Graphene and Superconducting (Yba2cu3o7-X) Thin Film – a Study on Electronic and Magnetic Transport Properties for Detectors Applications

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2017 Graphene and Superconducting (YBa2Cu3O7-x) Thin iF lm – A Study on Electronic and Magnetic Transport Properties for Detectors Applications Nandhagopal Masilamani University of Wollongong

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Recommended Citation Masilamani, Nandhagopal, Graphene and Superconducting (YBa2Cu3O7-x) Thin iF lm – A Study on Electronic and Magnetic Transport Properties for Detectors Applications, Doctor of Philosophy thesis, , University of Wollongong, 2017. https://ro.uow.edu.au/theses1/124

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Graphene and Superconducting (YBa2Cu3O7-x) Thin Film – A Study on Electronic and Magnetic Transport Properties for Detectors Applications

This thesis is submitted as part of the requirements for the award of the degree of

DOCTOR OF PHILOSOPHY

from the

UNIVERSITY OF WOLLONGONG

NANDHAGOPAL MASILAMANI, M.Sc.,

Faculty of Engineering and Information Sciences

Institute for Superconducting and Electronic Materials

AIIM Facility, Innovation Campus

Aug. 2017

CERTIFICATION

I, Nandhagopal Masilamani, declare that this thesis, submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy, in the School of Engineering Physics, Institute for Superconducting and Electronic Materials, University of Wollongong, is wholly my own work unless otherwise referenced or acknowledged. The document has not been submitted for qualifications at any other academic institution.

Nandhagopal Masilamani Wollongong 04 August 2017

DEDICATION

LORD KRISHNA

(Sarvam Krishnaarpanam)

Loka samastha sukino bhavantu

Ohm shanthi, shanthi, shanthi

(May all the beings in all the worlds be happy let there be peace, peace, and peace everywhere)

ABSTRACT

Miniaturization and performance improvements are driving the electronic industry to shrink the feature size of superconductor devices. Several important questions arise from this development. For example, how small can some devices be fabricated? How will it affect the device performance? Can new operating principles be implemented in nanoscale devices? What other applications exist for nanofabrication techniques?

Hence the goals of this Ph.D. thesis research were three-fold. First, using a scanning electron microscope (SEM) for electron beam lithography (EBL) to optimize, utilize/implement, characterize, and extend existing fabrication techniques and develop new ones (as described in Chapter 3). Second, establishing baseline fabrication processes for graphene-based Josephson junction devices and studying the electronic properties of few-layer graphene with superconducting electrodes. Finally, for superconducting single photon detector (SSPD) applications, exploring the properties of YBa2Cu3O7-x (YBCO) superconducting thin films with various buffers and substrates. Thorough theoretical and experimental studies were conducted based on existing designs and available instruments.

This Ph.D. thesis addresses nanostructure fabrication techniques based on EBL and their application to the creation and study of superconducting material for electron-transport studies. In this dissertation, I will first review the prior literature on superconductivity and the working principles of the Josephson junction and SSPD devices, along with the EBL fabrication technique. One of the aims of this thesis is to optimize the nanofabrication processes, such as the EBL and pulsed laser deposition (PLD) techniques. Electron beam lithography is one of the best methods to produce nanometer- scale patterns due to its resolution without a mask and its focus capability. The optimization and characterization of the minimum achievable feature sizes as small as 100 nm have been produced using the EBL system. It was achieved by modified a SEM and developing with a lift-off process which uses a novel (polymethyl-methacrylate (PMMA)/methyl methacrylate (MMA)) bilayer e-

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beam resist. Also, a hybrid focussed ion beam (FIB) and reactive ion-etching (RIE) process has been used to fabricate complete devices.

During the three and half years of my Ph.D. study, I started two projects that each lasted for about half of the total the time. The objective of the first research project was to develop, design, and fabricate advanced superconducting Josephson junctions on high quality graphene samples for application in the most sensitive devices known for sensing magnetic flux, superconducting quantum interference devices (SQUIDs), as well as superconducting oscillators and superconducting mixers in the high frequency regime. Graphene was investigated as an alternate barrier material (due to its tuneable electronic behaviour) for Josephson junctions by an electron- transport study at ISEM, UoW, Australia. This work presents experiments on the electrical properties and morphology of graphene. It includes an overview of the basic physical concepts relevant to the experimental results presented. In the experimental section, I fabricate a device by electron beam lithography (EBL) for making electrode contacts for electrical transport measurements on graphite flakes. I found that electrons in mesoscopic graphite pieces are delocalized over nearly the whole graphite piece down to low temperatures. Experimental studies of the I-V characteristics of Nb/Ti-carbon-Ti/Nb junctions describe the device characteristics at various temperatures.

High temperature superconducting thin films (YBa2Cu3O7-x) are emerging in Superconducting Single Photon Detector (SSPD) research as a novel replacement for conventional and semiconductor detectors. The final part of thesis is devoted to designing a fabrication process for building Superconducting Single Photon Detector (SSPD) devices. This study compares the performance of the YBCO film layer with optimized thickness, which constitutes the heart of the SSPD, with the best combination of substrate and buffer layer.

The major hindrance to this is the degradation of the superconducting properties of YBa2Cu3O7-x (YBCO) thin film with reduction of its lateral and longitudinal dimensions (i.e. film thickness and width of the stripe).

Furthermore, the surface of the film should be smooth to enable fabrication of the SSPD device. I have noticed that by optimizing the thickness of the buffer layer, the thickness of the YBCO ultra-thin film can be effectively reduced without significant degradation of its functional properties. In order to improve the quality of YBCO thin films, I exploited various buffer layers (i.e.

SrTiO3 (STO), CeO2, and PrBa2Cu3O7 (PBCO)) with thickness of 30 ± 5 nm prior to the YBCO deposition. These combinations of high quality films will allow the design a new class of SSPDs that is capable of the high sensitivity required of a single-photon detector.

ACKNOWLEDGEMENTS

This research would not have been possible without the help and support of a great many people. I would like to thank my supervisor Professor Alexey V. Pan for allowing me to do part of my thesis work in his Thin Film Technology (TFT) group at ISEM. He has closely followed this work and influenced it with many ideas and recommendations. His academic support, as well as numerous discussions, has often led me to find new perspectives or deeper insight into the subject. Thank you for teaching me, listening to me, and letting me argue with you. His constant monitoring, encouragement, and guidance throughout the course of this thesis and the experience that he has given me from time to time shall carry me a long way in the journey of life on which I am about to embark.

It would be unforgivable to mention anyone before my Co-Supervisor, Professor Shi Xue Dou, and I take this opportunity to express my profound gratitude and deep regard for him for providing the opportunity and support to work in ISEM, UOW as a PhD candidate.

Next, Darren Attard is at the top of my thank you, so I also take this opportunity to express a deep sense of gratitude to him. Since the start of my research, he has always been well supplied with valuable information and helpful to me as well as to others, which helped me in completing this task through various stages. He taught me almost everything I know about nanofabrication, as well as how to use SEM, EBL and Raman techniques, enabling me to master those techniques, thanks to his hands-on demonstrations and assistance, even when he was not at ISEM. Throughout my research, Darren always has been the first person to go to for advice and peace of mind, especially when things went wrong. He has been a mentor to me.

Special thanks go to Olga and Sergey, from whom I also learned a lot about thin film fabrication and its related characterization techniques, and with whom I did my TFT work. Also, I would like to say thank you to A/Prof. Joseph Horvat (HPS) and another member of the senior technical staff, David Wexler, for XRD and TEM assistance.

Additionally, thanks are owed to my remaining colleagues in ISEM and the TFT research group for sharing their experimental tricks, creative insights, and general opinions. And to all the basement inhabitants, particularly Fargol and Sujeewa, thanks vi

for your support when I needed it and for being such good friends to me. And to Abolfazl (Kian) and Anne, thanks for sharing the ups and downs of research life. Living with people from almost ten different countries has definitely expanded my world view. I have enjoyed our talks together so much, our crazy lunch conversations. I cherish them for their friendship, the many conversations and discussions about (not just) Physics, the balanced environment they contributed to, and for making my days easier (and often funnier). I will miss you all.

Many, many thanks go to the people who work “behind the scenes” and have interfaced me with the “world”. In particular I would like to thank, Dr. Tania Silver, for her undertaking the challenge of proofreading this thesis and reading more than I could ever hope for. I would like to express my gratitude to the members of the Dissertation Committee. Roberta, Crystal, Narelle, and Joanne were indispensable for the timely completion of official academic requirements, purchases, and administrative steps.

Moreover, I gratefully extend my sincere regards to all the non-scientific staff for the work of the machine shop: Rob Morgan, Paul and Laboratory Facility Manager David Mathew at ISEM, University of Wollongong. I am obliged to all staff members of ISEM for the valuable information provided by them in their respective fields. I am grateful for their cooperation during the period of my PhD.

Lastly, I want to thank almighty, my Amma (Gandhimathi), brothers (Kumar and Guru), and friends for their constant encouragement, without which this thesis/degree award would not possible. Finally, the greatest debt of gratitude is owed to my late Appa Masilamani Kishtappan, my lovable wife (Vanaja), son (Govardhanan) and upcoming new comer (expecting princess!!;)) to whom I dedicate this thesis as well. They are the roots I came from and the place where I belong and will always return to.

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TABLE OF CONTENTS CERTIFICATION………………………………………………………………..…...i

DEDICATION…………………………………………………………………...…...ii

ABSTRACT……………………………………………………………………...... iii

ACKNOWLEDGEMENTS…………………………………………………………..vi

TABLE OF CONTENTS………………………………………………………...... viii

LIST OF FIGURES…………………………………………………………………....x

LIST OF TABLES……………………………………………………...………...... xvi

SYMBOLS AND ABBREVIATIONS……………………………………………..xvii

Chapter 1……………………………………………………………………...……….1

1 Introduction and Literature Review………………………………………..………..1

1.1 Introduction of Superconducting Devices and It’s Application .…………….....1 1.1.1 Importance of miniaturization in Nanosciences and its trend to Superconducting device Technology...... 2 1.2 Superconductivity- An Introduction …………………………………...... ….5 1.3 Important Critical Parameters in Superconductors………………………...…...5 1.4 Types of Superconductors……………………………………………………..8 1.5 Flux Pinning Mechanism in HTS...... ……………………...………………...... 9 1.6 High Temperature Superconductors...... …………………………...…...11 1.7 Crystal Structure of YBCO………………………………………...………….12 1.7.1 Physical and Superconducting Properties of YBCO………………...….13

1.8 Critical Current Density (Jc) –A Key Parameter...... ………………..14 1.8.1 Major Issues and Crucial Factors of Thin Film Deposition...... 15 1.9 Why YBCO Photodetectors………………………………………...………....21 1.10 Introduction-Brief overview of Single Photon Detectors………………...…..22 1.11 Superconducting Single Photon Detector (SSPD)…...……………………....24 1.11.1 Properties of SSPDs.....………………………………………………....24 1.11.2 Working principle of SSPDs (SGK Hotspot Model)………...………....27 1.12 Photodetection and Photoresoponse Mechanism in YBCO Superconductors.29 1.12.1 Excitation below and above the energy gap ...... 29

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1.12.2 Hot electron effect- 2 Temperature model ...... 30 1.12.3 Photoresponse Mechanism in YBCO Superconductors...... 31 1.12.4 Kinetic Inductance Photoresponse ...... 32 1.13 Why Graphene? A Brief History..…………………………………...…….....33 1.14 Graphene Introduction...... ……………………...………………….34 1.15 Chemistry of Graphene-Structural Property ………………………………....35 1.16 Graphene Crystalline structure-Bravis Lattice.………………………...…....37 1.17 Electronics Properties of Graphene...………………………………………...40 1.18 Graphene based Josephson junctions..……………...……………………...... 44 1.19 Josephson junction device principle...... 45 1.19.1 Andreev Reflection………………………………………………….…..47 1.19.2 Time Reversal Symmetry…………………...…………………………..49 2 Investigtion of Graphene for Superonductor (Nb)-Graphene-Superconductor (Nb) junctions………...... ……………....52 2.1 Methods of Graphene Fabrication...... 53 2.2 Graphene Fabrication by Mechanical Exfoliation Method...... 54 2.3 Graphene Indentification by Optical Microscopy...... 56 2.4 Graphene Thickness Measurement by AFM...... 58 2.5 Surface Characterization of graphene by SEM...... 60 2.6 High Resolution-Transmission Electron Microscopy Images...... 61 2.7 Raman Spectroscopy- Graphene Layer Characterization...... 63 2.8 Raman Mapping...... 67 2.9 Patterning electrodes on Graphene by EBL...... 69 2.10 Oversize Patterns in EBL...... 70 2.11 Mix and Match Exposure...... 71 2.12 Junction Configuration-Device Packaging...... 75 2.13 I-V characteristics of Nb/Ti-Carbon-Ti/Nb junction...... 76 2.14 Theoretical Model for Nb/Ti-2D Carbon-Ti/Nb junction...... 80 2.15 Results of Nb/Ti-Carbon-Ti/Nb junction...... 86 3 Optimization of YBCO Thin film growth by Pulsed Laser Deposition (PLD) for Photon Detectors Applications…………………….……………………………..89 3.1 XRD Characterization of YBCO film………………………………………....91 3.2 Frequency dependent depositions of YBCO film…………..…………………93 ix

3.2.1 YBCO film grown at 1 Hz frequency………………...………………....93 3.2.2 YBCO film grown at 5 Hz frequency………...…………………………95 3.3 Thickness dependence of Critical temperature of YBCO films grown at different frequencies………………………………………………………...... 96 3.4 Thickness dependence of Critical current density of YBCO films grown at different frequencies………………………………………………………….98 3.5 Comparison of YBCO film grown at Different Frequency………..…...…...101 3.6 Details of YBCO deposition with different buffer layers…………………...... ……..102 3.7 Effect of Substrates on properties of YBCO films...... 105 3.7.1 STO buffer layer……………………………………………………….106

3.7.2 CeO2 buffer layer……………………………………………………....108 3.7.3 PBCO buffer layer……………………………………………………..110 3.8 YBCO bridge fabrication by Wet-etching ……………………...... ….....111 3.9 Transport Measurement of Patterned YBCO film……………………..…...... 113 4 CONCLUSITONS AND RECOMMENDATIONS…………………………....116 REFERENCES…………………...………………………………………………....120

LIST OF FIGURES

Fig: 1.1 Magnetic phase diagram of type I (a) and type II (b) superconductors……...8

Fig: 1.2 The evolution of the transition temperature (Tc) subsequent to the discovery of superconductivity, adopted from [45]…………………..……...... 11

Fig: 1.3 a) YBCO crystal structure [46]; b) phase diagram of YBCO with oxygen content [47]...... 12

Fig: 1.4 Schematics of the photogenerated (SGK) hotspot (a,b) and of the current- assisted formation of a normal barrier (c,d) across an ultrathin nanowire kept

at a temperature much lower than its Tc. Then black arrows indicate the flow of the supercurrent biasing the nanowire [125]……………………………..28

Fig: 1.5 sp2 hybridisation: shaded (unshaded) denotes weak (strong) bonds...... 36

Fig: 1.6 a) Hexagonal lattice structure of graphene, i.e., the unit cell b), Reciprocal space lattice points (dots) and the hexagonal first Brillouin zone (shaded) [160]. Figure adapted from [148]……………………………...……………37

Fig: 1.7 a) Sublattice vectors; b) first Brillouin zone [160]……...……...... …………38

Fig: 1.8 The electronic Band structure of graphene, modified from [169]. Then inset shows the Fermi cones …………………………………………………...…40

Fig: 1.9 Schematic diagram of the Josephson junction, adapted from [175]……...... 45

Fig: 1.10 Typical I-V curve of a Josephson junction …...…………………………...46

Fig: 1.11 a) Andreev retro-reflection; B) Specular Andreev reflection, adapted from [180]……………………………………………………………………….47

Fig: 1.12 a) Schematic of a planar Josephson junction, b) I-V measurement set-up ..50

Fig: 2.1 Single and few-layer graphene fabrication (synthesis) methods [194]...... 54

Fig: 2.2 a) Freshly cleaved flakes on 3M-Scotch tape. b) Homogenous distribution of flakes in the same type of (two samples) tapes……………………………..55

Fig: 2.3 (a) and (b) Optical microscope images of thin graphene sheets (2 different samples)…………………………………………………………………….57

Fig: 2.4 (a) to (f) Optical microscope images of thin graphene sheets, scale bar is 7.5 μm.…………………………………………………………………………..57 Fig: 2.5 a) 3-D AFM image, b) optical microscope, c) thickness profile (7.4 nm) of FLG flakes by AFM.………………………...... 58

Fig: 2.6 a) 3-D AFM image, b) optical microscope, c) thickness profile (5.2 nm) of FLG flakes by AFM.…………………...... 59 Fig: 2.7 a) 3-D AFM image, b) optical microscope, c) thickness (1.31 nm) profile of graphene flakes…………………...... 59

Fig: 2.8 (a) and (b) SEM images of multi-layer\broken-edge graphite layers; (c) folded surface of thin sheets. ……………………………………………….60

Fig: 2.9 a) and b) HR-TEM images of FLG flake, revealing the single layer graphene thickness as ~ 0.34 nm. The inset to (b) shows the corresponding selected area electron diffraction pattern, indicating an approximate [001] (or [0001]) orientation for several stacks of graphene layers…………………...……...61

Fig: 2.9 (c) Rolled up graphene layers near sample edge. d) Region of graphene believed to be one layer thick……………………………………………...62

Fig: 2.9 (e) and (f) images is before (left) and after (right) long exposure to the electron beam, showing the effects of radiation damage on thin samples at 200 keV………………………………………………………………….....63

Fig: 2.10 Raman spectra from several sp2 nanocarbon and bulk carbon materials, mainly monolayer graphene and HOPG spectra [200]……..………...……..64

Fig: 2.11 Raman spectrum of thick graphite flake; inset is optical image…………...65

Fig: 2.12 Raman spectra of Few-layer graphene (Red) (inset photograph) on Si/SiO2 (blue) substrate with thickness of 7.4nm …………………………………...66

Fig: 2.13 Optical images before (left) and after (right) the Raman laser treatment of a flake.………………...……………………………………………………....67

Fig: 2.14 Raman mapping of multi-layer graphene or graphite: (a) optical image, identified in red in (b). Scale bar is 1μm ……………………………...…....67

Fig: 2.15 Raman spectra with corresponding Raman mappings (insets) of graphite (ash gray) (a) and SLG (green) (b)……………………………………….....68

Fig: 2.16 General EBL procedure flow diagram...... 69

Fig: 2.17 Oversize exposure: (a) GDSII pattern, optical image of pattern before (b) and after (c) lift-off process …...... 71

Fig: 2.18 Mix-Match exposure: (a) GDSII pattern (contacts), (b) after exposure...... 72

Fig: 2.19 Contacts on a graphene flake through mix-match EBL exposure (Scale bar is 38 µm). Inset shows AFM image of the device G1 made on 148 nm thick carbon flake with its geometrical dimensions...…..……………………...... 73

Fig: 2.20 Process of fabricating graphene device through e-beam lithography...…....74

Fig: 2.21 (a). G1 and G2 devices, (b) G3 and G4 devices………………...………....75

Fig: 2.22 SEM image of the device G1 made on 148 nm thick carbon flake (a) and schematic of the I–V curve measurement (b)...... 78

Fig: 2.23 I–V curves of Nb/Ti–C–Ti/Nb device (G1) at various temperatures from 1.8 to 7.5 K (a). Numerical derivatives, dV/dI (V), for the I–V curves measured at different temperatures T, K (thin grey lines). Curves for 3.0, 4.0, and 5.0 K are arbitrarily shifted in vertical direction for clarity. Thick black lines are averaged curves (see text for details) (b)…...... …....79

Fig: 2.24 Various processes involved in the electric transport in a Nb/Ti–C junction: in process 1, an electron moving in 2D C flake from left can be either Andreev-reflected as a hole moving in opposite direction or normally reflected (not shown) from the interface A between the regions G″ and G′; inside the area G′, it can be either Andreev-reflected at the Nb/Ti–C interface I creating the Cooper pair in Nb (process 2), or continue moving in the graphite sheet ballistically (process 3). If the electron energy E is low (E ≪ xii

U0), the electron bounces many times back and forth between the two barriers at x = xA and x = xB (process 4) before it is either Andreev-reflected from the Nb/Ti–C interface or it escapes the contact region into the open C sections G″……………...... 81

Fig: 2.25 Calculated differential resistance of the Nb/Ti–C–Ti/Nb junction. A broad minimum in the vicinity of zero bias is caused by the reflectionless tunneling

inside the contact region (xA < x < xB). An even broader minimum at the voltages | V| ≤ 2 (ΔNb + ΔG′ )/e occurs due to the AR in the S–I–G′ subjunction (where ΔG′ is the proximity induced energy gap in the C under

the metal). Additional tunneling-like feature occurs at | V| ∼ 2 (ΔNb + ΔG′ +

ΔG″)/e where ΔG″ is the proximity induced gap in the open carbon regions G″ right outside the contact area (cf. Fig.2.23)…………………………………84

Fig: 2.26 The Nb/Ti–C–Nb/Ti junction which is composed of two Nb/Ti–C block contacts. Each of the Nb/Ti–C contacts is represented in our model by the double barrier S–I–G′–I–G″ junction (cf. Fig.2.23 in the main text) (a). The normalized “reflectionless” conductance σ(V) of the S–N–I–N junction

computed within the BTK model with the broken line trajectory ( r1 = 0). The energy gap is Δ = 1 + i · 0.002, transmission coefficient through the barrier I

is t1 = 0.3, 0.8, and 0.95 (b). The same characteristic as before but for the 2 straight line electron trajectory when r1 = Z1(2i – Z1)/(4 + Z1 ) (c). AR in the asymmetric S–I–S′ junction where S and S′ are superconducting electrodes characterized by different energy gaps Δ′ = 0.8Δ (d)…………………….....85

Fig: 3.1 X-ray diffraction patterns of YBCO thin films with different thicknesses (growth at different frequencies) on STO single crystal…………..……...... 92

Fig: 3.2 Tc values of YBCO film deposited at 1 Hz with different thickness……...... 94

Fig: 3.3 SEM images of YBCO films with different thickness deposited at 1 Hz frequency. Scale bar is 1 µm………………...……………………………...94

Fig. 3.4 Tc values of YBCO films with different thicknesses deposited at 5 Hz frequency...... 95

Fig: 3.5 SEM images of YBCO films with different thicknesses deposited at 5 Hz frequency. Scale bar is 1 µm……………………...………………………...95

Fig: 3.6 Critical temperature (Tc) of pure YBCO films with different thicknesses, grown on STO. YBCO film thickness: 125 nm (dark blue), 65 nm (light sea green), 28 nm (pink), 30 nm (red), and 15 nm (black)…………..……….....97

Fig: 3.7 Thickness dependence of critical temperature for YBCO films grown on STO substrates at different frequencies…………..………………………...... 97

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Fig: 3.8 Field dependence of critical current density (Jc) at 10 K of pure YBCO films with different thicknesses, grown on STO. YBCO film thickness: 125 nm (pink), 65 nm (light sea green), 28 nm (blue), 20 nm (red), and 15 nm (black)………………………...…………………………………………...... 99

Fig: 3.9 Field dependence of critical current density (Jc) at 77 K of pure YBCO films with different thicknesses, grown on STO. YBCO film thickness: 125 nm (pink), 65 nm (light sea green), 28 nm (blue), 20 nm (red), and 15 nm (black)………………………...…………………………………………...... 99

Fig: 3.10 Thickness (of YBCO film) dependence of critical current density at 10 K for magnetic fields of zero (black), 1 T (red), 2 T (blue), and 3 T (green) (growth at different frequencies)...... …………………...………...... 100

Fig: 3.11 Thickness (of YBCO film) dependence of critical current density at 77 K for magnetic fields of 0.02 T (black) and 0.24 T (red) (growth at different frequencies)...... ………………………...………………………...... 100

Fig: 3.12 Critical temperature of YBCO film made at different frequencies…...…..101

Fig: 3.13 SEM images of 50 nm thick YBCO film grown at different frequencies. Scale bar is 1 µm………………..………………………………………....102

Fig: 3.14 Surface morphology of YBCO films grown on STO (a), LAO (b), MgO (c), YSZ (d) substrates. Scale bar for all images is 1 µm. White arrow marks pointout the ab-oriented grains in LAO and voids or plate-like defects in YSZ……………...... …...…...105

Fig: 3.15 Images of YBCO thin films grown on STO buffer layer deposited on STO (a), LAO (b), MgO (c), and YSZ (d) substrates. Scale bar for all images is 1 µm. White arrow marks pointed the droplets (different sizes)……...... 107

Fig: 3.16 Morphology of YBCO thin films grown on CeO2 buffer layer deposited on STO (a), LAO (b), MgO (c), and YSZ (d) substrates. Scale bar for all images is 1 µm. White arrows pointed at various defects...... 108

Fig: 3.17 SEM images of surface morphology of YBCO thin films on STO (a), LAO (b), MgO (c), and YSZ (d) substrates with PBCO buffer layer. Scale bar is 1 µm………………………………...…………………………………..….110

Fig. 3.18 Meander line Structure (active area – 30 μm) of YBCO films on STO substrate with PBCO buffer after patterning (EBL): by wet etching (b) and its magnified image (a)...... 112

Fig.3.19 Critical temperature of YBCO/PBCO buffer on STO substrate before and after patterning by EBL...... 113

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Fig. 3.20: Critical current (I-V curve) measurement of YBCO with PBCO buffer on STO substrate (After patterning) by transport method ………..…………..114

LIST OF TABLES

Table: 1.1: Crucial factors and their effects on high quality thin films ………….....15

Table: 1.2 Physical parameters of YBCO [56] (ab)-along the ab plane, (c) along the

c-axis …………………………………………………………..………...... 17

Table: 1.3 Physical parameters of common substrates and buffer layers [56]…….....18

Table: 1.4 Performance and efficiency parameters for different types of Single Photon Detectors………………………………………………………………...... 22

Table: 2.1 Summary of the device parameters...…………....……………………...... 76

Table: 3.1 Parameters of YBCO film deposition by PLD for frequency study…...... 93

Table: 3.2 Properties of YBCO films grown on STO substrate at 1 Hz frequency.....95

Table: 3.3 Properties of YBCO films grown on STO substrate at 5 Hz frequency.....96

Table: 3.4 Properties of YBCO films grown on STO substrate at different frequencies...... 98

Table: 3.5 Lattice misfit values for Substrate/Buffer materials and YBCO thinfilm.103

Table: 3.6 Tc and ΔTc values (K) of YBCO Films grown on different Substrates ....103

Table: 3.7 PLD parameters of (optimized) YBCO thin film deposition...... 104

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SYMBOLS AND ABBREVIATIONS a,b,c dimensions of orthorhombic unit cell of YBCO

AC Alternating Current

AFM Atomic Force Microscopy

Ag Silver

Al Aluminium or Aluminum

Au Gold

AR Andreev Reflection

B (applied) magnetic field

Bc thermodynamic critical field

Bc1 lower critical field

Bc2 upper critical field

BCS Bardeen, Cooper, Schrieffer theory

BLG Bi-Layer Graphene

CB-CPW Conductor-backed coplanar waveguide

CC Coated conductor

CCD Charge Coupled Device

CO2 carbon dioxide

CW Continuous wave d film thickness, sample dimensions d distance between layers

DC Direct current

DCR Dark Count Rate

DE Detection Efficiency

DFT Density Functional Theory

DOS density of states

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E Energy or Energy of a Single Photon

E-beam electron beam

EBL Electron beam lithography

EBSD Electron backscattered diffraction

EDS Energy dispersive spectroscopy eV electron volts f Frequency

FET Field effect transistor

FIB Focussed ion beam

FIR far-infrared

FLG Few Layer Graphene

FL Lorentz force on flux line or Lorenz force density on flux line lattice

Fp pinning force on flux line per unit length or pinning force density on Flux Line Lattice

FWHM Full Width as Half Maximum

HeNe helium-neon (laser)

Hg Mercury

HTS High temperature superconductor

HSQ hydrogen silsesquioxane

Hc Critical Magnetic field

Hi irreversibility field

IBAD Ion beam assisted deposition

IC integrated circuit

Ic Critical current

InGaAs Indium Gallium Arsenide

IPA Isopropyl alcohol

IcRn Characteristic voltage xviii

IR Infrared

I-V Current-voltage

Jc Critical current density; usually defined by a voltage criterion

KID Kinetic Inductance Detector

ℓ mean free path of electrons

LAO Lanthanide Alumina oxide

LNA Low Noise Amplifier

LTS Low-temperature superconductor

M effective mass of quasiparticles moving in c-direction m effective mass of quasiparticles moving within ab-plane

MAR Multiple Andreev Reflection

MCP Multi Channel Plate

MPMS Magnetic property measurement system

MIBK methyl isobutyl ketone

MR Magnetoresistance

NA Numerical Aperture ns density of superconducting electrons

Nb Niobium

NbN Niobium nitride

NbTiN Niobium titanium nitride

Nd: YAG neodymium-doped yttrium aluminium garnet (laser)

