JP7342310B2 - Power supply device, superconducting device, superconducting device, and method for manufacturing a superconducting device - Google Patents

Description

Application of Article 30, Paragraph 2 of the Patent Act Oral presentation at the 2018 Spring (96th) Cryogenic Engineering and Superconductivity Society Research Presentation, May 28, 2018 (Date) [Publications, etc.] 2018 Fall (97th) 2018 Autumn 2018 (97th) Low Temperature Engineering and Superconductivity Society Research Presentation Oral Presentation, November 21, 2018 (Date) Low Temperature Engineering and Superconductivity Society Research Presentation Meeting Summary, https: //csj. or. jp/conference/2018a/3C. pdf, November 14, 2018 (date of publication) [Publications, etc.] 31st International Superconductivity Symposium (ISS2018) Oral presentation, December 12, 2018 (date of publication) [Publications, etc.] 31st International Superconductivity Symposium (ISS2018) Superconductivity Symposium (ISS2018) Lecture summary, https://iss2018. jp/abstracts-pdf. html, December 4, 2018 (date of publication) [Publications, etc.] 2019 66th Japan Society of Applied Physics Spring Academic Conference Oral presentation, March 10, 2019 (date of publication) [Publications, etc.] 2019 Summary of the 66th Spring Academic Conference of the Japan Society of Applied Physics, https://confit. atlas. jp/guide/event/jsap2019s/subject/10p-S224-3/advanced, February 25, 2019 (posting date)

The present disclosure relates to a power supply device, a superconducting device using the power supply device, a superconducting device that can be used in the power supply device and the superconducting device, and a method for manufacturing a superconducting device.

Superconductors, which have zero resistance at temperatures lower than their critical temperature, are being used as energy-saving devices. For example, Patent Document 1 discloses a rectifying element using a superconducting Josephson element. In particular, high-temperature superconductors such as cuprates, which become superconducting at the temperature of relatively inexpensive liquid nitrogen rather than expensive liquid helium, are expected to find applications in a wide range of fields.

JP 2018-170329 Publication

All of the superconductors currently discovered have a critical temperature below room temperature, so in order to maintain the superconductor in a superconducting state, it is necessary to continue cooling the superconductor to a temperature below the critical temperature. . Therefore, in order to reduce the energy consumption of a superconductor using a superconductor, it is also important to reduce the energy required to cool the superconductor.

The present disclosure has been made in view of such problems, and its purpose is to provide a technique for reducing energy consumption of a device using a superconductor.

In order to solve the above problems, a power supply device according to an aspect of the present disclosure includes a power receiving unit that receives AC power supplied from a power feeding unit in a non-contact manner, and a converter that converts the AC power received by the power receiving unit into DC power. It is equipped with a section and a section. The converter includes a superconducting device whose critical current value varies depending on the direction in which current flows.

A superconducting device according to another aspect of the present disclosure includes the above-mentioned power supply device, an electric wire formed of a superconducting material and for flowing a direct current converted by a conversion unit of the power supply device, and a superconducting device of the power supply device. and a cooling unit that cools the included superconducting material and the superconducting material forming the wire to a temperature lower than their critical temperatures.

According to the present disclosure, energy consumption of a device using a superconductor can be reduced.

FIG. 3 is a diagram showing current-voltage characteristics of a superconducting device according to an embodiment. FIG. 2 is a diagram showing waveforms of input AC current I and response voltage V in a half-wave rectifier circuit using a superconducting device according to an embodiment. FIG. 2 is a diagram showing a schematic diagram of the crystal structure of REBCO. FIG. 2 is a diagram showing the relationship between the oxygen content y and the lattice constant of SmBa ₂ Cu ₃ O _y (SmBCO). FIG. 3 is a diagram showing the relationship between carrier concentration and T _c with respect to oxygen amount y in REBCO. It is a figure which shows the solid solution limit with respect to RE3 ⁺ ion radius of REBCO. FIG. 3 is a diagram showing changes in T _c and lattice constant due to Sm/Ba substitution in SmBCO. It is a figure showing the structure of REBCO wire. FIG. 2 is a schematic diagram of a growth mode of epitaxial growth. FIG. 2 is a schematic diagram of lattice mismatch. FIG. 2 is a schematic diagram of a type 2 superconductor in a mixed state. It is a figure which shows the schematic diagram of each PC. FIG. 2 is a schematic diagram of a multilayer laminated thin film of BMO nanorods. FIG. 3 is a diagram showing potential energy U(x) versus distance x from the superconductor surface. FIG. 3 is a schematic illustration of a superconducting strip with asymmetric edge roughness. FIG. 2 is a schematic diagram of an L-shaped superconducting strip. FIG. 2 is a schematic diagram of asymmetric superconducting surface thickness modulation. FIG. 2 is a schematic diagram of an asymmetric pinning site array. FIG. 3 is a schematic diagram of asymmetric modulation of pinning site density. FIG. 2 is a schematic diagram of an asymmetric pinning channel. 1 is a schematic diagram of a PLD device used in this example. FIGS. 22(a) to 22(c) are schematic diagrams of each method. FIG. 2 is a schematic diagram of the structure of an IBAD-MgO substrate. It is a schematic diagram of parallel plate type RIE. It is a schematic diagram of δR. It is a figure which shows the procedure of bridge processing. FIG. 3 is a diagram showing conditions of annealing time and temperature. FIG. 3 is a diagram showing how a sample is attached to a rotator. FIG. 2 is a schematic diagram of measurement of the dependence of J _c on the angle of magnetic field application. FIG. 3 is a diagram showing how a sample is attached in measurement in an in-plane magnetic field. FIG. 3 is an example of current-voltage characteristics obtained from measurements and a schematic diagram of the measurements. FIG. 3 is a diagram showing an example of the measured non-reciprocal magnetic field dependence of I _c . 2 is a diagram showing AFM images of the surfaces of the IBAD-MgO substrate and LAO substrate used in Example 1. FIG. FIG. 3 is a diagram showing δω and δφ of IBAD samples and LAO samples fabricated with various film thicknesses. FIG. 3 is a diagram showing surface AFM images of a portion of an IBAD sample with various film thicknesses. FIG. 3 is a diagram showing the surface roughness δR of a 10 μm square area in IBAD samples and LAO samples with various film thicknesses. FIG. 3 is a diagram showing T _c and J _c in a self-magnetic field of IBAD samples and LAO samples with different film thicknesses. Asym. for T _c of the same sample and J _c in self-magnetic field. It is a figure showing ^MAX . Asym. at 77.3K for IBAD and LAO samples. ^MAX and Asym. =Asym. It is a figure which shows the relationship of magnetic field ^BMAX in ^MAX . Asym. of the IBAD sample at 77.3K. FIG. 2 is a diagram showing the magnetic field dependence of Asym. of LAO sample at 77.3K. FIG. 2 is a diagram showing the magnetic field dependence of Asym. of IBAD and LAO samples with different δω. It is a figure showing ^MAX . Asym. of IBAD and LAO samples with different δφ. It is a figure showing ^MAX . Asym. of IBAD samples and LAO samples with different film thicknesses. It is a figure showing ^MAX . FIG. 6 is a diagram showing B ^MAX of IBAD samples and LAO samples with different film thicknesses. Asym. of IBAD and LAO samples with different δR. It is a figure showing ^MAX . FIG. 3 shows B ^MAX of IBAD and LAO samples with different δR. FIG. 3 is a schematic diagram of nanorods for quantized magnetic flux. FIG. 3 is a diagram showing δω and δφ of IBAD-BHO3 volume % samples and LAO-BHO 3 volume % samples prepared with various film thicknesses. FIG. 6 is a diagram showing δω and δφ in LAO samples with various BHO addition amounts. FIG. 3 is a diagram showing surface DFM images of various BHO-doped LAO samples with a film thickness of about 300-400 nm. FIG. 3 is a diagram showing the surface roughness δR of IBAD samples added with 3 volume % BHO and LAO samples with various amounts of BHO added, which were prepared with various film thicknesses. FIG. 3 is a diagram showing Tc and _Jc in a self-magnetic field of LAO samples and IBAD samples with different film thicknesses and various amounts of BHO added. Asym. of LAO and IBAD samples with various BHO loadings. It is a figure which shows the relationship between ^MAX , _Tc , _{and Jc} in a self-magnetic field. FIG. 3 is a diagram showing the magnetic field dependence of J _c at 77.3 K, B//c for LAO samples with film thicknesses of about 200-300 nm and various amounts of BHO added. FIG. 3 is a diagram showing the dependence of J _c on the magnetic field application angle at 77.3 K and 1-5 T for LAO samples with various BHO addition amounts. Asym. FIG. 2 is a diagram showing the magnetic field dependence of Asym. in LAO samples with various BHO loadings. FIG. 2 is a diagram showing the magnetic field dependence of Asym. in LAO samples with various BHO loadings. FIG. 2 is a diagram showing the magnetic field dependence of Asym. in LAO samples with various BHO loadings. FIG. 2 is a diagram showing the magnetic field dependence of Asym. in LAO samples with various BHO loadings. FIG. 2 is a diagram showing the magnetic field dependence of Asym. in LAO samples with various BHO loadings. FIG. 2 is a diagram showing the magnetic field dependence of Asym. in LAO and IBAD samples with various BHO loadings. FIG. 3 is a diagram showing the relationship between ^MAX and B ^MAX . FIG. 3 is a diagram showing the dependence of I _c on the magnetic field application angle in an IBAD sample added with 3 volume % of BHO. Asym. It is a figure showing ^MAX . Asym. It is a figure showing ^MAX . Asym. It is a figure showing ^MAX . FIG. 6 is a diagram showing B ^MAX of LAO and IBAD samples with different film thicknesses and various BHO loadings. Asym. It is a figure showing ^MAX . FIG. 6 shows the B ^MAX of LAO and IBAD samples with various BHO loadings at different δR. FIG. 2 is a schematic diagram of changes in potential energy due to surface roughness and lattice strain. Asym. in LAO samples with different BHO loadings. It is a figure showing _MAX . FIG. 3 is a diagram showing factors for reducing the surface barrier in a BHO-added SmBCO thin film. Asym. It is a figure showing ^MAX . Asym. in LAO samples with various BHO loadings under various measurement temperature conditions. It is a figure showing ^MAX . FIG. 3 is a diagram showing B ^MAX in LAO samples with various amounts of BHO added under various measurement temperature conditions. FIG. 3 is a schematic diagram of magnetic field concentration due to δR. FIG. 3 is a diagram showing a schematic diagram of changes in U ₃ and U(x) due to δR. FIG. 3 is a diagram showing the relationship between ΔU _H and σ using the equation of the magnetic field dependent term ΔU _H. FIG. 3 is a diagram showing a schematic diagram of changes in U ₁ , U ₂ and U(x) due to δR. FIG. 4 is a diagram showing the c-axis length after oxygen annealing after etching of a sample with Tc>90K after etching and a superconducting non-transition sample. It is a figure which shows the surface DFM image of additive-free SmBCO thin film (Pure) before and after etching under various intensity|strength and time conditions. FIG. 3 is a diagram showing surface DFM images of a BHO-added SmBCO thin film (3% and 5% by volume of BHO) before and after etching under various intensity and time conditions. FIG. 6 is a diagram showing changes in δR (ΔRMS) before and after etching in samples etched at various intensities P and times t=30 minutes. FIG. 6 is a diagram showing ΔRMS for samples etched at various times t and intensity P=150W. FIG. 7 is a diagram showing Tc of pure samples and BHO-added samples etched with various intensities P. FIG. 7 is a diagram showing Jc (Jc/Jcas depo.) normalized by _Jc of unetched samples (as deposited) of Pure samples and BHO-added samples etched at various intensities P at 77.3K. . FIG. 3 is a diagram showing T _c of pure samples and BHO-added samples etched at various times t. Asym. It is a figure showing ^MAX . Asym. of the same sample. FIG. 3 is a diagram showing a diagram in which ^MAX and δR are plotted on the horizontal axis. Asym. It is a figure showing ^MAX . FIG. 3 is a diagram showing a schematic diagram of introducing a seed layer. It is a figure which shows the surface DFM image of the PrBCO Seed layer produced on the LAO substrate. FIG. 3 is a diagram showing δω and δφ of a PrBCO Seed layer formed at each film-forming substrate temperature. FIG. 3 is a diagram showing the T _c of SmBCO thin films with PrBCO seed layer introduced (IBAD-PrBCO-Pure samples) fabricated on IBAD-MgO substrates with various film thicknesses. FIG. 3 is a diagram showing J _c of SmBCO thin films (IBAD-PrBCO-Pure samples) with a PrBCO seed layer introduced on IBAD-MgO substrates with various film thicknesses. Asym. of IBAD-PrBCO-Pure samples with different film thicknesses. It is a figure showing ^MAX . FIG. 4 is a diagram showing B ^MAX of IBAD-PrBCO-Pure samples with different film thicknesses. Asym. of IBAD-PrBCO-Pure samples with different δR. It is a figure showing ^MAX . FIG. 3 shows B ^MAX of PrBCO Seed samples with different δR. Asym. in Pure sample. FIG. 3 is a diagram showing the relationship between ^MAX and the degree of lattice mismatch. Asym. at 77.3K. FIG. 3 is a diagram showing the relationship between ^MAX and B ^MAX . FIG. 2 is a diagram showing a laminated structure thin film into which BMO nanorods are introduced. 1 is a diagram schematically showing the configuration of a superconducting device according to an embodiment. 1 is a diagram schematically showing a method for manufacturing a superconducting device according to an embodiment. FIG. 2 is a diagram showing a schematic diagram of a parallel plate type RIE used in this example. It is a figure showing the change of the AFM image of the sample surface by RIE. FIG. 3 is a diagram showing a change in root mean square roughness δR (ΔRMS) of the surface before and after etching. FIG. 3 is a diagram showing changes in current-voltage characteristics of a thin film before and after etching. FIG. 3 is a diagram showing the magnetic field dependence of the asymmetry of the critical current value. FIG. 3 is a diagram showing the etching time dependence of the maximum value of the asymmetry of the critical current value. FIG. 1 is a diagram showing the configuration of a superconducting magnet system. It is a figure showing an example of composition of a conversion part. FIG. 3 is a diagram showing current resistance characteristics of a superconducting rectifier.

In an embodiment of the present disclosure, a power supply technique to a device using a superconductor will be described. In devices using superconductors, it is necessary to maintain the superconductor at a temperature below its critical temperature, which requires energy and cost for cooling. In applications such as conventional superconducting magnet systems, direct current is supplied from a DC power source to a superconducting electromagnet via a current lead, so heat intrusion via the current lead is unavoidable. Therefore, continuous cooling is required and a lot of energy is consumed. Moreover, when a large current is supplied to obtain a strong magnetic field, more heat enters the inside, which further increases the energy and cost for cooling.

Therefore, in the present disclosure, a technique is proposed for supplying power to a superconductor in a non-contact manner without using a current lead. In non-contact power transfer methods that use electromagnetic induction, etc., AC power is transferred, but since DC current needs to flow through devices such as superconducting electromagnets, the AC power transferred without contact is converted to DC power. There is a need to. Semiconductor diodes, which are conventional rectifying elements, have problems in that their carrier density decreases at low temperatures, resulting in a decrease in capacity, and that the rise voltage increases at low temperatures, resulting in increased loss. Therefore, in the present disclosure, AC power is converted to DC power using a rectifying element using a superconducting material that can perform rectification with low power consumption in a low-temperature environment.

First, in a first embodiment, a superconducting device having characteristics that can be used as a rectifying element and the content of research by the present inventors regarding the superconducting device will be described. Next, in a second embodiment, a power supply device using the superconducting device of the first embodiment as a rectifying element and a superconducting device using the power supply device will be described.

(First embodiment)
FIG. 1 shows current-voltage characteristics of a superconducting device according to an embodiment. The superconducting device according to the embodiment has asymmetric current-voltage characteristics in which the critical current value differs depending on the current direction under predetermined conditions. For example, when a magnetic field is applied in the direction perpendicular to the surface of the substrate, the superconducting device manufactured in the example described later shows that when a magnetic field is applied in the direction perpendicular to the surface of the substrate, current flows in the positive direction as well as in the negative direction. When the current is passed in the positive direction, it transitions to normal conduction at the same critical current value, but when a magnetic field is applied in a direction parallel to the surface of the substrate, the critical current value I when the current is passed in the positive direction, as shown in Figure 1. _c ^up is larger than the critical current value I _c ^down when the current flows in the negative direction, and asymmetry (I _c asymmetry) occurs in the critical current value. The superconducting device according to the embodiment can be used as a current-induced rectifier or the like by utilizing the dependence of the critical current value on the current direction.

FIG. 2 shows waveforms of input AC current I and response voltage V in a half-wave rectifier circuit using the superconducting device according to the embodiment. While the current value of the input AC current is smaller than _Ic , no voltage is generated, but when the value of the input AC current exceeds _Ic , a voltage is generated, so the response voltage V is half-wave rectified as shown in the lower part. Ru. The greater the asymmetry between I _c ^up and I _c ^down , the greater the rectification ratio, so it is desired to develop a superconducting device with a greater asymmetry between I _c ^up and I _c ^down .

Such asymmetry in the critical current value is thought to be due to the fact that the ease with which magnetic flux penetrates differs between the surface side of the thin film of superconducting material and the interface side with the substrate. In other words, the asymmetry of the critical current value is caused by the asymmetry of the shape, structure, crystallinity, etc. of the thin film of superconducting material, the shape, number, density, etc. of pinning centers and microfabrication formed inside or on the surface of the thin film, etc. This is thought to be caused by spatial asymmetry of potential energy due to asymmetry of distribution.

The content of the research conducted by the present inventors regarding the above-mentioned superconducting device will be described in detail below.

[Example]
The REBa ₂ Cu ₃ O _y (REBCO: RE is a rare earth element containing Y) high-temperature superconductor used in the examples can be used at an inexpensive liquid nitrogen temperature, has high superconducting properties, and is expected to be put into practical use. This is the material that is used.

[Crystal structure of REBCO]
REBCO has a perovskite structure. The perovskite structure is expressed by the composition formula RMO ₃ and has a cubic unit cell, with a metal element M at the body center, a metal element R at each vertex, and oxygen O at each face center. Due to the interaction with R, the regular octahedron formed by O with M at the center is easily distorted, and many substances undergo a phase transition to orthorhombic or tetragonal crystals.

FIG. 3 shows a schematic diagram of the crystal structure of REBCO. REBa ₂ Cu ₃ O ₇ has an orthorhombic structure, and REBa ₂ Cu ₃ O ₆ has a tetragonal structure. REBCO has a structure in which three layers of perovskite structures are stacked, and the perovskite structure containing RE is in an oxygen-deficient state. The superconducting current flows through the CuO ₂ surface, which is the bottom surface of the CuO ₅ square pyramid structure sandwiching the RE. This CuO ₂ plane is called a superconducting layer. On the other hand, the CuO chains and the BaO planes located above and below them are called insulating layers or block layers. Due to its crystal structure in which superconducting layers and insulating layers are stacked, REBCO has strong electrical anisotropy.

