Doping dependent transport in YBCO nanostructures: insights into the microscopic mechanism for high critical temperature superconductivity Thesis for the Degree of Erasmus Mundus Master of Nanoscience and Nanotechnology RANKO TOSKOVIC Promoter: Professor Floriana Lombardi, Chalmers University of Technology Co-Promoter: Associate Professor Frederik Denef, KU Leuven External Referee: Professor Göran Johansson, Chalmers University of Technology Department of Microtechnology and Nanoscience Chalmers University of Technology Göteborg, Sweden 2013 thesis for the degree of erasmus mundus master of nanoscience and nanotechnology Doping dependent transport in YBCO nanostructures: insights into the microscopic mechanism for high critical temperature superconductivity Ranko Toskovic This thesis was carried out as a part of the Erasmus Mundus Master program of Nanoscience and Nanotechnology with the trajectory Nanophysics KU Leuven - Chalmers University of Technology Department of Microtechnology and Nanoscience CHALMERS UNIVERSITY OF TECHNOLOGY Göteborg, Sweden 2013 Doping dependent transport in YBCO nanostructures: insights into the microscopic mechanism for high critical temperature superconductivity Ranko Toskovic Thesis for the Degree of Erasmus Mundus Master of Nanoscience and Nanotech- nology c�Ranko Toskovic, 2013 Quantum Device Physics Laboratory Department of Microtechnology and Nanoscience CHALMERS UNIVERSITY OF TECHNOLOGY SE-412 96 Göteborg Sweden www.chalmers.se Tel. +46-(0)31 772 1000 Cover: Printed by Chalmers Reproservice Göteborg, Sweden 2013 Abstract The microscopic mechanism responsible for superconductivity in high critical temperature superconductors (HTSs), almost three decades after their discovery, still remains unknown. It is widely believed that studies in the underdoped (UD) regime of these materials could shed light on this unresolved question. In this thesis project, a controllable and reproducible Pulsed Laser Deposition (PLD) growth of underdoped YBa2Cu3O7-δ (YBCO) films was done by changing only the post- annealing pressure. X ray diffractometry (XRD) scans of the films have shown a continuous YBCO unit cell expansion as the pressure decreased, indicating a reduction in the doping level of our films. Rather sharp resistance vs. temperature transitions obtained in our films indicate a high level of homogeneity. First steps towards optimization of the surface properties of the films have been also undertaken. A soft-patterning technique developed previously in our group, preserving homogeneity of submicron structures, was employed for nanorings’ patterning on the optimally doped films. Little Parks (LP) experiments were conducted on rings with different sizes. Cooper pairs have been identified as the predominant charge carriers in all the rings, as expected at the optimal doping level. Keywords: high critical temperature superconductivity, YBCO, Little Parks effect, underdoped and optimally doped films, nanorings Symbols Critical temperature Oxygen doping parameter Post-annealing pressure Deposition temperature Critical temperature oscillations amplitude Onset temperature of the resistive transition Resistive transition width Superfluid velocity Resistance Magnetic inductance Magnetic flux Magnetic fluxoid Magnetic flux quanta Radius of the loop enclosing Arm width of the ring Inner diameter of the ring Zero-temperature coherence length Abbreviations LTS Low critical Temperature Superconductor HTS High critical Temperature Superconductor YBCO Yttrium Barium Copper Oxide SC Superconducting OP Order Parameter BCS Bardeen-Cooper-Schrieffer UD Underdoped LAO Lanthanum Aluminum Oxide PLD Pulsed Laser Deposition XRD X-Ray Diffractometry PPMS Physical Properties Measurements System SEM Scanning Electron Microscopy AFM Atomic Force Microscopy MC Multiply Connected LP Little Parks MR Magnetoresistance FFT Fast Fourier Transform Contents 1 Introduction 1 1.1 Motivation …………………………………………………………………………..1 1.2 Theoretical background……………………………………………………………..3 1.2.1 Conventional vs. high critical temperature superconductivity……………...3 1.2.2 YBCO – structure, phase diagram and superconducting properties………..4 1.2.3 Little Parks effect…………………………………………………………...8 2 Deposition and characterization of YBCO films 13 2.1 The substrate choice………………………………………………………….…….13 2.2 Doping dependent YBCO films……………………………………………….…..14 2.2.1 Pulsed Laser Deposition……………………………………………….…..15 2.2.2 Characterization of YBCO films…………………………………………..17 2.2.2.1 Electronic properties……………………………………………..17 2.2.2.2 Crystallographic properties………………………………………21 2.2.2.3 Surface properties………………………………………………..24 3 Fabrication of optimally doped YBCO nanorings 27 4 Transport measurements 31 5 Conclusions and future outlook 41 Appendix A – XRD 43 Appendix B - PPMS 45 Acknowledgements 47 Bibliography 49 1 Chapter 1 Introduction 1.1 Motivation Since their discovery in 1986 [1], high- superconductors (HTSs) have attracted great attention due to their rather high critical temperature ( ) and ability to sustain large currents and magnetic fields while preserving the superconducting (SC) state, which can be highly useful for applications. Some knowledge on the symmetry of the order parameter (OP) has been collected [2]-[7]. It is well established by now that the dominant component of the OP in HTSs is of dx 2 -y 2 type. The microscopic theory providing explanation on the origin of superconductivity in these materials is still missing. The interplay between several degrees of freedom in these systems (charge, spin, orbit, lattice) requires further addressing for formulating the microscopic theory for HTSs. Two different streams have been followed in the attempts to provide an explanation. Some propose models which include phonon assistance in the formation of SC charge carriers, whilst reminding that if that is actually the case, the mechanism has to be more complex than the one proposed in the Bardeen-Cooper-Schrieffer (BCS) theory [8]. Others suggest models that include spin-spin interaction rather than the electron-phonon one [9]. In addition, the normal state of these materials introduces a peculiar behavior described by the existence of a gap in the electronic density of states in the underdoped (UD) regime 1 at temperatures higher than the critical one in the corresponding direction of the k space where the dx 2 -y 2 order parameter has its maximum [10] 1 More on different parts of the SC phase diagram can be found in section 1.2.2. Chapter 1 Introduction 2 [11]. Most importantly, it is not clear which type(s) of charge carrier is (are) responsible for SC transport in these materials. It has been suggested that studies in the UD regime could help gain more insight into the pairing mechanism in HTS materials. To identify the responsible charge carrier in the underdoped (and, also, in the optimally doped) regime, analyses of the Little Parks (LP) measurements have to be done. Rings are highly useful structures for investigating coherent quantum phenomena in SC state, such as the Little Parks effect [12]. This effect was firstly observed in low- superconductors (LTSs) [13]. In LTS systems LP oscillations are strictly periodical, identifying Cooper pairs ( ) as the charge carriers [13] [14]. In addition to the periodicity observed in LTSs, nanoscale rings patterned on HTS films are expected to show a crossover from to or flux periodicities [15]-[20]. Due to the surface problems we encountered, we could not probe these exciting predictions in our UD films. However, we did put to a test superconductivity in nanorings in the optimal regime and, as expected, charge carriers were found to be responsible for SC transport. Also, our measurements showed the advantage of the used patterning technique in preserving homogeneity in our rings, compared to similar work done by others [21], even though our rings are smaller in size and therefore more susceptible to damage induced by the fabrication process. The first part of this thesis work addresses the issues related to the growth of thin YBCO films in a controllable manner with reproducible superconducting properties in the UD regime. We have succeeded in changing the of the films by modifying only one parameter in the entire deposition process, that parameter being the pressure of post-annealing. The