PCB Printed circuit board

Pb Lead

PBCO PrBa2Cu3O7

PLD Pulsed laser deposition

PMMA Poly methyl methacrylate (electron beam resist)

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PMT Photomultiplier Tube

PPMS Physical properties measurement system

QHE Quantum Hall Effect

QKD Quantum key distribution

RABiTS Rolling assisted biaxially textured substrate

REBCO (Rare earth) Ba2Cu3O7

RF Radio frequency

Rn Normal state resistance

R Radius of Sphere

RSJ Resistively shunted junction

RIE reactive ion etching

SEM Scanning Electron Microscopy

SGS Superconductor-Graphene- Superconductor

SIS Superconductor-Insulator-Superconductor

SMF Single Mode Fiber

SNS Superconductor-Normal- Superconductor

SNSPD Superconducting nanowire single-photon detector

SPAD Single-Photon Avalanche Diode

STEM Scanning transmission electron Microscopy

STJ Superconducting Tunnel Junction

STO SrTiO3

SQUID Superconducting quantum interference device

T temperature

Tc Critical temperature

TCSPC Time Correlated Single-Photon Counting

TEM Transmission Electron Microscopy

TES Transition Edge Sensor

U pinning potential

UHV Ultra High Vacuum

VAP Vortex-antivortex pair

Vcrit voltage criterion used to determine Jc

Vg Gap voltage

XRD X-ray diffraction

YBCO Yttrium barium copper oxide (YBa2Cu3O7-x)

YSZ Yttria-stabilised zirconia

2DEG Two Dimensional Electron Gas

χ Susceptibility

λ penetration depth (magnetic)

λab penetration depth describing the decay length of currents parallel to the ab-plane

λc penetration depth describing the decay length of currents parallel to the c-axis

ξ Coherence length (Ginzburg Landau)

μ0 permeability of vacuum

ξab coherence length parallel to the ab-plane

ξc coherence length parallel to the c-axis

φ angle between current direction and component of magnetic field parallel to the ab-plane

ψ superconducting order parameter k = λ /ξ; Ginzburg-Landau parameter

Г =1/ε > 1; anisotropy parameter

ε = 1/ Г < 1; anisotropy parameter

εθ angle dependent anisotropy parameter xxi

δ parameter describing the oxygen content in YBa2Cu3O7-δ

λ Wavelength n An integer number

ε Relative dielectric constant: material dependent

τe Electron-electron elastic scattering time (Drude model)

τe-e Electron-electron inelastic scattering time

τe-ph Electron-phonon inelastic scattering time

τph-e Phonon-electron inelastic scattering time: τph-e (T) = τe-ph(T)

τesc Phonon escape time (from metal into substrate)

Δτ SNSPD timing jitter for photon detection w width of bridge μm d thickness of bridge μm

Edis Energy dissipated

To Operating temperature

Te electron temperature K

Tph phonon or lattice temperature K t reduced temperature = T/Tc t time tct response time tdead detector dead time

Δ Superconducting energy gap

Js supercurrent density

Jb Bias current density (uniform): jb = Ib/Acs

Jd Device current density

Rhotspot Resistance of a Hotspot

Ad Device (nanowire meander) detection area

xxii

ηd Intrinsic detection efficiency

C heat capacity J/cm3K

3 Cph phonon or lattice specific heat capacity J/cm K

Ce Electron heat capacity per unit volume

Ib Bias current

Is supercurrent l Length of bridge μm

Physical Constant c Speed of light: 2.998 x 108 m/s h Planck’ constant: = 6.626 10-34 J.s

ћ Reduced Planck’s constant: = h/2π = 1.055x 10-34 J.s

-15 2 Ф0 Magnetic flux quantum: = 2.07 x 10 T.m

-23 -1 kB Boltzmann’s constant = 1.381 x 10 J.K

-31 me mass of an electron: 9.1 x 10 kg e Charge of an electron : 1.6x 10-19 C

-12 -3 -1 2 2 ε0 Permittivity of free space: 8.85x10 m kg s C

-6 -2 μo Permeability of free space: 1.26x10 m.kg.C nair Index of refraction of air: 1.00

1 G = 10-4 T = 2.07 x 10-15 Wb

Boiling point of liquid nitrogen = 77.4 K

Boiling point of liquid helium = 4.2 K

ALL units are in SI unless specifically stated otherwise. The approximate values quoted here were used in all calculations unless otherwise stated.

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CHAPTER 1

1 Introduction and Literature Review

1.1 Introduction of Superconducting Devices and it’s Applications

One of the last century’s greatest discoveries in physics was superconductivity. Superconductivity (SC) has been challenging scientists to find a clear explanation of the basic theory, ever since superconductivity was discovered in 1911. The centennial of the discovery of superconductivity took place only five years ago. Since its discovery superconductivity has been applied in two completely different fields which are high power electrical and superconducting electronic applications. On the superconducting electronics applications, a completely different length scale active and passive superconducting devices are fabricated. Active ultra-sensitive SQUID magnetometers (two-and three-terminal devices, flux transformers) and NMR sensors, and passive microwave antennas and high-frequency (RF) cavities, filters are currently promising applications of superconductivity on a small length scale. These electronic measuring techniques provide us with the possibility to increase the sensitivity in many cases by orders of magnitude compared to techniques based on normal conducting circuits. In this thesis, superconductors will mostly be mentioned as being either low-Tc superconductors (LTS) or high-Tc superconductors (HTS).

Superconducting films (LTS and HTS) are the backbone of today’s and future superconducting electronic applications which range from material characterization, particle detectors, ultralow loss microwave components, medical imaging, and potentially scalable quantum computers, etc,. The majority of prospected electronic, power generation and distribution applications are made by HTS. Mainly, it has been concentrated on the YBCO/2G (Second Generation), which is the most popular among HTS due to the combination of unique characteristics such as convenient crystal structures (good scalability, smooth integration), high critical current density, ultra-low power consumption, absence of dissipation (which improves efficiency), coherence length with state-of the- art electronics, and relatively low level of 1/f noise [1] conditions available in cryogenic environments have led to the demonstration of various types of superconducting devices, for example detectors with unmatched performance. The other main

advantage with this material is the very low surface resistance, which are orders of magnitude lower than that of normal metals in the microwave frequency region. This makes these materials excellent candidates for microelectronics device applications [2, 3]. Microelectronics devices make use of HTS for detectors which measured magnetic flux and mm-wave radiation. Due to limited dimensions in size of the electronic devices are having small currents and current densities which are similar to those in large machines. In thin film form, HTS (YBCO superconductors) components can be considerably cut down in size and have adequate critical current densities. It seems reasonable to suggest that the use of HTS materials (YBCO superconductors) in applications involving electrical properties and magnetic field, implies the possibility of higher packing density on a circuit board or chip. Thus the possible use of HTS as passive circuit’s elements can confer a double advantage. For example, in SQUIDs with advantageous parameters like high critical current density, comparably low level of flux noise, and low level of inductance [4]. All of the above applications require the production of high critical current density superconducting films of HTS material. Such films must fulfil high requirements regarding material and electrical properties, (explained in below sections (1.8.1) with issues related to a proper choice of substrates, buffer layers for epitaxial growth), which are most helpful to give insight into the fundamental mechanisms governing superconductors.

1. 1. 1 Importance of miniaturization in Nanosciences and its trend to Superconducting Device Technology

The past few decades have seen an excellent growth in the microelectronics industry (starts at the end of the vacuum tube era [5]) and its associated technologies, such as bipolar junction transistor (BJT) [6], planar junction technology [7], 2-D monolithic integrated circuit (IC) [8]. According to Moore’s law, IC dimensions have been shrinking dramatically with even gate length down to 9 nm [9], which increasing the performance of devices. This revolution is going to continue for the foreseeable future and will require continued advances in fabrication technology, and they are becoming very established, however, fabrication issues are still in the evolving stage. This is because the nanofabrication researchers are still working on to miniaturization in size

(sub-nm range) by a controllable and reliable process in which new technological approaches are incorporated with existing technologies. The processing steps and materials involved in semiconductor or superconducting device fabrications are compiled in [10], [11] and Optical lithography [12] is the most mature of fabrication technologies, can also achieve sub 100 nm resolution. However, it has become impossible to extend optical lithography further into the deep nanoscale. For this purpose, several lithographic approaches have been used to achieve nanoscale fabrication of features, including electron beam lithography [12-14] (EBL), ion beam lithography (IBL), extreme ultraviolet lithography [12] (EUVL), nano-imprint lithography [12] (NIL), scanning probe lithography [12] (SPL), x-ray lithography [12] (XRL), and electron-beam-induced deposition (EBID). The overall goal is the practical and widespread use of devices and circuits based on quantum superconductivity. It will require a technology capable of providing sizeable quantities of these devices that are rugged and stable, and whose characteristics can be controlled and reproduced during fabrication. Superconductivity as a macroscopic quantum phenomenon offers a range of quantum effects such as tunneling, interference, phase transition and photoresponse that potentially benefit electronic and optoelectronic devices. To achieve this development, detector requires ultra-fast and ultra-sensitive (low noise, low power dissipation, etc.) digital read-out electronic devices such as superconducting single-flux-quantum (SFQ) logical devices, based on resistively shunted Josephson tunnel junctions [4], and imaging detectors such as Superconducting Single Photon Detector (SSPD) [15].

The superconducting state is sensitive to incident radiation at optical wavelengths [16], and the advent of thin film superconductors, microfabrication techniques, and laser sources allowed the first superconducting radiation detectors (e.g. infra-red detectors), bolometers to be demonstrated, as referenced in [17]. The new YBCO sensors could be capable of quick photoresponse in ultrafast photon detectors that would be of more practical use in communications and supercomputing systems, as well as in emerging applications in remote sensing and astronomical studies. Also, manipulation of single photon generation and detection technologies are important for several areas in quantum computing, where photons are used as quantum bits [18],

and quantum key distribution [19], where photons are used to securely transfer information over long distances.

These standard semiconductor microelectronic fabrication techniques have been utilized to produce batch quantities of superconducting quantum electronic devices and circuits. For instance, superconducting electronic technology enables the generation and detection of electromagnetic radiation at terahertz (THz) frequencies [20], a difficult frequency range above the reach of semiconductor devices and below that of optical devices. These main technological features which are needed are the same as those of semiconducting microelectronics, even though our particular materials and procedures are different in many cases. Consequently, I have been able to draw superconducting electronic circuits and devices with heavy reliance on semiconductor microelectronic fabrication technology.

In analogy with semiconducting microelectronic fabrication, the desired superconducting circuit elements are created by a sequence of manipulations of a thin- film parent material consisting of layers of superconducting and normal metals, and use bilayer, proximity-effect structures as the active circuit elements, which modify the electronic properties of the device on a microscopic scale. In developing this technology, I have designed the methods to be compatible, as much as possible, with the existing technology of semiconducting microelectronics, in order to take advantage of the highly developed state of that technology. In this work, I felt it was important to consider all the aspects of the complete steps in making superconducting microcircuits from design to packaging.

Before making any superconducting device (pattern/circuit design), one should understand that the phenomena of superconductivity or the mechanism of superconductivity, especially in high and low Tc superconducting thin films, is a debatable topic. This is because superconductivity theory can predict which materials may be superconducting. The theoretical understanding of superconductivity theory can be used for advanced research into further techniques that can improve the superconducting properties, which can lead to the use of these materials in various applications. Here, I describe the important basic properties and effects of superconductivity, which can be used to explain the fundamental physics behind a device’s performance of such as SSPD’s photoresponse mechanisms and electron 4

tunnelling in Josephson junctions. Individual characteristics of the phenomena of materials and devices will be discussed in other chapters.

1.2 Superconductivity- An Introduction

Soon after discovery of liquid helium by Heike Kamerlingh Onnes, he revealed that mercury metal abruptly lost its electrical resistance, which remained unmeasurable at all attainable temperatures below 4.15 K. He thus measured the first temperature dependence of resistivity (superconducting transition) curve in mercury, as presented in [21]. This phenomenon is now known as superconductivity, which means that the material undergoes a sharp phase transition between the resistive (above Tc) and superconducting (under Tc) states at this particular temperature is called the critical temperature Tc. Also, Onnes observed that above a certain current density, the mercury sample returned to the normal state from its superconducting state even though it might still be below its transition temperature. This threshold value was called the critical current density (Jc) [21]. Low temperature is not the only condition for superconductivity to occur, as magnetic fields higher than the critical magnetic field of the material also can affect the superconductivity. Magnetic fields above a certain field strength also destroyed the threshold value was denoted as the critical magnetic field (Hc) in Tesla (T), and it is different for each material [22]. The critical magnetic field (Hc) is also dependent on the temperature. It was found empirically that Hc(T) is quite well approximated by a parabolic law. The relationship between the critical magnetic field and the transition temperature of superconductors is given by 2 Hc(T) ≈ Hc(0)[1-t ] (1.1) where t = T/Tc is the reduced temperature.

1.3 Important Critical Parameters in Superconductors

From the application point of view, Superconductors are defined by three basic critical parameters: 1. Critical temperature (Tc) in Kelvin (K), 2. Critical magnetic -2 field (Hc) in Tesla, 3. Critical current density (Jc) in (A·m ). These parameters are often used to explain the superconductivity and its related effects in bulk and thin film

superconductors. The higher the above three values, the better will be the practical applications. The critical current depends on the shape (size and geometry) and material quality of the superconductor. These shape and material parameters are normally used to optimize the critical current density (Jc) value. So, these three critical parameters depend on each other, so we have the three critical parameters as Tc(H,J), Hc(T,J), and

Jc(T,H). Ref. [23] shows a diagram of these interdependent critical parameters of a superconductor and its critical surface between the superconducting and normal states. Superconductivity exists within the space covered under the dome (3D surface). This surface represents the maximum current density that a superconductor can carry as a function of temperature and magnetic field, with zero resistivity [23]. Perfect conductivity can be demonstrated by applying an external magnetic field to a superconducting ring and cooling it below the transition temperature. If the magnetic field is removed, induced current around superconducting ring flows continuously and produces its own magnetic flux for a huge number of years.

The first successful phenomenological description of superconductivity was provided by Walter Meissner and Robert Ochsenfeld [24], [25]. They observed that a superconductor was not only a perfect conductor (no electrical resistance), but also showed magnetic flux quantization and a perfect diamagnetism or Meissner effect: In the normal state, the magnetic field would pass through the material (T>Tc, B≠ 0), whereas in a superconductor (T

The magnetization M is defined as the dipole moment per unit volume. The magnetization of a non-equilibrium superconductor is not a spatially uniform quantity, as it is for single-domain ferromagnetic materials. The internal field B = H + 4πM [28]. This superconductivity phenomenon explained by the two-fluid model [29], in which superconducting electrons are different from normal electrons, and the two fluids play their different roles independently in a superconductor. Again “London Theory” [26] is used to describe this Meissner state in theoretically by using Maxwell’s equations, which is based on the following two London equations:

휕 E = (휆2휇 J ) (1.2) 휕푡 L 0 푠 2 퐵 = −curl (휆L휇oJ푠) (1.3)

푚 where 휆L = √ 2 (1.4) 휇0푛푠푒 is the London penetration depth [30] , m the effective electron mass, ns the density of superelectrons, and Js the supercurrent density. Typical values of λL range from 50 to 500 nm. The empirical temperature dependence of λ(T) can be approximated by 1 휆(푇) ≈ 휆(0)[1 − 푡4]− ⁄2 (1.5) Then the Ginzburg-Landau (G-L) theory [31] was extended the London macroscopic theory with a complex wavefunction, which is based on Landau’s phase-transition quantum mechanical theory. This theory introduced the idea of an order parameter, 푖휓 휓 = |휓|푒 , to describe the superconducting condensate, which is proportional to ns 2 (푛푠 = |휓(푥)| ), the local density of superconducting electrons in the London model, with ψ as a superconducting electron wavefunction. It was noted that the actual superconducting penetration depth (λ) was larger than the London penetration depth

(λL), which was observed experimentally. This depth discrepancy was solved by A. B.

Pippard, who introduced the concept of the coherence length (ξ0) by proposing a nonlocal generalization of the London theory in 1953. Half a century later only, two satisfactory microscopic theories of superconductivity phenomena were very well developed, one by three American physicists: J. Bardeen, L. N. Cooper and J. R. Schrieffer (BCS) and another by a Soviet scientist, Alexei

Abrikosov. The first theory of superconductivity in low Tc superconductors was expressed in terms of the electrons which carry charge in a superconductor. These will condense into pairs called “Cooper pairs” [32] at low temperature through an

attractive coupling with another electron with opposite spin and momentum via a phonon intermediary. The size of such a pair corresponds to the coherence length (ξ). In the superconducting state and in the absence of current flow, a Cooper pair is a system with zero momentum and zero spin like a boson. Hence, the total momentum of the pair is zero, so that it moves without scattering in the lattice, which leads to zero resistance. The microscopic BCS theory [33] provided a satisfactory justification of G-L theory, critical temperature limitation and explained many other properties of superconductors [34]. It could not explain, however experimental observations in high

Tc superconductors (HTS).

1.4 Types of Superconductors

In 1952, Alexei Abrikosov showed that the existence of two groups of superconductors could be distinguished [35] by a quasi-microscopic (flux vortex) theory of magnetization of alloys. The ratio κ = λ/ξ, known as the Ginzburg-Landau parameter, and is approximately temperature independent [36]. From this κ value, we can define the types of superconductors. In Type I (shown in Fig 1.1(a)) superconductors, those with 0 <κ< 1/√2, superconductivity exists only up to the breakdown field Hc(T), while in Type II, with κ> 1/√2, the division of the superconductor into superconducting and normal regions is energetically more beneficial. The type II superconductor (shown in Fig 1.1(b)) has two critical external magnetic fields, Hc1 and Hc2. If applied magnetic field is lower than critical field Hc1(T), it shows perfect diamagnetism, i.e. the Meissner effect, in Type II superconductors.

Fig: 1.1 Magnetic phase diagram of type I (a) and type II (b) superconductors. 8

Above Hc1, a type II superconductor does not show the Meissner effect. In this state, the material does not go directly into its normal state, but instead, the magnetic field is allowed to partially penetrate the superconductor. So, the magnetic flux (lines or vortices) can penetrate inside the superconductor in the form of filamentary structures, and current will circulate around these regions. Such circulating currents are called vortices, which arranged to form a hexagonal lattice in the region of between lower

(Hc1(T)) and upper (Hc2(T)) critical applied magnetic field. This state is called the mixed state or Shubnikov phase from the name of the first scientist to work on type-II superconductors, which comprise some metallic compounds and alloys, such as lead and bismuth alloys, and the entire HTS group. As the critical magnetic field or temperature is approached, the normal regions become more and more tightly packed, until the entire material is in the normal state.

Generally, most of the type II superconductors are suitable for all potential applications, due to their flux pinning properties and their higher Tc and Hc2, as well as their ability to carry high current (in the mixed state). Here, I have used both HTS (YBCO) and LTS (Nb) for making electronic devices, by using YBCO and Nb- Carbon (graphene layer) materials.

1.5 Flux Pinning Mechanism in HTS It is the structure of the quantised flux lines that create the flux pinning interaction. The superconducting order parameter,휓, has a zero point at the centre (where the superconducting electron density ns falls to zero) of the flux line with a sharp variation within the range (since the vortices have a normal core of radius) of the coherence length, ξ. In a vortex, the magnetic flux is concentrated within the range of the penetration depth, λ, from the centre. Hence, when the flux line moves to a region where the superconducting properties change spatially, it feels a change in the free energy, which results in the flux pinning interaction [37]. There are two types of pinning mechanisms available in vortex pinning, electrodynamic (magnetic) pinning and core pinning [38]. The first one is due to the perturbation of the supercurrents around vortices and of their local magnetic fields by the defects (natural or artificial). At point defects, core pinning is the origin of the attractive interaction between vortices and defects.

The presence of the Abrikosov lattice in HTS results in many new concepts that is not present in low temperature superconductors. The flux lines in YBCO are influenced by strong thermal and quantum fluctuations, resulting in several distinctive features, such as a vortex liquid phase below Hc2 and a vortex glass phase separated from the vortex liquid phase by the irreversibility field. The magnetic flux lines enter a type II superconductor in the form of tubular structures called flux lines or vortices, which consist of an integral number of a quantum known as a fluxon. Flux in theory is quantised as h/e, but measurement gives h/2e. Each fluxon or vortex containing a single flux quantum [36] is given by ℎ 휙 = = 2.075 × 10−15푊푏 (1.6) 0 2푒 The structure of a fluxon consists of a short-range (ξ) normal core surrounded by a long-range (λ) vortex of supercurrent. An applied current is passed through the superconductor in this mixed state, each vortex will experience a Lorentz force acting on the vortices. The flux lines start to move (transverse to the current) according to the action of the Lorentz force at right angles to both the direction of the flux penetration and the transport current which is given by

퐹⃗퐿 = 퐽⃗ × 퐵⃗⃗ (fL = J × 휙0) (1.7)

Where FL is the Lorentz force per unit volume on a flux bundle, fL is the Lorentz force per unit length of a single vortex 휙0, J is the current density, and B is the average magnetic field penetrating the superconductor.

There are certain sorts of defects or impurities in superconductors, such as dislocations, walls, grain boundaries, voids, etc., on which the magnetic flux gets trapped and which act as pinning centres for the vortices, keeping them from moving. The fluxoids (flux lines) then remain stationary, as long as there is present a flux pinning force at least equal to the Lorentz force FL acting to move the fluxoids across the sample. If the Lorentz force on the fluxoid is greater than the pinning force (Fp), the force resisting the fluxoid motion, the fluxoid begin to move across the sample. The energy dissipated by drag or viscous forces opposing this motion is supplied by the transport current. Hence, the movement of fluxoids causes resistivity (there is a voltage drop along the specimen). This fluxoid or vortex motion (without pinning) is called flux flow, and Jc is limited by the flux pinning in conductors, it is the source of 10

the resistance observed at currents greater than the critical current. Therefore, the better the pinning is, the higher the critical current density Jc will be.

1.6 High Temperature Superconductors

Even the BCS theory predicted that the Tc of superconductors could never be higher than 30 K. However, considerable work was devoted to finding superconductors with higher Tc values at the end of the 1980s. In 1987, Chu et al [39] synthesized a layered yttrium-barium-copper-oxide (YBCO) material (cuprate ceramic, or more exactly YBa2Cu3O7-x,where x is ~0.1) with transition temperature of

93 K. YBa2Cu3O7-x was the first material that shows a critical temperature above the boiling point of liquid nitrogen (77 K) and it is the most well-known example of high-

Tc superconductors (type-II superconductors) [25]. Indeed, the parent compounds of superconducting cuprates are antiferromagnetic Mott insulators.

Fig. 1.2 depicts the development of high Tc superconducting material between the years 1900 and 2007. In 2001, higher Tc values were discovered in the conventional superconductor MgB2 at 39 K [40], as well as in that same families of compounds with different variations [41-43]. The highest Tc ever reported was around 164 K for HgBaCaCuO compounds while under the pressure [44] in 1995. Researchers are still trying to discover superconductors with higher transition temperatures to realize room temperature superconductivity.

Fig: 1.2 The evolution of the transition temperature (Tc) subsequent to the discovery of superconductivity, adopted from [45]. 11

1.7 Crystal Structure of YBCO

Basically, all cuprate superconductors such as YBCO have a common crystal type known as the perovskite structure. The perovskites are minerals whose chemical formula is ABX3 or AB2X3.

Fig:1.3 a) YBCO crystal structure [46]; b): phase diagram of YBCO with oxygen content [47].

The single unit cell of YBCO is shown in Fig. 1.3(a) with the positions of the CuO planes. The reason for the HTSC behaviour in these compounds is believed to be that the superconductivity inherent within their CuO planes has 2- dimensional characteristics for carrier transport and not fully describable ─ not incredible for such a complicated structure.

Y-Ba-Cu-O structure is described as a system consisting of four different elements, in which three of them are metals. One can obtain superconducting and non- superconducting phases from different stoichiometry of these elements in this Y-Ba- Cu-O system. Hereafter in this thesis, I will only discuss the Y-Ba-Cu-O system of 1-

2-3 stoichiometry, i.e. YBa2Cu3O7-x (YBCO). For a true perovskite structure, however, the number of oxygen atoms should be 9, but the x value of YBa2Cu3Ox can achieve only 7. Thus, YBa2Cu3Ox is called an oxygen deficient or distorted perovskite structure.

The 1-2-3 high Tc superconductors form as planes of copper and oxygen atoms

(CuO2), which are sandwiched between layers containing the other elements such as Bi, O, Y, and Ba. The resulting YBCO unit cell is stacked in the following sequence:

CuO-BaO-CuO2-Y-CuO2-BaO-CuO-. The CuO2 plane has a square lattice formed by 12

copper ions bound to each other through oxygen ions. These layers are important in determining the electrical properties of 1-2-3 superconductors. The CuO and BaO chain layers provide the charge carriers in the CuO2 planes, so these layers are called charge reservoirs [48]. The electrical conductivity is higher in the ab-plane of YBCO compared with along the c-axis, due to one of the most important characteristics in high-temperature superconductors, the planar anisotropy.

1. 7. 1 Physical and Superconducting Properties of YBCO

As shown in Figure 1.3(a), the in-plane (ab-) dimensions and the c-axis dimensions do not have the same value, which leads to a strong anisotropy that is reflected in all the superconducting parameters (for example, λ, ξ) of HTSC (YBCO) superconductors. The same is true for resistivity measurements along the different crystal directions, with resistivity for c vs. ab in YBCO varying by about 5 to 7.

The crystal structure and lattice constants change with the oxygen deficiency (x), as well as the Tc, as shown in Fig. 1.3(b). The oxygen content (x) can be varied between 6 and 7 by adjusting the temperature and pressure [49] while doing film deposition in a PLD chamber. It also mainly depends on the both Cu2+ and Cu3+ being present in the YBCO structure. These ions are the “hole” reservoirs. Eventually, researchers found that the superconductivity that occurs in YBCO is due to Cooper pairs of holes, not Cooper pairs of electrons [50]. Due to an increased content of O2- in YBCO due to Cu3+, with relative proportion depending on the term 7-x in the chemical formula of

YBa2Cu3O7-x, there is a slight deficiency of oxygen. If the oxygen content (x) drops below 6.4, however, the superconductivity will disappear (although others have attained a very low Tc even at x < 6.4), and the material has a tetragonal structure. Whereas in the case of x = 0 to 0.5, YBCO has an orthorhombic room temperature phase with the lattice parameters a = 3.82 A˚, b = 3.89 A˚, and c = 11.68 A˚ [51] along the (100), (010), and (001) directions. Fig. 1.3(b) shows the phase diagram of the YBCO system as a function of oxygen content (x) with the variation of Tc. The oxygen content in YBCO determines the crystal structure and the hole concentration in the CuO2 planes, but this is stable only at temperatures below 500˚C. So, the highest Tc was obtained by the exact composition of YBa2Cu3O6.9, i.e. x = 0.1 [25]. To develope high Tc electronics, many approaches have been tried on YBCO [4, 52].

1.8 Critical current density (Jc) - A key parameter

One of the key parameters of a superconducting film is its critical current density (Jc). Achieving high critical current densities will bring us one step closer to high quality devices made from YBCO superconducting films. So, it is very important to understand the factors that adversely affect the Jc. The grain boundary induced reduction of Jc in high Tc cuprates is related to several mechanisms [53] relevant to the following factors: the microstructure of the thin film and weak links between grains [54], deviation from bulk stoichiometry in the vicinity of grain boundaries and their stress fields [55], the combined effects of the faceted microstructure of grain boundaries, and electric-charge inhomogeneities [53]. Superconducting thin films should be well textured to minimize weak links at high-angle grain boundaries, which can be used to carry high Jc [56].

Transport critical current (Ic) depends on the size of the superconductor, but Jc is a size independent and structure (microstructure) dependent characteristic. The microstructure provides numerous defects which can act as pinning centers. Also, while doing deposition of superconducting thin films at higher laser frequency, a high numbers of pinning centers are produced. Hence, this denser network of pins increases the pinning force (Fp calculated as Jc × Ba) and Jc of superconductors in the high applied magnetic field region.

Even though there are other critical parameters, such as magnetic field, temperature, and current, in thin film samples, the main important parameter is the critical current density (Jc), which is calculated from the critical current, Ic, divided by the cross- section of the specimen. The relationship between the thickness and the critical current density is very important for achieving higher device efficiency in many device applications. The thickness dependence of critical current density is still a controversial problem, and several explanations have been recently published [11-14].

