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.
vi
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
4 Introduction & Background
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
1.1 Metals and Insulators 5
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.
6 Introduction & Background
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]
1.1 Metals and Insulators 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.
8 Introduction & Background
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
1.1 Metals and Insulators 9
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
10 Introduction & Background
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
12 Introduction & Background
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.
1.2 Superconductors 13
(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)
14 Introduction & Background
(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
1.2 Superconductors 15
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)
16 Introduction & Background
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
1.2 Superconductors 17
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
18 Introduction & Background
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
1.2 Superconductors 19
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]
20 Introduction & Background
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
22 Introduction & Background
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
1.3 Conducting Polymers 23
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
24 Introduction & Background
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.
1.3 Conducting Polymers 25
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]
26 Introduction & Background
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.
28 Introduction & Background
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]
1.4 Ion Implantation 29
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
30 Introduction & Background
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]
1.4 Ion Implantation 31
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
32 Introduction & Background
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
1.4 Ion Implantation 33
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+
34 Introduction & Background
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
1.4 Ion Implantation 35
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.
36 Introduction & Background
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
38 Introduction & Background
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
1.5 Motivation and Applications 39
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
40 Introduction & Background
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
1.5 Motivation and Applications 41
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]
42 Introduction & Background
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
46 Methods and Techniques
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
48 Methods and Techniques
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
50 Methods and Techniques
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
2.2 Electrical Measurements 51
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
52 Methods and Techniques
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
2.2 Electrical Measurements 53
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
54 Methods and Techniques
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
2.2 Electrical Measurements 55
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.
56 Methods and Techniques
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,
2.2 Electrical Measurements 57
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.
58 Methods and Techniques
.
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
60 Methods and Techniques
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]
62 Methods and Techniques
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.
64 Methods and Techniques
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.
68 Effects of Substrate Morphology
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
70 Effects of Substrate Morphology
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
3.3 Results and Discussion 71
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
72 Effects of Substrate Morphology
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
3.3 Results and Discussion 73
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
ParallelPerpendicular
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
ParallelPerpendicular
0.8 1.2 1.6 2A
800 (Arb. Units)
(d)
300 K
77 K
ParallelPerpendicular
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
74 Effects of Substrate Morphology
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
ParallelPerpendicular
0.7 0.8 0.9 1A
600 (Arb. Units)
(b)
300 K
77 K
ParallelPerpendicular
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
ParallelPerpendicular
0.7 0.8 0.9 1 1.1A
800 (Arb. Units)
(d)
300 K
77 K
ParallelPerpendicular
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.
3.3 Results and Discussion 75
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
76 Effects of Substrate Morphology
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.
3.3 Results and Discussion 77
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.
78 Effects of Substrate Morphology
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 81
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
82The Competition Between Superconductivity and Weak Localisation in
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
4.3 Results and Discussion 83
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
84The Competition Between Superconductivity and Weak Localisation in
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.
4.3 Results and Discussion 85
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).
86The Competition Between Superconductivity and Weak Localisation in
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)
4.3 Results and Discussion 87
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
88The Competition Between Superconductivity and Weak Localisation in
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
4.3 Results and Discussion 89
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
90The Competition Between Superconductivity and Weak Localisation in
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
4.3 Results and Discussion 91
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).
92The Competition Between Superconductivity and Weak Localisation in
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.
4.3 Results and Discussion 93
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.
94The Competition Between Superconductivity and Weak Localisation in
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
4.3 Results and Discussion 95
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.
96The Competition Between Superconductivity and Weak Localisation in
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]
98The Competition Between Superconductivity and Weak Localisation in
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
102Metal-Mixed Polymers: Effects of Heavy-Element Implantation and
Applications
0 50 100 150 200
100
102
T (K)
Rs (
Ω/
)
ParallelPerpendicular
20 nm5 keV1x1015 ions/cm2
100 150 200 250 300
102
103
T (K)
Rs (
Ω/
)
ParallelPerpendicular
15 nm10 keV1x1015 ions/cm2
100 150 200 250 300
101
102
103
104
T (K)
Rs (
Ω/
)
ParallelPerpendicular
20 nm5 keV1x1015 ions/cm2
100 150 200 250 300
101
102
103
104
T (K)
Rs (
Ω/
)
ParallelPerpendicular
20 nm5 keV1x1015 ions/cm2
100 150 200 250 300
101
102
103
104
T (K)
Rs (
Ω/
)
ParallelPerpendicular
10 nm20 keV1x1015 ions/cm2
0 50 100 150 200
10−1
100
101
T (K)
Rs (
Ω/
)
ParallelPerpendicular
20 nm20 keV1x1015 ions/cm2
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/
)
ParallelPerpendicular
10 nm5 keV5x1015 ions/cm2
100 150 200 250 300
107
108
109
T (K)R
s (Ω
/ )
ParallelPerpendicular
15 nm5 keV5x1015 ions/cm2
100 150 200 250 30010
6
107
108
T (K)
Rs (
Ω/
)
ParallelPerpendicular
15 nm10 keV5x1015 ions/cm2
100 150 200 250 300
107
108
109
T (K)
Rs (
Ω/
)
ParallelPerpendicular
20 nm10 keV5x1015 ions/cm2
100 150 200 250 300
107
108
109
T (K)
Rs (
Ω/
)
ParallelPerpendicular
10 nm15 keV5x1015 ions/cm2
Figure 5.2: 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.
