Multilayering approach to enhance current carrying capability of YBa2Cu3O7 films

Transcription

1 University of Wollongong Research Online University of Wollongong Thesis Collection University of Wollongong Thesis Collections 2010 Multilayering approach to enhance current carrying capability of YBa2Cu3O7 films Serhiy Pysarenko University of Wollongong Recommended Citation Pysarenko, Serhiy, Multilayering approach to enhance current carrying capability of YBa2Cu3O7 films, Doctor of Philosophy thesis, School of Philosophy - Faculty of Arts, University of Wollongong, Research Online is the open access institutional repository for the University of Wollongong. For further information contact Manager Repository Services: morgan@uow.edu.au.

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3 Multilayering approach to enhance current carrying capability of YBa 2 Cu 3 O 7 films A thesis submitted in fulfilment of the requirements for the award of the degree of Doctor of Philosophy of UNIVERSITY OF WOLLONGONG by Serhiy Pysarenko Faculty of Engineering Institute for Superconducting and Electronic Materials January 2010

4 Declaration I, Serhiy Pysarenko, declare that this thesis, submitted in fulfilment of the requirements for the award of Doctor of Philosophy, in the Faculty of Engineering, 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. Serhiy Pysarenko Wollongong January 2010 i

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6 Acknowledgements I would like to thank my supervisors, Professor Shi Xue Dou and Associate Professor Alexey Pan for opening to me the possibility to do this work in their institute and for their financial and academic support as well as for the numerous fruitful discussions I had with them during the course of my PhD. I also would like to thank Ron Kinnell and all technical staff of the Faculty of Engineering for their technical support and their invaluable work in manufacturing and repairing parts for the PLD system as was required on many occasions during this work. Special thanks also go to Doctor David Wexler and Greg Tillman for their time and efforts spent in train me in the use of XRD, TEM and AFM, respectively. I would like to express my gratitude to Doctor Germanas Peleckis and Doctor Ivan Nevirkovets for dedicating their time and participating in fruitful discussions of various aspects of Chapters 3, 5, 6, 7. iii

7 iv I also wish to acknowledge the help I received from the ISEM academic staff members and PhD students, especially Doctor Joseph Horvat, for their helpful explanations about how to use of some equipment and Doctor Tania Silver for correcting some parts of my thesis. Finally I would like to thank my family members here in Australia as well as in Ukraine and on the other side of the world; they have constantly been encouraging me to complete the work; and it would have been really difficult to finish this work without their support. iv

8 Abstract High temperature superconducting (HTS) thin films deposited onto metallic substrates are known as coated conductors (CC) and are currently the most promising HTS candidates for wide-scale industrial applications. These films are fabricated from ReBa 2 Cu 3 O 7 (where Re is a rare earth element) ceramics and have very specific requirements with regard to their manufacturing and maintenance, due to their complex stoichiometry and large anisotropy. One of the most important problems studied by many researchers around the world is the improvement of critical current capability in such superconducting films. Structures consisting, for example, of both YBa 2 Cu 3 O 7 (YBCO) layers and layers of different superconductive or nonsuperconductive materials having a similar crystal structure are likely to have enhanced microstructural properties, and they are able to carry larger critical currents as compared to their monolayer counterparts. Such sandwich-like films are called multilayer structures. Usually, in order to increase the amount of electrical current being transported through a coated conductor, one needs to make necessary adjustments to the superconducting layer. An obvious way to enhance transport electrical current is to increase the thickness of the superconducting film. However, this approach has one very significant flaw: the fact that critical current density degrades with increasing thickness of the film. This phenomenon is widely observed in coated conductors, which are already used for transmission of electricity in electric motors and high-field magnets around the globe. The present work involves fundamental studies of the fabrication of multilayered v

9 vi structures on single crystal and metallic substrates with the emphasis on improvement of the critical current density and understanding the mechanisms responsible for the behaviour of the critical current in such superconducting multilayer thin films. Enhancement of the critical current density has been achieved, reaching 3.4 MAcm 2 at 77 K in YBa 2 Cu 3 O 7 /NdBa 2 Cu 3 O 7 based multilayers about 1 µm thick. This critical current density is higher than that for the best quality and optimal thickness YBa 2 Cu 3 O 7 monolayer films. Investigation of the crystal structure and electromagnetic properties of mono- and sandwich-like structures has been performed to clarify the origin of the critical current enhancement in the multilayer structures. It was found that, from the structural point of view, the multilayer films have much better microstructure and surface quality (i.e. the smoothness of the surface) than is the case for monolayer films. This is due to the increased filling factor in the multilayered structures, because the holes which are usually observed in the film, have been successfully eliminated. With one of the critical problems being solved, which is degradation of critical current due to thickness of the superconducting film, multilayer structures offer great potential to be utilized not only for electrical power transmission, but also, for example, in fabrication of superconducting electronic components, such as magnetic detectors, superconducting quantum interference devices, etc. Enhancement of the critical current capability of multilayer structures was investigated using a newly developed theoretical model. Mathematical modelling of critical current behaviour in thin superconducting films is one of the most complicated tasks of modern solid state physics. Theoretical investigation of multilayering is crucial for understanding the superconductivity and for further improvement of the superconducting properties of such structures. The qualitative analysis of electric current properties in superconductors can uncover the nature of the coexistence and interaction of two states: the solid state and the field state of the matter. The existing theory of vortex lattice behaviour in superconducting thin films in the field state of matter is an intriguing part of the research, as parameters controlling such a lattice vi

10 vii are controllable. By changing these parameters, a variety of structural defects and crystal characteristics on macroscopic and microscopic scales can be investigated. One of the major objectives of this PhD project was to develop a theoretical model that would allow modelling of critical current behaviour in superconducting films. The constraints and applicability of the model are discussed in accordance with experimental data and fitting procedures. Calculation results, obtained within reasonable approximations, can well describe various properties of the crystal structures of monolayer and multilayer thin films. An automated computer program was successfully designed on the basis of the statistical theory for the quantification of the crystal structure parameters in superconducting thin films. Observed data showed that multilayering is crucial to enhance the quality of the upper layers of the films and to increase the amount of dislocations that act as effective pinning centres, resulting in improved critical current carrying capability. During this work, a few additional related research problems have been addressed. An emphasis was put onto development of the pulsed laser deposition method (to prepare thin film samples of the highest quality) and investigation of the effect of Ag doping, which has a positive influence on the critical current carrying capability of YBCO superconducting films. Fabrication of high quality YBCO thin films implies usage of very reactive oxygen atmosphere and high temperature. These peculiarities make the process very sensitive to a number of various deposition parameters. Optimal deposition conditions were verified and, as a consequence, a new heater was designed and fabricated. As a result of this work, the amount of time required to be spent on optimization of deposition conditions has been considerably reduced. This, in fact, significantly increased the productivity of the pulsed laser deposition system. A comprehensive study of one deposition parameter, the target to substrate distance was performed. The obtained results showed that the target to substrate distance plays a crucial role in pulsed laser deposition of monolayer and multilayer structures. Special efforts were also dedicated to the investigation of Ag doping of the YBCO vii

11 viii superconducting thin films. It was found that doping strongly improves critical current at low applied magnetic fields. Research was directed towards uncovering the nature of advanced critical current carrying capabilities in Ag doped films. Microstructural analysis revealed that Ag doping leads to the enhancement of transparency for electrical current flow in the films. This is achieved in the process of deposition of the YBa 2 Cu 3 O 7 films, in which silver particles transfer extra energy to the YBa 2 Cu 3 O 7 ablated adatoms, thus ordering the microstructure during growth of the film. Moreover, the amount of silver which remains in the intergrain boundaries increases the transparency of films to the supercurrent flow and presumably plays a role as a barrier against oxygen depletion. viii

12 Contents Declaration i Acknowledgements ii Abstract v List of figures xii List of tables xx 1 Introduction to superconductivity and literature review Historical overview of superconductivity Two types of superconductivity Critical current and Bean s critical state model Structural and physical parameters of YBCO Properties of YBCO thin films Applications of superconductors HTSC for Coated Conductors (CC) Characterization methods and techniques Characterization of the thin film microstructure X-ray diffraction analysis Atomic force microscopy (AFM) Optical microscopy Scanning Electron Microscopy (SEM) Transmission electron microscopy (TEM) Profilometry ix

13 x CONTENTS 2.2 Electromagnetic characterization Magnetic measurements of critical current densities Magnetic measurements of critical temperatures Magneto optic imaging (MOI) Development and optimization of the pulsed laser deposition process Thin film growth technique Introduction to the growth of YBCO thin films Pulsed Laser Deposition (PLD) technique PLD system setup in the Institute for Superconducting and Electronic Materials Deposition procedure Development of PLD system in ISEM Study of optimal deposition conditions Study of target-to-substrate distance parameter Conclusion Critical current and pinning mechanisms in single-crystalline epitaxiallygrown YBCO thin films Outline Introduction Strong pinning considerations in YBCO films J c behaviour at different applied magnetic fields Model of critical current vs. applied magnetic field Development of the model of the critical current vs. applied magnetic field dependence Results and discussion Conclusion x

14 CONTENTS xi 5 Multilayer technique as an effective method to enlarge the critical current in YBCO films Outline Introduction and literature review Investigation of thin film current carrying capability as a function of film thickness YBCO/NdBCO multilayers Structural characterization of multilayer films Electromagnetic properties of multilayer films Multilayer YBCO/YBCO films Conclusion Multilayering for Coated Conductors Outline Introduction Optimization of Deposition Parameters Results and discussion Structural characterization of ISD-MgO templates Structural and electromagnetic characterization of CC Conclusion Silver doping of YBCO films Outline Introduction and literature review Sample preparation technique Structural characterization of doped and undoped films Electromagnetic properties of Ag doped and undoped films Conclusion Conclusions 183 xi

15 xii CONTENTS References 211 Publications 211 A Appendix A 213 xii

16 List of Figures 1.1 Phase diagram of Type-I (a) and Type-II (b) superconductors Magnetic flux penetration and current distribution in Type - II superconductor in according to the Bean critical state model Crystallographic structure of YBCO Schematic representation of YBCO quasi crystal Grain boundary created by rotation around an axis in the plane of the grain boundary Schematic view of various defects in thin films that can act as effective flux pinning sites [53] Schematic view of grain variety in YBCO film (quasi crystal). Misoriented grains form the network of ab-plane (also called in-plane) grain boundaries Schematic representation of Coated Conductor Schematic layout of the Bragg-Brentano geometry Schematic layout of the atomic force microscope Schematic layout of the optical microscope Schematic view of the scanning electron microscope Schematic view of the transmission electron microscope Schematic view of the stylus profilometer Schematic view of the MPMS xiii

17 xiv LIST OF FIGURES 2.8 Magnetic moment as a function of the external applied magnetic field for the determination of critical current density J c (B a ) Magnetic moment as a function of the temperature for the determination of critical temperature and transition width Schematic diagram of the Magneto Optic Imaging (MOI) principle used to obtain high quality MO images Schematic of the basic processes occurring in epitaxial growth Ambient oxygen pressure v.s. temperature phase diagram for YBCO according to Bormann and Nolting [115] Schematic view of the PLD system installed in the ISEM Schematic view of the deposition setup. During the deposition process this configuration makes it possible to switch targets without stopping the laser shoot The construction of the heater parts The positioning of the thermocouple on the surface of the removable plate Schematic presentation of the concepts of reproducible thin film deposition Normalized dependence of the magnetization on the oxygen pressure during deposition of the YBCO film Normalized magnetization versus deposition temperature of the YBCO film Dependence of the normalized magnetization on the substrate material Schematic representation of the arrangement of the target, substrate and ablated plume Normalized magnetization curves as a function of temperature for the YBCO films with 300 nm thickness deposited at different D T S xiv

18 LIST OF FIGURES xv 3.13 SEM images (a), (b), (c) of the surface morphology for YBCO films deposited at D T S =37 mm, 41 mm, and 46 mm; the film thickness is 450 nm in each case SEM images of the surface morphology for YBCO films deposited at D T S =37 mm (a) and 46 mm (b) with thickness of 1.6 µm and 1.3 µm respectively Critical current density (J c ) as a function of the applied magnetic field (B a ) for YBCO films with thickness of 300 nm TEM images of the inner structure of films deposited at D T S =37 mm(a) and 46 mm(b), respectively FESEM images (a) and (b) of the surface morphology for YBCO films taken at high resolution. A few grain boundaries within trenches are marked by white lines in the image at higher magnification (a) Schematic view of low-angle grain boundaries (a) and vortices pinned along them (b) STM image of YBCO film surface deposited on CeO 2 /Al 2 O 3 substrate [206] Typical experimental J c (T, B a ) curves (b) and the rate of J c (T ) degradation as a function of temperature encoded in parameter s: J c = J co (0)(1 T/T c ) s. Four different vortex modes are observed Out-of-plane edge dislocations in a LAB. Supercurrent J is flowing across the boundary and Abrikosov vortices are pinned at dislocations Schematic illustration of the theoretical model of J c behaviour on applied magnetic field in accordance with Ref. [205]. Free energy loss due to the elastic distortion of the VLL in the presence of linear defects as compared with the energy gain due to vortex pinning Calculated of dependencies J c (B a, τ)/j c (0, τ) on the dimensionless parameter b = (ν/(2µδ c )) 2 at different ν values according to the Equation xv

19 xvi LIST OF FIGURES 4.8 Probability function of grain sizes according to Equation Typical normalized critical current dependencies versus parameter b for different space-filling domain shapes: squares, rectangles and hexagons Typical normalized experimental critical current data versus magnetic field: (a) presents J c (B a ) curves normalized to J c (10K) on the vertical axis at different temperatures: 20 K, 30 K, 40 K, and 60 K, respectively; (b) presents J c (B a ) curves normalized to J c (10K) on the horizontal axis at different temperatures: 20 K, 30 K, and 40 K, respectively. The regions indicated by letters in (b) are the vortex pinning regimes: single vortex (A), small vortex bundle (B), large vortex bundle (C), and vortex creep (D) (a) Normalized experimental data of critical current dependencies versus magnetic field fitted by old model of equation (b) and (c) show the discrepancy between experimental and modelled data in low and high magnetic field regions, respectively (a) Original model [205] pinning potential. (b) Modified, pinning potential (see Equation 4.17) The approximation which was derived to simplify expression 4.17 in the in-plane projection Normalized experimental data of critical current dependencies versus magnetic field fitted by old model of Equation 4.16 and newly developed model of Equation The inset shows an enlargement of the higher critical current region Normalized experimental data on critical current dependencies versus magnetic field fitted by Equation (a) Statistical domain size distribution. (b) Critical current densities fitted by Equation SEM micrographs of the surface morphology of MS deposited film (a), and PLD film (b) xvi

20 LIST OF FIGURES xvii 5.1 SEM images of the surface morphology for YBCO films deposited at 2 Hz with the thicknesses: (a) 100 nm, (b) 345 nm, (c) 1820 nm, and at 6 Hz with thicknesses: (d) 50 nm, (e) 480 nm, (f) 1000 nm J c (d) dependencies at different fields and temperatures for YBCO films deposited at 2 Hz J c (d) dependencies at different fields and temperatures for YBCO films deposited at 6 Hz J c (T, B a ) dependencies for two samples deposited at 2 Hz and 6 Hz J c (T, B a ) dependencies for two samples deposited at 2 Hz and 6 Hz Normalized experimental data on critical current versus magnetic field for F(1000) and F(300) samples, fitted by equation The inset contains the domain size distribution functions Schematic view of the multilayer sandwich-type YBCO/NdBCO film structure SEM micrographs of the surface morphology of multilayer YBCO/NdBCO film (a,b) and an YBCO monolayer film (c,d) TEM images of the YBCO/NdBCO film multilayer: (a) extra amount of defects produced by the interfaces. Circled areas have denser defect structure, (b) and (c) formation of dislocations can be interrupted or initiated by the interfaces as well XRD θ 2θ scan data for the monolayer and multilayer films Critical current density as a function of applied magnetic field in double-logarithmic scales at 77 K. YBCO monolayer films with different thicknesses and two YBCO/NdBCO multilayers are shown for comparison Critical current density as a function of applied magnetic field in double-logarithmic scales at 10 K and 40 K. YBCO monolayer films with different thicknesses and two YBCO/NdBCO multilayers grown at different temperatures are shown for comparison xvii

21 xviii LIST OF FIGURES 5.13 Critical current density as a function of applied magnetic field in semilogarithmic scales with simulated curves (red colour). Inset demonstrates sufficient domain size distribution functions Critical current density as a function of applied magnetic field in semilogarithmic scales for YBCO/NdBCO multilayer films deposited at temperatures of 780 C and 800 C Schematic view of the multilayer YBCO/YBCO film structure SEM images of YBCO/YBCO multilayer (a) and YBCO/NdBCO multilayer (b) films deposited at D T S =41 mm Critical current density as a function of applied magnetic field in semilogarithmic scales for YBCO/YBCO multilayer, YBCO/NdBCO multilayer, and YBCO monolayer films Schematic view of the coated conductor configuration mastered within this work Comparison of transition curves of two samples deposited at different post-annealing conditions Comparison of transition curves obtained from AC magnetic susceptibility from PPMS measurements of two samples deposited under the same deposition conditions but on different substrate material Comparison of transition curves of two samples deposited under the optimal deposition conditions on different buffer layers Optical images of the ISD metallic surface before deposition at lower (a) and higher (b) magnification D surface obtained using AFM: (a) surface scan obtained from 5 µm 5 µm spot of single crystal SrTiO 3 substrate; (b) surface scan of 5 µm 5 µm area of metallic substrate (ISD-MgO template) SEM scan showing slightly tilted view of the metallic Hastelloy C276 substrate with ISD-MgO deposited buffer layer (see text for more details).156 xviii

22 LIST OF FIGURES xix 6.8 XRD scan results for two YBCO films of the same thickness, deposited on different substrates: SrTiO 3 and Hastelloy/ISD/CeO SEM images of the surface of the 0.5 µm thick (a,b), 1.7 µm thick (c,d), and 3.7 µm thick (e,f) YBCO films, respectively. Cracks appeared as a result of manipulation related to taking the images. Circled areas show holes in the structure Critical current density as a function of the thickness of YBCO films SEM images of the cross-section of two films deposited on the STO/ISD- MgO template: (a) monolayer film with the a thickness of about 3.7 µm, and (b) multilayer film with a thickness of about 3.5 µm Magneto-optical images of flux behaviour in 0.5 µm thick monolayer YBCO film deposited on ISD-Mg metallic template. (See detailed description in the text) Typical data of the normalized experimental critical current versus magnetic field XRD pattern of 2% Ag doped and undoped YBCO films. Two insets of Figure 7.1 visualise the two peaks (005) and (007) SEM images of undoped (a) and 2% Ag doped(b) YBCO thin films TEM images of 2% Ag doped (a,b) and of undoped (c) YBCO thin films. The circles enclose precipitates and second phases Normalized magnetization versus temperature dependencies for doped and undoped YBCO films Critical current density of doped and undoped YBCO thin films as a function of applied magnetic field at 10 K and 77 K Critical current density as a function of the YBCO film thickness. Asterisks mark the 2% Ag-doped film Normalized critical current density for pure and Ag-doped YBCO film DC normalized magnetization versus temperature and differential of this function is presented for Ag-doped YBCO film xix

23 xx LIST OF FIGURES 7.9 DC normalized magnetization versus temperature and differential of this function for pure YBCO film xx

24 List of Tables 3.1 Deposition parameters which are constant during target-to-substrate distance study. The thickness of the films investigated varied from 0.3 µm to 1.6 µm Structural parameters which were obtained during model fitting procedure Optimal deposition parameters which were used for multilayering CC study XRD FWHM values of the (005) peak, critical temperatures, and J c values measured at 77 K in self field for YBCO films deposited under optimal conditions Optimal deposition parameters which were used for silver doping study.170 xxi

25 Chapter 1 Introduction to superconductivity and literature review 1.1 Historical overview of superconductivity Heike Kamerlingh Onnes was the first physicist in the world to liquefy helium gas. This tremendous achievement enabled him to discover one of the most intriguing phenomenon in nature - superconductivity. Superconductivity was observed for the first time in purified mercury in 1911 [1] by Kamerlingh Onnes, who purified the liquid mercury and cooled it down to liquid helium temperature. While studying electrical resistivity in mercury and different metals as a function of the temperature, he discovered that the resistivity of mercury drops to zero at a temperature of 4.15 K. This temperature was called superconducting transition temperature (also called the critical temperature), in order to show the temperature point below which the new state was observed. Soon after this discovery, the same sharp decrease to zero was detected in the resistivity of other materials, the first known superconductors. The next step in the evolution of superconductivity research was investigation of electrical properties at cryogenic temperatures of intermetallic compounds, such as niobiumtin, vanadium-silicon, and niobium-titanium, which have been investigated since the 1930s.

26 2 Chapter 1. Introduction to superconductivity and literature review Increase of the critical temperature (T c ) is one of the main goals of superconductivity research; however, the path to high T c is very tortuous. Until the 1980s, all known superconductors had low T c, reaching a maximum of 23 K in NbGe [2; 3]. This imposed significant practical problems for real world applications because of need to use liquid helium as to reach such low temperatures, which requires substantial efforts and cost for its manipulation, transport, and storage. The breakthrough came in September 1986, when researchers Bednorz and Muller synthesized a copper based ceramic that was superconducting with the highest T c then known: 30 K [4; 5]. This breakthrough was the beginning of new era in superconductivity and the start of the race to higher T c superconductors, now called high temperature superconductors (also abbreviated as HTSC or HTS or high-t c ). The compound YBa 2 Cu 3 O 7, commonly named YBCO, was synthesized by Wu et.al. [6] in It was the first superconductor with a transition temperature above the liquid nitrogen boiling temperature, widening the potential superconductor applications to a significantly large extent, as liquid nitrogen is much cheaper and easier to handle as compared to liquid helium. One year later, superconductivity at temperatures as high as 110 K was discovered in Bi-2212 superconductor (Bi 1.72 Pb 0.34 Sr 1.85 Ca 1.99 Cu 3 O x ) [7]. Today, the highest known T c at atmospheric pressure is 138 K recorded in Hg 0.8 Tl 0.2 Ba 2 Ca 2 Cu 3 O 8.33 [8]. Superconductivity was first defined as an absence of resistivity, but later it was found that superconductors also exhibit amazing magnetic properties. In 1933 Walter Meissner and Robert Ochsenfeld discovered that superconductors could repel an applied magnetic field completely [9]. Two ears later Fritz and Heinz London were the first to explain this effect, known as the Meissner effect, using Maxwell s equations [10; 11]. Their theory showed the existence of a thin layer on the surface of the superconductor where the external field decays rapidly. The thickness of this layer is now known as the London penetration depth (λ). Since the discovery of superconductivity by Kamerlingh Onnes, major efforts have been made to explain this phenomenon from the theoretical point of view. In 1934,

27 1.1. Historical overview of superconductivity 3 Gorter and Casimir proposed the first model to describe superconductivity, the two fluid model [12]. This was a phenomenological model and two important assumptions were proposed. Firstly, the electrons of the superconductor were to be classified into two categories: the normal electrons and the superconducting electrons. Normal electrons obeyed Ohm s law, while superconducting ones did not. Secondly, the two fluids play their different roles in the superconductor independently. In 1950 Ginzburg and Landau used the Landau theory of phase transitions to investigate the transition from the normal to the superconducting state [13]. The theory described superconductivity in terms of an order parameter (ψ) and provided a derivation for the London equations. Both of the theories mentioned above are phenomenological in character. The theory of superconductivity made a significant advance in a very fruitful year, 1957, when two theories were proposed. One was proposed by Bardeen, Cooper, and Schrieffer (BCS) and another by Alexei Abrikosov. The first theory is also known as the BCS theory [14]. It is based on the phononmediated coupling of electrons with opposite momenta and spins to form pairs, known as Cooper pairs. The size of such a pair corresponds to the coherence length (ξ). This theory gives a good description of the superconductivity phenomenon in all metallic superconductors. However, it fails to fully explain some experimental observations in HTSC, such as their high T c. Independently, a young Soviet scientist Alexei Abrikosov discovered in the framework of Landau theory that the existence of two groups of superconductors can be distinguished [15]. The ratio κ = λ/ξ is known as the Ginzburg-Landau parameter, where λ is the penetration depth which describes the depth to which an external magnetic field can penetrate the superconductor. It has been shown that Type I superconductors are those with 0 < κ < 1/ 2 and Type II superconductors those with κ > 1/ 2. The next remarkable discovery was made in The quantum tunnelling effects in superconductors were theoretically described by the English student Brian Josephson. He predicted a current flow through a junction consisting of two weakly

28 4 Chapter 1. Introduction to superconductivity and literature review joined superconductors, separated by a very thin insulating barrier [16]. This theory was experimentally confirmed soon afterwards [17]. Three main effects predicted by Josephson were named DC, AC and inverse AC Josephson effects. These effects, now referred to as Josephson effects, are applied in superconducting quantum interference devices (SQUIDs), which are very sensitive magnetometers and are widely used in science and engineering. Two decades after the discovery of the HTSCs, two Japanese scientists J. Nagamatsu and N. Nakagawa announced the discovery of a new superconducting material. In 2001, they found superconductivity in MgB 2 at temperatures as high as 39 K [18]. This discovery stimulated considerable interest in superconducting research groups. The simplicity of fabrication and the low cost of MgB 2 attracted significant interest towards replacing existing superconducting magnets in various applications and verifying the mechanism of superconductivity in this material. Unfortunately, there is no widely accepted theory to explain major aspects of HTSC superconductivity and value of transition temperature in particular to date. The mechanism of high transition temperature in the HTSC remains in question, whether it is driven by electron-phonon coupling or electron-electron interactions which are more significant than electron-phonon interactions in the copper based ceramic. At present, a microscopic theory which accounts all the observed superconducting properties phenomena is still under considerable debate and only qualitative explanation mechanism is available. 1.2 Two types of superconductivity The previous section did not describe the behaviour of magnetic fields and current flows in superconductors. Here, a detailed physical picture of these processes will be summarized. Prior to about 1960, superconductors were interesting from the point of view of physics, but had no practical applications because they could not carry any significant amount of transport current. Only when the existence of two classes of superconductors was discovered did practical applications become possible. These

29 1.2. Two types of superconductivity 5 two classes of superconductors are distinguished as Type - I and Type - II superconductors, also known as soft and hard superconductors, respectively, because of the dramatic difference in their magnetic and current-carrying properties. There is such an enormous difference between current flow in these two types of superconductors that an entire industry is based on Type - II superconductors, while Type - I superconductors have only very limited application. In their experiments, Meissner and Ochsenfeld cooled a superconducting sample below T c and found that magnetic field was expelled from the sample. The phenomenon of repulsion of the magnetic field is produced by a thin screening current that flows around the edge of the superconducting sample and is known as the Meissner current. Figure 1.1: Phase diagram of Type-I (a) and Type-II (b) superconductors. In 1937, by studying the magnetic properties of 11 superconducting alloys, Shubnikov and collaborators observed an unknown superconductive state under high applied magnetic field. Later, this state was classified as the mixed or vortex state and named the Shubnikov state. Figure 1.1 illustrates how all superconductors are divided into two families: Type - I and Type - II superconductors. The response to an applied magnetic field is quite different in the two cases. In a Type - I superconductor, there is an exact cancellation of an applied magnetic field B a by an equal and opposite magnetization (M) up to

30 6 Chapter 1. Introduction to superconductivity and literature review so called critical magnetic field B c. Above the critical field B c, superconductivity vanishes (see Figure 1.1(a)). In a Type - II superconductor, the Meissner effect is partially circumvented. The magnetic field starts to penetrate into the material at a lower critical field, B c1, and penetration increases until the upper critical field B c2 is reached (see Figure 1.1(b)). At this stage the superconductor is fully penetrated by magnetic field and the normal state is restored. Thus, both magnetism and superconductivity can be found in a Type - II material, because it is energetically favourable to have many borders between superconducting and normal state regions, and the equilibrium configuration will be a mixture of the normal and superconducting zones. The first penetration of flux lines occurs in Type - II superconductors at B c1 where a single flux quantum Φ 0 = h/2e = Tm 2, defined by Abrikosov, occupies a core with an approximate radius equal to the coherence length ξ. The flux lines are associated with a normal core of radius ξ. These normal cores are surrounded by a vortex of supercurrent, which decays exponentially over a distance λ. This flux line lattice (FLL) exists in Type-II superconductors in a field range (see Figure 1.1(b)) starting from B c1, when the first vortex enters the superconductor, B c1 Φ 0 ln κ (1.1) 4πλ2 up to B c2, the upper critical field, when vortex normal cores start overlapping: B c2 = Φ 0 2πξ 2. (1.2) It is a worthwhile exercise to illustrate the applicability of this theoretical explanation using a real and well known Type - II superconductors, such as Nb 3 Sn and NbTi. In these superconductors magnetic flux lines penetrate the superconductor as soon as the magnetic field exceeds a particular value, usually around 0.01 T. However, superconductivity is not destroyed until the magnetic field exceeds 10 T or more. In this mixed state, large current densities of the order of 10 6 Acm 2 flow in the presence of large magnetic fields of about 6 T at 4.2 K.