Normally, Jc is considerably decreased with increasing thickness of the film to several micrometres. Knowing the surface characteristics is one of the key points in studying the pinning mechanism of YBCO films. Pure YBCO (as well as doped YBCO) films do not have a smooth surface, rather, it contains pores and precipitates (a-axis grains and large particles). Morphology characterization (by SEM) helps us to select the most effective area to draw the nanowires (meander lines) for single photon detector

fabrication. In order to achieve the standards requirements of detector technology and minimize deviation of the device characteristics, the thin film should have high superconducting properties with smooth surfaces on structurally “perfect” layers. The fundamental requirements for such systems are explained in following section.

1. 8. 1 Major issues and crucial factors for YBCO thin film deposition Being copper oxides, these YBCO materials are very poor conductors of electricity at room temperature, but below Tc (< 92 K) it allows great developments on superconductivity and superconducting electronics research to take place worldwide.

It can be prepared as single crystals, bulk polycrystalline material, or thin films on compatible substrates. Thin film superconductors usually have superior properties compared to the bulk materials, which have some practical limitations such as being too small and not flexible enough to use in superconducting magnets.

Table.1.1 Crucial factors and their effects on high quality thin films. Desired factors (cause) Effects Good lattice match Maximize crystalline perfection Provide film uniformity and enable Atomically smooth surface epitaxial growth Perfect flatness Provide mask definition Prevent excessive outgassing and improve No porosity film microstructure Mechanical strength Prevent film stress Thermal coefficient of expansion equal to Minimize film stress that of deposited film High thermal conductivity Prevent heating of circuit components Thermal stability Permit heating during processing Prevent damage and cracking during Resistance to thermal shock processing Chemical stability Permit unlimited use of process reagents Superconducting properties Permit high energy applications Low cost Permit commercial application

Even though significant research progress has been carried out on thin film PLD deposition of epitaxial metal oxides, there are still some fundamental issues and crucial factors which are yet to be dealt with. The foremost challenge is to reduce the deposition temperature for depositing epitaxial films while barring some chemical processes. Other factors involve the production of a precise composition with correct oxygen content and stable phases, good structure and morphology of the films, high degree of desired orientation, and issues regarding the nucleation and growth of the films. Major blockages to commercial success are achieving deposition over larger area substrates and finding low cost substrates that are compatible with the particular device. The interdependence of several parameters, for example, processing temperature and epitaxy, poses serious questions about the choice of optimum conditions, although there have been attempts to justify some of them for industry-scale production of thin films [57-59]. In this section, these problems and the ongoing efforts to deal with them are briefly elucidated. In order to avoid negative effects on high quality thin films, the above mentioned desired factors and their effects (listed in Table 1.1) will be considered before the discussion of deposition. Table 1.1 provides information on the most suitable list of desired properties for ideal substrates. Importance of suitable substrates and buffer layers for high quality YBCO thin films Suitable substrates are essential for achieving high-quality (homogenous flat surface with high superconducting properties) YBCO thin films for microminiaturized read-out electronic components. Such components must have the following fundamental requirements: small size, low surface resistance, high thermal, mechanical, and aging stability, low losses at high-frequency, and compatibility with the low-cost substrate that is used. These requirements can be fulfilled to a large extent by thin films of suitable materials. Hence, there is no ideal substrate available for high-Tc superconducting materials. Substrate suitability is mainly determined by matching of the crystal lattice (parameters) with the YBCO film, and the substrate should be single crystalline, with atomic smoothness over large distances (at least 10-20 mm size for research scale) and without inhomogeneity for epitaxial growth [60]. The better the matching of all these parameters, the more likely that high quality epitaxial growth will occur. To 16

preserve the lattice matching and also to avoid loss of adhesion or film cracking during thermal cycling, the thermal expansion coefficients of the substrate and the YBCO must be comparable over a wide temperature range. In addition to this, regardless of the specific film growth method used, the substrate must be unreactive (no chemical reactions) under the oxygen-rich ambient conditions required for growth and processing. Chemical reactions will result in a deviation from the desired phase growth [61]. In addition, adhesion of the YBCO thin films to a substrate is strongly dependent on the chemical nature, cleanliness, and microscopic topography of the substrate surface. Table 1.2 summarizes the physical parameters of YBCO film. Several other important electrical and thermal parameters in the selection of substrates and buffer layers are also given in Table 1.3. These data are from different manufacturers. YBCO superconducting film quality will mainly depend on both the underlying substrate and the buffer layer material properties. Table 1.2: Physical parameters of YBCO [56]. (ab)-along the ab-plane, (c) along the c-axis Physical Parameters YBCO Value

Critical Temperature (Tc) 92 K Crystal Lattice Parameters a= 3.82 A˚, b= 3.89 A˚, c/3 = 3.89 A˚ Coherence Length 15 A˚(ab), ~3-5 A˚(c) Penetration Depth 1400 A˚ (c), ~ 5×1400A˚(ab) Thermal Conductivity 3.2×10-2 Wcm-1K-1 (at 300 K) Specific Heat Capacity 0.39 J/gK Solid Absorption Coefficient (at 248 nm) 2.5×105 cm-1 Reflectivity (at 248 nm) 0.11

For analysis purposes, I took four different insulating, semi-metallic substrates, STO

[62], [63], LaAlO3 (LAO) [64], MgO [63], and Yttrium Stabilized Zirconia (YSZ) [65], whose physical properties make them suitable candidates for device fabrication and the best for epitaxial growth and excellent superconducting properties in the YBCO thin films to be deposited on them. Generally, a substrate should have high thermal conductivity, low microwave loss, and good acoustic matching with YBCO for device applications [66]. Here, I briefly introduce each of the substrates and buffer 17

materials that I used for YBCO film deposition with its physical and deposition parameters.

SrTiO3 (STO) is one of the most widely used substrates for growing high Tc superconducting thin films. STO possesses a perovskite structure, smooth, flat surface, high chemical stability and is a good lattice match with YBCO. STO has proved to be a reliable substrate for consistently producing high quality films, and its lattice constant is only about 2 % too large at 780˚C. Nevertheless, grain boundaries will form in the thin film due to the small thermal expansion mismatch between the substrate (single crystal) and thin film, and the large dielectric constant and poor high frequency properties of STO make it unacceptable for microwave device applications. Furthermore, this substrate is quite expensive. Due to the problems with STO mentioned above, MgO has received great attention, primarily due to its modest dielectric properties suitable for use in high frequency devices. It is one of the cheapest substrates and has good thermal expansion when matched with YBCO. The physical properties of MgO substrates are given in detail in Table 1.3.

Table 1.3: Physical parameters of common substrates and buffer layers [56].

Substrate STO LAO MgO YSZ CeO2 PBCO Al2O3

Crystal structure Cubic c/Rhom Cubic Cubic Cubic Orth. Trig.

Lattice mismatch (%) 2 3 9 5.8 4.9 1.8 11.2

Lattice parameter (Å) 3.902 3.8/5.3 4.213 3.73 5.411 3.88 4.73

Dielectric constant (ε) 277 24.5 9.65 25 17 - 9.34

Tan δ 6×10-2 3×10-5 5×10-4 8×10-3 5×10-4 3×10-5

Thermal Expansion 9 9.2 12.8 8.8 10 8.5 8.4 Coeff. (10-6C-1) Melting Point (˚C) 2080 2100 2825 2550 2900 2050

MgO (100) substrate has a rather big lattice mismatch with the YBCO lattice

(~9%), so the growth of epitaxial YBCO films with high Jc is problematic when compared to the optimum values obtained on perovskite substrates. However, under proper deposition condition, the high quality epitaxial YBCO films can be

successfully deposited on MgO. The disadvantage of MgO substrate is very sensitive to moisture (water vapour), and the poor reproducibility of the surface quality makes things still worse. The advantage of a LAO substrate is its small lattice mismatch, small thermal mismatch, and good chemical compatibility with YBCO. It is also a suitable material for high frequency application due to its low dielectric constant. LAO has a phase transition within the film deposition regime (at 800K), but the transition is second order [67]. Hence, LAO has been used successfully as a substrate material for YBCO.

Yttrium-stabilized zirconia (YSZ) is a substrate which has a cubic fluorite crystal structure with relatively large lattice mismatch (refer to Table 1.3) of 5.8 % with YBCO thin film, but it has been used extensively to grow high quality YBCO films [68]. A small degradation of superconducting properties occurs due to lattice mismatch and the formation of an intermediate layer of Ba2CuO2 (due to interfacial reaction between YBCO and YSZ). Although, highly epitaxial YBCO thin films with good superconducting properties, such as Tc of 86 K, are still (with CeO2 buffer layer) yielded. YSZ has also been frequently used as a buffer layer on reactive substrates, such as Si and Al2O3 (sapphire) [69, 70], for preventing interfacial reaction between the substrate and the thin film. One of the notable features of YSZ buffer layer on semiconductor (e.g. Si) substrates however is its permeability to oxygen, which may be useful in some HTS layers.

Another possible substrate is Al2O3 (sapphire), which is of interest as a substrate in view of its good high frequency properties and availability, although sapphire is chemically incompatible with YBCO at the high temperatures required for processing. These unwanted reactions can be reduced by introducing an appropriate buffer layer (YSZ) between them. Sapphire substrates are mostly used for detector devices, as this material has high thermal conductivity, which absorbs heat energy quickly and transmits it from the overlying film to the underlying substrates.

Since the discovery of YBCO, research has been carried out to find better buffer layers for epitaxial growth of YBCO thin films or multilayers for electronic device application [71-73]. A buffer layer can improve the epitaxial growth of YBCO films and also serve as an insulating (cap) layer, to avoid the degradation of the thin film’s superconducting properties (Tc), but the basic reason is to avoid chemical reactions 19

between the substrate and the YBCO film. So, the buffer layer must be chemically inert or allow no inter-diffusion or chemical reactions at interfaces. Choosing the buffer material with an appropriate lattice constant may improve the epitaxial quality of the film, and it may alter the grain boundaries in HTS film by changing the orientation of epitaxial growth [74].

PrBa2Cu3O7 (PBCO) is considered as the most suitable buffer layer for YBCO thin film in multilayer structures because of its structural and chemical similarity with YBCO. The growing conditions for PBCO are also very similar to those for YBCO [56, 75]. Earlier electrical studies on PBCO indicated that pure PBCO behaved like a semiconductor or an insulator [76]. There are many experimental results on YBCO/PBCO super lattices and YBCO/PBCO/YBCO superconductor-insulator- superconductor (SIS) trilayer junctions on different substrates [77, 78]. PBCO was successfully used as a buffer layer to block interfacial reactions and inter-diffusion between sapphire substrate and YBCO thin film, as confirmed by Auger Electron Spectroscopy (AES) and Transmission Electron Microscopy (TEM) [79]. Recently, there has been interesting reports on the electrical properties of PBCO thin film

(Blackstead et al. [80]) and bulk crystal (Z. Zou et al. [81]) with Tc>>92K and they discovered of inhomogeneous superconductivity in both material respectively. STO has been applied as a buffer layer when growing YBCO on MgO substrate. An STO buffer layer, however, allows control of the orientation of the YBCO c-axis on MgO substrate [82]. Nevertheless, the high dielectric constant of STO (ε =277 at room temperature) prohibits its use in high frequency applications.

CeO2 is one of the most suitable buffer layers for most substrates due to its compatibility with almost all substrates, especially sapphire. Mostly, this buffer can be used for extensive morphology studies, providing very smooth films and epitaxial growth of most thin films. For instance, if films are poor in some element they tend to have a pitted surface, while if rich, precipitate particles were seen. Outgrowths with a- axis orientation often have an elongated shape, because growth of crystallites within the ab-plane is much faster than in c-axis direction. In order to avoid those issues,

CeO2 is used as a buffer layer between the substrate and the YBCO film.

1.9 Why YBCO photodetectors

During the last decade, Superconducting Nanowire Single Photon Detectors (SNSPDs) were fabricated from Nb [83], NbN [84], NbSi [85], WSi [86], TaN [87], or MgB2 [88] superconductors and were operating below 4.2 K (for Nb) or 39 K (for

MgB2). By use of HTS based (YBCO) SNSPD is a challenging, but it shows an impressive promising due to their high operational temperatures, short coherence length, and ultrafast electron relaxation times, which have been studied recently [89], [90], [91], [92]. Obviously, there would be significant operational advantages in utilizing high temperature YBCO superconductors operating at much higher (up to 77 K) temperatures. They would allow substantially relaxed cooling requirements and assure portability of SSPD devices, so that low-cost cryocoolers could be used in read-out electronics applications such as SQUID and SSPD detectors with ultra-low noise.

The short superconducting coherence length [93] in combination with high Tc would provide an additional operating advantage over current conventional (Nb or NbN-based) superconducting photon counters. Defects (zero-dimensional impurities, atomic substitution, and vacancies) can act as strong pinning centers of vortices in HTS (particularly YBCO thin film) due to their dimensions on the order of the short coherence length of the materials (which means that even a single atomic site can have sufficient influence to locally suppress the superconducting order parameter). This form of pinning (where vortices do not move) is effective for high fields applied in-plane at low temperature (because the flux lines are lying in the plane of the YBCO material), leading to a sharp increase in the critical current density [94].

Moreover, the fast photoresponse (18 ps) of YBCO films enabled by the fundamentally small electron-phonon scattering time and the optical properties of low reflection and high absorption over a broad range of radiation frequencies make YBCO thin films well suited for broadband photodetectors, unlike semiconductor photodetectors, which are usually limited in wavelength sensitivity by the size of their band gaps. The reflectivity of YBCO is about 10 % from 1.5 eV to 3 eV [95], and the optical penetration depth at around 2 eV (620 nm, or red light) is δ = 90 nm [96]. So, YBCO based photon detectors might be useful for their sensitivity to a broad range of wavelengths (THz frequency) in the astronomical imaging and detector (HTS)

applications. YBCO microbridges have shown faster photoresponse to THz radiation [97, 98] than other types of photodetectors for optical up to infrared (IR) wavelengths.

1.10 Introduction – Brief overview of single photon detectors Almost all single-photon detectors convert a photon into an electrical signal of some sort. Detecting a single-photon is not an easy task, and even discriminating the number of incident photons is very hard. Because the energy of a single photon is so small (1 eV= 10-19 J), very high detection efficiency is required. Nowadays, many detectors have been developed for this by using different materials for converting a single charge carrier into a macroscopic current pulse. At present, the preferred types of existing commercial semiconductor based photon detectors, which include Avalanche Photodiodes (APD) [99] and Photomultiplier Tubes (PMT) [100] working at room temperature, have several drawbacks, such as high noise, low efficiency, long reset times (~100 ns), high dark count rates (~20 kHz) [101], and being limited to submicron wavelengths [102]. In contrast, superconducting detectors are very attractive for application in SPDs due to their quantum nature, enabling an ultrafast photoresponse, short timing jitter, and low noise [103].

Table.1.4 Performance and efficiency parameters for different types of single photon detectors. Detector Type Detection Dark Timing Max. Operating Spectral

(Material) Efficiency Count jitter δt Count Temp. (K) Range η(%), at Rate (ps) Rate (µm) λ=1.5(µm) (Hz) (FWHM) (MHz) PMT (InP/InGaAs) 2 100 300 10 200 0.3 – 1.7 [104] APD (InGaAs) [105] 10 16×103 55 100 240 <1.7 SSPD (NbN) [106] 57 - 30 1×103 1.5 1 - <5 TES (W) [107] 95 3 100×103 0.1 0.1 <2 (Vis- NIR)

A number of technologies based on superconducting materials have been developed for detecting single optical, ultraviolet (UV), and near infrared photons, as well as X- rays. These include superconducting (SIS) tunnel junction (STJ) detectors for optical and infrared photons [108], transition-edge sensors (TES) for visible and infrared

photons, Hot Electron Bolometer (HEB) [109], [110], [111], Pulsed THz [71] , and kinetic inductance detectors (KIDs) [112]. SSPDs are an attractive alternative in a number of fields in astronomy due to their low noise and high sensitivity over a wide spectral range (from Gamma rays to IR wavelengths with single photon sensitivity). The greatest disadvantages of these detectors are typically their large timing jitter (order of 100 ns), maximum count rates (order of kHz) and very low operating temperature (~100 mK), although they currently offer the highest detection efficiency. For example, TES detectors have 95% efficiency at a wavelength of 1550 nm [107] and are also optimized for sub-millimeter wave detection [113].

Furthermore, the experimental setup for read-out is complicated, requiring a cryogenic superconducting quantum interference device (SQUID) and only operating at very low temperatures (T<1 K – 100 mK [114]). Performance and efficiency parameters for different types of photon detectors are listed in Table 1.4. The use of LTS and their very low operating temperatures is a major drawback in

SSPDs. Hence, HTS have helped by increasing the operating temperature to LN2 temperatures, as well as their high absorption coefficient (with essentially the entire visible to millimeter wavelength), ultrafast response, and very low cost of production. Nevertheless, LTS bolometers operating at helium temperatures or below are consistently better than YBCO detectors at 90 K. The above sections (1.8-1.10) were clearly indicating the requirements on superconducting properties (as well as on the physical parameters of substrates and buffer materials) for the development of YBCO based thin films for detector applications (especially their Jc, Tc, critical dimensions, and spectral range). Among other HTS materials, YBCO could be more promising for radiation detectors (microbolometers) in the range of THz frequency due to its above mentioned potential with wide spectral sensitivity, as well as its high quality superconducting properties

(Jc, Tc) for use in SSPDs.

Hence I briefly describe the Superconducting Nanowire Single Photon Detector (SNSPD) and its photodetection and response mechanisms in YBCO thin films.

1.11 Superconducting Single Photon Detector (SSPD)

A new detector type, superconducting single photon detectors (SSPDs), is better able to address all the above requirements compared with other detectors. They are very fast and low noise single photon detectors. The SSPDs are very sensitive, and they can provide precise timing jitter FWHM, ~ 30 ps, timing information for electromagnetic radiation over a wide range of frequencies – from ultraviolet to low- energy, mid-wavelength infrared photons (1 – 3 μm wavelengths) [15, 20]. These features make SSPDs the most promising detectors for telecommunications and many other applications which require sensitivity to low-energy photons (due to interband excitations in superconductors, which have smaller band gaps than the alternatives, several meV only) The main reasons for the improvement in the sensitivity of the SNSPD detectors in particular at λ = 1550 nm (a wavelength where the solar background is low) are that there are more possibilities to associate signals from several spatial modes in high speed optical communications for astronomical observations. Many impressive demonstrations have been reported recently at this wavelength using high efficiency SNSPDs [106]. Overall, these requirements have provided the motivation to improve SNSPDs efficiency. Here, I have adopted SNSPDs as the one of the main objective of my thesis and focused on high quality surfaces of superconducting thin films for superconducting single photon detecting applications.

1. 11. 1 Properties of SSPDs

The overall performance of SSPD is characterized by the following important parameters: detection efficiency (DE), count rate, dark count rate, timing jitter. Detection Efficiency (DE): In the literature, there have been several ways to define the efficiency of SSPDs. Here the most used definitions will be presented. The most important quantity from the point of view of applications is the system detection efficiency (SDE), which describes the efficiency of a fiber-coupled detector. SDE is the product of the device single-photon detection efficiency (η) and the coupling efficiency (χ): SDE = η∙χ. η is defined as the number of individually measured events that are triggered by single-photons divided by the total number of photons incident on the detector. χ is defined as the ratio of the number of photons 24

that reaches the device active area to the number of photons coupled to the fiber. And, also η can be written as the product of the device absorbance (α) and the nanowire intrinsic single-photon detection efficiency (ηd), which means the probability of that the absorption of a photon in the nanowire triggers the resistive state formation: α∙ηd.

To assess the intrinsic detection efficiency (IDE or ηd) of an SNSPD, its depends on (the photon absorption model) the parameters of the superconducting material, on the nominal geometry of the device, and on its uniform cross section, which is extremely important [115]. Decreasing the nanowire width and it’s thickness increases the intrinsic efficiency of the device [116]. The following parameters, however, are basic key elements that effecting intrinsic detection efficiency (ηd) of the SSPDs in all methods. Geometry: The device geometry is shown in figure 1.8. Still there has been research is to find an ideal layout structure for SSPD. The nanowire geometries evolved from a single straight line [89] to much longer wires in meander design covering square [117] and circular areas [118]. Nanowire (shorter) array [119] also have a faster recovery (reset time) than a single meander, facilitating the development of larger-area devices. By using a meander layout with an optical cavity, provides efficient optical coupling and increases the probability of that a photon will be absorbed. Here, the structure of an SSPD is a thin (thickness ~4-10 nm) superconducting narrow nanowire (line width w = 50 to 120 nm) folded in a meandering or parallel pattern so as to form an 2 active area also called as a pixel. The typical detector active area is Ad (i.e. 10×10μm pixel size, which allows an efficient coupling with the core of optical fibres at telecommunication wavelengths [120]). To extend the sensitivity of DE of SNSPD to the longer wavelength, the nanowire width of SNSPDs needed to be drastically reduced and wider nanowires became negligible ‘DE’ at shorter wavelengths (higher energy photons) [121]. Also, the results of ref. [122] (concerning the influence of the width of nanowires on detection efficiency), indicated that the IDE spectra (performed at 0.94 Ic,e) collected at short wavelengths are constant (plateau of the spectrum) but at larger wavelengths as the photon energy decreases, the IDE makes a transition from the plateau to a steep decreasing slope.

Bias current: The detection efficiency depends on the bias current, as applying low current to the nanowire will have minimal efficiency, exponentially increasing at high bias current. Also, it depends on the impinging photon’s energy on the thinner and narrower wires of SSPD detectors [115], [121]. From the ref.83, the DE of SNSPD as a function of bias current showed (in the range of λ = 0.5-2.7 µm) a sigmoidal dependence on Bias current (IB) and saturated at some level (η = 4.5-5.5%) for IB

(depending on wavelength) sufficiently higher than the cutoff current Ico ~0.5 Ic (the nanowire critical current). As the wavelength was increased, Ico shifted to higher currents. At the above 3 µm, only the initial rise of sigmoid was observed, the DE (at 5 µm) was increased with higher bias current. Photon Energy: Detector property commonly varies with wavelength. The detection efficiency is generally lower for higher wavelengths (less energetic photons) than for smaller wavelengths. In ref. [87], shown that up to about 1µm wavelength, the DE is independent of photon energy at the bias current (IB) close to the Ic. And Ref.[121] says that beyond the cut-off wavelength (λmax), the detection efficiency is decreasing gradually. Temperature: When the temperature of the detector is decreased, the intrinsic detection efficiency (ηd) is increased [123] because IDE depends on the relative current Ib/Ic. Count rate: The number of single-photons detected per unit time is the count rate of a single-photon detector. Typically, the count rate is set by the reset time or dead time of a detector. Dark counts (DC) – or Erroneous photon detection: A dark count is when the single photon detector gives an output pulse when no photon in incident. DC rate (should be zero): rate of detector output pulses in the absence of any incident photon. This falls detection event depends on the detector material properties, detector biasing and external noise.

Detector Dead Time: The dead time or reset time (tdead) is the time it takes for the detector to reset to its initial detection event after a photon has been absorbed in the detector. It is the major limitation to the counting rate of an SSPD. The detection reset time is set by the electrical and thermal time constants of the nanowire (SSPD). To reduce the reset time of SSPDs, a shorter wire has a shorter reset time (although the

volume of the active area is reduced) and parallel geometry has a lower total kinetic inductance, leading to a decreased reset time. Timing jitter (Δt): Δt is the accuracy in the timing of a detection event. It is a time variation or uncertainty in the time from event to event in the delay between the following two events: Thus a certain time passes between when a photon hits the detector (the input of the optical signal) and when a voltage pulse caused by this photon is generated by the detector (the output of the electrical signal). This timing jitter (Δt) is the uncertainty in the time in which the photon is detected. 1. 11. 2 Working principle of SSPDs (SGK Hotspot model)

A single photon detection mechanism in superconducting nanowires was first proposed by Kadin et al. [124]. The working principle of SSPDs was first proposed in the Semenov, Gol’tsman, Korneev (SGK) hotspot model (2001) [125] in NbN nanowire. Even though, significant advances have been made in the modelling of these detectors [83, 126], the (SGK) hotspot model does not explain the temperature dependence of cut-off wavelength and often leads to inconsistencies. However, there has been different model of photon detection mechanism of SNSPD is available and it depends on the incoming photons energy and the superconductivity of the material. The models are Normal hard-core hot spot model [125], Diffusion-based refined (by quasiparticles) hotspot model [83], Vortex nucleation (Time Dependent Ginsburg-Landau TDGL) model Zotova et al [127], Quasi-static Vortex crossing model [128, 129]. All of the above mentioned vortex models are explain the observed detection probability beyond the cut-off energy [83, 129, 130] and have in common that the photon plays the major role in the detection process is to depress the superconducting gap. Subsequently, the depairing of a VAP [126] occurs in the superconductor or the crossing of a single vortex by a thermally activated fluctuation. In SSPD, the microscopic mechanism of photon detection is still under debate. Though, the working principle of SSPD is simply accepted by hotspot formation, which is discussed below. A superconducting nanowire (with a bandgap of 2Δ << hν) absorbs a photon with an energy E = hν at a temperature T well below the superconducting critical temperature

Tc, and the wire is driven with bias current Ibias slightly lower than or close to its critical current Ic (depicted in Fig. 1.4(a)). The event causes a local non equilibrium perturbation inside the wire. When a Cooper pair absorbs a photon of energy, a highly 27

excited quasiparticle (electron) with energy close to the incident photon energy is created. Due to the large physical size [coherence length] of a Cooper pair, only one electron absorbs a photon, while the second one becomes a low-energy quasiparticle (QP). Next, this excited (very hot) electron very rapidly (on a tens of femtoseconds time scale, according to all-optical pump/probe experiments) loses its energy via electron- electron (e-e) scattering and the production of secondary excited electrons [131]. The excited electron’s energy loss due to electron-phonon (e-p) scattering will become dominant. The excited phonons again break Cooper pairs and thus release a large amount of low energy excited quasiparticles. This is the reason for the generation of an avalanche of fast excited quasiparticles. As a consequence, a cascade of quasiparticle (QP) relaxation leads to a region of depressed superconductivity around the absorption site; i.e, so called, hotspot. After the formation of hotspot, the applying bias current will be expelled from the volume of the hot-spot occupies (Fig. 1.4(b) and (c)). This causes the current density to increase at the edges of the wire. In the case where this hot-spot region can cause a local phase transition in the nanowire towards its resistive state, the current density exceeds the critical current; and a resistive state across the strip is formed, as shown in Fig. 1.4(c).

Fig. 1.4 Schematics of the photogenerated (SGK) hotspot (a,b) and of the current- assisted formation of a normal barrier (c,d) across an ultrathin nanowire kept at a temperature much lower than its Tc. The black arrows indicate the flow of the supercurrent biasing the nanowire [125].

The switch between the superconducting state and the resistive state of the nanowire enables a voltage pulse over the SSPD to be measured with the proper read-out electronics. Thus, the measured voltage pulse is an indication that a photon has struck the nanowire. Eventually, the deposited energy in the strip is distributed over a large area and flows towards the substrate. Single electrons recombine into Cooper pairs, and the system recovers its equilibrium state. Hence, the hotspot heals due to relaxation and out diffusion of quasiparticles and finally collapses, so the superconductivity is restored, and the nanowire is ready to detect another photon (Fig. 1.4(d)). There has been lot of discussion in the literature, however, about the microscopic mechanism(s) responsible for photodetection in SNSPDs. A comprehensive description of the microscopic model which describes the diffusion behaviour of the hotspot region appears [124].

1.12 Photodetection and Photoresponse Mechanism in YBCO superconductors

One of the main motivations behind this work has been advancing the use of YBCO film for photon detector applications. In order to develop and improve the photon detector’s technology, we must understand the mechanism of photodetection and superconductivity of the material. A major influence on the detection mechanism of superconducting (high-Tc) materials is the incoming photon energy (Eph) which may be below or above the energy gap of the superconductor. Based on these excitations (such as short optical (above or over-gap) and THz (sub-gap)), the photodetection mechanism will varied. Also, understanding the origin of the fast photoresponse observed below Tc may also help to provide clues to the superconducting mechanism in the high-Tc oxides. In addition to that, each superconducting device has its own detection mechanism.