The crystal structure of REBCO changes depending on the amount of oxygen constituting the CuO chain. FIG. 4 shows the relationship between the oxygen content y and the lattice constant of SmBa ₂ Cu ₃ O _y (SmBCO). As y increases, the a-axis length becomes shorter and the b-axis length becomes longer, and they become equal at about y=6.36. At this time, the crystal structure changes from tetragonal to orthorhombic. Furthermore, as y increases, the c-axis length becomes shorter. This is because the upper and lower BaO surfaces are attracted by the doping of oxygen into the CuO chains. Further, a phase transition of the REBCO crystal structure occurs with respect to temperature. In the film formation temperature range of about 800° C., the amount of oxygen vacancies is large and the film becomes tetragonal, but at about 650° C. it transforms into orthorhombic crystal. Furthermore, the lattice constant of REBCO varies greatly depending on the RE element.

[Superconducting properties of REBCO]
The superconducting properties of REBCO are strongly influenced by changes in the crystal structure. FIG. 5 shows the relationship between the carrier concentration and T _c with respect to the oxygen amount y in REBCO. The carriers of REBCO are holes, and the carrier concentration can be controlled by y. T _c depends on the carrier concentration and has a maximum value. A state in which T _c takes a maximum value is called optimal doping, a state in which the doping is less than the optimal doping is called underdoping, and a state in which it is more than the optimal doping is called overdoping.

In REBCO, when the ionic radii of RE ³⁺ and Ba ²⁺ are close, the RE ³⁺ ion may substitute into the Ba ²⁺ site to form a solid solution of RE _1+x Ba _2-x Cu ₃ O _y . FIG. 6 shows the solid solubility limit versus RE ³⁺ ion radius of REBCO. The ionic radius of Ba ²⁺ is 0.143 nm, and the closer the RE ³⁺ ion is to the ionic radius of Ba ²⁺ , the larger the solid solution limit is and the more substitution occurs. This RE/Ba substitution changes the lattice constant and _Tc . FIG. 7 shows changes in T _c and lattice constant due to Sm/Ba substitution in SmBCO. As the amount of substitution increases, the a-axis length becomes shorter, the b-axis length and the c-axis length become longer, and the crystal changes from orthorhombic to tetragonal. Furthermore, as the amount of substitution increases, the carrier concentration on the CuO ₂ plane decreases, so T _c decreases.

[REBCO wire application]
Nb-Ti and Nb ₃ Sn are used in superconducting wires that are currently in practical use. Since these metal superconductors use expensive liquid He for cooling, they have a problem of high operating costs. On the other hand, REBCO high-temperature superconductors can use inexpensive liquid N ₂ for cooling, so it is expected that REBCO wires with low cooling costs will be put to practical use.

[Reducing the thickness of REBCO]
Since REBCO is a ceramic material, it is essential to combine it with a metal tape in order to give it mechanical strength and flexibility. Further, if there is a crystal grain boundary in the a-b plane in which crystals are bonded in a shifted manner and has electrical anisotropy due to the anisotropy of the crystal structure, the critical current density J _c decreases. Therefore, in order to produce a wire that can flow a large amount of current, it is necessary to achieve biaxial crystal orientation in the c-axis direction and the a- and b-axis directions. As a method for realizing the combination of REBCO with a metal tape and biaxial orientation, thinning using epitaxial growth is used.

The manufacturing process for superconducting thin films can be broadly classified into vapor phase epitaxy (VPE) and chemical solution deposition (CSD).

The VPE method is roughly divided into physical vapor deposition (PVD) and chemical vapor deposition (CVD). The PVD method is a method in which physical energy is injected into a single or multi-element solid material target to evaporate it and recrystallize it as a thin film on a substrate. PVD methods include sputtering that uses plasma to evaporate the target, pulsed laser deposition (PLD) that uses laser light, and molecular beam epitaxy (MBE) that uses electron beams and resistance heating. Epitaxy) etc. On the other hand, in the CVD method, a raw material gas containing the constituent substances of the target thin film is flowed into the space where the substrate is installed, and a thin film is created through chemical reactions in the gas phase and on the substrate surface through the excitation and decomposition of the molecules of the raw material gas. It's a method. In particular, a method using an organic metal as a material is called metal organic CVD (MOCVD). Although the VPE method allows the production of highly crystalline thin films with few pores and defects, it requires a vacuum device and is expensive. Furthermore, production of superconducting thin films using reactive co-evaporation by deposition and reaction (RCE-DR) has also been reported in recent years.

The CSD method is a method in which a starting material is diluted with a solvent, and a solution is applied onto a substrate by dipping the substrate into the solution and pulling it up, or by directly dropping the solution onto the substrate and performing spin coating. In contrast to the PVD method, the CSD method does not require a vacuum device and is therefore less costly and can produce a uniform thin film, but many pores and defects are formed in the thin film. Metal Organic Decomposition (MOD), which uses organometallic compounds as raw materials and is classified as a CSD method, is a method in which a raw material solution is applied to a substrate and heat treated, resulting in low equipment costs. In addition, it has a high yield of raw materials and is expected to be a low-cost wire manufacturing process.

In the RCE-DR method, each raw material is deposited using an electron beam on a substrate at a low substrate temperature under a low oxygen partial pressure to create an amorphous precursor, and then annealed in a high temperature furnace with a high oxygen partial pressure to form a thin film. This is a method for producing. High performance REBCO thin films can be produced relatively quickly.

[Structure of REBCO wire]
Currently, the metal tapes used for producing REBCO wire are substrates produced using two methods: IBAD (Ion-Beam-Assisted-Deposition) method and RABiTS (Rolling Assisted Biaxially Textured Substrate) method. It has become mainstream.

(a) IBAD method The IBAD method is a method of obtaining an oriented intermediate layer by irradiating an ion beam from a certain angle when producing an intermediate layer on a non-oriented metal tape. Due to the difference in etching rate for each crystal plane of the intermediate layer material, a specific crystal axis is fixed and oriented in the ion irradiation direction. By forming a film of REBCO on the intermediate layer produced by this method, a biaxially oriented REBCO superconducting layer can be produced. Yttria stabilized zirconia (YSZ), MgO, Gd ₂ Zr ₂ O ₇ (GZO), CeO ₂ or the like is used for the intermediate layer, and a strong alloy substrate can be used for the metal substrate. MgO, which is currently widely used as an intermediate layer material, can obtain sufficient orientation with a thin film thickness.

(b) RABiTS method The RABiTS method is a method in which a metal substrate is recrystallized by rolling or heat treatment to achieve biaxial orientation. Compared to the IBAD method, which requires a vacuum device or an ion beam device, it is easier to lengthen the length and is less expensive, but the orientation is inferior. The metal used is mainly Ni, which has a high degree of orientation, and in recent years, high-strength alloys made by adding Cr, W, etc. to Ni have been used.

FIG. 8 shows the structure of the REBCO wire. REBCO wire has a structure in which an intermediate layer, a superconducting layer, and a stabilizing layer are laminated on a metal tape, and such a wire is called a coated conductor.

(1) Intermediate layer If a superconducting layer is directly formed on a metal tape, there is a risk that the superconducting properties will be degraded due to diffusion of metal elements from the metal tape. Therefore, an intermediate layer is used to prevent the diffusion of metal elements from the metal tape into the superconducting layer. Furthermore, using a material with a lattice constant close to that of the superconductor as an intermediate layer serves to alleviate lattice mismatch and improve the orientation of the superconductor layer. Examples of the material for the intermediate layer include CeO ₂ , MgO, YSZ, and the like, and generally, a plurality of types of intermediate layers are used.

(2) Superconducting layer The superconducting layer is a layer in which REBCO is biaxially oriented on an intermediate layer. Elements such as Y, Sm, and Gd are used for RE.

(3) Stabilization layer The stabilization layer has the role of protecting the superconducting layer from the external environment. In addition, the role of thermal stabilization is to diffuse the heat generated from the broken part of the superconducting state to the outside and temporarily bypass the current, and the role of chemical stabilization is to prevent the REBCO layer from being exposed to moisture. There is. Ag or Cu, which has good thermal conductivity and electrical conductivity, is used as the material for the stabilizing layer.

[REBCO vapor phase growth]
Epitaxial growth in the vapor phase growth method, which is the mainstream manufacturing method for REBCO thin films, will be described. Epitaxial growth refers to the crystal growth of a substance with a specific orientation relationship with the parent phase that serves as a substrate. When the substrate and thin film are made of the same material, it is called homoepitaxial growth, and when the substrate and thin film are made of different materials, it is called heteroepitaxial growth.

[Growth style]
There are mainly four growth modes in epitaxial growth. FIG. 9 shows a schematic diagram of the growth mode of epitaxial growth.

(a) Frank-van der Merwe (FM) type The FM type is a growth mode in which thin films are regularly stacked one atomic layer at a time. This can be seen in homoepitaxial growth, where the interaction between the substrate and thin film is strong, and in heteroepitaxial growth, where the degree of lattice mismatch between the substrate and thin film is extremely small.

(b) Strenski-Krastanov (SK) type The SK type is a growth mode in which the layer grows one atomic layer at a time in the early stage of growth, and when the film thickness exceeds a certain level, three-dimensional islands grow thereon. This can be seen in heteroepitaxial growth when the degree of lattice mismatch between the substrate and the thin film is small.

(c) Volmer-Weber (VW) type The VW type is a growth mode in which three-dimensional islands grow from the initial stage of growth. A large degree of lattice mismatch between the substrate and the thin film is observed in heteroepitaxial growth.

(d) Two-dimensional island-like growth Two-dimensional island-like growth is a growth mode located between one-atomic phase growth and three-dimensional island growth. After one atomic layer of two-dimensional nuclei is generated on the substrate, new nucleation occurs on top of the two-dimensional nuclei before they cover the substrate surface. This growth mode is often seen in the growth of REBCO thin films.

When producing a thin film, which of these growth modes (a) to (d) is adopted is determined by many parameters such as lattice mismatch between the substrate and the thin film material, interfacial energy, and degree of supersaturation. In order to achieve FM type or two-dimensional island growth, which is the ideal growth mode for REBCO thin films, it is necessary to control these parameters.

[Lattice mismatch and critical film thickness]
The ratio of the difference in lattice constant between the substrate and the thin film material to the lattice constant of the substrate is called the degree of lattice mismatch. FIG. 10 shows a schematic diagram of lattice mismatch. In a thin film region, if there is lattice mismatch, the thin film lattice is distorted, resulting in coherent growth that maintains continuity at the interface. When the film thickness exceeds a certain value, dislocations are formed, the strain energy due to coherent growth is relaxed, and the film approaches the original lattice constant value of the thin film. The film thickness at this time is called the critical film thickness. From the mechanical equilibrium theory by Mathews and Blakeslee, the critical film thickness h _c is calculated by the following formula.
Here, b is Burgers vector, ν is Poisson's ratio, and f is the degree of lattice mismatch. The h _c of SmBCO calculated from the above equation is about 4 nm. It has been experimentally confirmed that h _c in YBCO is from several nm to about 20 nm.

[REBCO magnetic flux pinning]
In devices to which REBCO wire is applied, such as superconducting magnets, REBCO wire is used in a magnetic field. Since REBCO's superconducting properties deteriorate in a magnetic field, it is necessary to improve its superconducting properties in a magnetic field. Magnetic flux pinning is a method for improving superconducting properties in a magnetic field.

[Magnetic flux pinning mechanism]
REBCO is a type 2 superconductor and assumes a mixed state in which quantized magnetic flux enters and a part of the superconductor becomes normal conductive. FIG. 11 shows a schematic diagram of a type 2 superconductor in a mixed state. When a current flows through a type 2 superconductor in a mixed state, a Lorentz force F of F=J×B acts on the quantized magnetic flux using the current density J and the magnetic flux density B. When the quantized magnetic flux moves at a speed ν due to the Lorentz force, an electric field of E=B×ν is generated in the current direction according to the law of electromagnetic induction. Resistance is generated from the electromotive force generated by this. The resistance resulting from such magnetic flux movement is called flux flow resistance. Therefore, in order to prevent the occurrence of resistance in the mixed state, it is necessary to prevent the movement of the quantized magnetic flux. Stopping the movement of quantized magnetic flux is called magnetic flux pinning, and the pinning area is called the pinning center (PC).

In the mixed state, the quantized magnetic flux destroys some of the superconducting parts, making them normal, and penetrating into the superconductor. However, when a PC exists in a superconductor, it is more energetically advantageous for the quantized magnetic flux to penetrate into the pre-existing PC of the normal conductive part than to destroy the superconducting part and invade. Furthermore, when a current is passed through a superconductor, the quantized magnetic flux tries to move under the Lorentz force, but rather than newly destroying the superconducting part, it tries to stay in the PC. Therefore, the quantized magnetic flux is pinned to the PC.

The pinning force per _PC is called elemental pinning force f _p , and the pinning force per unit volume is called macroscopic pinning force F _p , where F _p =J _c ×B. Assuming that the number of PCs per unit volume is n, the relationship between F _p and f _p is expressed as F _p =f _p ×n. A PC introduced artificially is called an artificial pinning center (APC), and APC is introduced as a method for improving J _c in a magnetic field.

[Pinning center size effect]
In the previous section, the size of the defect was assumed to be about the same size as the quantized magnetic flux, but larger than the quantized magnetic flux. On the other hand, magnetic flux pinning is greatly influenced by the size of the PC. Below, we will discuss magnetic flux pinning in small defects and large defects with respect to quantized magnetic flux.

First, consider the case where the size of the defect is smaller than the magnetic flux and is spherical. When the radius r of the defect is smaller than the radius ξ of the magnetic flux, the volume in which the magnetic flux and the defect interact is (4/3)πr ³ , so the pinning energy U _p and the elemental pinning force f _p are expressed by the following equations. be done.
Therefore, the pinning force for small defects decreases proportionally to ^r2 . Therefore, very small defects will not work as a PC. Particularly in a high temperature region, the thermal energy k _B T increases and becomes equal to the pinning energy, so the pinning force becomes even smaller.

On the other hand, if the size of the defect is much larger than the magnetic flux, a large number of magnetic fluxes will interact with one defect. At this time, the elemental pinning force is similarly given by the above equation, but since the magnetic flux senses an energy change only at the normal-superconducting interface, the density of PC decreases and the pinning efficiency deteriorates. From the above, a columnar defect with a radius of about ξ and elongated in the direction of the magnetic flux lines is most effective as a PC. However, it can be said that columnar defects are effective only when the magnetic flux is in the longitudinal direction, and are not so effective in other directions. Conversely, columnar defects perpendicular to the direction of the magnetic flux lines have the function of promoting kink movement of the magnetic flux lines.

[Type of pinning center]
Pinning centers (PCs) are broadly classified into random pins and correlated pins. Furthermore, PCs are classified into 0-dimensional PCs, 1-dimensional PCs, 2-dimensional PCs, and 3-dimensional PCs based on their shapes. Random pins are randomly distributed inside the sample, and 0-dimensional PC and 3-dimensional PC correspond to random pins. Correlation pins are PCs that have a shape or distribution directionality in a certain direction, and correspond to one-dimensional PCs and two-dimensional PCs. However, it is possible to provide a correlation also to the three-dimensional PC by in-plane arrangement. FIG. 12 shows a schematic diagram of each PC. The characteristics of each PC will be described below.

(a) 0-dimensional PC
Zero-dimensional PC is PC due to point defects such as atomic deletions and substitutions. Since the size is on the atomic scale and smaller than the size of the normal conducting nucleus of the quantized magnetic flux, it is considered that the zero-dimensional PC is not an effective PC for pinning.

(b) One-dimensional PC
One-dimensional PCs include linear defects such as dislocations, columnar defects caused by heavy ion irradiation, and nanorods formed by introducing BaMO ₃ (BMO: M=Zr, Sn, Hf) into the REBCO thin film. . One-dimensional PC has anisotropy and has a strong pinning force against a magnetic field applied in the linear direction. Dislocations such as screw dislocations and edge dislocations are formed depending on the frequency of nucleation during crystal growth, so it is difficult to control their number density and shape. On the other hand, the number density and diameter of BMO nanorods can be controlled by controlling the film forming conditions such as the amount of BMO added and the film forming temperature. The one-dimensional PC of the c-axis correlation promotes magnetic flux movement under a magnetic field in the a-b plane direction, and is therefore caused by a decrease in J _c .

(c) 2D PC
A two-dimensional PC is a planar PC due to grain boundaries, twin boundaries, stacking faults, etc. It is an anisotropic PC and is effective against a magnetic field applied parallel to the surface direction. Compared to one-dimensional PC, more quantized magnetic flux can be pinned.

(d) 3D PC
The three-dimensional PC is an isotropically shaped PC such as a normal precipitate such as RE ₂ O ₃ or a solid solution due to RE/Ba substitution. In the BMO-added REBCO thin film produced by the MOD method, particle-like three-dimensional PCs of BMO are formed. Three-dimensional PC has no anisotropy and is effective for applied magnetic fields at any angle. On the other hand, the pinning force is weak compared to a one-dimensional PC or a two-dimensional PC. Although it is possible to control the number density and size of normal precipitates and solid solutions by controlling the amount added, it is difficult to control the distribution.

[REBCO pinning center]
It is difficult to produce a perfect single crystal of REBCO, and crystal defects are always included in the sample preparation process. Such naturally formed defects function effectively as PCs, and are expected to improve J _c in a magnetic field. The following PCs are listed as REBCO PCs.

(a) Random pins/oxygen vacancies REBCO is an oxide and generally contains oxygen vacancies, which are often distributed randomly forming clusters in the direction of the CuO chains. Since the oxygen vacancy is a small defect smaller than the coherence length, it is a random pinning with a small pinning force. It does not work as an effective PC at high temperatures, but it is thought to work as an effective PC at low temperatures because the coherence length becomes shorter.
・Normal conductive precipitates REBCO thin film contains normal conductive precipitates such as CuO and RE ₂ O ₃ during film formation. Since these precipitates are large compared to oxygen vacancies, they are random pins with a relatively strong pinning force, but their number density is small.

(b) Ab-plane correlation pin/intrinsic pin REBCO has a crystal structure in which CuO ₂ planes and block layers, which play a role in superconductivity, are alternately stacked in the c-axis direction. Due to the anisotropy of this crystal structure, the coherence length has anisotropy, and since the coherence length in the c-axis direction is shorter than the distance between _two CuO planes, the magnetic flux in the ab-plane direction is pinned to the block layer. PC resulting from such a crystal structure of REBCO is called an intrinsic pin or an intrinsic pin.
・Stacking faults Stacking faults are defects in which the regular stacking of atomic planes in a crystal is disrupted. Since REBCO has a layered structure, it is thought to contain many stacking faults. Stacking faults, like intrinsic pins, are correlation pins that effectively act on magnetic flux in the a-b plane direction parallel to the stacking direction.

