(σ

y / 1µ

S)

(b)

Fit

Figure 4.5: An Arrhenius plot of lnσy versus 1/T , where σy = R−1y for the 10 nm sample implanted

at: (a) 300 K, and (b) 77 K. In both cases an Arrhenius model only fits the data for T < 4 K. Howeverthe energy gaps, of ∆/kB = 0.6 K and 2 K for the 300 K and 77 K samples respectively, are too smallto suggest that the insulating behviour is a result of an energy gap at the Fermi level.

As a second alternative, we consider the possibility that the insulating behaviour is

instead due to weak localisation,[12] in which case the resistance should be proportional

to lnT as these are quasi-2D systems.[7] In Fig. 4.6, where we plot Ry versus lnT , a clear

linear trend emerges consistent with a weak localisation model. The strong linear dependence

suggests that the insulating behaviour of these systems is due to weak localisation. If this

is indeed the case, then insight may be gained into the relative disorder of the two systems

using Eqns. 1.9 – 1.11. Assuming that of all the parameters, the only difference between


the two samples is the electron’s mean free path (`), then the steeper gradient of the 77 K

sample’s data would indicate that it has a shorter mean free path of the two 10 nm samples

and is therefore more disordered. This is a somewhat surprising result given that the 20 nm

samples indicated that the higher implant temperature produced more disordered systems.

However, the inhomogeneity of the 10 nm samples makes the assumption of the two materials

only differing in ` a precarious one.

1.8 2.2 2.6 3.0 3.4

1.45

1.5

1.55

1.6

1.65

ln(T/1K)

Ry (

MΩ

)

(a)

1.8 2.2 2.6 3 3.4

2.5

3

3.5

ln(T/1K)

Ry (

MΩ

)

(b)

Figure 4.6: Two-terminal resistance versus lnT for the (a) 300 K and (b) 77 K samples. Thelinear dependence suggests that the origin of the insulating behaviour in these samples is due to weaklocalisation.

Weak localisation in 2D systems is also characterised by a negative magnetoresistance

(i.e., a resistance peak at B = 0), [12] and although, for the most part, this is seen for the

77 K sample [Fig. 4.4(b)] it is certainly not the case for the 300 K sample [Fig. 4.4(d)]. We

now suggest that this issue, of a local minima in the magnetoresistance for a weakly localised

system, can also be explained using a granular model. To do so, we will focus on the 10 nm

sample implanted at 300 K, as its behaviour is in the strongest disagreement.

In Fig. 4.7(a) and (b) we plot the magnetoresistance Rx(B) and Ry(B), respectively, at

a range of temperatures for the 10 nm sample implanted at 300 K [constant temperature

contours of Figs. 4.4(c, d)]. Concomitant with the temperature dependence of Rx presented

in Fig. 4.4(a), the Rx(B) data in Fig. 4.7(a) features a deep minimum centered at B = 0

and a field-induced transition to a normal state at a higher critical field Bc = 0.91 T. This

transition is relatively wide (∆Bc = 0.79 T) at T = 1.6 K, and the minimum rises rapidly as


Metal-Mixed Systems

the temperature is increased. In each case, however, the resistance becomes field-independent

for |B| & 1.5 T indicating the complete quenching of superconductivity in this sample. The

magnetoresistance data presented in Fig. 4.7(a) is quite similar to that observed in other

superconducting films [e.g., the 20 nm sample in Figs. 4.1(b, c)] except that in those samples

zero resistance is achieved. The absence of a zero resistance state in Fig. 4.7(a) indicates

that a sample-wide superconducting state has not been attained, despite clear evidence of

local superconductivity.

In contrast, the magnetoresistance along the y-direction [see Fig. 4.7(b)] shows both a

positive magnetoresistance (resistance increases with field), for |B| < 1 T, and a negative

magnetoresistance (resistance decreases with field), for |B| > 1 T. The two signs of the

magnetoresistance can be attributed to the competition between weak localisation and su-

perconductivity. To explain let us ignore, for a moment, the positive magnetoresistance for

|B| < 1 T and extrapolate the negative magnetoresistance to zero field. Doing so would

result in a broad peak in the resistance centered at B = 0 with a characteristic half-width

of order 3 T. This is a typical characteristic of weak localisation.[12] The magnitude of the

negative magnetoresistance diminishes with increasing temperature, as expected, given that

weak localisation is a quantum interference phenomenon. Now let us turn our attention back

to the positive magnetoresistance observed at smaller fields. This feature is very indicative

of local superconductivity in the sample. The crossover from positive to negative magne-

toresistance that occurs at B ∼ 1 T in Fig. 4.7(b), coincides with the critical field observed

in Fig. 4.7(a), adding support for this explanation for the B = 0 minimum in Ry. The

behaviour of the resulting magnetoresistance peaks is quite interesting. The field at which

the peak magnetoresistance is observed, Bpeak, is only weakly dependent on temperature,

and may be non-monotonic. However, it is difficult to make this statement definitively due

to the peak broadening as the temperature is elevated.

Defining the peak’s field location is straightforward but quantifying its height requires a

little more consideration. The resistance becomes constant in B at sufficiently high fields as

the effects of superconductivity and weak localisation are both quenched. Hence it makes

more sense to reference the peak height to the resistance at the maximum measured field

R(Bmax), than to R(B = 0), for example. This is particularly clear in Fig. 4.9, where


0

5

10

15

20

25

30

35

(a)1.6 K

4.7 K

Rx (

kΩ)

−3 −2 −1 0 1 2 31.3

1.4

1.5

1.6

1.7

1.8

(b)

1.6 K

4.7 K

Bpeak

∆ Ry

B (T)

Ry (

MΩ

)

Figure 4.7: (a) Rx and (b) Ry as a function of applied field, B, at several different temperatures forthe 10 nm sample implanted at 300 K. The Rx data has a deep minima centered at B = 0 that does notreach zero, indicating that the superconductivity in this sample is local and not global. In contrast, theRy data shows a broad negative magnetoresistance (peak) that diminishes with temperature, consistentwith weak localisation. The superimposed positive magnetoresistance feature (minima) is due to localsuperconductivity in the sample, and has the same width as the minima in (a). Bpeak and ∆Ry forT = 1.6 K are indicated in (b).


Metal-Mixed Systems

we use the same definition to quantify the peak height. Thus we define the peak height

∆R = R(T,Bpeak) − R(T,Bmax). In Fig. 4.8 we show the temperature dependence of the

peak height obtained in the y-direction, ∆Ry, in Fig. 4.7(b). No change in the temperature

dependence of the magnetoresistance peaks is observed at the resistive critical temperature

in the x-direction, and the peaks are observed at least up to the critical temperature of

bulk tin. This is consistent with a granular structure in which different grains become

superconducting at slightly different temperatures, beginning at about the Tc for bulk tin.

The competition between superconductivity and weak localisation in this sample is indicative

of a highly disordered and very anisotropic granular metallic film. We attribute the severity

of the electrical inhomogeneity to the system’s close proximity to a sharp metal-insulator

transition. The precise nature of the coupling between the grains is unclear and will require

further work. That said, we expect the coupling to be dependent on the nature of the

carbonised polymer matrix created by the ion-beam,[122] which fills the space between the

grains, as well as the size-distribution and morphology of the grains themselves. However,

on the weight of evidence presented in this chapter and in earlier work,[114] it is clear that

this material is granular.

4.3.3 Weak Localisation in Unimplanted Films with Metallic Con-

ductivity

We conclude this chapter by considering some data from an unimplanted sample with a much

higher conductivity, which provides an interesting counterpoint to the data presented for the

implanted samples. The nominal thickness of this sample is 20 nm. It was evaporated in a

separate batch to the 20 nm implanted samples and has a lower corner-to-corner resistance.

While at first sight this might be attributed to this sample being thicker, it should be

remembered that the implantation process spreads the evaporated film by up to ten times

its original thickness into the PEEK substrate.[96] This leads to some loss of metal due to

sputtering, [96, 114] which is the primary cause of the increased resistance after implantation

(as will be shown in chapter 5). The low and isotropic resistance in this sample makes it

ideal for four-terminal measurements.