1.12.1 Excitations below and above energy gap After the development of accelerators (coherent synchrotron radiation (CSR)), picosecond (ps) short pulses are used to evaluate the response time (non-bolometric features) of the YBCO thin-film detectors in sub-gap excitation. In the THz frequency range, the major energy in the form of ps pulses is generated by intensive CSR. Even if the incoming THz photon energy (1 THz = 4.1 meV) is smaller than the energy gap of YBCO [132], [71], the absorption of the THz radiation occurs by the Cooper pairs with a successive breaking of them. 29

The vortex based detection mechanism [132] well explains the excitations of the sub- gap range (ps THz pulses by CSR), in which the vortex-flow has been taken into account for the photoresponse in high-Tc YBCO. The incoming radiation is absorbed by the THz antenna (which is required to couple THz radiation to the YBCO detector), generating a rf-current (high frequency) which causes a rearrangement of the vortex lattice into a vortex line [132, 133] by the Lorentz force. The high frequency (rf-current) suppresses the order parameter in the superconducting bridge, which causes vortices to move and cross the bridge, which, in turn, gives rise to a voltage transient. The YBCO detector response to the continuous THz radiation is well explained by the bolometer model (working as a classical bolometer [92], [134], [135]). The response of an YBCO microbridge to above-gap [98] as well as to sub-gap excitations [71] shows small variances. YBCO thin film has already been studied in detail for its ultrafast photoresponse mechanism in over gap excitations in the wavelengths range from optical to infrared [92], [98, 136, 137], and it is widely based on the hot-electron effect, which is well described by the two-temperature or 2T- model [138], [137] (in which the electron and phonon subsystems are assigned temperatures Te and Tph, hence 2T-model [132]). This model is valid for nonequilibrium superconductors maintained at a temperature T near the Tc, where quasiparticles and phonons can be described by thermal, normal-state distribution functions, each with its own effective temperature. In above-gap experiments, the photon energy of incoming radiation was above the superconducting energy gap (∆) in YBCO (in the optical frequency range Eph > 1 eV, and ∆ ≈ 20-25 meV for YBCO [139]).

1.12.2 Hot-electron effect-Two temperature model

The generally accepted mechanism for photodetection is the hot-electron model, and it is in very good agreement with the 2T nonequilibrium heating model. The hot- electron phenomenon is that electrons excited by absorbed radiation destroy cooper pairs and produce hot electrons in the YBCO microbridge. Hence, the incoming radiation was directly absorbed in the microbridges by electrons.

An increased quasiequilibrium electron temperature Te is established within the thermalization time τth. The excess energy is then transferred to the phonons within

the e-p interaction time τe-ph, which increases the quasiequilibrium phonon temperature Tph. By electro-optical sampling technique [93] in YBCO, these two interaction times are measured in the sub-ps (τth =0.56 ps) and ps (τe-ph) range. Finally, within the phonon escape time τesc the energy is released to the substrate, which permanently remains at the bath temperature (Tb). Because all three processes occur simultaneously, the time for the microbridge to return to global equilibrium is a complicated function of aforementioned particular times. Simultaneously, In YBCO the specific heat capacity of the phonons Cph is much larger than the electron specific heat capacity Ce [Cph/Ce = 38] [93]. Therefore, on a femtosecond time scale, the hot- electron (non-thermal and thermal processes) and phonon (bolometric processes) subsystems are thermally decoupled (in the early stages of electron relaxation), and the energy backflow from the phonon to the electron system can be neglected. This explains the fast ps component in the photoresponse of YBCO microbridges. The following slow component is largely due to the cooling of phonons via escape to the substrate. 1.12.3 Photoresponse mechanism in YBCO superconductors

The mechanisms of photoresponse in superconductors have been divided into two types: (i) equilibrium or bolometric response and (ii) nonequilibrium response [140]. In the first type, the photon raises the temperature of the film and it change in the resistance is manifested as the photoresponse.

The photoresponse of YBCO thin film is comes under the nonequilibrium category [141]. The nonequilibrium type is created when the incoming radiation presumably breaks the superconducting cooper pairs (only in electron) and change in the quasiparticle density. An increase of population of low-energy quasiparticle leads to the suppression of superconductivity. In results, voltage shift in the resistive state is proportional to the concentration of low energy excess quasiparticles, the kinetic inductance signal in the superconducting state is proportional to the time derivative of the quasiparticle population. Also, R. Arpaia et al [141] says that there are two different photoresponse mechanisms responsible for the HTS in the presence of two distinct regimes. These two excitation regimes differ with respect to the ratio of the photon energy and the superconducting energy gap in YBCO.

Responses described by the detection mechanism, which includes a fast (nonbolometric) component in the beginning of the response corresponding to the hot electrons formation (electron thermalization on sub-ps time scale) and subsequent electron relaxation processes (e-p cooling on ps time scale). Then, the phonon subsystem of the film remains in thermodynamically equilibrium with the substrates and plays the role of the heat sink for electrons. The electron distribution function is controlled by the source of electromagnetic radiation and the electron relaxation mechanism. Finally, followed by a ns decay (bolometric response - slow component determined by the Kapitza resistance at the film-substrate interface [142]) corresponding to the cooling of the electrons and film phonons due to phonon escape from the film to substrate. Many research groups [134, 143-145] observed this bolometric response in YBCO thin films using pulsed-laser and synchrotron radiation sources from the visible to the infrared wavelengths. There have been a lot of response mechanisms involved in these wavelengths region, which means excitations above the energy gap. They are hot-electron effect-2T models (SNSPDs, YBCO micro-bridge detectors), vortex- assisted models (pulsed THz detectors), and kinetic-inductance photoresponse (described in the section below).

1.12.4 Kinetic-inductance photoresponse

The theory of kinetic-inductance photoresponse takes into account the change of the Cooper pair density induced by the absorption of over-gap photons. To observe this phenomenon the detector operation temperature has to be well below its critical temperature (T<< Tc) and photons with energy typically much larger than 2Δ. A typical kinetic-inductance response for a YBCO thin-film is demonstrated in [146], [93]. In that, the positive part of the transient represents the Cooper pair breaking process, while the negative part represents non-equilibrium cooper pair recombination processes (so called RT model). The RT model [147] assumes that there is a quick, intrinsic thermalization mechanism inside both the quasiparticle and phonon subsystems. So, the one of the applications of YBCO thin film is utilizing it in ultrafast photon detectors in the visible to THz frequency range, which depends on the potential for high thin film quality with the best combination of substrate/ buffer layers for various applications. 32

1.13 Why Graphene- A Brief History SQUID series arrays are ideal for read-out electronics of photon detector applications. Especially, transition edge sensors (TES), SSPD sensors, or as the amplifier stage for discrete two-stage applications. Hence, I have fabricated few nanostructured superconducting electronic devices, which can be used in modern detector physics research. These include niobium (low-Tc superconductor) and graphene nanostructure-based Josephson junctions fabricated with E-beam-lithography (EBL) and focused ion beam (FIB) patterning for optimising the graphene performance at low temperature for use in Josephson junctions for SQUIDs with high sensitivity. Graphene was investigated as an alternate barrier material (due to its tuneable electronic behaviour) for Josephson junctions by an electron-transport study. To study the superconducting behaviour of Niobium with the very interesting material graphene, which I now describe its structure and properties.

Graphene is being studied intensively throughout the world, because it is believed that it can play an important role in the electronics of the future and possibly replace the semiconductor age. Nowadays, many industries are attracted by carbon electronics because graphene has greatly superior properties compared to conventional materials, such as silicon and germanium. Graphene is not a semiconductor, but rather a semimetal, so the size of the current as well as the type of charge carrier also can be regulated in this material. Recently, researchers from TU Delft [148], for the first time, detected superconducting properties in a material composed of massless, relativistic electrons, which was nothing but graphene. They made their device from graphene material, which is attached to superconductors and also functions as a bipolar transistor for superconducting currents. It is worth looking at the history of graphene and its properties before studying them.

Approximately 7 decades ago, prominent theoretical physicists (Lev Landau and Rudolf Peierls) argued convincingly that the two-dimensional arrangement of atoms as in graphene materials is not a thermodynamically stable structure, a view later extended by Nathaniel Mermin [149] and supported by the fact that no two- dimensional crystals had been isolated. Nevertheless, the recent discovery of a graphene material in 2004 overturns the conventional understanding of the unstable

structure of 2-dimensional materials and has even led to 2010 Nobel prizes in Physics for its discoverers Andre Geim and Konstantin Novoselev. One of the most interesting properties of graphene is that the charge carriers inside it behave as mass chiral relativist particles [150], making it the first low-energy model system for studying 2+1 dimensional quantum electrodynamics. Apart from its unique electronic properties, graphene can also become superconducting through immediate proximity to a superconductor via the Josephson Effect. Thus, graphene Josephson junctions enable us to study the exceptional intersection of relativity and superconductivity, which has yielded such interesting results as specular Andreev reflection and the relativistic Josephson effect. This work examines only the very beginnings of what will likely be an important material of the future. Before going on to study the graphene devices, we need to know about the graphene natural properties. Since the twentieth century, organic molecules have been extensively studied by scientists because of their interesting electronic properties. As a consequence, organic electronics has nowadays become a growing field of interest, especially molecular electronics.

1.14 Graphene Introduction Graphite derives its name from the Greek "graphein", which means ‘to write’. Graphene is the name given to a 2-dimensional sheet of sp2-hybridized carbon (see Figure 1.5). It is an atomically-thin and flat, 2-dimensional single layer of conjugated sheet of six carbon atoms arranged in a hexagonal/honeycomb shaped lattice structure. These 2-dimensional sheets form the building blocks of graphite, made up of many layers of graphene. Since these newly-found carbon structures pose unique/wondrous properties due to quantum effects and lower dimensionality, they have generated intense research in many disciplines [151]. It is mother of all graphitic carbon forms. Graphite material is generally greyish-black, opaque, and has a lustrous black sheen. Graphene has distinct optical, electrical, and mechanical properties, all just because the carbon atoms have arranged themselves in different ways. Graphene is a really versatile material because its carbon atom has four valence electrons that can make different types of bonds with other carbon atoms. Observations of carbon crystalline molecular forms different from the graphite began in 1985 with the discovery of the nanoscale carbon molecules later named fullerenes, the most famous

of which is the C60 molecule [152]. A few years later, one-dimensional carbon nanotubes were discovered in 1991 [153]. Despite being a simpler and more versatile system to consider theoretically, graphene’s rise took place nearly a decade later than its isolation in 2003, when the group of Novoselov and Geim first reported that they had managed to create and detect two-dimensional single and few layer graphene [154]. Graphene has unusual electronic properties that may be useful in the design of new electronic devices. Recently there has been a great deal of interest in this high mobility, conducting material [155], [156], [157].

1.15 Chemistry of Graphene- Structural Property To understand the properties of graphene, we must first understand the structural arrangements and chemistry of graphene. Since carbon is the sixth element of the periodic table, each carbon atom has six electrons in two shells, with a ground state atomic configuration of 1s22s22p2. The two inner electrons are core electrons (1s2 orbitals) and the four outer electrons are valence electrons (2s22p2 orbitals), while the 2 inner shell electrons belong to the spherically symmetric 1s orbital that is highly bound. Carbon has 4 valence electrons, the wavefunctions of which mix easily, forming hybridizations. The valence electrons of carbon atoms are form the 2s, 2px,

2py, and 2pz orbitals. These orbitals give rise to the covalent bonds between neighbouring atoms in a molecule or a lattice. In order to create these molecular bonds, the 2s orbital hybridizes with the 2p orbitals to form spn orbitals (n = 1, 2, 3). Thus, three hybridization processes are possible: sp1 hybridization as in in acetylene (HC≡CH); sp2 hybridization as in graphite, carbon nanotubes, fullerenes, and graphene; and sp3 hybridization as in diamond. In graphene, due to the planar arrangement of carbon- carbon bonds (where each carbon atom is bonded to three others) the carbon atoms are in a sp2electronic configuration. In the sp2 configuration, the 2s orbital is mixed with only two of the three available 2p orbitals. Hence, the 2s orbital hybridises with the 2px and2py orbitals, forming three strong covalent ‘σ’ bonds with three neighbouring atoms in the plane, at an angle of 120° to one another [158]. These sp2 hybridization processes (Fig:1.5) yield high binding energies, resulting in strong covalent ‘σ’ bonds. This leaves one free electron per atom in a pz orbital,

perpendicular to the plane of the graphene sheet. This ‘σ’ bonds has consequences for the electronic properties.

Fig 1.5 sp2 hybridisation: shaded (unshaded) denotes weak (strong) bonds.

In more detail, the inner core electrons are strongly bound to the nucleus and do not interact with any neighbouring atoms, But, the 4 valence electrons do interact with the surrounding carbon atoms. In such interactions, each carbon atom forms 3 bonds with each of its neighbouring atoms. Three of those valence electrons only occupy the 2 planar sp hybrid orbitals made from the 2px, 2py, and 2s orbitals to form covalent in- plane (σ) bonds (shown in Fig. 1.5). These covalent σ bonds are oriented towards the neighbouring atoms, and the carbon-carbon σ bonds that are formed are strong enough to hold diamond together and give graphene comparable mechanical and thermal properties to diamond. The remaining 4th valence electron is not involved in covalent bonding, rather, it occupies a pz orbital (with the z-axis perpendicular to the plane), which forms a weak conducting ‘π’ bond with neighbouring atoms. Because the σ bonds are highly localised, the electrons in these orbitals do not take part in conduction, but the ‘π’ bonds are de-localised and are responsible for electronic conduction through graphitic structures. Overlap between pz orbitals results in loosely held free electrons in the π bonds; under illumination, they are responsible for the black colour of graphite. These ‘σ’ bonding electrons are very important in graphene, which gives an accurate description of electron correlation. This unique property can interact with the Dirac cone dispersion of π electrons by long range Coulomb interactions. The softness and lubricating nature of graphite arises from weak binding of the graphene sheets and weak van der Waals forces. The chemical and electronic properties of graphene are therefore determined by the valence electrons of a carbon atom in the 2s, 2px, 2py, and 2pz orbitals. There is a variety of structures (structures of different allotropes of carbon [159]) that can be formed through sp2 bonding hybridized systems in carbon. Structures can be

formed by cutting and folding the graphene, namely the zero-dimensional (0D) Buckminster fullerenes or buckyballs and the one-dimensional (1D) carbon nanotubes (CNTs) (with different types of CNT, termed armchair, chiral, and zigzag). By stacking many two-dimensional (2D) graphene sheets on top of one another, the common three-dimensional (3D) graphite structure is produced (e.g. diamond). Single layer graphene (SLG), also referred to as monolayer graphene, which consists of a single 2-dimensional sheet of sp2 bonded carbon in a hexagonal structure. (Graphene also forms the building blocks of the 0D allotropes.) Two or more stacked layers of graphene sheets are called bilayer graphene (BLG) and few layer graphene (FLG), respectively. All over in this thesis, the term graphene will be used to represent monolayer graphene unless otherwise mentioned.

1.16 Graphene Crystalline structure- Bravais Lattice To know more about graphene, we must first understand its lattice structure. The shape of graphene edges (armchair and zigzag) are playing important role in electrical properties, which is based on its crystalline structure. The crystal structure of graphene is a two-dimensional triangular Bravais lattice, which contains two carbon atoms (separated by the carbon-carbon bond length of 1.42 Å) per unit cell (dashed line), each placed on one of two sub-lattices, often labelled as the A and B sub- lattices, Fig. 1.6 (a). The basic periodic structure in graphene is made up of these two lattice points in a repeated lattice array formation.

1.42 A◦

Fig. 1.6 a) Hexagonal lattice structure of graphene, i.e., the unit cell, it contains two non-equivalent carbon atoms A and B. The lattice vectors are a1 and a2, and the three nearest neighbour vectors from sublattice B to sublattice A are shown. b), Reciprocal space lattice points (dots) and the hexagonal first Brillouin zone (shaded) [160]. Figure adapted from [148].

The periodic structure of the lattice can be understood in terms of the primitive unit cell. The primitive unit cell is an area (or volume, depending on the dimensionality of the crystal) element centred around a point in the reciprocal lattice, and it is the basic volumetric or areal element which acts as a building block to tile the area or volume of the full lattice. The primitive unit cell of the reciprocal lattice is called the first Brillouin zone and is shown in Fig. 1.6(b). It is interesting to note that the structure of the reciprocal lattice depends only on the shape of the Bravais lattice, that is, it depends only on the periodicity of the crystal lattice, and not its exact structure. The primitive unit cell with the full symmetry of the lattice is a hexagonal structure, as shown in Fig. 1.6(a). The area of the graphene unit cell is

3 3 퐴퐺 = 푎2 √ ≅ 5.22 Å2. The unit cell lattice is spanned by two vectors separated by 2 a 60° angle, a and b with length of 푎√3 ≅ 2.46 Å or 1.42 Å ×√3 = 2.46 Å, with dot 3 product 푎2. The lattice constant, a is given by 1.42 Å×√3 = 2.46 Å. All other lattice 2 sites are translations over the primitive unit vectors a1 and a2. These lattice vectors are described in [161] in great detail. The Bravais lattice of graphene consists of a unit cell with a basis of two carbon atoms (Fig. 1.6 (b)) with lattice vectors.

3푎 3 3푎 3 The basis vectors 푎 = ( , √ 푎), 푎 = ( , − √ 푎) (1.8) 1 2 2 2 2 2 Where a is the inter atomic distance (C-C = 1.42 Å) or the graphene bond length ° [162]. The basis vectors of the reciprocal lattice in k space are rotated 90 from a1 and a2, and the reciprocal lattice is again triangular with a hexagonal first Brillouin zone, see Fig. 1.7(b). The lattice vectors in reciprocal space are b1 and b2 (shown in Fig 1.7) given by 2휋 2휋 2휋 2휋 푏 = ( , ), 푏 = ( , − ) (1.9) 1 √3푎 푎 2 √3푎 푎

Fig.1.7 a) Sublattice vectors; b) first Brillouin zone [160].

The Brillouin zone (BZ) of graphene contains two non-equivalent K points, as there are two carbon atoms per unit cell of the Bravais lattice. In figure 1.7(b) the first Brillouin zone of grapheme is shown, including the high symmetry points in

2휋 momentum space: Γ = (0, 0), M =( , 0), K, K′. The particularly interesting points of 3푎 high symmetry, the K and K′points, have wavevectors:

2휋 2휋 2휋 2휋 퐾 = ( , ), 퐾′ = ( , − ) (1.10) 3푎 3√3푎 3푎 3√3푎

with (δi for i= 1, 2, 3), the three nearest neighbour vectors in real space from sublattice B to A are shown in Fig 1.7(a)). The three nearest-neighbour vectors in real space are

푎 푎 휹 = (1, √3); 휹 = (1, −√3); 휹 = −푎(1, 0) (1.11) 1 2 2 2 3

While the six second nearest neighbours are located at

′ ′ ′ 훿1 = ±풂1, 훿2 = ±풂2, 훿3 = ±(풂2 − 풂1) (1.12)

The importance of the K and K′ points are clear upon calculation of the band structure of graphene. The graphene band structure may be calculated using a tight-binding formulation which considers only the electrons in the pz orbital (with a hopping of electrons between nearest neighbour approximation atoms from sub-lattice A to B or B to A), and ignores any influence of the sp2electrons [163]. It is straightforward to show that the band structure derived from tight-binding mirrors these symmetries as represented in Fig. 1.8. Furthermore, the symmetric and anti- symmetric combinations of atomic orbitals lead to bonding (π) and anti-bonding (π*) orbitals, which cross at the Fermi level. At this energy, the density of states vanishes for charge neutral graphene. Normally, a material with two electrons per unit cell behaves as an insulator, but graphene, due to the band-crossing at the Fermi level, is classified as a semimetal. The band structure of graphene determines its electronic behaviour. 39

1.17 Electronic Properties of Graphene

Graphene is unique, in that has properties of both a metal and a non-metal. It is flexible, but not elastic and is highly refractory and chemically inert. There are a number of interesting answered and unanswered question related to the mechanical [164], optical [165] and magnetic [166] properties of grapheme, but the astonishing electronic properties of Graphenes are direct results of the peculiar band structure of graphene, a zero bandgap semiconductor with two linearly dispersed bands that at the corners of the first Brillouin zone. As an electronic material, graphene represents a new playground for electrons in 2, 1, and 0 or 2+1 dimensions, where the electronic properties are changed due to its linear band structure. Scattering is low in this material, allowing for the observation of the Quantum Hall Effect (QHE), and the unique band structure of graphene gives this old effect a new twist [167], [155]. Electron motion in graphene is equivalent to that of a neutrino or a relativistic Dirac electron with vanishing rest mass. This causes the appearance of a nontrivial Berry’s phase under 2π rotation in wavevector space, leading to the absence of backscattering. The conductivity of graphene is essentially independent of the Fermi energy and the electron concentration, as long as variations in effective scattering strength are neglected, and therefore, graphene should be regarded as a metal rather than a zero-gap semiconductor [168]. The special electrical properties of graphene can be derived from its band structure.

Figure.1.8 The electronic Band structure of graphene., modified from [169]. The inset shows the Fermi cones.

A tight-binding formulation which considers only the electrons in the pz orbital, and ignores any influence of the sp2 electrons that means considering the atomic structure

of graphene. The tight-binding Hamiltonian for electrons in graphene, considering that electrons can hop to both nearest- and next-nearest-neighbour atoms has the form

† † † 퐻 = −푡 ∑〈푖,푗〉,휎(푎휎,푖푏휎,푗 + H. c) − 푡′ ∑〈푖,푗〉,휎(푎휎,푖푎휎,푗 + 푏휎,푖푏휎,푗 + H. c) (1.13) Here, ћ = 1 scale units used t is the energy needed by an electron to move from one site to its nearest neighbour (hopping between different sublattices ─ i.e., from one sublattice to the other), and t′ is the next nearest-neighbour “hopping energy” (on the same sublattice), H. c is Hamiltonian constant. The notation is explained here as † follows: the operator 푎휎,푖 creates an electron with spin σ (σ= ↓, ↑) at a point R, indexed by i, on sublattice A. Similarly, 푏휎,푗 acts to annihilate an electron with spin σ on sublattice B at a point indexed by j. From the Hamiltonian, the energy bands (dispersion) are derived in the following form

′ 퐸±(풌) = ±푡√3 + 푓(풌) − 푡 푓(풌) (1.14)

√3 3 where, 푓(풌) = 2 cos(√3푘 푎) + 4 cos ( 푘 푎) cos ( 푘 푎) (1.15) 푦 2 푦 2 푥

In the vicinity of the K-point, electrons experience a linear energy-momentum dispersion relation, which is obtained by straightforwardly solving Eqs. (1.15) and (1.16), as the linear dispersion relation

퐸(풌) = ±휈퐹|ћ풌| (1.16) which corresponds to a cone-shaped band (fig. 1.8). Due to the linear spectrum, these electrons behave like massless particles with a constant speed of light equal to the

3푡푎 6 Fermi velocity νF = ≈ 1 ×10 m/s (where a = 1.42 Å is the lattice distance). This 2 property makes graphene special compared to conventional 2DEGs in which electrons are massive and have an energy dependent Fermi velocity. ћis Planck’s constant over 2π, and K is the wavevector with respect to k and K′. This first-order linear term gives rise to the so-called Fermi cones at the corners of the first Brillouin zone, shown in Fig. 1.8. As shown in Fig. 1.8, there is an electronic linear dispersion relation in the shape of the full band structure E(Kx, Ky), and in the inset also shows the enlarged structure of the energy bands close to the points labelled K and K′ in the BZ, often referred to as

Dirac points Quantum mechanical hopping between the sub-lattices leads to the formation of two energy bands. The origin of the upper conduction band is the anti- bonding orbitalsat E > 0, π* (positive), and the lower valence band originates from bonding orbitalat E <0, π (negative). They meet at six points, which are called the K- points (at E = 0). So the two π*-π bands intersect near the K-Dirac points at the edges of the first Brillouin zone [163], which yields the conical energy spectrum. The hexagon formed by six K-points defines the first Brillouin zone of the graphene band structure. In charge neutral graphene, the Fermi energy lies exactly at these Dirac points where there is a null in the density of states. Therefore, quasiparticles in graphene exhibit the linear dispersion relation with double valley degeneracy, and the graphene is called a zero-gap semiconductor. In contrast to the conventional metals and semiconductors, where the energy spectrum can be approximated by a parabolic (free-electron- like) dispersion relation, one can expect that graphene’s quasiparticles behave differently due to the linear spectrum. One of the factors which make graphene so attractive for research is the low-energy dynamics of electrons in graphene. Its low-energy quasiparticles are also formally described by the Dirac-Weyl Hamiltonian (as in Eq. (1.14)) rather than the usual Schrödinger equation, which is,

H = −iћvF σ∇, (1.17)

6 −1 where vF≈ 10 m·s is the Fermi velocity, σ = (σx, σy) are the Pauli matrices, and ∇= (∂x, ∂y). This description is theoretically accurate [162], [170], [171] and has also been experimentally proven [155]. From the point of view of its electronic properties, graphene is a two-dimensional zero-gap semiconductor. As a zero-gap semiconductor, outstandingly high crystal quality and high charge mobility are two of the wonderful properties of graphene. In fact, the charge carriers in graphene behave as massless chiral fermions [172], i.e., “relativistic” electrons. The analogy with massless Dirac fermions results from this unusual band structure (see Fig. 1.8), including notions of pseudo-spin and chirality found in relativistic quantum electrodynamics. The massless, linear dispersion gives graphene its unique electronic properties, extremely high mobility, and universal conductivity. The high charge mobility has attracted vast interest [167] in the field of device physics. In particular, mobilities on the order of 100,000 cm2·V-1·s-1 are

supposed to be possible, even at room temperatures. Such mobilities are possible in the case of high carrier density (n > 1 ×1012cm-2) and result in a mesoscopic system with transport in the ballistic regime (on the order of 1 µm). Other exciting transport properties of graphene include conductivity, where even in the limit of charge carrier density going to zero, a non-vanishing minimum conductivity, σmin, is measured. The singularity at the Dirac point was first verified experimentally by measuring half integer steps in the integer quantum Hall effect in graphene [155]. This and other anomalous Hall effects are believed to be based on grahphene’s chiral nature [173]. Additionally, this chiral nature gives rise to an additional phase in graphene, i.e., the Berry’s phase. Electrons in conventional materials have no Berry’s phase, but electrons in single layer graphene have a Berry’s phase of π, which means that an electron wavefunction acquires a phase of π after a rotation of 2π in momentum space around a K-point (or a closed trajectory takes place). The chiral nature of electron states in single-layer, as well as bi-layer, graphene is of crucial importance for electron tunnelling through potential barriers, and thus for the physics of electronic devices such as carbon transistors [157]. Another result of the Dirac cone band structure is that current in graphene can be carried by either electrons or holes. Electrons are filled states in the conduction band, above the intersection point of the Dirac cone, also known as the Dirac point, and holes are empty states in the valence band, which is below the Dirac point of the Dirac cone. We can control the current carrier by changing the carrier population in graphene to change its Fermi energy, most generally, by applying a voltage on the back of the substrate. It is known as a back gate voltage. Surprisingly, current can still be carried in the graphene at the Dirac point, where there should be no charge carriers.

Here, the charge is transferred via exponentially decaying modes, known as evanescent modes. The possibility of transmission for these modes obeys the same rules which describe diffusive modes in a disordered metal of the same conductivity. For this reason, transport in graphene at the Dirac point is known as the pseudo- diffusive mode [174]. Graphene is identified as the first material which supports Dirac fermions in two dimensions, and is therefore considered as an interesting material/playground for solid state physics. A description of the Josephson Effect in graphene based devices follows in the next. 43

1.18 Graphene based Josephson junctions

In this section, the basic theory of graphene’s superconductivity is presented along with the underlying microscopic theory of superconductor junctions. These are related to phenomena that are important for the measurements on the experimental SGS junction. As is well known, graphene gives a new twist to certain well-known processes such as Andreev reflection. Before describing the fabrication of the Josephson junction on graphene films, we must know the basics of superconductivity and its effects in graphene. The junction-related phenomena of Andreev reflection and the Josephson Effect are discussed in some detail. Josephsoneffect In 1962, a significant discovery was reported by Brian Josephson. He predicted that quantum tunnelling effects (a current flow through a junction consisting of two weakly joined superconductors, separated by a thin insulating barrier [175]) in superconductors were theoretically possible and three main effects were denoted as DC, AC and inverse AC Josephson effects, referred to collectively as Josephson effects. Soon afterwards, this theory was experimentally confirmed [176] and applied in superconducting quantum interference devices (SQUIDs), which are highly sensitive magnetometers that are broadly used in science and engineering.

Brian Josephson [175] predicted that in a superconductor-insulator-superconductor (SIS) junction, electron tunnelling by a special electron tunnelling mechanism, which involves a current carried by Cooper pairs could be observed, provided that barrier was thin. As discussed before, Graphene itself is not a superconducting material, but it takes on superconducting characteristics when in contact with superconductors due to proximity effects [110]. This effect was first observed by Heersche et al. in 2007 [148] and exhibits several remarkable properties (including Andreev reflection).

Such a superconductor-barrier-superconductor heterostructure is known as a Josephson junction. The wavefunctions of the two superconducting electrodes can overlap, allowing the tunnelling of Cooper pairs (Fig. 1.9). It is very significant that a supercurrent is only sustainable while the Cooper pairs are able to propagate through the middle material with phase coherence and time reversal symmetry, since both are mandatory requirements for the existence of Cooper pairs. Amazingly, graphene is capable of having both properties, and so is a suitable material for a Josephson

junction. Graphene can carry a supercurrent when it is placed between two superconductor electrodes, that is, where the proximity effect is possible due to the thin insulating barrier (≈ 10 Å). All the Cooper pairs in a boson condensate are in the same quantum state and can be described by a single wave function as follows: Ψ = |ΨѰ|푒푖휙푠 (1.18)

Where ϕs is the macroscopic quantum phase and |Ψ| is a measure of the Cooper pair density.