104Metal-Mixed Polymers: Effects of Heavy-Element Implantation and
Applications
100 150 200 250 300
107
108
109
T (K)
Rs (
Ω/
)
ParallelPerpendicular
10 nm20 keV5x1015 ions/cm2
100 150 200 250 30010
6
107
108
T (K)
Rs (
Ω/
)
ParallelPerpendicular
10 nm20 keV1x1016 ions/cm2
100 150 200 250 300
107
108
109
T (K)
Rs (
Ω/
)
ParallelPerpendicular
15 nm20 keV5x1015 ions/cm2
100 150 200 250 30010
6
107
108
T (K)
Rs (
Ω/
)
ParallelPerpendicular
15 nm20 keV1x1016 ions/cm2
100 150 200 250 300
108
1010
T (K)
Rs (
Ω/
)
ParallelPerpendicular
20 nm20 keV5x1015 ions/cm2
100 150 200 250 300
107
108
109
T (K)
Rs (
Ω/
)
ParallelPerpendicular
20 nm20 keV1x1016 ions/cm2
Figure 5.3: 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.
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
106Metal-Mixed Polymers: Effects of Heavy-Element Implantation and
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.
108Metal-Mixed Polymers: Effects of Heavy-Element Implantation and
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).
110Metal-Mixed Polymers: Effects of Heavy-Element Implantation and
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
112Metal-Mixed Polymers: Effects of Heavy-Element Implantation and
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.
5.5 Applications - Thermometers 113
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
114Metal-Mixed Polymers: Effects of Heavy-Element Implantation and
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.
5.5 Applications - Thermometers 115
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
116Metal-Mixed Polymers: Effects of Heavy-Element Implantation and
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
5.5 Applications - Thermometers 117
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.
118Metal-Mixed Polymers: Effects of Heavy-Element Implantation and
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.
5.5 Applications - Thermometers 119
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
120Metal-Mixed Polymers: Effects of Heavy-Element Implantation and
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.
122Metal-Mixed Polymers: Effects of Heavy-Element Implantation and
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.
130 Additional Thin Film Data
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.
132 Additional Thin Film Data
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.
134 Additional Thin Film Data
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
References
[1] D. J. Gundlach. Low Power, High Impact. Nat.Mater. 6, 173 (2007).
[2] S. R. Forrest. The path to ubiquitous and low-cost organic elctronic appliances on plastic. Na-ture 428, 911 (2004).
[3] C. Kittel. Introduction to Solid State Physics(John Wiley and Sons, 2005).
[4] N. W. Ashcroft and N. D. Mermin. Solid StatePhysics (Brooks Cole, 1976).
[5] G. Rickayzen. Green’s Functions and Con-densed Matter (Academic Press, 1980).
[6] P. A. Lee and T. V. Ramakrishnan. DisordedElectronic Systems. Rev. Mod. Phys. 57, 287(1985).
[7] P. Phillips. Advanced Solid State Physics(Westview Press, 2003).
[8] D. K. C. MacDonald and K. Mendelssohn. Re-sistivity of Pure Metals at Low Temperatures.Proc. Roy. Soc. A 202, 103 (1950).
[9] J. G. Analytis, A. Ardavan, S. J. Blundell,R. L. Owen, E. F. Garman, C. Jeynes, andB. J. Powell. Effect of Irradiation-Induced Dis-order on the Conductivity and Critical Temper-ature of the Organic Superconductor κ-(BEDT-TTF)2Cu(SCN)2. Phys. Rev. Lett. 96, 177002(2006).
[10] E. Abrahams, P. W. Anderson, D. C. Liccia-rdello, and T. V. Ramakrishnan. Scailing The-ory of Localization: Absense of Quantum Dif-fusion in Two Dimensions. Phys. Rev. Lett.42, 673 (1979).
[11] S. V. Kravchenko and M. P. Sarachik. Metal-insulator transition in two-dimension elec-tronic systems. Rep. Prog. Phys. 67, 1 (2004).
[12] G. Bergmann. Weak Localization in ThinFilms a time-of-flight experiment with conduc-tion electrons. Phys. Rep. 107, 1 (1984).
[13] G. Feher, F. R. C., and E. A. Gere. ExchangeEffects in Spin Resonance of Impurity Atomsin Silicon. Phys. Rev. 100, 1784 (1955).
[14] P. W. Anderson. Absense of Diffusion in Cer-tain Random Lattices. Phys. Rev. 109, 1492(1958).
[15] S.-A. Zhou. Electodynamic Theory of Super-conductors (Peter Peregrinus, 1991).
[16] G. J. Dolan and D. D. Osheroff. Nonmetallic
Conduction in Thin Metal Films at Low Tem-peratures. Phys. Rev. Lett 43, 721 (1979).
[17] B. L. Altshuler, A. G. Aronov, and P. A. Lee.Interaction Effects in Disorded Fermi Systemsin Two-Dimensions. Phys. Rev. Lett. 44, 1288(1980).
[18] E. Abrahams, S. V. Kravchenko, and M. P.Sarachik. Metallic behavior and related phe-nomena in two dimensions. Rev. Mod. Phys.73, 251 (2001).
[19] M. Y. Simmons, A. R. Hamilton, M. Pepper,E. H. Linfield, P. D. Rose, D. A. Ritchie, A. K.Savchenko, and T. G. Griffiths. Metal-InsulatorTransition at B = 0 in a Dilute Two Dimen-sional GaAs-AlGaAs Hole Gas. Phys. Rev.Lett. 80, 1292 (1998).
[20] D. Belitz and T. R. Kirkpatrick. TheAnderson-Mott transition. Rev. Mod. Phys.66, 261 (1994).
[21] D. J. Newson and M. Pepper. Anisotropic Neg-ative Magnetoresistance in a Variable-ThicnessElectron-Gas. J. Phys. C 18, 1049 (1985).
[22] A. M. Finkelstein. Weak Localization andCoulomb Interaction in Disorded-Systems. Z.Phys. B: Condens. Matter 56, 189 (1984).