31 1.2. Two types of superconductivity 7 The superconducting state has limits, not only with regard to higher temperatures and higher magnetic fields, but it is also limited by a maximum current density that can be carried through the superconductor. A simple relationship between current and magnetic field for a wire of radius R carrying current I leads to magnetic field at the surface B a = I/2πR. This means that the current cannot exceed a certain critical value that produces a critical magnetic field in the superconductor, which implies a maximum current I c = 2πRB c and critical current density J c = 2B c /R. Looking at Figure 1.1(a,b) and comparing the B c and B c1 for a Type - II superconductor should demonstrate the very limited critical currents due to small B c1, but this is not the case. As was mentioned, the real Type - II superconductors carry large current densities in the mixed state. Vortices which penetrate the superconductor are under the influence of the Lorentz force density F L = J B a, where B a is the applied magnetic field and flux lines have to move in a perpendicular to the J B a plane. Vortex movement, called as flux creep, leads to an induced voltage in the direction of the current and, therefore, to a finite linear resistivity [24; 25; 26; 27]. In real superconducting materials some inhomogeneities are always present. These inhomogeneities provide an effect called pinning, in which the inhomogeneities, acting as numerous pinning centres, pin magnetic vortices that penetrate into the sample with increasing applied magnetic field and prevent their movement. Hence, the Lorentz force is counteracted by a pinning force F pin. At zero temperature, voltage is observed only in the case when J exceeds the critical current density J c = F pin /B a. In the ideal superconducting sample (almost without inhomogeneities) at particular magnetic fields and temperatures vortices interact with each other by repelling each other to form a triangular lattice when the sample is in thermal equilibrium [15]. Such triangular vortex lattices can be observed in Type - II superconductors by using a so-called decoration experiment [20], where very fine particles of iron are allowed to settle on the surface of a superconductor in magnetic field. The flux line lattice can be disturbed from its ideal triangular structure by the presence of defects in the

32 8 Chapter 1. Introduction to superconductivity and literature review superconducting material [21]. 1.3 Critical current and Bean s critical state model For proper characterization of the performance of the superconducting material a precise model of the superconducting current flow has to be developed and appropriate equations must be derived to calculate it. To do so, one can imagine that the transport current is applied from the external source to infinite wire of radius R, which contains a large number of defects that can pin vortices. When it is postulated in Bean s critical state model [22; 23] that irrespectively to sample geometry the transport current and associated magnetic field B a which is lower then B c1 will be located at the outer part of the sample, i.e. surface of the wire. As soon as the field B a exceeds the critical value B c1, vortices will start to enter the body of the sample. While moving towards the center of the wire, the vortices will be pinned by the defects in the sample and, thus, will not be able to penetrate too far inside. This in fact means that a gradient of the vortex density will appear, which at a certain stage, will be the maximum possible gradient. This gradient corresponds to the critical value of the current as per the Maxwell equation B = µ 0 J (1.3) Thus, certain parts of the wire near the surface will carry critical current, while in the rest of the sample, there will be no current at all. This situation is illustrated in Figure 1.2 which shows the distribution of the magnetic field in a cylindrical wire when it carries a current J(x) (perpendicular to the x direction). The Bean s critical state model [22; 23] states that when the transport current increases, the vortices, while keeping the gradient of their density, will move closer to the center of the superconductor so that only a small central part of the wire will remain free of vortices and transport currents, while everywhere else the current J(x) will have the critical value J c. If the current is increased further, at some stage it will

33 1.3. Critical current and Bean s critical state model 9 Current density, J(x) Figure 1.2: Magnetic flux penetration and current distribution in Type - II superconductor in according to the Bean critical state model. reach a certain value I c, when the current density in any part of the wire will be of the critical value. This is called the critical state. In real superconducting wires, when both the applied magnetic field and the applied transport current are present, the physical picture is more complicated. The Bean s model conditions still apply, namely, wherever the current flows it flows at the critical density J c. The induced currents and fields combine with the applied fields to produce the balance of current densities and magnetic fields. For instance this behaviour occurs in a superconducting magnet wire wound as a solenoid to produce strong magnetic field. Using Bean s assumption that the current density is constant across the sample one can calculate the magnetic moment M for many sample geometries with an arbitrary cross-section. This is very useful as many single crystals can be described by such a geometry, which includes disks (pellets), flat samples, slabs and also thin films. An important application of the Bean model is the estimation of critical current of a sample from measuring the magnetization of the superconductor in an applied magnetic field. A certain resistance can be generated by applying a transport current to the superconducting sample, and this is caused by the motion of vortices. This motion is therefore disadvantageous. However, microstructural defects in the superconducting

34 10 Chapter 1. Introduction to superconductivity and literature review material can pin these vortices and impede such motion. Vortices trapped in these pinning sites are effective for blocking the motion of the whole flux line lattice due to the vortex interactions with each other [28]. The superconducting critical state corresponds to a metastable non-equilibrium state where the Lorentz force originating from the applied field is balanced by the pinning force, due to structural defects in the sample which block vortex motion [24; 26; 28; 29]. 1.4 Structural and physical parameters of YBCO As was mentioned, YBa 2 Cu 3 O 7 superconducting material, commonly named YBCO, was discovered in YBCO superconductor is a Type-II superconductor with a critical temperature of 92 K [32; 33]. It has a layered orthorhombic perovskite crystal structure [32], and its unit cell is composed of seven layers in the following order: A Cu-O layer with each copper atom being surrounded by 4 oxygen atoms; this plane consists of parallel Cu-O-Cu-O chains and is referred to as a Cu-O layer A Ba-O layer Another Cu-O layer, but this time, the copper atom is surrounded by 5 oxygen atoms, so it is usually referred as the Cu-O 2 plane A Y layer without any oxygen atoms A second Cu-O 2 plane A second Ba-O layer A second Cu-O layer Cu-O and Ba-O layers act as the charge reservoirs to assist strong superconductivity in the Cu-O 2 planes [33]. A schematic representation of the YBCO unit cell is shown in Figure 1.3. Generally, at room temperature, YBCO displays a metallic behaviour in the ab-plane, with electrical conductivity of the same order as in metallic alloys. Such metallic conductivity in the normal state is due to the copper-oxygen planes [33]. Along the c-axis, however, the electrical conductivity is much lower. Oxygen stoichiometry in YBCO can be illustrated by the parameter x in the YBa 2 Cu 3 O 6+x formula and is crucial to its superconductivity. It was eventually

35 1.4. Structural and physical parameters of YBCO 11 CuO layer CuO layer 2 Cu CuO layer 2 O CuO layer Figure 1.3: Crystallographic structure of YBCO. found that the superconductivity in YBCO is actually not due to Cooper pairs of electrons, but due to Cooper pairs of holes [28]. In the YBCO structure, both Cu 2+ and Cu 3+ are present, which is direct consequence of the oxygen non-stoichiometry in the material. These ions are the hole reservoirs. Their relative proportion depends on the stoichiometry of oxygen as the atoms of oxygen in the YBCO structure give O 2 ions. Thus, when the quantity of O 2 varies, the relative proportions of Cu 2+ and Cu 3+ also vary in order to maintain the electron neutrality of the YBCO material. In addition, if the proportion of Cu 3+ is too low, superconductivity through Cooper pairs of the holes can not occur. By increasing the content of O 2 in YBCO, one increases the proportion of Cu 3+ relatively to Cu 2+ and thus creates or improves the superconductivity due to the formation of Cooper pairs of holes. As a result, in YBa 2 Cu 3 O 6+x, when x < 0.4, the compound is an insulator, but for 0.4 < x < 1.0 the compound becomes a superconductor [34]. At x = 0.4, the YBCO crystal contains some oxygen vacancies, mostly in the Cu-O chains. These vacancies are filled when x increases up to 1 and the unit cell is similar to the one represented in Figure 1.3 [33].

36 12 Chapter 1. Introduction to superconductivity and literature review The highest T c is obtained for x =0.9, and so the exact composition of YBCO is generally described as YBa 2 Cu 3 O 6.9 [33]. As can be seen in Figure 1.3, the in-plane dimensions a and b are much shorter than the c-axis dimension c with a and b equal to 4 Å and c=12 Å (Angstrom unit 1 Å = m) [33]. Such a difference between the in-plane dimensions and the c-axis dimension leads to a strong anisotropy that is reflected in all physical parameters of the YBCO superconductor [33]: The penetration depth within the ab-plane is λ ab 1500 Å The penetration depth within the ac- and bc-plane is λ c 6000 Å The coherence length within the ab-plane is ξ ab 15 Å The coherence length within the ac- and bc-plane is ξ c 4 Å As a result of small coherence length the second critical field B c2 where the superconductor crosses over to the normal state and can be estimated from Equation 1.2 is also dependent on the crystallographic orientation for instance for ab-plane oriented magnetic field B ab c2 150 T and for ac- and bc-plane oriented magnetic field B c c2 40 T. It is worth noting that the coherence lengths of YBCO are comparable to the unit cell dimensions, which implies that any defects in the YBCO crystal structure can act as pinning centres [40]. In fact, as the vortex diameter corresponds to the coherence length, the defects are strong pinning centres when their dimensions are of the order of the coherence length. The high density of pinning defects arising from this short coherence length is thought to be the origin of the high J c values observed in YBCO films, as will be explained in the next sections. 1.5 Properties of YBCO thin films The peculiar anisotropic mechanical and electromagnetic properties, especially the superconductivity, of YBCO material have induced massive research and industrial efforts to create so-called quasi crystals of this material in the forms of thin films fabricated on mono- and polycrystalline substrates, coated conductors, and tapes.

37 1.5. Properties of YBCO thin films 13 At the same time polycrystalline superconducting bulks and single crystals are the most interesting forms for fundamental research. Figure 1.4: Schematic representation of quasi crystal of YBCO. A schematic representation of quasi crystal material is illustrated in Figure 1.4. The single crystal shown in Figure 1.4(1) can be presented as small crystallites perfectly matched to each other, which in metallurgy are also called grains Figures 1.4 (2) and (3). Figure 1.4(3) shows how the single crystal can be accurately split into a certain number of crystallites. All of the crystallites are spread evenly and are oriented in the ab-, ac- and bc-planes. quasi crystals are structural forms that are at the same time ordered and do not recur at precisely regular intervals. Figure 1.4(4) illustrates schematically this kind of crystal, where disorder is introduced into the ab-plane. Conventional physics determine the quasi crystals as structural forms which are both ordered and nonperiodic. Moreover, such a systems from one hand form the patterns that fill all the space but from another hand represent the lack of translational symmetry. Theoretically such a system has been investigated and predicted by Roger Penrose, who organised the so called tilings in such a way where tiles are non-periodic and are considered as aperiodic tiles [41]. The real picture of a quasi crystal is much more complicated, due to the varying grain sizes and orientations. However, all of the grains are oriented crystallographically in one par-

38 14 Chapter 1. Introduction to superconductivity and literature review ticular direction, i.e. perpendicular to the ab-plane. The interfaces between grains are called grain boundaries. Nowadays, the majority of quasi crystals are produced in the form of films. Grain boundaries can be classified according to the displacement and the rotation of the abutting crystallites, as shown schematically in Figure 1.5. For rotational grain boundaries a distinction is made between the tilt and twist (not shown) components of the misorientation. Here, tilt refers to a rotation around an axis in the plane of the grain boundary, while twist is rotation of the crystal grains around the axis perpendicular to the grain boundary plane. Figure 1.5: Grain boundary created rotation around an axis in the plane of the grain boundary. Bednorz and Muller [4; 5] in their pioneering work on high temperature superconductors predicted that grain boundaries generally limit the critical current density J c in the polycrystalline HTSC samples. Many groups have measured the currentcarrying properties of grain boundaries in samples prepared by the bicrystal technique [42; 43; 44; 45], where two single crystal substrates are joined with a predetermined misorientation angle between them. A large misorientation angle θ (see Figure 1.5) on the one hand and d-wave symmetry of the superconducting wave function responsible for superconductive current carriers anisotropy [46] with a very small coherence length of YBCO material on the other hand are serious drawbacks for the intergranular current carrying capabilities of the quasi crystals. To the

39 1.5. Properties of YBCO thin films 15 surprise of many researchers, it was found that the grain boundaries in YBCO films with very large misorientation angles generally act as Josephson junctions. These high-angle grain boundaries strongly impede the current flow and are referred to as weak-links. When characterized by these properties, grain boundaries in the HTSC differ fundamentally from their counterparts in classical metallic superconductors and MgB 2. Some differences in the behaviour of the grain boundaries can exist between films processed using different deposition methods [44]. The decrease of J c with the misorientation angle is not linear [44], but has been shown to be exponential [40] with a decrease in J c by one order of magnitude for every 11 [43]. Moreover, Ref. [44] showed that the transition from strong to weak-links with the misorientation angle between 7 and 10 is progressive at 77 K in zero applied magnetic field. This transition also occurs for larger angles (between 10 and 15 ) and at higher applied magnetic field fields. In order to overcome this problem, considerable research effort has been devoted towards fabrication of epitaxial YBCO films, with the goal of developing and improving deposition processes to manufacture films with ideal crystallographic alignment [40]. Epitaxial films have very high J c values, i.e. two to three orders of magnitude higher than the reported J c values for single crystalline samples [47]. These high values are considered to be due to the high density of different defects that are present in YBCO films which effectively act as pinning centres [48; 49; 50; 51]. Strong pinning is very important for practical applications, as it reduces the J c dependence on the applied magnetic field and on the temperature. Hence, a thorough understanding of the formation of pinning centres as well as pinning mechanisms related is required [51]. There are many different type of defects found in YBCO films: stacking faults in the ab-plane, lattice mismatch edge dislocations, twin boundaries, antiphase boundaries, low- and high-angle grain boundaries, etc. [52; 53] (see Figure 1.6). These defects are mostly formed during the deposition and growth processes of the film, and their density depends on the structure of the substrate and the processing conditions, as

40 16 Chapter 1. Introduction to superconductivity and literature review well as on the thickness of the film [43; 54]. Figure 1.6: Schematic view of various defects in thin films that can act as effective flux pinning sites [53]. The growth of YBCO films on flat substrates has been shown [47; 52; 55; 56; 57] to be largely governed by island-mode growth rather than by a layer-by-layer mechanism. The island-mode growth mechanism leads to the presence of spiral structures [47; 52], where each YBCO grain in the center contains a spiral dislocation (also known as a threading dislocation) extending through the whole film thickness (see Figure 1.6). These dislocations have diameter close to the YBCO coherence length and thus can act as pinning centres. The island growth mode, typically, also leads to a rough surface of the films, especially when the thickness of the film is increased. In particular, this growth mode leads to the formation of a network of grain boundaries that spread across the YBCO film, as shown in Figure 1.7. In terms of their shapes, all pinning sites can be classified into four categories as proposed in Ref. [58]: The volume pinning centres are defects with all dimensions larger than the vortex diameter. The planar pinning centres are defects with two dimensions larger than the vortex diameter. The linear pinning centres have only one dimension larger than the vortex diameter.

41 1.5. Properties of YBCO thin films 17 The point pinning centres have all their dimensions comparable or smaller than the vortex diameter. All of these defects can generally be observed in YBCO thin films. Grain boundaries, twin boundaries, antiphase boundaries, screw dislocations, edge dislocations, precipitates, surface roughness, and oxygen vacancies are all considered to be good candidates for pinning centres, but it is not yet fully understood whether or not one type of pinning center dominates the overall pinning mechanism in the YBCO thin films. Figure 1.7: Schematic view of grain variety in YBCO film (quasi crystal). Misoriented grains form the network of ab-plane (also called in-plane) grain boundaries. The oxygen defects known as oxygen vacancies, as point pinning centres, were first thought to be the main cause of the observed high J c values. However, further investigation showed that no modification of the J c is observed in single crystal samples when oxygen content is varied [47]. This fact rules them out as the dominating pinning centres in YBCO thin films. The contribution of point pinning defects can be increased and analysed by the deposition of YBCO thin films on a substrate with a modified surface. In Ref. [59] YBCO thin films were deposited on different single crystal substrates which were modified with silver nanodots. Obtained J c values were higher by up to one order of magnitude when compared to plain YBCO thin films. The authors explained this strong enhancement in J c by an increase in the density of point defects caused by the presence of the Ag nanodots, which consequently would increase the pinning strength. However, their results have not been reproduced in high quality YBCO

42 18 Chapter 1. Introduction to superconductivity and literature review thin films. It is thus possible that the presence of the Ag nanodots only leads to a higher crystallographic quality of the YBCO films, thus increasing their current carrying capabilities. Detailed investigation and discussion of the silver doping effect in YBCO thin films is presented in Chapter 7 in this work. Critical current deterioration under applied external magnetic field is governed significantly by linear and planar defects, which thus form the overall pinning strength of YBCO thin films [61; 62; 63; 64]. The majority of these defects are generated by the grain boundaries which usually are numerous in YBCO films (see Figure 1.7). Their central role in pinning mechanisms in YBCO films is illustrated in the forms of twin grain boundaries [65], low angle grain boundaries [43; 64], and antiphase boundaries [48; 49]. Linear defects have been shown to make a greater contribution to the pinning as compared to planar defects, point defects, or surface roughness [61; 62; 63; 64]. Anisotropy and the existence of an ensemble of defects also influence the behaviour of vortices and their movement in the superconductor. In c-axis oriented YBCO thin films, J c varies with the orientation of the applied field [35; 36]: at low field, J c is at a maximum when the field is oriented along the c-axis. At high field, however, J c variation as a function of the orientation of the applied field exhibits two maxima: one, when vortices are aligned with the Cu-O plane (external field parallel to the ab-plane), and second, when vortices are aligned with the c-axis (external field parallel to the c-axis) [37]. The authors of Ref. [37] explained this by the strong pinning force created by the presence of out-of-plane edge dislocations parallel to the c-axis (Figure 1.7). Moreover, it has been shown that, even at high fields, for which the density of vortices is higher than the density of linear defects, the pinning mechanism is largely determined by the presence of these linear defects [66]. In fact, at high magnetic fields, only a small portion of vortices is actually pinned, and there are vortex-vortex interactions which induce a collective pinning of the entire vortex lattice [66]. In addition, as YBCO is a layered HTSC, when magnetic field is applied along the c-axis and thus the flux lines are perpendicular to the Cu-O planes, vortices

43 1.5. Properties of YBCO thin films 19 have tendency to dissociate into weakly coupled pancake vortices [38; 39; 87; 88]. Refs.[67] and [63] propose the idea that the strength of pinning by linear defects is such that any contribution to J c from the roughness of the film surface or other similar defects is negligible. However, due to the strong decrease in the pinning strength when the film thickness is increased, several studies have suggested that the pinning role of the film surface can be more significant than the role of other pinning sources [68]. Numerous works have shown strong degradation of the microstructure with increasing thickness, d, of YBCO films [50; 56; 64; 69]. The reduction of J c values when the film thickness is increased is attributed more to the microstructure deterioration. On the other hand, the effect of the surface roughness should not be neglected: by using results of some magneto-optical observations [57], a model was developed demonstrating that attraction of the vortices towards the thinner areas of the films occurs, and it was estimated that 10% to 30% of the J c value was due to the surface roughness. In an effort to increase the transport current I (also called the engineering current), a large number of misleading results was produced, as critical current density J c decreases with increasing film thickness d above 200 nm, and this effect is independent of the deposition technique used to fabricate the film. This decrease is primarily supposed to be caused by a strong deterioration of the film microstructure as the deposited thickness is increased [56; 68; 69; 70; 71; 72], leading to the formation of voids, misoriented grains and a generally rougher surface. It was shown that no supercurrents are carried in the top layers of the YBCO film (above 2 µm), which have most degraded microstructure [70; 73]. On the other hand, it was shown that for films with d > 3 4 µm, J c also decreased in the lower layers close to the substrate. To overcome this problem, BaZrO 3 nanodots were introduced into the YBCO films to decrease the thickness dependence of J c due to the degradation of the microstructure [60]. It is important to note that the inverse J c (d) d 1/2 dependence varies when the

44 20 Chapter 1. Introduction to superconductivity and literature review magnetic field is increased: at high fields, the optimal thickness (thickness where the highest J c is obtained) tends to increase. This was explained in Ref. [76], as at low fields most of the current density is flowing near the surface (surface current) and is mostly influenced by the surface geometry of the superconducting YBCO films. This current flow represents a much higher fraction of the overall current in thinner films, leading to higher J c values at low fields in thinner films. On the contrary, at high fields, the currents which are flowing in the inner part of the sample dominate and, thus, the J c will be higher in thicker films. The same shift of J c (d) dependence towards higher optimal thickness is observed with increasing temperatures [75; 76; 77]. In order to circumvent the deterioration of superconducting properties with increasing thickness while still increasing the superconductor cross-section, multilayer films have been synthesized. The multilayering technique offers the possibility of keeping high J c values while increasing the YBCO film thickness, thus increasing the overall current carrying capabilities in the conductor. Different multilayer combinations have been tried: either with CeO 2 or with ReBCO (Re being a rare earth metal) [78; 64; 80]. These compounds are selected for deposition as interlayer materials as they have an excellent lattice parameter match with YBCO, have good chemical compatibility, and are thermally stable at YBCO deposition temperatures. Multilayer samples produced by Jia at al. [78] were reported to have J c values as high as about 1.4 MA/cm 2 at 75.2 K, even for thicknesses of 3.6 µm, and in some cases, the J c values obtained in multilayer films were as high as for thin monolayer YBCO films with optimal thickness [64; 80]. Chapter 5 is dedicated to the discussion and investigation of the multilayering effect on J c performance of YBCO superconductor films. 1.6 Applications of superconductors Absence of electrical resistivity and unique magnetic properties make superconductors the material of choice in a wide range of applications. In this Section some of the examples of applications of the superconductors are listed, along with the limi-

45 1.6. Applications of superconductors 21 tations that researchers are trying to overcome today. Superconductor applications can be divided into two main categories: high power applications, using the high current transport capabilities of the superconducting materials, and superconducting electronics, which use quantum properties of the superconductors. Superconducting transmission lines and cables, magnets, transformers, generators, fault current limiters, and energy storage devices fall into the first category of high power applications [40]. They all use the absence of electrical resistivity to surpass their conventional-material based counterparts [81]. In transmission lines, the use of superconductors not only permits a significant reduction of energy losses, but also makes it possible to carry a much higher amount of current for the same cross-sectional diameter of transmission line than in conventional cables [40]. Indeed, some researchers have already estimated that superconducting power cables could be as much as 7000% more space efficient than copper cable [82]. With the dramatic increase in energy demands around the globe, this is an important advantage. This extraordinary current carrying capability also makes superconductors the best candidates for the development of powerful magnets, delivering magnetic fields over 20 T. In fact, to generate magnetic field of the same magnitude, a superconducting magnet will be far smaller than a magnet made of copper wires. These powerful magnets play a crucial role in some impressive applications, such as magnetic levitation(maglev) trains, particle accelerators, fusion reactors, or magnetic resonance imaging (MRI). MagLev trains can levitate above the rails owing to the magnets in the railway and the superconducting magnets under the carriages, hence eliminating the losses due to friction, enabling once again a more efficient use of the energy. Very powerful superconducting magnets are also used in big research facilities such as particle accelerators or in fusion reactors to confine plasma, as is done in the International Thermonuclear Experimental Reactor (ITER), a fusion reactor project that is being developed in France. Furthermore, superconducting magnets are used in MRI (Magnetic Resonance Imaging) to provide medical researchers with another mean of

46 22 Chapter 1. Introduction to superconductivity and literature review non-destructive visualization of the structure and functions of the human body. Another large scale and high current application is in the field of energy storage. Since superconductors have no resistivity, a current can be stored in a superconducting loop and can be used as a readily available source of energy in the case of a power failure in the energy network system. Superconductor based energy storage units could increase stability of the entire energy network system, ensuring its maximum effective performance, and diminish the possibility of long power interruptions. Furthermore, a rapid transition from the superconducting state to the normal state when the superconducting material is affected by abnormally high current (above its J c ) can be used to build up ultra-fast fault current limiters [40]. Superconducting Quantum Interference Devices (SQUIDs) represent one of the best known examples of the application of superconducting materials in electronics. Today these devices are the most sensitive devices in the world for the detection of magnetic flux. They are the main components of magnetometers used in research laboratories and are also beginning to be used in hospitals in the field of biomagnetism (magnetoencephalography, magnetocardiography). SQUIDs are based on the Josephson junctions effect observed solely in superconducting materials. Josephson junctions are also an active area of research for the development of quantum computers with increased calculation speed [83]. Until recently, niobium alloys (NbTi, Nb 3 Sn) have been the favourite materials used for fabrication of magnet for MRI purposes. Indeed, they possess attractive mechanical properties and their T c is the highest among superconducting metallic alloys. However, these materials still need to be cooled down below 10 K, implying the use of liquid helium, which limits considerably any wider usage of superconductor based applications due to their high operational costs. The discovery of HTSC has opened new perspectives in terms of wider low cost applications. Today, the best candidates among HTSC for electrical current transmission are the two cuprate perovskites commonly referred to as Bi-2223 and YBCO as well as the newly discovered MgB 2 [18]. Although these superconductors are already used in

47 1.7. HTSC for Coated Conductors (CC) 23 real world applications, their potential has not yet been fully realized. Understanding current limiting mechanisms and methods to improve their processing technology are fundamental issues and are invaluable for advancement of their practical applications. 1.7 HTSC for Coated Conductors (CC) As shown in Section 1.1, the potential applications of superconductors have been apparent since superconductivity was observed for the first time by Kamerlingh Onnes. Kamerlingh Onnes could have imagined superconducting magnets that would have magnetic fields far beyond those produced by the usual iron magnets or solenoids. However, this vision had to wait for 50 more years, mostly because the physics of superconductivity in magnetic fields was not understood. The first step towards high field applications was made by Kunzler et al. [84] who showed that high-field applications were really possible, when Sn was drawn inside a Nb wire to form a brittle intermetallic Nb 3 Sn alloy. The current density of about 10 2 Acm 2 at 8.8 T and 4.2 K was staggering for that time and it was clear that with further development of superconductor technology even higher values could be achieved. At present, laboratory-scale superconducting magnets are very abundant, with some producing fields exceeding 20 T. These magnets, as well as those used for magnetic resonance imaging for medical purposes, use superconductor wires based on Nb 3 Sn or NbTi alloys. Although the material is metallic and readily available metal manufacturing techniques can be used to produce these wires, the major drawback is that Nb 3 Sn and NbTi have low T c. This implies that liquid helium must be used to reach temperatures at which the alloy becomes superconducting. Consequently, operational costs associated with cooling make these superconductors too expensive for replacement of conventional electrotechnology based on Cu and Fe, two cheap and well-studied materials. Prospects for the application of superconductors were changed dramatically by Bednorz and Muller. Shortly after their discovery, other copper based ceramics were found to be superconducting at temperatures as high as 138 K. This is well above

48 24 Chapter 1. Introduction to superconductivity and literature review the boiling point of liquid nitrogen at 77 K, thus giving a new boost to ideas for applications of superconductors in many fields. In 1987 Time magazine featured the discovery of high temperature superconductors and described HTSC as a startling breakthrough that could change our world. The fundamental novelty of HTSC materials was high T c, which implied a corresponding significant reduction of expenses would give HTSC materials an advantage in major applications. Many obstacles slowed the way toward practical HTSC applications. For instance, one obstacle was to learn how to make useful materials from brittle ceramic compounds that exist in multiple phases and morphologies. Another hurdle was to recognize the real advantages that HTSC offer to the applications and to realize these advantages in cost-effective products. High-temperature superconductors are among the most complex materials ever explored for practical applications. To realize the idea of producing a long-length superconducting wire for electrical transmission purposes, one would have to control many parameters: the chemical stoichiometry of the compound at elevated temperatures, the brittleness of this materials, and the volatility of some of the constituents. In addition, special needs must be satisfied for chemically nonreactive, lattice-matched, and thermally matched substrate material. Cost effective technology to form a wire long enough to be practically useful had to be developed. Moreover, high-power applications need flexible, robust, high-current wires that are kilometres in length. Generally, conductors for power applications are multifilamentary wires or tapes in which many superconducting filaments are embedded in a matrix of a normal metal, such as Cu or Ag [85]. When all of the requirements for the production of wire were considered, only two HTSC materials were identified as candidates for such applications: YBCO and Bi At present, only a few superconducting wire manufacturers are capable of delivering first generation (1G) HTSC wire to the market. The first generation superconducting wires are made using a mechanical deformation process that aligns crystalline Bi-2212 grains within the silver matrix, and thus minimizes the contri-

49 1.7. HTSC for Coated Conductors (CC) 25 bution of grain boundaries to the flow of electrical current. This type of wire is available as Ag-sheathed Bi-2212 with T c =108 K. These commercially available wires with cross-sectional dimensions in the range of to mm have critical current densities of 10 4 A/cm 2 in self magnetic field at 77 K (boiling point of liquid nitrogen) and are 1 km in length. Despite the fact that 1G conductors are able to carry currents as high as 100 A/cm width of engineering current, the cost of manufacturing of these wires is still too high for them to penetrate market at full scale and replace existing Cu and Fe based conductors. For electrical wire, the figure-of-merit for comparing costs of different materials at a particular operation point has been US dollars per kiloampere meter (USD/kA m). This reflects the twin purposes of a wire, namely, to carry high currents over great distances. The prices for 1G wires today are at approximately 100 USD/kA m, but the forecast for the years is at the level of 30 USD/kA m for operation at 77 K. It is known today the comparative tradeoffs between refrigeration and wire manufacturing costs, and recognising that NbTi cost 1 USD/kA m, Nb 3 Sn 8 USD/kA m (each at 4.2 K), and Cu cost 12 USD/kA m, Al 3.2 USD/kA m, Fe 0.5 USD/kA m (all at room temperatures), it is generally thought throughout the HTSC community that it will be necessary for HTSC wires to sell for about 10 USD/kA m in order to have substantial penetration to electrical power transmission markets. Practical design problems occur in the development of the joints to connect separate wire lots (done by a soldering process) and the fabrication of insulation (glass fibres, polyamides, also in the form of enamelled wire, and other types) since both disturb the thermal compactness. In recent years, a new strategy to improve the grain alignment and to achieve high current density in a wire with sufficiently low manufacturing costs is being researched. The strategy is to texture a flexible metal strip or its covering oxide layer, and then epitaxially deposit superconductor onto it. Once this so-called coated conductor or second-generation (2G) wire is mass produced, it could enable HTSC wire operating at 77 K to have a price/performance ratio at or even below that of the conventional copper wire found in power equipment. The engineering critical current of these wires

50 26 Chapter 1. Introduction to superconductivity and literature review matches or even exceeds that of the first generation wires, and the mechanical properties are also superior. Ambitious plans of the wire manufacturers envision that these wires will be introduced into a broad market in a few years to come. The estimated costs associated with the starting materials are very low, i.e. 6 USD/kA m and thus it is believed that effective application of superconducting technology for energy transmission can be realized by using superconducting film on metallic substrates. The dimensions of the conductors should be kept the same as for the presently used Bi-2212, which will allow the introduction of second generation conductors without significant redesigning of present manufacturing technologies. The total manufacturing prices will be reduced to the level of 30 USD/kA m over the next few years. The second-generation wires based on YBCO will inherently have some better characteristics than the first generation wires, allowing higher operating temperatures and larger mechanical strain. A schematic view of a coated conductor, consisting of a flexible metallic substrate, several buffer layers, an epitaxial superconducting layer and a cap protective layer, is shown in Figure 1.8. In order to obtain a biaxially textured superconducting layer with the minimum amount of high-angle, weakly conducting grain boundaries, biaxially textured substrates have to be used. Three techniques for producing biaxial texture in the substrate have been developed recently: ion beam assisted deposition (IBAD) of biaxially textured buffers on polycrystalline alloy substrates, epitaxial deposition of buffer multilayers on rolling assisted biaxially textured substrates (RABiTS), and inclined substrate deposition of buffers on polycrystalline alloy substrates (ISD). Generally speaking, the RABiTS method is distinctively different from the others (IBAD and ISD), as the texture is created in the tape prior to the formation of buffer layers. The other two methods, i.e. inclined substrate deposition and ion beam assisted deposition, are designed to cause crystal grain alignment of a buffer layer on top of non-textured high strength metallic substrates. The substrate strip made from polycrystalline nickel or nickel alloy consists of many smaller crystallites

51 1.7. HTSC for Coated Conductors (CC) 27 Cup - protection layer HTSC - YBCO Textured buffer layers Polycrystalline or textured Ni based alloy Figure 1.8: Schematic representation of Coated Conductor. without preferential orientation. making the strip notably non-textural. Recently, Malozemoff et al. [86] showed that coated conductors produced by the RABiTS technique can exhibit a performance of A/cm width at 77 K. This is well comparable to that of 1G superconducting wires. However, this is still below the 200 A/cm width threshold mark, which is considered to be the level that will enable broad market penetration for a wide variety of applications. At this stage, it is still not clear which technique will win out. The present design of coated conductors is such that a substrate thickness of µm is needed to support 1-5 µm of YBCO film, giving a superconductor fraction of only 5-10%. To increase the fraction of the superconductor, i.e. increase critical current, one should increase the thickness of the deposited HTSC. However, thicker YBCO layers tend to exhibit less epitaxy, more porosity, and thus smaller critical current densities. Degradation of the J c with increasing film thickness is a serious and poorly understood problem. Chapters 5 and 6 of this work have been dedicated to the investigation of the effects of multilayering for the improvement of critical current carrying capabilities of coated YBCO conductors.