2 2.5 3 3.5 4 4.50

0.02

0.04

0.06

0.08

0.1

T (K)

∆ R

y (Ω

)

Tc,x

sample Tc Sn

Figure 4.8: The peak resistance, ∆Ry = Ry(T,Bpeak) − Ry(T,Bmax), for data in Fig. 4.7(b)(the high resistance direction of the 10 nm sample implanted at room temperature) as a function oftemperature (Bmax = 3.5 T is the maximum field studied). The behaviour of the peaks does not changesignificantly at the temperature where the resistive transition is observed in the x-direction (marked inthe figure as ‘Tc,x sample’) and the peaks continue up until at least the Tc of bulk tin, also marked inthe figure, consistent with a granular structure.

Fig. 4.9 shows the measured four-terminal magnetoresistance for this sample at a variety

of temperatures between 1.3 and 5.0 K. Despite having a resistance that is six orders of

magnitude smaller than that reported in Fig. 4.7(b), a negative magnetoresistance is still

observed. The natural reaction is that this is also weak localisation, since the appearance of

weak localisation in low resistance thin films is certainly not unusual.[12] The central minima

observed in Fig. 4.9 due to superconductivity appears as a broad, flat-bottomed minima with

zero resistance, very similar to the 20 nm implanted samples’ data shown in Fig. 4.1(b, c),

indicating an electrically continuous, global superconducting state in this sample. This is

not surprising given this sample’s much lower normal resistance. Combining these negative

and positive magnetoresistance contributions together results in the appearance of ‘peaks’

in the magnetoresistance at the point of the field-induced superconductor-normal transition.


Metal-Mixed Systems

−1 −0.5 0 0.5 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.3 K

5.0 K

Bpeak

∆ R

B (T)

R (

Ω)

Figure 4.9: Four terminal magnetoresistance R at various temperatures between 1.3 and 5.0 Kfor the unimplanted 20 nm sample. Of particular note are the ‘peaks’ in the magnetoresistance on thenormal side of the field-induced superconducting-normal transition (cf. Figs. 1 and 2 in Ref [187] shownin Appendix B).

However, it is not quite so straightforward to attribute these peaks to competition between

weak localisation and superconductivity, because the question needs to be asked why similar

peaks do not occur in the implanted samples [see Figs. 4.1(b), 4.1(c) and 4.7(a)]?

A simple argument would be that the implantation spreads the film into the substrate,

increasing its thickness and making it three-dimensional. However, metal-mixing leads to

significant chemical binding between the metallic species and the polymer, [96, 114] which

should reduce the free electron density, increasing the Fermi wavelength and maintaining

the 2D limit. An interesting alternative to consider is that the peaks in the unimplanted

sample are not caused by weak localisation at all. Remarkably similar peaks are observed in

the magnetoresistance data obtained by Zuo et al. for the quasi-2D organic superconductor


0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5B

peak

(T

)

(a)

1.5 2 2.5 3 3.50

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

T (K)

∆ R

(Ω

)

(b)

Figure 4.10: (a) Location of the peaks in magnetic field, Bpeak, and (b) the peak resistancedefined as ∆R = R(T,Bpeak)−R(T,Bmax), where Bmax = 1.0 T, for data in Fig. 4.9 as a function oftemperature, for comparison with data in Refs. [187, 188] shown in Appendix B.


Metal-Mixed Systems

κ-(BEDT-TTF)2Cu(NCS)2. [187, 188]

The parallels between these two effects go beyond the similarities that are obvious to the

naked eye. The field at which the peak occurs, Bpeak, decreases linearly with temperature as

shown in Fig. 4.10(a). Further, the peak resistance, ∆R = R(T,Bpeak)− R(T,Bmax) where

Bmax = 1.0 T, increases with temperature as shown in Fig. 4.10(b). Zuo et al. reported both

of these effects in κ-(BEDT-TTF)2Cu(NCS)2, cf. Fig. 3 of Ref. [187] and Fig. 2 (inset) of

Ref. [188] (shown in Appendix B). The differing sign of the gradients for the data in Figs. 4.8

and 4.10(b) is consistent with the electrical properties (insulating versus metallic) of these

two samples. Further, the magnetoresistance peaks in the unimplanted sample [Fig. 4.10(b)]

are only observed below the superconducting critical temperature of bulk tin, suggesting that

the magnetoresistance peaks are intimately connected with the superconductivity. Zuo et al.

attributed the magnetoresistance peaks in κ-(BEDT-TTF)2Cu(NCS)2 to lattice distortion by

strong coupling to fluctuating vortices, [187] however, other mechanisms involving dissipation

and Josephson-junction effects have also been suggested.[189] Further, extensive studies of

the role of disorder in these materials have not shown any other signs of weak localisation.[9,

48]

Given the very different behaviour of the magnetoresistance peaks in the implanted and

unimplanted films, it seems reasonable to suggest that different physics may well be at play.

It is perhaps dangerous to suppose that the magnetoresistance peaks in our unimplanted films

have the same origin as that in κ-(BEDT-TTF)2Cu(NCS)2 without much more solid physical

evidence, given the important physical differences between the two materials systems.[49,

114, 160] However, the commonalities in the data are tantalizing, and further studies of this

phenomenon in both systems are certainly called for.

4.4 Summary

In this chapter results were presented of a study focusing on the effect implantation temper-

ature and initial film thickness have on nitrogen-implanted metal-mixed polymers. It was

found that thicker films produce more conductive samples, in agreement with the results

presented in chapter 3, and that under the implant conditions of 1016 N+/cm2 at 50 keV,

4.4 Summary 97

an initial film thickness of 10 nm produces highly inhomogeneous samples that are just on

the insulating side of a superconductor/metal-insulator transition. The anisotropic electri-

cal properties are consistent with a granular model of their structure. Further study of the

magnetoresistance of these inhomogeneous materials showed clear evidence of weak local-

isation in both the temperature dependence of the resistivity and the magnetoresistance.

However, weak localisation competes with superconductivity, leading to peaks in the magne-

toresistance. These magnetoresistance peaks differ in a number of important ways from the

peaks we have observed in the magnetoresistance of unimplanted films of SnSb on plastic

substrates. It is not yet clear whether this is because fundamentally different physics is at

play, or simply because the unimplanted films are much better metals. Intriguingly there

are strong similarities between the magnetoresistance of the unimplanted films and that of

κ-(BEDT-TTF)2Cu(NCS)2, which is a bulk layered crystal.[49, 187, 188]


Metal-Mixed Systems

For those who want some proof that physicists are human, the

proof is in the idiocy of all the different units which they use for

measuring energy.

Richard Feynman 5Metal-Mixed Polymers: Effects of

Heavy-Element Implantation and Applications

5.1 Introduction

While metal-mixing allows us to access the metallic side of the metal-insulator diagram,[50]

what is ultimately more desirable for an electronic material is tunability - the capacity to span

a large range in conductivity with a simple, reproducible and effective control parameter.

Although it was shown in chapter 3 that the conductivity can be controlled by the thickness

of the metal layer deposited on the polymer before implantation, it was later shown in

chapter 4 that doing so produces quite inhomogeneous metal-mixed samples with anisotropic

electrical properties as the metal thickness and the resulting conductivity are reduced.[160,

161] Furthermore, although it was shown in chapter 3 that the substrate morphology does not

affect the electrical properties of thin films prior to implantation, its effect on the conductivity

and tunability of metal-mixed systems is still unknown.

In this chapter, we will first determine what effect, if any, the substrate morphology

has. Following this, it will be demonstrated that a much more effective route to achieving

tunability in metal-mixed polymers is to use the very same sputtering process that was a

limitation when using a metal ion-beam to implant native polymer films. Metal-mixing with

an ion-beam consisting of heavier elements enhances the sputtering, thereby decreasing the

99

100Metal-Mixed Polymers: Effects of Heavy-Element Implantation and

Applications

net metal content of the implanted film. An added advantage of this approach is that it

allows one to start with a thicker metal layer, alleviating the problems with anisotropy in

lower conductivity films. It will be shown that it is possible to span the entire range from

metal/superconductor through to strong insulator using this approach, simply by tuning

the ion dose and beam energy. Finally, as a demonstration of a potential application for

these conductive ion-beam metal-mixed plastic films, we present proof-of-concept data for a

resistance thermometer made using this new material.