films we obtained showed not only reproducible superconducting properties, but also a high level of homogeneity, seen through rather sharp resistive normal-SC transitions. A confirmation of lower doping level in our films was found by X ray diffractometry (XRD) scans. The UD films have been deposited with the final goal of patterning and measuring devices on them, since, as stated above, the most exotic phenomena are expected for these doping levels. Unfortunately, the surface properties made our initial idea impossible to put into practice, since the submicron rings could not have been patterned on these films. The second part of my thesis was related to fabrication of nanorings and LP measurements performed on them. Fabrication was done on optimally doped commercial YBCO 1.2 Theoretical background 3 films with the idea of testing the soft nanopatterning technique previously developed in our group for nanowires’ fabrication [22]. The optimization of etching conditions done in this patterning technique previously yielded 40 nm wide nanowires with highly preserved pristine SC properties as in as-grown films, reflected in the critical current density approaching the theoretical depairing limit. However, the technique has never been used before for nanorings fabrication. By using it, we succeeded in patterning rings with arm’s width of 90 nm but at the cost of drop in compared to the as-grown YBCO films. 1.2 Theoretical background 1.2.1 Conventional vs. high critical temperature superconductivity Superconductivity, defined as the state of some materials occurring below a certain critical temperature, is described by two phenomena: resistance dropping to zero and magnetic field being expelled from the material. The last one, namely Meissner effect, is a characteristic of all superconducting materials. Whilst in Type I SC materials this is the only state allowed, in others, Type II materials, magnetic field can penetrate in form of vortices without destroying the superconducting state of the entire material. The BCS theory, explaining the microscopic mechanism behind this phenomenon, proposes a model of electron-phonon interaction which in turn results in two electrons of opposite spin and momentum overcoming the potential barrier of Coulomb repulsion and pairing up into a Cooper pair, the elemental carrier of superconductivity [8]. For materials that undergo SC transition at low temperatures (conventional or low- superconductors), this theory is in agreement with experiments. Every SC state is described by its order parameter, which contains information about the density of Cooper pairs and their unique phase. While LTSs are characterized by an isotropic s- wave order parameter, the Angle Resolved Photo Emission Spectroscopy (ARPES) reveals a different symmetry of the order parameter for HTSs. Namely, ARPES shows both gap like and Chapter 1 Introduction 4 gapless like excitations in HTSs by varying the direction in the k-space. The gapless like excitations are a clear signature of the OP with nodes. This is attributed to the anisotropic crystallographic structure. 1.2.2 YBCO – structure, phase diagram and superconducting properties YBCO represents the most studied material among HTSs. It belongs to the group of cuprates. This class of materials is characterized by the existence of CuO2 planes, which are believed to be responsible for superconducting transport in these materials [23] [24]. The structure of YBa2Cu3O7-δ, as shown in figure 1.1, is obtained by considering three perovskite type cells stacked on top of each other. A perovskite cell consists of two types of cations (A, B) and 3 oxygen anions. In YBCO, the A cation alternates between Y and Ba (Y cation in the middle and Ba cations in the bottom and the top cell), while the B cation is Cu for all three cells. YBCO can be considered as a “defected” perovskite. Vacancy of oxygen in the Y plane and on the top and bottom planes of the cell dissolves the three-dimensional oxygen lattice leading to two sublattices with reduced dimensionality, namely the Cu2O planes and the a-b chains. Yttrium and Barium atoms can be considered as fully ionic (Y 3+ and Ba 2+ ), acting as effective electron traps. Electrons found in their vicinity are localized, far from the Fermi level and, therefore, not mobile. Their role is to act as charge reservoirs for Cu2O planes and CuO chains. Copper atoms appear as double and triple ionized cations, Cu 2+ and Cu 3+ , which together with oxygen O 2- anions, represent the mobile charge sources. 1.2 Theoretical background 5 Figure 1.1: YBCO unit cell. The figure is after [25]. Structural and electronic properties of YBa2Cu3O7-δ are dependent on the oxygen content in the unit cell (figure 1.2). The parts of the unit cell susceptible to oxygen diffusion are the CuO chains. Pumping oxygen atoms in and out of these chains modifies the YBCO properties. When CuO chains are completely deprived of oxygen ( ), YBCO is an antiferromagnetic insulator with a tetragonal structure ( and lattice parameters equal – 0.386 nm). Oxygen doping makes YBCO conducting. This corresponds to decreasing from 1 to 0. For a certain value of , namely around 0.6, YBCO experiences a structural change from tetragonal to orthorhombic. This means that and are no longer the same with becoming slightly bigger than , due to the injection of oxygen atoms into the CuO chains. This point marks the beginning of the region referred to as the underdoped part of the superconducting dome. At this doping level conducting properties change as well – YBCO becomes a conductor, Chapter 1 Introduction 6 which below a certain temperature exhibits SC properties. Further increase in doping enhances SC properties of the material until an oxygen doping of 6.95 is reached [26]. This corresponds to and the highest possible (in phase diagram: top of the SC dome). YBCO containing this concentration of oxygen is referred to as optimally doped. At this doping level there are no oxygen vacancies - between every two Cu atoms in CuO chains there is one O atom. The normal state properties in this region (left part of the SC dome) are still not well understood. At these doping levels, above the critical temperature, in addition to gapless excitations (indication of the normal state), gap-like excitations (indication of the SC state) are found. This is one of the bottlenecks in creation of the HTS theory. Increasing the doping level beyond the optimal point (oxygen content greater than 6.95) brings further change in conducting properties of YBCO. Namely, the normal state resembles more the Fermi metal while the SC properties get depressed ( reduced). This part of the SC dome is labeled as the overdoped part. Figure 1.2: A simplified YBCO phase diagram. Compared to conventional superconductors, YBCO has a small coherence length ( ) and large London penetration depth ( ) as shown in table 1.1 (for comparison , 1.2 Theoretical background 7 ). This makes YBCO a Type II superconductor. Below there exist two distinct regions of superconductivity for these materials. Below the first critical field ( ), the superconductor is in the Meissner state. Between the first and the second critical field ( ), magnetic field enters the superconductor in a form of vortices. Vortices are normal regions whose size is determined by . Magnetic field penetrates these domains with quantized flux values, corresponding to flux quanta ( ). The length over which the field enters the SC material is determined by the circulating currents around the vortex core which disappear at distances larger than from the center. This state, characterized by coexistence of normal and superconducting regions, is called the mixed state. Increasing the field, the number of vortices increases until the second critical field is reached, when the distance between vortices becomes equal to the vortex core diameter and superconductivity gets completely destroyed. The lower critical field, , is rather low (around 0.01 T) and similar to the ones found in LTSs, while the upper one, , is extremely high (more than 100 T), which results in a high value for the critical current density (~ 10 8 A/cm 2 at 4 K). High critical temperature, critical current and upper critical field make this material extremely suitable for practical applications in many