[23] C. Castellani, C. Di Castro, P. A. Lee, andM. Ma. Interaction-Driven Metal-InsulatorTransition in Disorded Fermion Systems. Phys.Rev. B 30, 527 (1984).
[24] V. M. Pudalov, M. Dlorio, and J. W. Campbell.Hall Resistance and Quantized Hall-Effect toInsulator Transitions in a 2D Electron-System.JETP Lett. 57, 608 (1993).
[25] A. A. Shashkin, V. T. Dolgopolov, and K. G. V.Insulating Phases in a 2-Dimensional Electron-System of High-Mobility Si MOSFETS. Phys.Rev. B 49, 14486 (1994).
[26] A. A. Shashkin, V. T. Dolgopolov, K. G. V.,M. Wendel, R. Schuster, J. P. Kotthaus, R. J.Haug, K. von Klitzing, K. Ploog, H. Nickel, andW. Schlapp. Percolation Metal-Insulator Tran-sitions in the 2-Dimensional Electron-Systemof ALGAAS/GAAS Hetrostructures. Phys.Rev. Lett. 73, 3141 (1994).
[27] W. R. Clarke, C. E. Yasin, A. R. Hamilton,A. P. Micolich, M. Y. Simmons, K. Muraki,Y. Hirayama, M. Pepper, and D. A. Ritchie.Impact of long- and short-range disorder on the
141
142 References
metallic behaviour of two-dimensional systems.Nat. Phys. 4, 55 (2008).
[28] H. K. Onnes. Further experiments with liquidhelium D - On the change of the electrical resis-tance of pure metals at very low temperatures,etc V The disappearance of the resistance ofmercury. Akad. van Wetenschappen 14, 113(1911).
[29] W. Meissner and R. Ochsenfeld. Short initialannouncements. Naturwissenschaften 21, 787(1933).
[30] J. Bardeen, L. N. Cooper, and J. R. Schrief-fer. Microscopic Theory of Superconductivity.Phys. Rev. 106, 162 (1957).
[31] J. G. Bednorz and K. A. Muller. Possible High-Tc Superconductivity in the Ba-La-Cu-O Sys-tem. Z. Phys. B64, 189 (1986).
[32] A. Einstein. Quantum theory of mono-atomicideal gas. Akad. Wiss. pp. 3–14 (1925).
[33] R. A. Ogg. Bose-Einstein Condensationof Trapped Electron Pairs. Phase Separationand Superconductivity of Metal-Ammonia So-lutions. Phys. Rev. 69, 243 (1946).
[34] M. R. Schafroth. Superconductivity of aCharged Ideal Bose Gas. Phys. Rev. 100, 463(1995).
[35] M. R. Schafroth. Connection Between Super-fluidity and Superconductivity. Phys. Rev. 100,502 (1955).
[36] H. Frolich. Pauli exclusion principle forbids theformation of such a condensate. Phys. Rev. 79,845 (1950).
[37] L. N. Cooper. Bound Electron Pairs in a De-generate Fermi Gas. Phys. Rev. 104, 1189(1956).
[38] V. L. Ginzburg and L. D. Landau. Zh.Eksperim. Teor. Fiz 20, 1064 (1950).
[39] J. Bardeen, L. N. Cooper, and J. R. Schrieffer.Theory of Superconductivity. Phys. Rev. 108,1175 (1957).
[40] J. C. Maxwell. A Dynamical Theory of theElectromagnetic Field. Philosophical Transac-tions of the Royal Society of London 155, 459(1865).
[41] F. London and H. London. The electromag-netic equations of the superconductor. Proc.
Roy. Soc. A 149(A866), 0071 (1935).
[42] M. Tinkham. Introduction to Superconductivity(McGraw-Hill Inc., 1996).
[43] J. B. Ketterson and S. N. Song. Superconduc-tivity (Cambridge University Press, 1999).
[44] A. A. Abrikosov. On the Magnetic Propertiesof Superconductors of the Second Group. Sov.Phys. JETP 5, 1174 (1957).
[45] J. O. Indekeu and J. M. J. van Leeuwen. Inter-face Delocalization Transition in Type-I Super-conductors. Phys. Rev. Lett. 75, 1618 (1995).
[46] E. H. Brandt. Ginzburg-Landau vortex lat-tice in superconductor films of finite thickness.Phys. Rev. B 71, 014521 (2005).
[47] B. Rakvin, T. A. Mahl, A. S. Bhalla,Z. Z. Sheng, and N. S. Dalal. Measure-ment by EPR of the penetration depth in thehigh-Tc superconductors Tl2Ba2Ca2Cu3Ox andBi2Ca2SrCu2Ox. Phys. Rev. B 41, 769 (1990).
[48] B. J. Powell and R. H. McKenzie. Dependenceof the superconducting transition temperatureof organic molecular crystals on intrinsicallynonmagnetic disorder: A signature of eitherunconventional superconductivity or the atypi-cal formation of magnetic moments. Phys. Rev.B 69, 024519 (2004).
[49] B. J. Powell and R. H. McKenzie. Strong elec-tronic correlations in superconducting organiccharge transfer salts. J. Phys.: Condens. Mat-ter 18, R827 (2006).
[50] A. M. Goldman and N. Markovic.Superconductor-Insulator Transitions inthe Two-Dimensional Limit. Physics Today51, 39 (1998).
[51] N. Markovic, C. Christiansen, A. M.Mack, W. H. Huber, and A. M. Gold-man. Superconductor-insulator transition intwo dimensions. Phys. Rev. B 60(6), 4320(1999).
[52] M. Tinkham. Effect of Fluxoid Quantizationon Transitions of Superconducting Films. Phys.Rev. 129, 2413 (1963).