5.2 Sample Preparation

The samples discussed in this chapter were prepared in the manner outlined in § 2.1.2. Thin

SnSb films were deposited by thermal evaporation to a nominal thickness of 5, 10, 15 or

20 nm. The films were implanted using a Sn+,++ ion-beam with different combinations

of beam accelerating potentials (5, 10, 15 and 20 kV) and dose (1 × 1015, 5 × 1015 and

1 × 1016 ions/cm2). To discover what effect the substrate morphology has on the electrical

properties of implanted systems, a pair of samples, in four-terminal Hall bar configurations,

were prepared for each implant condition; one oriented parallel to the striations, the other

perpendicular. To ensure uniformity, both samples underwent film deposition and metal-

mixing at the same time.

Four-terminal electrical measurements were obtained as a function of temperature in one

of two similar experiments depending on the sample’s resistivity. Metallic samples with low

resistances were placed in a Oxford Instruments VTI system and had their 4T resistance

measured using a MM2000 Source-measure unit. Insulating, high resistance samples were

placed in an Oxford Instruments Optistat. The resistance measurements for these insulating

samples were obtained by applying a source voltage of up to 20 V using an Agilent E3640A

DC power supply, with the resulting source current measured using a Keithley 6485 Picoam-

meter. A Keithley 2400 Source Meter Unit in two-terminal mode was used to monitor the

output voltage during the measurement. In both experiments, measurements were taken

at one second intervals as the temperature was slowly varied from the cryostat’s maximum

temperature to its minimum and back to its maximum (see § 2.3.1 for details). The entire

5.3 Effect of Substrate Morphology on Metal-Mixed Polymers 101

cool-down/warm-up cycle took between 2.5 and 5 hrs.

5.3 Effect of Substrate Morphology on Metal-Mixed

Polymers

It was quickly found that all samples with an initial film thickness of 5 nm had resistances

too high to be measured (Rs > 10 GΩ/). This is not surprising as we found in chapter 3

that there was a metal-insulator transition for pre-implanted films at a thickness of 7 nm.

Determining the effect the substrate morphology has on the electical properties of thin films

(refer to chapter 3) was achieved by comparing the gradients of the conductivity-thickness

relationship between currents flowing parallel and perpendicular to the striations. Repeating

this analysis for this set of implanted samples is not possible for several reasons. Firstly,

the conductivity of the unimplanted films was only dependent upon the amount of metal

deposited on the substrate, which was characterised by the optical absorption. In this sample

set the conductivity was dependent upon the initial film thickness, the ion-beam energy and

the implantation dose, all of which alter the optical absorption in different ways (as it will be

shown below). Furthermore, there are at most four samples, for a given orientation, which

vary in only one parameter (i.e. same beam conditions with different film thickness), unlike

the twelve samples that only varied in film thickness used in chapter 3. Thus, establishing

trends like those shown in Fig. 3.7 is rather difficult.

Given this, we shall resort to directly comparing (where possible) the resistance-tempera-

ture relation between orientations. Figs. 5.1 – 5.3 shows comparisons for the fifteen implant

conditions where data was taken in both directions. These samples cover a wide range of

implant conditions and span from superconducting/metallic systems (Fig. 5.1) through to

strong insulators (Figs. 5.2 and 5.3). Examining the data one sees that over the temperature

range of these experiments Rs is generally higher (by a ratio of 2:1) in the perpendicular

direction, which indicates that the striations might have an affect on implanted systems.

If the striations do indeed have a negative affect on the conductivity in the perpendicular

direction, then for insulating systems this should be reflected in the gap, ∆/kB, and/or the


Applications

0 50 100 150 200

100

102

T (K)

Rs (

Ω/

)


20 nm5 keV1x1015 ions/cm2

100 150 200 250 300

102

103

T (K)

Rs (

Ω/

)



100 150 200 250 300

101

102

103

104

T (K)

Rs (

Ω/

)



100 150 200 250 300

101

102

103

104

T (K)

Rs (

Ω/

)



100 150 200 250 300

101

102

103

104

T (K)

Rs (

Ω/

)



0 50 100 150 200

10−1

100

101

T (K)

Rs (

Ω/

)



Figure 5.1: The temperature dependence of the sheet resistance for metal-mixed polymers atvarious implant conditions with a Sn ion beam. Data is shown for currents flowing parallel (solid line)and perpendicular (dashed line) to the substrate striations.

exponent prefactor, A, of Eqn. 1.8 as the resistance is directly dependent upon both these

parameters. Tab. 5.1 shows ∆/kB and A for the insulating systems shown in Figs. 5.2 and

5.3, where the top value for each implant condition is for the parallel direction and the

bottom value for the perpendicular direction.

Focusing on the gap first, we see that the perpendicular direction, which generally had

the higher Rs, has the larger value for ∆ seven out of eleven occasions. This is approximately

the same ratio as was found for Rs, which is not surprising since Rs is dependent upon ∆.

However, there is only a 64% correlation between any direction having both the higher Rs

and ∆. If the striations did cause an increase in the perpendicular direction’s resistance (as

was indicated in Figs. 5.1–5.3) then one would expect to see a larger correlation between

when it had the higher resistance while also having the larger gap than the 5 of 11 times

wittnessed here. Turning our attention to the prefactor, we see that the ‘higher-resistance’

5.3 Effect of Substrate Morphology on Metal-Mixed Polymers 103

100 150 200 250 300

107

108

109

T (K)

Rs (

Ω/

)



100 150 200 250 300

107

108

109

T (K)R

s (Ω

/ )



100 150 200 250 30010

6

107

108

T (K)

Rs (

Ω/

)



100 150 200 250 300

107

108

109

T (K)

Rs (

Ω/

)



100 150 200 250 300

107

108

109

T (K)

Rs (

Ω/

)





Applications

100 150 200 250 300

107

108

109

T (K)

Rs (

Ω/

)



100 150 200 250 30010

6

107

108

T (K)

Rs (

Ω/

)



100 150 200 250 300

107

108

109

T (K)

Rs (

Ω/

)



100 150 200 250 30010

6

107

108

T (K)

Rs (

Ω/

)



100 150 200 250 300

108

1010

T (K)

Rs (

Ω/

)



100 150 200 250 300

107

108

109

T (K)

Rs (

Ω/

)




5.4 Tunability 105

5× 1015 ions/cm2 1× 1016 ions/cm2

∆/kB (K) A (S) ∆/kB (K) A (S)10 nm 844 13.0

5 keV 745 13.315 nm 706 14.0

742 14.0

15 nm 658 12.110 keV 705 12.3

20 nm 699 12.5721 12.8

15 keV 10 nm 769 13.5719 13.3

10 nm 761 14.2 677 12.3871 13.4 715 11.8

20 keV 15 nm 773 13.6 694 11.8759 14.2 652 13.0

20 nm 705 14.4 721 12.0895 14.4 747 12.2

Table 5.1: Comparisons of the Arrhenius parameters of insulating Sn-implanted metal-mixed samples,produced using various fabrication conditions, oriented parallel (top value) and perpendicular (bottomvalue) to the substrate striations. The parameters are the gap, ∆/kB, and prefactor, A, of Eqn. 1.8.

perpendicular direction had the larger prefactor on only 6 (of 11) occassions. Although there

was better agreement with the perpendicular direction having both a higher resistance and

larger prefactor (5 of the total 6), if the striations did had any noticeable effect we should

still see a much larger proportion of the high-resistance direction having either the larger

gap or prefactor. Considering that there does not seem to be a correlation between any of

the parameters (Rs,∆ and A) and a particular direction, it appears clear that the substrate

morphology has no effect on the electrical properties of metal-mixed polymers. As such, the

sample orientation will be ignored below.