1.19 Josephson junction device principle

A Josephson junction is a device consisting of two superconducting electrodes S1 and

S2 separated by a thin insulating layer, a normal (non-superconducting) layer, or a weak link. We call this region the barrier region (see Fig. 1.9).

Fig. 1.9. Schematic diagram of the Josephson junction, adapted from [175].

Each electrode has its own macroscopic quantum state described by a wave function

i1 (which can be regarded as a superconducting order parameter): 1= n1e and

i2 2= n2 e for electrodes 1 and 2, respectively; here n1, n2 are the densities of the superconducting electrons, and 1 and 2 are the phases in electrodes 1 and 2, respectively. The wave functions decay within the barrier, but if the barrier width is less than the decay length, then the two functions overlap each other, as is schematically shown in Fig. 1.9. This is a “weak superconductivity” region; theoretical consideration of this system by Josephson [175] led him to conclusion that such a system can support a zero-voltage superconducting current (Josephson current) 45

according to the following equation: The voltage and current across a Josephson junction are given by

I = Icsin, (1.19)

where Ic is the critical current, that is the maximum supercurrent that the junction can support before switching to the dissipative state, and  is the phase difference (of the wavefunction across the two electrodes [177]) of the superconducting order parameters:  = (1 - 2).When a voltage is applied across the Josephson junction, the gauge-invariant phase difference will evolve according to

 2eV  , (1.20) t  Furthermore, this time derivative of the phase difference is proportional to the voltage across the weak link. This relation implies oscillating supercurrents at a frequency determined by the bias voltage, which was experimentally confirmed [176]. It turned out that those equations hold for more general ‘weak links’ between superconductors (S). A weak link can be formed by constriction or a non-superconducting material. Proximity induced supercurrents in non-superconducting materials have been observed in various materials [178, 179]. This relation gives rise to two possible effects- the DC and the AC Josephson effects. In the latter (at a voltage V 0), an AC current occurs in the Josephson junction with the oscillation frequency  = 2eV/h.

Fig.1.10. Typical I-V curve of a Josephson junction.

The DC Josephson effect occurs when we put a DC voltage across the Josephson junction. When this happens, the current begins to oscillate with time as 휙 grows

larger. Because of the small size of h, this oscillation is very fast and for most measurements will average out to zero.

When the voltage is near zero but ≠ 0, however, the oscillations will become slow enough to be picked up and will show up as a vertical line in a voltage vs. current plot. As the voltage increases, it will finally overcome the attractive interaction between the electrons in a Cooper pair, and the junction will become ohmic in its I-V 2∆ curve. This occurs when the voltage is equal to , where Δ is the energy gap for 푒 between the superconducting and the normal conducting states. For a typical I-V curve of a Josephson junction with a DC voltage bias, see Fig. 1.10.

If we apply an AC voltage signal on top of the DC voltage across the junction, we will see a DC component to the Josephson current when the frequency of the DC Josephson effect oscillations is a harmonic of the applied AC frequency. Typically, these frequencies are in the GHz range, the range of microwave radiation, and so rapidly oscillating AC voltages are often achieved by applying microwaves or radio frequencies (rf-frequency) from an antenna somewhere near the Josephson junction. Experimentally, the AC Josephson effect is typically seen as steps in the I-V curve of the Josephson junction.

1.19.1 Andreev Reflection

After single-layer graphene was introduced into experimental physics [154], numerous theoretical and experimental works appeared on Superconductor-Graphene- Superconductor (SGS) junctions.

Fig: 1.11 a) Andreev retro- reflection; b) specular Andreev reflection, adapted from [180].

A number of unusual effects were predicted in such junctions, associated with the possibility of realizing relativistic superconductivity induced in the graphene from the superconducting electrodes. One of these interesting effects is specular Andreev reflection. Due to the presence of a gap in the excitation spectrum of the superconductor, no electron states are available at energies E < Δ. In the superconductor, the wavefunction of the electron is exponentially damped on a length scale ξs = ћ휈퐹/(πΔ). As was shown by Andreev in 1954, Andreev reflection is a microscopic mechanism that converts normal current into supercurrent and vice versa, in which (in the classical case) an electron (hole) impinges on the SN junction from the N side to form a Cooper pair on the S side, while an electron is reflected as a hole (with the same momentum and opposite velocity) at the SN interface back into the N side exactly follows the path of the incident electron but in the opposite direction. Andreev reflection conserves momentum but does not conserve charge. (An SN interface where a hole of opposite charge (+e) and spin (-σ) is retro-reflected is shown in Fig. 1.11(a)). The missing charge (of 2e) is absorbed as a Cooper pair by the superconducting condensate. In graphene, in addition to this process, a specular Andreev reflection is possible, if the electron and hole belong to different (conduction and valence) bands [181], so that at the SN interface, its charge (-e) and spin (σ) are maintained, as shown in Fig. 1.11(b). That means, specular Andreev reflection is like in the usual Andreev reflection, the electron is converted into a hole, but the reflection angle is inverted. This behaviour can be observed in the differential conductance vs. voltage dependence of the SGS junction [182], [183]. The properties of Andreev reflection in graphene depend on whether it is in the doped (EF>> Δ) or undoped regime (EF = 0). This means that electrons that approach the NS interface with energy below the superconducting gap are Andreev reflected with unity probability, because Andreev reflection conserves chirality.

In the SNS junction, Andreev reflections leave a signature in the dissipative branch of the current-voltage characteristics. Even in the absence of phase-coherence, which is required for the Josephson effect, multiple Andreev reflections (MAR) at the two SN interfaces result in a subgap structure for bias voltages smaller than 2Δ/e. MAR were first proposed as an explanation for subgap structures by Klapwijk, Blonder, and

Tinkham [184]. At different bias voltages, MAR contribute to the current in the I-V characteristic.

1.19.2 Time Reversal Symmetry

Supercurrents in graphene are carried by both electron and hole Cooper pairs,which are symmetric about the Dirac point. Even in the pseudo-diffusive mode, the electronic transport in graphene is phase-coherent and obeys time-reversal symmetry (TRS). The dynamics of this superconducting graphene system must be described by the full two-valley, time reversal symmetric Hamiltonian. For the Hamiltonian of graphene to be time-reversal symmetric, E(k) = E(-K) is implied, even in the absence of a magnetic field and spin-orbit interaction. Nevertheless, in perfect graphene, the two valleys are independent and charge-carriers remain in the same valleys. The two electrons/holes in Cooper pairs are related to the time-reversed states, having opposite momentum and spin. For a low-energy charge carrier with momentum k in phase space, its time-reversed state, with momentum -k, occupies the opposite corner of the Brillouin zone. These two phases occupy different valleys, and so have opposite chirality. Because of this, the contact with a superconductor phase coherently couples the two valley states in graphene, which are otherwise decoupled. Charge carriers might experience effective TRS breaking, even in the absence of a magnetic field, although the effective TRS breaking due to second order corrections to the Hamiltonian is weak for low energies and imperfections in graphene such as ripples, lattice defects, and potential gradients. The carrier concentration in graphene is tuneable with a back-gate electrode, and hence, the conductance can be studied as a function of carrier density.

In order to observe this and other interesting effects, ballistic junctions are needed, where the graphene spacer is shorter than the electron mean free path in it. There are reports on Josephson junctions, where results have been interpreted in terms of ballistic transport [148], but later, the same results were explained in terms of diffusive transport [185]. Therefore, more experiments are needed to clarify the electronic transport issue.

For a ballistic Josephson SGS junction, Titov and Beenakker have shown [186] that e the critical current value is I  max(W / L,W /  ) , where L and W are the length c  F 49

and the width of the junction (Fig. 1.12);  is the superconducting energy gap, and F is the Fermi wavelength, F =ev/EF, where EF is the Fermi energy (calculated from the Dirac point) and v106 m/s.

Fig. 1.12a) Schematic of a planar Josephson junction, b) I-V measurement set-up.

Unlike the situation in ordinary SNS short ballistic junctions, where Ic does not depend on L, for graphene-based junctions, at the Dirac point, Ic scales as Ic1/L.

Since the normal state resistance RN  L, the product IcRN is independent of L and, at the Dirac point, IcRN  2/e.

Typically, in SGS Josephson junctions, Al is used for the superconducting electrodes.

Its critical temperature, Tc, is low (1.2 K), and the energy gap is small (0.175 meV), leading to low operation temperatures and a small Josephson critical current. In order to increase operation temperature and work with 4He (rather than with 3He), and obtain higher critical current that will allow for better comparison with theoretical predictions [181],[186], we propose to fabricate and study Nb-graphene-Nb junctions.

In this Literature Review, my progress toward this goal is presented with the primary emphasis on the most recent work, which includes in using the EBL technique is based on the possibility of drawing any pattern without the need for any other lithography technique or for multi-stage processes and pulsed laser deposition (PLD) techniques as applied to hybrid micro/nanoelectronics. The EBL machine in ISEM is capable of drawing both very large and very small size patterns.

CHAPTER 2

2 Investigtion of Graphene for Superonductor (Nb)-Graphene-Superconductor (Nb) junctions

This chapter is devoted to fabrication and characterization of the two-dimensional (2D) ballistic SNS junctions (where S and N denote an ordinary s-wave superconductor and a normally conducting spacer, respectively), where graphene (G) is the N material in this case. The main aim of the study was the electron transport in graphene-based devices, especially SGS junctions.

From the fundamental physics, as well as the practical point of view, it is interesting to fabricate and study these junctions where S electrodes have a higher critical temperature, Tc and there is minimal electronic mismatch between the S and N regions. Both electrodes were made from the same graphene sheet. One of the most promising devices, in terms of its excellent charge transport properties, is made possible by using Single Layer Graphene (SLG) or Bi-layer Graphene (BLG) as a junction material.

Graphene (G) is attractive as a barrier material for Josephson junctions due to high carrier mobility and unsurpassed flexibility in controlling its properties using various methods. In addition, such junctions offer an opportunity for physicists to study “relativistic” superconductivity [150] and unusual proximity effects [181]. Studying these effects and making useful devices is hampered, however, by the quality of the contacts between the G and metal banks [187-189], [190]. Due to the difference in the work functions between the G and metals, Schottky-type barrier may be formed at the interface, thereby significantly changing the transport properties of the metal/G devices.

In attempt to study Nb/G Josephson junctions, we tested transport properties of Nb(/Ti)–carbon(C)–(Ti/)Nb junctions fabricated on exfoliated graphite flakes. Characteristics of the junctions are strongly dependent on the interface properties. In spite of a high junction resistance, presumably associated with the formation of potential barriers at the Nb(/Ti)–C interfaces, the junctions display an overall metallic conductivity. A theoretical model is proposed to explain this behaviour.

The unique material properties of graphene make the device physics totally different from that of the conventional devices. Such devices are promising for development, e.g., of THz detectors and high-speed transistors; the latter was recently demonstrated by researchers from IBM [191, 192] and the University of California [193]. There is a plethora of interesting phenomena relating to the unique properties of graphene-based devices [160].

The technique used here to fabricate the devices includes mechanical exfoliation of graphene flakes and their characterization by Atomic Force Microscopy (AFM) and Raman spectroscopy. E-beam lithography was used to form the geometry of the devices, followed by deposition of thin-film metal leads/contacts using magnetron sputtering and lift-off. Of course, practical applications of such devices are limited due to the geometry of the devices which are made by EBL. The junction’s space and width plays a major role in its device efficiency. The performance of these devices may greatly exceed the present performance of semiconductor devices, ushering in a new era beyond the conventional semiconductor technologies. The device structure and characterization presented in this chapter provide useful information for further improvement of these emerging novel devices.

2. 1 Methods of Graphene Fabrication

A very broad range of graphene fabrication methods are now available and have been optimized to produce graphene single layers, ranging from bottom-up methods, such as decomposition of SiC or carbon, large area chemical vapour deposition (CVD) and chemical processing of graphite oxide, to top down methods, such as unzipping carbon nanotubes and the mechanical exfoliation method. The popular methods of producing or synthesizing single and few-layer graphene are depicted in Fig.2.1.

Another common graphene fabrication technique is to disperse graphene from solution, and sonication of graphite flakes is another possibility. The most widely used standard method of graphene fabrication, however, is mechanical exfoliation which occurs in daily life by writing with a graphite pencil on paper. The first true isolation of single layer graphene flakes was achieved by Novoselov et al. [154] by the mechanical exfoliation (Scotch tape) method.

Fig: 2.1 Single and few-layer graphene fabrication (synthesis) methods [194].

This is the best method to employ for device or electrical property studies. The mechanical exfoliation method is a very simple and low cost method of producing single-layer graphene samples.

Unluckily, this method has several issues, such as uncontrollability, which typically leaves the researcher with numerous sheets of varying thicknesses, so to find and pin down a single graphene sheet for study is like finding a needle in a haystack. It is relatively unsuitable for commercial applications due to the small scale production, but its high quality makes it ideal for use in industrial research or academic institutes to study the fundamental properties of graphene.

Recently, many attempts have been made to improve this exfoliation method to yield high quality single layer graphene, such as stamping methods by using silicon pillars (Liang, Fu et al. 2007) and the electrostatic voltage assisted method (Sidorov, Yazdanpanah et al. 2007) to separate graphene from the bulk crystals. Over the whole of this thesis work, however, this same mechanical exfoliation method is used to fabricate the graphene flakes.

2. 2 Graphene Fabrication – Mechanical Exfoliation method

Graphene and graphite are the 2-dimensional (sp2 hybridized) forms of carbon found in pencil lead. Graphite is a layered material formed by stacks of graphene sheets separated by 0.342 nm and held together by weak van der Waals forces (Kelly 1991). The weak interaction between the graphene sheets allows them to slide relatively easily across one another. The nature of this interaction between layers is not clearly 54

understood, however. The graphene flakes, derived from commercially available highly-oriented pyrolytic graphite (HOPG-10 × 10 ×1 mm) from SPI Supplies, USA, were prepared by the standard micromechanical exfoliation method as mentioned in [154] with small differences in the process.

First, a very important step for the preparation of single layer graphene is cleaning the substrates. Here, I used a fresh degenerately p++ type (1-10 ohm-cm) doped Si substrate capped with 300 nm thickness of thermally grown SiO2 oxide layer (from Siltronics Company, Germany) with predefined unique markers which were patterned by EBL. The process of cleaning the substrate starts with deionized water (5 min in ultrasonication), acetone (5 min. boiling + 5 min. ultrasonication), and then propanol

(5 min boiling + 5 min ultrasonication), followed by 5 min Ar-O2 plasma cleaning.

a) b)

Fig. 2.2 a) Freshly cleaved flakes on 3M-Scotch tape. b) Homogenous distribution of flakes in the same type of (two samples) tapes.

Then the HOPG flake is placed on the centre of a 13 × 2.8 cm2 piece of moderately sticky (3M-Scotch) tape (as shown in Fig. 2.2 (a)). Then the tape is subjected to a peeling (repeatedly folding and unfolding for > 40 times) process until it results in a homogenous distribution of graphite flakes over the entire tape (Fig. 2.2 (b)). The weak van der Waals bonding between the graphene layers in bulk graphite allows for the separation of individual layers, which preferentially stick to the tape. The exfoliated graphite sheets are transferred (deposited) by placing the very light coloured graphite covered side of the scotch tape to face down on the surface of the pre-patterned substrate without any air gaps or bubbles between them. To get good adhesion and avoid those bubbles, the surface of the tape with freshly cleaved graphite crystal) is very firmly pressed on the silicon wafer with thermally grown

SiO2and gently rubbed with a smooth tip for 45 to 50 seconds. Then, the substrate is

very gradually removed from the tape over the course of a more than 30 seconds to ensure that the graphene flakes are not damaged during the peel-off procedure.

In this way, graphite flakes of randomly varying thickness are deposited on the substrate. From an optical microscope image, the position of the flake relative to a unique marker set can be known for further processing. This array of unique markers is patterned on the substrate to identify the position of flakes for further processing under an optical microscope.

2. 3 Graphene Identification by Optical Microscopy Optical microscopy is the most fundamental and simple inspection technique that is used to identify and locate few-layer graphene flakes, including single layer graphene.

The main condition is that the thickness of the SiO2layer will be close to 260 - 320 nm [167, 195]) to enhance the colour contrast between thin graphene flakes and the back (bare Si) substrate. Graphitic films thinner than 50 nm are transparent to visible light, but nevertheless can easily be seen on the SiO2 substrate because of the added optical path that shifts the interference colours. The colour for a 300 nm SiO2 layer on a Si wafer is violet-blue, and the extra thickness due to graphitic films shifts it to blue. The shades of colour may vary slightly for different microscopes in different laboratory. This provides a natural marker that we use to distinguish between three groups of films that we refer to as single layer, bi-layer (2-layer), few-layer (3-10 layers), and multi-layer (more than 10 layers) graphene. Single atomic graphene layers are clearly visible under an optical microscope due to thin film interference effects [195, 196].

Here, I used a Nikon-Optical Microscope (LV-LH50PC) to identify few-layer (including single-layer) flakes. The samples were located by viewing the substrates under an optical microscope in reflection mode with a 100× objective and numerical aperture =0.95.The illumination was provided by an incandescent lamp (Halogen Filament-12 V 50 W). To reduce reflections from the back surface, substrates were placed on a diffusive black cloth. In order to get the highest possible contrast, the light source was altered through a pass-band filter.

Fig. 2.3 (a) and (b) Optical microscope images of thin graphene sheets (2 different samples).

Single and bi-layer graphene sheets were identified by colour interference under an optical microscope. Fig. 2.3(a) and (b), Fig. 2.4 a-f, shows the different samples on (Si) substrates. The size of the thin graphene flakes is typically a few square microns (although the aim was to obtain larger flakes). It was found that producing large size graphene can be mainly achieved by wafer cleaning. A high quality (better cleaned) wafer offers a better chance of getting large pieces [196]. A very clean wafer means that the distance between the wafer and the top graphite layer is very much smaller, so but the van der Waals forces between them are very much stronger. Therefore, single layer graphene is more likely to be absorbed on such a wafer.

Fig. 2.4 (a) to (f) Optical microscope images of thin graphene sheets, scale bar is 7.5 μm. 57

The following images (shown in Fig. 2.4(a-f)) are very thin flakes identified by optical microscope with the help of the unique pre-defined markers, with the process requiring nearly two hours for each sample. The colour variations are clearly visible under an optical microscope. All the images are of different sizes.

These optical images of thin graphite flakes are used in Raith drawing software to design and place the electrodes accurately on flakes. This optical observation is just making sure that the flakes of graphene are present, and it does not have thickness information. In order to find the thickness, I used AFM as the fundamental technique.

2. 4 Graphene Thickness Measurement by AFM

AFM can be used to further investigate the thickness and homogeneity of the graphene sheets. Here, all AFM images were collected on an Asylum Research MFP- 3D, which is operates under ambient conditions using silicon cantilevers with resonance frequencies of 250-330 kHz. Tapping or non-contact mode is used to characterize the thickness of few-layer graphene (FLG) samples. After the optical microscope observation, I used ambient AFM, which provides a straightforward means of spatial mapping, determining surface quality (homogeneity), and measuring the thickness of flakes with nanometer-scale spatial resolution.

Fig. 2.5 a) 3-D AFM image, b) optical microscope, c) thickness profile (7.4 nm) of FLG flakes by AFM.

This non-contact AFM mode was used to quantitatively measure the thickness of the sheets on the substrate which could be used to make the contacts/leads for the graphene properties measurements. Here, I show a few AFM topographical images of 58

FLGs and promising single-layer graphene sheets (SLGs) for thickness measurements. Each flake has a 3-dimensional AFM image (a) displayed with its optical micrograph (b) and its thickness profile (c) for comparison. The following images (Fig. 2.5, 2.6 and 2.7 (a-c)) are shown in the order of the thickness profile measurement by AFM from thicker to thinner few-layer graphene flakes.

a) b)

Fig. 2.6 a) 3-D AFM image, b) optical microscope, c) thickness profile (5.2 nm) of FLG flakes by AFM. The following image (Fig.2.7 (a-c)) shows one of the thinnest flakes, which I measured at 1.31nm by using tapping AFM.

Fig.2.7 a) 3-D AFM image, b) optical microscope, c) thickness (1.31 nm) profile of graphene flakes. The AFM measurement can be unreliable, however, and it has turned out that it does not provide conclusive information about the number of layers and determining the precise thickness [197, 198] for thinner sheets with only a few graphene layers (less 59

than 2-3 nm). Although, the theoretical value of the graphene layer thickness is 0.34 nm, the measured value varies. The thickness of a FLG layer was not always the same and in some cases I even observed that the value was varying on the same sample. This might be due to a free amplitude setpoint of the AFM cantilever, which can have a significant influence on the main signal for the topographical image [199]. To check the influence of the cantilever amplitude, I measured the thickness of various ranges of FLG flakes by using the free amplitude settings and keeping the set point of the cantilever amplitude at a constant value. Also, these inconsistencies in the measured thickness of FLG could be due to the relative thickness of the oxide layer formed during the measurement. Especially on graphite surfaces, capillary forces give strong attractive forces compared with other forces, and since under ambient conditions, a thin water layer is present on most surfaces, AFM can give different thicknesses with the height variance. This discrepancy can be explained by the difference in interaction strength between the cantilever tip and the SiO2 and also between the tip and the graphene. Before characterizing them with Raman spectroscopy, I used to study the morphology of thin graphene sheets by collecting electron microscope images.

2. 5 Surface Characterization of Graphene by SEM Graphene flakes were characterized by scanning electron microscope (SEM) images for surface qualities such as smoothness and uniformity. Here (at ISEM), two SEM machines were used in this work, a JEOL JSM and a FESEMJEOL 7500.

Fig. 2.8 (a) and (b) SEM images of multi-layer\broken-edge graphite layers; (c) folded surface of thin sheets.

LaB6 and tungsten filaments were respectively used as the electron gun source in these machines. Most SEM images were collected at various accelerating voltages

from low to high kV (0.5 kV to 10 kV), with a probe current of about 60 μA. The working distance was always kept around 8-10 mm for the best image of the specimen.

SEM images of mechanically exfoliated graphene on SiO2/Si substrate are shown in (Fig. 2.8(a-b), which clearly reveals how the graphene surface is arranged when the graphene is stacked as multi-layered graphite. They also reveal information on structure of graphene sheets surface. Fig. 2.8(a) and (b) shows low magnification surface images of a graphite flake with crumbled or wrinkled edges, which tells us how compactly stacked the graphene layers are at the broken edges, while Fig. 2.8(c) shows a higher magnification image of few-layer graphene with its puckered edges and its surface has without any organic or other contamination. The locations of the graphene flakes were registered under a scanning electron microscope using the high magnification (10,000×) voltage contrast imaging technique. These SEM images were used to draw the virtual electrode configurations in RAITH- EBL software.

2. 6 High Resolution-Transmission Electron Microscopy Images The following images are high-resolution transmission electron micrcoscope (TEM) images of graphene flakes, obtained by the mechanical exfoliation method. Here I performed the TEM images on cross-section of graphene layer with different electron diffraction patterns, which provide information on the thickness of the graphene film and its orientation relationship, respectively. For any TEM investigation, specimens must be very thin with a typical thickness of ~ 100 nm and transparent to electrons.

a) b)

Fig.2.9. a) and b) HR-TEM images of FLG flake, revealing the single layer graphene thickness as ~ 0.34 nm. The inset to (b) shows the corresponding selected area

electron diffraction pattern, indicating an approximate [001] (or [0001]) orientation for several stacks of graphene layers. To satisfy these requirements, graphene samples were prepared by using a liftout and Focused Ion Beam (FIB) milling at the Electron Microscopy unit, University of NewSouthWales, Australia. After FIB, the sample lifted out and placed on a holey- carbon coated copper grid for TEM imaging. For collecting HR-TEM images, a micromanipulator used to transfer graphene flakes onto a copper grid/mesh.

Each image has its own scale bar. Fig.2.9(a) shows the edge section of an image of a few-layer flake collected in high resolution (HR) TEM on a JEOL JEM 200 microscope, with a few dark lines, indicating ~10 layers. The individual layers can be clearly distinguished, and each single layer graphene sheet is approximately 0.34 – 0.5 nm in thickness, in agreement with the interlayer distance in bulk graphite.

The inset picture shown in Fig. 2.9(b) is a selected area electron diffraction (SAED) pattern, which indicates approximate [001] or (0001) orientation for several stacks of layers. The SAED pattern was measured, which helped to reveals the structure of the graphene. The pattern confirmed the proper arrangement of graphene’s hexagonal atoms, but some of the lattice planes were not bright due to an interference effect from the stacked layers, not just as they would appear from the individual lattice planes. A two white arrows marked on the sample in (b) show the position where a Moiree fringe was observed from the thicker graphene layers stacked in parallel. Fig.2.9(c) also shows the rolled up sheets at the end of a graphene flake, and (d) is an image of a single atomic layer surface with wrinkles.

c) d)

Fig. 2.9(c) Rolled up graphene layers near sample edge. d) Region of graphene believed to be one layer thick

Fig.2.9(e) and f) shows the effects before and after longer irradiation with the e-beam at 200 keV, on what are likely tri- and bi-layer graphene sheets, respectively. The individual layers are clearly visible from the broken edges in these HR-TEM images.

e) f)

Fig. 2.9(e) and (f) images is before (left) and after (right) long exposure to the electron beam, showing the effects of radiation damage on thin samples at 200 keV.

TEM is the finest way to find the layer thickness and understand the structure of graphene. TEM may not be always suitable, however, as it is a destructive analytical tool, and secondly, unlike nanotubes, a 2D crystal does not have a clear signature in transmission electron microscopy. Thirdly, it is very difficult to align 2D samples (single layer) exactly parallel to the electron beam, as they are not easily visible. The few-layer 2D crystal thickness is easily identifiable, however, because of the folded regions. To avoid these issues, Raman spectroscopy was used, as it is a reliable and qualitative method to determine the number of graphene layers.

2. 7 RAMAN Spectroscopy – Graphene Layer Characterization

An important reason for using Raman characterization is that this technique can distinguish the number of layers of graphene through applying the de-convolution method on the 2D bands, so that complete structural information about graphene can be obtained from Raman analysis. It has been widely used for studies of carbon materials, such as carbon nanotubes, synthetic diamonds, and graphene. Raman spectroscopy is a reliable technique which is often used to identify single layer graphene (SLG) [197, 198] and bi-layer graphene with their quality. The standard Raman spectra of several sp2 nanocarbon and bulk carbon materials, mainly monolayer graphene, and HOPG are shown in Fig. 2.10 from M. S.

Dressallhaus et al. [200], which was used as the reference to compare the Raman spectra of my exfoliated graphene (transferred to SiO2/Si substrates) samples.

Fig 2.10 Raman spectra from several sp2 nanocarbon and bulk carbon materials, mainly monolayer graphene and HOPG spectra [200].

The major intense Raman peaks are labelled on the graphene spectra. Here, the red and green coloured Raman spectra denote monolayer graphene and HOPG, respectively. This two (Green and Red color) spectra are used as the reference to compare with my exfoliated graphene sheet’s Raman spectra, which is shown in Fig. 2.11. In monolayer graphene, a D peak at 1350 cm-1 characterizes the defects in this sp2 carbon. Note the absent or undetectably small disorder D peak at 1350 cm-1. This ultra-high ratio of the G to the intensity of the 2D band (unmarked band at 2700 cm-1 in some of the spectra in Fig. 2.10) indicates the defect-free, high crystalline quality of the graphene (small 2D-band peaks). The distinct characteristics of the 2D peak of single and bilayer graphene at 2700 cm-1 are clearly identifiable. It is an unambiguous fingerprint of single-layer graphene with the linewidth of the 2D line approximately 33cm−1 (Fig. 2.10). The distinct feature of bi-layer graphene is a small peak above the frequency of the 2D line of SLG as in Ref. [200]. These preliminary measurements demonstrate that Raman spectroscopy is indeed a useful method to determine the layer thickness of a graphene sample. Note that some authors call the G' peak 2D and the G'' 2D' [201].

Raman spectroscopy was used to verify the number of graphene layers and check their quality. JOBIN YVON HORIBA JY HR800 Raman spectroscopy instrument, which was used in this work to collect the spectra of samples at the Polymer Research Institute (IPRI), in the University of Wollongong, Australia. For the acquisition, the 632.8 nm laser was focussed (100× objective, 60-120 s integration time) directly on the surface of the exfoliated HOPG, which was lying on the Si/SiO2 substrate. This was that the standard graphite Raman spectra could be seen (as shown in Fig.2.11), and the signal to noise ratio maximized.

Fig. 2.11 Raman spectrum of thick graphite flake; inset is optical image.