52 28 Chapter 1. Introduction to superconductivity and literature review

53 Chapter 2 Characterization methods and techniques Figure 2.1: Schematic layout of the Bragg-Brentano geometry. 2.1 Characterization of the thin film microstructure X-ray diffraction analysis X-ray diffraction (XRD) is the most convenient and straightforward tool to analyse the structural properties of prepared materials, whether they are quasi crystalline, monocrystalline, polycrystalline, or in powder form [90; 91; 92]. Schematic representation of diffractometry used in this work is illustrated in Figure 2.1. Basic parameters of typically used diffractometry (called also Bragg-Brentano

54 30 Chapter 2. Characterization methods and techniques geometry) are: (a) the incident angle, ω, is defined between the X-ray source and the surface of the sample; (b) the diffracted angle, 2θ, is defined between the incident beam and the detector angle; (c) the incident angle ω is always half of the detector angle 2θ. In this work, the crystallography of the majority of prepared thin film samples was analysed using a MAC-Science x-ray diffractometer equipped with θ-2θ scan function. In this instrument, the position of the sample is fixed, and the X-ray tube and the detector rotate at the same rate. The equipment uses a copper target in the tube as the X-ray source (wavelength = Å) for X-ray generation. The tube voltage during measurements is 40 kv, while the current is 20 ma. Another system used for characterization of the films is the GBC MMA diffractometer. The X-ray wavelength, and the operating voltage and current were the same as for the MAC-Science. In this instrument, the tube is fixed but the sample rotates at θ/min and the detector rotates at 2θ/min. Most of the scans of the thin films were taken between 5 and 55 at the rate of 2 per minute with a step size of For precise measurement of some characteristic peaks of the thin films the scan rate was decreased to 0.02 per minute, giving much better intensity readings. It is important to mention that one of the crucial aspects for obtaining good x-ray diffraction data is the alignment of the specimen in the equipment. A slight divergence of the sample orientation in the apparatus leads to significantly increased or decreased intensity of the measured peaks. Fine optimization of the sample alignment is crucial for adequate comparison of different thin film samples. To do so, all samples were placed onto a sample holder by using a little piece of Blu-Tac for alignment. Samples then were placed onto a metal disk and a small handheld press was used to evenly press the sample and thus obtain perfect horizontal orientation. The phase purity of the targets used for fabrication of thin film samples was also analysed by x-ray diffraction. As targets usually are very big bulks, only a small piece of material was used for structural analysis purposes. A small piece of target

55 2.1. Characterization of the thin film microstructure 31 material was crushed in an agate mortar and this powder was placed onto a special sample holder. The powder was secured on the sample holder by addition of a few drops of ethanol, which was then evapourated, and finally, a piece of glass was used to make the surface of the powder specimen flat Atomic force microscopy (AFM) Atomic force microscopy (AFM) is a method for measuring surface topography on a scale ranging from a few Angstroms to 100 micrometers. AFM is an extremely sensitive technique, which utilizes a reflective cantilever with a mounted nanoscale tip. a a a a a a a a Figure 2.2: Schematic layout of the atomic force microscope AFM uses a laser beam deflection system, where a laser beam is reflected from the back of the reflective AFM cantilever onto a position-sensitive detector. The detector usually consists of an array of photodiodes. In addition to basic AFM contact regime, the instrument is capable of producing images in a number of other modes, including tapping, magnetic force, electrical force, and pulsed force. In general, the sensitivity of the AFM equipment in vertical deflection at contact force mode is in the picometer (10 12 m) range. In contact mode, the AFM cantilever lightly touches surface of the sample [93]. The tip is then dragged by the instrument

56 32 Chapter 2. Characterization methods and techniques over the designated area on the sample. A motor driving the Z-axis motion of the scanner will react to the change of the deflection to make the force of the tip touching the sample approximately constant. The Z-motion is recorded as the height signal. In order to overcome the limitations of contact mode imaging, the tapping mode of imaging has been developed [94; 95; 96] where the cantilever is allowed to oscillate at a value close to its resonant frequency. When the oscillations occur close to a sample surface, the probe will repeatedly engage and disengage with the surface, restricting the amplitude of oscillation. As the surface is scanned the oscillatory amplitude of the cantilever will change as it encounter differing topography. By using a feedback mechanism to alter the Z-height of the piezoelectric-crystal and maintain a constant amplitude, an image of the surface topography may be obtained in a similar manner as with contact mode imaging. In this way as the probe is scanned across the surface, lateral forces are greatly reduced compared with the contact mode. Magnetic force imaging option creates images of the spatial variation of magnetic forces on a sample surface [93]. For that mode, the tip is coated with a ferromagnetic thin film. The system operates in non-contact mode, detecting changes in the resonant frequency of the cantilever induced by the magnetic field s dependence on tip-to-sample separation. Magnetic force imaging can be used to image naturally occurring and deliberately written domain structures in magnetic materials. Electric force imaging [93] mode of the AFM maps electric properties on a sample surface by measuring the electrostatic force between the surface and a biased AFM cantilever. Voltage between the tip and the sample has been applied while the cantilever hovers above the surface, not touching it. The cantilever deflects when it scans over static charges. In that mode, images contain information about electric properties such as the surface potential and charge distribution of a sample surface. That mode maps locally charged domains on the sample surface, similar to how magnetic mode plots the magnetic domains of the sample surface. The magnitude of the deflection, proportional to the charge density, can be measured with the standard beam-bounce system. Thus, electric force imaging option can be used to study the

57 2.1. Characterization of the thin film microstructure 33 spatial variation of surface charge carrier. For instance, electric force imaging option can map the electrostatic fields of a electronic circuit as the device is turned on and off. This technique is known as voltage probing and is a valuable tool for testing live microprocessor chips at the sub-micron scale. Pulsed force imaging mode of AFM is very similar to a contact mode operation, but the vertical motion of the probe avoids for the sample or the probe to suffer from damaging shear forces. Also, compared to an tapping mode that allows for elaborated surface analysis, the pulsed force imaging mode operation represents a powerful tool as it provides a convolution free characterization of topography, adhesion and stiffness properties. Pulsed imaging mode can be used to study non-homogeneous surfaces from many different materials such as polymer blends, composite materials and sticky surfaces [97]. All AFM measurements in this work have been performed in contact regime. The AFM system used for thin film characterization purposes was Dimension 3100 (Digital Instruments). The tips and cantilevers were standard Si 3 N 4 type with a tip-end radius of 20 nm. The scans were taken in the areas of the samples, which were selected as representative for a given thin film. The size of scanned area was 5 5 µm, with 512 lines being taken at 2 Hz. Height images were taken using a data scale of 500 nm; roughness data were also recorded. The Number Average Roughness (R AF M ) of the sample was chosen as the parameter specifying the roughness of the sample Optical microscopy Optical microscopy is a quick and effective tool to assess the surface quality of fabricated films [98]. Thin film surfaces can be viewed by optical microscopy; however, the resolution of a standard optical microscope with visible light diffraction is limited to a lateral resolution of about 0.5 µm with poor depth of field at high magnifications. It can be successfully used to observe structural integrity, for example cracks or scratches, and to some extent estimate the porosity of the films. In the schematic

58 34 Chapter 2. Characterization methods and techniques Human EYE Eyepiece Half-transparent mirror Light Objective lens Object Figure 2.3: Schematic layout of the optical microscope layout of the optical microscope (Figure 2.3), the light from the microscope lamp passes through the condenser, and then is reflected from or passes through the specimen. Such light is called direct light or undeviated light. The background light (often called the surround) passing around the specimen is also undeviated light. At the same time, some part of the light is deviated when it encounters parts of the specimen. Such deviated light (called diffracted light) is rendered one-half wavelength or 180 degrees out of phase with the direct light that has passed through the sample and is undeviated. The one-half wavelength out of phase, caused by the specimen itself, enables this light to cause destructive interference with the direct light; finally, both types of light arrive into the observers eye or camera through several apertures and lenses. A Leica DMRM Optical Microscope has been utilized in this work and was successfully used to capture images of film surfaces with magnifications varying from 100 to 500 times. A digital camera separated from the eyepiece lens was used to record high quality still images in electronic format Scanning Electron Microscopy (SEM) To investigate the microstructure, surface properties and elemental distribution in the samples, a JEOL 6460A Analytical Scanning Electron Microscope was used. The surface is viewed in an optical-like form. The operation principle of SEM is similar to

59 2.1. Characterization of the thin film microstructure 35 that used in optical microscopy. A schematic view of a scanning electron microscope is shown in Figure 2.4. Instead of visible light, SEM uses a focused beam of electrons. The secondary electrons are then reflected from the specimen surface and picked up by a detector and transformed into an image. The intensity and the angle of emission of electrons depend both on the surface topography and the material. This technique has high lateral and vertical resolution. The biggest difference between an optical microscope and the SEM is that latter uses scanning electron beam of a shorter wavelength [99; 100]. Because a stable electron beam usually can be obtained only in vacuum, the specimens are studied in vacuum. As a result, a sample suitable for SEM observation has to be solid to preserve integrity in the vacuum. SEM enables analysis of a wide range of materials and samples with resolution as high as 10 Å. The electron gun filaments used in this work were LaB 6 type and tungsten. LaB 6 uses lanthanum hexaboride cathode material which has improved stability, a long lifetime, and reduced aperture contamination effects. Electron source (electron gun) Scanning coil aaaaa aaaaa aaaaaaaaaaaa aaaaaaaaaaaa aaaaaaaaaaaa aaaaaaaaaaaa aaaaaaaaaaaa Figure 2.4: Schematic view of the scanning electron microscope. One of the main requirements needed to obtain good quality images is good electrical conductivity between the sample and the sample mount of the SEM. This is needed for good drainage of the electrons from the surface of the films. The accumu-

60 36 Chapter 2. Characterization methods and techniques lation of charge on the surface can result in an excessive brightness in the secondary electron image, a continuous image drift, and a blurred image under high magnification. In order to avoid accumulation of the charge, the films were electrically connected to the metallic SEM specimen stage by a conductive carbon tape or conductive silver paste. For a cross-sectional view of the samples, which is needed for estimation of the thickness of the samples, as well as for observation of various multilayers, samples were bent from flat to 90 angle (in the case of films deposited onto metallic substrates) or cut (in the case of single crystalline substrates) and attached with conductive silver paste to the sample holder in the perpendicular direction to the sample holder base Transmission electron microscopy (TEM) For investigation of the fine microstructure of the samples (down to atomic scale) transmission electron microscopy (TEM), a JEOL 2011 Instrument equipped with a JEOL energy dispersive spectroscopy (EDS) System has been used. This technique provides a much higher spatial resolution as compared to SEM and can facilitate the analysis of features at an atomic scale (i.e. in the range of a few Angstroms) using electron beam energies in the range from 60 to 350 kev. Generally, SEM is used to observe bulk specimens, and the image obtained shows the morphology of the surface [100]. For the specimens with rough surfaces, the morphology may change, depending on the view direction. For good TEM observation it is necessary to make the specimen thin enough to be able to transmit the electron beam; therefore, thin sections are cut from a bulk specimen for observations. This technique makes it possible to access and investigate the inner structure of the specimen. The information gathered is highly dependent on the origin of the specimen and the direction in which it was cut. Such a difference between SEM and TEM principles requires higher beam energies for the latter. A TEM uses an electron gun to produce the primary beam of electrons that is focused by lenses and apertures into a very narrow, coherent beam. This beam

61 2.1. Characterization of the thin film microstructure 37 Figure 2.5: Schematic view of the transmission electron microscope. then strikes the specimen and due to its high energy, some electrons are able to go through the sample; they are then collected at the other end by detectors, creating an image (see Figure 2.5). Crystalline materials are able to diffract the incident electron beam. Consequently, one can observe variations in local diffraction intensity, and then translate this to form an image. These patterns then can be used to analyse the crystallographic structure of the samples under investigation. For amorphous materials, contrast is achieved by variations in electron scattering, as the electrons experience the chemical and physical differences within the specimen. TEM is a challenging technique. Not only does it require expertise in the operation of the equipment, but the sample preparation is a scrupulous and lengthy process. For the cross-sectional observations, the samples were prepared at the Electron Microscopy Unit, University of New South Wales using a focused ion beam technique. The apparatus uses a fine, energetic beam of gallium ions that is scanned over the surface, of the specimen. At high beam currents, the gallium beam rapidly sputters away the specimen surface, allowing subsurface cross-sections to be patterned. When the energy of the beam is reduced and secondary electrons or ions emitted from the specimen surface are detected, high resolution images can be obtained as well.

62 38 Chapter 2. Characterization methods and techniques In this work, samples were analysed by TEM (JEOL, JEM 2010) which is available at the University of Wollongong. The beam energy was 200 kev, which corresponds to an electron wave length of Å Profilometry A stylus profilometer, a Veeco Dektak 6M, was used to determine the step height of the films deposited onto the single crystalline substrates. Steps on the substrate could be achieved by partially shielding the substrate during the deposition process. This instrument can measure small surface variation, which gives the profile of the vertical displacement of the stylus in contact with the sample as a function of position (see Figure 2.6). The basic profilometry measurement principle is as follows: the stylus is moved vertically in contact with the sample, and then moved laterally across the sample for a specified distance, speed, and contact force [101]. The height position of the diamond stylus generates an analog signal, and this is converted into a digital signal which is stored, analysed and displayed on the computer. The stylus tracking force can range from 0.03 to 40 mg. Figure 2.6: Schematic view of the stylus profilometer.

63 2.2. Electromagnetic characterization 39 The sample being investigated must be flat and levelled. With proper selection of the stylus force, both hard and soft materials can be measured. The maximum possible measurable step height is approximately 1 mm, while the smallest detectable one is about 10 nm. Generally, the instrument has a point-to-point resolution of 1 Å. Horizontal resolution of the device can be adjusted to less than 0.1 µm, depending on the scan speed and length. Vertical step resolution is limited mostly by the stylus tip radius of 12 µm. The step height is a direct measure of the film thickness, and can give information on the growth rate of the films under definite deposition conditions. In this work, the scans have been done with duration of 12 seconds over a length of 2 mm. 2.2 Electromagnetic characterization Magnetic measurements of critical current densities Knowledge of the amount of current that a given superconducting sample is able to carry is one of the most valuable pieces of data for development of superconductors, especially in view of future power applications such as superconducting wires, magnets, transformers or generators (see Section 1.6 for more details about superconducting applications). To measure this quantity, two types of techniques have been used in this work: magnetic and transport measurements. The majority of the measurements of the critical current have been undertaken using the Magnetic Property Measurement System (MPMS) manufactured by Quantum Design. This technique allows for an indirect measurement of the critical current as compared to electrical transport measurements. The magnetic moment of the sample is measured by a SQUID in the MPMS while the sample is moved through superconducting coils. The sample is located in the center of a superconducting solenoid producing magnetic fields up to 5 T. The sample space is filled with helium at low pressure at temperatures ranging from 2 to 400 K. The sensitivity of the system is 10 8 emu or Joule/T. This value is equivalent to the saturation magnetization

64 40 Chapter 2. Characterization methods and techniques Figure 2.7: Schematic view of the MPMS of an extremely small amount of six billionth (6/ ) of a cubic millimetre of iron or 1012 Bohr magnetons. The measurement system is fully computercontrolled and is operated 24 hours a day. Measuring sequences can be programmed in advance and are executed automatically without the user s intervention, except for changing samples and refilling the system with liquid nitrogen and helium. The magnetic signal of the sample is obtained via a superconducting pick-up coil with 4 windings (see Figure 2.7). This coil, together with a SQUID coil, is a part of a superconducting circuit transferring the magnetic flux from the sample to a SQUID device which is located away from the sample area in the liquid helium bath. This device acts as a magnetic flux-to-voltage converter. This voltage is then amplified and read out by the SQUID electronics. When the sample is moved up and down, it produces an alternating magnetic flux in the pick-up coil which leads to an alternating output voltage of the SQUID device. By locking the frequency of the readout to the frequency of the movement, the magnetometer system can achieve extremely high sensitivity for ultra-small magnetic signals as described above. To determine the J c, the magnetic moment m of the sample is measured in varying magnetic field in order to obtain a hysteresis loop for the sample (see Figure 2.8). The extracted value of the vertical width of the magnetization loop, m, is then

65 2.2. Electromagnetic characterization 41 Figure 2.8: Magnetic moment as a function of the external applied magnetic field for the determination of critical current density J c (B a ). used to calculate J c as a function of the applied field based on the critical state model [117; 118]: J c = D M m V (2.1) where D M is the demagnetization factor and V is the volume of the sample. D M depends on the sample shape and orientation with regard to the applied magnetic field. General, presentation of relationship between magnetic moment m and current density J(r) in an arbitrary shaped sample is given by m = 1 2 V 0 [r J(r)]d 3 r (2.2) where J(r) is current density and in according with critical state Bean model [117; 118] is constant across the sample and equal to critical current(see Section 1.3). It

66 42 Chapter 2. Characterization methods and techniques gives simple recalculations of the magnetic moment for any shaped sample of arbitrary cross-section to sample critical current at particular magnetic field orientation. In this work, the J c in thin films was calculated with the applied field perpendicular to the surface of the films (for derivation see [102]). In this case, J c can be expressed as: J c = M a ( 1 a 3b ) (2.3) for thin films, with a and b corresponding to the width and length dimensions of the sample (a b) and M = m/v (with the magnetization, M, is defined as the quantity of magnetic moment per unit volume: M = m/v ). For disk-like films, J c is calculated from the equation: J c = 3π M 4r d (2.4) where r d corresponds to the radius of the superconducting disk (for derivation see [102]). Magnetization loops were measured in accordance with a programmed sequence where the temperature during the measurement of the magnetization loop was constant. For each magnetic measurements of J c, the temperature was varied to study its influence on the J c behaviour as a function of the external magnetic field. Thus the dependencies of the critical current vs. external magnetic field, and of J c (B a ) on temperature J c (T ) were obtained and analysed in this work. Transport measurements were performed using the four-point probe method at 77 K in liquid nitrogen. In this measurement technique, four wires are connected to the sample with a specific orientation: the two outer leads deliver a transport current to the sample, while the two inner contacts are used to measure the voltage. In the superconducting state and when the current supplied is below the critical current I c, the current flows in the sample without dissipation, and thus no voltage will be measured between the two innermost contacts (except instrumental and contact voltages). However, when the applied current is increased above I c, the voltage will

67 2.2. Electromagnetic characterization 43 appear and will rapidly increase. As the transition from dissipation-free (superconducting state) to resistive (normal state) transport current is continuous, a criterion is needed to precisely determine I c in a reproducible way. Therefore, I c is generally defined as the value of the applied transport current for which the voltage increases above the value of 1 µv. As the voltage measured between the two inner contacts also depends on the distance between these contacts, the standard value is defined as 1 µv/cm with the two voltage contacts spaced by 1 cm on the sample. In fact, to calculate the critical current density it is necessary to divide I c by the cross-sectional area, S, of the sample: J tr c = I c S (2.5) assuming that the current is flowing through the whole cross-section of the sample. A magnetic field can be applied during the transport measurement in order to study the variation of J tr c with the applied magnetic field. However, in this work transport measurements were only done in self field mode (B a =0). Although both the techniques presented above give information about the current capabilities of the superconducting sample, a weak-link (crack, high angle grain boundary, or non-superconducting secondary phase) between the two voltage contacts in the transport measurement technique can affect the current path, in extreme cases blocking it. Another disadvantage of the electrical transport measurement method is the heating of the connecting wires and current contacts on the sample. In order to apply smaller currents during measurements, the films have to be patterned to create smaller current paths sized to µm width. Laser etching (patterning) or standard lithography methods in this case lead to the degradation of critical temperature and critical current of YBCO thin films. Hence, transport measurements of J tr c films reflect information about the current from a very local area of the whole thin film. On the contrary, the magnetic measurement of critical current density is nondestructive and demonstrates the average critical current value of the whole thin on

68 44 Chapter 2. Characterization methods and techniques film sample. Magnetic measurements have become more popular during the last two decades since the magnetometers and superconducting magnets have become commercially available. Moreover, the sample preparation procedure and measurements are much simpler than these for electrical transport method, resulting in higher yield of research papers published during the last few years in this field Magnetic measurements of critical temperatures In this work, the critical temperature T c of superconducting samples was determined via magnetic measurements conducted on the same MPMS equipment used for the determination of J c (Section 2.2.1). As explained in Section 1.2, Meissner current flows in a superconducting material at low temperature in a weak applied magnetic field. This Meissner current shields the superconductor from the magnetic field. It creates a magnetic moment, which has a direction opposite to the direction of the applied magnetic field. When the temperature is increased close to T c, magnetic flux begins to penetrate the sample, and the magnetic moment decreases. Above T c, the Meissner current completely disappears, and thus, the magnetic moment vanishes. Figure 2.9: Magnetic moment as a function of the temperature for the determination of critical temperature and transition width.

69 2.2. Electromagnetic characterization 45 The MPMS allows for measurement of the magnetic moment and its variation as the temperature is increased from below T c to above T c in a small applied magnetic field. In practice, the sample is cooled in zero field (ZFC) to a temperature of 10 K. Then, a weak magnetic field is applied, typically 25 Oe, and the temperature is progressively ramped to 93 K progressively. Around T c, the magnitude of the negative magnetic moment decreases dramatically, until it becomes zero when the sample reaches its normal state. In some cases, as it increases in the positive direction, the magnetic moment crosses the zero level line, but it soon drops back to zero value. Such transitions are shown in Figures 2.9 and The point where the magnetic moment reaches the zero level is identified as T c. In this work, the value of the transition width, T (see Figure 2.9), is defined from the m(t ) curve measured in the ZFC regime as well. This value is extracted from the difference between the two temperatures which correspond to m=0.4 and m=0.6 of the m(t ) curve, with m being normalized to the value of the moment at 10 K. The transition width is very important, because it shows the quality of the samples and together with critical temperature reflects the fraction of non-superconducting phase in the material Magneto optic imaging (MOI) A method to study magnetic and current-carrying properties of superconductors that allows visualization and measurement of the spatial distribution of the magnetic flux density in a sample is highly desirable. To understand the microscopic properties of superconducting thin films, such as magnetization, magnetic susceptibility, and critical transport currents, one needs to use some sort of local probe. Magnetooptical imaging is one of a very few tools that are suitable for these purposes (see overview Ref. [103]). The physical principle of magneto-optical measurement is based on the Faraday effect (Faraday rotation or magneto-optical effect). This effect based on the rotation of the polarization plane of a linearly polarized light beam when it passes through

70 46 Chapter 2. Characterization methods and techniques Camera and computer Exit analizer analyser Entrance polarizer Beam splitter Magneto-sensitive film Mirror Superconductor B a Solenoid Figure 2.10: Schematic diagram of the Magneto Optic Imaging (MOI) principle used to obtain high quality MO images. the sample in the direction of the force lines of an external applied magnetic field. In real experiments, the reflection scheme of the Faraday effect can be well applied to examine the magnetic properties at the surface of superconducting thin films. Figure 2.10 presents a schematic diagram of the Magneto-Optical Imaging (MOI) system based on the Faraday effect. Incident polarized light passes through the beam splitter and then is transmitted to a transparent magneto-sensitive indicator film, which is placed directly on the superconductor film, the light is reflected by the surface of the mirror. If a perpendicular external field is applied, the magnetization vector of each magnetic domain of the magneto-sensitive film is rotated in the direction of the local magnetic field, producing a perpendicular component of magnetization in the direction of the external field. This component makes the transmitted light Faraday rotated. As a result, the intensity of the reflected polarized light passing through the beam splitter and exit analyser is reduced, so the magneto-optical image becomes

71 2.2. Electromagnetic characterization 47 lighter. If the magnetic field is plotted as a function of space, the magneto-optical image has brighter and darker areas. The resulting picture consists of brighter areas, where the magnetic field is stronger, and darker ones, where the magnetic field is weaker. Detailed study of the greyscale of the image leads to the determination of the magnetic flux distribution in the sample. During the past several years, this technique has proved to be extremely useful for visualization of magnetoelectric properties of HTSC materials [103] due to its capability to observe dynamic processes i.e. observation of flux motion due to thermal activation or even quantum creep, and under the influence of transport currents. It has been shown that magneto-optical techniques are a unique tool to show that flux patterns are extremely sensitive to the presence of defects, structural inhomogeneities, etc. Moreover, magneto-optical images representing the magnetic field distribution are determined by the film s structure and are not affected by random external magnetic fields. In this work, we used a home-built MOI set-up for the characterization of the samples. The MOI set-up was constructed by Assoc. Prof. Alexey V. Pan at ISEM. The system can reach temperatures down to 1.9 K, owing to liquid helium cooling, and an external magnetic field of up to 0.1 T can be applied. Presented work used indicator (MOL) is ferromagnetic YIG film with in-plane magnetization. During the measurements, the MOI indicator is placed in the path of the light beam between the polarizer and the analyser, which are positioned at 90 degrees to each other. To capture magnetic features of the superconductors, a digital camera is attached to the microscope set-up.

72 48 Chapter 2. Characterization methods and techniques

73 Chapter 3 Development and optimization of the pulsed laser deposition process 3.1 Thin film growth technique Introduction to the growth of YBCO thin films The high temperature superconductor YBCO is believed to have enormous potential for a wide range of applications, i.e. SQUID devices, superconducting electronics, magnetic detectors, frequency filters for mobile communication operations, etc. Thus, this potential has driven significant efforts in exploring the fabrication of YBCO in the epitaxial form of thin films. As was mentioned in previous chapters, epitaxial films are the films having almost ideal crystallographic alignment and can be treated as quasi crystals. The term epitaxy, or epitaxial growth mode, comes from the beginning of the last century. Initially, epitaxy was associated only with oriented crystal growth mechanisms [104], but with increased availability of advanced materials analysis methods, one had to refer to epitaxy as relating to the atomic scale compatibility between the two crystal lattices. At present, the detailed crystallographic mechanism for successful epitaxial growth is still not completely understood. However, a simplified schematic of the physical picture of epitaxy can be drawn (Figure 3.1), where atoms are deposited onto a substrate.

74 Chapter Development and optimization of the pulsed laser deposition process Dropping particle Adatoms Substrate Figure 3.1: Schematic of the basic processes occurring in epitaxial growth. In general, particles or atoms emitted from the target material by laser light, electrical discharge or a radio frequency source are deposited (dropped) onto a substrate where they become adatoms, which jump around on the surface until they meet another deposited adatom. As soon as adatoms combine, they form nucleation centres, which form atomic size islands. Thus, the term epitaxy can be described as the process of the growth of a crystal of a particular orientation on the surface of the same type of crystal (homoepitaxy) or another crystal (heteroepitaxy), where the orientation is determined by the crystallographic orientation of the underlying crystal (substrate). Epitaxy itself is not the only requirement for synthesis of high quality YBCO film. Since YBCO is a compound with a complex crystal structure, stringent control of the chemical composition during the deposition process is essential. Even with the correct stoichiometric composition, the formation of a specific YBCO oxide phase requires optimization of both the temperature and the partial pressure of the chosen oxidizing species, consistent with the thermodynamic phase stability of the compound. Because the electronic properties of the superconducting YBCO are dependent on oxygen content, specific oxidation conditions after the film growth are generally required in order to achieve optimal oxygen doping, which makes the sample superconducting. These collective requirements can be satisfied for nearly all the techniques presently used for fabrication of YBCO thin films. Numerous deposition techniques are avail-

75 3.1. Thin film growth technique 51 able for the epitaxial growth of YBCO films. These include in-situ growth techniques, in which the correct crystallographic phase is formed as the material is being deposited, as well as ex-situ techniques, where a film that is either amorphous or a mixture of polycrystalline phases is deposited and then is subsequently annealed to form the desired YBCO superconducting phase. For the in-situ process, the kinetics of epitaxial film growth, along with the thermodynamic requirements for proper phase formation, typically require deposition at elevated temperatures ( C) in an oxidizing ambient atmosphere. In-situ deposition techniques usually consist of two steps: (1) deposition at high temperature (with the substrate temperature during deposition of YBCO varied depending on the process pressure from 650 C for low-pressure evapouration processes to 780 C for high-pressure sputtering processes; see Figure 3.2) and (2) post-deposition oxygen treatment during which the phase transition from the tetragonal to the superconducting - orthorhombic phase occurs. In-situ growth techniques that are being successfully employed in the synthesis of epitaxial YBCO films include so called physical deposition techniques, such as coevapouration [105; 106], molecular beam epitaxy (MBE) [107; 108], pulsed laser deposition (PLD) [109], and sputtering [110]. In physical deposition, the phase constituents are delivered as a flux of individual atoms, particles, clusters of particles or simple oxide species. Atomic-level control of the film-growth process is possible with most of these methods, thus enabling the formation of novel thin film structures [111; 112]. Other techniques that have proven to be useful in obtaining epitaxial YBCO films are metal-organic chemical vapour deposition (MOCVD) [113] and liquid-phase epitaxy (LPE) [114]. Discussions of the very general features and of the advantages and disadvantages of the most common deposition techniques can be found in the literature [105; 106; 107; 108; 109; 110; 116]. Typical preparation regimes for the different techniques are presented in oxygen pressure - temperature diagrams (see Figure 3.2 taken from Ref. [115]). The YBCO phase is stable in the regime indicated by the shaded area, which is divided into the tetragonal and orthorhombic phases. The deposition typically takes place in the

76 Chapter Development and optimization of the pulsed laser deposition process tetragonal regime; then, in-situ post-deposition treatments typically follow, leading to the orthorhombic phase (see routes (A) and (D) depicted in Figure 3.2). Figure 3.2: Ambient oxygen pressure v.s. temperature phase diagram for YBCO according to Bormann and Nolting [115] Pulsed Laser Deposition (PLD) technique The pulsed laser deposition technique was first used more than two decades ago. However, it underwent its renaissance when the technique was found to be the most convenient and efficient technique for synthesis of YBCO thin films. In PLD, a laser pulse strikes a solid bulk YBCO target. Some amount of the target material is evapourated in the form of a plasma plume. Part of the plume comes into contact with the surface of a heated substrate kept a few centimetres away from the target. The plume, consisting of the flowing particles of the YBCO lattice, attacks the substrate. The result is deposition of a thin film of YBCO material with the same chemical structure as the target. Thus, PLD offers numerous advantages, including film stoichiometry close to the target, a low contamination level, and a high deposition rate.

77 3.1. Thin film growth technique 53 The relatively easily accessible experimental parameters in PLD make it a very attractive technique for the synthesis of YBCO thin films. These parameters are the substrate temperature, the energy of the flowing particles, the relative and absolute flow rates of particles, and the pressure in the chamber. In order for any thin film technique to be highly suitable for the growth of YBCO films, the following conditions must be fulfilled: (a) the substrate temperature should be accurately controlled; (b) all atoms in the deposition flux should have a particular energy in order to promote surface diffusion, nucleation, and enough adhesion to stick to the surface; (c) the atoms of a multicomponent material should arrive in the precise relative amounts required for the final compound; and (d) all of the processing has to be undertaken in a high partial pressure of reactive gases such as oxygen to maintain stoichiometry of volatile species on heated substrates and to control the energy of the deposited flux. While some of the thin film deposition techniques mentioned in the previous section control two or three of the parameters well, only PLD meets all the criteria for the best deposition characteristics, especially precise relative arrival rate of atoms. In situ processing of YBCO thin films is facilitated by the non-equilibrium nature of the laser deposition. Plasma generated by laser irradiation of the target can be used to assist the growth of very high quality thin films at relatively low processing temperatures. The processing temperature in PLD is generally C lower than that used in other thin film growth techniques (see Figure 3.2). Atomically ordered layered structures can easily be fabricated by this technique. The cost advantage is attractive when one considers that PLD system can produce films with quality comparable to MBE systems that cost 10 times as much or more. Another advantage of the PLD, in terms of usage and cost, resides in the fact that the energy source that creates the plume of species, the laser, is independent from the deposition system. By moving various targets into and out of the beam complex structures with several layers of different materials can be obtained. Additionally, by using mirrors to change the beam path, several deposition systems can be installed around a single laser to

78 Chapter Development and optimization of the pulsed laser deposition process create a thin film deposition laboratory. method one of the most popular methods to deposit thin films. These advantages have made the PLD PLD system setup in the Institute for Superconducting and Electronic Materials The PLD system installed in the Institute for Superconducting and Electronic Materials (ISEM) consists of an oxygen-compatible vacuum chamber made by Neocera Inc. and an excimer laser made by Lambda Phyzik. The basic experimental design for existing thin film deposition system is similar to any other physical vapour deposition process. The apparatus installed in ISEM is depicted in Figure 3.3. A 52 litre spherical high vacuum chamber contains a sample heater, a manipulator, a target holder, and a shutter. The target holder block is mounted on a linear motion feedthrough which is used to exchange targets and rotate them at about 0.5 Hz, which is incommensurate with the laser repetition rate. Targets are installed on six target holders, and the substrate is mounted on a substrate holder, which acts as a substrate heater. The substrate holder has precise temperature control with a K - type thermocouple placed in the middle of it. The excimer laser (Lambda Phyzik - model Compex 301) which operates using a mixture of Kr - krypton and F - fluorine gases, generates pulses with a wavelength of 248 nm and is used for target deposition. An ultraviolet laser has been found to result in congruent deposition when the duration time is about ns and pulse repetition rates are in the range of 1-10 Hz, delivering a maximum energy of Joule/pulse. An aperture, called the beam limiter, is placed in the beam s way in order to cut out the non-uniform edges of the output laser beam. The actual laser influence is varied by either varying the laser output energy or by focusing the beam. The laser beam is focused by a perpendicularly assembled spherical lens with the focal length of 70 cm, which is situated outside the chamber. The focused laser beam is 45 from the target normal, and the plume is generally perpendicular to the target surface. The total energy loss at the lens and the window is less than 5%. Therefore,

79 3.1. Thin film growth technique 55 Plume Heater Target Focused laser beam Figure 3.3: Schematic view of the PLD system installed in the ISEM. throughout the text, laser energy is defined as the nominal energy detected by the inner Compex 301 laser detector, where the laser beam is coming out from the laser generator. The laser beam is admitted into the chamber via a specially coated quartz window. Transparent to the laser s wavelength, it is susceptible to damage if the energy density is too high or if the window is covered by dust particles. Moreover, the sides of the chamber contain several quartz windows: one to yield access to the chamber, while the others are for in-situ plasma diagnostics and monitoring of the position of the substrate in the plume. Vacuum in the chamber is achieved by a pump system which consists of a roughing pump (Varian SD-301) and a turbomolecular pump (Varian Turbo-V 550).