5.4 Tunability

In Fig. 5.4 we show the sheet resistance, Rs, versus temperature, T , for a selection of the

forty samples whose resistance was measured as part of this experiment. The most obvious

feature is that with small changes in the implant parameters, it is possible to span the entire


Applications

range from metal/superconductor, through to poor metals and moderate insulators, and

ultimately to strongly insulating films. The range covered by the data presented in Fig. 5.4

is quite remarkable, spanning over 10 orders of magnitude in resistance.

Comparing the measured resistances and implant conditions, the samples can be broadly

divided into three groups. The first group consists of samples with a 10 nm SnSb layer that

were implanted at the lowest dose of 1×1015 ions/cm2 with the lowest beam energies of 5 and

10 keV. This combination gives samples with very high resistances, too high to meaningfully

measure. Samples in this group are strongly insulating and sit at the far upper-right of

Fig. 5.4. Visual inspection of these samples is consistent with their very high resistivity,

they are far more transparent after implantation indicating a net loss of metal, but more

significantly, show no ‘greying’ of the polymer. Usually successful metal-mixing not only

distributes the metal layer into the polymer, it also leads to the graphitisation reported by

Osaheni et al.[122] for native polymers processed with an ion-beam. This graphitisation adds

a grey-brown tint to the samples and plays a significant role in enhancing the conductivity

of the metal-mixed films. We thus conclude that a low energy metal ion-beam results mostly

in sputtering, with the energy and dose being insufficient for graphitisation to occur. The

second group of samples consists of the remaining samples implanted to a dose of 1 ×

1015 ions/cm2 with either higher initial metal thickness and/or higher beam energy. These

samples are all metallic, sitting in the lower parts of Fig. 5.4 below Rs < h/e2 = 25.8 kΩ/,

and have a shiny, metallic appearance consistent with their low resistance. A photograph

of a metallic sample is shown in the lower inset of Fig. 5.4. The samples with the thickest

initial metal film undergo a superconducting transition to a sample-wide zero resistance state

at T = 3.6 K, consistent with our earlier work on superconductivity in these metal-mixed

polymer systems. The final group consists of all samples implanted with a dose higher than

1 × 1015 ions/cm2 irrespective of initial metal thickness and beam energy, and occupy the

middle-regions of Fig. 5.4. These samples all show insulating behaviour, and this group

reflects the important role that the balance between sputtering and graphitisation play in

the resulting resistivity of the film. For example, a 10 nm film implanted at 5 keV to a dose

1 × 1015 ions/cm2 has a very high resistance, and one would expect that if the dose was

increased to 1 × 1016 ions/cm2 that the resistance would be even higher due to increased

5.4 Tunability 107

0 100 200 30010

0

102

104

106

108

1010

T (K)

Rs (

Ω/

)

h/e2

kj

ihg

f

e

d

c

b

a

Figure 5.4: Sheet resistance, Rs, versus temperature, T , for a selection metal-mixed polymer filmsimplanted with an Sn+,++ ion beam at various energies, doses and initial film thicknesses. Despite thesimilar implant conditions, the observed resistance varied from a zero-resistance superconducting stateat low temperatures, through a metal-insulator transition at the quantum of resistance (∼ 25 kΩ) tostrongly insulating systems where the resistance could no longer be measured (Rs > 1010 Ω/). Thefabrication parameters for the data are: a (20 nm, 1× 1015 ions/cm2, 5 keV); b (15, 1× 1015, 20); c(15, 1× 1015, 10); d (10, 1× 1015, 20); e (20, 1× 1016, 10); f (15, 1× 1016, 20); g (10, 5× 1015, 10);h (10, 5× 1015, 20); i (20, 5× 1015, 20); j (10, 1× 1015, 5); k (10, 1× 1015, 10). The inset images arephotos of samples which produced data a (bottom) and i (top). As you can see the metallic sample ismuch shinier than the insulting sample, indicating that graphitisation has occurred in sample i.


Applications

sputtering. However, the resistance is actually lower and this is because the increased dose

leads to sufficient graphitisation to mitigate the effect of reduced metal content. Furthermore,

it was found that the resistance of samples implanted to a dose of 1 × 1016 ions/cm2 was

always lower than those implanted to a dose of 5× 1015 ions/cm2 (see Tab. C.1 for examples

at T = 100 K).

As both sputtering and graphitisation result in changes in visual appearance, it should

be possible to monitor both these effects via the sample’s optical absorption. To this end,

optical absorption spectra were obtained using a dual-beam Varian Cary 5000 UV-Vis-NIR

spectrometer between 400 and 800 nm. In Fig. 5.5 we present optical absorption spectra for

the films obtained in each case while changing just one fabrication parameter and keeping the

others constant. It was shown in the studies of unimplanted systems in chapter 3, that in-

creasing the film thickness increased the absorption across the 400 – 800 nm spectrum.[160]

Comparing this to Fig. 5.5(a) we can draw two conclusions. Firstly, the decrease in ab-

sorption is not constant across all wavelengths; there is a preferential decrease at longer

wavelengths. Indicating that the sputtering process, which thins films, causes samples to

become ‘redder’. Secondly, the decrease in absorption is not constant for all thicknesses,

indicated by the 5 nm sample ‘reddening’ more than the 20 nm sample. This suggests that

thinner films are less resistant to sputtering.

Now, if the only effect of the ion-beam was to sputter away metal, then increasing the

beam energy or dose would only result in reduced absorption, primarily at longer wave-

lengths, according to the data in Fig. 5.5(a). The data in Figs. 5.5(b) and 5.5(c) are ob-

tained from samples with a 20 nm thick film and show that the influences of the two beam

parameters are not so simple. In both cases, data from an unimplanted 20 nm film is pre-

sented for comparison (thick black line). Starting with the effect of beam energy at a fixed

but moderate dose [Figs. 5.5(b)], it is the lowest beam energy that actually has the lowest

absorption. Comparing with the trend in Fig. 5.5(a), this indicates that the film has been

significantly thinned by sputtering. As the beam energy is raised, the absorption actually

goes up not down for two reasons. First, for such high energies and thin films, an increase in

the beam energy only results in a relatively minor increase in the amount of sputtered ma-

terial for a given dose.[190] This makes sense, because the energy threshold for sputtering is

5.4 Tunability 109

0

0.5

1

5nm

10nm15nm

20nm(a)

Abs

0

0.5

1

Abs

(b)

Unimplanted

5kV10kV15kV20kV

400 500 600 700 800

0.5

1

Wavelength (nm)

Abs

(c)

1x1015 5x1015 1x1016

Figure 5.5: Absorption spectra for heavy-element metal-mixed plastics at: (a) 1× 1015 ions/cm2,20 keV at varying initial film thickness; (b) 20 nm, 5× 1015 ions/cm2ion at varying beam energy; and(c) 20 nm, 10 keV at varying implantation dose. We attribute the non-monotonic behaviour observedin panel (c) to the need for the film to be sufficiently thinned by the sputtering action of the ion-beambefore graphitisation of the polymer can proceed. Note that sputtering greatly increases transparencyat longer wavelengths (i.e., in the red part of the spectrum), while darkening due to graphitisation isgreatest for shorter wavelengths (i.e., blue side of the spectrum).


Applications

the surface binding energy of Sn (∼ 10 eV) and not the energy of the beam (∼ 10 keV).[110]

Second, the higher doses result in greater graphitisation, which is the origin of the increased

absorption, and the increasingly greyish hue that the films take with increased beam energy.

Graphitisation occurs due to the energy dissipated in atomic collisions within the sample as

the incident ions slow down and come to rest.[122] The number of collisions per incident ion

increases with energy, leading to the enhanced graphitisation referred to above.[191, 192] It

is interesting to note that the increase in absorbance graphitisation causes is favoured to

shorter wavelengths,[193] which is completely opposite to the affect sputtering has, which

decreases absorption primarily at longer wavelengths. Higher doses increase the probabil-

ity that the incident ions will penetrate the surface metal and lead to graphitisation of the

polymer.

Changing the dose at a beam energy of 10 keV [see Fig. 5.5(c)], further highlights the fact

that graphitisation is a process that requires significantly more energy/dose than sputtering.