Fig. 2.11 shows the Raman spectrum of graphene fabricated by mechanical exfoliation, in which the flakes are predominantly bilayer or few-layer graphene. This is a thick graphite flake, however, measured by using 632.8 nm laser power at 2-5 mW. The inset photograph is the optical microscope image of the thick graphite flake. The dominant peaks are the G peak, signature of sp2 bond stretching, the D peak, indicative of the presence of aromatic rings and defects, and the 2D peak, indicating a fourth order scattering process [198], [202]. The peaks and bands in the spectrum are related to the different vibration modes in the material. It highlights the radial breathing modes (RBMs) in the low-frequency region. In the calibration

spectrum (green), the G peak is observed around 1578 cm-1, which results from an in- plane optical mode (E2g) phonon, close to the Γ point, and the 2D or G' peak at 2682 cm-1 is very pronounced, even though the D peak cannot be resolved. The D peak, near 1400 cm-1, is proportional to the defect density and was not observed in the HOPG sample, but the region is marked for reference. Other important peaks can include the D peak near 1620 cm-1 (not visible) and the 2D' or G'peak near 3250 cm-1 just visible. The spectrum in Fig. 2.12 does not display a G peak at desired wavenumber (1585 cm-1) for the sample shown in inset photograph was Few-layer graphene. The measured graphene sheet (as shown in Fig. 2.5 has an AFM-determined height of 7.4 nm, which is very much thicker sample with approximately 20 layers of graphene sheets (in violet colour in inset photograph). This is also one of the main reasons why the finger print of SLG could not be observed. The thick layer (scroll) lying over the Si/SiO2 substrate gave a backscattering effect during the Raman measurement.

360 ------Si/SiO2 substrate 3 500 ------Few-layer graphene 3 000

2 500

2 000

1 500 1144.59

1 000 2 D 1193.03 500 2519.08

0 500 1 000 1 500 2 000 2 500 3 000 3 500 Wavenumber (cm-1)

Fig. 2.12 Raman spectra of Few-layer graphene (Red) (inset photograph) on Si/SiO2 (blue) substrate with thickness of 7.4nm.

In theory, the G peak intensity decreases for thinner layers, while the peak shifts to higher wave numbers at the same time. The 2D peak is broader for a thick layer compared to a thin layer. The distinct feature of bi-layer graphene is a small peak above the frequency of the 2D line of single layer graphene.

In order to avoid damage to the high quality few-layer samples, the laser was not focused for long integration time and close to area where the contacts were fabricated. Fig. 2.13 depicts the effects of irradiation with the laser (long integration time 60-120 s) and the power of the laser (5 mW) by showing the same flake before and after Raman measurement.

Fig. 2.13 Optical images before (left) and after (right) the Raman laser treatment of a flake.

2. 8 Raman Mapping Raman mapping was conducted by using the same JOBIN YVON HORIBA JY HR800 via an optical (Raman) microscope, under 633 nm laser excitation in the backscattering configuration at room temperature. Raman mapping images of few- and single-layer graphene are identified at the edge of a thick sample, which are shown in Fig. 2.14(a) and (b).

Fig.2.14. Raman mapping of multi-layer graphene or graphite: (a) optical image, identified in red in (b). Scale bar is 1μm.

Raman imaging in the form of 100-point mapping was conducted on a few samples. The spectra were acquired via 10 × 10 (100 point) mapping in the vicinity of the actual EBL patterned area, with two spectra acquired and averaged at each point. Since most of these mapping points resulted in “dead scans” with no graphene present, these “flat” spectra were discarded for the statistical analysis. All summarized data were normalized to the 303 cm-1 mode in silicon as it was the back substrate of the graphene samples. (Dead scans on Si with no graphene signature were discarded).

Both multi-layer graphite and single layer graphene were observed in the sample. SLG can be able to clearly seen in the mapping image as the green colour at the edges (Fig. 2.14 (b)) is identified as single-layer graphene.

Fig.2.15 Raman spectra with corresponding Raman mappings (insets) of graphite (ash gray) (a) and SLG (green) (b).

As shown in the spectra in Fig. 2.15(a) and (b), on the edge or scroll of the graphite -1 flakes there is a clear indication of a strong G peak at 1585 cm , representing the E2g in-plane vibrational modes. A small disorder D band appears about 1350 cm-1 in the presence of the aromatic rings and defects which are close to the edge of the single layer graphene flake. The D band corresponds to the in-plane A1g (LA) zone-edge mode [203]. This disordered D band is induced due to SiO2 layer on Si substrate effects, surface contamination, and many peaks caused by single and multiple- resonance effects [204].

These strange properties of the monolayer graphene’s Raman peaks were also enhanced by their dependence on both the material structure and external factors, such as temperature, pressure, doping, and the environment [205]. I did not measure some of very thin layer pristine graphene flakes for device fabrication purposes.

2. 9 Patterning Electrode on Graphene by Electron Beam Lithography (EBL) After verifying the number of layers, I used direct in-situ e-beam writing to make the contact electrodes, wires, contact pads and arrays of markers with designed narrow gaps in a layer of resist. Each lithography system is assigned its own exposure procedure and working sequence. The EBL process comprises several steps. The schematic flow diagram in figure 2.16 explains the operational procedure of the EBL system at ISEM.

Figure 2.16: General EBL procedure flow diagram. 69

The e-beam nanolithography was performed using a conventional SEM (JEOL 6460) integrated with a Raith pattern generation system and a high-mechanical-precision stage to fabricate the electrodes/wires on the graphene. This device fabrication helps in studying the novel transport properties of such patterned graphene. Before transferring the graphene flake, a series (array) of unique features are patterned onto the substrate by using EBL. These unique features labelled with numbers or letters allowed us to easily find flakes and then reference them in future lithography steps such as mix-match and over-lay procedures. To begin, the substrate is spin-coated with a double e-beam resist layer for an undercut profile, which was done using methyl methacrylate (MMA) and poly (methyl methacrylate) (PMMA) resist. On these resist coatings, EBL is a very precise and high-resolution, direct- writing method for forming patterns in a layer of material.

2. 10 Oversize patterns in EBL Usually, EBL is not advisable for bigger or oversize patterns, due to time concerns and resolution issues with drift in stage movement. Generally, it’s drawn by stitching method, in which the large size patterns must be broken down into many smaller WF ones and depending on the pattern size. But, Here I used another method, which is the high end usage of SEM at ISEM clean room facility. The maximum working distance (48 mm) is used to cover the working area for oversize patterns without any stitching or mix-match procedure. Moreover, only a negligible amount of error (± 0.5 µm) occurs in pattern resolution after exposure. The electron beam used for this exposure is high beam current compared to the beam used for high-resolution patterns, due to larger pattern size. Fig. 2.17 shows optical images (b, c) of a cross mark pattern, which is a 10 µm size mark aligned at 60 µm distances to cover the whole (5 mm × 5 mm) area. Additionally, big alignment marks are situated at every 180 μm distance in this 5 × 5 mm size (Fig. 2.17(a)) pattern.

Each row and column mark will have unique features to differentiate it from surrounding features. This helps in finding a specific exposure area or finding the samples, and the marks are very useful in the mix-match type of exposure (explained in the next section) as alignment marks. The typical exposure field used for these oversize patterns is 5 mm × 5 mm on a 1 cm × 1 cm wafer with a thickness of 300 nm PMMA. At the 48 mm working distance, the whole 5 mm × 5 mm working area with

8× magnification. The beam current used for a 5 mm × 5 mm field is 0.087 pA with 15 kV accelerating potential and ‘48’ spot size. By using the large WD, the overall image of the Chessy pattern will be rotated and deflected more, so that the stage movement error will be higher. To avoid these errors, it is necessary to adjust the rotation position manually and set the (u,v) position in the centre of the wafer to draw the oversize patterns (not on the bottom of the wafer).

Thicker and high-atomic weight metals such as gold (Au) are preferred for coating on alignment marks after the development process. A 50 nm coating provides enough thickness for a stronger secondary electron signals, even though it is covered by an e- beam resist for the mix-match EBL process.

Figure 2.17: Oversize exposure: (a) GDSII pattern, optical image of pattern before (b) and after (c) lift-off process. Those arrays of small crisscross ‘Au’ alignment marks were made by optical or E- beam lithography (1 cm × 1 cm) or EBL (5 mm × 5 mm) at the beginning of the mix- match procedure (explained in next section).

2. 11 Mix-Match Exposure The Mix& Match technology has long been used by the microfabrication facilities to utilize their lithography equipment more efficiently. One of the most efficient ways to utilize the EBL system is by using a mix-and-match process for reducing the principal costs and increasing throughput yield in a semiconductor manufacturing company. Mix-match fabrication is a highly challenging procedure, since much effort needs to 71

be spent on alignment. The intention in the mix-match process done with EBL alone is to minimize the sample contamination and also achieve high resolution for submicron size features. Sometimes, combining photolithography with EBL is preferred to using a mix-match process, but this depends on the size of the features. Usually, it involves a multi-level lithography step. In this process, exposing a pattern into an existing pattern (exposing large structures consisting of wires, pads and several alignment marks) or overlapping the patterns made by photolithography or electron beam lithography on the specimen. This process use different alignment schemes, also different maximum field sizes.

Sample preparation  Expose the (first layer is smaller writefield size for contacts) smaller pattern by using pre-aligning marks to precisely locate these smaller or finer ‘contacts’ on desired place on the wafer.  Then expose the large patterns (second layer is bigger writefield size for wires), which is overlay the smaller patterns. These large patterns must have markers for the smaller field.

Figure 2.18: Mix-Match exposure: (a) GDSII pattern (contacts), (b) after exposure.

Generally, a minimum of two patterns will be needed for mix-match exposure and several global marks to match those two patterns by alignment (rotational and shift displacement of stage from sample). Hence, it is necessary to prepare the pre-defined marks on the substrate and design the whole pattern (including alignment marks, contacts, wires, and pads) in the GDSII database (pattern generator) (Fig. 2.18). In the 72

two patterns, the contacts are drawn in one layer, and wires and contacts in another layer. While drawing, the small working area (contacts) in one pattern overlays the large area (wires, pads) the other and both should have the same centre (u, v) values of field. The substrate has at least a 4 × 4 matrix array of cross marks inserted with a mark scan box, or each mark is labelled with unique indexing (as shown in Figs. 2.17 and 2.18 for oversize patterns) to make it easy to locate or identify the area of interest. The size of the global alignment mark depends on the pattern requirements. A calibrated write field is selected for both patterns before the mix-match process. The SEM images of thin graphite flakes are imported as GDS II data files in the Raith software program, in which the electrode is designed. After formation of the e-beam resist mask, a bilayer of Ti (2 nm) and Nb (40 nm) is deposited using DC magnetron sputtering, followed by lift-off in acetone. These metallic depositions allow easy measurement access and the titanium ensures a good electrical contact to the graphene. One of the typical configurations of the fabricated device is shown in Fig. 2.19. Here, I made the electrodes at separate distances ranging from 150 nm to 800 nm, and the devices were fabricated in invasive probe geometry (As shown in Fig. 1.18 b). Finally, the sample is ready to be mounted in a chip carrier and wire-bonded.

38µm

Bonding Pads

Junction Area

L = 0.43 µm W = 10 µm Alignment Mark T = 148 nm Ti/Nb = 2/40 nm

Fig.2.19. Contacts on a graphene flake through mix-match EBL exposure (Scale bar is 38 µm). Inset shows AFM image of the device G1 made on 148 nm thick carbon flake with its geometrical dimensions. 73

The whole fabrication process for the electrodes is illustrated in Fig.2.20 as step-by- step. Mainly it contains four steps as follows: 1. Wafer cleaning by ultrasonication in Pirana solution followed by de-ionised water, isopropyl alcohol, and acetone, respectively.

2. Spin coating of e-beam resist on ultrasonically treated Si/SiO2 clean substrates. 3. E-beam exposure by standard conventional EBL to pattern contacts, wire and pads (mix-match exposure). 4. Sputtering the metal coating of Ti/Nb and lift-off process. Metal deposition typically is done by e-beam evaporation and RF-magnetron sputtering.

Fig.2.20 Process of fabricating graphene device through e-beam lithography. On the one hand, e-beam lithography on graphene has the advantage that it can pattern leads of arbitrary configuration with very small spacing (tens of nm) between them. On the other hand, the main disadvantage is that the graphene will be exposed to many chemicals, which may introduce organic pollutants into the graphene and affect its properties and nature.

A total four devices were fabricated and tested. Graphite flakes were deposited onto oxidized Si substrates by mechanical exfoliation of highly oriented pyrolytic graphite (HOPG). Using e-beam lithography, a PMMA mask was patterned on the graphite flakes. Then 2 nm of Ti was deposited, followed by 40 nm of Nb, to form devices G1 and G3; in devices G2 and G4, 40 nm thick Nb film was deposited directly onto the flakes. Prior to deposition of the Ti and Nb layers, 4 nm of the surface layer were removed from device G1 (made on thicker flake) by ion milling; no ion milling was used for devices G2 to G4 (which involve thinner flakes). The thickness of the flakes was measured using AFM (inset of Fig. 2.19). The device parameters are summarized in Table 2.1. Figure 2.24 (a) shows an SEM image of a typical device structure; Fig. 2.24 (b) shows a schematic of the I–V curve measurement.

2. 12 Junction Configuration –Device Packaging

The substrates with the devices (samples) on them were glued (using a varnish) to a chip-carrier plate with Cu contact pads to which Cu wires were soldered by ultrasonic bonding. Because the electrical contacts on the chip are separated from the substrate by a 300 nm thin silicon oxide layer, the bonding has to be done carefully in order to prevent gate leakage. Then, the device contact pads and the plate contact pads were wire-bonded; the plate itself was glued (using the same varnish) to a standard MPMS Quantum Design probe, and the sample wires were connected to the probe wires using screws. The probe was placed into the PPMS Quantum Design apparatus to perform I- V characterization. As shown in Fig. 2.21 (a), and (b), four devices were fixed in two different chip-carrier plates. The four devices were designated as G1, G2, G3, and G4.

a) G1 G2 b) G4 G3

Fig. 2.21 (a).G1 and G2 devices, (b) G3 and G4 devices.

Device dimensions are given in the following Table 2.1, with details of the graphene thickness (measured by AFM), electrode materials and gap length.

Table 2.1 Summary of the device parameters. Material of leads Gap Device Device Flake thickness (in parentheses between resistance at 5 K Number by AFM (nm) thickness in nm) Leads (nm) and 5 mV(Ω) G1 Ti(2)/Nb(40) 430 148 224 G2 Nb(40) 640 19 … G3 Ti(2)/Nb(40) 440 9 369 G4 Nb(40) 170 8 600

2. 13 I-V Characteristics of Nb/Ti – Carbon – Ti/Nb Junction

In order to record I–V curves, dc current from a battery-powered, computer- controlled power source was fed into the junction in steps of about 0.06 μA; the voltage across the junction was amplified and acquired by the computer using a National Instruments analog-to-digital converter.

Devices measurements were carried out in a Quantum Design PPMS cryostat at temperatures down to 1.8 K using a two-probe method. Due to the latter, the measured resistance (see Table 2.1) contains a 25 Ω contribution from the wires. Measurable characteristics were obtained for devices G1, G3, and G4; the resistance of the device G2 was too high to be measured with our technique. The measured characteristics of the different devices were similar and displayed a nonlinearity of the I–V curve which was most pronounced for device G1. The I–V curves of this latter device, taken at various temperatures, are shown in Fig. 2.23 (a). The junction resistance increases significantly with increasing temperature starting from about 7.0 K, indicating the beginning of transition of the Nb film into a resistive state (the critical temperature, Tc, is reduced for a 40 nm-thick Nb film as compared with usual Tc ≈ 9.0 K for our thicker films). At the temperatures of the experiment, a Josephson current was not observed in the I– V curves. In order to see if the I–V curves have nonlinearities, we differentiated them numerically to obtain dV/dI vs. V dependences. The most pronounced features were observed for sample G1 (see Fig. 2.23 (b)). Numerical differentiation typically results in “noisy” curves. Better results can be obtained using ac modulation, a “physical differentiation” technique; however, in these preliminary experiments, we used the available digitized data, which already showed interesting properties. Specifically, we 76

found that the differential resistance shows structure associated with the superconducting transition in Nb, and an overall metallic-like conductivity (initial portion is concave up), in spite of a high junction resistance presumably associated with the formation of potential barriers at the Nb/Ti–C interfaces. In order to better reveal the features in the noisy dV/dI vs. V dependences, we smoothed the curves using an adjacent averaging algorithm available from commercial software. As a result of averaging we obtained two traces (black curves) corresponding to “forward” and “backward” current ramping for the dependences taken at specific temperatures. Reproducibility of these traces, especially at the lowest temperatures, and the symmetry of the positions with respect to zero voltage (designated by arrows) argue that the observed nonlinearities are associated with the physical properties of the system and are not spurious. In samples G3 and G4 the nonlinearities were weaker, and the resistance of the junctions was higher, as shown in Table 2.1. Below we consider properties of the sample G1 in a more detail. The dimensions of our sample as determined by AFM (inset of Fig. 2.19) are: Nb/Ti lead spacing, L = 430 nm; junction width, W ≈ 10 μm; and flake thickness is 148 nm.

Given this thickness, the electric properties of the flake should be regarded as those of the graphite. Then, assuming that the resistivity of graphite is about 9 × 10 –6 Ω·m, and taking into account its temperature dependence [206], we estimate that the resistance of our junction should be about 6 Ω; in fact, it is 224 Ω at low temperatures. Excluding the contribution of 25 Ω from the wires and 6 Ω from the graphite flake, we obtain a resistance of 193 Ω, which is probably originating from the interfaces between the Ti/Nb and the graphite flake.

Assuming that the two interfaces are identical, with an average area of A = 1 μm × 10 μm, we obtain the specific tunneling resistance (R × A) of the interface to be of the order of 10 –5 Ω cm 2, indicating a rather strong barrier. It is known that such a barrier appears at the metal–G interface due to the different electron concentrations and work functions [190], [207].

Fig.2.22. SEM image of the device G1 made on 148 nm thick carbon flake (a) and schematic of the I–V curve measurement (b).

At lower temperatures, features are observed in the dV/dI(V) dependences (marked by arrows in Fig. 2.23 (b)). It is interesting to compare characteristic energies of these features with the Nb energy gap, Δ. Using the Bardeen–Cooper–Schrieffer (BCS) relation 2Δ/ kBTc = 3.52 (where Δ is the superconducting energy gap, kB is the –5 Boltzmann constant, kB = 8.62 × 10 eV/K), with Tc ≈ 7 K as deduced above, we obtain an estimated maximum value Δ ≈ 1 meV. Because the device consists of two Nb/Ti–C junctions connected in series, one may expect manifestation of the gap-sum feature at about 2 mV; however, we observe a conductance peak within a voltage range of about ±1 mV (see curves for 1.8 K), and the conductivity anomalies at higher voltages (∼4 and 7 mV). The first feature (conductance peak around zero voltage) may be indirectly related to the gap but rather to a contribution of the “reflectionless” Andreev reflection (AR) process (see our theoretical model below). The features at about 4 and 7 mV (Fig. 2.23 (b)) are unusual. A similar anomaly (as well as metallic junction type) was observed by Choi et al. [190] for devices reported to be made from monolayer graphene [208]. The peaks at V > 2Δ/e can appear if the energy gap is induced in C, as explained in the next section. Further investigation is required to establish the nature of these features. For this study, most important is the fact that the device conductance has a maximum at zero voltage (i.e., it is of metallic-type). Metallic type of conductivity takes place in junctions with high-conductive channels. Also, the conductance may continuously increase with voltage if the barrier is not rectangular but its width decreases with

energy; it is suggested that the metal–G interface barrier has essentially a triangular shape [190], [208]. The barrier is probably also asymmetric, as follows from the asymmetry of the dV/dI(V) dependences with respect to zero voltage (cf. Fig. 2.23(b)). However, if a nonrectangular barrier is the only reason for the increase in the conductance, then it should not have an inflection point, as indicated here and in Refs. [208-210]. Therefore, we have to look for another mechanism for such behavior. First, we analyze the junction resistance in a more detail. In general, there are three contributions to the junction resistance: (i) the Schottky barrier resistance due to difference of the work functions; (ii) a contribution due to a change in the number of channels for quantum tunneling from three-dimensional (3D) metallic electrode into the essentially two-dimensional (2D) graphite flake; and (iii) the resistance of the flake itself (estimated to be 6 Ω for the device G1); and (iv) a finite resistance originating from the mismatch of electronic properties between the two regions—the C just below the metal (G′), where electronic structure is modified due to the contact with the metal, and the open C region (G″). A schematic cross-sectional view of the device structure is shown in Fig.2.24.

Fig. 2.23. I–V curves of Nb/Ti–C–Ti/Nb device (G1) at various temperatures from 1.8 to 7.5 K (a). Numerical derivatives, dV/dI (V), for the I–V curves measured at different temperatures T, K (thin grey lines). Curves for 3.0, 4.0, and 5.0 K are arbitrarily shifted in vertical direction for clarity. Thick black lines are averaged curves (see text for details) (b).

One can separate the contributions (i) and (ii) to the interface resistance from the experimental data by analyzing the ratio of the excess zero-voltage conductance (measured at a very low temperature) to the normal state conductance. We estimate 79

this ratio by comparing zero-voltage differential resistance values at 1.8 K (the lowest temperature accessible in this experiment) and 5.0 K. The choice of the curve for 5.0 K is dictated by the fact that, at higher temperatures, an increasing overall shift of the differential resistance curve appears, indicating that some regions of the Nb leads become resistive below an estimated Tc value of 7 K; this makes the curves for higher temperatures unsuitable for the estimation. Then from the results shown in Fig. 2.23 (b) we obtain an excess resistance for the 5.0 K curve of 2.7 Ω, which implies that the excess zero-voltage conductance due to contribution (ii) above is about 1.4% of the interface conductance. For the qualitative consideration, most important is presence of an excess conductance (the true value should be even slightly larger), which we discuss below.

2. 14 Theoretical Model for Nb/Ti-2D- carbon-Ti/Nb junction

A theoretical model proposed here is based on single-layer graphene that is a 2D material. The junction region in our devices contains many carbon layers; i.e., it is a graphite flake rather than graphene (although in the literature even multilayered carbon samples have been often referred to as graphene). However, the epitaxial graphite is highly anisotropic material with the conductivity along the crystal planes being hundreds of times larger than across the planes [163]. For this reason, we believe such a model can qualitatively explain transport properties of our system, specifically, the large value for the junction resistance (R0 = 193 Ω in device G1) coexisting with the metallic-like shape of the dV/dI(V) curves at T < Tc , Nb as seen in Fig. 2.23 (b). On one hand, the overall high value of dV/dI(V) indicates that a low-transparency barrier is formed at the metal/carbon interface. On the other hand, the metallic-like shape of dV/dI(V) implies that the electric transport involves AR process that usually occurs at high-transparency interfaces. These two apparently contradictory facts can be reconciled within a model in which the metal/2D C contact is simulated by double- barrier S–I–G′–I–G″ junctions connected in series. The model is based on the modified BTK theory [184]. We shall show that the model qualitatively explains the experimental data taking into account the nanodevice geometry and the assumed interface structure. More technical details of the model are explained in the Appendix.

An important distinction between the junction considered within the BTK model [184] and our device is the change of electron state dimensionality 3D → 2D in the tunnelling process between the Nb/Ti electrode (S electrode) and the C in the latter case. The number of quantum channels in 2D C is finite, which limits the tunnelling probability from Nb/Ti into C. Another difference between the BTK model and our geometries stems from a specific electron momentum conservation in our case. On one hand, only the electrons with momentum p⊥ perpendicular to the interface contribute to the conventional tunnelling (CT) between the Nb/Ti (S-electrode) and 2D carbon. On the other hand, only the electrons whose momentum p∣∣ is parallel to the interface actually contribute to the AR process. This is due to the fact that the AR occurs on a much longer scale, of the order of the coherence length in 2D C ξG , rather than the regular tunnelling across the C layers which occurs on a scale of order the lattice constant a [211]. Yet another difference between the model of Ref. [184] and our model is that, in the 1D geometry

[184], an electron incoming from the N electrode reverses its momentum (px → – p x) after being normally reflected from the S/N interface barrier. For finite interface barrier strength Z ≠ 0 this causes suppression of the electric current at voltages

|V| < ΔS/e. In our geometry this does not happen since during the reflection at the S–I–G′ interface the x-component of the electron momentum is not reversed, px → px.

Fig.2.24. Various processes involved in the electric transport in a Nb/Ti–C junction: in process 1, an electron moving in 2D C flake from left can be either Andreev- reflected as a hole moving in opposite direction or normally reflected (not shown) from the interface A between the regions G″ and G′; inside the area G′, it can be either Andreev-reflected at the Nb/Ti–C interface I creating the Cooper pair in Nb (process 2), or continue moving in the graphite sheet ballistically (process 3). If the electron 81

energy E is low (E ≪ U0), the electron bounces many times back and forth between the two barriers at x = xA and x = xB (process 4) before it is either Andreev-reflected from the Nb/Ti–C interface or it escapes the contact region into the open C sections G″.

In this model, it involves two very different characteristic scales—an “access” length

[212], LT , and the coherence length in 2D C, ξG , which are related as LT ≪ ξ G . The short length LT ≈ a characterizes CT of electrons between the 3D Ti/Nb electrode and

2D carbon perpendicular to the Nb/Ti–C interface (p⊥ ≠ 0). The much longer ξG is related to AR at the 3D/2D Ti/Nb–C interface which occurs in parallel with the

Nb/Ti–C interface (p∣∣ ≠ 0). This is shown schematically in Fig.2.24 as process 2. Additionally there is another AR at the transitional G′/G″-region between the C section under the metal contact G′ (highlighted by lighter color in Fig.2.24) and the C outside the contact region G″. We assume that the G′/G″ interfaces are characterized by potential barriers A and B shown in lower panel of Fig.2.23 and located at x = xA,B.

The superconducting order parameter, ΔG, induced due to the proximity effect, is finite not only in G′, but also in the uncovered C section G″ and spreads outside the contact area on the coherence length scale ξG. Thus the main contribution to the junction resistance comes from the CT through the Nb/Ti–G′ and G′/G″ interfaces.

The CT, acting during the first stage, actually restricts the AR to just a small fraction of electrons coming from Nb to C. The next stage is dominated by AR which takes place on a much longer spatial scale ξG. This AR process involves only the electrons whose momentum is parallel to the barrier component, i.e., p∣∣ ≠ 0. In the latter case, since the contact length Lc = LG′ + 2 LG″ (see Fig.2.24) is Lc ≫ a, the electrons spend much longer time Lc/vF near the barrier before being Andreev-reflected (here vF is the

Fermi velocity in C). Because Lc/vF ≫ τT (where τT is the CT time through the Nb/Ti– G′ barrier), the prolonged stay of electrons near the Nb/Ti–G′ barrier strongly increases probability of the AR T2 as compared to the CT probability T1 for electrons with p∣∣ ≠ 0. Another important contribution comes from the “reflectionless” AR which happens when an electron spends sufficient time in vicinity of the N/S interface. The corresponding dwell time, τd, should much exceed the duration of an individual AR process, τAR, which is the case for an electron residing in the region G′.

Furthermore, the τd is energy dependent. In our theoretical model we assume that the prolonged dwell time in the region G′ is caused by multiple reflections of electrons back and forth from the barriers A and B (see Fig.2.24). In this model, the energy dependence of the τd naturally originates from the energy dependence of transparencies of the barriers A and B. At low energies, E ∼ 0, the barriers are thicker and thus less transparent, which corresponds to a longer dwell time τd ≫ τAR. An electron tends to bounce several times between the barriers A and B before leaving the region G′. The barriers are thinner and more transparent as the electron energy increases, which makes the dwell time shorter, τd ∼ τAR. For this reason, the probability of the “reflectionless” AR is higher at low energies, and a conductance peak appears around zero voltage. We believe the feature within the voltage interval of about ±1 mV (cf. Fig.2.24(b)) is caused by this process. The peak width is determined by the energy dependence of the transparencies of the barriers A and B rather than by the Nb energy gap magnitude.