80 Chapter Development and optimization of the pulsed laser deposition process Deposition procedure The preparation procedure for the deposition can be started the day before the actual deposition takes place, as the chamber has to be pumped to Torr vacuum. The surface of the heater or removable plate is polished with sandpaper to remove oxides or residues from previous depositions. After that, the plate is cleaned with acetone and dried by flowing nitrogen or compressed air. Simultaneously, the substrate is cleaned with acetone and dried as well. The substrate then is placed on top of a small drop of conductive silver paste. Some pressure has to be applied to the substrate to spread the silver paste uniformly to the edges of the substrate. A heater gun is used to dry the substrate within 5-10 minutes to get rid of wet solvents and acetone. At the same time any dust particles attached to the substrate are removed as well. Then the removable plate is installed onto the heater in the chamber. It is very important to have good thermal contact across the whole substrate, heater surface, or removable plate, as otherwise the substrate temperature is not homogeneous enough, resulting in poor quality YBCO films. Targets of the desired materials have to be polished and mounted onto rotating target holders. Then the chamber is evacuated by the roughing pump to reach the forevacuum. When the chamber pressure is below 100 mtorr, the turbomolecular pump is switched on. After all these steps are accomplished, the heating process can be started. The pressure in the chamber could rise with temperature due to outgassing from the vacuum parts. In order to bake the vacuum parts in the chamber, a 200 C temperature must be applied until the next day, when deposition is made. After completion of the preparation process, the deposition of the films can be performed on the same day, but it usually is carried out on the next day. The vacuum pressure in the chamber has to be around Torr. A heating temperature of approximately 780 C is applied. The final step before the deposition is to adjust the ambient oxygen pressure. The pressure level in the chamber should be about 300 mtorr for YBCO deposition. For some other non-superconductive materials such as CeO 2 or silver the background gas pressure should be different and has to be

81 3.1. Thin film growth technique 57 experimentally obtained during the optimization process. At this stage, the rotation motor of the target holder is turned on. Prior to deposition, the target surfaces have to be cleaned with the laser beam. To achieve homogenous films, the plasma plume of particles has to be directed towards the center of the substrate by adjusting the manipulator position. The deposition starts with by turning on the laser at the selected pulse-repetition rate (usually 5 Hz). The length, the colour, and the shape of the plume all depend on the ambient oxygen pressure. At low pressures ( Torr), the center of the plume is barely recognizable, which makes it difficult to properly adjust the position where laser pulses hit the target. This is a particular problem when depositing silver. Typically, the deposition time of YBCO film is 5-10 minutes and the resulting thickness of the deposited layer is approximately nm. Therefore, the deposition time can be shortened (to about 5-7 minutes) if the target-to-substrate distance is smaller or the oxygen pressure is lower, so that the plume is longer and wider. All parameters, such as the oxygen pressure and the substrate temperature are very important and have to be stable during deposition. After the deposition, the rotating motor is turned off, the laser is switched off, the post-annealing process begins. This step is necessary to allow the formation of the orthorhombic superconducting lattice phase (for instance, route (D) shown in Figure 3.2). The temperature of the substrate is decreased to 400 C within 30 minutes. This decrease has to be slow in order to avoid sudden changes in the substrate temperature. Approximately at 500 C, the chamber is filled with oxygen to a pressure of 1 atmosphere. The system is left in this state for at least one hour to ensure sufficient oxidization of the film. After annealing, the heater power is reduced down slowly to prevent the film from cracking due to a sudden drop in temperature. A slightly different post-annealing technique is applied when YBCO material is deposited onto metallic substrates covered with buffer layers (see details in Chapter 6). The heater and targets have to be cooled down for a few hours to room temperature and, usually, the deposited film is taken out of the chamber on the same

82 Chapter Development and optimization of the pulsed laser deposition process day. The removable plate or whole manipulator with the heater is quickly placed on the table. The substrate is removed gently from the surface to avoid bending by pushing the substrate with tweezers and scalpel. The film is stored in a small paper package, and the packages are further stored in a desiccator filled with silica gel to avoid chemical reaction with water in the air. In some cases, a passivation of the films by deposition of a silver layer is done to protect the YBCO film from degradation and to form a base for electrical contacts. YBCO target Rotation direction Silver target Laser beam-target Interaction areas Direction of switching between two targets Laser beam Figure 3.4: Schematic view of the deposition setup. During the deposition process this configuration makes it possible to switch targets without stopping the laser shoot. The majority of monolayer films produced by this technique were used to achieve the goals in this work. In order to make the multilayered superconducting structures, the sequential deposition of one target material after another was applied. The interval between the depositions of YBa 2 Cu 3 O 7 and NdBa 2 Cu 3 O 7 materials was 60 seconds. In cases where buffer layers were deposited before the superconducting films, the interval was 5-15 minutes due to the different substrate temperature and

83 3.1. Thin film growth technique 59 oxygen pressure applied. To introduce controllable amounts of silver particles into the superconducting YBCO film a new method was developed, which has not been previously described in the literature. The usual and easiest way to add dopants to the growing film during the PLD process was by using simple replacement of a segment of the target material with the dopant material. In this method the concentration of doped material is adjustable by the sizes of the segment introduced into the target. The bigger the angle of the segment is, the higher the amount of additional material that is deposited from the target. In this work a totally different approach was implemented. To introduce silver particles as a dopant material, a target switching method has been applied. The main idea of this method was to place two rotating targets Ag and YBa 2 Cu 3 O 7 as close to each other as possible (see Figure 3.4). During the operation of the laser, this particular configuration allows one to swap targets between them, which results in controllable numbers of shots directed to each of the target materials. This method leads to fine, very tuneable doping and a procedure with no interruptions, allowing homogenous embedding of the dopant material in the film matrix. Results of this method are reported and discussed in Chapter Development of PLD system in ISEM A few distinctive changes have been applied to the PLD system during this work. Initially, the system was designed in 1997 by Neocera, Inc. ( In general, the system is capable of producing quality films. However, while operating the system, several problems have been identified. The architecture of the substrate holder with the installed heater did not satisfy our requirements. For instance, the arrangement of the working parts did not allow for positioning inside the chamber when it was pumped, preheated and ready for deposition. This small adjustment was necessary from one deposition to another in order to put the substrate exactly within the center of the plume. The plume and the relative position of the substrate in it is

84 Chapter Development and optimization of the pulsed laser deposition process the central factor to obtain high quality YBCO thin films. Proper calibration of the position alone can require 5-7 depositions, and it is very time consuming. Additionally, the old sample holder required constant removal of the entire assembly to change each substrate between depositions. Moreover, the thermocouple was positioned in the center of the heated disk and at least 5 mm away from the mounted substrate. To overcome these drawbacks a new substrate manipulator was purchased and fitted into the existing setup. This manipulator consisted of a new substrate heater and removable substrate holder, and most important, allowed movement of the substrate in three directions during deposition. The new low-voltage heater needed an additional transformer and temperature controller to be installed as well. A sliding removable plate was designed that would be easily extracted from the chamber though the access window. The access window with removable sample plate enabled deposition to be performed much more quickly and simply. However, this design had further flaws. Due to the movement of the removable plate relative to the surface of the heater, the thermal transfer was not sufficient. Consequently, a temperature gradient of 250 C between the inner heater temperature and the temperature on the surface of the removable plate was observed. The working temperatures in our experiments were in the range of C. It means that the heater was working on the upper limit of its heating capability. It is important to note that the heater was constructed from nickel chromium alloy, and the maximum heating element temperature itself is about 1250 C. This specification implies a shorter lifetime of the heater. After two months in operation this heater had become useless, and it became apparent that a new heater must be designed if extensive and long-term experiments were planned to be performed in this PLD system. Several commercially available heaters on the market, both boron nitride and silicon nitride based heaters, were available. They were unnecessarily bulky, brittle, and expensive. We required a heater that would be inexpensive and simple in design. As such simple requirements could not be fulfilled by commercially available heaters,

85 3.1. Thin film growth technique 61 it was decided to manufacture and design a home-built heater, which would employ conduction heating of the removable plate with a mounted substrate and would be able to withstand an oxygen environment at temperatures of up to 850 C. The operation rate should also correspond to as low a fraction of its rated power as possible. The power required to achieve a particular temperature may be kept low by reducing the surface area of the heater and by reducing its effective emissivity. The emissivity may effectively be handled by a single radiation shield. In some cases two or three shields had to be employed. Additionally, the losses to power leads and mechanical support of the heating elements play a role in heat leakage. In principle, every heater which has even one Watt power, with enough insulation, could reach temperatures of 1000 C. Yet, one thousand Watt heater with high heat losses will be still incapable of reaching 500 C. Figure 3.5: The construction of the heater parts. The diagrams of the heater support, radiation shield, and removable plate are shown in Figure 3.5. The heating element (not shown) has to be bent into a flat, spiral-like configuration to be mounted between the radiation shield and the removable plate. Three screws allow for simple substrate mounting and good contact with the heating spiral. A 1.6 mm diameter hole was drilled inside the removable plate to

86 Chapter Development and optimization of the pulsed laser deposition process install a grounded thermocouple. The end of the thermocouple was placed exactly under the substrate mounting area. After careful investigation, it was obvious that a thermal gradient between the substrate and the thermocouple was unavoidable. To circumvent this disadvantage, the tip of the thermocouple had to be placed as close to the substrate as possible, making the difference between the real and measured substrate temperature about 2-4 C. The mask The substrates (a) The thermocouple tip (b) The thermocouple sheath Figure 3.6: The positioning of the thermocouple on the surface of the removable plate. Figure 3.6(a) and (b) shows two variants of the thermocouple mounting on the removable plate. The thermocouple, which was fabricated in the ISEM s workshop, is unsheathed and is depicted in Figure 3.6(a) with two mounted substrates. To obtain good thermal contact with the metallic plate, we screwed and cemented the tip of the thermocouple with silver paste. The great disadvantage of this temperature control method was in the difficulty of cleaning the plate after each deposition. To prepare the plate before each deposition the thermocouple had to be disassembled. After two or three times the thermocouple was broken due to mechanical bending.

87 3.1. Thin film growth technique 63 Figure 3.6(b) shows the new design of the plate. A sheathed and grounded thermocouple was purchased. The removable plate was thick enough to drill a 1.6 mm diameter hole to install the thermocouple in the body of the plate parallel to its surface (see Figure 3.6(b)). Moreover, special gold coated connectors were made to allow easy removal of the thermocouple wires from the chamber. All of these developments significantly improved temperature control and decreased the time required for optimization of deposition. The importance of precise temperature control during deposition is discussed in the next section Study of optimal deposition conditions Successful thin film deposition can only be achieved if the effects of the growth parameters are well understood. The key aspect of good deposition is the optimization and reproducibility of these parameters. The parameters which determine the kinetics of the growth of YBCO films, their epitaxy, microstructural evolution, and, hence, the physical properties of the films grown by PLD can be divided into three categories. All of these categories can be summarized as shown in Figure 3.7. One group of parameters corresponds to the parameters related to the laser beam - target interaction; the second group reflects all the parameters associated with the ablating plume, while the third group of parameters is related to the substrate and superconducting film itself. There are, of course, parameters which are relevant to the particular chamber or preparation procedure. They are quite reproducible within one set of experiments when substrates from the same batch are used with the same target. In addition, the flux of contaminants which comes with the flux of film material and is incorporated into the film during deposition has to be taken into account and is strongly dependent on the base pressure, pumping speed, and pre-deposition chamber cleanliness. Detailed modelling and studies of the laser - target interaction can be found in Refs. [119; 120; 121; 122]. It is understandable that the local temperature of the target increases due to the absorption of the laser light, and almost immediately the

88 Chapter Development and optimization of the pulsed laser deposition process Figure 3.7: Schematic presentation of the concepts of reproducible thin film deposition. top surface of the target begins to evapourate. The heat required for vapourization is supplied from a layer below the top surface. Thus, surface evapouration provides a cooling mechanism which can lead to a higher temperature of the layer below the surface than the temperature of the evapourating surface layer. If the temperature of this subsurface layer is high enough to result in vapourization, then the underlying material will burst out from the target, taking the surface layers with it and forming a highly directed plume of ablated material above the target. High speed of evapouration leads to a congruent nature of the deposition process, as there is no time for component atoms to decompose [123; 124]. During this work, in order to have a process which allowed for good reproducibility of the laser - target interaction, the targets were polished before each deposition with fine sand paper. Moreover, they were kept in a desiccator to avoid unwanted reactions with the water vapour in the air. It is important to note here that laser beam wavelength and the pulse duration are out of our control. The use of the 248 nm laser wavelength is close to optimal, because the shorter the wavelength of the laser, the smaller is the amount of particles

89 3.1. Thin film growth technique 65 in the film (see Ref. [142]). The laser beam focus is also well reproducible, and different target surfaces of different target materials have to be placed to the same plane to be in the same focus position. The laser energy parameter must be optimised and controlled from one deposition to another because the excimer lasers tend to decrease their output power due to gas aging effects. As has been mentioned, the optimal energy to be used is one where the laser optical system is not affected, which in our case is Joule/pulse, and the size of the plume is about 5-7 cm. It is obvious that some parameters from the first group (Figure 3.7) determine the parameters in the second one. For example, the energy density and focusing of the laser beam change the shape and size of the plume and the homogeneity of the components in it. At the same time, studies of the plume and its interactions are complicated because of its kinetic nature. Simply, the plume has two notably visible features: (a) it is directed in a perpendicular direction to the target surface, and (b) it is brightly coloured. For illustration, the colour is green for the deposition of copper, silvery blue for iron rich compounds, and blue with red outer edges for the deposition of YBCO in oxygen. Using an analogy with the well-known flame tests, it may be assumed that the colours arise from the electronic excitation of different spectroscopic species inside the plume. However, one should remember that visible emission from exited states in the plume comprises just one observable component of the plume [143], although, non-emitting ground state atoms, ions, and molecules are observable by optical absorption spectroscopy as a slower component in the plume transport (see Ref. [143; 144]). The pressure gradient within the plume is greatest in the perpendicular direction to the surface of the target, and so the constituents of the plume have the greatest velocities in this direction too. Time-of-flight studies of the plume just above the deposition threshold have recorded ionic velocities of the order of 100 m/s, corresponding to energies of ev [125]. This leads to the forward directional characteristic of the deposition process. Theoretical analysis [126] predicts that velocities of the

90 Chapter Development and optimization of the pulsed laser deposition process species within the plume should display a mass dependence weaker than the thermal dependence (where the velocity is inversely proportional to the square root of the mass) due to the collisions within the plume. Indeed, time-of-flight measurements of the velocities of Cu +, Ba + and Y + ions at several centimetres from the target surface determined that all three species had almost the same velocity [127]. The existence of this area supports the presence of an optimal target-to-substrate distance (see Section 3.2). The initial expansion of the plasma is one-dimensional in a distance comparable to the laser spot diameter. In this dense region, the plasma is heated by absorption of the laser beam to temperatures of several thousand degrees. Beyond this heating zone, the plasma expands in the three-dimensional manner. The typical time of flight before collision with the substrate position is around several microseconds. At such temperatures, ionization due to collisions is expected to be negligible [128], and so the laser beam itself must be the dominant source of ionization, even during very short durations of 25 ns. The high energy of the plume leads to a pressure of more than mtorr, which drives the expansion into the background gas [145; 146]. In this work, YBCO films were grown reactively in oxygen with an optimised pressure of 300 mtorr. Collisions with oxygen slow down the deposition products, causing a shortening and rounding of the plume shape, which is significant above 300 mtorr [129]. At the collision interface between the plume and the ambient oxygen, oxide formation occurs, and, in particular, yttrium oxide and barium oxide are produced [130; 131]. These oxides appear to lead to a distinct reddening of the edges of the plume. The ionic content of the plume decreases in the oxygen environment [132]. Clearly, the physics and the chemistry of the plume, and the propagation of the plume front, which is the result of interaction with background oxygen, are important areas to study. These aspects are outside the framework of this thesis, and only a brief study of the influence of the position of the substrate in the plume will be provided in the next section. It is worth mentioning that the parameters in the second group (Figure 3.7) are

91 3.1. Thin film growth technique 67 dependent on each other as well. For instance, the background oxygen pressure can affect the size of the plume and, as a result, the position of the substrate in it [139]. Systematic optimization of deposition conditions in this work has been undertaken to eventually obtain the best performance and structure of YBCO thin films. The optimization means that we kept the deposition parameters of YBCO film (see Figure 3.7) unchanged while, for example, the substrate temperature and oxygen pressure during deposition were varied in order to obtain the highest critical temperature and critical current density, and the narrowest transition in the superconducting film. Optimization of each parameter was made under conditions in which other parameters were nearly optimised. As was mentioned above, some of the parameters are not independent of each other, and further discussion will be provided. The preparation and quality of the substrate and target materials depend on predeposition processing, i.e. cleaning and polishing, and are considered well-reproducible parameters. Hence, only film growth temperature and conditions which drive the plume have to be optimised during deposition experiments. Before beginning the study of each new series of samples, several films were deposited in order to optimise the background oxygen pressure (P O2 ), deposition temperature (T D ) and the distance between the target and the substrate (D T S ). Optimization of the annealing procedure and annealing temperature (T P A ) has been done for films deposited on metallic substrates (see Chapter 6). These were investigated by relating superconducting transition temperatures and their transition widths to deposition parameters. The initial point of optimizations performed in this work was optimization of background oxygen pressure, which was then retained for all further depositions. Figure 3.8 shows the results of the oxygen pressure optimization. It is clear that T c of YBCO thin films is highly sensitive to the deposition parameter P O2. The most obvious explanation for this is in thermodynamic consideration of the plume, where the ambient pressure has to have an optimal value in order for the deposited film to achieve the needed stoichiometry (see Section 1.5).

92 Chapter Development and optimization of the pulsed laser deposition process Normalized Magnetization, M/M(10 K) Y; P O2 =250 mtorr; T c =87.50 K Y; P O2 =300 mtorr; T c =89.91 K Y; P O2 =350 mtorr; T c =89.34 K Temperature, K Figure 3.8: Normalized dependence of the magnetization on the oxygen pressure during deposition of the YBCO film. The second deposition parameter to be optimised was the deposition temperature. Figure 3.9 demonstrates how sensitive the critical temperature and transition width are to the parameter T D. Therefore, a particular substrate temperature is an important parameter for optimization, influencing crystallisation processes and the mobility of the adatoms across the substrate [147; 149; 152; 151]. Moreover, in Refs. [153] and [154], the mobility of the cations, which is proportional to T D, leads to less disorder between Y and Ba atoms in resulting thin YBCO films. At the same time, high deposition temperature T D < 830 C leads to the formation of excessive amount of YBa 2 Cu 4 O 6+x planar defects and columnar-like defects (Ba-Cu-O nanocolumns) (see Refs. [156; 155]) To produce crystalline, c-axis oriented YBCO films on different substrate materials, the substrate temperature has to be varied within the range of C. Therefore, some compromises are required. For example, better quality (in terms of high crystallinity and T c ) is achieved when the films are deposited at higher temperatures, but they show lower critical current [73]. In order to obtain films with maximum critical current and critical temperatures that are still high, additional depositions and measurements at the final stage of optimization have to be applied.

93 3.1. Thin film growth technique 69 Normalized Magnetization, M/M(10 K) Ysto; T c =85.25 K; T D =775 o C Ysto; T c =89.91 K; T D =780 o C Ysto; T c =88.78 K; T D =785 o C Temperature, K Figure 3.9: Normalized magnetization versus deposition temperature of the YBCO film. Substrate material is also a very important factor influencing the quality of the films. Generally, we can distinguish between two classes of substrates: 1. compatible substrates onto which YBCO film can be deposited without a buffer layer, and 2. non-compatible substrate materials, which have to be covered with an epitaxial buffer layer prior to deposition of the YBCO film due to large lattice mismatch and/or chemical reaction between the substrate and the YBCO material, or due to missing in-plane orientation (e.g. for deposition of biaxially oriented YBCO on metallic substrates or technical substrates such as Si and Al 2 O 3 ). Deposition onto compatible substrates is much easier as compared to type 2 substrates. Typical type 1 substrates are SrTiO 3, MgO, and yttrium stabilized zirconia (YSZ). Buffer layers could profitable be added in a few cases of the compatible substrates, e.g. a CeO 2 buffer layer reduces the probability of a-axis growth when deposited onto YSZ substrates. Additionally, CeO 2 has proven to be the most effective buffer layer owing to its favourable film growth characteristics, minimal chemical reaction, and good lattice match with YBCO (see review Ref. [74]). Optimal deposition conditions which are best for one substrate material are not necessarily the same for different kinds of substrate. Figure 3.10 shows the result

94 Chapter Development and optimization of the pulsed laser deposition process Normalized Magnetization, M/M(10 K) YSTO; P -0.1 o2 =300 mtorr; T D =780 o C YMgO; P -0.2 o2 =300 mtorr; T D =780 o C Temperature, K Figure 3.10: Dependence of the normalized magnetization on the substrate material. of one deposition on two single crystal substrates: SrTiO 3 (STO) and MgO. It is clear that the optimal conditions for the STO substrate are not suitable for the MgO substrate. In this work, various substrate materials were used, such as STO, YSZ, MgO and LaAlO 3. All of them have different optimal deposition conditions. Due to high sensitivity of superconducting properties to the deposition conditions, many different conditions have been tried. Critical temperature and critical current density were also found to vary with the target-to-substrate distance. Detailed study of this deposition parameter will be described in the next section. 3.2 Study of target-to-substrate distance parameter. It is well known [130; 131] that placing the substrate at different positions with respect to the plume produces films surfaces with different surface roughness. Within the plume, the roughness of the film is on the scale of 500 nm. When the substrate is

95 3.2. Study of target-to-substrate distance parameter. 71 placed at the edge of the plume, the roughness is on the scale of 200 nm. In the case when the film is grown beyond the plume, the roughness is on the scale of 100 nm. A recent target-to-substrate investigation has been done based on energy dispersive X-ray spectroscopy [141]. The films are Cu-rich if the D T S is large (substrate is placed out of the plume edge) and, on the other hand, Cu-deficient if the D T S is short, when the substrate is placed close to the target. The typical resultant dependencies of the critical temperature and critical current density of YBCO films on the D T S follow a Gaussian distribution with their maxima at some particular target-to-substrate distance [73; 150]. However, these targetto-substrate distances are not the same for critical temperature and critical current density. Moreover, the best critical current properties are produced with the substrate placed at the edge of the plume; growth within or beyond the plume both result in poorer transport properties [73]. Therefore a controllable compromise has to be made between the surface morphological properties, critical temperatures, and critical current properties of the films being grown. At the beginning of this work, the effect of the target-to-substrate distance was understandable and controllable when the distance was varied in the range from 30 mm to 70 mm, because the total size of the plume was around mm. Generally speaking, the size of the plume is difficult to determine just by a human eye due to its high intensity and very short life time. Hence in our laboratory it was impossible to make substrate positioning exactly at the edge of the ablating plume. Therefore, the use of terminology such as the edge of the plume or substrate placed in the edge of the plume is totally inappropriate, as there is a large error in actual determination of these parameters. Operation of a defined and well controlled target-to-substrate distance parameter is much more useful, leading to a reproducible formation of thin films. A conclusion was drawn that it is possible to optimise the deposition process to obtain films with desired electromagnetic properties. During the optimization process, the surface morphology, critical temperature, and critical current density as a

96 Chapter Development and optimization of the pulsed laser deposition process Target-to-substrate distance D TS aa aa aa aa aa aa aa aa aa Figure 3.11: Schematic representation of the arrangement of the target, substrate and ablated plume. function of the target-to-substrate distance were systematically studied. These results were crucial in order to establish fabrication of thin films of controllable quality. The target-to-substrate distance (D T S ) was changed in order to set the substrate in a few different positions relatively to the plasma plume (see Figure 3.11). achieve reproducible results, all other deposition parameters (see Section 3.2) were kept unchanged during these experiments (see Table 3.1). Table 3.1: Deposition parameters which are constant during target-to-substrate distance study. The thickness of the films investigated varied from 0.3 µm to 1.6 µm. To Deposition parameter Value Laser beam energy, Joule/pulse 0.4 Laser beam repetition rate, Hz 6 Deposition temperature, C 780 Background oxygen pressure, mtorr 300 Substrate material SrTiO 3 Figure 3.12 illustrates how superconducting transition behaviour is affected by the target-to-substrate distance parameter. It can be seen clearly that the highest critical temperature and narrowest transition width is achieved when the deposition

97 3.2. Study of target-to-substrate distance parameter. 73 Normalized Magnetization, M/M(10 K) ; T c =89,58 K film deposited at D T-T = 37 mm ; T c =90,56 K film deposited at D T-T = 41 mm Y730; T c =88,33 K film deposited at D T-T = 46 mm Temperature, K Figure 3.12: Normalized magnetization curves as a function of temperature for the YBCO films with 300 nm thickness deposited at different D T S. parameter D T S is about 41 mm. With changing deposition conditions, so that the D T S is closer or farther than the particular optimal distance, the samples are less crystalline and have less superconducting phase. Moreover, a significant decrease or increase in D T S, e.g. D T S =34 mm or D T S =56 mm, respectively, leads to a large drop in the critical temperature T c to about 86 K and widening of the transition width to about 4-6 K (magnetization curves not shown). Figure 3.13 shows the influence of the target-to-substrate distance parameter on the surface morphology of the YBCO films. SEM images of films deposited for different D T S are obtained from tilted surfaces of thin films. The three SEM images presented in Figure 3.13(a), (b) and (c) correspond to D T S = 37mm, 41mm, and 46mm, respectively. It is clear that the surface morphology strongly changes with D T S. Roughness of the film deposited at D T S =37 mm is larger than that for the film deposited at D T S =46 mm. Poor surface smoothness of the films deposited at D T S =37 mm is a result of poor connection between YBCO grains (see

98 Chapter Development and optimization of the pulsed laser deposition process Figure 3.13: SEM images (a), (b), (c) of the surface morphology for YBCO films deposited at D T S =37 mm, 41 mm, and 46 mm; the film thickness is 450 nm in each case. Figure 3.13(a)). With increasing D T S from 41 mm to 46 mm, the surface morphology becomes smoother (see Figure 3.13(b) and (c), respectively). This is the result of good coalescence during the thin film growth process. The evolution of the film surface morphology can be very well illustrated by the number and shape of voids in the films. Their size and density are larger in film deposited at D T S =37 mm. In Figure 3.13(a) voids merge, forming extended valleys. In contrast, the density of voids is seemingly lower and their size is much smaller for films obtained at D T S =41 mm and 46 mm. The average grain size also changed from smallest (about nm) to largest (1000 nm) in films deposited at D T S =41 mm and 46 mm, and at D T S =37 mm, respectively. Previous publications point out that different grain size is mostly a result of different types of substrate materials or different dopants used in the PLD technique [134; 135]. Our results demonstrate that deposition parameters can influence grain size, too. Large size particles (of the order of 0.5 µm) are found in films deposited at D T S =46 mm (see Figure 3.13(c)). These particles are clusters of the target material deposited onto the substrate. It is interesting to note that there are no particles on the surfaces of the films deposited at D T S =37 mm and 41 mm. It is reasonable to assume that kinetic energy of these big particles in the plasma plume at distances D T S =37 mm or 41 mm is so big that they can not precipitate successfully on the surface of the substrate [137]. On the other hand, large particles formed at the

99 3.2. Study of target-to-substrate distance parameter. 75 longer distance of D T S =46 mm have lower energy, and hence, they could efficiently precipitate on the surface of the film. Observed morphological evolution could be interpreted according to the nucleation and growth model. In this model, the degree of nucleus coalescence depends on the kinetic energy of adatoms on the surface of the growing film [130; 131]. All particles, ions, atoms, and clusters, coming from the plasma plume become the adatoms on the surface of the growing film (see Section 3.1.1). Hence, the closer the substrate is placed to the target (small D T S parameter), the higher is the kinetic energy of the adatoms. Moreover, they have extra relaxation (reaction) time, which lets them interact with other adatoms on the surface. A result of this strong bonding is incomplete coalescence, which leaves voids between the grains. On the other hand, the adatoms on the substrate surface at large D T S have lower kinetic energy. Therefore, the time for interaction with the surface adatoms is enough to fill holes and voids. That is why the surface of the film deposited at D T S =46 mm is much smoother than that for the other films. Figure 3.14: SEM images of the surface morphology for YBCO films deposited at D T S =37 mm (a) and 46 mm (b) with thickness of 1.6 µm and 1.3 µm respectively. Confirmation of this scenario can be evidenced for thicker films where the surface morphology takes a longer time to form and the surface is generally much rougher (see Section 1.5 and Chapter 5). Further evolution of surfaces can be well illustrated, as in Figure Figure 3.14(a), (b) reflects the surface morphology of YBCO films with

100 Chapter Development and optimization of the pulsed laser deposition process thicknesses of 1.6 µm and 1.3 µm deposited at D T S =46 mm and 37 mm, respectively. It is clearly visible that the surface of the film deposited at D T S =37 mm is very rough and looks like a surface consisting of separated grains. In contrast, the surface of the film deposited at D T S =46 mm looks much smoother and denser. In Figure 3.15, one can see the magnetic field dependence of the critical current density J c. A slight decrease of J c (B a ) when 0 T < B a < T is observed for the film deposited at D T S =46 mm, whereas no J c degradation is seen for the films deposited at D T S =37 mm and 41 mm. This decrease of J c for the first film is consistent with the decreased critical temperature of the film, as depicted in Figure At the same time, degradation of he critical current value at high magnetic fields (1 T) occurs for the film deposited at D T S =37 mm, but the films deposited at D T S =41 mm and 46 mm do not show this behaviour. This behaviour could be attributed to a lower amount of defects in the film which act as effective pinning centres (see Section 1.5). Critical current density, J c (10 10 A/m 2 ) film depozited at D T-T =37 mm film depozited at D T-T =41 mm film deposited at D T-T =46 mm T = 77 K 1E Applied magnetic field, B a (T) Figure 3.15: Critical current density (J c ) as a function of the applied magnetic field (B a ) for YBCO films with thickness of 300 nm. Figures 3.16(a) and (b) contains TEM pictures of two multilayered films deposited

101 3.2. Study of target-to-substrate distance parameter. 77 at D T S =37 mm and 46 mm, respectively. The details of the deposition technique that was used to fabricate such multilayered structures is explained in Section High quality layers can be seen in Figure 3.16(b), and the structure of the film looks uniform. On the other hand, the TEM image of the film deposited at D T S =37 mm represents a structure with destroyed layers and has a high density of voids (see Figure 3.16(a)). Figure 3.16: TEM images of the inner structure of films deposited at D T S =37 mm(a) and 46 mm(b), respectively. The results presented in this section clearly demonstrate the existence of optimal deposition conditions, which have been realized in film deposited at D T S =41 mm. This YBCO film can carry higher critical current at B a =0 T, T =77 K and B a =1 T, T =77 K as compared to its counterparts obtained at D T S =37 mm or 46 mm. The combination of strong crystallinity (see Figure 3.12) and the existence of effective pinning centres (see Figure 3.15) is the main advantage of optimally deposited YBCO thin films. As was demonstrated previously, the position of the substrate with respect to the plasma plume during the PLD process plays a crucial role in the formation of YBCO films. The surface and interior morphology of YBCO films, deposited at different target-to-substrate distances, can be transformed from very porous and rough

102 Chapter Development and optimization of the pulsed laser deposition process to smooth and dense. The resultant electromagnetic properties can be associated with morphology differences as well. The results presented can be explained on the basis of the gradient in the kinetic energy of particles in the plasma plume and the Stranski-Krastanov growth model, where mixed, layer and island growth modes occur [158]. Despite the different velocities of different particles in the plasma (due to their masses [127; 157]) they form a sharp front with the size of several millimeters [143]. According to various models available in the literature, the plume front appears to be unaffected by the background gas pressure for the first microsecond of its flight. It them slows considerably, which the is consistent with the appropriate decelerating Law: D T S =α t 0.4 p - (shock model), or D T S =β (1 e γ t p ) - (Drag model), where the parameters α=1.26 cm/µs, β=3 cm, γ=0.36 µs 1 and t p is the time. Consequently, the particles in the plume hit the surface of the substrate or surface of the growing film with kinetic energies which are dependent on the position in the plume. As a result, the closer the substrate is placed to the target, the larger becomes the surface mobility and diffusion of adatoms on the surface. Adatoms with high energy can move longer distances on the surface and coalesce to form large nuclei. In this way, large nuclei grow much faster and form granulated structures. Eventually this growth model is manifested as in Figure 3.14(a). This film has good crystallinity (see Figure 3.12), but nevertheless has the interior structure presented in Figure 3.16(a). On the other hand, as the target-to-substrate distance becomes larger, the mobility of adatoms at the surface is reduced. Adatoms have less kinetic energy and can be completely incorporated into existing inter-lattice outgrowths. Consequently, the surface formation process becomes more uniform and, therefore, the surface becomes much smoother (Figure 3.14(b)). Further increase of parameter D T S leads to insufficient kinetic energy of adatoms, which prevents particles having a good orientation on the surface. As a result, the strain in the crystal lattice increases significantly in the growing layers. Thus, significant deterioration of crystallinity occurs, and, consequently, there is a decrease of critical temperature and critical current density in the

103 3.3. Conclusion 79 YBCO films. Moreover, results found from energy dispersive X-ray spectroscopy [141] showed that YBCO films change their stoichiometry: they become Cu-rich if the substrate is placed beyond the plume, and Cu-deficient if the substrate is placed close to the target. Compositional variations in superconducting films are attributed to the different atomic velocities of the particles in the plasma if the substrate is placed out of optimal range. The particle velocities show a weaker than inverse square root dependence with molecular weight [126]. This yields formation of films which are not completely stoichiometric and have poor superconducting properties. At this stage, it is possible to speculate on the correlation between two deposition parameters. There is similarity of the effects of substrate temperature (T D - deposition temperature parameter) and kinetic energy of the plume particles (D T S - target-to-substrate deposition parameter). The kinetic energy of adatoms on the surface of a growing film has two components: kinetic energy inherited from the laser plume and the energy obtained from the heated substrate. The combination of these two energies determines the growth mechanism and final microstructure of the deposited films. Generally speaking, similar effects have been recognized in ion beam deposited films [159], where more highly accelerated ions strike the surface of the target. Particles in the plume have higher kinetic energy and, generally, improve the film quality. Therefore, there is a possibility of creating high quality films which can be either deposited at lower substrate temperatures by using high kinetic energy of the plume particles, or with lower kinetic energy of ablated species by using higher substrate temperatures. 3.3 Conclusion The deposition technique to obtain superconducting thin films used in this work has been described. The availability of different target materials in the PLD chamber and in-situ deposition process itself have allowed us to deposit multilayer structures as well as silver doped YBCO films. Significant modification of the existing heater has been conducted in order to shorten the deposition optimization time. Such a heater

104 Chapter Development and optimization of the pulsed laser deposition process has better temperature control, which is a highly important deposition parameter. Systematization of all deposition parameters has been done in this Chapter. All these parameters have been described and their interconnections discussed. Furthermore, a most efficient route to optimise deposition parameters has been demonstrated. In the last two sections of the Chapter, we also examined how the quality of YBCO films fabricated by the PLD method is strongly dependent on deposition parameters. Separate investigation of the deposition parameter D T S has revealed its very important role in determining the microstructure and electromagnetic features of the superconducting YBCO films. In our work we have found an optimal zone, where D T S =41 mm. YBCO films fabricated in this optimal zone have smooth surface morphology and the greatest critical current value over the whole range of applied magnetic field. Film formation mechanism was explained using nucleation and growth model. Appropriate control of the D T S parameter together with the substrate temperature and oxygen background pressure allows for an optimised PLD technique.