[53] I. S. Beloborodov, K. B. Efetov, A. V. Lopatin,and V. M. Vinokur. Transport Properties ofGranular Metals at Low Temperatures. Phys.Rev. Lett. 91, 246801 (2003).
References 143
[54] D. Dalidovich and P. Phillips. Fluctuation Con-ductivity in Insulator-Superconductor Transi-tions with Dissipation. Phys. Rev. Lett. 84,Dalidovich2000 (2000).
[55] D. G. McDonald. The Nobel Laureate Ver-sus the Graduate Student. Phys. Today 54, 47(2001).
[56] B. D. Josephson. Possible new effects in su-perconductive tunnelling. Phys. Lett. 1, 251(1962).
[57] B. D. Josephson. Coupled Superconductors.Rev. Mod. Phys. 36, 216 (1964).
[58] K. K. Likharev. Superconducting Weak Links.Rev. Mod. Phys. 51, 101159 (1979).
[59] P. W. Anderson and J. M. Rowell. ProbableObservation of the Josephson SuperconductingTunneling Effect. Phys. Rev. Lett. 10, 230(1963).
[60] S. Shapiro. Josephson Currents in Supercon-ducting Tunneling: The Effect of Microwavesand Other Observations. Phys. Rev. Lett. 11,80 (1963).
[61] P. W. Anderson. Theory of Dirty Superconduc-tors. J. Phys. Chem. Solids. 11, 26 (1959).
[62] S. Qin, J. Kim, Q. Niu, and C. Shih. Supercon-ductivity at the Two-Dimensional Limit. Sci-ence 324, 1314 (2009).
[63] Y. Li, C. L. Vicente, and J. Yoon. Transportphase diagram for superconducting thin filmsof tantalum with homogeneous disorder. Phys.Rev. B (2009).
[64] B. G. Orr, H. M. Jaeger, and A. M. Goldman.Local superconductivity in ultrathin Sn films.Phys. Rev. B. 32, 7586 (1985).
[65] H. M. Jaeger, D. B. Haviland, A. M. Goldman,and B. G. Orr. Threshold for superconductiv-ity in ultrathin amorphous gallium films. Phys.Rev. B. 34, 4920 (1986).
[66] A. F. Hebard and M. A. Paalanen. Magnetic-field-tuned superconductor-insulator transitionin two-dimensional films. Phys. Rev. Lett. 65,927 (1990).
[67] S. Okuma, T. Terashima, and N. Kukubo.Anomalous magnetoresistance near thesuperconductor-insulator transition in ultra-thin films of a−MoxSi1−x. Phys. Rev. B. 58,2816 (1998).
[68] T. Baturina, D. Islamov, J. Bentner, C. Strunk,M. Baklanov, and A. Satta. Superconductiv-ity on the localization threshold and magnetic-field-tuned superconductor-insulator transitionin TiN films. JETP Lett. 79, 337 (2004).
[69] M. Ma and P. A. Lee. Localized superconduc-tors. Phys. Rev. B 32, 5658 (1985).
[70] R. C. Dynes, J. P. Garno, and J. M. Row-ell. Two-Dimensional Electrical Conductivityin Quench-Condensed Metal Films. Phys. Rev.Lett. 40, 479 (1978).
[71] D. B. Haviland, Y. Liu, and A. M. Gold-man. Onset of superconductivity in the two-dimensional limit. Phys. Rev. Lett. 62, 2180(1989).
[72] D. Voss. Cheap and cheerful circuits. Nature407, 442 (2000).
[73] H. Shirakawa, E. J. Louis, A. G. MacDiarmid,C. K. Chiang, and A. J. Heeger. SynthesisOf Electrically Conducting Organic Polymers- Halogen Derivatives Of Polyacetylene, (Ch)x.J. C. S. Chem. Comm. 16(16), 578 (1977).
[74] C. K. Chiang, C. R. Fincher, Y. W. Park, Jr.,A. J. Heeger, H. Shirakawa, E. J. Louis, S. C.Gau, and A. G. MacDiarmid. Electrical Con-ductivity in Doped Polyacetylene. Phys. Rev.Lett. 39, 10981101 (1977).
[75] A. J. Heeger. Nobel Lecture: Semiconductingand metallic polymers: The fourth generationofpolymeric materials. Rev. Mod. Phys. 73, 681(2001).
[76] A. G. MacDiarmid. Nobel Lecture: ”Syntheticmetals”: A novel role for organic polymers.Rev. Mod. Phys. 73, 701 (2001).
[77] H. Shirakawa. Nobel Lecture: The discovery ofpolyacetylene film - The dawning of an era ofconducting polymers. Rev. Mod. Phys. 73, 713(2001).
[78] T. Ishiguro, H. Kaneko, Y. Nogami, H. Ishi-moto, H. Nishiyama, J. Tsukamoto, A. Taka-hashi, M. Yamaura, T. Hagiwara, and K. Sato.Logarithmic temperature dependence of resis-tivity in heavily doped conducting polymers atlow temperature. Phys. Rev. Lett. 69, 660(1992).
[79] H. Wu, G. Zhou, J. Zou, C. Ho, W. Wong,
144 References
W. Yang, J. Peng, and Y. Cao. Efficient Poly-mer White-Light-Emitting Devices for Solid-State Lighting. Adv. Mater. 21, 4181 (2009).
[80] B. O’Regan and M. Gratzel. A low-cost, highefficiency solar cell based on dye-sensitized col-loidal TiO2 films. Nature 353, 737 (1991).
[81] B. C. Thompson and L. M. J. Frechet. Poly-merFullerene Composite Solar Cells. Angew.Chem. Int. Ed 47, 58 (2008).