Summarizing, all the electrons with p⊥ ≠ 0 contribute into CT although its probability could be small due to presence of a finite interface barrier. On the other hand, only a small fraction of electrons with p∣∣ ≠ 0 contribute to AR from the Nb/Ti–G ′ interface, although the AR process probability is high. The associated transmission factors are small in the first case and much larger in the second case, which explains the apparent contradiction of the observed behaviors. The calculations have been performed by solving the Dirac equation for G and using the S-matrix technique extended to include superconducting correlations [150, 181]. Since the real device (cf. Fig.2.22) has two metal-carbon contacts, each of them assumed to have the double barrier S–I–G′–I–G″ structure shown in Fig.2.24, the device is modelled by two S–I–G′–I–G″ junctions connected in series. Here S stands for the superconducting metal, I is the interface barrier, G′ is the carbon under the contact, G″ is the open carbon. The computed differential resistance dV/dI(V) of such a double barrier S–I–G′–I–G″ junction is shown in Fig.2.25 where we used the S–I–G′ subjunction transparency, T1 = 0.04, and the G′–I–G″ subjunction transparency,

T2 = 0.65. One sees three pronounced features in the dV/dI(V) curve. The feature within the voltage range ±1 mV corresponds to reflectionless tunneling, as described above. More specifically, as an electron traverses the contact area enclosed between the two barriers at x = xA and x = xB , it either can be Andreev-reflected with 83

probability T1 at the S–I–G′ interface, or it can be normally reflected (or transmitted) with probability R2 (T2) at the G′–I–G″ interface barrier. The number of reflections depends on the electron's energy since the transparency of the potential barriers at x = xA and x = xB is energy-dependent. At low energies, the electron can bounce back and forth several times which increases the AR probability considerably [210]. This results in a pronounced minimum in the dV/dI(V) curve in the vicinity of V = 0. The second feature at V ∼ 2 (ΔNb +ΔG′)/ e is related to AR in the S–I–G′ subjunction. Here AG is the proximity energy gap induced in the layer adjacent to the metal. There are two such S–I–G′ subjunctions in the measurement circuit which yields the coefficient

2. The third feature at V ∼ 2 (ΔNb + ΔG′ + ΔG″)/e corresponds to AR at the G′–I–G″ subjunction which is connected in series with the S–I–G′ subjunction. Similarly, since there are two G′–I–G″ subjunctions in the circuit, it also gives the factor 2. Note that the shape of the feature at V ∼ 2(ΔNb +ΔG′)/e is different from the shape of another feature at V ∼ 2(ΔNb +ΔG′ +ΔG″)/e. The difference comes from different geometry of the S–I–G′ and G ′–I–G″ subjunctions. During the reflection in the S–I–G′ junction, the x-component of the electron momentum is not reversed, px → px, whereas it is reversed in the reflection process at the G′–I–G″ subjunction, resulting in px → – px.

The calculated data reveal an excess conductance at voltages | V| ≤ 2 (ΔNb + ΔG′)/e for

1 > T2 > 0.5, in qualitative agreement with our experimental observation.

Fig: 2.25. Calculated differential resistance of the Nb/Ti–C–Ti/Nb junction. A broad minimum in the vicinity of zero bias is caused by the reflectionless tunnelling inside the contact region (xA < x < xB). An even broader minimum at the voltages | V| ≤ 2

(ΔNb + ΔG′ )/e occurs due to the AR in the S–I–G′ subjunction (where ΔG′ is the proximity induced energy gap in the C under the metal). Additional tunneling-like feature occurs at | V| ∼ 2 (ΔNb + ΔG′ + ΔG″)/e where ΔG″ is the proximity induced gap in the open carbon regions G″ right outside the contact area (cf. Fig.2.24). 84

Similar excess conductance has been reported not only for superconductor–graphene– superconductor junctions [208], [209, 210], but also for the Nb/Pd–CNT–Pd/Nb junctions (where CNT stands for carbon nanotube) [213, 214], implying that our model may be applicable for a broader class of systems than considered here.

FIG.2.26. The Nb/Ti–C–Nb/Ti junction which is composed of two Nb/Ti–C block contacts. Each of the Nb/Ti–C contacts is represented in our model by the double barrier S–I–G′–I–G″ junction (cf. Fig.2.24 in the main text) (a). The normalized “reflectionless” conductance σ(V) of the S–N–I–N junction computed within the BTK model with the broken line trajectory ( r1 = 0). The energy gap is Δ = 1 + i · 0.002, transmission coefficient through the barrier I is t1 = 0.3, 0.8, and 0.95 (b). The same characteristic as before but for the straight line electron trajectory when r1 = Z1(2i – 2 Z1)/(4 + Z1 ) (c). AR in the asymmetric S–I–S′ junction where S and S′ are superconducting electrodes characterized by different energy gaps Δ′ = 0.8Δ (d).

The computed conductance is represented in Figs. 2.26 (b) and 2.26 (c). In Fig. 2.26(b), we plot the conductance of the S–N–I–N block junction assuming that there is no conventional reflection at the N–I–N interface (i.e., we set r1 = 0 according to

our broken-line trajectory model). From Fig. 2.26(b), one can infer that the conductance vs. voltage dependence follows the shape of the barrier less AR, while its 2 amplitude is strongly reduced due to the low-tunneling amplitude, 푡1 ≪ 1, through the interface barrier I. For comparison, Fig. 2.26(c) represents results for the conventional BTK model that assumes the electron trajectory is a straight line and the reflection

2 coefficient is finite and defined as r1=Z1(2i−Z1)/(4+푍1 ) ≠ 0.

As an illustrative example, first assume that no superconducting proximity gap is induced in C. We then represent the S–I–C–I–S junction as a combination of two S–

N–I–N and N–I–N–S block junctions. In the simplest approximation Z2 = 0 (i.e., there are no barriers at the S/N and N/S interfaces). Then, in the one-dimensional BTK

2 model, one gets r1=Z1(2i−Z1)/(4+푍1 ) . On the other hand, in our broken-line model, we use r1 = 0. The other parameters are common for the both cases,

2 (1) (2) (2) t1=(1+iZ1/2)/(1+푍1 /4), 푡퐴 =0, t2=1/u0, 푟퐴 = (v0/u0), r2=0, and 푡퐴 =0. We also consider an additional contribution from multiple AR processes occurring when an electron bounces back and forth inside the contact region G′. Such multiple processes are illustrated in Fig.2.24. The multiple AR scenarios takes place as follows. An electron e enters the contact region G′ from the uncovered C section G″ Since there are two potential barriers separating the G′ and G″ regions [210, 215] after entering G′, the electron is Andreev-reflected many times inside G′ before it exits into G″ region.

2. 15 Results of Nb/Ti-Carbon-Ti/Nb junction

A more realistic correspondence with the experimental data can be achieved if assume that a finite superconducting energy gap is induced in carbon as a result of the proximity effect. Then have an S–S′–I–N block junction rather than an S–N–I–N junction. Qualitative agreement with the experimental data shown in Fig. 2.24 can be obtained if assume that the energy gap Δ′ induced by the superconducting metal electrode in the carbon region G′ (i.e., S′) is only slightly smaller than Δ in S. The S–S′–I–N–I–S′–S junction is composed of two S–S′–I–N and N–I–S'–S block junctions (cf. Fig. 2.26(a)); its calculated differential resistance dV/dI vs. voltage V is shown in Fig. 2.25. The calculation shows that there is a visible suppression of the resistance at voltages –(ΔNb + ΔG)/e < V < (ΔNb + ΔG)/e occurring when the AR 86

probability 1 > T2 > 0.5. In our experiment, the excess Andreev conductance (which corresponds to the suppressed differential resistance) occurs in the bias voltage interval corresponding to four S–I–S′ junctions connected in series. The two junctions originate immediately from the Nb/Ti–C 3D/2D interfaces, whereas two additional S′–I–S″ junctions are formed inside the carbon layer between the region underneath of metal (G′) and outside adjacent region (G″) as shown in the lower panel of Fig.2.24. The four junctions connected in series thus provide the bias voltage interval

−4(ΔNb + ΔG)/e < V < 4(ΔNb + ΔG)/e (where (ΔNb + ΔG)/e ∼ 1.9 mV) for the excess Andreev conductance (suppressed resistance). Similar phenomena have been reported recently for the Nb/Pd/CNT/Pd/Nb junctions [213, 214]. More details of Fig.2.26 is given and explained in appendix of Ref. [216]. Experimental data on Nb(/Ti)–C–(Ti/)Nb junctions reveal a strong barrier at the metal–C interfaces, which probably results in suppression of Josephson current in the devices down to 1.8 K. However, the device conductivity is metallic-type, which is not expected for the strong interface barriers. A theoretical model is presented which explains this apparent contradiction in terms of two tunneling processes: CT between the Nb(/Ti) electrode and 2D carbon, and the second process, associated with the AR which also involves “reflectionless” processes. The associated transmission factors are small in the first case and much larger in the second case, leading to a noticeable contribution of the AR to the conductivity.

CHAPTER 3

3 Optimization of YBCO thin film growth by Pulsed Laser Deposition (PLD) for photon detectors Applications

This chapter is dedicated to finding a suitable combination of substrate and buffer layer that has been optimized for high quality superconducting thin films of

YBa2Cu3O7-x (YBCO). It has to be a smooth surface, which can be used for photon detector nanowire fabrication. Superconducting properties of YBCO film on various substrates and also buffer- layered YBCO thin film properties for optimization of critical current density (Jc) and critical temperature (Tc) in various applied magnetic fields and at various temperatures were determined by transport and magnetic measurements in a Magnetic Properties Measurement System (MPMS). Apart from the superconducting characterization aspects, the thickness of YBCO film with high quality superconducting properties was optimized in terms of its structural dimensions (suitable geometry) for nanowires patterning or device fabrication by Electron Beam Lithography (EBL) techniques, and chemical etching. This optimized patterning structure can be used in the Superconducting Single Photon Detector (SSPD) to increase the device efficiency. I have investigated the properties of 65 ± 5 nm thick YBCO films grown simultaneously (explained in this chap.3) on different substrates (i.e. SrTiO3, LaAlO3, MgO and Yttrium Stabilized Zirconia (YSZ). By optimizing the deposition rate (repetition rate in Hz) of the PLD system for some substrate/buffer material combinations, the surface morphology of the YBCO film was effectively improved, and there was only a small or no degradation of their critical temperature values. These structures point the way to further development of fabrication technology for YBCO-based SSPD devices. A comprehensive analysis of the structural and electromagnetic properties of ultra-thin films will be presented, and their applicability for SSPD application will be discussed. Since the successful demonstration of in-situ preparation of YBCO thin films with high Tc and high Jc by the PLD technique by Venkatesan et al. during late 1987 [217, 218], it has been a widely used technique to prepare epitaxial thin films of any oxide material, including HTS materials. Among the various fabrication techniques, PLD

produces films with high quality and maintains the same stoichiometry as the target material [219]. In-situ YBCO superconducting thin films were fabricated by the Pulsed Laser Deposition (PLD) technique. An excimer KrF laser (Lambda Physik COMPex 205) source (wavelength λ = 248 nm) was used to evaporate YBCO and buffer targets with 450 mJ pulsed laser energy. A multi-target holder allowed simultaneous mounting of buffer and YBCO targets [220]. The surface quality of the initial YBCO film is crucial for device fabrication. To achieve a high efficiency SSPD device, the sample (YBCO thin film should be ≤ 10 nm thick [103] and structured into ~100 nm wide wires) must have high quality superconducting properties including a smooth surface, high critical temperature Tc, narrow transition width, ΔTc, and high critical current Ic. These requirements are quite difficult to meet due to the structural complexity of YBCO films. In [221], demonstrated that reduction of YBCO film thickness from 90 nm to 28 nm leads to degradation of its critical temperature from 89 K to ~70 K. Structuring of the film also causes degradation of the physical properties of YBCO structures. 500 nm wide and 12 nm thick YBCO wires, however, that are functional below 65 K have recently been realized with the help of Focused Ion Beam (FIB) milling [222].

Moreover, the film properties (Tc, the super current, Is) can be affected by the presence of extended imperfections or defects such as grain boundaries, droplets, etc., [223]. Recently, great efforts have been focused on its surface morphology and high

Tc for SSPD and other research related applications [224]. In addition, recent studies suggest that the fine grain morphology of the high temperature superconducting (HTS) oxide thin film enhances its optical detection sensitivity [225], and it is also suggested that the edge roughness of the superconducting thin film enhances the detection efficiency of SSPD detectors [226]. In order to increase the surface quality (smoothness) of YBCO thin films, introduced a buffer layer between the substrate and the HTS film as mentioned in [62], which can work in a similar way to YBCO multilayering [220], [227]. The latter was found to dramatically improve the surface smoothness, as well as electrical properties of YBCO thin film [220] and step-edge Josephson junctions [228]. Our choice of buffer layer is based on the parameters (listed in Table 1.1), such as lattice mismatch, chemical stability at higher temperature (~780˚C), and a good structural match with the superconducting films and the 90

underlying substrates. Based on the above criteria, I have chosen three different materials for buffer layers, SrTiO3 (STO) [229], CeO2 [65], and PrBa2Cu3O7 (PBCO) [230]. These buffers have received great attention due to their compatible properties (listed in Table 1.1) with YBCO thin films and substrates.

3.1 X-Ray Diffraction (XRD) characterization of YBCO film

XRD is a highly versatile and straightforward technique used for identifying the crystalline phases present in the films and for analysing the various structural properties, such as stress, grain size, phase composition, crystal orientation, and defects composed of different phases for any form of the material, such as quasi-, mono-, and polycrystalline-like thin films, powder, and bulk samples [231, 232] . This section provides an overview of the XRD analysis techniques that were used to characterise the thin film quality. Samples were mounted using modelling clay (Blu- Tac™), manually centred and rotated for maximum diffraction intensity in GBC- MAC-Science X-ray diffractometer.

A typical XRD pattern of an epitaxial YBCO thin film, with a single orthorhombic phase and c-axis orientation, should only reveal the presence of (00l) peaks, and the c-axis lattice parameter is c = 11.68 A˚. The distance between successive planes for the orthorhombic phase can be expressed by [233]

1 ℎ2 푘2 푙2 = + + 푑2 푎2 푏2 푐2

By using this formula one can predict that the interlayer (c-axis) distance of YBCO will be in the XRD pattern.

From Fig. 3.1 the x-rays are reflected from both the YBCO thin film and the STO single crystal substrate. As STO is a (110) single crystal, its peaks in the XRD patterns representing the reflected in-phase X-ray scan only occur at the (001) and (002) planes, as shown in Fig. 3.1. For epitaxial YBCO thin films, as they have only the (00l) lattice arrangement, the peaks in Fig. 3.1 for STO substrates, the (001) and (002) peaks appear close to the (003) and (006) YBCO peaks, respectively, as mentioned in Ref. [234].

X-RD pattern of YBCO films with diff. thickness (diff. frequency) d = 30 nm, 300 s (f = 1 Hz) d = 50 nm, 440 s (f = 1 Hz) 1.0 d = 55 nm, 440 s (f = 2 Hz) d = 125 nm, 180 s (f = 5 Hz)

0.8 YBCO YBCO (006)

0.6

STO STO (002) YBCO YBCO (003)

0.4 STO (001) YBCO(005)

Normalized Intensity, cps Intensity, Normalized 0.2

YBCO YBCO (007) YBCO YBCO (004)

0.0

20 30 40 50 60 2(degree)

Fig. 3.1 X-ray diffraction patterns of YBCO thin films with different thicknesses (growth at different frequencies) on STO single crystal.

Film thickness is not linearly increasing with the laser frequency (50 nm thick film at f=1 Hz and 55 nm thick film at f=2 Hz) by PLD method. The reason behind of this thickness irregularity is from the thin film growths (island growth mode) mechanism, which may be arise from the following reasons like oxygen pressure in PLD chamber, the distance of target-substrate, fluctuation of power of laser and the different (lasing) gas container. The YBCO film with different thickness that was deposited at 780˚C shows very good epitaxial growth, with (00l) peaks only, as shown in the X-ray diffraction pattern in the Fig. 3.1. Oxygen content is an important factor that decides the superconducting properties of YBCO. For a good quality film, the oxygen deficiency x has to be smaller than 0.07 [235]. The oxygen deficiency of an YBCO film can be calculated, as mentioned in Ref. [235], by investigating the ratios between the intensities of the various (00l) peaks. The (006) and (005) peaks are the strongest peaks in YBCO films deposited on STO substrate, but their ratio cannot be used for this purpose, since the (006) YBCO peak overlaps the (002) peak of STO. Hence, I chose the reflection of the (005) and (004) peak can be used to determine x and their ratio of I(005)/I(004) is calculated based on the models established by

Ref. [236]. The ratio of I(005)/I(004) = 13, which corresponds to x = 0.07 (see Fig. 11 in

Ref. [235]). This means that the film is fully oxygenated. So, the films are closer to the optimum for which x should be < 0.07.

3.2 Frequency dependent deposition of YBCO film

To find the optimized thickness of the YBCO film and the buffer layer (for photon detector applications), contributing to a high critical temperature and smoother surface morphology, I have deposited films at different frequencies (repetition rate in Hz) and deposition times in PLD to achieve a reasonable thickness and smoother surface by optimized laser frequency. Table 3.1 shows the parameters used to deposit the YBCO film for this frequency study.

Table.3.1. Parameters of YBCO film deposition by PLD for frequency study.

Parameters Value Temperature 780˚C

Pressure of O2 300 mTorr Laser energy 450 mJ Substrate-target 30-50 mm distance Dt-s

Initially, I chose three different laser frequencies with small differences, such as 1, 2, and 5 Hz for YBCO film deposited only on STO substrates. As in Reference [62], I selected STO substrate, which has good chemical stability, and small lattice misfit, and thus leads to the best quality YBCO thin films. In this range of frequency difference, the film surface may be smooth enough, with fine grain size in a controlled manner, that it will be feasible to make nanowires on it.

A profiler (Veeco Dektak-6K) is used to identify the step height (thickness) of films deposited onto single crystal substrates and for measuring the length and width of bridges in patterned films.

3.2.1 YBCO film at 1 Hz frequency At each frequency, YBCO films were grown with different deposition times to have various ranges of thickness. The following graph (Fig. 3.2) shows the magnetic

moment of YBCO film deposited at 1 Hz frequency with three different thicknesses, and its Tc (Fig. 3.2) was measured by the magnetic inductive method using MPMS.

T =71.3 K, d=15 nm(150 s) YBCO on STO substrate at f=1 Hz c T =80.5 K, d=30 nm (300 s) All T measured at 25 Oe c c T =90 K, d=50 nm (440 s) c 0.0

-0.2

-0.4

-0.6 Moment (a.u)

-0.8

-1.0 T =780c, dis=70 mm, PO =300 mTorr s 2

0 20 40 60 80 100 Temperature (K)

Fig. 3.2: Tc values of YBCO film deposited at 1 Hz with different thicknesses.

Fig. 3.3: SEM images of YBCO films with different thicknesses deposited at 1 Hz frequency. Scale bar is 1 μm.

Fig. 3.3 clearly indicates the surface morphology of YBCO films in three different thicknesses produced at 1 Hz frequency. As shown in Fig 3.3(a), the 15 nm thick YBCO film has a very much smoother surface than the thicker YBCO films, but it also has a lower Tc value of 71 K with highest the transition width of 42 K (see Table 3.2). This thinner film has more fine (in size) droplets and pits on its surface. But, 30 nm and 50 nm thick films have sensible Tc (shown in Fig 3.2) values, which are above 77 K, and the transition width (see Table 3.2) is gradually reduced when the thickness of the YBCO film is increased. Both films had inhomogeneous surfaces (shown in Fig 3.3 (b) and (c)) with more inclusions of pits and droplets. 94

Table 3.2: properties of YBCO films grown on STO substrate at 1 Hz frequency. Deposition time YBCO thickness Tc (K) ΔT (K) (s) 150 15 71 42 300 30 80.5 30 440 50 90 17

3.2.2 YBCO film at 5 Hz frequency

Here, I used the higher frequency of 5 Hz to deposit YBCO film on STO substrates with different deposition times for different thicknesses. These higher frequency films have higher Tc values compared with lower frequency (1 Hz) deposition of YBCO film.

YBCO on STO substrate at f=5Hz T =84.47K, d=28 nm (40s) c All T measured at 25 Oe T =87.07K, d=47 nm (95s) c c T =89.96K, d=125 nm (180s) c 0.0

-0.2

-0.4

-0.6 Moment(a.u)

-0.8

-1.0 T =780C, PO =300 mTorr s 2

0 20 40 60 80 100 Temperature (K)

Fig. 3.4: Tc value of YBCO film with different thicknesses deposited at 5 Hz frequency.

Fig. 3.5: SEM images of YBCO films with different thicknesses deposited at 5 Hz frequency. Scale bar is 1 μm. 95

As shown in Fig. 3.4, all YBCO the films have Tc value higher than 84 K with different ranges of transition width (mentioned in Table 3.2). Fig. 3.5 shows the surface of the YBCO films with three different thicknesses deposited at 5 Hz frequency on STO substrates. The two thinner films show higher ΔTc compared to the highest thickness sample (Fig.3.5), but all the films have many droplets and other defects (compare with 1 Hz film), which give their surfaces high roughness.

Table 3.3: Properties of YBCO film grown on STO substrate at 5 Hz frequency.

Deposition time YBCO thickness Tc (K) ΔT (K) (s) (nm) 40 28 84.47 25 95 47 87.07 43 180 125 89.96 9

When the frequency of laser pulses is increased, the YBCO film is not smooth enough, and it has defects such as droplets, outgrowths, and dips on the surface. Hence, the lower frequency samples have smoother surfaces, and higher frequency samples have higher Tc. In addition, I have tried to make samples with 2 Hz frequency for higher Tc and smoother surface.

3.3 Thickness dependence of critical temperature of YBCO films grown at different frequencies

Figure 3.6 compares all YBCO films with respect to their critical temperatures

(Tc), were measured by the magnetic inductive method in MPMS. These films were deposited on STO single crystal to optimize the frequency of laser pulses and find the optimum value of YBCO film thickness.

T =71.3K;d=15nm(150s)f=1Hz c YBCO on STO substrate at diff. freq T =80.5K;d=30nm(300s)f=1Hz c All T measured at 25 Oe T =90K;d=50nm(440s)f=1Hz c c T =89.63K;d=65nm(440s)f=2Hz c T =84.47K;d=28nm(40s)f=5Hz c T =87.07K;d=47nm(95s)f=5Hz 0.0c T =89.96K;d=125nm(180s)f=5Hz c

-0.2

-0.4

-0.6 Moment(a.u)

-0.8

-1.0 T =780c, dis=70 mm, PO =300 mTorr s 2

20 40 60 80 100 Temperature (K)

Fig. 3.6: Critical temperature (Tc) of pure YBCO films with different thicknesses, grown on STO. YBCO film thickness: 125 nm (dark blue), 65 nm (light sea green), 28 nm (pink), 30 nm (red), and 15 nm (black).

Fig. 3.6 shows the critical temperature measurement for pure YBCO films grown on STO substrates at different frequencies by the PLD method. On reducing the thickness of YBCO film, it’s Tc and ΔTc value become worse due to the inhomogeneous surfaces with more inclusions of pits, droplets and mainly the amount of superconducting material is very less (i.e, thin films).

ExpDec2 Fit of Critical Temperature, T (K) YBCO on STO substrate @ diff. freq. c Critical Temperature of All Frequencies, Tc (K) All T measured at 25 Oe Transition Width of All Frequencies, T (K) c c Reciprocal Fit of Transition Width, T (K) Tc 45c 90 40

(K) 85 35

(K)

c T

30 

80 25

20 75

Transition Width, Critical Temperature, Critical T

70 10 T = 780c, dis = 70 mm, PO = 300 mTorr s 2 5 0 20 40 60 80 100 120 140 Thickness, d (nm)

Fig. 3.7: Thickness dependence of critical temperature and Transition Width for YBCO films grown on STO substrates at different frequencies. 97

For low frequency (1 Hz) growth, samples have Tc around 70- 80 K with less thickness (15 to 30 nm), while the high frequency (5 Hz) samples have higher Tc around 90 K with thickness ranging from 28 to 125 nm, which is good indication for optimizing the frequency for PLD operation. Table 3.4: Properties of YBCO film grown on STO substrate at different frequencies YBCO Critical Transition Deposition Deposition Thickness, Temperature, Width, frequency, Time, s d (nm) Tc (K) ∆Tc (K) Hz 150 15 71 42 1 40 28 84.47 25 5 300 30 80.5 30 1 95 47 87.07 43 5 440 50 90 17 1 440 65 89.63 19 2 180 125 89.96 9 5

From the frequencies of 1, 2 and 5 Hz samples, reasonable Tc and ΔTc with less thickness is obtained from samples made at frequencies1 and 2 Hz, which can be the optimum frequencies for PLD operation to attain higher Tc with less thickness. Fig. 3.7 shows the thickness dependence of the critical temperature and transition width for YBCO films deposited at different frequency. It gives the entire trend for the critical temperature (Red curve in Fig. 3.7 is “Exponential Decay 2” means Two- phase exponential decay function with time constant parameters) and transition width (Blue curve in Fig. 3.7) dependence on thickness in YBCO films. The sample critical temperature is gradually saturated at a certain thickness, which is around 125 nm. Those values can be fitted by the exponential decay formula. Also, Transition width of the sample is steadily decreased (values fitted by reciprocal formula) while its thickness was increased. Moreover, the physical properties and deposition details of YBCO grown on STO substrate at different frequencies have given in Table.3.4.

3.4 Thickness dependence of critical current density of YBCO films grown at different frequencies. Figures 3.8 and 3.9 show the field dependence of the critical current density of YBCO films deposited on STO single crystal substrates, which were measured at 10 K and 77 K, respectively. Fig. 3.8 shows the results of the 10 K measurement for the 98

J of YBCO film with diff. thickness (diff. frequency) c 2 d = 15 nm 150 s ,J =3.20E10A/m ;T =71.36 K c c 2 1E12 d = 20 nm; 42 s, J =4.83E10A/m ; T =80.48 K c c 2 d = 28 nm; 40 s, J =7.42E10A/m ;T =84.47 K c c 2 d = 65nm; 95 s, J =8.49E10A/m ;T =87.07 K c c 2 d = 125nm; 180 s, J =4.70E11A/m ;T =89.96 K c c

1E11

2 Measured at T = 10 K A/m

c D =70 mm

t-s J

1E10

0.0 0.5 1.0 1.5 2.0 2.5 3.0 Field (T)

Fig. 3.8: Field dependence of critical current density (Jc) at 10 K of pure YBCO films with different thicknesses, grown on STO. YBCO film thickness: 125 nm (pink), 65 nm (light sea green), 28 nm (blue), 20 nm (red), and 15 nm (black). different thicknesses of YBCO samples from 15 to 125 nm, deposited by changing the frequency and deposition time. All films were deposited at same distance (70 mm) from target to substrate, and the other optimum parameters were used for YBCO deposition.

2 d = 13nm; 150 s, J =1.86E8A/m ; T = 71.36K c c ) 2 d = 20nm; 42 s J =6.93E8A/m ; T = 80.48K c c 2 d = 28nm; 40 s , J =1.79E9A/m ; T = 84.47K 1E11 c c 2 d = 65nm; 95 s, J =5.58E9A/m ; T = 87.07K c c 2 d = 125nm; 180 s, J =4.54E10A/m ; T = 89.96K 1E10 c c

1E9

2 Measured at T=77K

A/m c 1E8J

1E7

0.0 0.1 0.2 0.3 0.4 0.5 Field (T)

Fig. 3.9: Field dependence of critical current density (Jc) at 77 K of pure YBCO films with different thicknesses, grown on STO. YBCO film thickness: 125 nm (pink), 65 nm (light sea green), 28 nm (blue), 20 nm (red), and 15 nm (black). 99

11 The thickest YBCO film is 125 nm, for which Jc reaches its maximum of 4.7 × 10 A/m2 at 10 K, (just 4.5 × 1010 A/m2 at 77 K), and for the 65 nm thick YBCO sample, 10 2 9 2 the critical current density (Jc) is 8.49 × 10 A/m at 10 K,(5.58 × 10 A/m at 77 K). 10 2 The thinnest YBCO film (15 nm) has the smallest Jc, 3.2 × 10 A/m at 10 K (1.86 × 8 2 10 A/m at 77 K), which can be explained by the lowest Tc of this film which has inadequate amount of current carrying materials or more possibly by poor growth mechanism (likely 3-D growth rather than 2-D growth) for this thickness, so that there is an inhomogeneous surface with droplets or grains that are not connected well with each other. At higher temperature measurements of critical current density (Fig. 3.9), curves for the thinner samples appear to waver due to weak signal, so we get high noise level (as the field is increased).

J of YBCO film with diff. thickness (diff. frequency) c

0T 1T 2T

1E11 3T

A/m c

J 1E10 Measured at T = 10 K

D = 70 mm t-s

1E9

0 20 40 60 80 100 120 140 Film Thickness d (nm)

Fig. 3.10: Thickness (of YBCO film) dependence of critical current density at 10 K for magnetic fields of zero (black), 1 T (red), 2 T (blue), and 3 T (green) (growth at different frequencies).

Thickness = 15, 20, 28, 65,125nm 0.02T 0.24T

1E10

1E9 2

A/m

c Measured at T=77K

J 1E8

1E7

0 20 40 60 80 100 120 140

Film Thickness d (nm)

Fig. 3.11: Thickness (of YBCO film) dependence of critical current density at 77 K for magnetic fields of 0.02 T (black) and 0.24 T (red) (growth at different frequencies). 100

Figs. 3.10 and 3.11 show the thickness dependence of Jc for different applied magnetic fields from zero field to 3 T, and 0.02 to 0.24 T, respectively. They clearly indicate that the critical current density Jc is decreases sharply when the thickness of YBCO film is decreased at the different temperatures of 10 K and 77 K, respectively (for thickness less than 150 nm). Especially for the lower thickness range from 15 to

30 nm, Jc is drastically decreased. This can be explained by the fact that the volume of current carriers is less when the thickness of YBCO film is reduced and the microstructure is poor, so the superconductivity properties worsen as well. There is the exact opposite behaviour for the thicker films, which start above 1 μm thickness. This study firmly indicates that the optimum thickness of YBCO film should be around above 125 nm at 2 Hz frequency for the PLD operating conditions at TFT group in ISEM, which gives high quality of superconducting properties.