105 Chapter 4 Critical current and pinning mechanisms in single-crystalline epitaxially-grown YBCO thin films 4.1 Outline The following chapter briefly describes theoretical approaches which were applied to explain dependence of critical current on applied magnetic field. A theoretical model combining stochastic and physical predefinitions was developed to fit the experimental J c (B a ) curves. Calculation of the thin film crystal structure parameters based on experimental data has been undertaken. 4.2 Introduction Type II superconductors can carry bulk currents only if there is a macroscopic gradient of flux density (or magnetic field) in the superconductor. This implication is clear from the Maxwell equation (see Section 1.3): B = µ 0 J (4.1)

106 Chapter Critical current and pinning mechanisms in single-crystalline epitaxially-grown YBCO thin films A macroscopic gradient of magnetic field can be sustained by pinning of the vortices at certain points which are microstructural defects. Increasing temperature and magnetic field weaken the potential wells at which vortices are pinned, thus lessening J c (B a, T ). Flux pinning is determined by spatial interaction of the vortex lines with these microstructural imperfections due to the local interactions of associated screening currents and normal cores with pinning centres. Moreover, the vortex lattice structure is subject to the Lorentz force of the macroscopic current: B J = F L (4.2) Critical current density J c (B a, T ) is then defined by the balance of the pinning and Lorentz forces, F L =F pin, where F pin is the volume summation over all microstructural pinning defects in a strongly interacting network of flux lines. Hence superconductors can carry non-dissipative current density up to some J c value. When the current density exceeds J c, a superconductor switches into a dissipative, vortex flow (or flux flow) state driven by the Lorentz force. This description of flux pinning immediately suggests that it is necessary to tailor the defect structure of the conductor to maximize J c. A simple relation can be derived to see the relationship between non-destructive macroscopic critical current density and pinning force [160]: B J c = F pin (4.3) It is clear that a pinning force generated by defects determines the behaviour of the critical current at an applied magnetic field in any superconducting single crystal or superconducting thin film. In single YBCO crystals, vortices are mostly weakly pinned by randomly distributed point defects [47]. In contrast, YBCO thin films have strong pinning present due to a much larger amount of defects and can carry very high critical currents up to 10 6 Acm 2 at 4.2 K and 10 5 Acm 2 at 77 K [161; 162]. Strong vortex pinning is an important aspect of YBCO thin films, but the nature of the defect type which is responsible for the observed large current densities in thin

107 4.2. Introduction 83 films remains unresolved. Many different defects can act as strong pinning sources: twin boundaries [163], low angle grain boundaries [164; 165; 166], large extended precipitates [167] or oxygen vacancies [168], surface roughness [169; 170], and also screw dislocations [168; 171; 172; 173; 174]. From the theoretical point of view the maximum possible current flowing in a superconductor is limited by the gap energy or binding energy of Cooper pairs. It means that as soon as a current carrier - Cooper pair reaches the energy comparable with its own coupling energy, the superconducting state can not exist in material. This current is known as so called depairing current density J d. According to the Ginzburg Landau theory, the depairing current density: J d (T ) = Φ 0 3 3/2 πµ 0 λ 2 (T )ξ(t ) (4.4) where Φ 0 is the single flux quantum, Φ 0 = h/2e = Tm 2, the vacuum permeability µ o = 4π 10 7 NA 2, and λ(t ) and ξ(t ) are the penetration and the coherence lengths, respectively. In according with Gorter and Casimir phenomenological model [12], and Bardeen, Cooper, Schrieffer (BCS) theory [14] the two characteristic lengths depend on temperature according to relations: λ(t ) = λ(0)(1 (T/T c ) 4 ) 1/2 and ξ(t ) = ξ(0)(1 (T/T c ) 4 ) 1/2, so if one takes from Ref. [33] ξ(0)=1.5 nm and λ(0)= 150 nm, near 0 K the depairing current density J d Am 2. Other Refs. [176; 177; 178; 219; 181; 179] address ways to explain J c by artificially introducing various types of defects, such as columnar defects, antidotes or impurities. These studies were undertaken on samples with an artificially induced defect structure. Some of them used doping or heavy ion irradiation, or specially chosen techniques such as miscut, bicrystal substrates in order to study various pinning mechanisms. Among them, an extensively studied method to increase critical current density in single crystals is irradiation by heavy ions [176; 177; 178]. Columnar tracks with diameters of Å are formed to constitute effective linear pinning centres. As a result, critical current is increased by one order of magnitude. However, even after heavy ion irradiation, the critical current of single crystals is still two orders of

108 Chapter Critical current and pinning mechanisms in single-crystalline epitaxially-grown YBCO thin films magnitude lower than that of thin films [176; 175]. In fact, the critical current density of thin YBCO films is already close to the depairing current. Typical J c of thin films is % of J d. Introduction of artificial defects into the film has proven to be less effective than for single crystals, since the current is increased by typically a factor of 2 at low temperatures [35; 183; 184]. However, as has been mentioned above, studies dedicated to determining the dominant defects responsible for pinning formation have not been able to demonstrate a direct relationship between critical current values and specific pinning centres. The study of pinning mechanisms and creep of the vortex lattice in a HTSC presents quite a tremendous task, if studied in its full complexity. The reason for the complexity of this task can be attributed to the significant dispersion of length scales that are used for accurate description of physical processes. First, there are several classes of disorders which have the potential to produce pinning. Second, there is the vortex line lattice, which is temperature and applied magnetic field dependent. The smallest length scale involved is the coherence length ξ, which describes the extent of the vortex cores responsible for the coupling of the flux line lattice to the pinning potential. The largest are microstructural pores or nonsuperconductive phases which could accommodate groups of flux lines. In relation to the vortex lines, all defects can be divided into two types: correlated and uncorrelated disorder. For instance, grain boundaries, screw dislocations, twin boundaries, and large extended precipitates are typical examples of correlated disorder along the c-axis, as shown in Figure 1.6. They can pin the flux lines alongside almost uniformly, assuming that the vortex is oriented directly along the c axis. Typically representative of uncorrelated disorder are oxygen vacancies, which are the most discussed defect in the literature and are called point-like disorder. Point-like defects are often suggested to compose a very effective ensemble of point pinning centres in YBCO material. Recent scanning tunnelling measurements directly confirm the role of oxygen vacancies in pinning [180]. However, in YBCO thin films, point defects are actually very weak pinning centres, so it is necessary to have large

109 4.2. Introduction 85 numbers of such defects in the film to pin a flux line lattice. In this case, it is the stochastic fluctuations in defect concentration that lead to the pinning. This type of pinning is often referred to as a collective pinning mechanism [186; 187] when many vortices move as a unit or in large groups under the action of perturbing forces. It was intensively studied in the middle of 60-th by Anderson, Kim and Tinkham [17] when the pinning mechanisms had been substantial part of interest for industrial production of superconductor wires. Collective pining was established by Larkin and Ovchinnikov [186; 187], and was refined later by Feigel man et al. [188] and Nattermann [189] by extending the theory to small current densities, by Feigel man and Vinokur [190] to include thermal fluctuations, and by Blatter et al. [191] to include quantum creep; [192] takes into account the anisotropy. The basic assumption of collective pinning theory is the existence of quantized magnetic flux lines with a correlation length of L c which are rigid and can not bend to accommodate the nearest pinning centres present nearby. When a single vortex is pinned by many pinning centres, which are randomly distributed and have a random pinning force, the vortex tries to increase its pinning energy by taking advantage of as many pinning centres as possible, and at the same time, the vortex wants to remain straight in order to minimize its elastic energy. As a result of this competition between pinning and elastic energy, the vortex breaks up in correlated pieces with the correlation length L c. This picture works very well in describing the situation in single YBCO crystals, but it is not very appropriate for strong pinning in thin YBCO films. In particular, it can not explain the plateau-like features in J c (B a,t ) dependencies that are observed in thin films at low magnetic fields, nor the J c (B a,t ) dependence in high magnetic fields, as shown by strong magnetic field dependence of Figure Many important results on pinning are presented in two detailed Refs. [185; 193]. However, collective pinning is a complex stochastic problem even for the simple case, where single vortex pinning occurs, and to date, there are still substantial disagreements between theory and experiment. Certain works [188; 190; 191; 185] demon-

110 Chapter Critical current and pinning mechanisms in single-crystalline epitaxially-grown YBCO thin films strate a number of flux lattice phase diagrams and contain qualitative descriptions of critical current behaviour in applied magnetic field. Hence, the universal formula for J c (B a ) dependence which would be true within all ranges of applied magnetic field can not be derived from the collective pinning theory. Therefore, one common prediction of this theory is that flux creep leads to the so-called interpolation formula that interpolates a wide range of experimental data: J c (T, t) = J c0 [1 + (µkt/u 0 )ln(1 + t/t 0 )] 1/µ (4.5) Here J c0 is the critical current in the absence of flux creep, U 0 is the pinning barrier at zero current, and t and t 0 are the characteristic experiment time and an effective attempt time, respectively. The exponent µ depends on the dimensionality and particular flux-creep behaviour [194]. The vortex-glass model [195; 196] predicts µ to be a universal exponent less than unity. Feigelman et al. [188] predicted differences in µ as a function of the field and temperature. Generally speaking, µ is an exponent describing the degree of nonlinearity, acquiring different values depending on the actual collective flux creep regime: 1/7 for single-vortex mode, 5/2 for small bundle mode, and 7/9 for large bundle vortex creep mode. When µ = 1/7, the flux creep is dominated by the motion of individual flux lines at low magnetic fields and in the low-temperature region. At higher temperatures and fields, µ is 3/2 due to the collective creep of small vortex bundles, and finally at still higher fields and temperatures, where the bundle size is much larger than the London penetration length, µ is 7/9. These different µ values indicate different critical current behaviour at different applied magnetic fields and could sufficiently identify the pinning modes in superconducting samples. A model alternative to the collective pinning model was developed by Mezzetti et al. [197], to describe the J c (B a ) behaviour in thin YBCO films. It was assumed that grain boundaries in the film are junctions, playing the role of hidden weak links. Most of the defects are considered as insulating nanoscale zones with the carrier density and the order parameter reduced [164; 165]. Transport of Cooper pairs

111 4.2. Introduction 87 through such junctions occurs via tunnelling, and the boundary interfaces themselves can enclose a certain amount of magnetic flux [198]. From the theoretical point of view, weak links between the grains can be effectively described as a random array of parallel Josephson junctions, with statistically distributed lengths. Such a network can be thought of as a one-dimensional array meandering in two-dimensional space. Macroscopic critical current can be obtained by integration of the critical current of each junction, which is given by a Fraunhofer-like expression. According to Mezzetti s model, fitting of measured magnetic field dependence of the critical current density, J c (B a ), has been attempted [197]. The distribution of the lengths of Josephson junctions has been calculated. This approach fits experimental current density well at intermediate temperatures, but no proof is given as to the actual existence of such a network of planar defects in YBCO films. Grain boundaries manifest themselves as the source of effective pinning centres rather than Josephson junctions. Moreover, this model can not explain the temperature dependence of J c (B a ) in magnetic field when J c starts to fall significantly with increasing field, nor the field dependence at low (T < 0.3 T c ) temperatures. In our work we assumed that in the case of strong pinning, which is presumably dominant in crystalline YBCO films, vortices are pinned over their full length by extended defects. This assumption is based on the topology of the vortex itself which is linear object and can be captured over a considerable portion of its length. Extended defects are responsible for correlated disorder and can be manifested as columnar defects which locally suppress the superconducting order parameter. In order to analyse the magnetic field dependence of the critical current density J c (B a,t ) a theoretical model [205] of critical current behaviour based on strong pinning by rows of columnar defects in the superconducting YBCO film was chosen. Development and analysis of the experimental data revealed that parameters of the crystal structure can be obtained when the model is applied and fitted to the J c (B a,t ) curves. The following sections will provide details of the model and its development.

112 Chapter Critical current and pinning mechanisms in single-crystalline epitaxially-grown YBCO thin films 4.3 Strong pinning considerations in YBCO films Epitaxial thin YBCO films grow usually as slightly misoriented island-like crystallites (see Section 1.5). This island growth mode leads to the formation of grains and a network of grain boundaries that pierce the entire film thickness (see Figure 1.7). It has been shown in Ref. [199] that thin YBCO films obtained by sputtering or by the PLD technique have the island structure, with the diameter of such islands (or grains) being typically nm, separated by deep trenches up to 20% of the film thickness. By means of wet chemical etching in a 1.0 vol% Br-ethanol solution, the linear defect density was obtained. Most linear defects are situated in the trenches resulting in a linear relationship between the grain density and the linear defect density. It has been shown [199] that the defects are non-randomly distributed, with almost no defects situated close to each other. As the defect density in films remains constant up to certain thickness, dislocations are formed at the substrate-film interface and persist up to the surface of the YBCO film, i.e. they thread through the entire film parallel to the c-axis. In our work we clearly observed granulated thin YBCO films. Examples of such films have been shown in Chapter 3 (Figure 3.13). Figure 4.1 presents a highresolution image of the surface of typical YBCO film deposited during this work. A few grain boundaries within trenches are marked by white lines in Figure 4.1(a). grain (a) (b) grain boundary 100nm 100nm Figure 4.1: FESEM images (a) and (b) of the surface morphology for YBCO films taken at high resolution. A few grain boundaries within trenches are marked by white lines in the image at higher magnification (a). A schematic view of a film interior consisting of coalesced grains is presented in

113 4.3. Strong pinning considerations in YBCO films 89 Figure 4.2(a). Various degrees of misalignment between adjacent grains are visible. When the misorientation between the grains is small, the boundary is called a lowangle boundary (LAB), where the misorientation angle θ (see Figure 1.5) varies from 0.5 to 7 [44; 165; 200]. Such a LAB consists of an array of dislocations termed out-ofplane edge dislocations. Frequently, regions of material separated by low-angle grain boundaries are described as sub-grains. When the misorientation becomes larger, the atomic arrangement at the boundary is more complicated and varies significantly with the angle of misorientation. Generally speaking, the LAB network forms relatively regular chains of edge dislocations with mean spacing d r, which is related to the misorientation crystallite boundary angle θ. In accordance with Frank s formula, d r = b /(2sin(θ/2)), where b 0.4 nm is the Burgers vector with a magnitude close to those of the lattice constants along the a and b axes. Assuming that 0.1 < θ < 5, we obtain 230 nm < d r < 5 nm, respectively. Taking into account the average grain size of about 500 nm and d r 50 nm, the estimated density of linear defects in the film depicted in Figure 4.1 is m 2. This is two orders of magnitude larger than in Ref. [51] where the dominating pinning defects were presumably screw dislocations. (a) (b) Vortices Figure 4.2: Schematic view of low-angle grain boundaries (a) and vortices pinned along them (b). In general, LABs form a two-dimensional network with the dimensions of the

114 Chapter Critical current and pinning mechanisms in single-crystalline epitaxially-grown YBCO thin films grains distributed randomly about some mean value. Depending on the technology and particular growth parameters used to grow the films, the mean dimensions of the grains can range from a few to several hundreds of nanometres. For instance, it can be seen clearly with the aid of scanning tunnelling microscopy (STM) in Figure 4.3 taken from Ref. [206] that the grain size is quite small in comparison with the grains in our thin films. Taking into account the mean grain size value and the mean intergrain misorientation angle in our film depicted in Figure 4.1, the amount of effective pinning centres in the form of out-of-plane edge dislocations, n oped, can be estimated as n oped m 2. Calculation of the density of vortices, n v, at 0.1 T magnetic field gives n v m 2. It seems quite reasonable to assume that our YBCO films have an amount of dislocations that is large enough to pin the vortex lines corresponding to magnetic fields up to 1 T. Figure 4.2(b) represents schematically how vortices can be pinned by a row-of-out of plane edge dislocations within LABs with a length of about 700 nm. Figure 4.3: STM image of YBCO film surface deposited on CeO 2 /Al 2 O 3 substrate [206]. 4.4 J c behaviour at different applied magnetic fields Typical experimental data on critical current density as a function of the applied magnetic field is depicted in Figure 4.4(b). Analysis of the set of J c (B a ) curves leads

115 4.4. J c behaviour at different applied magnetic fields 91 to the estimation of J c (T ) dependencies. The interpolation formula of collective pinning theory presented in equation 4.5 can be approximated to a relation such as J c (T ) (1 T/T c ) s. The parameter s in this case is proportional to the abovementioned exponent µ and is responsible for collective creep regimes. The set of J c (B a ) curves measured at T = 5 K, 10 K, 20 K, 30 K, 40 K, 50 K, 60 K, 70 K, 77 K and 80 K was transformed to set of J c (T ) curves at some particular applied magnetic fields (see the chosen star-like points in Figure 4.4(a)). Then, each J c (T ) curve has been analysed in order to be extrapolated by the function: J c (T ) = J co (1 T/T c ) s (4.6) where J co =J c (5K). The dependence of the extracted parameter s on magnetic field is depicted in Figure 4.4(a). Analysis of the behaviour of the parameter s in varying applied magnetic field revealed that pinning properties in the film can be divided into at least four regimes: (i) single vortex pinning; (ii) small vortex bundle pinning, (iii) large vortex bundle pinning, and (iv) vortex creep or flow. This is in good agreement with collective vortex pinning theory. The parameter s has been obtained for several different YBCO films (figure not shown). These films have different thicknesses and electromagnetic properties, or were prepared by different techniques and conditions. Observed behaviour of s shows that YBCO films demonstrate the existence of the four vortex regimes. Such vortex modes can be slightly shifted within the magnetic field scale and temperature range, but the vortex behaviour remained consistent with collective creep theory [185]. Qualitative descriptions of the critical current density versus applied magnetic field can be found in Refs. [51; 197; 206; 207; 208]. According to these works the field dependence of J c (B a ) can be divided into several segments corresponding to definite magnetic field intervals. Low magnetic field, also called self-field mode, can be characterized by values of J c (B a ) that are almost independent of the applied field. This behaviour is clearly seen in Figure 4.4(b) in the single vortex regime. The

116 Chapter Critical current and pinning mechanisms in single-crystalline epitaxially-grown YBCO thin films large Figure 4.4: Typical experimental J c (T, B a ) curves (b) and the rate of J c (T ) degradation as a function of temperature encoded in parameter s: J c = J co (0)(1 T/T c ) s. Four different vortex modes are observed. authors in Ref. [62; 51] call attention to the presence of a correlation between the observed J c (B a ) curves and the structural defects in the films. For example, in Ref. [51] it was pointed out that the value of the characteristic field B at which the transition from the low-field plateau to the region of strong field dependence J c (B a ) occurs is related to the value of the dislocation density in the film. It was considered in Ref. [51] that dislocations responsible for such a characteristic field B and for high critical current densities are the screw dislocations. From the author s point of view the characteristic field B can be attributed to the matching effect, i.e. when the number of vortices closely matches the number of dislocations in films. However, the amount of dislocations existing in films is underestimated in

117 4.5. Model of critical current vs. applied magnetic field 93 Ref. [51] by one to two orders of magnitude (see Ref. [211]). Moreover, the characteristic field interpretation has one important disadvantage, e.g. at the characteristic field one usually expects an increase in current, instead of the measured degradation [210]. This fact indicates that the explanations of B behaviour and its origin provided by Dam et al. [51] could be incomplete. At higher fields, J c (B a ) begins to decrease and three others vortex modes can be distinguished: the small vortex bundle regime, the large vortex bundle regime and vortex creep or flow. With increasing B a the amount of vortices penetrating the YBCO film increases. In this situation, vortices start to organize themselves into a vortex line lattice(vll) as so-called vortex bundles. That is why the collective pinning theory was named as collective, i.e. a bunch of vortices form a vortex bundle. In Ref. [51; 206; 209]), the authors identify an intermediate interval of the J c (B a ) curve as the part where J c falls off by a nearly inverse square-root law, J c (B a ) B 1/2, after which the current begins to fall off with increasing field in proportion to a higher power J c (B a B 1 ). Different vortex regimes, which appear with increasing magnetic field and are shown in Figure 4.4, are responsible for such different rates of critical current degradation. Klaassen et al. in Ref. [66] associated the dislocation density in YBCO films with different pinning regimes: plastic or collective pinning. 4.5 Model of critical current vs. applied magnetic field In order to develop a theoretical model of critical current behaviour in applied magnetic field, an explicit explanation of the original model has to be made. Initially, such a model was presented in Ref. [205] by Fedotov. This section will provide details of this model with some discussion on different important aspects related to our work and schematic figures. Figure 4.5 shows a schematic representation of the existence of the out-of-plane edge dislocations within the LAB. Out-of-plane edge dislocations have non-superconducting

118 Chapter Critical current and pinning mechanisms in single-crystalline epitaxially-grown YBCO thin films J J LAB flux line ~3 nm vortices ~150 nm the area of elastic stain produced by out-of-plane edge dislocation ~10 nm Figure 4.5: Out-of-plane edge dislocations in a LAB. Supercurrent J is flowing across the boundary and Abrikosov vortices are pinned at dislocations. cores surrounded by a stress-strain field area, where T c is locally suppressed. Their cores are not shown but have diameters of 5-7 interatomic distances in the ab-plane, i.e nm. The local area where the elastic strain suppresses T c is about 10 nm in diameter (see right part of Figure 4.5). Such columnar rows of normal holes in the superconducting YBCO film form a kind of fence network which is transparent to supercurrent (shown by arrows). When the magnetic field is applied parallel to the LAB, the areas with suppressed T c around each of the dislocation lines plays the role of a potential well to pin the flux. Evidently. it is when the flux line is placed within a columnar defect that the pinning force is at a maximum and the pinning regime is strong. At the same time the spaces between the dislocations are still transparent to the supercurrent flow (see Figure 4.5). Such a structure is capable of a having maximum supercurrent density which is limited by transparency of the LABs on the one hand and the effectiveness of pinning centres at preventing any depinning on the other hand. In other words, the amount of out-of-plane edge dislocations (OPED) and their spatial distribution must result in a particular critical current behaviour. Thus one has to assume that vortices and dislocations appear to be parallel to

119 4.5. Model of critical current vs. applied magnetic field 95 each other; the free energy loss due to the elastic distortion of the vortex line lattice (VLL) in the presence of linear defects has to be compared with the energy gain due to vortex pinning. This in fact means that the energy gain due to the vortex pinning in the equilibrium state should be greater than the energy loss due to the VLL strain (see Figure 4.6). So vortices may be assumed to have two definite states: pinned with pinning energy ε pin = ε pin (0) and unpinned with ε pin = 0. It is quite natural to consider that a number of vortices remain unpinned and are in a space free of LAB, e.g. inside of the grain (see Figure 4.6). The density of pinned vortices, n pin, is determined by the following factors: (i) the density and spatial configuration of the pinning centres (i.e., OPED cores) within a random network of LABs, (ii) by the temperature or, more exactly, by the temperature-dependent pinning energy - ε pin, and (iii) by the field-dependent VLL constant a. The ratio of pinned vortices to the total amount of the vortices in the film, i.e. n pin / n v, is the accommodation function of a distorted VLL pinned by an ensemble of OPED cores. This accommodation function is a key characteristic of the discussed model [205]. The main assumption of the model is that the accommodation function averaged over a certain macroscopic area is invariant in the presence of an applied current. Redistributed unpinned vortices (free vortices) with concentration n v - n pin remain at their positions due to the electromagnetic interaction with neighbouring vortices pinned by OPED. The vortices could be rigidly pinned altogether as a lattice if the total Lorentz force F L is balanced by the total pinning force F pin. Thus, the condition of collective depinning of a distorted VLL from a statistical ensemble of identical OPED cores can be written as: n pin (B a, T ) F pin F L = 0; or n pin(b a, T ) n v (B a ) n v (B a ) = F L F pin (4.7) This consideration is very important because it is relevant to the statistical nature of this model. The ratio n pin / n v, i.e. the accommodation function, is the only unknown variable for obtaining the magnetic field and temperature dependencies of J c (B a,t ) according to Equation 4.2.

120 Chapter Critical current and pinning mechanisms in single-crystalline epitaxially-grown YBCO thin films Figure 4.6: Schematic illustration of the theoretical model of J c behaviour on applied magnetic field in accordance with Ref. [205]. Free energy loss due to the elastic distortion of the VLL in the presence of linear defects as compared with the energy gain due to vortex pinning. The positive energy, ε d, of the VLL elastic strain arising when a vortex line is displaced as a whole from its equilibrium position in the VLL by a small distance δ can be taken from the VLL elastic shear modulus C 66 described in Ref. [185] (see Figure 4.6): ε d (δ) = C 66 (B a )δ 2 wherec 66 = φ 0B a (8πλ) 2 = ε o 4a 2 (4.8) At the same time, the value of the pinning potential energy required to pin a flux line by an OPED core within vortex displacement R can be derived from Ref. [185; 214]:

121 4.5. Model of critical current vs. applied magnetic field 97 ε pin (R) = ε 0 2 r 2 c R 2 + 2ξ 2 ; if r c/ 2ξ 1 (4.9) ε pin (0) = ε ( ) 0 2 ln 1 + r2 c ; if r 2ξ 2 c / 2ξ 1, and R = 0 (4.10) ε pin (R) = ε ( ) 0 2 ln 1 r2 c ; if r R 2 c / 2ξ 1 (4.11) where R the distance of the vortex displacement from the center of the pinning site and r c is the radius of the OPED. The vortex pinning is energetically beneficial if the condition ε v ε d (δ)+ε pin < 0 for the vortex energy is fulfilled. Thus, assuming the condition from Equation 4.9, the critical value of the vortex displacement, i.e. δ c (δ c δ), up to which the vortex remains pinned in the potential well of the OPED core with small insulating core is: δ c = (2r c /ξ o )(φ o τ/b a ) 1/2 (4.12) where τ = (1 T/T c ). Generally speaking, δ c should characterize the distance from a node of the VLL in equilibrium state to the nearest LAB between domains (see Figure 4.6). On the other hand, if the mean linear domain size L > d r, the probability of vortex being captured by one of the pinning centres should be equal to the product of the probability of finding a VLL node inside a domain of a certain size and shape, and the probability of finding it at a distance δ c from the domain boundary. It has been shown in Ref. [215] that all grains are randomly distributed in size and their dimensions L x and L y can be described by a statistical distribution function. A Gamma type distribution has been used to describe grains in YBCO films. Hence, the probability distribution of finding a domain with dimensions of L x, L y against dimensions X, Y, respectively, is:

122 Chapter Critical current and pinning mechanisms in single-crystalline epitaxially-grown YBCO thin films W (L x, L y ) = L ν 1 x L ν 1 y e (L x+l y )/µ (µ ν Γ(ν)) 2 (4.13) where Γ(ν) is the complete gamma function and µ and ν are scale and shape parameters, respectively [216]. Taking into account that the domains are rectangular with independent random distributions of their dimensions L x, L y (see Figure 4.6), the probability of vortex being captured by one of these dislocation potential walls in the boundary of the L x L y domain is: 1 if L x, L y 2δ c, P (L x, L y, δ c ) = 1 (L x 2δ c )(L y 2δ c ) L xl y if L x, L y > 2δ c. (4.14) where δ c is the critical distance from the grain boundary to the vortex which has to be pinned. Integration of the probability at that site of a regular VLL will fall within a domain mosaic structure for all possible sizes, leading to the following expression in terms of the fraction of pinned vortices: 2δc n pin (B a ) n v (B a ) = J c(b a, τ) J c (0, τ) = W (L x, L y )dl x dl y + 0 [ + W (L x, L y ) 1 (L (4.15) x 2δ c )(L y 2δ c ) ]dl x dl y 2δ c L x L y Integration of Equation 4.15 with the distribution density of gamma type given by Equation 4.14 yields the following result (see Appendix A for a derivation): n pin (B a ) n v (B a ) = 2Γ(ν + 2; 2µδ c) Γ 2 (ν + 2; 2µδ c )+ 4µδ c ν + 1 (1 Γ(ν + 1; 2µδ c))(1 Γ(ν + 2; 2µδ c )) (4.16) 4µ2 δ 2 c (ν + 1) 2 (1 Γ2 (ν + 1; 2µδ c ))

123 4.5. Model of critical current vs. applied magnetic field 99 Thereby, Equation 4.16 can describe the critical current density normalized by the plateau value versus applied magnetic field and temperature, but only through the parameter of the vortex trapping area of a dislocation δ c. As has been shown, the parameter δ c is proportional to τ/b a ) 1/2. If parameter b = (ν/(2µδ c )) 2, then the fraction n pin (B a )/n v (B a ) = J c (B a, τ)/j c (0, τ) in Equation 4.16 can be plotted. Figure 4.7 shows different accommodation function behaviour, i.e. critical current as a function of different ν parameters. It can be seen that curves have a plateau at small b and then, after the change in curvature, the sharpness of which increases with increasing ν, a region of logarithmic dependence. After that the dependence J c (B a, τ)/j c (0, τ) vs. b becomes weak. An important feature arising from Figure 4.7 has yet to be mentioned. Fitting of the experimental data depends on parameter ν, which is responsible for the grain size distribution. The grain size distribution is a probability density function, which is presented in Figure 4.8. It can be seen that the steepness of the slope of the intermediate part of the J c (B a, τ)/j c (0, τ) curve is responsible for the statistical distribution of grain sizes in the films. It should be noted that the volume of the thin film can be composed not only of Figure 4.7: Calculated of dependencies J c (B a, τ)/j c (0, τ) on the dimensionless parameter b = (ν/(2µδ c )) 2 at different ν values according to the Equation 4.16.