[82] A. Dodabalapur, L. Torsi, and H. E. Katz. Or-ganic Transistors: Two-Dimensional Transportand Improved Electrical Characteristics. Sci-ence 268, 270 (1995).
[83] J. L. Reddinger and J. R. Reynolds. Molec-ular engineering of pi-conjugated polymers(Springer, Berlin, 1999).
[84] W. Brutting. Physics of Organic Semiconduc-tors (Wiley, 2005).
[85] Z. Gadjourova, Y. G. Andreev, D. P. Tunstall,and P. Bruce. Ionic conductivity in crystallinepolymer electrolytes. Nature 412, 520 (2001).
[86] K. Lee, S. Cho, S. H. Park, A. J. Heeger,C. W. Lee, and S. H. Lee. Metallic transportin polyaniline. Nature 441, 65 (2006).
[87] H. A. Jahn and E. Teller. Stability ofPolyatomic Molecules in Degenerate ElectronStates. Proc.Roy. Soc. A 161, 200 (1937).
[88] H. Hettema. On the Theory of the Interac-tion Between Electronic and Nuclear Motionfor Three-Atomic Bar Shaped Molecules. Quan-tum Chemistry: Classical Scientific Papers 8,61 (2000).
[89] D. Song, S. Zhao, F. Zhang, Z. Xu, J. Li,X. Yue, H. Zhu, L. Lu, and Y. Wang. A key is-sue of organic light-emitting diodes: Enhancinghole injection by interface modifying. J. Lumin129, 1978 (2009).
[90] S. Gledhill, B. Scott, and B. A. Gregg. Organicand nano-structured composite photovoltaics:An overview. J. Mater. Res. 20, 3167 (2005).
[91] M. Nowak, S. D. D. V. Rughooputh, S. D. D.V. andS. Hotta, and A. J. Heeger. Polarons andbipolarons on a conducting polymer in solution.Macromolecules 20, 965968 (1987).
[92] S. Kohne, H. Schirmer, O. F.and Hesse, T. W.Kool, and V. Vikhnin. Ti3+ JahnTeller Po-larons and Bipolarons in BaTiO3. J. Supercon
12, 193 (1999).
[93] J. Roncali. Conjugated Poiy(thiophenes): Syn-thesis, Functionalizatlon, and Applications.Chem. Rev. 92, 711 (1992).
[94] T. A. Skotheim and J. R. Reynolds. Handbookof Conducting Polymers (CRC Press, 2007).
[95] A. Brown, D. Jarrettb, C. P.and de Leeuwa,and M. Mattersa. Field-effect transistors madefrom solution-processed organic semiconduc-tors. Synth. Met. 88, 37 (1997).
[96] E. Tavenner, P. Meredith, B. Wood, M. Curry,and R. Giedd. Tailored conductivity in ionimplanted polyetheretherketone. Synth. Met.145(2-3), 183 (2004).
[97] H. Kuninaka, K. Nishiyama, I. Funaki, T. Ya-mada, Y. Shimizu, and J. Kawaguchi. PoweredFlight of Electron Cyclotron Resonance Ion En-gines. Journal of Propulsion and Power 23, 544(2007).
[98] J. W. Mayer, L. Eriksson, and J. A. Davies.Ion Implantation in Semiconductors (Aca-demic Press, 1970).
[99] E. Rimini. Ion Implantation: Basics to De-vice Fabrication (Kluwer Academic Publishers,1995).
[100] S. Moffatt. Ion implantation form the past andinto the future. Nucl. Instr. and Meth. Phys.Res. B 96, 1 (1995).
[101] N. Bhor. Phil. Mag. 25, 10 (1913).
[102] J. J. Thomson. Phil. Mag. 13, 561 (1907).
[103] J. J. Thomson. Proc. R. Soc. London 99, 87(1921).
[104] G. Dearnaley, J. H. Freeman, and J. Nelson,R. S. adn Stephen. Ion Implantation (North-Holland Publishing Company, 1973).
[105] R. Ohl. Bell Syst. Tech. J. 31, 104 (1952).
[106] P. D. Townsend, P. J. Chandler, and L. Zhang.Optical Effects of Ion Implantation (Cam-bridge University Press, 1994).
[107] W. A. Grant, R. P. M. Procter, and J. L. Whit-ton, eds. Surface Modification of Metals by IonBeams (Elsevier Applied Science, 1987).
[108] S. Coffa, G. Ferla, F. Priolo, and E. Rimini,eds. Ion Implantation Technology (Elsevier,1995).
References 145
[109] M. Natasi, J. W. Mayer, and J. K. Hirvonen.Ion-Solid Interactions: Fundamentals and Ap-plications (Cambridge University Press, 1996).
[110] D. Carter and D. G. Armour. The interactionof low energy ion beams with surfaces. ThinSolid Films 80, 13 (1981).
[111] V. C. Long, S. Washburn, X. L. Chen, and S. A.Jenekhe. Hall-effect study of an ion-bombardedpolymer. J. Appl. Phys. 80(7), 4202 (1996).
[112] D. S. Gemmel. Channeling and related effectsin the motion of charged particles through crys-tals. Rev. Mod. Phys. 46, 129 (1974).
[113] Z. A. Iskanderova, J. Kleiman, W. D. Morison,and R. C. Tennyson. Erosion resistance anddurability improvement of polymers and com-posites in space environment by ion implanta-tion. Mater. Chem. Phys. 54, 91 (1998).
[114] A. P. Micolich, E. Tavenner, B. J. Powell,A. R. Hamilton, M. T. Curry, R. E. Giedd, andP. Meredith. Superconductivity in metal-mixedion-implanted polymer films. Appl. Phys. Lett.89, 152503 (2006).