At a dose of 1× 1015 ions/cm2, there is very little graphitisation, and as a result very little

change in the absorption spectrum, aside from an offset corresponding to a reduction in

metal thickness. As the dose is further increased, there is a net reduction in absorption

(primarily at longer wavelengths) due to a loss of metal from sputtering, followed by a net

increase (primarily at shorter wavelengths) due to graphitic carbon. These changes in the

spectra with dose in Fig. 5.5(c) confirm that the impact of the ion-beam is first on the metal

content and then on the graphitic content of the sample. This can be explained by the

screening effect of the metal layer deposited on the surface, which restricts the ion-beam’s

access to the polymer at first, but as the metal is gradually broken up and sputtered away

by the incident ions, graphitisation can proceed at an increasing rate. It is interesting to

note that the intermediate dose of 5 × 1015 ions/cm2 corresponds to crossing from metallic

conductivity to insulating conductivity in Fig. 5.4, which occurs due to the loss of metal

from the sample by sputtering.

The optical absorption can be utilised beyond simply telling us about the physics of

implantation and metal-mixing in these samples. The contradicting changes in absorption

resulting from the implantation-induced sputtering and graphitisation could be utilised as

a method for characterising the samples if they were to be developed for applications. This

5.5 Applications - Thermometers 111

would allow for reel-to-reel processing, where sheets of plastic are coated with metal films

and implanted within the same apparatus, with both processes being monitored in situ via

the absorption spectra. A schematic diagram of this is shown in Fig. 5.6.

EvaporatorIon Beam

Spectrometer Spectrometer

Figure 5.6: A diagram illustrating how large scale production of metal-mixed polymers could beachieved. The flexible nature of plastics would allow for reel-to-reel processing. Film deposition andion-implantation could be done simultaneously within the same apparatus, while both being monitoringin situ via their absorption spectra.

5.5 Applications - Thermometers

Having demonstrated that one can tune the conductivities of the Sn+,++ implanted polymers,

we now turn to a discussion of an important application for these samples. Materials with

predictable and reproducible temperature-dependent properties are widely used in thermom-

etry applications. Thermometers based on electrical resistance are particularly favourable

due to the ease with which they can be coupled into electronic circuits for digital read-out,

control and actuation, etc. As stated earlier, the most common resistive thermometers con-

sist of either platinum films (e.g., the PT100), ceramics (e.g., RuO2 or BaTiO3) or polymer

films loaded with carbon black (e.g., the polyswitch [156]) or metal powder.[157] However,

reproducible thermal characteristics are not the only requirement in such devices; low cost,

ease of production, and durability are also paramount. Another desirable quality is tunabil-

ity, particularly in resistance thermometers with a negative temperature coefficient, which

are often insulators with an exponential temperature dependence. With such sensors, if


Applications

the resistance is too high/low, the change in resistance corresponding to a given change in

temperature becomes too large/small to accurately measure, and so designing the sensor to

have the ideal resistance for a given range is important.[194]

The ion-beam metal-mixed polymer system presented here has all of these features. The

material can be produced at low cost, using facilities already widely used in the device

industry (e.g., a thermal evaporator and a kV-range ion-implanter). Furthermore, as we show

in this chapter, the resistance of a given sample at a particular temperature can be easily

tuned over a wide range by varying the implant parameters. Meaning that this one material

system can be used for thermometry at a very wide range of temperatures from millikelvin

through to the PEEK substrates’s glass transition temperature of 143 C, and possibilly

even approaching the melting point of PEEK at 343 C. The potential of this material as

a low temperature thermometer is evident in Fig. 5.4, with the conductivity profile of these

samples being the same as those currently being widely used in commercial applications (as

it will be shown below). To determine the suitability of using these materials in resistance-

based temperature sensors, we shall now compare the performance of three metal-mixed

samples (henceforth samples A-C) to that of currently commercially used devices (a PT100

film sample) in measuring the temperature between the melting and boiling points of water.

In order to obtain temperature readings the samples must first have their resistance

profile calibrated to a temperature scale. This was achieved by placing the four samples on

a EchoTherm hot plate, precise to 0.5 C, while the two-terminal resistance was calibrated

between 20 and 135 C. A two-terminal measurement was taken for two reason: firstly, the

vast majority of commercial RTDs only make use of two probe measurements; and secondly,

the contact resistance of the three metal-mixed samples (∼ 1 Ω) were negligible compared

to the samples’ room temperature resistance (∼ 1 MΩ). The temperature readings of the

hot plate were cross checked by a Digitech QM1320 thermocouple, precise to 1 C, whose

probe was placed in contact with the sample. The temperature of the hot plate was slowly

varied in 5 C increments. The PT100 sample gave a smooth, monotonic, reproducible curve

when calibrated against both the hot plate and thermocouple, as shown in Fig. 5.7. This

is not surprising given that PT100 is an industry standard. The calibration curves of the

metal-mixed samples, on the other hand, are a little more exotic.


20 40 60 80 100110

115

120

125

130

135

140

145

T (° C)

R2T

(Ω

)

Hot PlateThermocouple

Figure 5.7: Calibration curve of a PT100 resistive sample. Notice that the curve is equally smoothwhether calibrated against the hot plate or thermocouple.

When sample A was heated to 100 C, the resistance decreased in a smooth, mono-

tonic fashion as shown in Fig. 5.8(a). However, when the sample was cooled, the data,

although still smooth and monotonic, did not reproduce the data taken as the temperature

was increased [see Fig. 5.8(b)]. It was found that the resistances obtained on the cool-down

(squares) were lower than on the warm-up (circles). When reheated to 135 C from room

temperature, the resistance reproduced the data of the previous cool-down, and extrapolated

nicely when the temperature surpassed the previous cycle’s maximum [Fig. 5.8(c)]. When

cooled however, the resistance once again produced a nice smooth curve that was lower than

the warm-up [Fig. 5.8(d)]. When the sample was heated for a third time up to to 105 C,

the data once again followed the previous cycle’s cool-down. However, this time when cooled

the data reproduced the warm-up [Fig. 5.8(e)]. Repeated cycles between 105 C and room

temperature confirmed this reproducible trend [Fig. 5.8(f)].

In addition to this unusual electrical behaviour, there are two prominent differences when

comparing sample A’s appearance before and after heating. Firstly, prior to heating it is


Applications

4

6

8

10

12(a)

R2T

(M

Ω)

(b)

4

6

8

10

12(c)

R2T

(M

Ω)

(d)

20 40 60 80 100 120

4

6

8

10

12(e)

T (° C)

R2T

(M

Ω)

20 40 60 80 100 120

(f)

T (° C)

Figure 5.8: Calibration data of sample A, which shows rather peculiar behaviour. (a) As the sampleis heated to 100 C the resistance produced a neat curve. (b) When cooled, the data does not reproducedata taken during the warm-up. (c) When reheated to 100 C the data reproduces the previous cool-down and extrapolates in a smooth continuous manner. (d) After reaching a new maximum temperaturesample A’s resistance is once again lower than the warm-up. (e) However, when reheated to 105 Cthe data reproduces the previous cycle’s cool-down on both the warm-up and cool-down. (f) Repeatedcycles between room temperature and 105 C confirm this reproducible trend. The decrease in resistancecaused by heating is attributed to the sample being annealed.


possible to see the substrate striations, which appear as faint lines, running parallel across the

surface. Post heating the surface has a smoother, glazed appearance. Secondly, the clarity

and transparency of the sample has greatly increased. Unfortunately, due to the sample

being attached to a glass slide with double sided tape it was impossible to take absorption

spectra to gain a quantitative measure of this change.

We attribute the electrical and visual changes of sample A to annealing. By heating the

sample the bonds between molecules, mixed-metal and the newly formed graphitic carbon are

allowed to realign. Given that the PEEK is amorphous to begin with, and the implantation

process is rather random and ballistic, it is easy to suggest that the structure of metal-

mixed polymers are far from optimised regarding charge transport. Thus, any realignment

of the bonds should have a positive affect on the material’s conductivity, which is what was

observed. Given that annealing is used so prevalently to increase the conductivity of ion

implanted semiconductors[99, 104, 106] it seems more than reasonable to suggest that doing

so has the same effect for metal-mixed polymers.