superconducting devices. Anisotropy in the YBCO structure translates into anisotropy of the characteristic SC length scales as well, namely and . Anisotropy in , i.e. in the size of a Cooper pair, reflects the fact that superconductivity is not equally strong in all directions, while anisotropy in , i.e. in the length over which the magnetic field penetrates the superconductor, induces anisotropy in magnetic properties of these materials. - (nm) (nm) 135 1000 1.6 0.24 Table 1.1: Coherence length ( ) and London penetration depth ( ) in plane ( - ) and along - axis for the optimally doped YBCO [27] [28]. As explained above, this material has a remarkable property of switching from insulating state to a superconducting one with a broad superconducting span, by changing the doping level. The maximum measured in YBCO is 92K (optimal doping) [29]. This high value cannot be Chapter 1 Introduction 8 derived from the BCS theory. Another curiosity arises from the small value of the coherence length in this material [27]. Namely, coherence length not being large enough to cause the overlap of the wavefunctions belonging to electrons from adjacent CuO2 planes, cannot be the cause for the phase coherence between the Cooper pairs in this material. There has to be another mechanism, different from the BCS one, responsible for this. Some suggest existence of an imaginary component of the order parameter in c-axis direction causing wavefunctions’ overlapping [30]. 1.2.3 Little Parks effect Measurements on resistance vs. magnetic field, , in the vicinity of (Little Parks) provide information on the value of the charge responsible for the electric transport. In particular, the period of oscillations unambiguously identifies the charge carriers, which is of outmost importance for better understanding of the mechanism behind superconductivity in high- materials. In addition to the periodicity observed in LTSs, submicron rings patterned on HTS films are expected to show different field dependent features, namely and periodicities [15]-[20]. For a multiply connected (MC) superconductor (superconductor enclosing a region of a normal material or simply a hole), London introduced the concept of a fluxoid: with as the penetration depth, the super-current density vector, the surface vector and being the ordinary magnetic flux enclosed by the loop: ( – the magnetic inductance vector). 1.2 Theoretical background 9 Combining (1) and (2) with GL expressions for penetration depth and current density of a thin film: gives: ( - the mass of a Cooper pair, - the charge of a Cooper pair, – the Cooper pairs’ density, - the Cooper pairs’ velocity and - the Cooper pairs’ momentum in a magnetic field). Applying Bohr-Sommerfeld motion quantization condition to relation (3): leads to the final fluxoid expression: ( - Planck’s constant, – integer)2. This expression reveals the discrete nature of the fluxoid penetrating the MC superconductor. It can only exist as an integer multiple of flux quanta: 2 The expression is not a consequence of the semi-classical Bohr-Sommerfeld formalism and London equations only. It follows in the same form from the GL theory alone. The condition of the complex superconducting OP being single valued puts a constraint on the phase change around the loop which has to be a multiple of : , which results in the same condition for the fluxoid quantization. Chapter 1 Introduction 10 If a magnetic field is applied to a thin-wall cylinder with radius , the magnetic flux inside the cylinder will be given as 3 : Putting (4) and (5) into (1), the superfluid velocity is obtained as follows: For a given field , the energy of super-currents in the cylinder will have a minimum for those values of that allow for the minimum in the superfluid velocity and that choice of will allow the system to remain superconducting at the highest possible temperature. In this way, will be a periodic function of (figure 1.3). The free energy density of a thin film is given by4: where is the free energy of the normal state, the slope of the curve in the vicinity of 5 and the curvature of the same curve at . Minimizing this expression for the free energy of a thin film for a given , the optimum value for the superfluid density at any given position inside a superconductor is derived: where is the SC order parameter deep inside a superconductor in the absence of the external field and transport current, and is the coherence length. At the normal-SC transition, one might argue that , from which a constraint on can be obtained: 3 No distinction should be made here between the applied filed and the field inside a cylinder, since we are investigating the shift in , where , so and the fields are the same. 4 Here, the field term is neglected, since its value is smaller than the kinetic energy of the current by a factor of the order of the ratio of the cross-sectional area of the conductor to and this ratio is large for thin conductors. 5 at . 1.2 Theoretical background 11 From (6) and (7): Equating this expression with the GL coherence length near for the clean limit (the mean free path larger than the coherence length 6 ): one finds the expression for variations in at the transition: where is the zero temperature coherence length. From this, the maximum depression in is expected when and the relative variation reaches . It should also be noted here that the radius of the cylinder should not be very large to allow for the oscillations to be detected. Given that the rings on optimally doped YBCO films show resistive transition at ~ 80 K, and taking , cylinders with radius not larger than ~ 160 nm are required to induce oscillations larger than 1 mK. 6 We did not perform measurements for determining the mean free path in our SC films. However, the typical values are in the range of hundreds of nm’s. Chapter 1 Introduction 12 Figure 1.3: Variation of (up) and (bottom) as a function of the magnetic field through a hollow cylinder in the LP experiment. The depression in is proportional to (scallop shaped curve at the bottom). This figure is after [12]. In order to experimentally verify this theory, one utilizes the finite width of the resistive transition. Upon applying magnetic field near transition point the resistance oscillations are measured. Their amplitude ( ) can be converted to via the following expression: This relation is not entirely quantitatively correct, since the slope of the transition, , has been observed to depend on the field , causing the inferred to depend on the resistance level choice within the transition. Still, this serves as a satisfactory method for extraction from LP experiments [12]. From figure 1.3, it is clear that the period of LP oscillations is determined by . Measurements performed so far, both on LTS and HTS structures, show this value to be the same as the one Little and Parks originally obtained: . This value for the flux quanta identifies Cooper pairs as the charge carriers. To argue in favor of different charge carriers responsible for transport in HTS structures, different values for flux quanta ought to be observed, since their charge enters in the denominator of the expression determining the flux quanta. 13 Chapter 2 Deposition and characterization of YBCO films 2.1 The substrate choice The second part of this thesis, being the fabrication of rings scaled down to tens of nm’s on YBCO films, underlines the necessity of growing homogenous films with surface roughness in the range of few nm’s. When depositing films, the substrate-film interface influences to a certain extent the morphology of the film grown. Several substrate-related factors need to be considered: lattice mismatch, thermal expansion coefficient mismatch (depositions done at high temperatures – typically several hundred °C), structural phase transitions of the substrate (twinning). The mismatch in the lattice parameter and possibly in the thermal expansion coefficient between the substrate and the material deposited represents the main source of strain and stress in films. Furthermore, if the in-plane lattice parameters ( and ) of the substrate are equal (forming a square-like pattern on the surface), twinning of YBCO films occurs when growing in direction. Namely, the small difference of 1% between the and parameters of the YBCO unit cell results in an unpredictable lateral direction of growth, i.e. while stacking laterally, YBCO unit cells could experience a rotation of 90° in the plane perpendicular to the -axis. This is reflected through the intrinsic twin domains 7 of the YBCO. However, what proved to be a bigger challenge in growing YBCO films with good surface properties is the twinning of the substrate. This type of twinning is a different phenomenon compared to the YBCO twinning discussed 7 Here, a domain is defined as a -axis grown stack of YBCO cells with a single lateral growth direction – or . Twin domains differ only in the lateral direction of stacking. Chapter 2 Deposition and characterization of YBCO films 14 above and represents a temperature induced structural transition of the substrate lattice. 