[115] A. Persaud, J. A. Liddle, T. Schenkely, J. Boko,T. Ivanov, and I. W. Rangelow. Ion Implanta-tion with Scanning Probe Alignment.
[116] S. H. Sperling. Introduction to Physical Poly-mer Science (Wiley, 2006).
[117] J. Comyn, L. Mascia, G. Xiao, and B. M.Parker. Plasma-treatment of polyetheretherke-tone (PEEK) for adhesive bonding. Int. J. Ad-hes. Adhes. 16, 97 (1996).
[118] H. Li, R. Fouracre, M. Given, H. Banford,S. Wysocki, and S. Karolczark. The effectson polyetheretherketone and polythersulfone ofelectron and gamma irradiation. IEEE Trans-actions on Dielectrics and Electrical Insulation32, 1527 (1999).
[119] Y. Wu, T. Zhang, Z. H., X. Zhang, Z. Deng,and G. Zhou. Electrical properties of polymermodified by metal ion implantation. Nucl. Instr.and Meth. Phys. Res. B 169, 89 (2000).
[120] Y. Q. Wang, R. E. Giedd, M. G. Moss, andJ. Kaufmann. Electronic properties of ion-implanted polymer films. Nucl. Instr. and Meth.Phys. Res. B 127/128, 710 (1997).
[121] S. R. Forrest, M. L. Kaplan, P. H. Shmidt,
T. Venkatesan, and A. J. Lovinger. Large Con-ductivity Changes In Ion-Beam Irradiated Or-ganic Thin-Films. Appl. Phys. Lett. 41(8), 708(1982).
[122] J. A. Osaheni, S. A. Jenekhe, A. Burns, G. Du,J. Joo, A. J. Epstein, and C. S. Wang. Spec-troscopic and Morphological-Studies of HighlyConducting Ion-Implanted Rigid-Rod and Lad-der Polymers. Macromolecules 25, 5828 (1992).
[123] Z. J. Han, B. K. Tay, P. C. T. Ha, M. Shak-erzadeh, A. A. Cimmino, S. Prawer, andD. McKenzie. Electronic conductance of ionimplanted and plasma modified polymers. Appl.Phys. Lett. 91, 052103 (2007).
[124] Z. J. Han and B. K. Tay. Electrical Conductiv-ity of Poly(ethylene terephthalate) Modified byTitanium Plasma. J. Appl. Polym. Sci. 107,3332 (2007).
[125] R. C. Powles, D. R. McKenzie, N. Fujisawa,and D. G. McCulloch. Production of amor-phous carbon by plasma immersion ion implan-tation of polymers. Diam. Rel. Mat. 14, 1577(2005).
[126] T. Hioki, S. Noda, M. Sugiura, M. Kakeno,K. Yamada, and J. Kawamoto. Electrical AndOptical-Properties Of Ion-Irradiated OrganicPolymer Kapton-H. Appl. Phys. Lett. 43(1),30 (1983).
[127] G. R. Rao, E. H. Lee, and L. K. Mansur. Struc-ture and dose effects on improved wear proper-ties of ionimplanted polymers. Wear 162-164,739 (1993).
[128] G. R. Rao, E. H. Lee, and L. K. Mansur. Wearproperties of argon implanted poly(ether etherketone). Wear 174, 103 (1994).
[129] D. R. McKenzie, K. Newton-McGee, P. Ruch,M. M. Bilek, and B. K. Gan. Modification ofpolymers by plasma-based ion implantation forbiomedical applications. Surface & CoatingsTechnology 186, 239 (2004).
[130] P. K. Haff and Z. E. Switkowski. Ion-Beam-Induced Atomic Mixing. J. Appl. Phys. 48,3383 (1977).
[131] J. M. Valles Jr, R. C. Dynes, and J. P. Garno.Superconductivity and the Electronic Densityof States in Disorded Two-Dimensional Metals.Phys. Rev. B 40, 6680 (1989).
[132] T. Ishiguro, K. Yamaji, and G. Saito. Organic
146 References
Superconductors (Springer, Berlin, 2001).
[133] A. Tracz, J. Wosnitza, S. Barakat, J. Hagel,and H. Muller. Superconducting properties oforganic composites: blends of βco-(ET)2I3 withparaffin and polycarbonate. Synth. Met. 120,849 (2001).
[134] A. Tracz, J. K. Jeszka, and A. Sroczyriska.Colourless, transparent conductive polymerfilms with ultrathin networks of organic crys-tals. Adv. Mat. Opt. Elect. 6, 335 (1996).
[135] J. K. Jeszka, A. Tracz, A. Srozynska, J. Ulan-ski, H. Muller, T. Pakula, and M. Kryszewski.Direct preparation of polymer composites with?-ET2I3 polycrystalline layers. Synth. Met.103, 1820 (1999).
[136] E. E. Laukhina, V. A. Merzhanov, S. I. Pesot-skii, A. G. Khomenko, E. B. Yagubskii, J. Ulan-ski, and J. K. Jeszka. Superconductivity inreticulate doped polycarbonate films, containing(BEDT-TTF)2I3. Synth. Met. 70, 797 (1995).
[137] A. M. Goldman. Superconductor-insulatortransitions in the two-dimensional limit. Phys-ica E 18(1-3), 1 (2003).
[138] J. M. Kosterlitz and D. J. Thouless. Order-ing, Metastability And Phase-Transitions In 2Dimensional Systems. J. Phys. C 6(7), 1181(1973).
[139] V. M. Vinokur, T. I. Baturina, M. V. Fistul,A. Y. Mironov, M. R. Baklanov, and C. Strunk.Superinsulator and quantum synchronization.Nature 452(7187), 613 (2008).