124 Chapter Critical current and pinning mechanisms in single-crystalline epitaxially-grown YBCO thin films Figure 4.8: Probability function of grain sizes according to Equation rectangular shaped grains with an independent random distribution of L x and L y, but also of differently shaped grains. In order to clarify the influence of the grain shape, three accommodation functions for different grain shapes: squares, rectangles and hexagons have been tried. The calculated (see Figure 4.9) dependencies are very close to each other. Hence, the difference in the slope near the inflection point can be neglected. This means that the ideal detailed physical picture of domain shapes and their size distributions in the film is not critical to the J c (B a, τ) analysis, and rectangular-shape grains will be considered further. To analyse the typical experimental data, two sets of normalized J c (B a ) curves in Figure 4.10 (a) and (b) have been plotted. Figure 4.10(a) presents J c (B a ) curves normalized to the J c (10) at different temperatures: 10 K, 20 K, 30 K, 40 K and 60 K respectively. Figure 4.10(b) illustrates additional normalization on the horizontal axis. It can be seen that the curves are nearly identical, i.e. have the same shape, up to a particular temperature. To visualize this feature the normalized J c (B a ) curves are drawn in Figure 4.10(b) with the magnetic field axis scaled to J c (B a ) at 10 K. This scaling illustrates that an inherent shape of critical current density curves is maintained until a particular temperature, T T A. Above T T A, the J c (B a ) curves are no longer self-similar, due to greater thermally activated depinning effects [217; 218; 219].

125 4.5. Model of critical current vs. applied magnetic field 101 Figure 4.9: Typical normalized critical current dependencies versus parameter b for different space-filling domain shapes: squares, rectangles and hexagons. Looking at Figure 4.10, we can identify that T T A is between 40K and 60K. The same behaviour of the critical current can be found in the region from 100% to 60% of the critical current onset which can be termed as zones A, B, C and D (see Figure 4.10). As was shown in Section 4.4, the shape of the critical current curves is the combination of various interactions: (i) the interplay between thermal fluctuations, (ii) vortexvortex interactions, and (iii) the interaction of the vortex core with the versatile defect structure. According to Figures 4.7 and 4.10, the proposed model describes magnetic field behaviour of the critical current density over the entire magnetic field range quite well. At low magnetic fields, statistically, the amount of vortices in the sample is so small that probability that a vortex will find a pinning center and be pinned is about 1. Physically, the vortices are strongly pinned by OPED in the LAB, resulting in a nearly plateau-like J c (B a ) behaviour, which occurs from 100% to 90% of the critical current onset (zone A). Further increase of the applied magnetic field up to 0.3 T (intermediate magnetic field range corresponding to zones B and C) leads to a decrease of the critical current density to 60% of the maximum value. This intermediate range can be associated with the small vortex bundle mode and large vortex bundle modes (see Section 4.4),

126 Chapter Critical current and pinning mechanisms in single-crystalline epitaxially-grown YBCO thin films Figure 4.10: Typical normalized experimental critical current data versus magnetic field: (a) presents J c (B a ) curves normalized to J c (10K) on the vertical axis at different temperatures: 20 K, 30 K, 40 K, and 60 K, respectively; (b) presents J c (B a ) curves normalized to J c (10K) on the horizontal axis at different temperatures: 20 K, 30 K, and 40 K, respectively. The regions indicated by letters in (b) are the vortex pinning regimes: single vortex (A), small vortex bundle (B), large vortex bundle (C), and vortex creep (D). meaning that the vortices begin to interact with each other intensively. At magnetic fields higher than 0.3 T, vortex creep or depinning mode is observed, which corresponds to zone D in Figure This regime can be characterized by thermally activated hopping of vortex bundles within potential wells under the action of any finite driving force, e.g. F L or F pin. In Refs. [66; 72], a strong pinning mode is discussed, and Refs. [38; 201] describe weak collective pinning regimes within the D zone. In principle, the ideal pinning mechanism is unachievable in real YBCO films at high magnetic field due to the simple fact that all pinning sites, i.e. OPED, are occupied by vortex lines, but some of the vortices have still to be trapped by weaker pinning centres such as point-like defects. This situation is unavoidable at high magnetic field where critical current is determined by the interplay of pinning centres

127 4.5. Model of critical current vs. applied magnetic field 103 of different strengths rather than strong or weak pinning separately. The resulting picture is a combination of both pinning mechanisms, and hence, the modelling of critical current behaviour is a very complicated task. Due to the complexity of processes at high magnetic field the area of low and intermediate applied magnetic fields can be used to analyse the grain structure and out-of-plane edge dislocations in epitaxially grown YBCO films. Figure 4.11 shows how J c (B a ) curves were fitted using Equation A good agreement between critical current curves measured by the SQUID magnetometer was obtained for the descending part of the curves, although discrepancies in the Figure 4.11: (a) Normalized experimental data of critical current dependencies versus magnetic field fitted by old model of equation (b) and (c) show the discrepancy between experimental and modelled data in low and high magnetic field regions, respectively.

128 Chapter Critical current and pinning mechanisms in single-crystalline epitaxially-grown YBCO thin films fitting were observed for two regimes: low and high magnetic fields (Figures 4.11(a,b) respectively). The discrepancy between experimental and modelled curves at high field is due to a few reasons. Firstly, this model does not take into account the point-like pinning defects, e.g. oxygen vacancies [168] or precipitates [167]. Secondly, induced elastic distortion, leading to the elastic energy of the VLL is dependent not only on the shear module C 66, but is dependent on the bulk elastic module C 11 and the tilt elastic module C 44 [188] as well. The discrepancy at high magnetic fields was circumvented in Ref. [37] in part by introducing a so-called geometrical factor. The introduced geometrical factor has not been explained completely. Moreover, this factor was used only for the analysis of the data in the high magnetic field part of the J c (B a ) curve. In such form, the application of this geometrical parameter is quite artificial. Thus, adding the influence of the C 44 and C 11 moduli must be considered and can provide satisfactory fitting in the high magnetic field region. More detailed discussion of this problem will be addressed separately. 4.6 Development of the model of the critical current vs. applied magnetic field dependence The normalized and scaled critical current curves in Figure 4.10(b) clearly demonstrated that J c (B a ) curves can be identical up to some temperature T T A. Furthermore, high magnetic field J c (B a ) behaviour demonstrates a complicated mechanism that has to be accounted for in the discussed model. The above mentioned model was developed and applied to the critical current curves at low and intermediate magnetic fields. A further modification of the model was introduced by replacing the existing pinning potential. The original model proposes a potential wall which looks like a trench. Within this trench there is no modulation of different pinning centres, although the existence of OPED points to a significantly modulated landscape

129 4.6. Development of the model of the critical current vs. applied magnetic field dependence 105 within the potential wall (see Figure 4.6). Figure 4.12(a) is derived from the original work [205] and the potential shown in Figure 4.12(b) was used in our work to develop the new revised model. (a) (b) ε pin ε pin X X Y Y Figure 4.12: (a) Original model [205] pinning potential. (b) Modified, pinning potential (see Equation 4.17). The new potential depicted in Figure 4.12(b) is created by an infinite chain of insulating cores of OPED which are periodically distributed along the X axis. This potential was described in Ref. [214]. An expression for the pinning potential of a vortex on a periodic chain of dislocations is (taken from Ref. [214]): 2π 2 rc 2 ε pin (x, y) = ε o d 2 ξ 2 + ỹ 2 cosh sinh ξ 2 + ỹ 2 ξ 2 + ỹ 2 cos x (4.17) where ξ = 2π 2 ξ d ; x = 2π 2 x d ; ỹ = 2π 2 y d.

130 Chapter Critical current and pinning mechanisms in single-crystalline epitaxially-grown YBCO thin films As can be seen, the modulation of OPEDs within the LAB by means of a new potential (Equation 4.17) leads to the appearance of an important parameter, i.e. the distance between dislocation cores, d r. Comparison of these potentials demonstrates the existence of a peculiar anisotropy of the pinning potential when pinning forces are different along all directions. The same conclusion was reported in [202] recently, where particular attention was paid to the enhanced anisotropy of vortex pinning in YBCO single crystal. The authors predicted and observed experimentally the interaction of an individual vortex with the local disorder potential. Enhanced vortex pinning anisotropy was explained in single YBCO crystal by clustering of oxygen vacancies. It is quite reasonable to assume that such a vortex pinning anisotropy exists in thin YBCO films, where oxygen vacancies and OPED act as pinning centres together, thereby strengthening the anisotropy. Figure 4.13: The approximation which was derived to simplify expression 4.17 in the in-plane projection. To get the explicit function for the interaction between pinning centres and vortices within the X-Y plane the projections of pinning potential have been calculated for differen energies. These projections can be observed as bright concentric lines in the X-Y plane (see Figure 4.12(b)). As a matter of fact, 87% of the projections as derived from Equation 4.17 can be reasonably well fitted by the equation for a

131 4.6. Development of the model of the critical current vs. applied magnetic field dependence 107 superellipse [221] (see Figure 4.13). In practice, the same form of approximations is revealed and used in work [202]. Superelliptical equation can be presented in single form as: 1 = ( ) m ( ) n X Y + (4.18) d r /2 δ c where m and n both representing power coefficients. The fitting results, which are presented in Figure 4.13, revealed that the power coefficients are about 1.8 in value. With such interaction between pinning centres and vortices within the X-Y plane taken into account, it is immediately apparent that the area to pin the vortices has to be reduced. From Figure 4.13 it can be seen that the area between two horizontal lines (at a distance of 2δ c ) is transformed to an area enclosed within the superellipse. Taking into account the nature of the accommodation function, i.e. critical current behaviour from the previous Section, the ratio of the area of the vortices pinned by the new potential to the area of the vortices pinned by the old potential is the new probability coefficient in Equation 4.16, namely, the shape coefficient, K sh. This coefficient can be calculated as the ratio of the area under superellipse (dr /2) 0 δ n c (1 (X/d r /2) m ) 1/n dx to d r /2 δ c in the first quadrant of Figure This proportionality of the reduced area of pinned vortices can be rewritten in the following form: K sh (t) = 1 t t 0 (1 z m ) 1/n dz (4.19) where t = d r /2δ c. To derive new conditions to express the probability of vortices being captured in pinning areas, a calculation of total probability by simple multiplication has to be made [216]. The calculation yields the fraction of pinned vortices is determined by the following expression:

132 Chapter Critical current and pinning mechanisms in single-crystalline epitaxially-grown YBCO thin films [ n pin (B c ) = K sh (t) 2Γ(ν + 2; 2µδ c ) Γ 2 (ν + 2; 2µδ c )+ n(b c ) 4µδ c ν + 1 (1 Γ(ν + 1; 2µδ c))(1 Γ(ν + 2; 2µδ c )) ] 4µ2 δc 2 (ν + 1) (1 2 Γ2 (ν + 1; 2µδ c )) (4.20) Despite the complexity of Equation 4.20, the fitting results showed that the goodness factor (R-Squared) of the fitting is This can be seen clearly in Figure 4.14 where the star-like points present correspond to the experimental data, the black solid line to the fitted data, while the old fitting model is depicted as a dotted line. All fitting procedures were executed by means of the program Origin Pro 7.0. Programs were created under the Origin C part of Origin Pro 7.0. Origin C is a full-featured high level programming language based on the ANSI C programming language syntax. In addition, Origin C supports a number of C ++ features and a few C features. Origin C programs are developed in Origins Integrated Development Environment (IDE) that is called the Code Builder. Code Builder includes an editor, a workspace window, a debugger with variables and a watch window, a call stack, an output window, a command console, and a compiler and a linker. Origin C functions can be compiled into object code, loaded, and then run inside of Origin Pro 7.0. Using Origin C, we took full advantage of Origins many data import, data handling, graphing, analysis, and image export capabilities. To use the incomplete gamma functions in calculations, the built-in Code Builder was used. The Origin C ++ programming language syntax code was compiled into object code, loaded, and then run inside Origin Pro 7.0. To speed up the fitting process, Origin s non-linear regression method based on the Levenberg-Marquardt (LM) algorithm was used instead of the Simplex minimization method. The LM algorithm provides a nonlinear numerical solution to the problem of minimizing a function on the parameter space of the function. Minimization is especially effective when nonlinear programming is applied instead of standard linear minimization as

133 4.6. Development of the model of the critical current vs. applied magnetic field dependence 109 Figure 4.14: Normalized experimental data of critical current dependencies versus magnetic field fitted by old model of Equation 4.16 and newly developed model of Equation The inset shows an enlargement of the higher critical current region. in least squares curve fitting.

134 Chapter Critical current and pinning mechanisms in single-crystalline epitaxially-grown YBCO thin films 4.7 Results and discussion Let us note here that both fitting curves in Figure 4.11 at fields higher than 0.7 T, are situated below the experimental data. The newly developed model postulates a lower pinning area in comparison with the old model, because the area of pinning sites was reduced by the new shape coefficient K sh and as a result, in the low magnetic field zone A (see Figure 4.11), has much better fitting results. Lack of pinning in the high field region can be partially solved by adding more interaction between vortices. The influence of the C 44 and C 11 moduli can be added into Equation 4.8 when applying the model at high magnetic fields. These moduli are derived from Ginzburg-Landau theory [13] and are slightly modified in the microscopic theory of Gorkov [203; 204]. They are magnetic field and temperature dependent and could be significant in superconductors with λ/ξ = κ 1 (see Section 1.1) as follows: C 66 = (B 2 c2/µ 0 )b(1 b) 2 (1/8k 2 )(1 1/2k 2 )(1 0.58b b 2 ); (4.21) C 11 (k) = (B 2 c2/µ 0 )(1 1/2k 2 )(1 + k 2 λ 2 ) 1 (1 + k 2 ξ 2 ) 1 ; (4.22) C 44 (k) = (B 2 c2/µ 0 )((1 + k 2 λ 2 ) 1 + k 2 λ 2 ); (4.23) where b = B a /B c2, k = (2b) 1/2 /ξ is so called radius of the circularized Brilloin zone; λ = λ/(1 b) 1/2 and ξ = ξ/(2 2b) 1/2 (see Refs. [222; 223]). Modulus C 66 in Equation 4.21 is slightly different from the one used in Equation 4.8. The expression of C 66 taken from Equation 4.21 to fit the experimental data (not shown) was applied. The fitting results were slightly better, but were still not adequate to fit the high

135 4.7. Results and discussion 111 magnetic field region completely. It is reasonable to assume that implementation of two additional moduli, i.e. C 11 and C 44, would yield a better approximation to fit the experimental data. Unfortunately, this is not as straightforward as one would like. Due to the vector nature of these moduli, it is necessary to introduce a third dimension (Z) into the model, which would account for three-dimensionality. Therefore, our two-dimensional model has to be further developed to enable transformation from a two-dimensional form to a three-dimensional one. It is highly desirable to be able to use a three-dimensional model for analysis of critical current, as such a model would allow critical currents to be described as a function of film thickness. Figure 4.15: Normalized experimental data on critical current dependencies versus magnetic field fitted by Equation It is worth noting that our model describes the temperature dependence J c (B a, τ), where τ = (1 T/T c ). The shapes of the curves of J c (B a, τ) are identical up to the temperature where thermally activated depinning effects are significant (see Section 4.4). The higher the temperature, the further the J c (B a, τ) dependencies shift to the low field region (as can be seen in Figure 4.10(a)). Above T T A, which is about 50K for our samples, J c (B a ) is no longer self-similar (Figure 4.10(b)). The detailed

136 Chapter Critical current and pinning mechanisms in single-crystalline epitaxially-grown YBCO thin films behaviour of these dependencies has different and very temperature range specific characteristics. Besides previously discussed temperature effects in the theory, there are two more ways to account for the temperature effects that can be considered: 1) is to take into account of additional thermo-activation energy in Equation 4.8, and 2) is to artificially increase parameters of the VLL elements, i.e. the size of the vortex normal core and the vortex screening current radius. However, in this case, the VLL loses its ability to verify real parameters of the film structure adequately, which leads to an increase in the size of the dislocations, their statistical distribution, and inter-dislocation distances. Within the framework of the above mentioned assumptions we have fitted our experimental curves at 77 K (see Figure 4.15(a)) and determined the parameter ν. It can be seen that the curvature of the J c (B a ) plot becomes steeper in the descending region (see for comparison the descending parts in Figure 4.15(a) and 4.15(b)). Remembering the tendency of ν to become larger as the descending part of accommodation function becomes steeper (see Section 4.5 and Figures 4.7 and 4.8), this parameter is equal to 40 and 200 for Equations 4.20 and 4.16 at 77 K, respectively. We have also found that parameter ν is 1.7 and 2.3, respectively, for these Equations at a temperature of 10 K. As we mentioned before, this feature of parameter ν can be attributed to the size of the normal vortex core ξ(t ) which is proportional to 1/ 1 T/T c. On the one hand, as temperature increases towards the critical temperature T c, the value of ξ(t ) becomes larger. On the other hand, the real defect and average grain size remains unchanged, and thus, interaction of modified VLL with the real structure becomes fuzzier. That is why hypothetically the probability density function of the dislocation sizes becomes broader (see Figure 4.8). Another conclusion is apparent as well. When the data is fitted using Equation 4.20 the fit is significantly constrained by parameter ν, because at 77 K, the descending part of curve is not fitted well even at ν = 200; see Figure 4.15(a), where the slope of fitting curve is not good enough. In contrast, the newly developed Equation 4.20 allows for

137 4.7. Results and discussion 113 better fitting at high temperatures, revealing the advantages of our development. Further into our investigation, we have revealed an interesting feature of the important parameter d r which reflects the distance between OPEDs within the LAB. In order to adequately fit experimental J c (B a ) curves at 77 K (see Figure 4.15(a)) the value of parameter d r had to be increased. In accordance with the working model, this indicates that the number of OPEDs becomes somehow smaller at higher temperatures. Evidently, the real number of defects in the film is constant at all temperatures in the same sample. The explanation of this discrepancy between the real situation and the model is driven by the VLL. At higher temperatures, the changed VLL structure does not allow detection of the real dislocation structure with good enough resolution. Therefore, we can conclude that the fluxon s normal core size becomes larger at higher temperatures, but the real size of defects is still small. Thus not all OPEDs can be verified at these high temperatures. Once again, we should consider that at high temperatures and high magnetic fields the pinning mechanism is a combination of several mechanisms. As soon as we reach the temperatures where thermally activated depinning occurs, the pinning regime becomes weaker, because the pinning potential is smoother. Furthermore, at higher magnetic fields, vortices expel each other from the LAB to the inner part of the grains. These grains can be envisioned as very small single crystals or crystallites, which are rich in uncorrelated disorder [180]. This disorder, which is mostly inside of the grains, acts as an additional pinning source [37]. If this important point is considered, the modification of the theoretical model becomes very complicated. The point-like defects are randomly distributed within the entire thickness of the film. Consequently, to bring the calculation of additional pinning potential into the existing model, a transformation of the model to a three-dimensional model has to be exercised. Our approximation model has been used for practical comparison of two different YBCO films. Analysis of the experimental data clearly showed the workability of the developed model. Two sets of experimental critical current curves were fitted to

138 Chapter Critical current and pinning mechanisms in single-crystalline epitaxially-grown YBCO thin films Figure 4.16: (a) Statistical domain size distribution. (b) Critical current densities fitted by Equation verify the dislocation structure. The fitting has been applied to the critical current curves of YBCO films which were grown by the magnetron sputtering (MS) technique and by the PLD method. The MS technique was used for fabrication of YBCO films in the Institute for Metal Physics (Kiev, Ukraine), and details of the fabrication of the films can be found in Ref. [64]. As can be seen in Figure 4.16(b), the experimental data were fitted with good precision, with R-squared The characteristic field B 0 was introduced from conditions 2µδ ν(2δ/l) ν(b 0 τ/b a ) 1/2, and B 0 = 8rcφ 2 0 /(ξ0l 2 2 ), where r c is the radius of the non-superconducting dislocation core (see Figure 4.3). Physical understanding of the characteristic field B 0 comes from the conditions B a = B 0 and 2δ = L which in fact help us to understand that up to the magnetic field B 0, the area of vortices where they can be pinned is about the average size of grains in the film. Moreover, the concluding ratio: (2δ) 2 /L 2 = B 0 /B a turns into a limiting case where the area of the entire average domain L 2 has 100% ability to pin, i.e. (2δ) 2 /L 2 = 1. In this case, J c (B a ) should be independent of B a. The independent fitting parameters ν

139 4.7. Results and discussion 115 and d r were obtained during the fit. Mean domain sizes L(L x, L y ) were estimated from the value of B 0 and the assumption originating from Equation 4.9 that r c /ξ 0 = 0.5. The sizes were found to be quite close to each other: L MS =122 nm for MS film and L P LD =138 nm for the PLD film. (a) 200nm (b) 200nm Figure 4.17: SEM micrographs of the surface morphology of MS deposited film (a), and PLD film (b). The domain size distributions obtained in accordance with the fits for both films are depicted in Figure 4.16(a). The parameter ν clearly illustrates that the dispersion of the domain size of the MS deposited film is slightly higher than that of the PLD film. It is worth noting that the usual film growth rate for the MS is one order of magnitude lower than for the PLD process, and domains in MS film should be more ordered and larger than in PLD film. In order to determine the crystal parameters of both films, XRD texture analysis was undertaken. For representative purposes, the XRD data of the (005) peak full width at half maximum (FWHM) was chosen. The PLD film has FWHM(005)=0.19, and the MS deposited film has FWHM(005)=0.27. This indicated that PLD films had better crystallinity. The relatively better crystal structure in the PLD film can be attributed to the statistical distribution of domain sizes. The narrow peak of the probability function suggests minimal distortion in the

140 Chapter Critical current and pinning mechanisms in single-crystalline epitaxially-grown YBCO thin films crystal structure, and parameter ν has to also be smaller (see for reference Figures 4.7 and 4.8). An obvious explanation of this result lies in the fact that different substrates were used for the growth of these films. The magnetron sputtered film was grown on CeO 2 buffered sapphire substrate, while the PLD film was deposited on to the SrTiO 3 substrate, which is nearly ideally compatible with the YBCO lattice structure. Moreover, Figures 4.17(a) and (b) qualitatively illustrate the surface morphology difference of both films. It is quite difficult to valuate and collect the statistics about the real domain sizes of these films but it is evidently visible that the surface of the PLD film (see Figure 4.17(b)) is comprises from more uniform domains then the surface of the MS deposited film (see Figure 4.17(a)). The third fitting parameter d r that was analysed showed the average distance between OPED in the LAB. d MS r =28 nm for the MS deposited film, which is smaller than d P r LD =32 nm for the PLD film. The average density of columnar defects can be calculated from evaluation of the d r and L parameters for both films. It is clear that this density is slightly larger for the MS film than that for the PLD film. Hence, a stronger pinning of individual vortices in the system of linear defects in the grain boundaries is observed at low applied magnetic fields. To the contrary, the value of the J c (0) of the MS deposited film is smaller by a factor of 2.83 than that for the PLD film, which supposedly was affected by the transparency of the film structure as explained, in Ref. [217; 214]. In general, the developed model describes the critical current density behaviour quite well, and the resultant crystallographic parameters can be extracted from analysis of the J c (B a ) curves with good approximation. 4.8 Conclusion In conclusion, a statistical model to analyse and explain critical current density behaviour in thin YBCO films was developed. Using the assumption of a statistically independent distribution of grain sizes, dislocations, defects, and vortex lattice sites, we have obtained a general expression for J c (B a, τ). A new pinning potential was

141 4.8. Conclusion 117 introduced into the theoretical model in order to account for the discreteness of dislocations in the LABs. For any grain shapes with respect to their characteristic linear dimension size L, the resulting magnetic-field dependence of the critical current density can be used to fit experimental data over a wide range of magnetic fields. The value of the parameter ν in this approximation is responsible for the distribution function of the grain sizes, and also can be interpreted as a parameter governing distortion of the crystal structure of the sample. At the same time, the value of the characteristic field B 0 of the transition from the plateau to the logarithmic dependence depends on the value of the average grain size L itself for any ν. It was shown that the observed dependencies can be explained by considering that in the absence of a magnetic field, the critical current density is limited by the transparency of the low-angle grain boundaries.

142 Chapter Critical current and pinning mechanisms in single-crystalline epitaxially-grown YBCO thin films

143 Chapter 5 Multilayer technique as an effective method to enlarge the critical current in YBCO films 5.1 Outline Multilayering is a methodology which includes control of the different materials involved and interfaces obtained in a sequential fabrication process. Thin film multilayers are artificially fabricated materials that consist of thin slabs of various layers deposited sequentially on a substrate. Generally speaking, when the individual layer thicknesses are comparable with certain physical length scales for electronic interactions, the electromagnetic properties of the complete structure take on new characteristics, which can be quite different from the electromagnetic properties of the individual layers. Use of this method is very common and runs from state-of-the-art semiconductor technology to magnetostrictive actuators and magnetic multilayered recording materials. Special features of materials which are obtained from multilayer structure interfaces and improvement of some important film qualities facilitate the application of such methods despite their complexity. In this chapter, multilayering and its positive influence on the current carrying

144 Chapter Multilayer technique as an effective method to enlarge the critical current in YBCO films properties of YBCO films are presented and discussed. The initial part of the Chapter is dedicated to studies concentrated on the clarification of the origins of critical current degradation in YBCO films and optimization of the single layer thickness to maximize their critical current carrying capabilities. The second section deals with the preparation and characterization of superconducting multilayered films. Lastly, the newly developed statistical model described in Chapter 4 has been applied to explain critical current behaviour in fabricated films, with all the results summarized. 5.2 Introduction and literature review It has been found that a superconducting multilayered structure usually shows behaviour different from that of its monolayer counterpart, such as the crossover phenomenon [224], anomalous upper critical field behaviour [225; 226], the scaling effect [227], and enhanced anisotropy in the pinning energy [228]. There have been a number of experimental reports on multilayered superconducting alloys [226; 229], including HTSC [230; 231; 232; 233] as well. The majority of multilayered superconducting structures have been designed to enhance critical current or critical temperature behaviour. The purpose of the studies presented in this Chapter was to enhance the critical current capability of YBCO films by means of the multilayering technique. As was shown in Section 1.7, to fabricate coated conductors, several approaches have been developed by different research groups around the world. Regardless of what technique is used, the goal is to produce conductors with a high critical current. The US Department of Energy goal for the year 2010 is to make a 1 cm wide cable capable of carrying a 1 ka overall current, also known as the engineering current. Unfortunately, the achievement of this goal by simply increasing the thickness of superconducting wire is impossible (see review [53]). Further, it was shown in Section 1.5 that the critical current density of an YBCO film is a function of the film thickness (d) for films formed on either single crystal substrates or metallic alloy substrates. High critical current densities of over 1 MA/cm 2

145 5.2. Introduction and literature review 121 at liquid nitrogen temperature have been achieved easily for YBCO films having thicknesses in the range of nm. However, critical current density tends to decrease with increasing YBCO film thickness. For example, critical current density saturates to a value of around 1 MA/cm 2 at 77 K for YBCO films deposited onto single crystal substrates having a thickness over 1000 nm [70]. Critical current density is slightly lower for YBCO films deposited on metallic substrates, where different buffer layers are deposited and used as a template. It should be pointed here that, although high J c (d) results have been shown for films deposited on metallic substrates, most deposition techniques, representing considerable microstructural diversity, have produced equally high or even higher J c values [234; 235; 236]. Unfortunately, J c (d) drops rapidly as the films become thicker. So, the source of critical current degradation is a more general problem rather than being specific to a particular deposition method or substrate material. Moreover, often this phenomenon in J c (d) curves is misinterpreted, as every deposition method is capable of producing films that have no or very little critical current degradation as a function of thickness [237]. However, the absolute value of J c in such cases is typically two or even three times lower. Thus, strong thickness dependence is better characterized as a sharp increase from a relatively flat baseline as the films are made thinner. Generally speaking, interpretations of critical current density degradation J c (d) can be divided into two groups: fundamental vortex pinning mechanisms and thickness dependent material microstructure evolution. The first interpretation comes from collective pinning theory, which was originally developed by Larkin and Ovchinnikov [187]. It is based on the concept that vortex line elasticity limits bending over short distances, i.e. the correlation length L c (see Chapter 4.2). If the thickness d is lower than the correlation length along the c- axis direction, pinning forces accumulate statistically along rigid vortex segments and, thus, grow in proportion to d 1/2 [239]. As the film thickness increases, the Lorentz force, which is proportional to d, can only remain in balance with pinning

146 Chapter Multilayer technique as an effective method to enlarge the critical current in YBCO films forces by reducing the current density, so that the J c (d) decreases as d 1/2. When d d crit is larger than the Larkin correlation length and vortex bending becomes less restricted, with both the pinning and Lorentz forces now proportional to d, J c (d) becomes independent of film thickness [39]. However, there is a problem with this explanation: traditional estimates give the Larkin correlation length as about several interatomic distances in the ab-plane of L c nm, which is very small in comparison with the observed 0.5 µm < d crit < 1 µm [70; 240; 241; 242; 243; 244]. However, recently it was shown [237] that the Larkin correlation length can indeed approach a few micrometers, if the collective pinning model incorporates a multiscale pinning potential that is an appropriate combination of point-like uncorrelated and correlated disorder. According to Ref. [237], pinning defects have a pin interaction range, r p, which is much greater than the coherence length ξ. Such a size can produce large plastic deformations of vortices rather than the small elastic deformations produced only by uncorrelated defects. So, the model presented in Ref. [237] predicts a crossover thickness d crit as large as 1-2 µm, in agreement with the observed J c (d) dependence for many PLD films [240; 241; 242; 243; 244; 245; 246; 247]. Ref. [248] shows qualitative consistency with many studies of the angular dependence of J c, which also reveal more evidence for correlated pinning along the c-axis in PLD films. Such a multi-scale pinning model also predicts the J c (d) d 1/2 thickness dependence of J c (d), but the magnitudes of J c and d crit can vary depending on the particular defect microstructure and thus on the YBCO film growth conditions. Another interpretation of critical current density degradation J c (d) is related to microstructural degradation, which consists of a decrease in the total film transparency to current flow and an evolution of the pinning mechanisms. The quality of the epitaxial coating and hence, J c is best near the substrate. As the film grows thicker, current-blocking defects such as more highly misoriented grains, cracks, or voids become more prevalent. This deterioration of crystalline and/or morphological quality has been observed in YBCO films made by a variety of deposition methods. Thus, many studies have been performed to establish a quantitative correlation be-

147 5.2. Introduction and literature review 123 tween observed microstructural decay and the J c thickness dependence. Ref. [242] has reported that in one such case, it was found that YBCO films above a certain thickness carried no supercurrent at all, due to the transition to a very porous microstructure. A few years later, the authors of Ref. [247] minimized this problem by using smoother metallic substrates. There was still a thickness dependence J c (d) that showed a rather moderate decreasing and was slightly shifted to the higher thickness region. This shows that, even when microstructural decay has been minimized, thickness dependence still persists. The last concept that can be used to explain J c (d) degradation as a consequence of microstructural degradation is related to a pinning source degradation mechanism which is correlated to the flux pinning at YBCO film interfaces. If the density of pinning defects, for instance, OPED, is at a maximum at thicknesses of µm rather than in the upper volumes of the film, the thickness dependence of the critical current in the framework of the existing pinning model (see Chapter 4) leads to reduction of J c (d). In accordance with TEM and electron backscattering diffraction (EBSD) studies [249; 250], the OPEDs within the LAB structure network initially formed in YBCO films evolve with the film thickness. Initially, when the film thickness is just a few atomic layers, a very high density of all types of dislocations is accumulated (up to cm 2 ). The authors of Refs. [249; 250] proposed that dislocations located at the interface are arranged chaotically as a so-called dislocation forest. During further growth of the YBCO film, the randomness and disorder of the dislocation nanostructure remain significant until the film thickness reaches approximately nm. The critical thickness depends on the substrate material and deposition parameters. At higher thicknesses, nm, remarkable changes in the dislocation distribution are observed [251]. The dislocation forest is gradually rearranged into a dislocation wall surrounding areas with a lower number of dislocations arranged within the LAB. Hence, a very high defect density which appears in a thin layer of YBCO close to the substrate interface could explain the cause for the decrease of J c (d) as d 1/2.