8 Unlike the YBCO twinning domains, the substrate induced ones are easily visible as stripes on the YBCO films’ surface. Twin boundaries in the substrate surface, when translated into the YBCO film, cause suppression of the superconducting order parameter and the critical current density [31], as well as the vortex pinning [32] and the dc flow of Abrikosov vortices under the action of the Lorentz force (the vortices move preferentially along the grain boundaries, including the twin ones) [31] [33]. 9 All of the work presented in this chapter is dedicated to YBCO deposited on Lanthanum Aluminum Oxide – LaAlO3 (LAO) with (100) crystal orientation. LAO belongs to the group of substrates with an intrinsic problem of twinning [34] [35]. Decreasing the temperature, at 534 °C the LAO crystal lattice undergoes a structural change from a cubic type (with a lattice parameter at deposition temperatures around 800 °C) to the rhombohedral one (with a rhombohedral angle 90.096° and a lattice parameter ). 10 The other two substrates used in this work for YBCO deposition, LSAT 11 and MgO, do not exhibit twinning phenomena. However, due to the time limitations within which this project had to be performed, no significant results have been obtained on LSAT and MgO. 2.2 Doping dependent YBCO films Electronic properties of YBCO are determined by the oxygen content in the unit cell, as described in section 1.2.2. Finding the deposition conditions for the optimal growth of YBCO (highest ) while simultaneously optimizing the surface of the films, was the first step towards controllable underdoped films deposition. The next step was finding the deposition parameters that influence the doping level to the extent of enabling going from the top of the superconducting dome to the extremely UD regime. The deposition technique explored for 8 It should be noted here that the temperature induced structural transitions do not represent a characteristic of all crystals. 9 All these electronic and magnetic features are caused by the YBCO film twinning as well. 10 YBCO undergoes a structural transition at ~ 400 °C from a high temperature oxygen-deprived tetragonal phase (with a = 3.86 Å and c = 11.79 Å) to an orthorhombic one (with a = 3.82 Å, b = 3.89 Å and c = 11.68 Å) [41] [42]. 11 Lanthanum Strontium Aluminum Tantalum Oxide 2.2 Doping dependent YBCO films 15 growing SC films was the Pulsed Laser Deposition (PLD). The crystal structure of the films was subsequently characterized by the X-ray diffractometer and resistive transition detected using Physical Properties Measurement System (PPMS). 2.2.1 Pulsed Laser Deposition Physical principles behind the PLD are described as follows. A highly energetic laser beam in the UVA range hits the target (the desired material for deposition) in pulses with duration of the order of nanoseconds. The target, being locally heated in this way, gets ablated, given that the laser energy is sufficiently high. Each pulse can be divided into two parts. In the beginning of the pulse, a vapor is formed in front of the target. During the second part of the pulse, the pressure and the temperature increase due to energy absorption, which results in partial ionization followed by the vapor expansion and formation of the plume. The plume, consisted of atoms, molecules, ions, electrons and atomic clusters, condenses on the heated substrate placed against the target (figure 2.1). Figure 2.1: A sketch of the PLD system (taken from [36]) used for the YBCO deposition (left) and a picture of the plume inside the chamber during the deposition (right). Chapter 2 Deposition and characterization of YBCO films 16 Many deposition parameters influence the final characteristics of the film growth: the fluence of the laser beam (ratio between the energy of the beam and the surface of the focal point on the target), the pulse rate, the distance between the target and the substrate, the background gas pressure, the temperature of the substrate. Finding the right set of values for all these parameters in order to obtain a film with desired doping and surface properties is a challenging task. Another difficulty reflects in the fact that the optimal growth on different substrates requires different deposition conditions. The key property of the plume susceptible to all of these parameters is the kinetic energy of the atoms and ions reaching the substrate. The growth of homogeneous, relaxed, defect-free films is actually confined to a narrow energy range. If the kinetic energy is very high, re- sputtering from the film can occur, while, on the other hand, if it is too low, the atoms/ions do not have enough mobility to rearrange themselves on the surface. While the aforementioned parameters affect the kinetics of the particles between the target and the substrate, the substrate temperature affects their surface kinetics. Again, a range of temperatures is allowed to grow high quality films. If the temperature is too high, interdiffusion between the substrate and the film can occur; if the temperature is too low, the atoms/ions will not be mobile enough to find the best site to occupy. As will be shown later, the deposition temperature has a large influence on the smoothness of the films’ surface. For the purposes of this thesis, 50 nm YBCO films were deposited which was followed by an ex-situ 50 nm gold (Au) film evaporation soon afterwards to protect the YBCO films from oxygen diffusion. The highest obtained in YBCO films was reported on LAO substrates with 001 crystal orientation (~ 92 K). In our films, the highest onset temperature for the normal – superconducting transition found was 91.3 K with a transition width of 1.6 K (table 2.1 – sample nr. 1). This film was deposited under the pressure of 0.6 mbar at 865 °C. Slow cooling rate followed, with one hour of post-annealing at 550 °C. After the deposition, the pressure in the chamber was set to 650 torr and the sample was held at that pressure until the temperature fell below 50 °C. This sample will be referred to as the optimally doped one from now on. 2.2 Doping dependent YBCO films 17 2.2.2 Characterization of YBCO films 2.2.2.1 Electronic properties The oxygen content of the YBCO unit cell proved to be mostly dependent on the post-annealing procedure. Data on the deposition conditions used and the corresponding resistive transitions of the films are shown in Table 2.1. The measurements performed on some of these samples are presented in Figure 2.2. Sample number [°C] [mbar] [torr] (865 – 550) °C [°C/min] [min] (550 – 50) °C [°C/min] [K] 1 865 0.6 6.5·10 2 10 60 15 91.3 2 865 0.6 6.5·10 1 10 60 15 91.1 3 865 0.6 6.5·10 0 10 60 15 91.1 4 865 0.6 6.5·10 1 30 1 40 90.8 5 865 0.6 6.5·10 0 30 1 40 91.2 6 865 0.6 4.5·10 -1 30 1 40 90.4 7 865 0.6 4.5·10 -2 30 1 40 87.6 8 865 0.6 2·10 -2 30 1 40 83.7 9 865 0.6 1.5·10 -2 30 1 40 82.3 10 865 0.6 1.2·10 -2 30 1 40 72 11 865 0.6 1·10 -2 30 1 40 63.6 12 865 0.6 7.5·10 -3 30 1 40 62 13 865 0.6 4.5·10 -3 30 1 40 58.8 Table 2.1: Summary of the c-axis oriented YBCO 50 nm films deposited on LAO (001): deposition conditions - temperature ( ), pressure ( ); post-annealing parameters – pressure ( ), Cool Down Rates ( ) I and II, post-annealing time at 550 °C ( ); transition parameters – transition onset temperature ( ). Chapter 2 Deposition and characterization of YBCO films 18 Figure 2.2: Resistive transition measurements on nine 50 nm c-axis oriented YBCO films deposited on LAO (001) with different post-annealing pressures, ranging from 6.5·10 2 torr (optimally doped YBCO) to 4.4·10 -3 torr (YBCO film with the lowest doping). The resistances are normalized with respect to resistance values at 95 K (normal resistance). Decreasing the post-annealing pressure by factors of 10 and 100 (compared to the optimal film) resulted in almost the same onset temperature (samples nr. 2 and 3). No change was observed for these pressures by increasing the post-annealing cooling rate (samples nr. 4 and 5). By decreasing the post-annealing pressure by another factor of 10 (making it equal to the deposition pressure) and keeping the faster cooling rate, a very sharp transition (< 1 K) was observed with a drop in of almost 1 K (sample nr. 6). All the subsequent samples (as well as the three previous ones) were characterized by a post-annealing procedure with a fast cool down with only 1 min of post-annealing at 550 °C. Decreasing the post-annealing pressure by another factor of 10 resulted in the first significant drop in (~ 4 K) compared to the optimal film 50 55 60 65 70 75 80 85 90 95 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 Temperature [K] N o rm a liz e d r e s is ta n c e 6.510 2 torr 4.510 -1 torr 4.510 -2 torr 210 -2 torr 1.510 -2 torr 1.210 -2 torr 110 -2 torr 7.510 -3 torr 4.510 -3 torr 2.2 Doping dependent YBCO films 19 (sample nr. 7). The most pronounced changes of were observed to happen in a very narrow range of pressures: 4.5·10 -2 - 4.5·10 -3 torr (figure 2.3). Figure 2.3: Onset transition temperature of YBCO films deposited with different post-annealing pressures (presented in a log scale). 10 -5 10 0 10 5 55 60 65 70 75 80 85 90 95 Post-annealing pressure [torr] O n s e t tr a n s it io n t e m p e ra tu re [ K ] Chapter 2 Deposition and characterization of YBCO films 20 Figure 2.4: Graph illustrating the definition of the transition width ( ) given as the difference between the onset transition temperature ( ) and the critical temperature ( ). and are defined as temperatures at which the resistance drops to 10% and 90% of the normal state resistance ( ), respectively. [K] [K] 91 1.6 91 1.2 90 0.9 87 1.4 83 2.7 82 2.6 72 3.4 63 3.6 62 3.3 58 1.8 Table 2.2: Transition widths ( ) corresponding to the onset transition temperatures ( ) of YBCO films presented in Figure 2.2. Low values of (table 2.2) indicate sharp resistive transitions, characteristic of highly homogeneous films. A trend in increase is observed when going deeper into the UD regime. Small doping variations in the film could account for this, given that the slope of the SC dome increases when moving from the (flat) optimally doped part to the UD one (figure 1.2). 2.2 Doping dependent YBCO films 21 An attempt to observe SC transition below 4.5·10 -3 torr failed. Namely, we deposited two films under the same conditions as for the other UD films, but with post-annealing at 1.5·10 -3 torr and 2·10 -6 torr. The films showed metallic behavior down to 4 K. 2.2.2.2 Crystallographic properties When pumping out oxygen atoms from the CuO chains of the YBCO unit cell, the cell expands in the -axis direction. To study the structural deformation of the YBCO unit cell in our UD films, XRD scans were done on the optimally doped film and several UD ones (figures 2.5 and 2.6). Figure 2.5: scans performed on six YBCO films with different post-annealing pressures. Three peaks are observed in the (35-50)° range of the angle: the (005) YBCO and (006) YBCO reflections and the (002) LAO. Shift to the left is observed for every peak as the pressure decreases. Chapter 2 Deposition and characterization of YBCO films 22 Figure 2.6: (005) YBCO peak from scans performed on the optimally doped (blue) YBCO film and the most underdoped (brown) YBCO film. A shift to the left, corresponding to the increase of the YBCO unit cell height, is observed in the UD film compared to the optimal one. From Bragg’s law, it follows that the distance between the crystallographic planes is inversely proportional to the angle at which a peak of certain order is observed 12 . So, the scans in figures 2.5 and 2.6 show an expansion of the YBCO unit cell in a direction perpendicular to the CuO2 planes with the decrease in the post-annealing pressure. This serves as a definite proof that by changing only the post-annealing pressure we obtained YBCO films with different oxygen concentration. XRD data on underdoped YBCO films are summarized in table 2.3 and figure 2.7. 12 For further information on XRD system and measurements, the reader is referred to Appendix A (XRD). 37.8 37.9 38 38.1 38.2 38.3 38.4 38.5 38.6 38.7 10 -1 10 0 2Theta-Omega [°] N o rm a liz e d i n te n s it y 6.510 2 torr 4.510 -3 torr 2.2 Doping dependent YBCO films 23 Sample number Post-annealing pressure [torr] YBCO unit cell height [Å] 1 6.5·10 2 11.69 3 6.5 11.7 6 4.5·10 -1 11.72 7 4.5·10 -2 11.74 12 7.5·10 -3 11.764 13 4.5·10 -3 11.783 Table 2.3: YBCO unit cell height obtained from the scans of the (005) YBCO peak on films with different post-annealing pressures. Figure 2.7: YBCO unit cell height as a function of the post-annealing pressure (samples from the Table 3.2). The data is presented in a log scale. 10 -4 10 -2 10 0 10 2 10 4 11.68 11.69 11.7 11.71 11.72 11.73 11.74 11.75 11.76 11.77 11.78 Post-annealing pressure [torr] Y B C O u n it c e ll h e ig h t [Å ] Chapter 2 Deposition and characterization of YBCO films 24 2.2.2.3 Surface properties When depositing superconducting films, one needs to reach compromise conditions for obtaining films with the desired SC properties and good enough surface properties for device patterning. Our YBCO films deposited by PLD show that these two requirements are somewhat conflicting, i.e. improving the surface of the film leads to lower and wider transition, compared to the case when no surface optimization was done. Scanning Electron Microscope (SEM) pictures were taken on several films. SEM images on the optimally doped film and one of the underdoped ones are presented in figure 2.8. These scans show particle-like features on our surfaces, as well as oriented domains. The origin of the particle-like features is still under investigation. On the other hand, the oriented domains are a signature of an a-axis growth of YBCO. Their elongated appearance comes as a consequence of growth velocities having different values in different directions ( , , ). The size of the surface features varies from tens of nm’s (particles) to several μm’s (particles and a-axis domains). An increase in particles’ density was noticed with a decrease in the post-annealing pressure. As mentioned in section 2.2.2.1, a loss of superconducting behavior in UD films is observed below 4.5·10 -3 torr. We attribute this to very bad surface conditions in the UD regime which could easily result in formation of regions of non-SC material enclosing entire loops that could account for metallic behavior down to very low temperatures. 2.2 Doping dependent YBCO films 25 Figure 2.8: SEM pictures of the optimally doped (up) YBCO film (6.5·10 2 torr) and underdoped (down) YBCO film (4.5·10 -3 torr) before surface optimization. The scans on two comparable length scales are presented (left – larger, right – smaller). Regardless of the lack of knowledge on the origin of these surface shapes, some improvements have been made in depositing films with smoother surfaces. Different approaches have been used - changing the energy of the laser, its pulse rate, the substrate-target distance. However, the parameter that proved to influence the surface properties the most was the temperature during the deposition ( ). After several chamber passivations, by decreasing from 865 °C to 780 °C, we obtained better surface properties for YBCO grown on LAO (figure 2.9). From this figure, it is clear that more work on optimizing the deposition conditions for better surfaces is needed, especially for UD films. Chapter 2 Deposition and characterization of YBCO films 26 Figure 2.9: SEM pictures of the optimally doped (up) YBCO film (6.5·10 2 torr) and underdoped (down) YBCO film (1·10 -2 torr) after first attempt of surface optimization (several passivations and a deposition temperature decrease). The scans on two comparable length scales are presented (left – larger, right – smaller). 