[140] K. Yamada, B. Shinozaki, and T. Kawaguti.Weak localization and magnetoconductance inpercolative superconducting aluminum films.Phys. Rev. B 70(14), 144503 (2004).
[141] J. Hua, Z. L. Xiao, D. Rosenmann, C. Be-loborodov, U. Welp, W. Kwop, and G. W.Crabtree. Resistance Anomoly in DisorderedSuperconducting Films. Appl. Phys. Lett. 90,072507 (2007).
[142] C. A. M. dos Santos, C. J. V. Oliveira, M. S.da Luz, A. D. Bortolozo, M. J. R. Sandim,and A. J. S. Machado. Two-fluid model fortransport properties of granular superconduc-tors. Phys. Rev. B 74(18), 184526 (2006).
[143] M. Oszwaldowski, T. Berus, and V. K. Dugaev.Weak localization in InSb thin films heavilydoped with lead. Phys. Rev. B 65(23), 235418
(2002).
[144] K. Myojin and R. Ikeda. Effect of in-plane linedefects on field-tuned superconductor-insulatortransition behavior in homogeneous thin film.J. Phys. Soc. Jpn 76, 094710 (2007).
[145] S. Gunes, H. Neugebauer, and N. S. Sari-cifci. Conjugated Polymer-Based Organic SolarCells. Chem. Rev. 107, 1324 (2007).
[146] C. D. Dimitrakopoulos and P. R. L. Malenfant.Organic Thin Film Transistor for Large AreaElectronics. Adv. Mater. 14, 99 (2002).
[147] V. Subramaniam, J. Frechet, P. C. Chang,D. C. Huang, J. B. Lee, S. E. Molesa, A. R.Murphy, D. R. Redinger, and S. K. Volkman.Progress Towards Development of All-PrintedRFID Tags. Materials, Processes, and Devices.Proc. IEEE 93, 1330 (2005).
[148] D. T. McQuade, A. E. Pullen, and T. M. Swa-ger. Conjugated Polymer-Based Chemical Sen-sors. Chem. Rev. 100, 2537 (2000).
[149] S. R. Forrest, D. C. Bradley, and M. E. Thomp-son. Measuring the Efficiency of Organic Light-Emitting Devices. Adv. Mater. 15, 1043 (2003).
[150] N. D. Robinson and M. Berggren. ConjugatedPolymers: Processes and Applications (CRCPress, 2007).
[151] Y. Liang, Z. Xu, J. Xia, S. Tsai, Y. Wu, G. Li,C. Ray, and L. Yu. For the Bright FutureBulkHeterojunction Polymer Solar Cells with PowerConversion Efficiency of 7.4%. Adv. Mater.22, 1 (2010).
[152] M. A. Green, K. Emery, K. Hishikawa, andW. Warta. Solar Cell Efficiency Tables. Prog.Photovolt: Res. Appl 17, 320 (2009).
[153] E. S. P. Smits, S. G. J. Mathijssen, P. A.van Hal, S. Setayesh, T. C. T. Geuns, K. A.H. A. Mutsaers, E. Cantatore, H. J. Won-dergem, O. Werzer, R. Resel, M. Kemerink,S. Kirchmeyer, A. M. Muzafarov, S. A. Pono-marenko, B. de Boer, P. W. M. Blom, andD. M. de Leeuw. Bottom-up organic integratedcircuits. Nature 455, 956 (2008).
[154] H. Klauk, U. Zschieschang, J. Pflaum, andM. Halik. Ultralow-power organic complemen-tary circuits. Nature 445(7129), 745 (2007).
[155] M. Fisher and J. Sikes. Electronic Noses &Sensors for the Detection of Explosives (NATO
References 147
Science Series, 2004).
[156] F. A. Doljack. Polyswitch PTC devices -A new low-resistance conductive polmer-basedPTC device for overcurent protection. IEEETrans. On Comp., Hybrids and Manuf. Tech-nol. 4, 372 (1981).
[157] R. Strumpler. Polymer composite thermistorsfor temperature and current sensors. J. Appl.Phys. 80, 6091 (1996).
[158] TC. Guide to Thermocouple and ResistanceThermometry.
[159] URL www.wikipedia.org.
[160] A. P. Stephenson, U. Divakar, A. P. Micolich,P. Meredith, and B. J. Powell. Preparation ofmetal mixed plastic superconductors: Electricalproperties of tin-antimony thin films on plasticsubstrates. J. Appl. Phys. 105, 093909 (2009).
[161] A. P. Stephenson, A. P. Micolich, U. Divakar,P. Meredith, and B. J. Powell. Competition be-tween Superconductivity and Weak Localizationin Metal-Mixed Ion-Implanted Polymers. Phys.Rev. B 81, 144520 (2010).
[162] A. P. Stephenson, A. P. Micolich, K. H.Lee, P. Meredith, and B. J. Powell. Atunable metal-organic resistance thermometer.ChemPhysChem 12, 116 (2011).
[163] J. R. Atkinson, J. N. Hay, and M. J. Jenkins.Enthalpic relaxation in semi-crystalline PEEK.Polymer 43, 731 (2002).
[164] F. N. Cogswell. Thermoplastic Aromatic Poly-mer Composites (Buttwerworth-Heinemann,1992).
[165] J. E. Harris and L. M. Robeson. IsomorphicBehavior of Poly(aryl ether ketone) Blends. J.Polym. Sci. Polym. Phys. 25, 311 (1987).
[166] W. J. Brennan, H. S. Munro, and S. A. Walker.Investigation of the ageing of plasma oxidizedPEEK. Polymer 32, 1527 (1991).
[167] L. J. Matienzo. Surface reactions of poly(etherether ketone) with He2+ ions. Polymer 32,3057 (1990).