148 Chapter Multilayer technique as an effective method to enlarge the critical current in YBCO films A possible means of improvement of critical current carrying capabilities was proposed in Ref. [253; 252] where the effectiveness of interfaces towards better J c (d) performance was confirmed, partly by using an interlayer of CeO 2 between adjacent YBCO layers. Initially, authors declared that the reduction of the structural degradation, such as the porosity in the top region of the multilayer films, was responsible for the improved current carrying capability of the films. However, this hypothesis was not consistent with the obtained results, probably because of lack of electrical contacts between the individual YBCO layers. Due to the insulating nature of the CeO 2 layers, the proper analysis of vortex lattice behaviour in such multilayered films is possible within framework of our developed model (Chapter 4), but only with transformation to three-dimensional form. The following section deals with determination of the parameters influencing degradation of the critical current density as a function of film thickness. 5.3 Investigation of thin film current carrying capability as a function of film thickness Understanding the mechanisms that are affecting critical current behaviour in YBCO films is crucial. Such an analysis may shed light on the particular pinning mechanism leading to the inverse dependence of J c in the films, since vortex pinning is strongly affected by temperature and magnetic field. In this Section, we show that YBCO films obtained by pulsed laser deposition exhibit maximum J c at a certain optimal thickness. This optimal thickness range migrates to larger thicknesses as applied magnetic field and temperature increase. Two series of YBCO thin films having different thicknesses deposited at different deposition rates (2 Hz and 6 Hz) were prepared under identical conditions. The thickness of the films investigated varied from 50 nm to 2000 nm. The target-tosubstrate distance was fixed at 46 mm. During deposition the substrate temperature and oxygen pressure were 780 C and 300 mbar, respectively.

149 5.3. Investigation of thin film current carrying capability as a function of film thickness 125 Figure 5.1: SEM images of the surface morphology for YBCO films deposited at 2 Hz with the thicknesses: (a) 100 nm, (b) 345 nm, (c) 1820 nm, and at 6 Hz with thicknesses: (d) 50 nm, (e) 480 nm, (f) 1000 nm. Figure 5.1 shows the influence of the deposition rate and the film thickness on the surface microstructure of the YBCO films. Both sets of films demonstrate that the surface roughness and the number of holes increase as the thickness is increased. The films deposited at the pulse rate of 2 Hz will be called as S (thickness in nm) films, and these deposited at 6 Hz rate F (thickness in nm) films (with the letters S and F are chosen as reference to slow and fast, respectively). The films S(100), S(343), S(1820) have more holes than the films F(50), F(480) and F(1000). Moreover the average diameter of the holes in the S films is approximately a factor of 1.5 larger than for F films. These are about 300 nm and 200 nm respectively. In general, holes and trenches in the films are observed as a result of incomplete coalescence of the films. In our case, the incomplete coalescence is the most pronounced in the thick S(1820) film due to a slower, ordered growth mode. This demonstrates that during the half second between shots, significant nucleus ripening has been occurring. The same conclusion was reached in Ref. [147] where it was shown that film coalescence occurs at smaller thicknesses for faster deposition rates, according to conventional nucleation and growth theory, where nucleus aging or ripening is an important process, because the supersaturation during each laser shot is high (see Ref. [148]). This implies that larger holes (a rougher surface) would

150 Chapter Multilayer technique as an effective method to enlarge the critical current in YBCO films create larger obstacles to current flow in the upper layers of YBCO, decreasing the effective cross-sectional area and, thus, lowering the total critical current [242]. Figure 5.2: J c (d) dependencies at different fields and temperatures for YBCO films deposited at 2 Hz. Moreover, in the S(1820) film (see Figure 5.1(c)), the holes combine forming extended valleys. This is in contrast to the lower layers, which exhibit a rather continuous and smooth structure (Figure 5.1(a)). Figures 5.2 and 5.3 present the J c dependence as a function of the thickness for the films deposited at the 2 Hz and the 6 Hz deposition rates, respectively. The curves are presented for different applied fields of 0-5 T. The set of J c (d) curves in Figure 5.2 clearly demonstrates that the common trend where J c (d) is inversely proportional to d is modified at 40 K and 77 K at higher fields. In this region of temperature and magnetic field, J c (d) curves display increasing J c with increasing d at small thicknesses, reach a maximum point, and then follow the inverse J c (d) dependence at higher thicknesses. In contrast, for the films deposited at 6 Hz shown in Figure 5.3, the dependence is notably modified only at 77 K and applied magnetic field 0.05 T.

151 5.3. Investigation of thin film current carrying capability as a function of film thickness 127 These modification trends imply that there is a range of thicknesses where the critical current densities are at a maximum, and this so called optimal thickness range is moved towards larger thickness with increasing temperature and magnetic field. This means that the films with optimal thicknesses around nm have stronger pinning properties at larger fields and higher temperatures. Presumably, films with optimal thicknesses have larger numbers of defects with slightly larger dimensions, enabling them to accommodate vortices with diameters that increase with temperature. Figure 5.3: J c (d) dependencies at different fields and temperatures for YBCO films deposited at 6 Hz. A weaker shift of the optimal thickness with magnetic field and temperature that was observed for the films deposited at 2 Hz (in comparison with that for the films deposited at 6 Hz) indicates weaker pinning for films deposited at the slower rate. This can be explained from the point of view of more ordered growth (see Ref. [147]). For this type of growth, the nuclei turn into bigger grains, lessening the LAB network and probably the amount of OPED. Moreover, the larger holes and trenches that are observed in thick films due to the coalescence that happens at larger thickness cannot

152 Chapter Multilayer technique as an effective method to enlarge the critical current in YBCO films pin vortices effectively. The comparison of J c (B a ) curves for two films, S(345) and F(300), is shown in Figure 5.4. The critical current density is larger for the F(300) film over the entire field range, which again can be explained by the larger number of effective pinning centres created in the 6 Hz films. Similar behaviour can be observed in Figure 5.5 for the thickest samples. However, the differences between the curves at large fields diminish, which indicates a lesser difference between pinning defects in thick films. Figure 5.4: J c (T, B a ) dependencies for two samples deposited at 2 Hz and 6 Hz. At small fields, where the largest currents flow through the films, the 6 Hz film still has larger J c values. This could be due to smaller percolation in the upper layers, in agreement with Figure 5.1, and, thus, a larger effective cross section for the current flow in the 6 Hz films. In contrast, the behaviour of films with smallest thicknesses d < 100 nm changes qualitatively. J c at self field is larger for the S(100) film than for the F(50) film, as illustrated in Figures 5.2 and 5.3, respectively. This might be explained by lesser percolation and higher effective cross-section to current flow of the films at these thicknesses. The more ordered crystal structure of the films formed at slow deposition rates has larger average grain size, L, and presumably smaller amounts of OPEDs. Consequently, quasi-particles are scattered less and render a

153 5.3. Investigation of thin film current carrying capability as a function of film thickness 129 more transparent structure than in the films deposited faster (see the schematic view in Figure 4.5 illustrate that). Hence, larger currents can be achieved for the slowly deposited films, especially in small fields. Figure 5.5: J c (T, B a ) dependencies for two samples deposited at 2 Hz and 6 Hz. In accordance with the proposed theoretical model in Chapter 4, Figure 5.6 shows the fitting results for the F(300) and F(1000) films. The parameters of grain sizes L and inter-dislocation distance d r between OPEDs within the LAB are very close: L F 300 = 138 nm, d F r 300 = 32 nm, and L F 1000 = 143 nm, d F r 1000 = 40 nm for the F(300) and F(1000) films, respectively. However, the parameter d r is slightly bigger for the F(1000) film. This could be explained by a minor reduction in the number of dislocations in the upper layers of the films. Furthermore, the thicker film has parameter ν F (1000) =2.48, and this parameter is responsible for the statistical distribution of grain sizes (see inset in Figure 5.6). This wider distribution can be interpreted as consistent with microstructural degradation in thick films. The analysis of the observed features of the J c (B a ) and J c (d) curves is in good agreement with a pinning mechanism that exists in YBCO films on out-of-plane dislocations (predominantly edge dislocations - OPED), which are formed at the filmsubstrate interface due to the crystal-lattice mismatch between them (see Sections 5.2

154 Chapter Multilayer technique as an effective method to enlarge the critical current in YBCO films Figure 5.6: Normalized experimental data on critical current versus magnetic field for F(1000) and F(300) samples, fitted by equation The inset contains the domain size distribution functions. and 4.6, and Ref. [251]). Structural degradation with increasing thickness indicates that the influence of OPEDs for large thicknesses is only slightly reduced. On the other hand, the upper layers of the films, starting from about 500 nm thickness, have been shown to have no significant influence on the vortex pinning mechanism in the films, despite the significant structural changes observed. Indeed, the optimal film thickness with the largest critical current varies between 100 and 500 nm. The role of the upper layers in the current-carrying capacity can be considered from the point of view of how quickly the microstructure deteriorates. This means that the increase in the total cross-section of the films (in order to increase the total J c ) is counteracted by the microstructural degradation, reducing the effective cross-section for current flow. The observed thickness behaviour points out the important role of structural transparency for the current flow in the films, which is particularly pronounced at low fields and large currents (see Ref. [254]). A few important conclusions can be drawn from the data presented data. Critical current performance at applied fields and liquid nitrogen temperature has been

155 5.4. YBCO/NdBCO multilayers 131 presented for YBCO films deposited at the 6 Hz rate. The optimal thickness range where the critical current is at a maximum is from 100 nm to 500 nm, because the vortex pinning is governed mainly by the OPEDs and the amount of them in that area. In order to obtain thicker films having these maximum critical current densities, i.e. without the microstructural degradation, multilayer structures consisting of several layers of optimal thickness have to be created. 5.4 YBCO/NdBCO multilayers The requirements of good epitaxy and chemical compatibility which were discussed in Chapter 3 imply the best material choices for fabrication of interlayers in our multilayered structures. Instead of using well-known dielectrics such as CeO 2 or STO, we have chosen to the superconducting material NdBa 2 Cu 3 O 7 (NdBCO). Bulk NdBCO material has a superconducting transition temperature of about 96 K [255]. Thin NdBCO films demonstrate a critical transition temperature at about 93.5 K which is the highest among ReBa 2 Cu 3 O 7 compounds, where Re is a rare earth material such as Nd, Sm, Eu, Gd, etc. (see Ref.[256]). In fact, NdBCO compound is very promising as a possible substitute for YBCO, in the form of stoichiometric melttextured samples or thin films, exhibiting higher critical current density in magnetic field than YBCO (see Ref. [257; 258]). Multilayered structures were obtained as was described in Chapter 3 by using the PLD process. In order to make multilayered superconducting structures, sequential depositions of one target material after another were used. The time gap between depositions was 60 seconds and was used for rotating the YBCO and NdBCO targets. A schematic view of the resultant structure is presented in Figure 5.7. A 270 nm thick YBCO layer was deposited first, then a 20 nm thick NdBCO film was deposited, followed by a 270 nm YBCO layer, then 20 nm of NdBCO, and a 270 nm YBCO layer. By means of scanning electron microscopy both NdBCO layers were identified to be present in the film. The corresponding structures can be seen in the image with the highest magnification (see Figure 5.7).

156 Chapter Multilayer technique as an effective method to enlarge the critical current in YBCO films Figure 5.7: Schematic view of the multilayer sandwich-type YBCO/NdBCO film structure Structural characterization of multilayer films In Figures 5.8(a) and (b) the typical surface of a thick YBCO/NdBCO multilayer at different scales is shown. For comparison purposes, an YBCO monolayer film having a thickness of 1 µm is shown in Figures 5.8(c) and (d) on the same scale. As can be seen, the multilayered film shows dramatically different morphology as compared to the monolayer film. The multilayer exhibits an extremely smooth surface with only few hole-like features, very few droplets or outgrowths, and no sign of even the slight bumpiness which is observed for the 1 µm monolayer counterpart in Figure 5.8(d). In contrast to the multilayer, the YBCO monolayer film has numerous holes, which are characteristic of poorer coalescence in this composition (see Section 5.3). Some of the holes 0.2 µm in diameter on the surface and corresponding structural inhomogeneities extend almost throughout the entire thickness of the film. In addition, some droplets or outgrowths up to 1 µm in size can be found on the surface of the 1 µm monolayer film. The resultant surface appears to be very rough. It is important to note here that the surface structure of the YBCO/NdBCO multilayer is independent of the deposition temperature range that was used in

157 5.4. YBCO/NdBCO multilayers 133 Figure 5.8: SEM micrographs of the surface morphology of multilayer YBCO/NdBCO film (a,b) and an YBCO monolayer film (c,d). this work (see Chapter 3 on deposition temperature). This indicates that improved smoothness results not from different (improved) growth conditions, but from intrinsic relaxed strain in the crystal lattice of the YBCO as a result of multilayering with NdBCO. The crystal lattice strain relaxation is presumably achieved through the creation of additional dislocations at the interfaces between the YBCO and NdBCO layers due to the mismatch between their crystal lattices. Indeed, the ratios between the crystal lattice parameters are quite similar for the YBCO-STO interface (for the parameter a : Å / Å = ; for b : Å / Å = ) and for YBCO-NdBCO interfaces (for a : Å / Å = ; b : Å / Å = 0.992). This leads to the assumption that all interfaces act in a similar way, with a slightly larger number of dislocations to be expected from the STO-YBCO interface than from the YBCO-NdBCO one [211]. In fact, not only does NdBCO have a positive influence on the formation of the YBCO structure, but the underlying YBCO layers have positive effects on the growth of NdBCO layers. YBCO layers also promote easier growth of the NdBCO layers. The YBCO layers act as seed layers for NdBCO growth in a similar way to that described

158 Chapter 5. Multilayer technique as an effective method to enlarge the 134 critical current in YBCO films Figure 5.9: TEM images of the YBCO/NdBCO film multilayer: (a) extra amount of defects produced by the interfaces. Circled areas have denser defect structure, (b) and (c) formation of dislocations can be interrupted or initiated by the interfaces as well. in Ref. [259]. As a result, the relaxed, seeded crystal lattice experiences improved growth conditions for achieving high quality multilayers with large thicknesses, as is evident from the wider temperature range for deposition. TEM observation provides us with more detailed information on the inner parts of the YBCO/NdBCO multilayer films. This, in fact, leads to a better understanding of the observed improvements in these films. First of all, interfaces between the layers are barely distinguishable on the crystal lattice layer scale, as shown at high magnification in Figure 5.9(c). The layers are observed to interrupt dislocations and ab-phase growth, as well as initiating dislocations, as in Figure 5.9(b) and (c). The largest density of defects is observed immediately above the STO-YBCO interface (see Figure 5.9(a)). However, the interfaces between the NdBCO/YBCO layers produce

159 5.4. YBCO/NdBCO multilayers 135 a considerable number of additional defects, as can be seen in Figure 5.9(a). Despite the almost similar mismatch between STO-YBCO and NdBCO-YBCO lattices, the formation of defects at the interfaces of NdBCO/YBCO appears to be less favourable than at the STO/YBCO interface. The XRD θ 2θ patterns of the monolayer and multilayer films are shown in Figure All seven (00l) peaks are visible, indicating that the grains in the films are c-axis oriented [90; 212]. Additionally, splits in all the (00l) peaks in the multilayer film are observable, confirming the scenario of the crystal lattice mismatch between YBCO and NdBCO materials. Figure 5.10: XRD θ 2θ scan data for the monolayer and multilayer films. Usually, the amount of disorder in the films can be evaluated by measuring the integrated intensity of (005) and (006) peaks, as in Ref. [212]. In our case, this method could not be applied as the (006) peak overlaps with (002) SrTiO 3 peak. On the other hand, another integrated peak ratio can be used for these purposes. The ratio of integrated intensity of the (005) and (007) peaks is also valid for estimating cation disorder, i.e. Y + and Ba + cation substitution. The (005)/(007) ratio decreased with the increasing of c-axis lattice parameter, suggesting that a larger amount of cation disorder is present in the multilayered film. Hence, the (005)/(007) ratio decreased

160 Chapter Multilayer technique as an effective method to enlarge the critical current in YBCO films from 12.9 in the monolayer film to 3.5 in the multilayered one due to the additional cation disorder that was present in the multilayered structure. It is logical to propose that the disorder is located mostly in the areas shown in Figures 5.9(a,b,c), i.e. the YBCO-NdBCO interfaces, which act as effective pinning sites Electromagnetic properties of multilayer films In Figure 5.11, the J c (B a ) data for three YBCO monolayer films: 0.1, 0.3 and 1 µm thick, are presented. Additionally, the J c (B a ) data for the YBCO/NdBCO multilayer film with thickness of 0.85 µm is shown as well. Figure 5.11 shows the critical current vs. applied magnetic field behaviour at 77 K in order to demonstrate the advantages of the multilayering method for superconductor wire applications (see Chapter 1). Figure 5.11: Critical current density as a function of applied magnetic field in double-logarithmic scales at 77 K. YBCO monolayer films with different thicknesses and two YBCO/NdBCO multilayers are shown for comparison. The J c (B a ) dependencies of the multilayers outperform all monolayer YBCO films over nearly the entire field range. The only exception, where J c of the 0.1 µm thick

161 5.4. YBCO/NdBCO multilayers 137 film is larger than that for the multilayer film, is for very small fields < T at T = 77 K. As we can see from Figure 5.11 the J c enhancement of the multilayered film as compared to the monolayer film of similar thickness is remarkable: the critical current of the multilayer is greater by a factor of > 2 at zero field and by a factor of > 3 at 1 T. The J c is also larger over the entire measured temperature range (see Figures 5.11 and 5.12). Figure 5.12: Critical current density as a function of applied magnetic field in double-logarithmic scales at 10 K and 40 K. YBCO monolayer films with different thicknesses and two YBCO/NdBCO multilayers grown at different temperatures are shown for comparison. Unexpected behaviours can be seen in Figures 5.11 and 5.12, namely, larger supercurrents are observed in multilayered films at low magnetic fields. One should expect an opposite effect: at low magnetic field critical currents in thinner films should be larger [260]. Judging from the obtained experimental data, this contradiction can be explained by the dominant role of current transparency effects in the low magnetic field regime (see Chapter 4). As was explained and shown in Section 5.3, the thinner the film is, the lesser the amount of defects that is present in its structure, and hence, there is higher transparency to current flow. At low temperatures, a multilayer s crit-

162 Chapter Multilayer technique as an effective method to enlarge the critical current in YBCO films ical current is larger in the small field range due to the lesser scattering of charge carriers in the modified defect structure (see Figure 5.12). The characteristic field B can be determined as the 99% offset of the critical current curve criterion (see Chapter 4). It can be seen from Figures 5.11 and 5.12 that this field for a multilayer film is always larger than for any monolayer films. This feature can be explained by aforementioned assumption in Section that the number of OPEDs i.e. dislocations within the LAB in multilayer films is larger. Figure 5.13: Critical current density as a function of applied magnetic field in semilogarithmic scales with simulated curves (red colour). Inset demonstrates sufficient domain size distribution functions. In order to evaluate the structural parameters of the YBCO/NdBCO multilayer films, the theoretical model proposed in Chapter 4 has been utilized. The resulting fits are plotted in Figure Structural parameters obtained as a result of fitting the curves are presented in Table 5.1. The inset of Figure 5.13 indicates the evolution of the statistical distribution of domain sizes in the three films with different thicknesses: 300 nm, 1000 nm (both monolayers), and an 850 nm multilayered film, respectively. The thicker monolayer

163 5.4. YBCO/NdBCO multilayers 139 film demonstrates widest distribution of domain sizes (ν = 2.48) and the smallest amount of pinning sites. At the same time, the multilayer film has a larger amount of pinning sites as was observed in the TEM images (see Figure 5.9). These are most likely to originate from the YBCO-NdBCO interfaces. Furthermore, the grain size distribution function for the multilayered film is very close to that of monolayer film, with parameters ν=1.87 and ν=1.67, respectively. The average grain size L and the inter-dislocation distance d r of the multilayer film is slightly lower than respective values for its monolayer counterpart. This can be due to an increase in the total amount of grains and dislocations in the multilayer film. Finally, the role of multilayering can be interpreted as cloning of microstructural properties of the bottom single layer in the upper layers without any structural degradation. Figure 5.14 represents different J c (B a ) curves for different YBCO/NdBCO multilayer films deposited at temperatures of 780 C and 800 C. At magnetic fields higher than 0.7 T, the multilayer film deposited at 800 C possesses stronger pinning properties than the 780 C film. This indicates that multilayer structures are very sensitive to the deposition temperature parameter T D, and to variations of the defect structure formation. This in fact implies that desirable pinning properties are achievable by changing the deposition temperature Multilayer YBCO/YBCO films Multilayer films containing only YBCO layers have been prepared in order to investigate the influence of the interlayer material and the presence of interfaces on Table 5.1: Structural parameters which were obtained during model fitting procedure. Description of the sample Parameters: ν L d r YBCO monolayer 0.3 µm film nm 32 nm YBCO monolayer 1.0 µm film nm 40 nm YBCO/NdBCO multilayer 0.85 µm film nm 24 nm

164 Chapter Multilayer technique as an effective method to enlarge the critical current in YBCO films Figure 5.14: Critical current density as a function of applied magnetic field in semi-logarithmic scales for YBCO/NdBCO multilayer films deposited at temperatures of 780 C and 800 C. the superconducting properties of the multilayered structures. By layer composition, these films were identical to these having NdBCO interlayers. In other words, YBCO films were grown by interrupting the deposition for the same time interval which was technologically needed to grow the comparable YBCO/NdBCO multilayer; the structure of these films is shown in Figure The surface of the YBCO/YBCO multilayer shown in Figure 5.16(a) is only slightly better than the surface of the YBCO films shown in Figure 5.8(c) and (d) and clearly worse, with larger diameter holes, than the surface of the YBCO/NdBCO multilayer films shown in Figure 5.16(b), Figures 5.8(a) and (b). The distance between the substrate and the target during deposition was D T S =41 mm for the multilayer films shown in Figures 5.16(a) and (b). As was mentioned in Section 3.2, the surface morphology is dependent on the deposition parameter D T S which might affect the structure significantly. This fact can be clearly seen by comparison of the

165 5.4. YBCO/NdBCO multilayers 141 Figure 5.15: Schematic view of the multilayer YBCO/YBCO film structure. two SEM images of YBCO/YBCO and YBCO/NdBCO multilayer films presented in Figure 5.16(a) and (b), and Figures 5.8(a). Figure 5.16: SEM images of YBCO/YBCO multilayer (a) and YBCO/NdBCO multilayer (b) films deposited at D T S =41 mm. Both multilayers, YBCO/YBCO and YBCO/NdBCO, deposited at D T S =41 mm, exhibited a similar critical current enhancement compared to the YBCO monolayer film with the same thickness of 1 µm (see Figure 5.17), which was deposited at D T S =46 mm. The J c enhancement, which becomes pronounced up to 1 T applied field, indicates that the microstructure of the multilayers has been modified due to the

166 Chapter Multilayer technique as an effective method to enlarge the critical current in YBCO films presence of the interfaces. Microstructural peculiarities of the YBCO/NdBCO multilayer films have already been discussed in the previous section. On the other hand, microstructural properties of the YBCO/YBCO multilayer have to be addressed separately. First, there is no difference between the lattice parameters of alternating YBCO-YBCO layers. This is an important difference from NdBCO containing samples, as there is virtually no possibility of introducing an extra amount of dislocations within the multilayered structure, i.e. OPEDs within the LAB. Second, the interfaces provide microstructure-related improvements which can be presumably be associated with extended periods of time for adatoms to find their accommodative sites on the surface during the waiting time between the deposition of the individual layers. This extended mobility may result in strain release of the lattice in a similar way to the NdBCO interlayers leading to a J c enhancement and some surface smoothness, as is demonstrated in Figure 5.16(b). Figure 5.17: Critical current density as a function of applied magnetic field in semi-logarithmic scales for YBCO/YBCO multilayer, YBCO/NdBCO multilayer, and YBCO monolayer films.

167 5.5. Conclusion Conclusion In summary, a multilayering approach has been realized to satisfactorily overcome the usual decrease in J c of superconductive films with increasing film thickness d. The optimal thickness range of YBCO monolayer films has been verified and used to design multilayer structures. Fabricated multilayered films exhibited superior electromagnetic properties as compared to thick monolayer YBCO films over practically the whole temperature and applied magnetic field ranges. The reasons for such enhancement have been found in the well developed microstructure of multilayered YBCO films. The observed results signify a remarkable step for the manufacture of coated conductors and will enable the production of coated conductors with industrially required current capacities. A statistical model developed in this work and described in Chapter 4 has been successfully applied to the analysis of monolayer and multilayered structures. It has been shown that parameters extracted from the fitting procedure adequately describe the microstructural peculiarities not only for monolayer but for multilayered films as well. The resultant applicability of developed model in Chapter 4 can be considered being an effective tool to verify microstructural properties of quasi crystal superconducting thin films.

168 Chapter Multilayer technique as an effective method to enlarge the critical current in YBCO films

169 Chapter 6 Multilayering for Coated Conductors 6.1 Outline This Chapter is dedicated to the investigation and application of the multilayering method for fabrication of coated conductors(cc). The following sections will provide general information about CCs, and some peculiarities of the deposition process of YBCO films on metallic substrates, as well as giving analysis of the obtained results. Evolution of the microscopic structure with increasing film thickness of the monolayer and multilayer structures will be discussed. At the end of this Chapter, multilayering and its positive influence on the current-carrying properties of CC will be presented and discussed. 6.2 Introduction As was mentioned in Section 1.7, second generation (2G) CC consists of a flexible substrate (a metallic template with several buffer layers), an epitaxial superconducting layer, and, lastly, a layer of stabilizer (see Figures 1.8, 6.1). In order to obtain a biaxially textured superconducting layer with the minimum amount of high-angled,

170 146 Chapter 6. Multilayering for Coated Conductors weakly conductive grains, biaxially textured substrates have to be used. Three techniques for producing biaxial texture in the substrate have been discussed: ion beam assisted deposition (IBAD) of biaxially textured buffers on polycrystalline alloy substrates, epitaxial deposition of buffer multilayers on rolling assisted biaxially textured substrates (RABiTS), and inclined substrate deposition of buffers on polycrystalline alloy substrates (ISD). Figure 6.1: Schematic view of the coated conductor configuration mastered within this work. In terms of functionality, buffer layers play a key role in coated conductor technology. The main purpose of the buffer layers is to provide a continuous, smooth, and chemically inert surface for the growth of the YBCO film, while maintaining the biaxial texture from the RABiTS substrate to the HTSC layer (see Ref.[89]) or create a texture by IBAD and ISD (see Refs.[279; 265]). The texture of the buffer layers is characterized in the same way as the texture of a substrate. XRD and XRD-pole scans provide important information about the buffer-layer growth and the quality of the grown films. Buffer layers also serve an important role in preventing metal diffusion from the substrate into the superconductor. They also act as oxygen diffusion barriers to avoid undesirable metallic substrate oxidation. Buffer layers must also

171 6.2. Introduction 147 provide mechanical stability and good adhesion to the substrate. For that purpose, it is important that buffer layers match both lattice constants and the coefficient of thermal expansion of the substrate and the YBCO layer (see Section 3.2). Buffer layers should also be continuous, crack-free, and as dense as possible. Even though oxide buffer layers are much thinner ( nm) than the metallic layer 100 µm, deposition of three buffer layers by vacuum deposition techniques accounts for over 20% of the total conductor cost. Hence, a considerable and concentrated effort is devoted to the development of a scalable, high-rate, high-quality buffer-layer deposition process. ISD is a simplest method to obtain an in-plane aligned buffer layer, which is achieved by inclining a metal substrate relative the plasma plume in the vacuum chamber [262; 263]. If compared to IBAD, the ISD process is fast and easy to scale up. In addition, its production speed is over 1 m/hour, which is much faster than around 0.1 m/hour for the IBAD technique. With these merits, ISD is the most industrially favourable method to fabricate substrates for the superconducting layer [264; 265]. One of the other advantages of the ISD technique is that it does not need an assisting ion source and it is independent of the recrystallisation properties of the metallic substrate [266; 267]. Although ISD is simple and fast, some disadvantages do exist. For example, the degree of in-plane and out-of-plane misalignment of the crystal lattice in buffer layers, which is often characterized by full width at half maximum (FWHM) of peaks an X-ray measurement, is larger than that in IBAD or RABiTS [264; 265]. There is also a slight tilt of this crystal lattice orientation compared to the substrate normal, which originates from substrate inclination. This angle is usually about 7-10 [267]. As a result, HTSC films directly deposited on ISD templates buffered by an MgO layer (ISD-MgO) show a rough surface similar to roof-tile patterns, which is observed on the underlying MgO buffer layer [267]. In most cases these misalignments and tilting are to the most important reasons for decreased J c in ISD conductors. If an additional YSZ layer with CeO 2 on top of the ISD-MgO template is deposited (see

172 148 Chapter 6. Multilayering for Coated Conductors Ref. [268]), this additional double buffer layer (YSZ/CeO 2 ) results in better crystal structure alignment in YBCO film, which leads to notable enhancement of critical current density. Finding a simpler (single) buffer layer structure, which would be equivalent to the properties of the double buffer layers is a challenging task, because the more complex the buffer layers structure is, the more expensive the wire production would be [269]. Another well known problem discussed in Sections 5.2 and 5.3 in relation to YBCO films is the inverse proportionality of the critical current density to their thickness (d): J c 1/d 1/2. Gradual deterioration of the critical current density occurs with increasing superconductor thickness. In order to overcome this problem, multilayered structures YBCO/NdBCO have been proposed and employed, as described in the previous Chapter. They allow us significantly improve the current-carrying ability for rather thick films. Moreover, pinning properties have been enhanced, and the overall microstructure of the superconducting films has become much denser and more ordered [64; 270]. This has led to the significant enhancement of the critical current density over the entire field range and extremely smooth surface of the multilayers. The presents of interfaces and layers has been found to be responsible for the performance and structure improvements [64; 270]. In Ref. [253], critical current J c (d) improvement has also been obtained in coated conductors on IBAD templates using a non-superconducting interlayer of CeO 2. The problem of the surface degradation was partially fixed by fabricating multilayered YBCO/CeO 2 films. Three YBCO layers 1.1 µm thick were alternated with intervening CeO 2 interlayers, providing the solution to decreasing the roughness of the film. However, it should be pointed out that it is necessary to make electrical contact to each YBCO layer due to the insulating nature of the CeO 2 interlayers. While this can be accomplished by suitable patterning at the ends of longer tapes, this difficulty can be overcome altogether by replacing CeO 2 interlayers with superconductors such as NdBCO as it described in the previous Chapter 5 and our Ref. [64].