27 Chapter 3 Fabrication of optimally doped YBCO nanorings Nanofabrication process used to pattern YBCO films is depicted in figure 3.1. Figure 3.1: Nanofabrication scheme used for YBCO nanorings, displaying the most important steps: 1) YBCO deposition and gold evaporation; 2) carbon (C) evaporation and double-layer resist spin coating; 3) resist development after e-beam lithography; 4) chromium (Cr) evaporation; 5) Cr lift off; 6) oxygen (O) plasma etching of the uncovered C; 7) Ar + ion beam etching; 8) O plasma removal of the residual C. Chapter 3 Fabrication of optimally doped YBCO nanorings 28 The method we used for deposition of YBCO films resulted in obtaining films with reproducible SC properties. However, the surface properties were substantially worse, making patterning of nanodevices impossible. Regardless, we wanted to test the fabrication procedure optimized previously in our group for the fabrication of nanowires to realize nanorings. We resorted to using commercial (001) YBCO films produced by THEVA. This company produces only YBCO films close to the optimally doped regime. The THEVA YBCO films used had a 30 nm thickness, were c-axis oriented, grown on (100) MgO and covered with 30 nm of gold (Au). The films had a of 87 K and a sharp transition with a width of 1 K. Detailed description of all the steps with the relevant used parameters is given below: a) Additional 20 nm of Au was evaporated on top of the YBCO/Au bilayer after isopropyl alcohol (IPA) and nitrogen (N) cleaning. The layer of Au disables oxygen diffusion out of YBCO and protects the film from contamination and physical damage caused by the subsequent fabrication steps. b) As hard mask, we used an 80 nm amorphous C layer. The deposition chamber for the evaporation of C was pumped down to ~ 2·10 -7 mbar, followed by a C target pre-ablation (needed to clean the target) and titanium (Ti) ablation (needed to decrease the pressure after the C pre-ablation) which provided the recovery of the previous base pressure of ~ 2·10 -7 mbar at which the C deposition was finally done. The evaporation rate was rather low (~ 1 nm/s) to ensure uniformity of the C film. c) Low power oxygen plasma etching (50 W) was performed for 5 s to clean the surface from undesired particles coming from the C evaporation chamber. d) IPA cleaning in the spin coating machine was done prior single-resist spinning. The resist ZEP 520 A 1:1 was spun and baked at 95 °C for 7 min. The thickness of the resist is directly related to the spinning speed. We achieved a thickness of ~ 100 nm with the speed of 5500 rpm. 29 e) Nanostructures were defined by e-beam lithography (EBL) at 100 kV. The steps after e-beam exposure are crucial for getting reproducible structures at nanoscale. f) The exposed part of the resist was developed in hexylacetate for ~ 20 s followed by a short rinsing of 3 s in IPA to stop developing. This creates an undercut in the developed structure that facilitates the lift-off. g) Low-power oxygen plasma etching (50 W) was performed for 5 s to clean the surface from residual parts of the exposed resist. h) A thin layer (12 nm) of chromium (Cr) was evaporated with a low evaporation rate (1 Å/s). i) Lift-off of Cr on the top of the remaining resist was done in a 1165 removal at 50 °C for ~ 15 min followed by ~ 10 s in a low-power ultrasonic bath. Additional ~ 5 min of removal in the 1165 bath and 3 min of rinsing in IPA were done to ensure complete removal of the unexposed resist. j) Low-power oxygen plasma etching (50 W) was performed for 22 min to remove the C not covered by Cr. k) Argon (Ar) ion etching was used to remove the Au and YBCO layers’ parts not covered by Cr. The ion etching parameters need to be well controlled, since high power argon ions (Ar + ) can change severely the film stoichiometry. Small changes in etching parameters proved to strongly affect the transport properties of nanostructures, in particular the critical current ( ) and its dependence on . So, the acceleration voltage was chosen high enough to etch the film (below that value the film is not etched but made amorphous), while the etching time is calibrated so to minimize Ar + ions interaction with YBCO/Au rings. For our rings, we used ~ 60 min etching with an accelerating voltage of 300 V and a current density of 0.056 mA/cm 2 , at a chamber pressure of 1.6·10 -4 mbar. During the etching, the Cr over the structures is removed, as well as part of the C. Atomic Force Microscope (AFM) pictures of our rings showed an over-etch of ~ 10 nm in the substrate. l) Low power oxygen plasma etching (50 W) was performed for 18 min to remove the remaining C on top of the rings. Chapter 3 Fabrication of optimally doped YBCO nanorings 30 Having a protective Au layer during the fabrication and not removing it at the end of the process, has proven to help in preserving the pristine SC properties of YBCO in nanostructures comparable to the as-grown films [22]. 31 Chapter 4 Transport measurements Rings are useful tools when investigating quantum effects coming from the mesoscopic confinement of the superconducting state. In particular, Little Parks measurements on superconducting rings reveal the type of charge carrier in these materials. Previously, in high- materials, LP was measured on micron sized hole arrays [37] and single rings with inner diameters and arm widths of the order of hundreds of nanometers [21]. An array of nanorings can introduce artifacts in the measurement due to the higher order harmonics, which appear when flux quanta enter not just the measured ring, but also several other cells in the array. In a single loop, on the other hand, there is no convolution of the fundamental period of the loop with the periods coming from other cells and therefore, intrinsic effects related to the magnetoresistance (Little Parks) in a single loop can be more easily distinguished. Here, we report on LP measurements on single YBCO rings with dimensions that have not been reached before (inner diameter and arm width smaller than 100 nm). Rings with several different submicron sizes have been patterned on 30 nm thick optimally doped YBCO films. Five nanorings have been measured, selected from three different chips, with different inner diameters and arm widths. In this chapter, isothermal magnetoresistance (MR) measurements on two rings which differ to the largest extent geometrically (inner diameters of 70 nm and 260 nm and arm widths of 160 nm and 90 nm, respectively), will be presented. The resistance vs magnetic field measurements were performed at several temperatures of the resistive transition of these devices above , which is defined here as the temperature below which the measured resistance becomes smaller than the noise level of the measurement set-up. No resistive transition of the larger YBCO areas, such as wiring and pads, was observed, as expected, considering the resistance was measured in a four probe Chapter 4 Transport measurements 32 configuration 13 . Four electrodes, two voltage and two current ones, were attached closely to the rings (tens of nm’s distance), so as to detect the resistive transition of the rings only. The resistance has been measured as a function of the magnetic field at several temperatures between and the onset transition temperature. We selected a (-0.2 – 0.2) T field range (low field), in which several oscillations are observed. Obtained resistance oscillations in this field range were superimposed on a parabolic background coming from the screening currents in the arms of the rings [38]. In the wider ring (figure 4.2), more clear oscillations have been observed in a narrower field range: (-0.1 – 0.1) T, so the further analysis of the data for this ring followed on this range only (due to negligible background noticed in the data for the narrower ring, presented in figure 4.3, the data from the entire field scan range was used without parabolic subtraction for that ring). The background (in the case of the wider ring) was subtracted by a parabolic fit of the form: with . Using a three-parameter fit takes into account not only the curvature in the data (parameter ), but also a zero-field shift (parameter b) and average resistance (parameter c) which increases upon moving from a point towards , i.e. upon approaching the normal state. Obtained plain oscillations were a subject of a Fast Fourier Transform (FFT) analysis. FFT spectrum of R(B) oscillations reveals the period of MR oscillations: with being the radius of the SC loop enclosing the flux in the ring (cylinder). The type of the charge carrier responsible for coherent transport in the ring can be now readily inferred by comparing the value obtained for from (9) with the following expressions: In all our rings, measurements displayed periodicity of the magnetic flux enclosed by loops with diameters equal or close to the average ones obtained by AFM. Given that the rings were 13 For further information on the measurement system, the reader is referred to the Appendix B (PPMS). 