(c) c-axis correlation pin/crystal grain boundary The crystals constituting the polycrystalline body have different crystal orientations from adjacent crystals. Therefore, discontinuous interfaces between adjacent crystals become grain boundaries. The grain boundaries act as a two-dimensional PC for magnetic flux in the B//c direction.
・Twin boundary A twin is a collection of two crystals of the same type with different crystal orientations, and a plane that is a mirror image of the plane of the two crystalline solids that become the twin is called a twin boundary. . REBCO undergoes a phase transformation from tetragonal to orthorhombic due to the difference in oxygen content. At this time, strain occurs due to the difference in lattice constants, and to alleviate the strain, a twin boundary is formed with the (110) plane as the twin plane. Since the lattice is disordered at the twin boundary, it acts as a PC.
- Screw dislocations Screw dislocations are generated by lattice disturbances, grain boundaries, stacking faults, etc. during crystal growth. Due to the shift of the crystal lattice in the c-axis direction, it acts as a one-dimensional PC for the magnetic flux in the B//c direction.

[Artificial Pinning Center (APC)]
In order to improve J _c in a magnetic field, various attempts have been made to introduce APC into superconductors. Among them, BMO nanorods have a very high pinning characteristic against a magnetic field in the direction in which their columnar shape extends, so they are attracting attention as being very effective in improving J _c in a magnetic field. In this section, we will discuss the BMO nanorods and APCs with a laminated structure that are used in this example.

[BaMO ₃ nanorods]
In 2004, JL Macmanus-Driscoll and colleagues at Los Alamos National Laboratory introduced BaZrO ₃ (BZO) into YBCO thin films on single-crystal or metal substrates in order to improve the superconducting properties of YBCO thin films in a magnetic field. BZO has a perovskite structure similar to YBCO, has a high melting point, and is a chemically stable material. BZO was selected because it had the same crystal structure as YBCO and was thought to grow heteroepitaxially within the YBCO thin film to form nano-sized particles. When a thin film was fabricated using a YBCO sintered target mixed with BZO, an evaluation of the dependence of J _c on the magnetic field application angle revealed that J _c was significantly improved with respect to the applied magnetic field of B//c. Microstructural observation using a cross-sectional transmission electron microscope (TEM) confirmed that nano-sized rod-shaped BZO was mixed with particle-shaped BZO and self-organized in the c-axis direction of YBCO. This is the first report of BMO nanorods. Furthermore, in 2005, Y. Yamada et al. of ISTEC (International Superconductivity Industrial Technology Research Center) created a YBCO thin film on a metal substrate using the PLD method using a YBCO sintered target mixed with YSZ. It was confirmed that BZO grows continuously in a columnar shape from the substrate interface toward the thin film surface. After that, searches for nanorod materials were carried out all over the world, and it was revealed that BaSnO ₃ (BSO) and BaHfO ₃ (BHO) form nanorods. Furthermore, it has been reported that Ba ₂ RETaO ₆ , Ba ₂ RENbO ₆ , and Ba ₂ RERuO ₆ having a double perovskite structure also form nanorods.

It is known that BMO nanorods are formed only in the case of vapor phase growth such as PLD or CVD, and that BMO is introduced in the form of particles without forming nanorods in chemical solution methods such as MOD.

[APC with laminated structure]
In order to improve the superconducting properties of REBCO wire in an isotropic manner, it is considered that the introduction of three-dimensional APC is effective. However, it is generally difficult to control the size and distribution of three-dimensional APC. Therefore, T. Haugan et al. proposed a multilayer structure in which a YBCO matrix and Y ₂ O ₃ were alternately laminated for a YBCO thin film fabricated by the PLD method, and succeeded in introducing particle-like three-dimensional APC. There have also been reports on the use of BZO and BSO as APC materials. However, these stacked structures are pseudo multilayer structures in which a small amount of APC material is deposited on top of the REBCO layer, and then a REBCO layer is stacked, and the growth of REBCO and APC is independent, so the particle size (c-axis direction (height) cannot be controlled. Therefore, it was confirmed that the particle size could be controlled by using BSO as the APC material and laminating multiple layers of a BSO-doped SmBCO layer and an undoped SmBCO layer. By combining BMO nanorods whose in-plane density can be controlled and a multilayer structure, three-dimensional APCs with controlled size and distribution can be introduced. FIG. 13 shows a schematic diagram of a multilayer stacked thin film of BMO nanorods. The size, density, and distribution of such a stacked APC can be controlled. Therefore, the possibility of J _c non-reciprocity is expected not only by improvement of J _c but also by asymmetric modulation of the pinning potential by changing the size and distribution of APC in a gradient manner.

[Effect of superconductor surface and magnetic flux]
A shielding current flows in a region with a circumferential radius of about λ around the normal conducting core, and the quantized magnetic flux receives magnetic interaction from a non-uniform portion with a size of about λ. The surface barrier on the superconductor surface or at the superconductor-normal conductor interface is one type of magnetic interaction, and together with the magnetic flux pinning due to the pinning center in the bulk of the superconductor explained in the previous section, it is a determining factor for I _c . sell. This section describes surface barriers and the effects of surface conditions that affect them.

[Surface barrier]
A surface barrier is a potential barrier that occurs at the surface of a superconductor when magnetic flux attempts to enter the superconductor. Surface barriers were proposed by Bean and Livingston. The Bean-Livingston surface barrier model deals with what happens to the magnetic field in which magnetic flux lines enter a superconductor with respect to the lower critical magnetic field H _c1 when a surface exists. When considering the penetration of magnetic flux into the surface of a superconductor, it is necessary to consider the surface magnetic field that attenuates at a distance λ from the surface, and the magnetic field of the magnetic flux lines and their mirror images. The interaction with the mirror image is due to magnetic interaction. Assuming magnetic flux exists on the surface of a superconductor, the shielding current circulating around the magnetic flux is distorted from a perfect circle, so a force acts on the magnetic flux in a direction that makes it energetically stable. This effect can be explained by assuming a mirror image on the outside of the superconductor. Since an attractive force acts between the magnetic flux and its mirror image, a force acts in a direction that forces the magnetic flux on the surface out of the superconductor.

When the GL parameter κ is large, the potential energy U(x) when magnetic flux penetrates a distance x from the superconductor surface in an external magnetic field H is derived by the following equation.
The first term represents the self-energy of the magnetic flux lines, the second term represents the energy due to the interaction between the magnetic flux lines and the mirror image, and the third term represents the energy due to the surface magnetic field. K ₀ is a modified Bessel function of the second kind. FIG. 14 shows potential energy U(x) versus distance x from the superconductor surface. U(x) has a peak when the external magnetic field H is as low as the upper critical magnetic field H _c1 . Even if H exceeds H _c1 , magnetic flux cannot enter the superconductor due to the surface barrier, but as the external magnetic field H further increases, the surface potential energy increases and the barrier to magnetic flux entry decreases. At a certain magnetic field _Hs , the barrier to entry disappears and magnetic flux begins to enter.

[Effect of surface condition]
Surface barriers become important at high temperatures where bulk pinning decreases. In particular, when discussing the transport properties of superconducting thin films in an in-plane magnetic field, it is necessary to consider the size of the surface barrier depending on the surface morphology. The Bean-Livingston surface barrier explained in the previous section assumed the penetration of quantized magnetic flux into a perfectly flat, infinitely long parallel surface. However, in reality, it is difficult to achieve such a completely ideal surface, and the surface of the superconductor may become rough, and the chemical composition of the compound may vary. Such surface imperfections reduce the surface barrier. Factors that reduce the surface barrier on the surface of a superconducting thin film include the following factors.
・Surface roughness, defects near the surface, and gradient changes in surface superconductivity parameters

[Non-reciprocity of superconducting properties]
Breaking of spatial or time symmetry in physical systems can lead to non-reciprocity in physical properties such as optical, magnetic, and electrical properties of materials. The non-reciprocity treated in this embodiment is a property that when a magnetic field is applied to a superconductor, a current direction dependence (rectification effect) occurs in the motion of quantized magnetic flux. As a result of the rectification of the quantized magnetic flux, a current direction dependence occurs in the critical current I _c . This non-reciprocal electrical conduction property of superconductors is expected to be applied to future low-energy rectifying devices using superconductors. Furthermore, such a rectifying effect is also called the ratchet effect, and research on the dynamics of quantized magnetic flux in superconducting ratchets is expected not only for device applications but also for modeling biological ratchets. Various theoretical and experimental reports have been made regarding the non-reciprocal quantized magnetic flux motion of superconductors and the resulting non-reciprocal electric conduction properties. Many of these properties are due to the spatial asymmetry of potential energy due to the asymmetric shape and structure of the superconductor and the asymmetric shape and distribution of pinning centers. In this section, we will discuss approaches to achieve these nonreciprocal superconducting properties.

[Nonreciprocity of superconductors with asymmetric shapes and structures]
Various reports have been made regarding the non-reciprocal superconducting properties caused by the shape and structure of superconductors that are asymmetrical with respect to the current direction. Initial studies reported asymmetric flux pinning in Nb twinned samples. In this report, when the pinning force was measured for a current perpendicular to the magnetic field parallel to the twin interface, the pinning force changed by about twice as the current direction was reversed. This non-reciprocity is due to the fact that the crystal axis directions of the two crystals are asymmetric with respect to the magnetic field.

Non-reciprocal superconducting properties focusing on the surface structure of superconductors have been reported, and the non-reciprocity is caused by surface barriers of different sizes at different superconducting interfaces. Regarding low-temperature superconductors, when a magnetic field was applied in the in-plane direction of a Pb _0.9 Bi _0.1 thin film, an asymmetry was observed in the magnitude of I _c with respect to the current in two directions perpendicular to the magnetic field. . In this case, the quantized magnetic flux enters from the top or bottom surface (substrate interface) of the thin film depending on the current direction. The difference in surface barrier size due to the difference in roughness between the two superconducting interfaces is thought to be the cause of the non-reciprocity. Similarly, I _c asymmetry in an in-plane magnetic field has also been observed in Nb thin films. A similar I _c asymmetry due to an asymmetric surface barrier has also been achieved by superconducting nanobridge processing or edge processing on one side of a superconducting strip. FIG. 15 shows a schematic diagram of a superconducting strip with asymmetric edge roughness. Regarding high-temperature superconductors, the asymmetry of I _c in an in-plane magnetic field in a thin film of YBCO added with 5 mol% Yb ₃ TaO ₇ has been reported. In this case, in addition to the difference in roughness between the surface of the superconducting thin film and the substrate interface, the lowering of the surface barrier due to the lowering of T _c near the substrate interface is considered to be the cause of the asymmetry of I _c .

Asymmetry in Ic due to the asymmetric shape of the superconducting strip has also been reported. It has been reported that an asymmetrical I _c with respect to the current direction can be obtained in an L-corner shaped Al strip. FIG. 16 shows a schematic diagram of an L-shaped superconducting strip. This asymmetry is due to the current crowding effect at the inner corner, and it is easier for magnetic flux to penetrate from the inner corner than from the outer corner. It has been confirmed that if the corners are sharp, the current crowding effect becomes large, but if the corners have curvature, the current crowding effect is reduced.

In addition, rectification properties in superconductors with crystal structures with broken spatial symmetry have also been reported. High rectification characteristics in a perpendicular magnetic field have been obtained by an electric double layer transistor structure using a MoS ₂ thin film.

[Non-reciprocity of superconductors with nanostructures created by microfabrication]
With the development of microfabrication technology, research on the dynamics of quantized magnetic flux by introducing various pinning nanostructures into superconductors has been actively conducted, and rectification of quantized magnetic flux has been reported. There are a wide variety of pinning structures utilized. In the following, we will discuss pinning nanostructures that provide nonreciprocal superconducting properties.

(a) Asymmetric modulation of superconducting surface thickness Since the energy of magnetic flux lines is proportional to the length of magnetic flux lines, an asymmetric pinning potential can be constructed by asymmetric changes in the superconductor's thickness. FIG. 17 shows a schematic diagram of asymmetric superconducting surface thickness modulation. Rectification of the quantized magnetic flux due to the thickness change or step of the sawtooth-shaped asymmetric slope has been observed in numerical simulations and experiments.

(b) Asymmetric shape of pinning site By controlling the shape and size of the pinning site, a locally asymmetric pinning potential can be constructed. FIG. 18 shows a schematic diagram of an asymmetrically shaped pinning site array. Rectification of quantized magnetic flux by pinning centers such as antidots of various shapes such as rectangles and triangles has been reported. Rectification has also been provided by arrays of large and small antidot pairs, sawtooth modulation of pinning site size, and asymmetrical arrangements.

(c) Asymmetric density modulation of pinning sites Even with isotropically shaped pinning sites, by controlling the density distribution, it is possible to configure non-local and overall modulation of the pinning potential. FIG. 19 shows a schematic diagram of asymmetric modulation of pinning site density. Sawtooth modulation of the pinning density and rectification of the quantized magnetic flux by a pinning site array with a wedge-shaped asymmetric shape distribution have been reported. These are due to the asymmetric potential formed by the pinned quantized magnetic flux, which rectifies the unpinned quantized magnetic flux between the pinning sites.

(d) Asymmetric structure of magnetic dots/magnetic loops Pinning using magnetic structures such as magnetic dots and magnetic loops suppresses local superconductivity due to the proximity effect and reduces the shielding current of the magnetic dipole moment and quantized magnetic flux. Due to interaction. It has been reported that the rectifying effect due to the proximity effect is similar to that of anti-dots due to triangular magnetic dots. On the other hand, it has been reported that the rectification caused by the dipole moment of the magnetic loop has unique characteristics that are different from the rectification effects of other pinning structures, such as the direction of rectification does not reverse even if the magnetic field is reversed. Furthermore, the pinning potential can be tuned by adjusting the in-plane magnetic field of the magnetic loop.

(e) Asymmetric weak pinning channel A weak pinning channel is a channel structure in which a part of the strong pinning layer of a two-layer superconducting thin film exhibiting strong pinning force and weak pinning force is removed. Since there is only a weak pinning layer inside the channel, by adjusting the magnetic field, the quantized magnetic flux outside the channel is pinned by the strong pinning layer, and the quantized magnetic flux inside the channel can move. FIG. 20 shows a schematic diagram of an asymmetric pinning channel. Rectification of quantized magnetic flux by an asymmetric channel shape consisting of a series of triangles has been reported.

In the rectification of quantized magnetic flux by nanostructures as described above, reversal phenomena due to interactions between magnetic fluxes that depend on the magnitude of the magnetic field and temperature have been observed in many cases. Factors for reversing the rectification direction include the following parameters.
・Interaction between magnetic flux lattice and pinning potential shape ・Magnetic field penetration length relative to modulation length of pinning potential ・Density of quantized magnetic flux

Ratchet effects using Josephson junctions and arrays thereof have also been reported, and are expected to be put to practical use, particularly in the electronics field. Rectification in superconductor systems without spatial asymmetry of pinning potential has also been reported. For example, rectification of quantized magnetic flux and pumping phenomena have been reported by applying a temporally asymmetric magnetic field to a Bi ₂ Sr ₂ CaCu ₂ O _8+δ crystal. Furthermore, asymmetric current-voltage characteristics have been reported by applying a combination of a plurality of harmonic alternating currents to a structure including a unique Josephson junction of a Bi ₂ Sr ₂ CaCu ₂ O _8+δ crystal. These are caused by the fact that the quantized magnetic flux is divided into a pancake vortex and a Josephson vortex due to the large anisotropy of the Bi ₂ Sr ₂ CaCu ₂ O _8+δ crystal structure, and the two interact.

[Purpose of this example]
In this example, the aim was to realize non-reciprocal superconductivity characteristics (current direction dependence of I _c ) toward the development of a superconducting diode using a REBCO high-temperature superconducting thin film. In order to obtain I _c that is asymmetric in magnitude depending on the current direction, it is necessary to control the effect of stopping or moving the quantized magnetic flux. As a means of achieving this, we focused on the magnetic flux pinning structure on the surface, bottom, and inside of a superconducting thin film in an in-plane magnetic field, and aimed to rectify the quantized magnetic flux according to the current direction by controlling these thin film structures. Using SmBCO as a superconducting material, we produced a thin film without the addition of APC and a thin film in which BMO nanorods were introduced by adding BHO, which is one of the APC materials. In addition, we fabricated thin films with various thicknesses and amounts of BHO added using different substrates, and examined changes in non-reciprocal superconducting properties depending on the thickness, surface roughness, substrate, and nanorod number density of the superconducting thin film. In addition, we evaluated non-reciprocity in various magnetic fields and temperatures in order to elucidate the causes of non-reciprocity. Furthermore, for the purpose of improving non-reciprocity, we investigated thin film surface processing using reactive ion etching and introduction of a PrBCO seed layer.

[experimental method]
[Method for producing SmBCO superconducting thin film]
The PLD method used in this example is a type of physical vapor deposition (PVD) method. The PLD method is a film formation method using laser ablation. Laser ablation is a phenomenon in which when a high-power laser is irradiated onto a solid (or liquid) surface, plasma is generated and constituent substances on the solid surface are evaporated and released. The characteristics of the PLD method are shown below.
・There is little compositional deviation between the target (raw material sintered body) and the thin film.
・Film formation is possible in a wide range of atmospheres and pressure conditions.
・By installing multiple targets in the chamber, it is possible to create a thin film with a multilayer structure.
・Film thickness can be easily controlled by controlling the number of laser pulses.
- Vacuum equipment is relatively simple because energy is injected from outside the chamber.
Due to these characteristics, the PLD method is suitable for producing REBCO thin films.

[Principle and overview of PLD method]
FIG. 21 shows a schematic diagram of the PLD device used in this example. This PLD device is composed of a laser oscillation source, a vacuum chamber, a vacuum pump, and an oxygen introducing section. The vacuum chamber used was equipped with a heater to heat the substrate and a shutter to prevent molecular radiation to the substrate during pre-ablation. Pre-ablation is ablation performed before the start of film formation in order to remove impurity particles on the target surface. A KrF excimer laser (COMPex20 manufactured by Lambda Physik, excitation wavelength λ = 248 nm) and a Nd:YAG laser (ALC-YAG-90 manufactured by Amister Inc., excitation wavelength λ = 266 nm) were used as laser oscillation sources. A chamber using a KrF excimer laser can accommodate up to four targets, and the revolution of the targets can be controlled by a computer. Up to three targets can be installed in the chamber using the Nd:YAG laser, and the revolution of the targets is manually controlled.

Excimer lasers are characterized by high output, high efficiency, and short wavelength. Furthermore, the wavelength of an excimer laser is determined by the type of mixed gas. The principle of generation of KrF excimer laser is as follows. By discharging in a mixed gas of Kr and F ₂ , F ₂ is decomposed and excited, and combines with Kr to form a KrF excimer, which is an unstable diatomic molecule. The light emitted when the KrF excimer decomposes and falls to the ground state causes stimulated emission in other excimers, and phase-aligned light with a wavelength λ=248 nm is emitted. The laser beam is further amplified by a resonator to oscillate a high-energy laser beam.

Compared to excimer lasers, Nd:YAG lasers are characterized by smaller equipment and lower running costs. The generation principle of the Nd:YAG laser is as follows. The Nd:YAG crystal is a crystal in which Y in a garnet-structured crystal (YAG crystal) made of Y ₃ AlO ₁₂ is partially replaced with Nd. By applying external energy to the Nd:YAG crystal from a flash lamp, electrons in the crystal are excited and enter a population inversion state. The light emitted when the excited electrons fall to the ground state causes other electrons to be stimulated to be emitted, thereby emitting light with a uniform phase and a fundamental wavelength λ=1064 nm. The laser beam is further amplified by a resonator to oscillate a high-energy laser beam. Further, by transmitting the light through a wavelength conversion crystal, it can be converted into a second harmonic wave (532 nm) and a fourth harmonic wave (266 nm). In this embodiment, a fourth harmonic wave having a short wavelength and high energy was used.