Similar behaviour was observed during the calibration cycles of samples B and C [data

shown in Figs. 5.9(a) and (b) respectively], which involved two cycles between room temper-

ature (RT) and 120 C followed by, two cycles for sample B and three cycles for sample C,

between RT and 105 C. In both samples, the resistances measured during a cool-down from

a record high temperature were lower than those recorded on the warm-up to the record

high. This is in agreement with the behaviour observed for sample A. However, although

the drop in resistivity, which we attribute to annealing, was present, the observed change

in visual properties that occurred for sample A were not present in samples B or C. This is

not necessarily a surprising result, as the maximum temperature samples B and C reached

was 15 degrees below that for sample A. Given that such significant changes occurred in

sample A (i.e. the glazed appearance), which require a cooperative effort from the polymer’s

molecules,[195, 196] despite the sample never being heated as high as the glass transition

temperature of PEEK, raises the suggestion that metal-mixing has lowered Tg to somewhere

between 120 and 135 C. This could possibly be a result of a new material being formed (cf.

the raising of T (Rmax) in chapter 4). Annealing metal-mixed polymers could provide yet

another means with which the electrical properties of these systems, and the temperature


Applications

range of a thermometer based on these materials, could be tuned.

60

80

100

120

140

T (° C)

R2T

(kΩ

)

(a)

20 40 60 80 100 120

1

1.5

2

T (° C)

R2T

(M

Ω)

(b)

Figure 5.9: Calibration curve of samples (a) B and (b) C, which involved two cycles between roomtemperature (RT) and 120 C followed by, two cycles for sample B and three cycles for C, between RTand 105 C. The annealing behaviour observed in Fig. 5.8 for sample A is present in samples B and C.

Upon completion of the calibration measurements, the performance of the four ‘ther-

mometers’ (samples A-C and the PT100 sample) was compared between the melting and

boiling points of water. This was achieved by placing the four samples in a conical flask filled


with polydimethylsiloxane oil (Dow Corning 200 Fluid, 100 cSt). The flask was then placed

in a water bath, which acted as a thermal reservoir. Initially, the water temperature was

maintained at zero degrees (using ice) until the flask, oil and samples came to thermal equi-

librium (i.e. all resistance and temperature measurements became constant). After which,

the water temperature was slowly raised to boiling point over the course of 11 hours. The

two-terminal resistance of the PT100 and metal-mixed samples was measured using a Keith-

ley 2400 source meter unit. The probe of the Digitech thermocouple was also placed within

the flask of immersion oil as an independent means of determining the oil temperature. The

measured temperatures during this experiment are shown in Fig. 5.10 as a function of time.

0 100 200 300 400 500 6000

20

40

60

80

100

Time (s)

T (

° C

)

PT100Sample ASample BSample C

Figure 5.10: Temperatures measured using a PT100 resistive element sample (found in platinumresistance thermometers) and three metal-mixed polymers. The temperatures of all four ‘thermometers’are in strong agreement over the entire range. The step-like nature of the data reflects the variable rateof heating.

The temperatures reading of all four ‘thermometers’ are in strong agreement over the

entire 100 degree temperature range. The step-like nature of the data reflects the variable

rate of heating. To assess their relative performance, the temperatures recorded by each

‘thermometer’ were compared to each other. This analysis is shown in Figs. 5.11.


Applications

(b)

PT100 vs B

0

50

100(a)

PT100 vs A

T (

° C

)

(d)

A vs B

0

50

100(c)

PT100 vs C

T (

° C

)

0 50 100

(f)

B vs C

T (° C)0 50 100

0

50

100(e)

A vs C

T (° C)

T (

° C

)

Figure 5.11: Comparisons between the temperatures given by the four thermometers shown inFig. 5.10. A straight line with a gradient equal to unity would indicate two identically performingthermometers.


As a quantitative measure of performance, the root-mean-squared difference (residual)

was calculated, relative to the behavior of two identically performing thermometer, which

would give a perfectly linear relation with a gradient equal to unity. The residuals are

reported in Tab. 5.2. It can be seen that the residual values for the metal-mixed plastics are

all lower that of the PT100 sample, which indicates that, of the four, the PT100 sample was

in the strongest disagreement. This may just be a reflection of the similarities samples A

– C share due to their common makeup, but it may also indicate the superior performance

of the metal-mixed materials. Given their smaller residual values, and the uniformity of the

data shown in Fig. 5.10 it seems apparent that the theremometers based on metal-mixed

polymers performed at least as well as the more conventional PT100 thermometer.

(C) PT100 Sample A Sample B Sample CPT100 0 1.27 0.68 1.19

Sample A 1.27 0 0.71 0.50Sample B 0.68 0.71 0 0.64Sample C 1.19 0.50 0.64 0

Average 1.04 0.83 0.68 0.78

Table 5.2: Root-mean-squared values of residuals between comparisons of temperature readings givenby a platinum resistance sample (PT100) and three metal-mixed polymers (samples A-C). The lowervalues given by the metal-mixed samples indicate that they are at least as goods as the more conventionalPT100 sample.

Finally, in order to test the stability of these thermometers in a real-world application,

sample A (which had the largest residual value of the three metal-mixed thermometers) was

used to monitor the temperature of a well insulated, sound-proof wooden box containing

an Alcatel 65 m3/hr rotary pump used to run the VTI system. There was a fan-driven

continuous flow of air through the box via a pair of baffled ports on either side of the box.

Sample A was mounted inside the box next to the remote probe of a (commercially available)

Dual Inline 211c digital thermometer (the digital read-out module was located outside the

box), accurate to 0.1 C, used for monitoring and thermal cut-out of the pump. During

normal operation the temperature in the pump enclosure ranges between 21 and 37 C.

The sample resistance was measured, in a two-terminal configuration, using a Keithley 2000

multimeter to drive a constant current of 1 µA through the sample to ensure Joule heating

did not contribute errors to the measurement. Two-terminal resistance measurements were


Applications

made using a Keithley 2400 source meter unit during the daily warm-up and cool-down of

the pump box over a period of 2–3 weeks during the experiment in which low-temperature

data for Fig. 5.4 were obtained. Throughout the experiment good agreement was found

between sample A and the digital thermometer, as shown in Fig. 5.12.

21 25 29 33 37

11

12

13

14

T (°C)

R2T

(M

Ω)

21 25 29 33 37

11

12

13

14

T (°C)

R2T

(M

Ω)

Figure 5.12: Two-terminal resistance of sample A measured at temperatures close to room tem-perature attained in a sound-proof box containing a rotary pump used to run the VTI system. This datarepresents a proof of concept test to determine if metal-mixed polymers are suitable materials for usein resistance-based thermometers. The line of best fit is shown in red. Note that no care was taken toensure that the reference thermometer and sample A were in thermal equilibrium with each other or theirsurroundings. Resistance measurements were accurate to 5 significant figures, equating to a precisionof less than 5 millidegrees at 25 C providing an appropriately accurate calibration is undertaken.