33 patterned on the optimally doped films, no other types of periodicity ( or ) were expected to present themselves. A potential uncertainty in data analysis related to inadequate geometrical design of the rings needs to be noted here. FFT spectrum is given as a function of and the peak position corresponding to a certain type of a charge carrier is given as a reciprocal value of the expression defined by (9). Therefore, from (9) and (10) it is clear that the FFT peak position ( ) is proportional to the squared radius of the superconducting loop and to the charge value of the carrier in question ( , or ). Due to the finite width of the ring, in order to avoid an overlap of the regions in which the three different periodicities ( , and ) are expected to appear, the following conditions have to be fulfilled: where subscripts in and out refer to the inner ( ) and outer ( ) radius of the ring (figure 4.1). Both conditions, in combination with (9) and (10), give rise to the following requirement on and : Figure 4.1: A sketch of the nanoring with current leads. Chapter 4 Transport measurements 34 For a fixed arm width of the ring, , condition (11) puts a lower bound for the inner diameter 14 : (12) In the ring #1 (wider ring), whose dimensions after patterning (figure 4.2a) do not comply with the relation (12), an overlap of regions in which and periodicities could appear with the peak position takes place, so it is not possible to state unequivocally which type of charge carriers is responsible for the transport properties based on MR measurements on this ring only (figure 4.2e). In the ring #2 (narrower ring), where dimensions (figure 4.3a) are closer to fulfilling the condition (11), the overlap between the three periodicity regions does not occur in the position of the peak (figure 4.3d). Based on the facts that the two rings were patterned on the optimally grown YBCO and that they differ only in dimensions, one could argue that the superconductivity observed in both rings is established by Cooper pairs and no other type of carriers. Due to the nanofabrication limitations which do not allow for patterning of structures with feature dimensions as small as the coherence length in HTSs, detection of vs magnetic field oscillations is somewhat challenging in these materials, given the amplitude of these oscillations is proportional to . As stated in 1.2.3 section, measured resistance oscillations can be related to the oscillations via relation (8). Amplitude of oscillations ( ) depends on the temperature at which the MR was acquired. The largest values obtained in our rings, 80 mK, are 1-2 orders of magnitude larger than the values predicted by the theory for clean superconductors, , assuming a zero-temperature coherence length of 1.5 nm. This large discrepancy is consistent with previous measurements on HTS structures [37] and conventional systems [38] and has been attributed to the fact that in theory sharp resistive transitions are considered [38], whilst the R(T) characteristics of submicron rings on thin films typically have a broader transition. 14 It should be mentioned here that conditions (11) and (12), even though valid, are not important for our rings, considering that they have been patterned on optimally doped YBCO, in which one does not expect nor charge carriers. The fulfillment of the condition stated through (11) and (12) will be necessary for rings patterned on underdoped films. 35 Contrary to the results previously reported on HTS rings with sizes comparable to ours [21], our measurements show no additional periodic peaks in the FFT spectra of the R(B) data. Moreover, our peak is displayed with a width ~ 8 times narrower. Both of these improvements we achieved could be ascribed to the soft-patterning technique we used and the Au layer which was not removed from the YBCO structures even after the fabrication was completed. It is our belief that due to these reasons, we maintained the homogeneity of YBCO films after patterning with smaller number of regions with suppressed superconducting properties as compared to previous works [21]. As reported previously [21], to avoid a situation of rings becoming superconducting while current leads being normal, we made the current leads larger compared to the arm width of the rings, as can be seen in figures 4.2a and 4.3a. This allows for non-equilibrium effects induced by the normal leads and responsible for critical current enhancement near and order parameter suppression at lower temperatures [39], to be negligible compared to the shielding currents in the loop responsible for the LP effect. Detailed description on the measurement results for each ring is given under the corresponding figure (figures 4.2 and 4.3). Chapter 4 Transport measurements 36 Figure 4.2: Ring on the optimally doped 30 nm 001-oriented YBCO on 100-cut MgO (film #1). 37 (a) AFM picture (inner diameter 70 nm; arm width 160 nm; average roughness < 1 nm). (b) The corresponding resistive transition of the ring ( ). (c) Resistance measurements at six temperatures above Tc in the (-0.2 – 0.2) T magnetic field span. Parabolic fits in the (-0.1 – 0.1) T field range are depicted by black lines. (d) Resistance oscillations in the (-0.1 – 0.1) T field range obtained after subtracting the parabolic fit ( ) 15 . Note that at the lowest temperature, the oscillations are not clear due to the fact that at that temperature, the resistance of the ring, being almost at , is comparable or smaller than the noise level. Also, in the FFT spectrum of the MR oscillations, a low frequency component appears. It is very pronounced at the lowest temperature and even larger than the h/2e peak at the highest temperature. The presence of this component is not connected to any intrinsic properties of the ring. On the contrary, its origin lies in parabolic fitting curve subtraction. Another peculiarity has been observed in the collected MR data for this ring. Namely, the peak that occurs at the highest temperature, coming from the maximum in resistance at zero-field, is not well understood. This feature has been ascribed to the existence of grain boundaries in YBCO films [40]. (e) FFT spectrum of the plain oscillations. Red, orange and green lines on the FFT graph correspond to , and domains, respectively. A FFT peak at 22 (1/T) corresponds to the SC loop with 241 nm diameter, which is fairly close to the AFM extracted average loop diameter of 230 nm. 15 is obtained using approximation formula (8) and using expression . Chapter 4 Transport measurements 38 Figure 4.3: Ring on the optimally doped 30 nm 001-oriented YBCO on 110-cut MgO (film #2). 