The principle of the PLD method is as follows. The oscillated laser beam is reflected by a reflecting mirror, passed through a mask, focused by a condensing lens, and irradiated onto the target surface in a vacuum chamber through a laser introduction window. The reflective lens has the role of adjusting the trajectory of the laser beam, and the mask has the role of controlling the size of the laser beam and adjusting the energy distribution. Molecules on the target surface are ablated (evaporated) and excited by the focused laser light, creating a columnar plasma called a plume. At this time, constituent substances are decomposed and released from the target into particles such as atoms, molecules, and ions, which reach and deposit on the substrate placed opposite to form a thin film.

[Thin film production by PLD method]
The thin film manufacturing procedure is shown below.
(1) The target surface was polished with sandpaper (#220, #2000) because the unevenness of the target surface causes deformation and inclination of the plume, and the generation of droplets where target pieces adhere on the substrate.
(2) A target and a substrate were placed in a chamber, and vacuum was drawn using a rotary pump. Note that since the target installation surface is horizontal, a certain degree of adhesive strength is required. In this example, targets were bonded using carbon conductive tape, which has high adhesive strength and good thermal conductivity and is highly durable against heat during film formation.
(3) When the pressure inside the chamber reached 500 mTorr or less, further evacuation was performed using a turbo molecular pump connected in series to the rotary pump.
(4) When the pressure in the chamber reached 4 mTorr or less, the turbomolecular pump was switched off and oxygen was introduced. The displacement was adjusted using the valve of the rotary pump so that the oxygen partial pressure was 400 mTorr.
(5) The temperature of the heater was raised from room temperature to the temperature of the film forming substrate over about 20 minutes. During this time, in order to remove impurities on the target surface, pre-ablation was performed by rotating and revolving the target with the shutter closed.
(6) When the temperature of the film-forming substrate was reached, the film was waited for about 2 minutes to stabilize the temperature.
(7) The shutter was opened and the target was irradiated with a laser to form a film. During film formation, in order to maintain the oxygen partial pressure at 400 mTorr, the exhaust volume was adjusted as appropriate using a rotary pump. Note that no mask was used during laser irradiation.
(8) After the film formation was completed, the rotary pump was switched off, and the oxygen partial pressure in the chamber was set to about 200 Torr to lower the substrate temperature.
(9) When the substrate temperature reached 100° C. or lower, the chamber was opened to the atmosphere and the target and substrate were taken out.

[Target production procedure]
Since the composition of the target affects the composition of the thin film, the target needs to have high density and high purity. This section shows the fabrication procedure. The target raw material powders are Sm ₂ O ₃ (purity 99.9%), BaO ₂ (purity 99.9%), CuO (purity 99.9%), and HfO ₂ (purity 98.0%) manufactured by Kojundo Kagaku Co., Ltd. ), Pr ₆ O ₁₁ (purity 99.9%) was used. To produce the SmBCO target, SmBCO+BHO mixed target, and PrBa ₂ Cu ₃ O _y (PrBCO) target, powder was dried and fired using a small electric furnace (NHK-170) manufactured by Nichito Kagaku Co., Ltd. A BaHfO ₃ (BHO) target was produced by firing using a small electric furnace (KBF-314N) manufactured by Koyo Thermo Systems Co., Ltd.

(a) Preparation of SmBCO target (1) Since Sm ₂ O ₃ is hygroscopic, it was heat-treated in the air at 990° C. for 12 hours and dried.
(2) The dried Sm ₂ O ₃ , BaO ₂ , and CuO were weighed according to the desired composition, mixed in an agate mortar for about 3 hours, and then calcined in the air at 700° C. for 17 hours.
(3) After mixing the calcined raw materials with an agate mortar and pestle for about 3 hours, pressurize at 40 MPa using a hydraulic press machine (P-16B manufactured by Riken Kiki Co., Ltd.) to form a cylindrical pellet, and Calcining was performed at 850° C. for 17 hours.
(4) After the same treatment as in step (3), calcination was performed at 900° C. for 35 hours in the air.
(5) After the same treatment as in step (3), firing was performed at 940° C. in the air for 36 hours, then turned over and further baked at 990° C. in the air for 36 hours.

(b) Preparation of BHO target (1) BaO ₂ and HfO ₂ were weighed according to the desired composition, mixed in an agate mortar for about 3 hours, and then calcined in the air at 900° C. for 24 hours.
(2) After mixing the calcined raw materials in a mortar for about 3 hours, the pellets were pressurized at 40 MPa using a hydraulic press to form cylindrical pellets, and calcined in the air at 1550° C. for 24 hours.
(3) It was turned over and further baked at 1600° C. for 24 hours in the air.

(c) Preparation of SmBCO+BHO mixed target (1) Follow steps (1) to (4) in “(a) Preparation of SmBCO target” and mix the SmBCO target before firing in a mortar for about 2 hours to form a powder. did.
(2) Procedures (1) to (3) of "(b) Preparation of BHO target" were performed, and the BHO target after firing was mixed in a mortar for about 2 hours to form a powder.
(3) Mix the SmBCO powder and BHO powder from steps (1) and (2) to the desired amount of BHO added, mix in a mortar for about 2 hours, and pressurize at 40 MPa using a hydraulic press. It was molded into a cylindrical pellet, heated in the air at 940°C for 36 hours, turned over, and further baked in the air at 990°C for 36 hours.

(d) Preparation of PrBCO target (1) Since Pr ₆ O ₁₁ is hygroscopic, it was heat-treated at 990° C. for 12 hours in the air and dried.
(2) The dried Pr ₆ O ₁₁ , BaO ₂ , and CuO were weighed according to the desired composition, mixed in an agate mortar for about 3 hours, and then calcined in the air at 700° C. for 17 hours.
(3) The calcined raw materials were mixed in an agate mortar for about 3 hours, then pressurized at 40 MPa using a hydraulic press to form into cylindrical pellets, and calcined in the air at 850° C. for 17 hours.
(4) After the same treatment as in step (3), calcination was performed at 900° C. for 35 hours in the air.
(5) After the same treatment as in step (3), firing was performed at 940° C. in the air for 36 hours, then turned over and further baked at 990° C. in the air for 36 hours.

[Method of adding BaMO ₃ ]
In this example, BaHfO ₃ (BHO) was introduced as an artificial pinning center (APC). BHO is a type of perovskite metal oxide called BMO (M=Zr, Sn, Hf). There are three methods shown below as methods for adding BMO to REBCO using the PLD method. FIGS. 22(a) to 22(c) show schematic diagrams of each method.

(a) Mixed target method As shown in Figure 22(a), this is a method in which a desired amount of BMO is mixed in and sintered during the production of a REBCO target to produce a BMO-added thin film. be. Since BMO can be added relatively easily, it is suitable for wire applications. However, since the amount of BMO added for each target is constant, it is necessary to fabricate a plurality of targets in order to fabricate thin films with different amounts of BMO added.

(b) Modified target method During thin film production, as shown in Figure 22(b), a BMO sintered body processed into small pieces was placed on a REBCO target, and REBCO and BMO were alternately deposited by rotation of the target and BMO was added. This is a method for producing thin films. The amount of BMO added can be easily changed depending on the area of the BMO sintered body. However, the drawback is that if the laser hits the edge of the installed BMO sintered body, the plume will tilt and the amount of addition will become uneven.

(c) Target exchange method As shown in FIG. 22(c), this is a method in which REBCO and BMO targets are prepared and alternately deposited during thin film production to produce a BMO-added thin film. The amount of BMO added can be easily controlled by the number of laser pulses irradiated to REBCO and BMO. However, this method has the disadvantage that it takes a long time to form a film because it takes time to replace the target.

[Film-forming substrate]
The substrate is the base on which the thin film is deposited and has a great influence on the crystallinity of the epitaxially grown thin film. Therefore, it is necessary to select a substrate that suits the purpose. The properties required of the substrate are shown below.
・Crystal structure is similar to thin film material, and lattice misfit is small.
・Thermal expansion coefficient is similar to that of thin film materials.
・No reaction or diffusion with thin film materials.
・There is no structural phase transition below the film formation temperature.

In this example, an IBAD-MgO substrate and a LaAlO ₃ (LAO) (100) single crystal substrate were used. FIG. 23 shows a schematic diagram of the structure of the IBAD-MgO substrate. The IBAD-MgO substrate has a structure in which a plurality of intermediate layers are laminated on a metal tape. The role of each layer is shown below.

(a) Hastelloy C276
It is an alloy of Ni with Cr and Mo added. Excellent durability, corrosion resistance, and heat resistance.
(b) Gd ₂ Zr ₂ O ₇ layers
Manufactured by ion beam sputtering method. It has the role of preventing metals such as Ni from diffusing from Hastelloy.
(c) Y ₂ O ₃ layer Similar to the Gd ₂ Zr ₂ O ₇ layer, this layer serves to prevent metals such as Ni from diffusing from Hastelloy. It also plays a role in alleviating the lattice mismatch between Gd ₂ Zr ₂ O ₇ and MgO.
(d) IBAD-MgO layer This is a layer in which MgO is biaxially oriented by the IBAD method.
(e) LaMnO3 layer
Manufactured by RF-sputtering method. It plays a role in alleviating the lattice mismatch between MgO and _CeO2 .
(f) CeO ₂ layer Produced by PLD method. Since CeO ₂ grows in a self-oriented manner, its in-plane orientation improves even without assistance from an ion beam or the like. The orientation tends to improve as the film thickness increases, and the orientation of this layer affects the crystallinity of the superconducting layer.

In this example, in order to consider the influence of the roughness of the bottom surface of a superconducting thin film, a REBCO thin film was fabricated using a single crystal substrate whose surface was smooth at the molecular level. Table 1 shows the characteristics of various substrates. In this example, LAO, which has a small lattice misfit and a coefficient of thermal expansion close to that of SmBCO, was selected among single crystal substrates.

[Reactive ion etching]
Reactive ion etching (RIE) is classified as dry etching, which is a processing method using gas using plasma. RIE is a highly accurate anisotropic etching process using physical sputtering using ions and chemical reaction using reactive gas, and is often used in the production of semiconductor devices. In this example, for the purpose of flattening the surface of the SmBCO thin film, an attempt was made to process the surface of the thin film by RIE.

FIG. 24 shows a schematic diagram of parallel plate type RIE. The physical etching principle of RIE is as follows. Two parallel plate electrodes are installed in a vacuum container, and a sample is placed on one side. A high frequency power source is connected to the sample side (cathode) of the electrode, and the other side (anode) is at ground potential. By applying a high-frequency voltage between parallel plate electrodes, the etching gas in the chamber (in this example, a mixed gas of CF ₄ and O ₂ ) is dissociated into ions and radicals by electron collision, and the ions and electrons enter a plasma state. Form. Since the mobility of electrons is much greater than that of ions, the plasma potential is positive. Furthermore, when the cathode electrode is positive, electrons are accelerated toward the electrode and negative charges are accumulated. When the cathode electrode is negative, positive ions are accelerated toward the electrode, but their mobility is low, so the amount accumulated is extremely small. Furthermore, since the blocking capacitor insulates the cathode electrode from the high-frequency power source, the electrons accumulated in the electrode are not discharged, and the cathode has a negative potential. Therefore, an ion sheath is formed between the plasma and the cathode electrode, resulting in a potential difference. This is called the sheath potential. Since the ion sheath is formed perpendicular to the sample, ions accelerated by the sheath potential impact the sample perpendicularly, causing anisotropic etching.

The RIE processing in this example was performed using a parallel plate type RIE device (RIE-10NRT manufactured by Samco Co., Ltd.). Table 8 of Example 3 shows the conditions of various parameters of RIE. The sample was placed on a quartz plate and etched. Note that the etching conditions were examined by keeping the etching gas conditions constant and varying the etching intensity and time.

[PrBa ₂ Cu ₃ O _y Seed layer]
The base layer upon which a thin film is deposited has a great effect on the crystallinity of the epitaxially grown thin film. By using a material having a lattice constant close to that of the Upper layer as the Seed layer, it is possible to alleviate strain caused by lattice misfit at the interface between the Upper layer and the substrate. In this example, in order to alleviate the lattice strain at the bottom surface of SmBCO (substrate side interface), PrBCO, which is the same rare earth oxide as SmBCO in the Upper layer but is a normal conductor, was introduced as a seed layer. PrBCO has a very similar lattice constant to SmBCO, and the lattice misfit is as small as 0.26%. Therefore, by introducing a PrBCO seed layer with good crystallinity, the interface strain of SmBCO can be more relaxed than when no PrBCO seed layer is introduced. Furthermore, it has been reported that when a PrBCO Seed layer-introduced SmBCO thin film is fabricated on an IBAD-MgO substrate, it is possible to suppress the decrease in T _c due to the diffusion of Ce from CeO ₂ on the outermost surface of the IBAD-MgO substrate to SmBCO. . From the above, by using the PrBCO Seed layer, it is possible to produce an SmBCO Upper layer having a good interfacial structure with less strain and solid phase diffusion of the substrate material.

On the other hand, when PrBCO and SmBCO are stacked, there is a concern that the T _c of SmBCO will decrease due to diffusion of Pr into SmBCO. ( _{Y 1-x} , _Pr It has been reported that conductive transition no longer occurs. Therefore, it is necessary to appropriately set the temperature for forming the thin film in order to prevent Pr from diffusing. If Pr is diffused under the optimum temperature conditions for film formation of SmBCO, it is considered that the film needs to be formed at a certain temperature lower than the optimum temperature conditions for SmBCO when no seed layer is used. Therefore, in this example, an attempt was made to fabricate an SmBCO thin film into which a PrBCO seed layer was introduced using the low temperature growth (LTG) method proposed by our group. The LTG method is a method in which REBCO of the Seed layer is produced at a relatively high temperature, and then REBCO of the Upper layer is produced at a relatively low temperature. By using the LTG method, it is possible to produce a c-axis oriented REBCO thin film at a relatively low temperature at which c-axis alignment is normally difficult. Even in a report on an SmBCO thin film into which a PrBCO seed layer was introduced, which was fabricated by the LTG method, an increase in the a-axis grain mixture ratio was not confirmed at temperatures lower than in an SmBCO thin film into which no PrBCO seed layer was introduced. Based on the above, the LTG method was used as a thin film manufacturing method that achieves both maintenance of good crystallinity of the PrBCO Seed layer and SmBCO Upper layer and prevention of Pr diffusion.

[Evaluation method of SmBCO thin film]
The produced thin film was evaluated for crystal structure, surface and microstructure observation, compositional analysis, and superconducting properties. Each evaluation method is shown below.
・Crystal structure evaluation X-ray diffraction (XRD) method ・Surface structure observation Atomic force microscope (AFM)
・Composition analysis Inductively-coupled plasma spectroscopy (ICP)
・Film thickness evaluation White microscope ・Superconductivity property evaluation Physical properties measurement system (PPMS)

[Crystal structure evaluation]
The crystal structure of the produced thin film was evaluated using X-ray diffraction. In this example, 2θ-ω measurement, rocking curve measurement, and φ-scan measurement were performed using a multifunctional X-ray diffraction device ATX-G for surface structure evaluation manufactured by Rigaku. Each measurement method will be described below.

(a) 2θ-ω measurement The X-ray incident angle ω is changed by rotating the sample, and the sample is irradiated with X-rays from the X-ray source. At this time, the X-ray detector is placed at a position at an angle 2θ which is twice ω. In this example, measurements were performed while changing the 2θ range from 5° to 80°. Through this measurement, it is possible to evaluate the orientation of the sample, the presence or absence of different phases, and the c-axis length. Plot the c-axis length obtained from the peak of the (00n) plane on the vertical axis and the Nelson-Riley (NR) function shown below on the horizontal axis, and use the least squares method to calculate the exact value from the extrapolated value where the NR function becomes zero. The c-axis length was determined.

(b) Rocking curve measurement
In rocking curve measurement, ω and 2θ are fixed at the peak angle of the (005) plane obtained in 2θ-ω measurement, and ω is varied within a range of ±1° from that angle to measure diffracted X-rays. . From the half-value width δω of the peak of the (005) plane obtained from this measurement, it is possible to evaluate the variation in crystal orientation with respect to the c-axis direction of the substrate. The smaller δω is, the better the c-axis orientation is.

(c) φ-scan measurement By rotating the α-axis, the X-ray source and detector are installed at a position where the diffraction peak from a specific surface of the thin film can be obtained, and by rotating the sample by φ within the plane. , the in-plane orientation of a thin film can be evaluated. In this example, the peak of the (102) plane of SmBCO was used, and the range of φ was set to ±100°. The variation in crystal orientation in the in-plane direction can be evaluated from the half-width δφ of the peak obtained from the measurement. The smaller δφ is, the better the in-plane orientation is.

[Surface structure observation]
Dynamic force mode (DFM) of an atomic force microscope (AFM), which is a type of scanning probe microscope, was used to observe the surface structure of the thin film. The AFM used in this example was SPI3800 manufactured by SII nano technology. The probe is attached to the tip of the cantilever, and in AFM, the probe is constantly brought into contact with the sample surface with a small force, and the probe is attached so that the force is constant, that is, the amount of deflection of the cantilever is constant. Surface information is obtained by horizontally operating the piezoelectric element while controlling the distance between the surface and the sample. An optical lever method is used to detect the amount of deflection. The reflected light from the semiconductor laser irradiated onto the back surface of the cantilever is guided to a four-part photodiode in the photodetector. Since the reflection angle of the laser changes due to the deflection of the cantilever, the center position of the laser hitting the four-split photodiode shifts and the voltage difference between the photodiodes changes. By detecting this, the displacement of the cantilever is measured. DFM is one of the measurement modes of AFM, in which the probe is brought close to the sample surface while the cantilever is vibrated at about the resonance frequency by a piezoelectric element, and a laser beam is applied to the back of the cantilever so that the vibration amplitude is constant. , surface information can be obtained by detecting changes in amplitude due to atomic forces with a photodetector. DFM is suitable for measuring soft samples or samples with adsorption force that are difficult to measure with contact-type AFM.

In this example, the surface roughness δR was evaluated using the analysis results of the root mean square roughness based on the surface information of a square area of 10 μm on a side. FIG. 25 shows a schematic diagram of δR.

[Composition analysis]
For compositional analysis, evaluation was performed by inductively-coupled plasma spectroscopy (ICP) using Thermo iCAP6200DUO manufactured by Thermo Scientific. In ICP, a sample dissolved in an acidic solution is sprayed into Ar plasma to excite the constituent elements of the sample, and the unique emission spectrum of each element generated when the excited atoms return to the ground state is analyzed by spectroscopy. This is a method for quantitatively measuring the constituent elements of a sample. In this example, a standard solution of the element to be evaluated was diluted with dilute nitric acid, and a calibration curve of spectral intensity and concentration was drawn using the diluted standard solution, thereby using it as a reference for the unknown concentration of the sample. The standard solutions used in this example are Kanto Kagaku Co., Ltd. 1000 mg/l samarium standard stock solution, praseodymium standard stock solution, barium standard stock solution, copper standard stock solution, cerium standard stock solution, yttrium standard stock solution, calcium standard stock solution, lanthanum standard stock solution, zirconium standard stock solution. A diluted solution (blank, 0.01,0 .1, 0.5, 1.0 ppm) were used.