[168] A. Mackova, V. Havranek, V. Svorcik,N. Djourelov, and T. Suzuki. Degradation ofPET, PEEK and PI induced by irradiation with150 keV Ar+ and 1.76 MeV He+ ions. Nucl.Instr. and Meth. B 240, 245 (2005).
[169] V. Svorcik, K. Proskova, V. Rybka, J. Vacik,V. Hnatowicz, and Y. Kobayashi. Changesof PEEK surface chemistry by ion irradiation.Mater. Lett. 36, 128 (1998).
[170] URL www.pag.lbl.gov.
[171] URL www.eeel.nist.gov.
[172] L. van der Pauw. A Method of Measuring Spe-cific Resistivity and Hall Effect of Discs of Ar-bitarty Shape. Philips Res. Repts. 13, 1 (1958).
[173] L. van der Pauw. A Method Of Measuring theResistivity and Hall Coefficient on Lamellae ofArbitary Shape. Philips Technical Review 26,220 (1958).
[174] Oxford Instruments Optistat Operators Hand-book.
[175] G. Binnig, C. F. Quate, and C. Gerber. AtomicForce Microscope. Phys. Rev. Lett. 56, 930(1986).
[176] F. J. Giessibl and C. F. Quate. Exploringthe Nanoworld with Atomic Force Microscopy.Physics Today 59, 44 (2006).
[177] M. Strongin, R. S. Thompson, O. F. Kam-merer, and J. E. Crow. Destruction of Su-perconductivity in Disordered Near-MonolayerFilms. Phys. Rev. B. 1, 1078 (1970).
[178] H. Raffy, R. B. Laibowitz, P. Chaudhari, andS. Maekawa. Localization and interaction ef-fects in two-dimensional W-Re films. Phys.Rev. B. 28, 6607 (1983).
[179] J. M. Graybeal and M. R. Beasley. Localizationand interaction effects in ultrathin amorphoussuperconducting films. Phys. Rev. B. 29, 4167(1984).
[180] S. Kobayashi, Y. Tada, and W. Sasaki.Two-dimensional random array of Josephson-coupled fine particles. Physica B 107, 129(1981).
[181] A. E. White, R. C. Dynes, and J. P. Garno.Destruction of superconductivty in quench-condensed two-dimensional films. Phys. Rev.B 33, 3549 (1986).
[182] M. Kunchur, Y. Z. Zhang, P. Lindenfeld, W. L.McLean, and J. S. Brooks. Quasireentrant su-perconductivity near the metal-insulator transi-tion of granular aluminum. Phys. Rev. B. 36,4062 (1987).
148 References
[183] H. M. Jaeger, D. B. Haviland, B. G. Orr, andA. M. Goldman. Onset of superconductivity inultrathin granular metal films. Phys. Rev. B40, 182 (1989).
[184] A. Gerber, T. Grenet, M. Cyrot, andJ. Beille. Double-Peak Superconducting Transi-tion in Granular L-M-Cu-O (L=Pr,Nd,Sm,Eu;M=Ce,Th) Superconductors. Phys. Rev. Lett.65, 3201 (1990).
[185] K. E. Gray and D. H. Kim. Interlayer Tun-neling Model for the c-axis Resistivity in High-Temperature Superconductors. Phys. Rev. Lett.70, 1693 (1993).
[186] M. V. Kartsovnik, G. Y. Logvenov, and N. D.Kushch. Interlayer magnetotransport in κ-(BEDT-TTF)2X superconductors. Synth. Met.103, 1827 (1999).
[187] F. Zuo, J. A. Schlueter, M. E. Kelly, andJ. M. Williams. Mixed-state magnetoresis-tance in organic superconductors κ-(BEDT-TTF)2Cu(NCS)2. Phys. Rev. B 54, 11 973(1996).
[188] F. Zuo, J. A. Schlueter, and J. M. Williams.Interlayer magnetoresistance in the organic su-perconductor κ-(BEDT-TTF)2Cu[N(CN)2]Brnear the superconducting transition. Phys. Rev.B 60, 574 (1999).
[189] J. Singleton. Studies of quasi-two-dimensionalorganic conductors based on BEDT-TTF usinghigh magnetic fields. Rep. Prog. Phys. 63, 1111(2000).
[190] P. Sigmund. Theory of Sputtering. I. SputteringYield of Amorphous and Polycrystalline Tar-gets. Phys. Rev. 184, 383 (1969).
[191] B. S. Elman, M. S. Dresselhaus, G. Dressel-haus, E. W. Maby, and H. Mazurek. Ramanscattering from ion-implanted graphite. Phys.Rev. B 24, 1027 (1981).
[192] M. S. Dresselhaus and R. Kalish. Ion Implan-tation in Diamond, Graphite and Related Ma-terials (Springer-Verlag, 1992).
[193] X. L. Ding, Q. S. Li, and X. H. Kong.Effect of Repetition Rates of Laser Pulseson Micorstructure and Optical Properties ofDiamond-Like Carbon Films. Int. J. Mod.Phys. B 23, 5671 (2009).
[194] L. C. Inc. Temperature Measurement and Con-trol Catalog. Tech. rep., Lakeshore Cryotronics
Inc. (2004).
[195] R. D. Andrews. Transition Phenomena andSolid-State Structure in Glassy Polymers. J.Polym. Sci: C 14, 261 (1966).
[196] J. M. O’Reilly and F. E. Karasz. Specific HeatStudies of Transition and Relaxation Behaviorin Polymers. J. Polym. Sci: C 14, 49 (1966).
[197] Industrial platinum resistance thermometersand platinum temperature sensors. Tech.rep., International Electrotechnical Commis-sion (2008).