39 (a) AFM picture (inner diameter 260 nm; arm width 90 nm; average roughness ~ 1 nm, corresponding to one YBCO unit cell). (b) The corresponding resistive transition of the ring ( ). (c) Resistance oscillations in the (-0.2 – 0.2) T field range without subtracting the parabolic fit ( ). (d) FFT spectrum of the oscillations in the narrow field range: (-0.1 – 0.1) T. Red, orange and green lines on the FFT graph correspond to , and domains, respectively. A FFT peak at 46 (1/T) corresponds to the SC loop with 350 nm average diameter, which coincides with the AFM extracted average loop diameter. Chapter 4 Transport measurements 40 41 Chapter 5 Conclusions and future outlook In this thesis work we have developed a PLD procedure for deposition of thin -axis oriented YBCO films on LAO (001) substrates with different superconducting properties. The procedure allows for reproducible vs. post-annealing pressure characteristics in the underdoped part of the SC dome down to 58 K. Submicron size nanorings were patterned on the optimally doped films and Little Parks oscillations identifying Cooper pairs as charge carriers detected. Continuation of this work could follow two trajectories – one moving along the line of the UD part of the superconducting dome and the other one covering the remaining, overdoped, part. Our UD stopping point of 58 K should be breached, given that the most exotic phenomena are expected to be observed in the highly UD regime. It is our belief that the particle- like features on our surfaces are preventing us from detecting the SC state below this point on the dome. Growth conditions for obtaining defect-free surfaces (which are also necessary for nanoscale device patterning) need to be optimized. A few attempts proved the deposition temperature to be the key parameter in tuning the surface properties. This would allow for investigation of the LP effect in this regime and possible verification of predicted and flux periodicities. Some improvement in the surface appearance has already been made on optimal YBCO grown on LAO by decreasing the deposition temperature to 780 °C. Furthermore, the task of optimizing the growth of UD -axis YBCO films on LSAT and MgO in a reproducible manner could be undertaken, followed by the same fabrication and measurement procedure performed on films deposited on LAO. By doing this, one could attribute the possibly observed and oscillations to the low oxygen level in YBCO rather than to some substrate induced effect. Chapter 5 Conclusions and future outlook 42 To complete the story related to doping dependence of SC properties, an entire SC dome should be covered. By ex-situ ozone treatment of the optimally doped YBCO films one reaches the overdoped regime. The work on this has already been started in our group and the first results are encouraging. The films obtained on MgO (110) show a drop in compared to the optimal ones, while the XRD scan displays a peak shift to the right, corresponding to the shrinkage of the YBCO cell in -direction which is a signature of a higher oxygen concentration in YBCO. Ultimately, devices would be patterned on these films as well, and MR measurements performed, in order to learn more about superconducting mechanism in this doping regime. 43 Appendix A - XRD XRD has become one of the most common characterization techniques for investigating crystallographic structure of materials. Many applications, ranging from analyzing substrate materials, layered structures, thin films, interfaces, determination of composition and thickness measurements, have made it an irreplaceable tool in studies on structural properties of materials. XRD is based on Bragg’s diffraction (figure A.1). The incoming X-ray beam hits the electrons in the atoms of the crystal lattice. The electrons become the sources of secondary spherical waves. These waves get annihilated in most directions through destructive interference. However, if the scattering centers (scatterers) are located periodically in planes equidistantly separated by a distance , the waves originating from the scatterers will constructively interfere only if their path difference, , equals the multiple number of incoming beam wavelengths : (Bragg’s law). Only at the angles obeying the Bragg’s law, the incoming rays get deflected from the surface and form a reflection spot in the diffraction pattern. Figure A.1: Bragg’s diffraction. Appendix A - XRD 44 The three main parts of the X-ray diffractometer are the source of the X rays, the specimen on which the incoming X rays get scattered and the detector of the scattered X rays (figure A.2). There are several XRD measurements done for different purposes. For the film characterizations done in this thesis, two are relevant: scan (also denoted as ) and scan (also denoted as the rocking curve measurement). The scan provides out-of-plane information about the crystal lattice. Here, it was used to determine the lattice parameter of the YBCO unit cell in the growth direction of the film (perpendicular to the substrate). In this kind of the scan, the angle is kept constant by changing simultaneously the and angles. The scan provides information about the film quality. The full width half maximum (FWHM) of the diffraction peak is inversely proportional to the dislocation density in the film. Here, only the angle is kept constant while is changed constantly throughout the scan. Figure A.2: XRD measurement set-up with the important angles: – the angle between the incoming X-ray beam direction and the specimen surface; – the angle between the incoming X-ray beam direction and the scattered X-ray beam direction. 45 Appendix B - PPMS Electrical characterization of the films was done with PPMS. This system was designed to measure film sheet resistance at a range of temperatures and magnetic fields. The main part of the system is the PPMS probe, a tube containing the high-vacuum sample chamber and control systems of temperature and magnetic field. The sample is glued on a sample holder (puck) and connected with the circuit with gold wires. The puck is put into the bottom of the probe where it reaches an electrical connector. In this system, the problem of thermal gradients is avoided by pumping helium and nitrogen into an annular region surrounding the sample chamber, disabling direct contact of the sample with the gases. Cooling annulus is equipped with thermometers (figure B.1). Figure B.1: Scheme of the PPMS system. Appendix B - PPMS 46 For films deposited for the purpose of this thesis, PPMS has been used to obtain their resistive transition curves. Resistance measurements were done using a four point probe method (figure B.2). The sample is connected to the measurement circuit through two current probes (used to run the current through the sample) and two voltage probes (used to measure the voltage drop over the sample). However, each of these four probes has three intrinsic resistances of its own that need to be taken into account. First, the probe has its own resistance ( ). Furthermore, the physical contact of the probe with the sample gives rise to the probe contact resistance ( ). Finally, the current spreads into the film from the tip of the probe, creating the spread resistance ( ). The four probe measurement eliminates the problem of the current probes’ stray resistances and to a large extent of the voltage ones as well. The reason for the last one lies in the high impedance of the voltmeter that makes the voltage drops over the voltage probe stray resistances very small (figure B.3). Hence, the voltmeter reading is very close to the real voltage drop over the sample. Figure B.2: Sketch of the four probe measurement set-up on a sample mounted on a PPMS puck. Figure B.3: Equivalent circuit for four point probe measurement of the film resistance. Indexes 1 and 4 correspond to the current probes, and 2 and 3 to the voltage ones. 47 Acknowledgements My ‘thanks’ goes to: …my supervisor, Prof. Floriana Lombardi, for being convincing in persuading me to join her group and invoking interest in me for this field of science; for the highly valuable guidance throughout the work that followed; for somewhat ‘unconventional’, but rather appreciable direct approach in communication …my daily supervisor, Riccardo Arpaia, for all the early mornings, long days and late nights in the cleanroom and the lab; for the endless patience tested many times by numerous questions coming from my side during so many discussions; for being very successful in pedagogically approaching to me …Prof. Thilo Bauch, for introducing me to this group; for helping Floriana and Riccardo with reading and correcting this report …Sophie Charpentier, for all the help with the measurements …Reza Baghdadi, for my very first days in the cleanroom …Marco Arzeo, for the help with the simulation and the mask design parts …the entire group for a warm welcome; for all the kindness throughout this period; for making the time spent working on this thesis not only beneficial, but also enjoyable …MC2 for providing an amazing work environment …Prof. Frederik Denef, for the enthusiasm with which he accepted to be a co-promoter of this thesis and the support along the way …my EMM Nano coordinators for the enormous help in crucial moments …my family and everyone else whose acts caused me making a step towards the point of writing this last line 49 Bibliography [1] J. 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