In this example, a sample solution was prepared by dissolving the sample in 20 ml of 10% diluted nitric acid, and the concentration of each constituent element was measured by spraying it into Ar plasma, and the composition ratio and film thickness of the sample were evaluated. The film thickness was calculated using the following formula.
Here, C [ppm] and M are the mass concentration and atomic weight of each constituent element. V [cm ³ ] is the volume of the sample solution, n _SmBCO is the number of moles of SmBCO in the sample solution, _NA is Avogadro's number, l [Å] is the lattice constant of SmBCO, S [cm ² ] is the surface area of the sample, t [nm] is the film thickness.

[Film thickness evaluation]
The thickness evaluation of the thin film on the single-crystal substrate in this example was performed using an ECLIPSE LV150N white light microscope manufactured by Nikon, along with the evaluation by ICP described in the previous section. In addition, evaluation results of ICP are used for evaluation of film thickness in the following examples. A white light microscope can perform step measurement using two-beam interferometry. The incident light from the light source is split by a half mirror in the two-beam objective lens, and the transmitted light is incident on the surface of the measurement sample and reflected. On the other hand, the reflected light enters the reference surface (reflection mirror) and is reflected. Each reflected light beam is imaged on the camera surface. At this time, if there is no phase difference in the reflected light at a measurement point on the sample, it will be the brightest, and if there is a 1/2 wavelength shift, it will be the darkest. In other words, an optical path difference occurs in the reflected light depending on the unevenness of the sample surface, and interference fringes are formed. By analyzing images of interference fringes, surface roughness and step height can be measured.

[Superconducting property evaluation]
The superconducting properties of the thin film were measured using a DC four-probe method using a physical property measurement system (PPMS) MODEL 6000 manufactured by Quantum Design. In the DC four-terminal method, the current terminal and voltage terminal are connected separately. If the sample resistance is sufficiently small compared to the internal resistance of the voltmeter, almost no current will flow through the voltmeter. Therefore, wiring resistance and contact resistance can be ignored, and the resistance of a sample with low resistance can be accurately measured.

The AC transport measurement system (ACT) option was used to measure the superconducting properties. Using the ACT option, four types of electrical transport measurements are possible: resistivity, Hall coefficient, IV curve, and critical current. In measuring the IV curve, it is possible to measure the current-voltage curve including positive and negative currents from a specified maximum current or from zero by stepping the DC current. Note that the maximum current range that can be measured by specifying a lamp sequence is the range from zero to specified maximum current (positive) to specified maximum current (negative) to zero. However, since the current steps per quadrant are limited to a maximum of 256 steps, the positive and negative current-voltage curves in the I _c nonreciprocal measurements were measured individually (the ramp sequence used was zero → Specified maximum current (positive) or zero → specified maximum current (negative), each with 256 steps).

The AC transport option of the PPMS used in this example has a limitation in that it can only flow a maximum current of 2A. Therefore, we performed a bridge process to limit the current flowing through the sample. FIG. 26 shows the procedure of bridge processing. After placing a mask on the sample as in (1), Ag coating was performed as in (2). Ag coating was performed using QUICK COATER SC-701 manufactured by Sanyu Denshi Co., Ltd. Thereafter, as shown in (3), the film was masked with a silver wire and aluminum foil, and laser etching was performed using a Nd:YAG laser for about 5 minutes at moderate laser energy. The width of the bridge was approximately 50-100 μm, and the length was approximately 1 mm. Thereafter, oxygen annealing was performed at 350° C. for 2 hours in an oxygen flow atmosphere. FIG. 27 shows the annealing time and temperature conditions. In addition, terminals were attached to the sample by indium crimping. As superconducting properties, critical temperature T _c , magnetic field dependence of critical current density J _c , dependence of J _c on magnetic field application angle, and J _c nonreciprocity were measured. Each measurement method is described below.

- T _c measurement T _c was measured by passing an alternating current of 0.01 mA through the sample while lowering the temperature from 95 K at a rate of 0.3 K/min, and measuring the temperature dependence of the alternating current electrical resistivity. The temperature at which the electric field becomes 10 μV/cm was interpolated from the measurement results and defined as T _c .

- Magnetic field dependence of J _c The magnetic field dependence of J _c was measured by measuring the current-voltage characteristics of the sample while applying a magnetic field in a direction perpendicular to the substrate surface of the sample. The current when the electric field generated between the voltage terminals was 1 μV/cm was defined as the critical current _Ic , and the value obtained by dividing _Ic by the cross-sectional area of the bridge was defined as _Jc . Measurements were performed at a magnetic field range of 0-9T and a temperature of 77.3K.

- Dependence of J _c on magnetic field application angle The dependence of J _c on magnetic field application angle was measured using a PPMS rotator. FIG. 28 shows how the sample is attached to the rotator. Moreover, FIG. 29 shows a schematic diagram of measurement of the dependence of J _c on the magnetic field application angle. J _c was measured by rotating the sample to change the applied angle θ of the magnetic field from −130° to 130°. At this time, the current I and the magnetic field B were always perpendicular to each other in order to perform measurements under a transverse magnetic field where the Lorentz force on the magnetic flux is maximum. Measurements were performed at a magnetic field of 1-5T and a temperature of 77.3K.

-Measurement of I _c non-reciprocity In the measurement of I _c non-reciprocity in this example, a magnetic field was applied in the direction perpendicular to the current direction (B⊥I) and in the in-plane (B//ab) direction of the thin film. FIG. 30 shows how a sample is attached for measurement in an in-plane magnetic field. The magnetic field application direction of the PPMS used in this example was from the bottom to the top of the device. Therefore, a jig was made from a copper plate and attached to the sample holder, and the sample was fixed to the jig so that a magnetic field was applied in the in-plane direction of the sample. In order to evaluate I _c nonreciprocity, I _c magnetic field dependence was measured at a temperature of 65-85 K and a magnetic field of 0-9 T. FIG. 31 shows an example of the current-voltage characteristics obtained from the measurement and a schematic diagram of the measurement. In each magnetic field, I _c is measured twice for each positive and negative current direction, and using the average value, the non-reciprocal Asym. was calculated.
Here, I _c ^down is a critical current for a current in the direction in which the Lorentz force applied to the magnetic flux is directed from the surface of the superconducting thin film to the bottom surface (substrate side), and I _c ^up is a critical current in the opposite direction. FIG. 32 shows an example of the measured non-reciprocal magnetic field dependence of I _c . In most samples, the magnetic field dependence had positive or negative peaks at low magnetic fields below 1 T, so the maximum value of nonreciprocity in the magnetic field dependence was determined as Asym. It was defined as ^MAX . Furthermore, since the current upper limit of the ACT option of the PPMS is 2A, some samples were measured at a current upper limit of 5A by connecting a 2182A voltmeter manufactured by KEITHLEY and a 6242 current source manufactured by ADCMT to the PPMS. Table 2 shows the correspondence between the terminals of channels (Ch) 1 and 2 of the sample pack for 5A measurement and the pins of the DB25 connector. The voltmeter and current source were computer controlled using Laboratory Virtual Instrumentation Engineering Workbench (LabView) manufactured by National Instruments.

[Example 1: Non-reciprocal superconducting properties of SmBCO thin film]
For the development of REBCO high temperature superconducting diodes, I _c nonreciprocity (I _c asymmetry) depending on the current direction of the REBCO thin film is required. The I _c of a superconductor in a magnetic field is due to the motion of the quantized magnetic flux in the superconductor. Therefore, in order to control I _c , it is necessary to control the movement inside the superconductor and the penetration of magnetic flux into the superconductor. Therefore, factors necessary for I _c asymmetry include asymmetry of magnetic flux pinning inside the thin film and asymmetry of the surface barrier at the magnetic flux entry surface of the thin film. If the flux pinning structure inside the thin film is symmetric, an asymmetric surface barrier at the flux entry surface would be required to achieve I _c asymmetry. I _c asymmetry due to surface barrier asymmetry is often reported. Particularly in high-temperature superconductors, it has been reported that I _c asymmetry in the in-plane magnetic field of YBCO thin films is associated with the surface barrier, but the thin film structure and conditions that can achieve high asymmetry, as well as the degree of asymmetry, have been reported. There are still many aspects that are unclear as to whether this can be achieved. Therefore, in Example 1, the purpose was to realize asymmetric I _c in a REBCO thin film and to elucidate the parameters of the thin film structure that contribute to the I _c asymmetry. In a REBCO thin film in an in-plane magnetic field, the plane of entry of the quantized magnetic flux is the top or bottom surface of the thin film (substrate-thin film interface). The size of the surface barrier depends on the surface structure such as the roughness and defects of the magnetic flux entry surface. Therefore, in order to achieve surface barrier asymmetry, it is considered important to control the structure of each interface so that the surface barrier size differs between the top and bottom surfaces of the thin film. The roughness of a thin film surface generally increases as the film thickness increases. Furthermore, the condition of the bottom surface of the thin film changes depending on the material and quality of the substrate on which the thin film is formed. In this chapter, we will fabricate SmBCO thin films of various thicknesses on two different types of substrates (LaAlO ₃ (LAO) substrate and IBAD-MgO substrate), and discuss the film thickness, surface roughness, crystal orientation, and film formation of SmBCO thin films. We investigated the influence of the substrate on I _c asymmetry in an in-plane magnetic field.

[Preparation and properties of thin film]
In order to control the surface roughness of SmBCO thin films, we fabricated SmBCO thin films with various thicknesses, and investigated structural changes such as crystal orientation and surface morphology of the thin film depending on the film thickness and deposition substrate, as well as basic superconductivity. Characteristics were evaluated.

[Preparation of thin film]
Tables 3 and 4 show the conditions for producing SmBCO thin films. The thin film using the IBAD-MgO substrate was produced by a KrF excimer laser, and the thin film using the LAO substrate was produced by the PLD method using a Nd:YAG laser. FIG. 33 shows AFM images of the surfaces of the IBAD-MgO substrate and LAO substrate used in Example 1. The surface roughness of the IBAD-MgO substrate was about 3 nm, and the surface roughness of the LAO substrate was about 0.3 nm. Hereinafter, a sample fabricated on an IBAD-MgO substrate will be referred to as an IBAD sample, and a sample fabricated on an LAO substrate will be referred to as an LAO sample.

[Crystal structure]
XRD measurement confirmed that SmBCO had good c-axis orientation in all samples. FIG. 34 shows δω and δφ of IBAD and LAO samples made with various film thicknesses. The dotted and broken lines indicate the average values of the samples for each substrate. The average value of δω was 0.45° for the IBAD sample and 1.38° for the LAO sample, and the average value of δφ was 0.21° for the IBAD sample and 0.96° for the LAO sample. Regarding the LAO sample, both δω and δφ showed good orientation regardless of the film thickness of the sample. Regarding the IBAD samples, although variations were observed in both δω and δφ in samples with small film thicknesses of about 250 nm or less, δφ was smaller than the δφ value of 1.6° of the CeO ₂ layer of the substrate in most samples, which was good. It has an in-plane orientation.

[Surface morphology]
FIG. 35 shows surface AFM images of a portion of an IBAD sample with various film thicknesses. It was confirmed that crystal grains and grain boundaries became coarser as the film thickness increased. Moreover, FIG. 36 shows the surface roughness δR of a 10 μm square area in IBAD samples and LAO samples with various film thicknesses. In the IBAD sample, there was a strong tendency for δR to increase as the film thickness increased. There was a tendency for δR to be larger for the IBAD sample than for the LAO sample, but this is because the surface roughness (3 nm) of the IBAD-MgO substrate is different from the surface roughness (3 nm) of the LAO substrate from the above AFM measurement results. This is thought to be because the surface roughness is larger than 0.3 nm) and the surface roughness is large from the early stage of thin film growth.

[Superconducting properties]
Figure 37 shows the T _c and J _c in the self-magnetic field for IBAD and LAO samples with different film thicknesses. Furthermore, _FIG . 38 shows the _Asym . Indicates ^MAX . Most of the samples exhibited high superconducting properties with T _c of 90 K or more and J _c ^self of more than 1 MA/cm ² . There were also some samples with small film thickness and low J _c ^self . The reason for this is thought to be that the sample had a relatively low _Tc . In addition, Asym. Regarding ^MAX , no correlation was found between T _c and J _c .

[J _c non-reciprocity of SmBCO thin film]
The correlation between J _c nonreciprocity, magnetic field, crystal orientation, film thickness, surface roughness, and film-forming substrate will be described.

[Magnetic field dependence]
Figure 39 shows the Asym. ^MAX and Asym. =Asym. The relationship between magnetic field B ^MAX at ^MAX is shown. Figure 40 shows the Asym. shows the magnetic field dependence of Figure 41 shows Asym. of the LAO sample at 77.3K. shows the magnetic field dependence of Asym. of each sample. showed positive or negative peaks (Asym. ^MAX ) in low magnetic fields below 1 T. In particular, Asym. B ^MAX of samples with ^MAX greater than 10% was 0.2 T or less, and concentrated in a relatively low magnetic field. From this, it is inferred that the obtained I _c asymmetry is due to the surface barrier that is effective in low magnetic fields.

[Crystal orientation dependence]
Figure 42 shows the Asym. of IBAD and LAO samples with different δω. Indicates ^MAX . FIG. 43 shows Asym. of IBAD and LAO samples with different δφ. Indicates ^MAX . Regarding δω, no systematic change was observed in both the IBAD sample and the LAO sample. On the other hand, regarding δφ, the smaller δφ is, the more Asym. A tendency for ^MAX to be large was observed. The crystallinity of thin films contributes to the generation of defects inside the thin film. Therefore, it is presumed that the larger δφ is, the more defects such as stacking faults are formed inside the thin film. These defects act as pinning centers within the thin film, which leads to Asym. This may have contributed to the decrease in ^MAX .

Let us consider the influence of magnetic flux pinning (bulk pinning) due to defects inside the thin film on the I _c asymmetry. First, the determining factors of _Ic include the surface barrier at the interface (top surface and bottom surface) of the thin film and the bulk pinning inside the thin film. Comparing the two, in the sample with a large δφ, the influence of bulk pinning became larger as the number of defects inside the thin film increased. Therefore, it is thought that the influence of the surface barrier was relatively small compared to bulk pinning. That is, in samples with large δφ, bulk pinning became the main determinant of I _c , and the I _c asymmetry due to the asymmetric surface barrier was attenuated. Therefore, in order to reduce the influence of bulk pinning in order to realize I _c asymmetry, it is considered necessary to fabricate an SmBCO thin film having the following two types of structures.
・Thin film with few defects that become pinning centers inside the thin film.
・A thin film with a structure that alleviates magnetic flux pinning inside the thin film.

[Film thickness dependence]
FIG. 44 shows the Asym. Indicates ^MAX . Figure 45 shows the B ^MAX of IBAD and LAO samples with different film thicknesses. Asym. For both ^MAX and B ^MAX , no clear correlation with film thickness was confirmed.

[Surface roughness dependence]
First, we consider the expected asymmetry results from the surface roughness perspective. The surface barrier decreases as the roughness of the magnetic flux entry surface of the superconductor increases. The magnetic flux entry surface depends on the current direction and is the thin film surface or the bottom surface. First, the roughness of the bottom surface of the thin film is the roughness of the substrate surface, and is approximately constant if the substrate is the same. Therefore, in terms of roughness, the surface barrier at the bottom of the thin film is constant. On the other hand, the roughness δR of the thin film surface differs depending on the sample. Therefore, the asymmetry of the surface barrier is expected to change with changes in δR of the thin film surface. When comparing the δR of the thin film surface and the bottom surface, δR of the thin film surface is larger than that of the thin film bottom surface. Therefore, the surface barrier of the thin film is smaller than that of the bottom of the thin film, and magnetic flux easily penetrates from the thin film surface. In particular, Asym. The sign of is negative by definition. And Asym. ^MAX is expected to monotonically decrease (increase in the negative direction) as δR increases.

Figure 46 shows Asym. of IBAD and LAO samples with different δR. Indicates ^MAX . Both the IBAD sample and the LAO sample have Asym. The values of ^MAX were not regular and no clear correlation was confirmed. This result was contrary to the above-mentioned prediction. Therefore, Asym. Let's compare the top three samples with ^MAX of 15% or more. Asym. ^MAX is 29.8%, 20.6%, and 17.6%, δR is 25.5nm, 37.1nm, and 43.6nm, and Asym. The sample with higher ^MAX has smaller δR. This is consistent with the above prediction. The δφ of these samples is 0.82°, 0.93°, and 0.90° C., respectively, and these are also samples with relatively low δφ shown in FIG. 43. Therefore, since the influence of bulk pinning is small in samples with low δφ, Asym. There is a possibility that the correlation between ^MAX and δR has become significant. FIG. 47 also shows the B ^MAX of IBAD and LAO samples with different δR. No clear correlation between B ^MAX and film thickness was confirmed.

[Dependency on film-forming substrate]
Comparing the IBAD and LAO samples, the LAO sample has a higher Asym. There was a tendency for ^MAX to be positively large. The LAO samples had all positive Asym. between 3.8 and 29.8%. ^MAX , IBAD samples have positive or negative Asym. It is ^MAX . First, the difference in the magnitude of the asymmetry is thought to be due to the difference in crystal orientation of the thin film. Comparing the IBAD sample and the LAO sample, the IBAD sample has a large δφ, so many fine defects such as stacking faults are formed inside the thin film, and it is thought that the influence of bulk pinning was large and the asymmetry was small. In the LAO sample, δφ is relatively small and the crystal orientation is good compared to the IBAD sample, so it is thought that the influence of bulk pinning is small and the asymmetry is large. Next, we will discuss the reason why the asymmetry sign was positive in the LAO sample. From the viewpoint of the surface barrier, a positive sign of asymmetry means that, by definition, it is easier for magnetic flux to penetrate from the bottom of the thin film than from the surface of the thin film. As mentioned in the previous section, it is expected that the interface roughness will exhibit negative asymmetry, so it is thought that there is a parameter that has a greater effect on the surface barrier than the interface roughness. One of the parameters is the strain at the bottom of the thin film. The effect of strain will be discussed below. Strain occurs at the bottom of the thin film due to lattice mismatch between the crystal lattices of the substrate and the thin film. Therefore, near the interface of the thin film, T _c decreases and superconductivity is not exhibited. Since the strain is relaxed as the thickness of the thin film increases, a layer with a gradient in T _c is formed. On surfaces with such gradient superconducting parameters, the surface barrier decreases. Therefore, it is thought that the strain at the bottom of the thin film reduces the surface barrier, making it easier for magnetic flux to penetrate from the bottom, resulting in positive asymmetry.