173 6.3. Optimization of Deposition Parameters Optimization of Deposition Parameters For our studies, commercially available ISD-MgO metallic templates from THEVA were used in our sample preparation. These templates are made of 10 mm wide and 100 µm thick non-magnetic Hastelloy C276 substrate, which is buffered with an MgO layer with total thickness of 3.9 µm. The MgO buffer layer consists of a primary 3.6 µm thick layer deposited by the ISD technique and the final layer 0.3 µm thick grown by the co-evapouration technique. This layer serves to close the gaps between the large MgO columns and to establish an appropriate surface quality for the subsequent coatings. On top of the MgO layer, different thin buffer layers made of SrTiO 3 or CeO 2 have been grown in our PLD chamber. Then, the YBCO superconducting thin films were deposited. The preparation and basic deposition techniques for growing thin YBCO film on metallic substrate were the same as for deposition on single crystal substrates described in Chapter 3. The post-annealing procedure for our CC was slightly changed, as it consisted of two stages. After deposition, the temperature was lowered to 700 C and for 60 minutes, films were annealed in 1 atmosphere of oxygen pressure. Then, the temperature was decreased to 400 C within 30 minutes, and the film was annealed at the same oxygen pressure during 1 more hour. Finally, the temperature was ramped down to 30 C within 30 minutes. Figure 6.2 demonstrates the superconducting transition curves of two YBCO films obtained with different post-annealing procedures. It can be clearly seen that the new prolonged post-annealing process leads to a shorter superconducting transition width and a higher transition temperature. Presumably, this optimised post-annealing method helps to avoid formation of micro-cracks during the cooling procedure. It is believed that such micro-cracks are formed due to different coefficients of thermal dilatation of the substrate and film materials. We can speculate that during the annealing, extra oxygen content can be absorbed by superconductive YBCO film, thereby increasing the critical temperature. Before using CeO 2 and SrTiO 3 materials to create buffer layers on top of an ISD-

174 150 Chapter 6. Multilayering for Coated Conductors Normalized Magnetization, M / M(10 K) Hastelloy C 276 / ISD / CeO 2 / YBCO Standart 400 o C postannealed sample with T c =82.6 K Optimized postanneling method at 700 o and 400 o C; sample with T c =89.1 K Temperature, K Figure 6.2: Comparison of transition curves of two samples deposited at different post-annealing conditions. MgO template, the deposition of the YBCO film directly onto the ISD-MgO surface was undertaken to verify the capability of the ISD-MgO template itself to serve as an effective buffer layer. A routine optimization procedure to verify the optimal deposition parameters for YBCO film deposited on ISD-MgO metallic template has been conducted. Figure 6.3 shows two transition curves of YBCO films deposited on single crystal SrTiO 3 substrate and on ISD-MgO template at the same time. The data presented in Figure 6.3 were obtained from AC magnetic susceptibility measurements at a magnetic field of 2 Oe. It can be seen that at the same optimal deposition conditions (background oxygen pressure - P O2, deposition temperature - T D, distance between target and substrate - D T T ) the transition temperature is higher and the transition width is substantially smaller for YBCO film deposited on single crystal substrate. The next step of our work was to compare and choose between two buffer layers materials: CeO 2 and SrTiO 3. The results are shown in Figure 6.4. Two transition

175 6.3. Optimization of Deposition Parameters 151 Normalized AC Magn.Susceptibility, M / M(5 K) ISD-MgO template / YBCO; T c =73.0 K STO single crystal / YBCO; T c =91.3 K Temperature, K Figure 6.3: Comparison of transition curves obtained from AC magnetic susceptibility from PPMS measurements of two samples deposited under the same deposition conditions but on different substrate material. curves of two samples deposited under the optimal deposition conditions on different buffer layers are presented. Generally speaking the YBCO films produced on top of SrTiO 3 buffer layers demonstrate better electromagnetic properties than films deposited on CeO 2 buffer layers. An explanation for this feature can be found in the lattice mismatch between these materials (see Section 5.4.1). For instance, the misfit between SrTiO 3 and the YBCO lattice is about 1.5%. That is why SrTiO 3 material has widely been used as a single crystal substrate or buffer layer [274] in traditional YBCO films epitaxial growth. Moreover, it has been found in Refs. [274; 275] that SrTiO 3 can grow with high epitaxy on MgO (a=0.421 nm) by domain matching epitaxy, even with a lattice misfit as high as about 7.4%. CeO 2 material is slightly worse in this respect for YBCO growth, but it is still chemically stable and structurally compatible to YBCO with unit cell (CeO 2 : a=b=0.541 nm), equal to the diagonal length of the a-b lattice

176 152 Chapter 6. Multilayering for Coated Conductors Normalized Magnetization, M / M(10 K) ISD-MgO template / CeO 2 / YBCO ISD-MgO template / STO / YBCO Temperature, K Figure 6.4: Comparison of transition curves of two samples deposited under the optimal deposition conditions on different buffer layers. plane in the YBCO unit cell (see Section 3.2 and Section 1.4). The optimal deposition parameters shown in Table 6.1 were used to create a series of monolayer and multilayer films with a single SrTiO 3 buffer layer. Table 6.1: Optimal deposition parameters which were used for multilayering CC study. Deposition parameter Value Laser beam energy, Joule/pulse Laser beam repetition rate, Hz 5 Deposition temperature, C 780 Background oxygen pressure, mtorr 300 Buffer layer material SrTiO 3 The laser beam was focused onto a rotating YBCO target at an energy density of 6.7 J/cm 2, which is larger then the 3.6 J/cm 2 used in Section 3.1 and Chapter 5. The substrates, i.e. ISD-MgO templates with dimensions of 2 5 mm were cut from

177 6.4. Results and discussion 153 the strip, mounted on a removable part of the heater with silver paste, and heated to the desired deposition substrate temperatures, as was described in Section 3.1. The optimised distance between the target and substrate was D T S =60 mm, which is larger then for the experiment undertaken in Chapter 5. This D T S distance satisfies the requirements described in Section 3.2, where the tip of the plume was touching the substrate. Before the deposition of YBCO film, a thin buffer layer of SrTiO 3 was deposited in the same PLD chamber at a laser repetition rate of 1 Hz. The substrate deposition temperatures were T D =820 C for SrTiO 3, and T D =780 C for YBCO, respectively. The deposition time for the SrTiO 3 buffer layer was 5 min, and the resultant thickness of this buffer layer was 90 nm, as was verified with help of the Dektak Surface Profiler. The YBCO film thickness was varied from 0.5 µm to 4 µm by changing the deposition time. 6.4 Results and discussion Structural characterization of ISD-MgO templates With the help of an optical microscope, images of the metallic ISD-MgO templates were obtained. Figures 6.5(a) and (b) demonstrate the surface quality of these metallic templates at low and higher magnifications, respectively. Two features are clearly visible on these images. First, grain boundaries originating from the metal substrates can be easily recognized in Figure 6.5(b) because the MgO layer is transparent to light. Second, the wave-like surface quality probably results from the rolling method used to get 100 µm thin and 10 mm wide metallic strips from Hastelloy C 276 material. Two black arrows in Figure 6.5(a) indicate the general rolling direction. On the one hand, the image with the higher magnification, Figure 6.5(b), has its focused area in the center. On the other hand, there are unfocused areas on the left and right sides as well. This is evidence that the focused and unfocused parts of the image are not in the same plane, so that the surface is wavy.

178 154 Chapter 6. Multilayering for Coated Conductors Figure 6.5: Optical images of the ISD metallic surface before deposition at lower (a) and higher (b) magnification. Surface areas were analysed by AFM. Data obtained from the surface scan were carried to a matrix format, and a 3D surface was simulated using Origin Pro 7.0. Figure 6.6 illustrates two surfaces: (a) is obtained from a 5 µm 5 µm scan of a single crystal SrTiO 3 substrate, and Figure 6.6(b) is obtained from a 5 µm 5 µm surface area of an ISD-MgO metallic template. It can be seen in Figures 6.6(a) and (b)that the surface roughness is different for these substrates. The roughness measured by AFM is rather smooth with R A F M 1-2 nm for the SrTiO 3 single crystal substrate, whereas the metallic ISD-MgO template revealed a root mean square (RMS) parameter of R A F M 8-10 nm. Moreover, valley type surfaces are also visible on the ISD-MgO metallic template as discussed above. Figure 6.7 shows the surface morphology of the ISD-MgO metallic template obtained using the scanning electron microscopy. The top and bottom images were taken with lower and higher magnification, respectively. The lower part of the SEM image is an area that is free from the MgO buffer layer, where the Ni-based Hastelloy C 276 substrate is visible. It represents the same granular type of surface which was observed using the optical microscope. The inset in Figure 6.7 shows an enlargement of the area marked by the square. The roof-tile-shaped surface is clearly visible in the inset. The side view reveals a denser top MgO layer deposited by co-evapouration method; this layer fills up the gaps between the columnar grains of the ISD deposited MgO layer. In spite of the roof-tile surface, the MgO template is potentially a good buffer material for further

179 6.4. Results and discussion 155 Figure 6.6: 3D surface obtained using AFM: (a) surface scan obtained from 5 µm 5 µm spot of single crystal SrTiO 3 substrate; (b) surface scan of 5 µm 5 µm area of metallic substrate (ISD-MgO template). epitaxial growth of YBCO films. Results on finding the optimal buffer layer are described in the previous section; it was demonstrated that SrTiO 3 yields better quality YBCO films Structural and electromagnetic characterization of CC Crystallographic and superconducting properties of YBCO films deposited under optimal deposition conditions are listed in Table 6.2. All superconducting films listed in the table are 0.5 µm thick. X-ray diffraction scan results are shown in Figure 6.8. The results reveal that Table 6.2: XRD FWHM values of the (005) peak, critical temperatures, and J c values measured at 77 K in self field for YBCO films deposited under optimal conditions. Num. Sample type FWHM (005) T c,k T,K J c,10 6 A/cm 2 1 YBCO/STO single crystal YBCO/ISD-MgO template YBCO/CeO 3 /ISD-MgO template YBCO/StTiO 3 /ISD-MgO template

180 156 Chapter 6. Multilayering for Coated Conductors Figure 6.7: SEM scan showing slightly tilted view of the metallic Hastelloy C276 substrate with ISD-MgO deposited buffer layer (see text for more details). the intensities of the reflection signals from YBCO films deposited on single crystal substrates and from YBCO films deposited on ISD-MgO metallic templates are very different, in spite of the fact that the thickness of these films is the same (see Figure 6.8). The signal is two orders of magnitude lower for the YBCO films deposited on the ISD-MgO metallic template than that for YBCO films deposited on the single crystal substrate. In addition, in the first case, the FWHM of the (005) peak is about a factor of 2 larger compared to that of the YBCO film on the single crystal substrate. It is known that quasi-single crystal YBCO thin films have strong XRD signals from all (00l) peaks with small FWHM. Hence, lower intensity of these peaks and larger FWHM indicate that significant in-plane and out-of-plane misorientations exist between adjacent grains in YBCO films deposited on the ISD-MgO metallic templates. A few XRD scans were carried out at different in-plane angles for all samples.

181 6.4. Results and discussion 157 During these diffraction scans, the pattern and intensity of the (00l) peaks of samples 1, 3, and 4 were the same, but the (00l) peaks of sample 2 were hardly visible. This finding indicates that samples 1, 3, and 4 have a well ordered grain structure with the c-axis parallel to the normal of substrate, while sample 2 has misaligned grain orientation. Figure 6.8: XRD scan results for two YBCO films of the same thickness, deposited on different substrates: SrTiO 3 and Hastelloy/ISD/CeO 2. The surface topology of the YBCO films deposited on the SrTiO 3 /ISD-MgO templates is shown in Figure 6.9. This set of SEM images shows the evolution of the surface morphology with increasing the thickness. The YBCO films with thickness of 0.5 µm, 1.7 µm, 3.7 µm are presented in Figure 6.9(a),(b), Figures 6.9(c),(d), Figures 6.9(e), (f), respectively. For better comparison, the images shown in Figure 6.9 are presented on different scales of 10 µm and 1 µm. The granular structure is an attribute of all the films. In contrast with the YBCO films presented in Figure 5.1, the YBCO/SrTiO 3 /ISD-MgO structure displays worse coalescence. Moreover, the surface of these films shows morphology characterized by deep pores and holes (circled in Figure 6.9(b)-(f)). Formation of the pore-like structure might be related to the

182 158 Chapter 6. Multilayering for Coated Conductors intrinsic strain of the YBCO lattice in the vicinity of the roof-tile-shaped ISD-MgO buffer layer (shown in the inset of Figure 6.7). It is clear that the 0.5 µm thick YBCO film in Figure 6.9(a) has the smoothest surface, without the holes which are seen in Figure 6.9(c) and(e). A minimum number of the droplets, as shown in Figure 6.9(a), is also characteristic only of the 0.5 µm YBCO film. The thicker YBCO films (1.7 µm and 3.7 µm) have rougher surfaces. The surface structure of the 0.5 µm and 1.7 µm thick films is visibly denser than that Figure 6.9: SEM images of the surface of the 0.5 µm thick (a,b), 1.7 µm thick (c,d), and 3.7 µm thick (e,f) YBCO films, respectively. Cracks appeared as a result of manipulation related to taking the images. Circled areas show holes in the structure.

183 6.4. Results and discussion 159 of the 3.7 µm thick films. Moreover, the film with the thickness of 3.7 µm has an average grain sizes of the order of 1 µm, which is larger than the size of the grains depicted in Figure 6.9(b) and (d). It is reasonable to assume that this is a result of coalescence of smaller grains from lower layers, as seen in Figure 6.9(d). All these facts imply that the structural degradation is an inevitable result of increased film thickness during pulsed laser deposition. The most interesting results of our investigation of microstructure effects on critical current density were obtained when the multilayering technique described in Chapter 5 was transferred to metallic substrates. In order to improve the critical current density of thicker films, two multilayered sandwich type YBCO/NdBCO structures were deposited on the optimised STO/ISD-MgO metallic templates. A series of alternating 0.4 µm thick YBCO layers and interlayers of 30 nm thick Nd- BCO were deposited to obtain two multilayered films with resultant 1.26 µm and 3.5 µm thicknesses. Figure 6.10 shows critical current density versus film thickness. It was revealed that the critical current density of the 1.26 µm thick YBCO/NdBCO multilayer is larger than that of the monolayer with the thickness of 0.5 µm at all measured temperatures and magnetic fields. Critical current density, J c (10 10 A/m 2 ) B a = 0 T T = 10 K YBCO/NdBCO multilayers YBCO monolayer B a = 0 T Film thickness, d (nm) T = 77 K YBCO/NdBCO multilayers YBCO monolayer Figure 6.10: Critical current density as a function of the thickness of YBCO films. The reason for the critical current density enhancement in the multilayers can

184 160 Chapter 6. Multilayering for Coated Conductors be attributed to different structural features of these films. The SEM images of the monolayer YBCO film 3.7 µm thick and the multilayer 3.5 µm thick YBCO/NdBCO film are presented in Figure 6.11(a) and 6.11(b), respectively. Both monolayer and multilayer films have microstructural imperfections, i.e. holes. The internal structure of the monolayer film demonstrates a number of holes which have the sizes from 0.3 µm to 1 µm. On the other hand, the multilayer film shows fewer of the holes which are formed mainly between columnar grains. Figure 6.11: SEM images of the cross-section of two films deposited on the STO/ISD-MgO template: (a) monolayer film with the a thickness of about 3.7 µm, and (b) multilayer film with a thickness of about 3.5 µm. The monolayer film with a thickness of 3.5 µm demonstrates the three-dimensional random growth mode, where the grains are interlaced with one another and straight columns are not formed. This random growth mode is a result of the continuous deposition process where the YBCO plume particles arrive continuously. This leads to accumulated crystal strain, favoured by the imperfect alignment of the buffer layer, which can be released by creation of holes. These holes form the porous structure shown in Figure 6.11(a). Alternatively, the YBCO/NdBCO multilayer film shows columnar structure. In that case, a mixture of two-dimensional and three-dimensional columnar island growth mode is realized, due to interruptions during deposition to introduce interlayers. Interruptions of the YBCO plume particle flow lead to relaxation of the crystal structure accruing at the interfaces. This leads to a reduction in the number of holes. Moreover, introduction of the NdBCO material that has

185 6.4. Results and discussion 161 lattice parameters very close to those of YBCO also relieves the accumulated strains effectively [64]. However, starting from the thickness of about 1.9 µm, some columns demonstrate incomplete coalescence and diverge. This sort of microstructural imperfection leads to critical current density degradation. This is because the structural peculiarity is likely to result in highly percolative supercurrent flow with reduced effective cross-section, which leads to suppression of the current flow in the upper part of the multilayered films. This problem may be solved by optimization of the YBCO film structure on the top of the optimised buffer layer. Thus, we can conclude that multilayering contributes to the stress relieving mechanism, which decreases the porosity and increases the critical current density in YBCO films. Figure 6.12: Magneto-optical images of flux behaviour in 0.5 µm thick monolayer YBCO film deposited on ISD-Mg metallic template. (See detailed description in the text) Figure 6.12(a,c) and (b) presents magneto-optical (MO) images of one YBCO/STO/ISD-

186 162 Chapter 6. Multilayering for Coated Conductors MgO sample collected under different conditions. The images (a,c) were taken when sample was cooled in T from above T c to 50 K, and then the magnetic field was removed (the so called field-cooled (FC) regime). In that remnant state, when magnetic field is applied perpendicular to the film surface, the sample retains trapped flux. The amount of flux is determined by the sample temperature, the magnitude of the applied field, and the local critical current densities. The trapped flux will also interact with an induced anti-flux, creating annihilation zones, areas where the net field is zero. The annihilation zones, which can be seen in Figure 6.12(c), remain dark in MOI. However the dark areas are not always annihilation zones; areas that are not superconducting at the local field and temperature will also be dark due to the absence of trapped flux. To avoid misinterpretation of these areas, an analysis of MO images obtained in the zero-field cooled (ZFC) regime has to be provided. Figure 6.12(b) shows an image which was collected after cooling in zero field to 4.38 K, and then magnetic field of T was applied. The bright areas indicate magnetic flux penetration, while the dark area corresponds to flux shielding. Magnetic flux enters the sample from the edges and propagates preferentially along weaker-linked regions such as grain boundaries. Dark areas are electromagnetically well-connected regions, while the lighter ones are areas with flux network penetration. The flux is attracted to stay within areas where the superconducting order parameter is depressed, e.g. in the grain boundaries. The pattern and average separation of the bright lines in the images in Figure 6.12(c), which map the flux distribution, can be attributed to characteristics of the grain structure of the underlying metallic template, which were shown in Figure 6.5. Almost the same magneto-optical images were obtained from YBCO films deposited on top of RABiTS templates, according to Ref. [280]. The authors pointed out that the origin of these bright lines in the MO images begins in the grain structure of the underlying metallic substrate. Taking into account optical images of the surface of the metallic substrate before deposition (presented in Figure 6.5) and the SEM image from Figure 6.7, a clear conclusion on the influence of the grain structure

187 6.4. Results and discussion 163 of the metallic template on the structure of the upper layers (ISD-MgO, STO, and YBCO) can be reached. Generally speaking, the strain produced in the areas of the grain boundaries can be transferred through buffer layers to the top YBCO film. This is probably due to the temperature treatment, both at the YBCO deposition and the post-annealing stages. Furthermore, an additional network of sub-millimeter size defects is created and plays a role as a barrier to current flow. In practice, we can see two networks of barriers to current flow: one is created by the µm micrometer grains of YBCO visible in Figure 6.9, and the other by µm grains of the underlaying metallic substrate. In order to apply the model developed in Chapter 4, we have to take in to account two functions to express the networks of grains of different sizes for current percolation, as well as the role they play as effective pinning sites. Normalyzed Critical Current, J c (B a ) / J c (0) K B a (10K)/B a (T)=1 20K B a (10K)/B a (T)= K B a (10K)/B a (T)= Magnetic field, B a (T)/B a (10K) Zones where curves are not self-similar. Figure 6.13: Typical data of the normalized experimental critical current versus magnetic field. Prior to starting the fitting procedures on the obtained J c (B a ) curves, an attempt was made to normalize them and scale them up. Typical normalized experimental

188 164 Chapter 6. Multilayering for Coated Conductors J c (B a ) curves have been plotted in Figure Figure 6.13 presents J c (B a ) curves normalized to J c (0) at different temperatures: 10 K, 20 K, and 40 K, and scaled up to be at 10 K along the magnetic field axis. One important feature that can be seen in Figure 6.13 is the absence of identical behaviour in the J c (B a ) dependencies at temperatures higher then 10 K, as was mentioned in Section 4.5. The curves are not self-similar at temperatures > 10 K in all vortex modes.it is reasonable to assume that, firstly, the pinning mechanism is different in YBCO films deposited on single crystal substrates and those deposited on metallic ones due to difference in ensembles of pinning defects. Secondly, thermal activations effects probably become more pronounced in YBCO films deposited onto the ISD-MgO template. This can be seen if one compares the following scaling ratios for the J c (B a ) dependencies taken at different T: B a (10 K)/B a (20 K)=1.45 and B a (10 K)/B a (20 K)=2.65 for YBCO/STO film (Figure 4.10 (b)) and B a (10 K)/B a (20 K)=1.75, B a (10 K)/B a (20 K)=3.15 for YBCO/STO/ISD-MgO film (Figure 6.13). Thirdly, the critical current density can be also interpreted as a current tunnelling through the network of grain boundary channels played the role of hidden weak links, as Mezzetti considered in his work [197]. SEM observations of the granularity and the MO imaging of the irregular flux penetration in the YBCO films deposited on metallic template point out to this scenario. Consequently, the critical current behaviour at applied magnetic fields can be theoretically described by random array of parallel Josephson junctions with statistically distributed lengths. We applied the fitting to one J c (B a, 10 K) curve and obtained the parameter ν=36.9 responsible for the statistical distribution of the grain sizes in the YBCO film. This parameter is largest among those J c (B a, 10 K) curves which were obtained from YBCO/STO films. Such a value of that parameter can reflect a large variety of grain or domain sizes in the YBCO/STO/ISD-MgO film, and it is consistent with the existence of above-mentioned pinning networks: one micrometer size and the other sub-millimeter size.

189 6.5. Conclusion Conclusion During the optimization of the deposition process, it was shown that in order to deposit good quality thin films on metallic substrates, a single layer of the SrTiO 3 material has been found to be most suitable as a buffer material between the ISD-MgO metallic template and the YBCO superconducting film. This finding was predicted and expected because of the minimal lattice mismatch between the YBCO and STO latices. Monolayer and multilayer sandwich-like structures of different thicknesses were successfully fabricated. Analysis of the obtained dependences of the critical current degradation on the film thickness was conducted for monolayer and multilayer structures in accordance with the microstructural experimental data. The unavoidable degradation of J c for thicker monolayer YBCO films has been studied. Introduction of the multilayered structure approach was successful in term of achieving the highest critical current density, i.e. high critical current was obtained for the 1.26 µm thick multilayer film. The higher J c obtained in multilayered films was not related to better surface morphology (as revealed in the previous Chapter). It has become clear that enhanced critical current capability is a result of advanced interior microstructure of the YBCO films deposited on metallic template. From our point of view, to obtain thicker multilayered films with improved critical current density and the required denser structure to industrial production of CCs with the largest possible critical current capabilities, further optimization of the PLD process parameters should be undertaken. It has been shown that CCs constructed on ISD-MgO metallic template poses fabrication induced microstructural features which limits the microstructure transparency to supercurrent flow. Additional grain boundary network of micrometer size, created by incompatible thermal expansion coefficients between metallic template and upper ceramic layers, might be unavoidable factor for CC microstructure, which plays a role of additional barrier to current flow.

190 166 Chapter 6. Multilayering for Coated Conductors

191 Chapter 7 Silver doping of YBCO films 7.1 Outline This Chapter deals with an investigation of silver doping effects on the electromagnetic properties of YBCO thin films. An introduction of the basic principles and literature data on Ag doping effects in bulk and thin YBCO superconductors will be presented. This will be followed by a microstructural and electromagnetic investigation of Ag doped YBCO films prepared in ISEM. The Chapter will conclude with an explanation of results and discussion on the origins of improved critical current density in Ag doped YBCO films. 7.2 Introduction and literature review An artificial addition of a very small percentage of foreign atoms into the regular crystal lattice is defined as doping. Historically, doping processes were revealed and implemented to the semiconductor industry to fabricate semiconductors with specifically designed magnetoelectric properties. In superconductors, the doping method has been widely used to change their magnetoelectric properties and has great potential to tailor the superconducting properties of YBCO films in a positive way. To produce high quality coated conductors (CCs), methods which increase criti-

192 168 Chapter 7. Silver doping of YBCO films cal current densities have to be investigated. In Refs. [281], [283], and [45], BaZrO 3, Y 2 O 3, and Ca dopant materials have been explored to enhance critical current carrying capabilities of YBCO films. Results obtained in these works can be separated into two categories: (a) some dopants act as effective pinning centres, which lead to maximization of the critical current in applied magnetic fields [281; 283]; (b) dopants increase transparency to the current flow in YBCO films, thereby raising the total critical current in YBCO films [45]. Due to the presence of large amounts of inherent nanosized defects in YBCO films (see Chapter 1), research and development of controllable doping materials and their effects on superconducting properties is a very difficult task. Silver doped YBCO thin films and their bulk counterparts were fabricated by several groups [284; 286; 285; 124; 288; 287; 289]. Most of the results demonstrated improvement in the microstructure, and consequently, the critical current density. The positive influence of Ag doping on YBCO films is mainly attributed to improved intergranular coupling resulting from bigger grain size and better in-plane orientation, rather than from the increased number of pinning centres or enhanced pinning force [124; 290; 291]. Also, it was reported in Ref. [291] that Ag doping results in enhanced kinetics of oxygen diffusion in bulk HTSC materials. The technical advantages of Ag use in fabrication of YBCO films can be realized in the following areas: (i) obtaining high overall J c, (ii) lower reactivity with background air and, as a result, stability in the environment, (iii) reduction of the contact resistance. As was mentioned in Chapter 1, high J c in coated conductors, enabling their applications, is a result of YBCO quasi crystal texturing. In other words, it is necessary that c-axis in the film grains is perpendicular to the substrate surface and have good in-plane orientation. Oxygen diffusion along the c-axis is known to be lower than in the ab- plane. In order to oxygenate films completely, the presence of short-circuit paths for fast oxygen diffusion into the entire thickness of the film is required. It was shown in Refs. [287] and [136] that silver situated in the LAB of the film may allow rapid oxygen diffusion into the body of the YBCO film. The authors

193 7.3. Sample preparation technique 169 explain that this happens irrespective of the deposition technique used. YBCO films need to be oxygenated (annealing stage, Chapter 3.1) over their entire thickness in order to have high current-carrying ability. It is a well known fact that films deposited on substrates always develop strain. The strength of strain depends on the extent of lattice mismatch between the substrate and the film. In the case of free-standing bulk samples, only volume expansion stresses are present during tetragonal-to-orthorhombic transformations. In thick films, substrate-film interface stress is also present in addition to the volume stress. The creation of defects to accommodate these stresses by adding small amounts of silver indirectly affects the oxygen diffusion in YBCO films. Deposited Ag nanodots on STO substrates in Ref. [292], prior to the growth of superconducting BaSrCa 2 Cu 3 O x film, were shown to enhance the critical current density behaviour in magnetic fields. This enhancement was explained as being due to lattice mismatch and chemical poisoning. Due to these reasons, the superconducting phase does not form right above the nanodot. Consequently, this creates large number of extended and effective pinning centres, which help to increase the critical current density of the whole film. As the concentration of Ag in doped thin YBCO films is of the order of a few percent, the resultant fabrication cost of a coated conductor with Ag does not increase significantly. Therefore, it is believed that Ag doping is very attractive for fabrication of coated conductors on a large scale. To expedite introduction of Ag doping into industry it is necessary to investigate the influence of Ag doping on the electromagnetic properties of YBCO superconductor in detail. Understanding of silver doping effects will clarify whether Ag doping results in improvement of critical current flow itself or if it is the pinning properties of the films which are enhanced. 7.3 Sample preparation technique Silver doped and undoped YBCO thin films were deposited in accordance with the deposition process described in Chapter 3.1. The optimised deposition parameters

194 170 Chapter 7. Silver doping of YBCO films are presented in Table 7.1. Table 7.1: Optimal deposition parameters which were used for silver doping study. Deposition parameter Value Laser beam energy, Joule/pulse 0.36 Target-to-substrate distance, mm 37 Laser beam repetition rate, Hz 5 Deposition temperature, C 780 Background oxygen pressure, mtorr 300 Substrate material SrTiO 3 After deposition, the films were annealed at 400 C for about 60 min before they were cooled down to room temperature. The film thickness was varied from 400 nm to 1000 nm. The Ag doping level in the fabricated YBCO films was 1%, 2%, 5.8%, 11% percent of silver. The laser shot repetition rate was kept constant at 5 Hz. The duration of ablation and the number of shots for each target material were calculated to match the desired requirements. As a result, the relative concentration of Ag in the doped films was calculated. This calculation method has one inherent flaw, i.e., uncertainties in evaluation of the deposited material in the film volume. However, these uncertainties were neglected as the results were repeatable and did not change from one deposition to another. 7.4 Structural characterization of doped and undoped films Figure 7.1 shows the XRD patterns of pure and Ag doped YBCO films. It is well known that quasi-single crystal YBCO thin films yield strong XRD signals from all (00l) peaks with well ordered crystallized single orthorhombic phase. Both undoped and doped films demonstrate this feature. However, it can be seen clearly that the full width half maximum (FWHM) of the most dominant (00l) peak of 2% in Ag doped film is smaller than for the undoped ones. A smaller FWHM indicates better crystallinity of the 2% Ag doped film. Two

195 7.4. Structural characterization of doped and undoped films FWHM FWHM FWHM 1.32 FWHM Intensity, arbitrary units (005)-peak (007)-peak YBCO 2% Ag doped YBCO (001) (002) (003) (004) (005) Angle 2 (deg.) (006)+STO(200) (007) Figure 7.1: XRD pattern of 2% Ag doped and undoped YBCO films. Two insets of Figure 7.1 visualise the two peaks (005) and (007). other representative peaks, i.e. (005) and (007), are shown in insets of Figure 7.1 for better comparison. To estimate the amount of Y + and Ba + cation substitution, i.e. cation disorder, comparison of the (005)/(007) peaks ratio was used in the same way as it was described in Section The 2% Ag doped YBCO film has (005)/(007)=5.36, whereas pure YBCO film has (005)/(007)=2.16. There is evidence that the enlarged value of the (005)/(007) ratio in the 2% Ag doped sample is not due to the deoxygenation of the film [294]. The reason for such a conclusion is that there is virtually no difference in the critical transition temperature of doped and undoped films. In fact, these observations indicate that cation disorder in undoped YBCO thin films is larger than in Ag doped ones. To detect the existence of silver in thin films a conventional XRD method was applied. Doped films did not all show any peaks corresponding to pure Ag or other Ag

196 172 Chapter 7. Silver doping of YBCO films containing phases. This is consistent with the results obtained by Singh in Ref. [286]. Singh investigated the amount of Ag in the patterns by means of energy dispersive X-ray analysis. This analysis showed that the characteristic Ag signal was very small, i.e., less than %(atomic) in the film. We speculate that this disappearance of Ag can be explained by the very large diffusion length of Ag adatoms on the substrate during deposition at the temperature of 780 C and pressure of 300 mtorr. Before re-evapouration silver particles interact with YBCO adatoms on the surface, and due to the non-reactivity of Ag, its particles are turned away from areas where formation of grains occurs. It is reasonable to assume that Ag particles can settle in intergrain regions, e.g. grain boundaries. Thus, the kinetic energy from Ag adatoms can be transferred to adatoms forming the YBCO lattice. A very similar scenario of structure improvement due to Ag doping was proposed in [286]. The authors have argued that the great increase in grain size and the grain alignment over and above levels possible by normal growth conditions were because of enhanced supply of active oxygen due to the better surface mobility provided by the doped Ag particles. SEM images of Ag doped and undoped YBCO thin films are shown in Figure 7.2. It is clear that the surface morphology of the films is practically indistinguishable. This feature is characteristic of all YBCO films deposited at D T T = 37 mm (see Chapter 3.1). It is obvious that Ag doping does not influence the surface morphology of the YBCO films deposited under the above-mentioned conditions. Figure 7.2: SEM images of undoped (a) and 2% Ag doped(b) YBCO thin films. In order to understand the peculiarities of the inner structure of the doped and

197 7.4. Structural characterization of doped and undoped films 173 undoped films, transmission electron microscopy experiments were performed. Figure 7.3(a) shows TEM cross-sectional image of the 2% Ag doped sample. The YBCO [001] orientation is perpendicular to the substrate plane. Precipitates and second phases are circled in the image, and their sizes are in the nm range. It can be seen clearly that the majority of them are formed as elongated particles. A magnified image of one of these particles is presented in Figure 7.3(b). One can easily note that the particle is quite well embedded in the YBCO matrix despite its ab-plane orientation. Figure 7.3: TEM images of 2% Ag doped (a,b) and of undoped (c) YBCO thin films. The circles enclose precipitates and second phases. It is worth mentioning here that in the 2% Ag doped YBCO film precipitates have a preferred orientation in the direction parallel to the ab-plane. In contrast, precipitates of undoped YBCO films are oriented randomly. Figure 7.3(c) shows an example where one particle is elongated along the c-axis. Taking into account