It should be noted that no care was taken to ensure that either the sample or the com-

mercial thermometer were in equilibrium with each other or their surroundings. Also, there

is some hysteresis in the data, due to oppositely-directed lag in the warm-up and cool-down

cycles. Despite this, a smooth, monotonic relationship between the resistance and temper-

ature is clearly evident. In the later stages of this experiment, it was possible to use this

calibration to predict the measured pump-box temperature to within 1 C using the mea-

sured sample resistance. The measured resistance for sample A was stable to 5 significant

5.6 Summary 121

figures, which is 2 orders of magnitude better than the digital thermometer used for the test,

preventing us from directly determining the precision of our metal-mixed PEEK thermome-

ter. However, with an appropriately precise calibration, the stability reported above would

equate to a precision of 5 millidegrees at 25 C, which exceed the IEC 60751 requirements

for Class A thermometers by a factor of 3.[197]

5.6 Summary

In conclusion, we have shown that the tunability of ion-beam metal-mixed polymer films

can be significantly enhanced by utilising the added sputtering that results from exposure

to an ion-beam consisting of heavier elements such as Sn. With an appropriate choice of pa-

rameters we can access the full range of conductivities from metal/superconductor through

to strong insulators, without the anisotropy and difficulties in control that occur when at-

tempting the same by tuning the pre-implant metal thickness and using a lighter element

ion-beam (e.g., N+). As a result of the combined effects of sputtering and graphitisation of

the polymer, the mapping of implantation parameters to the final conductivity of the film is

not straightforward, but can be assessed by optical absorption, which may ultimately prove

to be a useful technique in commercial production of this material. Heating of the samples

resulted in significant changes in the optical and electrical properties, indicating that further

control of the material’s properties can be gained via annealing. With a view towards appli-

cations, it has been demonstrated that these metal-mixed polymer films have considerable

potential for use as temperature sensing elements. Comparisons between the performance

of three metal-mixed polymer based resistance thermometers and a PT100 thermometer be-

tween 0 and 100 C showed that the low-cost, robust metal-mixed plastics performed at least

as well as the industry standard, and exceeded the requirements for class A thermometers.


Applications

Whatever you do will be insignificant, but it is very important

that you do it.

Mahatma Gandhi 6Conclusions

This project set out to understand the electronic properties of a recently discovered class of

materials, metal-mixed polymers, with a major focus of this research being to gain control

of these properties. To do so required understanding of the system both before and after

implantation.

We began, in chapter 3, by determining the electrical properties of thin SnSb films on

PEEK substrates (i.e. metal-mixed systems prior to implantation). It was shown that the

morphology of thin metal films was dominated by that of the substrate. However, we demon-

strated that this need not be an issue in determining metal content as the optical absorption

of the films at a fixed wavelength provides a reliable and reproducible characterisation of

the relative film thickness. Comparisons of the conductivity for currents flowing parallel and

perpendicular to the substrate’s prominent striations revealed that they have no effect on the

electrical properties of unimplanted systems. It was found that there exists a metal-insulator

transition at a film thickness between 7 and 8 nm. The chapter concluded by showing that

as the film thickness is reduced, the superconducting transition in the unimplanted thin films

is broadened, but the onset of the transition remains at the transition temperature of bulk

Sn.

The focus moved onto metal-mixed systems in chapter 4 by studying the effects implan-

tation temperature and film thickness have on nitrogen implanted materials. Comparisons

of 20 nm films implanted at 77 K and 300 K showed that the lower implant temperature pro-

duced samples with lower residual resistances, which had sharper superconducting transitions

123

124 Conclusions

(smaller ∆Tc and ∆Bc) that occurred at relatively higher fields and temperatures (although

still suppressed from the Tc of Sn). From this we concluded that the higher implant tempera-

ture results in greater disorder. Measurements of 10 nm implanted films indicated that they

had just crossed over to the insulating side of a thickness-induced superconductor-insulator

transition. The electrical properties of these thinner samples were highly anisotropic, which

showed many intriguing features, including unusual peaks in the two-terminal magnetore-

sistance. We compared these peaks to similar ones seen in a 20 nm unimplanted system,

but it is not yet clear whether the underlying physics causing these features is the same

for both samples. We concluded that the observed behaviour in the metal-mixed systems

was due to the competition between superconductivity and weak localisation in a network

of superconducting and insulating grains.

Continuing the study of implanted system, but now with a Sn+,++ beam, in chapter

5 four key results were obtained. Firstly, it was determined that the substrate striations

have no affect on the electrical properties of implanted systems, indicating that metal-mixed

polymers are remarkably robust to variations in the substrate morphology. Secondly, by

utilising sputtering, which had previously been regarded as a drawback of using ion beam

consisting of heavier elements (i.e. Sn), we showed that it is possible to overcome the issue

of inhomogeneity that plagues thinner films by being able to start with thicker ones. Fur-

thermore, using this technique we were able to vary the resistivity of metal-mixed polymers

by over 10 orders of magnitude with only minor changes in the film thickness, implantation

dose and beam energy. The third result was that annealing these materials can result in

significant changes in their electrical and optical properties. Including annealing with im-

plant temperature, pre-implant film thickness, implantation dose, beam energy and species,

gives a total of six parameters, which we have shown can be used to control the electrical

properties of metal-mixed polymers. Finally, it was demonstrated that metal-mixed poly-

mers are well suited for use in resistance based temperature sensors. Comparisons against

an industry standard (PT100) between 0 and 100 C indicated that metal-mixed polymers

performed at least as well and exceeded the standards set for class A thermometers. Given

that low-cost, large-scale production of these systems is easily attainable, it appears that

metal-mixed polymers have great potential in the world of soft electronics.

6.1 Future Work 125

6.1 Future Work

Although the understanding of metal-mixed polymers has been greatly increased as a result

of the research contained in this thesis, there are still many questions left unanswered and

many new ones that have arisen from these results.

There is still further insight to be gained by studying the optical properties of these sys-

tems. The studies undertaken here only involved absorption measurements, however photons

can also be reflected or transmitted. Thus the behaviour seen in the absorption spectrum

does not tell the whole story of the sputtering and graphitisation processes. Further insight

into this interplay could also be gained via X-ray photoelectron spectroscopy. Such mea-

surements would be invaluable in determining the degree of graphitistation. Furthermore,

comparing XPS measurements of the samples studies in chapter 5 to those made on nitrogen

implanted metal-mixed systems by Tavenner et al. would allow the effect the implanted ion’s

mass has on the system’s bonds to be determine directly. Given the changes that occur from

annealing (colour, transparency and conductivity), it is clear that chemical bonds have been

altered. As such, XPS would also be very useful in the future studying the effect annealing

has on metal-mixed polymers.

Atomic force microscopy is another experimental technique that would be very beneficial,

as it would allow direct comparison to the unimplanted films, thereby revealing how resistant

the polymer is to implantation. AFM could also be used to help characterise annealing-

induced changes, and help verify any change in the glass transition temperature.

A technique yet to be applied to the study of metal-mixed polymers is magnetic sus-

ceptibility measurements. Such experiments, which determine the superconducting volume,

would give the first direct indication of the metal content within the samples. Compar-

isons of these values with the metal content of the pre-implanted film would help determine

the degree of sputtering present in the implantation process. Furthermore, susceptibility

measurements could help determine the size of the superconducting grains.

Given the tunable electronic properties of these systems, they appear ideal for study-

ing the superconductor-metal-insulator transition, which would benefit the developement of

these materials for use in soft electronics applications. Furthermore, given their disordered

126 Conclusions

2D nature, and the results presented in chapter 4, it appears there may be a lot interesting

and exotic physics to be studyied in metal-mixed polymers.

There are of course the many different combinations of metals, polymers and implant

conditions that need to be studied, as the prospect of mixing niobium films is certainly an

intriguing one. Given more time, all these topics would have been investigated, but, after

all, a Ph. D. can only go for so long.

AAdditional Thin Film Data

A.1 IV Sweeps of SnSb Thin Films

0 0.5 1 1.5 2 2.50

0.5

1

1.5

Current (µA)

Vol

tage

(m

V)

R4T

= 595 Ω

5 nm ||

0 0.5 1 1.50

2

4

6

8

Current (mA)

Vol

tage

(V

)

R4T

= 5670 Ω

5 nm ⊥

0 0.2 0.4 0.6 0.80

0.2

0.4

0.6

Current (µA)

Vol

tage

(m

V)

R4T

= 661 Ω

6 nm ||

0 5 100

1

2

3

Current (mA)

Vol

tage

(V

)

R4T

= 279 Ω

6 nm ⊥

Figure A.1: IV sweeps of 5 and 6 nm SnSb films on PEEK substrates at 300 K.