Next, we will discuss the asymmetry of the IBAD sample from the perspective of substrate parameters. Comparing the IBAD-MgO substrate and the LAO substrate, first, the roughness of the IBAD-MgO substrate is greater than that of the LAO substrate. Therefore, contrary to the experimental results, it is predicted that the IBAD sample is more likely to allow magnetic flux to enter from the bottom surface than the LAO sample, and exhibits a positive asymmetry. However, since the effect of strain is greater than the roughness of the bottom surface of the thin film, it is thought that the difference in roughness depending on the substrate had a small effect on the surface barrier. Next, when comparing the magnitude of lattice mismatch between the IBAD-MgO substrate and the SmBCO of the LAO substrate, the lattice mismatch of the LAO substrate is larger than that of the IBAD substrate. Therefore, in the IBAD sample, the strain at the bottom of the thin film is smaller than in the LAO sample, and the surface barrier is larger, so it is considered that magnetic flux is less likely to penetrate from the bottom of the thin film. As a result, the IBAD samples had small positive asymmetry, and depending on the sample, the surface barrier at the bottom surface was larger than the thin film surface due to surface roughness, and it is considered that negative asymmetry was exhibited.

[Brief Summary]
In this example, in order to realize J _c non-reciprocity (I _c asymmetry) of REBCO thin films, SmBCO thin films with various thicknesses were fabricated on two different substrates, an IBAD-MgO substrate and an LAO substrate. , we evaluated the influence of SmBCO thin film structure on its I _c asymmetry. The findings obtained are shown below.
(1) In the IBAD sample, Asym. ^MAX was obtained, but Asym. There was no correlation between the size of ^MAX and the structure of the sample.
(2) The LAO sample has a small δφ and a relatively small δR, and the maximum Asym. ^MAX was obtained.
(3) Asym. It was confirmed that the magnitude of ^MAX has a correlation with δφ. This suggests that in samples with many defects inside the thin film, I _c is determined by bulk pinning at the defects, which alleviates the influence of the surface barrier. Therefore, it was suggested that in order to obtain high asymmetry, it is necessary to reduce the effect of bulk pinning while maintaining the asymmetry of the surface barrier.
(4) When comparing the IBAD sample and the LAO sample, a high degree of asymmetry was obtained in the LAO sample, but this difference in asymmetry is thought to be due to a difference in the orientation of the crystals in the thin film. It is thought that the LAO sample had greater asymmetry because both δω and δφ were smaller than the IBAD sample.
(5) The asymmetry signs of the LAO samples were all positive. Therefore, magnetic flux is more likely to penetrate from the bottom of the thin film than from the surface of the thin film. This suggests that lattice strain due to lattice mismatch at the bottom of the thin film contributes to reducing the surface barrier, and that lattice strain has a greater effect on reducing the surface barrier than the roughness of the thin film surface.

The above results indicate that in order to realize the I _c asymmetry of the SmBCO thin film due to the asymmetry of the surface barrier, it is necessary to alleviate the magnetic flux pinning inside the thin film. Furthermore, if the effect of magnetic flux pinning inside the thin film is small, it is possible to control the asymmetry by controlling the structure of the thin film surface and bottom surface.

[Example 2: Non-reciprocal superconducting properties of SmBCO thin films with various _BaHfO3 addition amounts]
For the development of REBCO high temperature superconducting diodes, asymmetry of I _c according to the current direction in the REBCO thin film is required. It is believed that the I _c asymmetry of the REBCO thin film in an in-plane magnetic field can be realized by the asymmetry in the size of the surface barrier at the surface and bottom of the thin film. From Example 1, it was inferred that bulk pinning caused by defects inside the SmBCO thin film suppressed the I _c asymmetry caused by the asymmetric surface barrier. Based on this result, the following two structures were proposed to realize I _c asymmetry.
・Thin film with few defects that can become pinning centers inside the thin film.
・A thin film with a structure that alleviates magnetic flux pinning inside the thin film.

Regarding the former structure, it is thought that defects generated during thin film fabrication can be reduced to some extent by slow film formation with low supersaturation, but REBCO is an oxide and has a large potential for crystal anisotropy. There are limits to how much defects can be reduced inside the thin film because it contains many defects. For the latter structure, mitigation of bulk pinning by the introduction of nanorods is proposed. BaMO ₃ (BMO: M=metal) is a typical nanorod material. BMO nanorods are introduced parallel to the c-axis of REBCO during vapor phase growth. FIG. 48 shows a schematic diagram of nanorods for quantized magnetic flux. In the magnetic field in the B//c direction, the nanorod and the magnetic field direction are parallel, and the quantized magnetic flux is pinned along the nanorod, so the nanorod becomes an effective pinning center. On the other hand, in the in-plane magnetic field of B//AB, the nanorods and the magnetic field direction are perpendicular, and the nanorods do not function as pinning centers. Rather, it is thought that it acts to promote the movement of the quantized magnetic flux pinned to other defects in the REBCO thin film. In REBCO thin films in which irradiation defects and c-axis correlation pins of BMO nanorods have been introduced, a decrease in J _c in an in-plane magnetic field has been confirmed, and although it is not clear, this is due to the magnetic flux motion promoting effect of the c-axis correlation pins. It could be something. Therefore, it is considered that bulk pinning can be alleviated by introducing BMO nanorods into the REBCO thin film.

This example aimed to realize I _c asymmetry in a REBCO thin film into which BMO nanorods were introduced and to elucidate the thin film structure that contributes to I _c asymmetry. A SmBCO thin film doped with BaHfO ₃ (BHO), which is one of the BMO materials that form nanorods in REBCO thin films, was prepared, and the I _c asymmetry was evaluated. The effects of the crystal orientation, film thickness, surface roughness, film-forming substrate, and amount of BHO added on the I _c asymmetry in an in-plane magnetic field of the BHO-doped SmBCO thin film were evaluated.

[Preparation and properties of thin film]
In order to realize the high non-reciprocal superconducting properties of SmBCO thin films, we prepared BHO-doped SmBCO thin films of various thicknesses and evaluated their thin film structures and basic superconducting properties.

[Preparation of thin film]
Tables 5 and 6 show the conditions for producing the BHO-added SmBCO thin film. A thin film using an IBAD-MgO substrate was produced by a KrF excimer laser, and a thin film using a LaAlO ₃ (LAO) substrate was produced by a PLD method using an Nd:YAG laser. BHO was added using a mixed target method. The amount of BHO added was 3% by volume for the IBAD sample, and 2, 3, 5, and 10% by volume for the LAO sample. The laser energy density was optimized for each additive amount.

[Crystal structure]
XRD measurement confirmed that SmBCO had good c-axis orientation in all samples. FIG. 49 shows δω and δφ of IBAD-BHO3 vol% samples and LAO-BHO3 vol% samples prepared with various film thicknesses. The average value of δω is 0.67° for the IBAD-BHO3 volume% sample and 0.26° for the LAO-BHO3 volume% sample, and the average value of δφ is 1.90° for the IBAD-BHO3 volume% sample, LAO- It was 1.22° for the BHO3 volume % sample. Regarding δω, both the IBAD-BHO 3 volume % sample and the LAO-BHO 3 volume % sample did not change with respect to the film thickness, and exhibited good orientation comparable to that of the Pure sample. Regarding δφ, there were many variations from sample to sample for IBAD-BHO3 volume % samples, and some samples had a value of δφ larger than 1.6° of the CeO ₂ layer of the substrate. Figure 50 shows δω and δφ in LAO samples with various BHO loadings. For reference, the BHO-free sample of Example 1 (LAO-Pure) is also plotted. The average value of δω was 0.32° for the 2 vol% BHO sample, 0.26° for the 3 vol% BHO sample, 0.24° for the 5 vol% BHO sample, and 0.28° for the 10 vol% BHO sample. The average value of δφ was 1.14° for the BHO2 volume% sample, 1.22° for the BHO3 volume% sample, 1.23° for the BHO5 volume% sample, and 1.20° for the BHO10 volume% sample. As for δω, it does not change with respect to the film thickness at all additive amounts and has good orientation. Regarding δφ, the difference in orientation depending on the amount of BHO added is small, but for all addition amounts, there is a large variation from sample to sample when the film thickness is smaller than about 300 nm, but the orientation is lower than when the film thickness is large. I understand that. This is considered to be because when the film thickness is small, the relaxation of crystal lattice strain due to lattice mismatch is small.

[Surface morphology]
FIG. 51 shows surface DFM images of various BHO-doped LAO samples with film thicknesses on the order of 300-400 nm. Unlike the isotropic concentric or polygonal step shape of the additive-free SmBCO thin film shown in Example 1, petal-shaped surface steps were observed at all BHO addition amounts. This is a characteristic step shape observed when nanorods are formed, and from this it is considered that nanorods are formed at least near the thin film surface in the samples with all additive amounts. Moreover, FIG. 52 shows the surface roughness δR of IBAD samples added with 3 volume % BHO prepared with various film thicknesses and LAO samples with various amounts of BHO added. Regarding IBAD samples, there is a large variation in δR from sample to sample. This is thought to be because the film formation rate differed from sample to sample due to the instability of the laser energy. Regarding the LAO sample, δR tended to become relatively large as the film thickness increased.

[T _c and J _c ]
FIG. 53 shows T _c and J _c in a self-magnetic field for LAO samples and IBAD samples with different film thicknesses and various amounts of BHO added. Samples with a thickness of 200 nm or less have large variations in T _c , but most samples with a thickness of 300 nm or more exhibit high characteristics with T _c of 91 K or more and J _c of 1 MA/cm ² or more. Figure 54 shows the Asym. The relationship between ^MAX , T _c , and J _c in the self-magnetic field is shown. Similar to the Pure sample without BHO shown in Example 1, the Asym. No correlation was confirmed between ^MAX and T _c or J _c .

[Magnetic field dependence of J _c ]
FIG. 55 shows the magnetic field dependence of J _c at 77.3 K, B//c for LAO samples with film thicknesses of about 200-300 nm and various added amounts of BHO. For comparison, the magnetic field dependence of J _c of an SmBCO thin film (LAO-Pure) without BHO addition is also shown. Compared to the Pure sample, in the BHO-added sample, J _c is improved in the entire magnetic field region at all BHO addition amounts, and a plateau region in which J _c is slowly attenuated is confirmed. This is considered to be because BHO nanorods are formed in the BHO-added sample and effectively pin the magnetic flux in the B//c direction. Furthermore, the lower the amount of BHO added, the larger the J _c was in a low magnetic field, and the higher the amount of BHO added, the larger the J _c was in a high magnetic field. This suggests that the number density of BHO nanorods increases as the amount of BHO added increases. Since the number density of BHO nanorods increases as the amount of BHO added increases, it is thought that J _c in the high magnetic field region is improved by shifting the matching magnetic field to the high magnetic field side.

[Magnetic field application angle dependence of J _c ]
FIG. 56 shows the dependence of J _c on the magnetic field application angle at 77.3 K and 1-5 T for LAO samples with various BHO addition amounts. A peak in the B//ab direction exists in the samples with all BHO addition amounts. This is considered to be because the stacked structure and stacking faults of the SmBCO crystal lattice function as pinning centers. In addition, the J _c in the B//c direction is greatly improved and has a peak in the samples with all BHO addition amounts. This is considered to be because the BHO nanorods function as pinning centers. In the magnetic field near the plateau termination magnetic field of the J _c -B curve for each BHO addition amount in FIG. 56, the peak in the B//c direction is a relatively large peak compared to the peak in the B//ab direction. It is suggested that continuous nanorods parallel to the c-axis direction are formed at all BHO addition amounts.

Comparing the magnitude of the peak in the B//ab direction depending on the amount of BHO added, at 1T, the peak in the B//ab direction is smaller in the BHO 3 volume % sample than in the BHO 2 volume % sample. In the high magnetic field of 5T, including BHO 5% and 10% by volume samples, the peak in the B//ab direction becomes smaller as the amount of BHO added increases, which is due to the higher density of nanorods. This is thought to be due to the promotion of magnetic flux movement in the //ab direction. On the other hand, the BHO 5% and 10% by volume samples have larger peaks in the B//ab direction at 1T than the 3% by volume BHO samples. This may be due to an increase in stacking faults due to the interfacial strain of the BHO nanorods introduced at a higher density, which may result in enhanced magnetic flux pinning in the B//ab direction.

[J _c nonreciprocity of BHO-doped SmBCO thin film]
In the previous section, we described the crystal structure, surface morphology, and superconducting properties of the fabricated thin film. In this section, we will discuss the correlation between J _c non-reciprocity, magnetic field, crystal orientation, film thickness, surface roughness, film forming substrate, amount of BHO added, and measurement temperature.

[Magnetic field dependence]
FIG. 57 shows the Asym. shows the magnetic field dependence of Figures 58 to 62 show Asym. shows the magnetic field dependence of Asym. of each sample. showed positive or negative peaks in low magnetic fields below 1 T. Figure 63 shows the Asym. The relationship between ^MAX and B ^MAX is shown. In particular, Asym. The B ^MAX of samples with ^MAX greater than 20% was 0.2 T or less, and was concentrated in a relatively low magnetic field. Comparing B ^MAX of positive asymmetry and negative asymmetry, B ^MAX of negative asymmetry is distributed in a lower magnetic field than B ^MAX of positive asymmetry. Comparing the IBAD sample and the LAO sample among the BHO3 volume % samples, the B ^MAX of the IBAD sample is distributed in a lower magnetic field than the B ^MAX of the LAO sample.

Previous research on YBCO thin films in an in-plane magnetic field has also confirmed a positive asymmetry peak below about 0.2 T. However, negative peaks like those confirmed in FIGS. 61 and 62 have not been reported. This is considered to be due to the effect of introducing BHO nanorods. The discussion will be discussed in the following sections.

FIG. 64 shows the dependence of I _c on the magnetic field application angle in the IBAD sample added with 3 volume % of BHO. Since the closer to the B//ab direction, the larger the difference in I _c when comparing symmetrical magnetic field directions, it is inferred that the I _c asymmetry is due to an asymmetric surface barrier.

[Crystal orientation dependence]
Figure 65 shows the Asym. Indicates ^MAX . Moreover, FIG. 66 shows the Asym. Indicates ^MAX . For the LAO sample, Asym. for δω and δφ. No change in ^MAX was confirmed. The increase in the absolute value of asymmetry with a decrease in δφ, which was confirmed in the Pure sample, was not confirmed, so the introduction of nanorods eased the magnetic flux pinning at defects inside the thin film, and the amount of defects inside the thin film decreased. Asym. It is considered that the magnitude of the absolute value of was not changed. Unlike the Pure sample, the IBAD sample has a high Asym. of about 40% even in the sample with a large δφ. ^MAX has been obtained, and the larger δω and δφ, the greater the asymmetry. However, due to the small number of IBAD samples, Asym. A more detailed study is required in the future regarding the relationship between crystal orientation and crystal orientation.

[Film thickness dependence]
FIG. 67 shows the Asym. Indicates ^MAX . Both the IBAD sample and LAO sample are Asym. No clear correlation between ^MAX and film thickness was confirmed. FIG. 68 also shows the B ^MAX of LAO and IBAD samples with different film thicknesses and various BHO loadings. No clear correlation was confirmed between B ^MAX and film thickness.

[Surface roughness dependence]
FIG. 69 shows the Asym. Indicates ^MAX . First, regarding the LAO sample, Asym. A relatively clear correlation between ^MAX and δR was confirmed. Asym. There is a tendency for ^MAX to decrease monotonically. Among them, the larger the amount added, the more Asym. The slope at which ^MAX decreases becomes smaller. In the sample with the largest addition amount of 10% by volume of BHO, Asym. ^MAX has no correlation with δR and remains almost constant at about -10%. Also, in the IBAD-BHO3 volume % sample, Asym. It was confirmed that ^MAX monotonically decreased as δR increased. However, the rate of decrease was smaller in the IBAD sample than in the LAO sample. In addition, Asym. The maximum value of ^MAX is 40.5% at δR=21.8nm, and when comparing LAO samples, the same high Asym. ^MAX was obtained. Asym. The monotonically decreasing tendency of ^MAX is considered to be due to the decrease in the surface barrier of the thin film surface as the surface roughness δR increases.

Figure 70 shows the B ^MAX of LAO and IBAD samples with various BHO loadings at different δR. In the BHO2 volume % and 3 volume % samples exhibiting positive asymmetry, it was confirmed that B ^MAX tends to increase as δR increases. The reason why B ^MAX tends to be large in samples with large δR is considered to be the effect of a barrier (escape barrier) when magnetic flux leaves the superconductor. FIG. 71 shows a schematic diagram of changes in potential energy due to surface roughness and lattice strain. However, details of the potential energy change will be described later. The size of the escape barrier tends to increase as the potential energy of the magnetic flux lines at the interface increases. Therefore, the larger the magnetic field, the larger the escape barrier, and the escape barrier remains even beyond H _s . Of the surface roughness and lattice strain, which are factors that reduce the surface barrier for magnetic flux penetration mentioned above, surface roughness in particular is due to the local concentration of the magnetic field in the concave portions of the thin film surface. It is also thought to be a factor that increases potential energy and increases the escape barrier. That is, depending on the roughness of the thin film surface, the escape barrier at the thin film surface becomes larger than the escape barrier at the bottom surface of the thin film. It is thought that the harder it is for the magnetic flux to escape from the superconductor, the larger _Ic becomes.Asym. The contribution to ^MAX is a shift in the negative direction. This is consistent with the experimental results. From the above, it is thought that samples with large δR tended to have large B ^MAX due to the influence of the escape barrier. On the other hand, the reason why no correlation between B ^MAX and δR was observed in the 5% and 10% BHO samples is considered to be due to the influence of the nanorod number density. Details will be described later.

[BHO addition amount dependence]
Figure 72 shows the Asym. Indicates ^MAX . |Asym. The maximum value of ^MAX | was 32.8% at 2% by volume of BHO, 39.2% at 3% by volume, 16.4% at 5% by volume, and 10.2% at 10% by volume. In addition, Asym. The sign of ^MAX is positive for 2% by volume and 3% by volume, and negative for 5% by volume and 10% by volume. From this, the highest Asym. It was shown that the amount of BHO added to achieve ^MAX was about 3% by volume. Asym. depending on the amount of BHO added. It is inferred that the change in the magnitude and sign of ^MAX is due to the change in the number density of BHO nanorods. This suggests that the nanorods had the effect of reducing the surface barrier. In particular, it is thought that the surface barrier reduction effect of the nanorods was small at the bottom of the thin film and large and significant at the surface of the thin film. One of the reasons for this may be that nanorods are not formed on the bottom surface of the thin film, but to confirm this, it is necessary to observe the cross-sectional fine structure of the thin film. However, many of the previous studies in which BHO was added to SmBCO reported that nanorods were observed penetrating the bottom surface of the thin film, so the BHO nanorods were introduced penetrating through the bottom surface of the BHO-added SmBCO thin film fabricated in this example. There is a high possibility that Therefore, the discussion will be based on the assumption that nanorods also exist at the bottom of the thin film.