3.5 Comparison of YBCO film grown at Different Frequency

In the above studies, I compared samples for the best YBCO film with both high superconducting properties and a smoother surface. For comparison, I have taken the same thickness of around 50 nm for YBCO films grown on STO substrates at different frequencies, 1, 2, and 5 Hz. As shown in Fig. 3.12, the highest (90 K) Tc was achieved at 1 Hz frequency with a narrow transition width (ΔTc), which was very similar to the 2 Hz frequency sample. Unfortunately, the higher (5 Hz) and lower (1 Hz) frequency sample seems to have a rough surface with more droplets and pits, which were denser than in the 2 Hz sample (Fig. 3.13(b)).

YBCO on STO substrate at diff. freq. T =90 K, d=50 nm (440 s)f=1 Hz All T measured at 25 Oe c c = Tc 89.63 K, d=55 nm(440 s) f=2 Hz

Tc=87.07 K, d=47nm(95 s) f=5 Hz 0.0

-0.2

-0.4

-0.6 Moment (a.u)

-0.8

-1.0 T =780c, dis=70 mm, PO =300 mTorr s 2

0 20 40 60 80 100 Temperature (K) Fig. 3.12: Critical temperature of YBCO film made at different frequencies.

101

Fig. 3.13: SEM images of 50 nm thick YBCO film grown at different frequencies. Scale bar is 1 μm.

The surface roughness in the 5 Hz sample (Fig. 3.13(b)) is higher, which reduces the

Tc (~ 87 K) compared to the 2 Hz sample. The thickness of the YBCO sample grown at 2 Hz frequency was thicker than for the other frequency sample, to which this higher Tc value may be attributed. By compare with other frequency samples, the

2 Hz frequency deposition of YBCO sample shows sensible high Tc (89.63 K), a reasonably narrow transition width (ΔTc = 19 K) and mainly has a smoother surface with very less droplets and pits, which can be used for nanowire or strip fabrication on it. The other samples (Fig. 3.13(a) and (c)) do not show a smoother surface.

3.6 Details of YBCO deposition with different buffer layer

I have coated STO, LAO, MgO and YSZ substrates (all (001) oriented) with STO,

CeO2, and PBCO buffer layers and finished with deposition of the YBCO. The misfit values, δ, based on the a-lattice parameter values of the YBCO thin film and substrate/buffer materials are listed in Table 3.5.

Substrate preparation Here, YBCO thin films were deposited using PLD on various commercially available insulating single-crystal substrates, including STO, LAO, MgO, YSZ, and R-Al2O3, that were polished on one side. The sizes of substrates (subject to change from the requirements of devices) that were generally 5 mm× 5mm × 0.2 mm, as specified in the three different sizes, 5 × 5, 3 × 3, and 10 × 10 mm2. These substrates were cleaned prior to the YBCO deposition with acetone for few minutes in an ultrasonic bath and then blown dry with nitrogen gas, as substrates with degraded or contaminated surfaces will reduce the film critical current density [237] for many substrates,

102

TABLE 3.5 LATTICE MISFIT VALUES FOR SUBSTRATE/BUFFER MATERIALS AND YBCO THIN FILM. Misfit, δ, % a-lattice Material STO CeO PBCO parameter, nm YBCO 2 buffer buffer buffer YBCO 0.382 - 2.3 29 1.5 STO 0.391 2.3 - 38 0.8 LAO 0.379 0.8 3 43 2.4 MgO 0.421 9 7 29 8 YSZ 0.514 25 24 5 25 CeO2 0.541 - - - - PBCO 0.388 - - - -

TABLE 3.6

TC AND ∆TC VALUES (K) OF YBCO FILMS GROWN ON DIFFERENT SUBSTRATES.

No buffer STO buffer CeO2 buffer PBCO buffer Substrate Tc ∆Tc Tc ∆Tc Tc ∆Tc Tc ∆Tc STO 89.6 13 86.5 20 86.1 20 89.9 23 LAO 90.0 12 87.7 21 85.7 >60 89.5 26

MgO 81.4 >60 87.7 18 81.4 >60 - - YSZ 81.3 16 - - 86.1 18 85.8 >60 especially MgO. For all kinds of substrates, the surface should be very smooth, as otherwise the growth template will be partially or completely suppressed. Generally, the substrates are bought from manufacturer as finished with mechanically and chemically polished so that the surface roughness is 0.5 to 4 nm over the area of 5 × 5 mm2 (mentioned in Materials Safety Data Sheet) as well as I measured those substrates (with ~50 nm thick laser ablated films) for a root mean square surface roughness of typically 5 nm (Average value) by Atomic Force Microscopy scans (scan area is 2 x 2 μm). Here, I describe the basic properties of several substrates which can be used for YBCO film deposition in electronic and microwave devices.

Substrate temperature of 780 C and oxygen pressure of 300 mTorr were maintained during deposition of the buffer layers and the YBCO. The oxygen pressure for CeO2

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deposition was reduced to 150 mTorr, as larger grains are formed in CeO2 thin films deposited at higher oxygen pressure [238]. From the frequency studies, the following PLD operating parameters (listed in Table 3.7) were used for the buffer and the YBCO film. The excimer laser was fired for 240 s at 1 Hz repetition rate for all buffer layers and 440 s at 2 Hz for YBCO.

This resulted in thickness of 30 ± 5 nm for the buffer layers and 65 ± 5 nm for the YBCO films, as measured by a mechanical stylus profiler (Dektak-6M). Following the YBCO deposition, the films were quickly cooled down to 400˚C and annealed at this temperature for 60 min in 1 atm oxygen pressure.

A Field Emission Scanning Electron Microscope (FESEM; JEOL 7500) was used to investigate the surface morphology of the thin films with and without buffer layers.

The YBCO thin film critical temperature (Tc) and its transition width (∆Tc) were measured in the Magnetic Properties Measurement System (MPMS, Quantum

Design). Properties of the resulting YBCO films (Tc and ∆Tc) are summarized in Table 3.6.

Table.3.7. PLD parameters of (optimized) YBCO thin film deposition.

Parameters YBCO Buffer layers

Temperature 780˚ C 780˚ C

Deposition time 440 s 240 s

Repetition rate 2 Hz 1 Hz

300 mTorr (except CeO2 with 150 Pressure of O2 300 mTorr mTorr)

Laser energy 450 mJ 450 mJ

Dt-s 40-50 mm 40-50 mm

Film Thickness 60-70 nm (± 5) 30-35 nm

Dt-s is the distance between the substrate and the target material in PLD chamber. The optimized parameter conditions of YBCO (65 nm) and Buffer layers (30 nm) are given for a particular thickness range.

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3.7 Effect of substrate on properties of YBCO films

Fig. 3.14 shows the surfaces of YBCO thin films grown directly on the studied substrates. A strong correlation between the surface morphology, the physical properties of the YBCO films, and the type of the substrate can be observed.

Films grown on substrates with small misfit (δ<2.4%) to the YBCO lattice parameters (i.e. STO and LAO) exhibit smooth surfaces with only a few voids 200-300 nm in diameter [Fig. 3.14(a, b)]. Their Tc values are as high as 90 K, and the width of transition temperature is quite narrow (~12-13 K, Table.3.6) at the applied magnetic field of 2.5 mT. Small ab-oriented grains, as can be seen in Fig. 3.14 (b) (some of them marked by arrows), are the result of twinned grain boundaries in the LAO substrate [239].

Fig. 3.14: Surface morphology of YBCO films grown on STO (a), LAO (b), MgO (c), YSZ (d) substrates. Scale bar for all images is 1 μm. White arrow marks point out the ab-oriented grains in LAO and voids or plate-like defects in YSZ.

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When δ is larger (9% for MgO or 25% for YSZ), the YBCO film grows with high angle grain boundaries [240], which result in the formation of larger (~ 700 nm) voids [Fig. 3.14(c)] or localized plate-like defects [marked by arrows in Fig. 3.14(d)] that occur due to different types of angle oriented epitaxial relations between the YBCO and the YSZ substrate [241].Tc values are reduced to ~81 K, and poor homogeneity of these films is evidenced by the large ∆Tc values (16 K for YSZ or 60 K for MgO substrates).

Our cross-sectional investigations of thin YBCO films by Transmission Electron Microscopy (TEM) [242] revealed that initial layers of epitaxial growth can be (locally) altered near the substrate (as a result of its degraded quality). The thickness of this layer varies from 3 nm (for LAO) to 10 nm (for MgO). Clearly, the existence of such a defective layer in an YBCO film with reduced thickness (<10 nm required for SSPD [103]) will negatively and drastically affect its electrical properties. Our

TEM investigations of STO/La0.7Ca0.3MnO3 (LCMO) superlattices on LAO substrate [243] revealed perfectly epitaxially grown layers (including initial stage) of (3 nm thick) LCMO material on (30 nm thick) STO buffer. The structures of the LCMO and YBCO compounds are identical, and thus a similar effect is expected for YBCO films. For this reason, we have introduced various buffer layers 30 nm thick between the YBCO and the substrate, and their effects are described below.

3.7.1 STO buffer layer

Fig. 3.15 shows surfaces of YBCO films on different substrates coated by an STO buffer layer. In YBCO samples with an STO buffer grown on STO, LAO, and MgO substrates [Fig. 3.15(a-c)], the density of voids is increased (compared to Fig. 3.14), but their size is generally reduced (<100 nm for STO and LAO, and <500 nm for MgO). These samples have improved surface morphology. We attribute this to the fact that the STO buffer layer forms a more relaxed, atomically better adjusted surface for YBCO epitaxial growth. As a result of the small misfit between YBCO and the STO lattice (δ = 2.3%, Table.3.5), an STO buffer layer favors formation of an YBCO coating with fewer defects. A few larger outgrowths [shown by arrows in Fig. 3.15(a, b)] and ab-oriented grains in Fig. 3.15(b)] appeared on the surfaces of samples grown on STO and LAO substrates compared to samples without a buffer layer (Fig. 3.14).

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Fig. 3.15: Images of YBCO thin films grown on STO buffer layer deposited on STO (a), LAO (b), MgO (c), and YSZ (d) substrates. Scale bar is 1 μm. White arrow marks pointed the droplets (different sizes)

Interestingly, this observation correlates with the preceding studies, where larger density and size of outgrowths were observed when the thickness of the YBCO layer was increased [221], [244]. Thus, the introduction of a buffer layer may have similar effects to increasing the thickness of YBCO film.

For STO and LAO substrates, Tc values were slightly decreased (down to 87 ± 0.5 K) and ∆Tc values increased (up to 21 K) compared to the reference samples (without buffer layer). This indicates that the overall homogeneity of these films is reduced on introducing an STO buffer layer. This is likely due to the fact that the thickness of the buffer layer is not optimized. For instance, a thinner layer of STO buffer on STO substrate may enable growth of the buffer layer with a smoother surface and fewer defects. The STO buffer increases the lattice misfit between YBCO and LAO (from

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0.8% to 3%, Table 3.5), which likely degrades the surface quality of the STO buffer layer, affecting the homogeneity of the final YBCO film.

The physical properties of the film on MgO substrate are notably improved (Tc =

87.7 K and ∆Tc = 18 K, Table 3.6). This correlates with the minimized δ (from 9% to 2.3%) between the bare MgO and the YBCO that is enabled by the STO buffer. Also, this result implies that for materials with larger lattice misfit, increasing the buffer layer thickness may allow more efficient defect annihilation and thus can be beneficial for fabrication of YBCO films with better structural/superconducting quality. For YSZ substrate having δ of 24% with STO buffer, YBCO film did not grow epitaxially [Fig. 3.15(d)], and no superconducting behaviour was detected in this sample.

3.7.2 CeO2 buffer layer

Fig. 3.16: Morphology of YBCO thin films grown on CeO2 buffer layer deposited on STO (a), LAO (b), MgO (c), and YSZ (d) substrates. Scale bar for all images is 1 μm. White arrows pointed at various defects.

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CeO2 has a lattice constant of 0.541 nm, and direct calculation yields a large lattice misfit between CeO2 and YBCO (δ = 29 %). CeO2 (100) is commensurate with YBCO (110), however which reduces misfit with the a (b) lattice parameter of YBCO to ~0.2% (1.7%) and makes CeO2 an excellent template for YBCO film growth [238], [240]. The sample on STO substrate [Fig. 3.16(a)] has a reasonably smooth surface, but the introduction of CeO2 buffer leads to degradation of Tc and ∆Tc values compared to the sample without CeO2 buffer. Note that Tc and ∆Tc are similar for the YBCO sample with STO buffer (Table 3.6). The surface morphology of YBCO thin films grown on STO and YSZ substrates with a CeO2 buffer layer [Fig. 3.16(a, d)] has a large volume of outgrowths compared to the reference samples [Fig. 3.14(a, d)]. Effect of outgrowths and their origin should be investigated further. They may be correlated with reduced epitaxial quality of a relatively thick (30 nm) buffer layer. According to observations of [243], a buffer layer has high density of defects (misfit dislocations) as a result of stress relaxation. These defects would create ideal spots for the formation of different types of angle oriented YBCO grains. Their nucleation should start at the interface between the buffer layer and the YBCO thin film, locally threading through all the YBCO film thickness. This would be an undesirable arrangement, because these different types of angle oriented YBCO grains will affect current flow in regular YBCO structures (stripes in the case of SSPD). Therefore, further TEM study is necessary to explain the origin of the observed outgrowths.

Previous studies suggested that CeO2 is a good buffer for LAO substrate. Although these materials have large lattice misfit in the (100) plane (δ = 43%, Table 3.5), it is reduced to 3.6% for (110) CeO2 planes parallel to (100) LAO, which results in the formation of good quality (001) oriented YBCO thin film [72], [64]. Our YBCO sample grown on LAO substrate has a Tc value of 85.7 K, but its homogeneity is quite poor. This is evident from the surface morphology with deep trenches [Fig. 3.16(b)] and the large transition temperature width (>60 K, Table 3.6. The reason for these observed properties is not clear, but it may be related to the different fabrication parameters (compared to those in [72], [64]) or the poor quality of the underlying LAO substrate.

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The YBCO sample fabricated on MgO substrate [Fig. 3.16(c)] exhibited a structure with large grains and a rough surface. Its physical properties are similar to those of the reference sample (Tc = 81 K, ∆Tc > 60 K, Table 3.6). We anticipate that the structural and electrical quality of this sample are degraded as a result of chemical reaction between the MgO and CeO2 materials, which may occur at higher (>700 C) fabrication temperatures [245]. (Note that the deposition temperature in this work is 780 C for all samples).

The CeO2 buffer notably improves the surface of YBCO film grown on YSZ substrates [Fig. 3.16(d)]. This is likely to be the result of small misfit between YSZ and CeO2 materials (δ = 5%, Table 3.5). This sample has the highest Tc value of

86.1 K (among others grown on YSZ substrate) and a small ∆Tc of 18 K (Table 3.6).

3.7.3 PBCO buffer layer

Fig 3.17: SEM images of surface morphology of YBCO thin films on STO (a), LAO (b), MgO (c), and YSZ (d) substrates with PBCO buffer layer. Scale bar is 1 μm.

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PBCO buffer is structurally and chemically compatible with YBCO. The small lattice misfit between YBCO and PBCO (δ = 1.5%, Table 3.5) enables fabrication of high quality, ultrathin YBCO films [71, 73, 246]. YBCO films grown on STO [Fig. 3.17 (a)] and LAO [Fig. 3.17 (b)] substrates with PBCO coating have significantly improved surface morphology. The number of voids and the size of outgrowths are notably reduced. This result is correlated with small lattice misfit of PBCO buffer, and STO (δ = 0.8%, Table 3.5) and LAO (δ = 2.4%, Table 3.5) substrates. Note that all ab-oriented grains (typical of LAO substrate) on the surface of the YBCO coating are effectively blocked by the PBCO buffer. Tc values for these samples are similar to those of YBCO on bare substrates (~90 K). ∆Tc is slightly increased (Table 3.6), however, indicating an increased level of inhomogeneity in these films, which is introduced by the PBCO buffer.

MgO substrate was found to be incompatible with PBCO material [Fig. 3.17(c)] with the fabrication parameters used, and no Tc value could be measured. We propose that a lower deposition temperature (~700 0C) should be used in order to eliminate interaction between the PBCO and MgO materials [4]. YBCO film on YSZ substrate has large-angle grain boundaries, resulting in formation of voids [~300 nm in diameter, Fig. 3.17(d)]. The Tc value remains relatively high (86 K, similar to the sample with a CeO2 buffer layer), but ∆Tc of 60 K suggests degraded epitaxial growth conditions in this sample.

Optimization of PBCO buffer layer thickness is likely necessary for further improvement of YBCO superconducting and structural properties. As suggested in [73], [71], reduction of the PBCO buffer layer thickness (down to 15 nm) may result in higher quality thin YBCO films.

3.8 YBCO bridge fabrication by wet etching After the fabrication of the optimized YBCO thin film will be ready for draw meander line structure by EBL. Here, I used the conventional etching method, which is done by immersion of the sample, using wet etchants. The immersed samples remain in a chemical etchant solvent for a specific period of time, are transferred to a rinse bath for acid removal, and thereafter, are transferred for a spin-dry or blown-air step. Etching uniformity and process control are enhanced by the addition of heaters and agitation devices, such as ultrasonic waves for the immersion tanks. 111

Wet etchants for YBCO are chemically selected for their ability to uniformly remove the top layers of samples without attacking the underlying material. These etchants must only react with the YBCO and leave the substrate and the resist intact. The most widely used common wet etchants for YBCO are bromine (non-aqueous) in methanol, ethylene diamine tetraacetic acid (EDTA) [247], dilute sulphuric acid [248], nitric acid, and citric acid [249]. Although structure sizes down to micron feature sizes are possible, chemical wet etching causes problems in providing smooth side walls by undercutting the photoresist stencils. Another problem is that the water in aqueous solutions reacts with YBCO and degrades the superconducting properties.

Fig. 3.18: Meander line Structure (active area - 30 μm) of YBCO films on STO substrate with PBCO buffer after patterning (EBL): by wet etching (b) and its magnified image (a).

EDTA and dilute sulphuric acid were used to etch the YBCO thin film in this work. The chemical solutions were diluted in de-ionized (DI) water. The sample was then immersed in the acid in an ultrasonic bath. The etching time was dependent on the thickness of the YBCO film. Most of the YBCO samples were etched within 5-10 seconds. When the substrate under the YBCO layer became visible, the sample was removed from the solution, rinsed in DI water, and checked under the microscope.

The utilisation of wet etching may be limited by a number of considerations, such as the pattern sizes (~ 3 μm or larger), the sloped sidewalls from isotropic etching, the requirement for rinse and dry steps, and the toxicity of wet chemicals. Dry etching is mostly advisable for YBCO film compared with wet etching technique.

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3.9 Transport measurements of patterned YBCO film

Before patterning, Tc = 90.47 K,

After patterning, Tc = 88.38 K 1.0

0.8 f = 1 Hz, t = 440 s 0.6 Bridge width (w)=30m, d = 58 nm

0.4

NormalizedVoltage 0.2 Tc= 89.88 K by Mag. induc.method

0.0

0 20 40 60 80 100 Average Temperature (K)

Fig. 3.19: Critical temperature of YBCO/PBCO buffer on STO substrate before and after patterning by EBL.

For comparison of superconducting property, a 58 nm thick YBCO film with a PBCO buffer layer grown on STO substrate (same sample as in Fig. 3.17) had its critical temperature measured before and after patterning by the transport measurement method in MPMS. Fig. 3.19 shows (black curve) that the critical transition temperature Tc for the unpatterned (or before patterning) sample to become superconducting is 91.7 K. For the same sample, the Tc is around 89.88 K (in Fig. 3.16) by the magnetic inductive method, which reveals the accuracy of the value of the higher Tc from transport measurements. The red curve is the critical temperature of the same sample measured by the four probe method, but after (Fig. 3.19) pattering by the EBL technique using the wet etching method.

The critical transition temperature Tc for the (~30 μm) bridge structures to become superconducting is typically around 88.38 K, which is lower than before patterning of the same sample. After patterning, the Tc and transition width (ΔTc) values are degraded due to the chemical processing involved during wet etching. However, it shows reasonable value of the critical temperature of the patterned sample to do further optimizing research on size of the YBCO microbridge with threshold thickness of the film. Already discussed [132], (SUST, vol.27, 2014 and 113

App.Phys.Lett.vol.104,2014) about the dependency of Tc and ∆Tc with the film thickness, in which it shows sharply decreases the both values with film thickness.

Finally, the other important superconducting property of the sample is critical current density, which can be measured from current-voltage (I-V) characteristics. The critical current was typically (Ic= 0.047 A) measured from the (30 μm width) meander patterned sample by applying current (I = 0.1 A) at 77 K in the transport method. Critical current of the 58 nm thick YBCO/PBCO/STO sample is determined with the 1 μV/cm criterion from the I-V curve (shown in Fig. 3.20). Above this critical current, it clearly indicates that there is no sharp superconducting transition, which may occur due to the energy dissipative in the movement of vortices. These observations are already explained (in sec. 1.11.2) clearly by many research groups [132, 141].

Fig. 3.20: Critical current (I-V curve) measurement of YBCO with PBCO buffer on STO substrate (After patterning) by transport method.

From the I-V measurement (at T=77 K), critical current density (Jc) is calculated by using Jc = Ic /Area, i.e., area = width (30 μm) × thickness (58 nm). For the 30 μm width, the bridge patterned sample has reasonable critical current density (Jc), which 10 2 is around 2.70 × 10 A/m , and the critical temperature (Tc) is 88.38 K. The results are showing the high quality superconducting properties, which are promising enough to encourage proceeding with the best combination of substrate/buffer/YBCO layered meander line structures for SSPD detector applications.

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4 CONCLUSIONS AND RECOMMENDATIONS

Summary

This thesis dissertation has explored the superconducting thin film’s electronic properties by fabricating and characterizing them in electronic devices. Chapter 1 began by an overview of the basic concepts of superconductivity with the electrical and structural properties of graphene and YBCO systems, along with our current understanding of SSPD and Josephson junction device principles. The photoresponse of the YBCO detector as observed in the optical and THz regime has been described and also explained by the various detection mechanism models. Chapter 2 provided a detailed overview of EBL techniques, which are used in this work. I demonstrated advanced methods, such as constructing oversize patterns, the mix-match process, and line resolution tests on various thicknesses of resist layer. Here, I listed only some of the progress made in EBL techniques. I have been investigating the possibility of extreme usage of an EBL machine without any mask and other (optical) lithographic methods. All the complex e-beam exposure parameters have been optimized such as exposure conditions, WF alignment, the development environment, and the lift-off process.

This work

 Showed that it is possible to design patterns with 1nm resolution using the GDSII database;  Optimized the bilayer resist profile and lift-off process;  Produced various sizes of high quality pitch lines and gratings (> 80 nm);  Fabricated micron-size features on oversize (5 mm × 5 mm) patterns with highly reliable results at ~ 50 mm working distance by EBL;  Wrote and attached high quality of nano- and micron-size patterns accurately by the mix-match process without using any other photolithographic process.

Beyond this, the EBL technique will be used to fabricate nano-/micron-scale devices on different types of material (thin films) to study their electronic and related properties.

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Hence, I used this optimized EBL technique to fabricate graphene-based Josephson junctions and characterized them for possibility of supercurrent through selected barrier materials. This was relevant to the experimental results presented in the same chapter. In this study, an attempt was made to develop a fabrication process for optimization of graphene based Josephson junctions. Graphene film was fabricated by the mechanical exfoliation (scotch tape) method and it was patterned directly by using PMMA as a positive resist on EBL without transferring the pattern. The process developed for fabricating monolayer graphene and patterning junction electrodes within the superconducting coherence length (superconducting wavefunction electrodes) seems promising for fabrication of nanoscale Josephson junction and SQUIDs. The overall results (including I-V characterization) are listed below:

 Successful fabrication of sub-micrometer size junctions on graphite/carbon flakes was demonstrated using available e-beam lithography.  Superconductor-Carbon-Superconductor junctions have been characterized at temperatures down to 1.8 K; their characteristics displayed overall nonlinearity and anomalies at V 0. To establish the nature of these anomalies, further study is required.

There are still many interesting new problems to address with graphene based Josephson junctions. An intriguing and potentially revolutionary application which remains largely unexplored for atomically thin graphene flakes is selective ultra-thin barrier membranes, which should be as thin as possible to increase supercurrent flow in a junction device. Hence, further studies are required, including on reducing the junction length, the formation of junctions on single-layer graphene, and studying their properties to obtain Josephson tunnelling, especially the dependence of the differential conductance on the junction length.

Chapter 3 presents the results on YBCO superconducting thin films that were fabricated and studied for SSPD device fabrication. The influence of different buffer layers on the superconducting properties of YBCO thin films deposited on various substrates has been investigated. By introducing buffer layers, we were able to change the YBCO film surface morphology and superconducting properties (Tc). Generally, improvement of the surface morphology was observed in the structures where

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materials have a small lattice misfit (in preferred orientation). On the basis of the results observed, it was concluded that:

 STO and LAO substrates with or without a PBCO buffer layer are the most promising for the following SSPD device fabrication process. They yield films

with smooth surfaces and relatively high Tc values.  Although MgO and YSZ are more attractive for application in devices, the quality of YBCO films grown on these substrates can only be improved by introducing a buffer layer. In particular, an STO buffer layer notably improves

the properties of YBCO film grown on MgO substrate, while CeO2 is the best buffer layer for YSZ.  Additionally, 30 μm of meander line structure was fabricated on an YBCO layer with PBCO buffer on top of an STO substrate. The patterned film 10 2 exhibited a reasonable critical current density. Jc was around 2.70 × 10 A/m , and the critical temperature was 88.38 K.

These results [250] demonstrate that more work should be done in order to improve the homogeneity and superconducting properties (Tc and ∆Tc, as well as supercurrent

Ic) of YBCO films for application in SSPDs. One of the approaches to this is optimization (surface quality, thickness) of particular buffer layers suitable for particular substrates, which are revealed in this work. With the dry-etching technique, we can achieve very narrow strips. Once superconducting thin films are fabricated, it is necessary to optimize the patterning of these thin films. The resolution of EBL must be optimized to obtain a better defined nanostructure. It can be done by optimizing the exposure parameters for a special resist such as HSQ or a negative resist, which can be also used to invert the pattering structure.

For example, simple analysis of the developed films, combined with other results worldwide, will give a clear picture of where they can be used. As in Ref. [251], high 6 2 Tc SNSPD is possible based on YBCO/STO with Jc = 14 × 10 A/cm at Tc = 78 K, and these results are similar to those for our low (15 nm) and medium thickness (60 nm) YBCO samples on STO substrate without any buffer layer. Also, the same thickness of the samples deposited on a sapphire substrate for photoresponse studies of YBCO microbridges led to high Tc and Jc [132].

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The following combinations of films, such as YBCO/MgO and YBCO/YSZ, were used as sub-millimeter (0.1-1 mm) wave superconducting bolometers (Tc ~90 K) [252]. Also, a nano SQUID made by YBCO (50 nm)/MgO was constructed, having 7 2 Tc = 85 K and Jc = 7-9 × 10 A/cm [253]. It could be used in quantum meterology and nanoscience as a highly sensitive magnetic sensor with ultra-low noise.

A PBCO layer was used as a buffer as well as a cap layer for an YBCO film with a 10 nm thick microbridge based (PBCO/YBCO/PBCO) HEB constructed by e-beam lithography and the ion milling process [109]. This kind of bolometer has also shown potential for application in THz imaging [254] and astronomy [255]. YBCO exhibits high Tc and ultrafast (ps range) dynamics of nonequilibrium quasiparticles, but also high optical absorption, which all make it a good candidate for making advanced SNSPDs. So, YBCO on STO substrate with or without PBCO buffer layers is suitable to build detectors with sensitivity to single photons. Hence, the optimal selection of the superconductor and substrate materials is very essential in detector applications.

From this thesis work, patterning technology for micrometer (or nano-meter sized) YBCO detectors is embedded with the EBL and etching (both ion milling and wet etching). The transport measurements (IV and DC characteristics) of YBCO bridges has shown almost the same values of superconducting properties, which could be promising for high-Tc SNSPD fabrication, as well as for the other detector applications such as fast THz detectors, bolometers, and HEB mixers. Except for the cryogenic requirements and the inconsistency of etching on the YBCO structure, YBCO seems to be a good candidate for advanced SNSPD detectors. If the YBCO based SNSPDs have high fabrication limitations, the next best choice of YBCO goes to the THz detectors in which YBCO could be a very promising material and meet all requirements with fewer drawbacks due to sensitivity.

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