127

128 Additional Thin Film Data

0 0.05 0.10

5

10

15

20

Current (µA)

Vol

tage

(m

V)

R4T

= 12.6 MΩ

7 nm ||

0 5 10 150

5

10

15

Current (mA)

Vol

tage

(V

)

R4T

= 909 Ω

7 nm ⊥

0 5 10 15 200

0.5

1

1.5

2

2.5

Current (mA)

Vol

tage

(V

)

R4T

= 125 Ω

8 nm ||

0 5 10 15 200

0.5

1

Current (mA)

Vol

tage

(V

)

R4T

= 67.9 Ω

8 nm ⊥

0 5 10 15 200

0.5

1

1.5

Current (mA)

Vol

tage

(V

)

R4T

= 74.3 Ω

9 nm ||

0 5 10 15 200

0.5

1

Current (mA)

Vol

tage

(V

)

R4T

= 67.3 Ω

9 nm ⊥

Figure A.2: IV sweeps of 7 – 9 nm SnSb films on PEEK substrates at 300 K.

A.1 IV Sweeps of SnSb Thin Films 129

0 5 10 15 200

0.2

0.4

0.6

0.8

1

Current (mA)

Vol

tage

(V

)

R4T

= 49 Ω

10 nm ||

0 5 10 15 200

0.2

0.4

0.6

0.8

Current (mA)

Vol

tage

(V

)

R4T

= 45.9 Ω

10 nm ⊥

0 5 10 150

0.1

0.2

0.3

0.4

0.5

0.6

Current (mA)

Vol

tage

(V

)

R4T

= 35.2 Ω

12 nm ||

0 5 10 15 200

0.1

0.2

0.3

0.4

0.5

0.6

Current (mA)

Vol

tage

(V

)

R4T

= 34.4 Ω

12 nm ⊥

0 5 10 15 200

0.1

0.2

0.3

0.4

0.5

Current (mA)

Vol

tage

(V

)

R4T

= 26.3 Ω

14 nm ||

0 5 10 15 200

0.1

0.2

0.3

0.4

0.5

Current (mA)

Vol

tage

(V

)

R4T

= 25.3 Ω

14 nm ⊥

Figure A.3: IV sweeps of 10 – 14 nm SnSb films on PEEK substrates at 300 K.


0 5 10 15 200

0.1

0.2

0.3

0.4

Current (mA)

Vol

tage

(V

)

R4T

= 18.9 Ω

16 nm ||

0 5 10 15 200

0.1

0.2

0.3

0.4

Current (mA)

Vol

tage

(V

)

R4T

= 23.1 Ω

16 nm ⊥

0 5 10 15 200

0.1

0.2

0.3

Current (mA)

Vol

tage

(V

)

R4T

= 16.5 Ω

18 nm ||

0 5 10 15 200

0.1

0.2

0.3

0.4

Current (mA)

Vol

tage

(V

)

R4T

= 19.6 Ω

18 nm ⊥

0 5 10 15 200

0.1

0.2

0.3

Current (mA)

Vol

tage

(V

)

R4T

= 17.5 Ω

20 nm ||

0 5 10 15 200

0.1

0.2

0.3

0.4

Current (mA)

Vol

tage

(V

)

R4T

= 19.5 Ω

20 nm ⊥

Figure A.4: IV sweeps of a 16 – 20 nm SnSb films on PEEK substrates at 300 K.

A.2 Absorption Spectra of Thin Films 131

0 5 10 15 200

50

100

150

Current (mA)

Vol

tage

(m

V)

R4T

= 8.62 Ω

30 nm ||

0 5 10 15 200

50

100

150

Current (mA)

Vol

tage

(m

V)

R4T

= 7.67 Ω

30 nm ⊥

Figure A.5: IV sweeps of a 30 nm SnSb films on PEEK substrates at 300 K.

A.2 Absorption Spectra of Thin Films

400 450 500 550 600 650 700 750 800

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

5 nm6 nm7 nm

8 nm9 nm

10 nm

12 nm

14 nm

16 nm18 nm

20 nm

30 nm

λ (nm)

Abs

(ar

b. u

nits

)

Figure A.6: Absorption spectra of SnSb films on PEEK substrates at various nominal thicknesses.


400 500 600 700

0.4

0.45

0.5

0.55

0.6

0.65

5 nm

A (

arb.

uni

t)

λ (nm)400 500 600 700

0.45

0.5

0.55

0.6

0.65

0.76 nm

A (

arb.

uni

t)

λ (nm)

0.5

0.55

0.6

0.65

0.7

0.757 nm

A (

arb.

uni

t)

0.6

0.65

0.7

0.75

0.8

0.85

8 nm

A (

arb.

uni

t)

0.55

0.6

0.65

0.7

0.75

0.89 nm

A (

arb.

uni

t)

0.6

0.65

0.7

0.75

0.8

0.8510 nm

A (

arb.

uni

t)

Figure A.7: Absorption spectra of SnSb films on PEEK substrates at nominal thicknesses between5 and 10nm.

A.2 Absorption Spectra of Thin Films 133

400 500 600 7000.7

0.8

0.9

112 nm

A (

arb.

uni

t)

λ (nm)400 500 600 700

0.8

0.9

1

1.1

1.2

14 nm

A (

arb.

uni

t)

λ (nm)

1

1.1

1.2

1.3

1.4

16 nm

A (

arb.

uni

t)

1.1

1.2

1.3

1.4

1.5

18 nm

A (

arb.

uni

t)

1.1

1.2

1.3

1.4

20 nm

A (

arb.

uni

t)

1.6

1.7

1.8

1.9

2

2.1

2.2

30 nm

A (

arb.

uni

t)

Figure A.8: Absorption spectra of SnSb films on PEEK substrates at nominal thicknesses between12 and 30nm.

BMagnetoresistance of Organics Charge

Transfer Salts

Figure B.1: Magnetoresistance of κ-(BEDT-TTF)2Cu(NCs)2 as a function of field at low temper-atures (T < 5 K). The field is applied perpendicular to the conducting plane. The inset is an expandedview of R(H) at T = 2 K. Plot taken from Zuo et al.[187]

135

136 Magnetoresistance of Organics Charge Transfer Salts

Figure B.2: Magnetoresistance of κ-(BEDT-TTF)2Cu(NCs)2 as a function of field at temperaturesbetween 5 and 10 K. The field is applied perpendicular to the conducting plane. The inset includesnormal state R(H) at T = 11 K. Plot taken from Zuo et al.[187]

Figure B.3: Location of the peak resistance in field, Hpeak, of the data shown in Figs. B.1 and B.2as a function of temperature. Plot taken from Zuo et al.[187]

137

Figure B.4: Interlayer resistance of κ-(ET)2Cu(N(CN)2)Br as a function of temperature near Tc.Data was taken while a field was applied perpendicular to the places of the crystal (therefore parallel tothe current). The inset is the R(T ) for the whole temperature range. Plot taken from Zuo et al.[188]

138 Magnetoresistance of Organics Charge Transfer Salts

CSheet Resistance of Metal-Mixed Polymers

1× 1015 ions/cm2 5× 1015 ions/cm2 1× 1016 ions/cm2

Rs(T = 100 K) (Ω/) Rs(T = 100 K) (Ω/) Rs(T = 100 K) (Ω/)10 nm Rs > 1010 1.59× 109

Rs > 1010 1.20× 109

5 keV 15 nm 1.41× 109

1.74× 109

20 nm 15.1154

10 nm Rs > 1010 4.72× 108

9.43× 105

10 keV 15 nm 62.5 1.98× 108 4.42× 105

1100 3.33× 108

20 nm 14.9 4.30× 108 5.45× 105

6.44× 108

10 nm 1.67× 109

15 keV 1.13× 109

20 nm 1.95× 109

10 nm 58.6 2.53× 109 2.02× 108

7090 1.74× 109 2.48× 108

20 keV 15 nm 68.5 1.73× 109 1.43× 108

2.48× 109 3.47× 108

20 nm 19.8 1.64× 109 3.21× 108

17.8 1.47× 109 5.01× 108

Table C.1: The sheet resistance of Sn+,++-implanted metal-mixed polymers at T = 100 K, for variousimplant conditions. The top value within each cell is Rs for a sample oriented parallel to the substratestriations and the bottom value is for samples oriented perpendicular to the striations.

139

140 Sheet Resistance of Metal-Mixed Polymers

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