First, the effect of reducing the surface barrier by nanorods will be described below. The magnitude of the surface barrier reduction effect by nanorods seems to be related to the coherence length ξ. In this example, the fine structure of the nanorods was not actually observed by TEM observation, etc., but the diameter of BHO nanorods was observed to be about 10 nm in previous research. This is a size close to ξ (ξ _ab ) in the a-b plane direction, which is about 3 nm. Since the thin film production conditions are similar, it is assumed that BHO nanorods with similar diameters are formed in this example as well. The reason why nanorods exhibit strong magnetic flux pinning when parallel to the magnetic field is that nanorods with a magnetic flux of about 2ξ _ab are easily felt as pinning centers. This is considered to be the same with regard to magnetic flux penetration and promotion of magnetic flux motion when the nanorods are perpendicular to the magnetic field. When nanorods exist at the interface of a thin film, it is thought that in a low magnetic field, the magnetic flux bends and penetrates along the nanorods, as shown in the figure. Therefore, it is considered that when the size of 2ξ _ab is close to the diameter of the nanorod, the effect of promoting magnetic flux penetration becomes large, and the reduction of the surface barrier becomes large.

Next, we will discuss the difference in the surface barrier reduction effect of nanorods on the surface and bottom of the thin film. The difference in the surface barrier reduction effect of the nanorods on the surface and bottom of the thin film is thought to be due to the difference in the size of ξ between the surface and bottom of the thin film. According to GL theory, the coherence length ξ changes depending on T _c as expressed by the following equation.
At the bottom of the thin film, lattice distortion occurs due to lattice mismatch with the substrate, so T _c is low, that is, ξ is large compared to the surface of the thin film. Therefore, since the magnitude of ξ with respect to the nanorod diameter is large at the bottom surface of the thin film, the effect of promoting magnetic flux penetration by the nanorods is small, and it is considered that the reduction in the surface barrier is small. From the above, the factors for reducing the surface barrier in the BHO-doped SmBCO thin film can be summarized as shown in Table 7 and FIG. 73. First, since the bottom surface of the thin film has small roughness and the effect of nanorods is also small, the main factor in reducing the surface barrier on the bottom surface of the thin film is lattice strain. Therefore, if the substrate is the same, there is no difference in the surface barrier of the bottom surface of the thin film depending on the sample, and it can be said that it is constant. On the other hand, there are two main factors for reducing the surface barrier on the thin film surface: surface roughness and nanorods, which are parameters that vary in size depending on the sample.

Taking these things into consideration, the Asym. The reversal of the sign of ^MAX will be explained. Asym. Focusing on the sign of ^MAX and the asymmetry of the surface barrier, Asym. From the definition of positive Asym. indicates that the barrier on the surface of the thin film is larger than the barrier on the bottom surface. Asym. The opposite is true when is negative. First, in the case of low addition of BHO, as in the Pure sample, the surface barrier of the bottom surface is small due to the strain on the bottom surface of the thin film, so the positive Asym. Indicates ^MAX . On the other hand, the higher the addition of BHO, the higher the number density of nanorods, so the effect of reducing the surface barrier on the thin film surface increases, and the surface barrier on the thin film surface becomes smaller. Asym. The sign of ^MAX is reversed to negative.

Asym. The decrease in the rate of decrease in ^MAX is also considered to be due to the increase in nanorod number density. Among the factors that reduce the surface barrier on the thin film surface, the effect of reducing the surface barrier due to δR is dominant at a low nanorod number density. On the other hand, at a high nanorod number density, the effect of reducing the surface barrier by the nanorods becomes dominant, so it is thought that the change in asymmetry with respect to δR becomes small. From the above, the Asym. It is thought that the rate of decrease in ^MAX has decreased. Furthermore, for the same reason, it is considered that no correlation between B ^MAX and δR was confirmed in the BHO-rich sample.

[Dependency on film-forming substrate]
Comparing the IBAD sample and the LAO sample from FIG. 70, it was confirmed that the IBAD sample had a smaller rate of decrease in asymmetry with respect to δR than the LAO sample. The degree of lattice mismatch of CeO ₂ and LAO on the surface of the IBAD-MgO substrate with SmBCO is 0.64% and 1.44%, respectively, and when comparing the magnitude of lattice strain on the bottom surface of the thin film depending on the type of substrate, LAO Since the lattice mismatch and lattice strain are smaller in the IBAD sample than in the sample, the IBAD sample is expected to have less asymmetry than the LAO sample. However, this contradicts the results. Therefore, it is considered that this change in asymmetry is not due to a difference in the film-forming substrate. Comparing the film formation conditions of the IBAD sample and the LAO sample, the film formation rate of the IBAD sample is about four times slower than that of the LAO sample. Therefore, it is considered that nanorods with a larger diameter are formed in the IBAD sample than in the LAO sample. Therefore, since the nanorod diameter was closer to 2ξ in the IBAD sample than in the LAO sample, it is considered that the surface barrier reduction effect by the nanorods was large and the asymmetry was positively large.

[Temperature dependence]
Figure 74 shows the Asym. Indicates ^MAX . Moreover, FIG. 75 shows the Asym. Indicates ^MAX . For the BHO2 volume %, 3 volume %, and 5 volume % samples, many samples showed Asym. A change in ^MAX was confirmed. In many cases, Asym. The magnitude of ^MAX decreased from positive to negative as the temperature went from low to high in the order of 65.0, 77.3, and 85.0K. However, although not shown in the figure, in the region lower than 65.0K, Asym. It has been confirmed that the absolute value of ^MAX tends to decrease. This is considered to be because the influence of the surface barrier becomes less obvious as the magnetic flux pinning due to minute defects inside the thin film increases as the temperature decreases.

Asym. Let us consider the reason why ^MAX shifted in the negative direction. One possible reason for the positive asymmetry to approach zero is due to the approach to T _c . Since _Ic approaches zero regardless of the current direction, Asym. It is considered that the absolute value of ^MAX decreases. However, most of the samples produced in this example had a T _c of over 90K, which is far from the maximum measurement temperature of 85K, so this is unlikely to be the main factor. Also, this is a positive to negative Asym. Reversal of the sign of ^MAX and negative Asym. I cannot explain the improvement in ^MAX . The next consideration is the factor of temperature change in the magnetic field entry length λ. λ changes depending on the temperature as expressed by the following formula.
Therefore, the higher the temperature, the larger λ becomes. λ (λ _c ) in the c-axis direction at 77.3K is about 90 nm. In contrast, the surface roughness δR is approximately 15-90 nm. Further, the critical film thickness of SmBCO is approximately 2-10 nm at the SmBCO, CeO ₂ and LAO interfaces. Therefore, the magnitude of lattice strain is considered to be small compared to surface roughness. Particularly at high temperatures, the non-superconducting region (dead layer) below _Tc becomes thicker, so the effective strain region becomes smaller. Furthermore, it is considered that the smaller the size of these surface structures is relative to λ, the smaller the contribution to the surface barrier, which is electromagnetic interaction. Therefore, at high temperatures where λ is large, the surface barrier reduction effect due to lattice strain becomes small. On the other hand, the surface barrier reduction effect due to surface roughness remains even at high temperatures compared to the effect due to lattice strain. Furthermore, considering that nanorods also have a surface barrier reduction effect on the thin film surface, the higher the temperature, the larger the surface barrier at the bottom of the thin film relative to the surface barrier at the thin film surface becomes. It is considered that a shift of ^MAX in the negative direction has occurred. Moreover, such an asymmetry change is caused by the Asym. It is thought that this also caused an inversion of ^{the MAX} sign. In some samples, Asym. Reversal of ^MAX sign has been confirmed.

Asym. Regarding the cause of the reversal of ^{the MAX} sign, it is also possible that the interaction between magnetic fluxes is the cause. It has been reported in many cases that the asymmetry of the magnetic flux motion due to the interaction between magnetic fluxes is reversed with respect to the measured temperature and magnetic field, in relation to the width d of the potential barrier and the density of the quantized magnetic flux. These reversals occur because the quantized magnetic flux overcomes the pinning potential due to the repulsion between the magnetic fluxes, thereby changing the easy direction of the magnetic flux motion. However, in order for the reversal to occur, it is assumed that the magnetic flux interstitial distance is smaller than d. The surface roughness of the sample in which reversal was observed in this example was approximately 30 nm. The magnitude of the magnetic field that provides this level of magnetic flux lattice distance is approximately 2T, assuming a triangular lattice. However, in the B//ab direction, the magnetic flux lattice is distorted by the layered structure of SmBCO, so the actual value of the magnetic field is smaller than this. From the anisotropy of λ, it is thought to be about 1/3, about 0.6T. However, in this embodiment, Asym. The value of B ^MAX of the sample in which the sign of ^MAX was reversed was about 0.2T, which is smaller than 0.6T, so Asym. It is considered that the reversal of the sign of ^MAX is not due to interaction between magnetic fluxes.

For the 10 volume % sample with high BHO addition, Asym. The change in ^MAX was small. The reason for this is thought to be that, due to the large number density of nanorods, nanorods were the dominant factor in reducing the surface barrier on the thin film surface, and the influence of surface roughness was small. In other words, with high addition of BHO, Asym. It is thought that along with the decrease in the correlation change with ^MAX roughness, the correlation change with temperature due to roughness also decreased.

FIG. 76 shows B ^MAX in LAO samples with various BHO loadings under various measurement temperature conditions. Regardless of the amount of BHO added, it was confirmed that in most samples, the higher the measurement temperature, the lower the B ^MAX . This is thought to be because the magnetic field at which the surface barrier is effective decreases as the temperature increases. The magnetic field H _s when the magnetic flux enters the superconductor is related to H _c1 . In particular, in the Bean-Livingston surface barrier model, H _s on an ideal surface is derived as follows.
Further, the lower critical magnetic field H _c1 depends on λ as described below and changes with temperature.
Therefore, the higher the temperature, the smaller H _c1 becomes, and therefore the smaller H _s becomes. Therefore, it is thought that B ^MAX decreased because the magnetic field in which the surface barrier is effective decreases as the temperature increases.

[Consideration of surface roughness and lattice strain for surface barrier]
From the results in the previous section, it was inferred that the thin film surface roughness δR and lattice strain contributed to the reduction of the surface barrier. In this section, we will discuss the contribution of each thin film structure to the surface barrier. Here, the potential U(x) with respect to the distance x from the superconductor surface is expressed by the following equation as described above.
The first term represents the self-energy of the magnetic flux lines, the second term represents the attractive potential due to the interaction between the magnetic flux lines and the mirror image, and the third term represents the repulsive potential due to the external magnetic field.

First, it is thought that the contribution of δR to the reduction of the surface barrier is mainly due to local magnetic field concentration due to the dense quantized magnetic flux in the uneven surface portion. FIG. 77 shows a schematic diagram of magnetic field concentration due to δR. An increase in local magnetic field concentration corresponds to an increase in H in the third term (U ₃ ) in the above equation. Therefore, an increase in δR contributes to an increase in _U3 . Figure 78 shows a schematic diagram of the change in _U3 and U(x) with δR. An increase in δR increases the magnetic field H and increases U ₃ . It is thought that this makes the slope of U(x) gentler and reduces the surface barrier. For example, F. Bass et al. derived the magnetic field dependent term ΔU _H of the surface barrier of a superconductor surface with roughness σ as shown in the following equation, and confirmed that the surface barrier decreases as σ increases. FIG. 79 shows a relationship diagram between ΔU _H and σ using the formula.

On the other hand, lattice strain contributes to lowering the T _c of superconductors. Since λ increases due to a decrease in T _c , this is considered to contribute to a decrease in the first term (U ₁ ) and second term (U ₂ ) in the above equation. FIG. 80 shows a schematic diagram of changes in U ₁ , U ₂ and U(x) due to δR. It is believed that the gradient reduction of U ₁ and U ₂ makes the gradient of U(x) gentler and reduces the surface barrier.

[Brief Summary]
In this example, in order to realize I _c non-reciprocity (I _c asymmetry) of REBCO thin films, SmBCO thin films with various thicknesses were fabricated on two different substrates, an IBAD-MgO substrate and an LAO substrate. , we evaluated the influence of SmBCO thin film structure on its I _c nonreciprocity. The findings obtained are shown below.
(6) SmBCO thin films containing 2, 3, 5, and 10% by volume of BHO were prepared. At J _c in a magnetic field of 77.3 K in the B//c direction, the higher the addition of BHO, the greater the improvement in J _c in the high magnetic field. Furthermore, a relatively large peak was observed in the B//c direction in the dependence of the angle of application of the J _c magnetic field at 77.3K. These results suggested that continuous BHO nanorods were introduced in the c-axis direction at a number density that corresponded to the amount of each added.
(7) In the BHO-added sample, Asym. No decrease in ^MAX was confirmed. This is considered to be because the magnetic flux pinning caused by defects inside the thin film was alleviated by the nanorods.
(8) Among the LAO samples, the maximum Asym. It showed ^MAX 39.2%. It was shown that the optimum addition amount to achieve high asymmetry of the BHO-doped SmBCO thin film was 3% by volume. The IBAD-BHO 3% by volume sample also had the same maximum Asym. It showed ^MAX 40.5%.
(9) Asym. A tendency for ^MAX to decrease monotonically was confirmed. This is considered to be because the surface barrier of the thin film surface was lowered due to surface roughness.
(10) Asym. The rate of decrease in ^MAX decreased as the amount of BHO added increased. The sample containing 10% by volume of BHO had almost constant Asym. regardless of δR. It showed ^MAX . This is considered to be because the effect of δR was dominant as a factor for reducing the surface barrier on the thin film surface when BHO was low added, but as the number density of nanorods increased, the effect of nanorods became dominant.
(11) Asym. ^MAX is all positive, Asym. ^MAX is positive or negative depending on the sample, and Asym. ^MAX was all negative. This shift in the negative direction of the asymmetry with respect to the increase in the amount of BHO added is considered to be due to an increase in the surface barrier reduction effect of the thin film surface as the number density of nanorods increases.
(12) It seems that the reduction of the surface barrier by the nanorods had a large effect on the surface of the thin film, but the effect was small on the bottom of the thin film. This is considered to be because the coherence length ξ is large because T _c is low at the bottom of the thin film.
(13) Asym. It was confirmed that ^MAX tends to shift in the negative direction as the measurement temperature increases. In addition, some samples showed a reversal of the sign of the asymmetry. Furthermore, it was confirmed that B ^MAX tends to decrease as the measurement temperature increases. These are considered to be caused by temperature changes in the magnetic field penetration depth λ.
(14) The contribution of δR to the reduction of the surface barrier is thought to be due to local magnetic field concentration due to the dense quantized magnetic flux in the surface unevenness. Therefore, it is considered that δR contributes to an increase in the repulsive potential due to the external magnetic field and reduces the surface barrier. On the other hand, lattice strain contributes to lowering the T _c of superconductors. Therefore, the lattice strain is thought to contribute to the reduction of the self-energy of the magnetic flux lines and the attractive potential due to the interaction between the magnetic flux lines and their mirror images, thereby reducing the surface barrier.

The above results suggested that the parameters contributing to the magnitude of I _c asymmetry due to the asymmetric surface barrier in the BHO-doped SmBCO thin film are the thin film surface roughness, nanorods, and strain at the substrate interface. It was also shown that a high positive I _c asymmetry can be achieved by reducing the roughness of the thin film surface with a low addition of BHO3 volume %. Furthermore, it was suggested that the I _c asymmetry could be further improved by further flattening the surface of the SmBCO thin film.

[Example 3: Non-reciprocal superconducting properties of SmBCO thin film surface-treated by reactive ion etching]
For the development of REBCO high temperature superconducting diodes, non-reciprocity of J _c (asymmetry of I _c ) depending on the current direction of the REBCO thin film is required. One way to achieve I _c asymmetry is to utilize the asymmetric surface barrier of REBCO thin films. In Example 2, it was suggested that by reducing the surface roughness of the REBCO thin film, the surface barrier on the thin film surface was reduced and a large I _c asymmetry could be realized. Therefore, it is expected that the asymmetry of I _c will be improved by further reducing the surface roughness of the REBCO thin film and making it planar. In Example 2, a sample with small surface roughness was obtained by making the film thickness relatively thin. However, in order to ensure current capacity, it is necessary to improve the asymmetry of I _c even in a thick thin film. In addition to film thickness control, the following method can be considered as a method for planarizing the REBCO thin film.
- Flattening during thin film fabrication by depositing REBCO in layers layer-by-layer.
・Flattening of the thin film surface by etching.

The former method requires appropriate selection and control of many parameters, such as the lattice constant and surface condition of the substrate, and control of supersaturation and oxygen partial pressure during thin film fabrication. On the other hand, it is thought that the latter method can be easily processed by post-processing the produced thin film. Etching of the REBCO thin film requires a process that does not cause any physical damage such as cracks to the REBCO thin film during etching, and does not cause any chemical reaction between REBCO and the etching mediator, which does not deteriorate the superconducting properties. is necessary. Therefore, dry etching that does not use liquid chemicals is considered to be superior. However, it is necessary to select optimal conditions so as not to damage the thin film. One of the dry etching methods is reactive ion etching (RIE). RIE is an etching method using gas using plasma, and is the main processing method for semiconductor devices.

In this example, the purpose of this embodiment was to improve the I _c asymmetry by flattening the surface of the REBCO thin film by etching it. RIE was selected as the etching method, and the I _c asymmetry was improved by applying RIE to the SmBCO thin film. The RIE conditions of etching intensity and etching time were investigated, and the effects on the surface structure and I _c asymmetry of the SmBCO thin film were evaluated.

[Surface processing by reactive ion etching]
In this example, for the purpose of improving the non-reciprocal superconducting properties of the SmBCO thin film, the SmBCO thin film was subjected to surface processing by RIE, and the surface structure and changes in T _c and J _c before and after etching were evaluated.

[Reactive ion etching conditions]
The prepared SmBCO thin film was fabricated on a LaAlO ₃ (LAO) substrate by the PLD method using an Nd:YAG laser. Three samples were prepared in one film formation, and RIE processing was performed on two of them. The remaining sample was not subjected to RIE processing and was evaluated as a comparative sample. Table 8 shows the RIE etching conditions. The sample was placed on a quartz plate and etched. The etching gas conditions were kept constant, and the etching intensity and time were varied. The etching gas conditions were set with reference to the conditions used for Si etching by RIE. As etching samples, an additive-free SmBCO thin film (Pure sample) and a BHO-added SmBCO thin film (3 volume % BHO sample and 5 volume % BHO sample) with a film thickness of 600 to 1000 nm were used.

[Change in crystallinity]
FIG. 81 shows the c-axis length after oxygen annealing after etching of the sample with T _c >90K after etching and the superconducting non-transition sample. It was confirmed that the c-axis length of the sample that did not undergo superconducting transition after etching was extended. Therefore, the reason why superconducting transition did not occur due to etching is considered to be due to oxygen vacancies. However, since superconducting transition did not occur even in samples with a relatively small degree of elongation of the c-axis length, it is possible that the cause is other than oxygen vacancies.

[Change in surface morphology]
FIG. 82 shows surface DFM images of the additive-free SmBCO thin film (Pure) before and after etching under various intensity and time conditions. FIG. 83 shows surface DFM images of a BHO-doped SmBCO thin film (3 and 5 volume % BHO) before and after etching under various intensity and time conditions. Regarding the Pure sample, it was confirmed that as the etching intensity or etching time increased, fine holes with a diameter of several tens to hundreds of nanometers and a depth of 2 to 5 nm were formed on the thin film surface. In particular, when the etching strength was high at P=300W, the surface was covered with many craters and had a rough surface. When compared under the same etching conditions, it can be seen that the number of holes in the BHO-added sample is greater than in the Pure sample. Furthermore, in the BHO-added sample, in addition to the fine holes confirmed in the Pure sample, relatively large holes with a diameter of about several hundred nm and a depth of several tens to several hundred nm are also formed. FIG. 84 shows changes in δR (ΔRMS) before and after etching in samples etched at various intensities P and times t=30 minutes. FIG. 85 shows the ΔRMS for samples etched at various times t and with an intensity P=150W. Here, in order to take into account the roughness due to the presence of holes generated by etching, and due to the influence of precipitates and problems with resolution, the evaluation of δR was performed in a relatively narrow area of 4 nm square. Note that ΔRMS is the value of the difference obtained by subtracting δR before etching from δR after etching. In other words, if ΔRMS is negative, δR decreases, indicating that the thin film surface is flattened. Conversely, if ΔRMS is positive, it means that δR is increasing. First, regarding the etching strength, it can be seen that ΔRMS decreases the most at P=150W, indicating flattening. However, when P=200W or more, the decrease in ΔRMS decreases, and when P=300W, it increases, and the thin film surface becomes rough. This is considered to be because as the etching intensity increases, fine holes are generated on the thin film surface and increase in number. Furthermore, with respect to the etching time, in the same sample, ΔRMS decreased as the etching time increased, and the surface of the thin film became more planarized as the etching time increased. It is believed that the increase in roughness due to holes was small because the increase in the number of holes due to the increase in etching time up to 120 minutes was smaller than that due to the increase in etching intensity.

The reason why holes are formed on the surface of the thin film will be explained. Since the etched area is uniform, it is thought that the formation of holes is due to preferential etching of areas with weak atomic bonding strength. Possible weak points include dislocation defects in the SmBCO crystal or the BHO nanorod interface in the BHO-added sample. The diameter of the hole in the Pure sample is relatively small, and it is presumed that this hole was formed by cutting away the dislocation portion. On the other hand, in the BHO-added sample, in addition to small holes, many relatively large holes, which are not observed in the pure sample, are also formed. Therefore, it is thought that the relatively large holes seen in the BHO sample were formed by cutting away the nanorod portion.

[Changes in T _c and J _c ]
FIG. 86 shows the T _c of Pure samples and BHO added samples etched at various intensities P. T _c is almost constant until P = 150 W, but T _c drops significantly below 77.3 K at 200 W or more. In addition, FIG _. 87 shows the J _c (J _c /J _cas ^depo. ). For the Pure sample, up to P=150W, J _c does not change depending on the presence or absence of etching. On the other hand, for the BHO-added sample, it can be seen that J _c decreases at P=150W. In particular, the decrease in J _c is large in the sample with a high addition of 5% by volume of BHO. From the above, it was shown that the etching strength that can maintain the superconducting properties of the SmBCO thin film at 77.3K is about 100-150W when the etching time is 30 minutes. FIG. 88 shows the T _c of Pure and BHO-doped samples etched at various times t. It can be seen that T _c does not decrease until t = 30 minutes, but after t = 30 minutes, T _c decreases to below 85K. Therefore, it was shown that at an etching intensity of 150 W, the etching time that can maintain the superconducting properties of the SmBCO thin film at 77.3 K is up to about 60 minutes.

Since the decrease in T _c and J _c occurs as the etching intensity or etching time increases, the etching process is considered to be the cause. A possible cause of the decrease in T _c and J _c is an increase in temperature due to high-energy ion bombardment. It is thought that oxygen in SmBCO diffused due to the temperature rise, causing oxygen vacancies. The fact that the c-axis length of the sample that no longer undergoes superconducting transition due to etching is extended also suggests that oxygen in SmBCO is deficient and the sample is in an underdoped state. If the deterioration of superconducting properties is due to oxygen vacancies, improvement can be expected by optimizing the oxygen annealing conditions. Further, as improvements in etching, there are a method of using intermittent etching to suppress temperature rise, and a method of cooling the sample using a refrigerant.

[J _c non-reciprocity of SmBCO thin film surface-treated by reactive ion etching]
J _c nonreciprocity (I _c asymmetry) of SmBCO thin films subjected to RIE processing under various etching conditions (intensity and time) was evaluated. Changes in I _c asymmetry due to consideration of each etching condition will be described.

[Etching strength dependence]
FIG. 89 shows the Asym. Indicates ^MAX . As shown in the previous section, the sample etched at P=200W or more did not show superconducting transition at 77.3K, so 150W is the maximum value of P. For both the Pure sample and the BHO-added sample, almost no change was observed at P=100W, but Asym. It was confirmed that ^MAX becomes positively large. This is considered to be because δR was reduced by etching, which suppressed the reduction in the surface barrier on the thin film surface. Moreover, FIG. 90 shows Asym. of the same sample. A diagram in which ^MAX and δR are plotted on the horizontal axis is shown. The smaller δR is, the more Asym. A tendency for ^MAX to become positively large was generally confirmed. From the above, it was confirmed that RIE processing with an etching time of 30 minutes and an etching intensity of 150 W tends to improve the I _c asymmetry of the SmBCO thin film at 77.3K.

[Etching time dependence]
FIG. 91 shows the Asym. Indicates ^MAX . At t=60 minutes, Asym. Although ^MAX increased positively, Asym. ^MAX has decreased. Asym. at t=60 minutes. The positive increase in ^MAX is considered to be due to the suppression of the reduction in the surface barrier on the thin film surface due to etching. On the other hand, Asym. The decrease in ^MAX is considered to be due to T _c decreasing to 78.0K, which is very close to the measured temperature of 77.3K. Based on the above, it was confirmed that RIE processing at an etching intensity of 150 W and an etching time of 30 to 60 minutes tends to improve the I _c asymmetry of the SmBCO thin film at 77.3K.

[Brief Summary]
In this example, in order to improve the J _c non-reciprocity (I _c asymmetry) of the REBCO thin film, the SmBCO thin film fabricated on the LAO substrate was subjected to surface processing by RIE, and the surface structure of the SmBCO thin film and the I _c non-reciprocity were improved. The effects on reciprocity were evaluated. Etching intensity and etching time were investigated as etching conditions. The findings obtained are shown below.
(15) In the Pure sample, the surface roughness of the thin film surface decreased as the etching intensity increased. However, when the etching strength was 300 W, the surface appeared to be covered with many craters, and the roughness increased. Furthermore, the surface roughness of the thin film surface decreased as the etching time increased. Therefore, it was shown that the surface of the thin film was flattened by surface processing by RIE. However, the surface roughness of the BHO-added sample increased slightly due to the formation of relatively large holes.
(16) As the etching intensity increased, fine holes were formed on the thin film surface. Further, even with an increase in etching time, fine holes were formed on the surface of the thin film. In the BHO-added sample, many holes with larger diameters were formed compared to the Pure sample. It is thought that these were formed by cutting dislocation defects or nanorod parts in the SmBCO thin film.
(17) As the etching intensity and etching time increased, the superconducting properties of T _c and J _c deteriorated. In particular, the deterioration was greater in the BHO-added sample than in the pure sample. This may be due to the temperature increase due to ion bombardment or the formation of holes.
(18) In both the Pure sample and the BHO-added sample, the I _c asymmetry improved by 77.3 K at an etching time of 30 minutes and an etching intensity of 150 W. In the Pure sample, the I _c asymmetry improved to 77.3 K even at an etching strength of 150 W and an etching time of 60 minutes. This improvement in I _c asymmetry is considered to be due to the reduction in surface roughness of the thin film surface.

The above results suggest that the I _c asymmetry is improved by the asymmetric surface barrier in the SmBCO thin film subjected to RIE processing. This improvement is thought to be due to flattening of the thin film surface. Furthermore, as the optimum etching conditions for improving I _c asymmetry at 77.3K, an etching intensity of 150 W and an etching time of 30 to 60 minutes were found.

[Example 4: Non-reciprocal superconducting properties of SmBCO thin film with seed layer introduced]
For the development of REBCO high-temperature superconducting diodes, J _c nonreciprocity (I _c asymmetry) depending on the current direction of the REBCO thin film is required. It is believed that the I _c asymmetry of the REBCO thin film in an in-plane magnetic field can be realized by the asymmetry in the size of the surface barrier at the surface and bottom of the thin film.

In Example 3, an attempt was made to improve the I _c asymmetry by controlling the thin film surface structure by subjecting the SmBCO thin film to surface processing using reactive ion etching. On the other hand, the results of Examples 1 to 3 suggested that magnetic flux penetration in the in-plane magnetic field of SmBCO thin films with no or low addition of BHO is dominated by penetration from the bottom surface rather than from the thin film surface. Therefore, it was inferred that the lattice strain caused by the lattice mismatch at the substrate interface had a large effect of reducing the surface barrier at the bottom of the thin film. From this, it is expected that I _c asymmetry can also be controlled by controlling the strain at the bottom of the thin film. However, it is necessary to discuss in more detail whether the reduction of the surface barrier at the bottom of the thin film is due to lattice strain.

The magnitude of lattice strain at the bottom of the thin film depends on the magnitude of lattice mismatch between the thin film crystal and the substrate crystal. Therefore, it is considered that the lattice strain at the bottom of the thin film is alleviated by introducing a material having a lattice constant close to that of the thin film crystal and a small lattice mismatch as the seed layer. FIG. 92 shows a schematic diagram of introducing a seed layer. It is thought that the influence of lattice strain on the surface barrier can be discussed by evaluating the I _c asymmetry of a thin film incorporating such a seed layer. Furthermore, by relaxing the lattice strain at the bottom of the thin film, it is expected that reduction in the surface barrier at the bottom of the thin film will be suppressed. In other words, by introducing the seed layer with small lattice mismatch, the negative asymmetry Asym. is expected to improve.

PrBa ₂ Cu ₃ O _y (PrBCO) is a candidate for the seed layer material of the SmBCO thin film. PrBCO is the same rare earth oxide as SmBCO and has a layered perovskite structure, but it does not exhibit superconductivity and has a lattice constant very close to that of SmBCO, so the lattice mismatch is very small at 0.26%. Additionally, there are reports of producing an Upper layer of YBCO or SmBCO on a PrBCO Seed layer.

This example aimed to elucidate the thin film bottom structure that contributes to the I _c asymmetry of REBCO thin films, and to control and improve the I _c asymmetry by controlling the bottom structure. By introducing PrBCO, which has a very small lattice mismatch, as a seed layer, the lattice strain at the bottom of the SmBCO thin film was alleviated. Then, the influence of the PrBCO seed layer on the I _c asymmetry in the in-plane magnetic field of the SmBCO thin film was evaluated.

[Preparation of thin film]
We investigated the conditions for forming the PrBCO Seed layer and SmBCO Upper layer. We also evaluated the thin film structure and basic superconducting properties.

[Preparation of PrBCO Seed layer]
The surface morphology and crystal orientation of the Seed layer greatly affect the crystal orientation and superconducting properties of the Upper layer. This section describes the conditions for manufacturing the PrBCO seed layer. Table 9 shows the conditions for producing the PrBCO Seed layer on the LaAlO ₃ (LAO) substrate. In order to search for the optimum deposition substrate temperature for the PrBCO Seed layer, deposition was performed while varying the deposition substrate temperature from 780 to 860°C.

FIG. 93 shows a surface DFM image of the PrBCO Seed layer fabricated on the LAO substrate. Two-dimensional nucleus growth of PrBCO was confirmed at all deposition substrate temperatures. Moreover, it was confirmed by XRD measurement that PrBCO was oriented along the c-axis at all film-forming substrate temperatures. FIG. 94 shows δω and δφ of the PrBCO Seed layer deposited at each deposition substrate temperature. Both δω and δφ showed the smallest values at 860°C. Therefore, it was confirmed that PrBCO exhibits the best biaxial orientation at 860°C. Therefore, in this example, 860° C. was selected as the substrate temperature for forming the PrBCO Seed layer. Note that this temperature condition was the same as the temperature of the film-forming substrate for SmBCO without using a seed layer.

[Preparation of SmBCO Upper layer]
A PrBCO Seed layer was formed on the LAO substrate at a film formation substrate temperature of 860°C, and then an SmBCO Upper layer was formed at 860°C. In a sample with an Upper layer thickness of 150 nm, T _c was 89.6 K and 77.3 K, and J _c of the self-magnetic field was 140 kA/CM ² , showing lower superconducting properties than the SmBCO thin film that does not use a seed layer. . The reason for this was thought to be that Pr diffused into the SmBCO Upper layer and _Tc decreased, so samples were prepared with film thicknesses of 200, 300, and 600 nm, but superconducting transition was confirmed in all of them. There wasn't. Next, an attempt was made to fabricate a sample in which the temperature of the substrate on which the Upper layer was formed using the LTG method was lowered. A sample was prepared by keeping the temperature of the Seed layer deposition substrate at 860°C and setting the Upper layer deposition substrate temperature to 780°C. When fabricated with film thicknesses of 200, 300, and 600 nm, _Tc decreased as the film thickness increased, to 88.4, 50.0, and 44.6K, respectively. The highest T _c of the sample with a film thickness of 100 nm is 77.3 K, and the self-magnetic field J _c is 2.0 kA/CM ² . Even in the LTG sample, the superconductivity is lower than that of the SmBCO thin film that does not use a seed layer. Ta.

Furthermore, since it has been reported that SmBCO was fabricated on an IBAD-MgO substrate while maintaining its superconducting properties, we attempted to fabricate an SmBCO thin film with a PrBCO seed layer introduced using an IBAD-MgO substrate. The manufacturing conditions are shown in Table 10.

FIG. 95 shows the T _c of PrBCO Seed layer-introduced SmBCO thin films (IBAD-PrBCO-Pure samples) fabricated on IBAD-MgO substrates at various film thicknesses. FIG. 96 shows the J _c of PrBCO Seed layer-introduced SmBCO thin films (IBAD-PrBCO-Pure samples) fabricated on IBAD-MgO substrates with various film thicknesses. Although almost the same T _c was obtained regardless of the film thickness, it was confirmed that J _c tended to decrease as the film thickness increased. It is thought that the reason for the decrease in J _c is that the diffusion of Pr into the SmBCO Upper layer increased due to the longer film formation time, but a more detailed evaluation is required in the future.

[J _c non-reciprocity of SmBCO thin film with PrBCO introduced as a seed layer]
In the previous section, the manufacturing conditions and superconducting properties of the PrBCO Seed layer and SmBCO Upper layer were described. In this section, we will discuss the correlation between J _c nonreciprocity and surface roughness, and the effect of the seed layer.

[Film thickness dependence]
FIG. 97 shows the Asym. Indicates ^MAX . For reference, an LAO-Pure sample and an IBAD-Pure sample without the seed layer of Example 1 are also shown. Similar to the Pure sample without a seed layer, the IBAD-PrBCO-Pure sample is Asym. No clear correlation between ^MAX and film thickness was confirmed. Figure 98 shows the B ^MAX of IBAD-PrBCO-Pure samples with different film thicknesses. No clear correlation was confirmed between B ^MAX and film thickness.

[Surface roughness dependence]
Figure 99 shows the Asym. Indicates ^MAX . LAO-Pure and IBAD-Pure samples without a seed layer are also shown. Similar to the Pure sample without a seed layer, the IBAD-PrBCO-Pure sample is Asym. No clear correlation between ^MAX and film thickness was confirmed. Figure 100 shows the B ^MAX of PrBCO Seed samples with different δR. No clear correlation was confirmed between B ^MAX and film thickness.

[Effects of introducing PrBCO Seed layer]
Figure 101 shows Asym. The relationship between ^MAX and the degree of lattice mismatch is shown. The horizontal axis plots the lattice mismatch between SmBCO and the interface material. The interfacial materials are LAO for LAO-Pure samples, CeO ₂ for IBAD-Pure samples, and PrBCO for IBAD-PrBCO samples. The lattice mismatches of LAO, CeO ₂ , and PrBCO with SmBCO are calculated to be 1.44%, 0.64%, and 0.26% from their respective lattice constants. As the lattice mismatch degree increases, Asym. A tendency for ^MAX to increase in the positive direction was confirmed. From this, it can be seen that the lattice distortion due to lattice mismatch is Asym. It was suggested that it greatly contributed to ^MAX . Furthermore, this tendency is considered to be due to the fact that as the lattice mismatch at the substrate interface increases, the lattice strain increases and the surface barrier at the bottom of the thin film decreases. When considering the material for the seed layer, since PrBCO has a very small lattice mismatch with SmBCO, even if a material with a smaller lattice mismatch can be used, a negative Asym. ^MAX may reach a plateau. On the other hand, by introducing a material having a large lattice mismatch with SmBCO into the Seed layer, positive Asym. It is expected that ^MAX will be improved. FIG. 102 shows Asym. The relationship between ^MAX and B ^MAX is shown. No change in B ^MAX due to the interface material was confirmed.

[Brief Summary]
In this example, we fabricated an SmBCO thin film in which PrBCO was introduced as a seed layer, with the aim of elucidating the thin film bottom structure that contributes to the I _c asymmetry of REBCO thin films, and controlling and improving the I _c asymmetry by controlling the bottom structure. We then evaluated the influence of the SmBCO bottom structure on its I _c nonreciprocity. The findings obtained are shown below.
(19) Even when PrBCO was introduced as a seed layer on the IBAD-MgO substrate, an SmBCO Upper layer that maintained superconducting properties could be fabricated.
(20) Similar to the SmBCO thin film in which PrBCO was introduced as a seed layer, no clear correlation was confirmed between the film thickness and δR.
(21) It was confirmed that as the magnitude of lattice mismatch of the interface material of the SmBCO thin film increases, the I _c asymmetry of the Pure sample tends to increase positively. This suggests that the main factor that reduces the surface barrier at the bottom of the thin film is the strain caused by lattice mismatch.

The above results suggest that I _c asymmetry changes by changing the interface material of the SmBCO thin film. It was also suggested that positive I _c asymmetry can be improved by introducing a material with a large lattice mismatch with SmBCO as a seed layer. Moreover, further improvement of I _c asymmetry is expected by combining the introduction of the seed layer and the introduction of nanorods.

[Summary]
From the above results, it is effective to introduce nanorods and flatten the thin film surface by adding BHO at a low addition of about 3 volume %, and to introduce a seed layer of a material with a large lattice mismatch with SmBCO to achieve a high positive asymmetry. It has been suggested.

In this example, the I _c asymmetry was realized or improved from three points: introduction of BHO nanorods, surface roughness (surface processing), and introduction of a seed layer. It was also found that each of these contributes to the magnitude of asymmetry. By combining structural control of the surface, bottom, and interior, it is expected that even higher _Ic asymmetry can be achieved. In this example, we attempted to realize I _c asymmetry by asymmetry of the surface barrier. On the other hand, it is expected that I _c asymmetry can also be achieved by making the internal magnetic flux pinning structure asymmetric. One method is to use a layered structure thin film into which BMO nanorods are introduced, as shown in FIG. 103. It is expected that an asymmetric pinning potential can be realized by changing the amount of BMO added in each layer in a gradient manner.

Furthermore, in order to realize a superconducting diode, it is necessary to increase the current capacity. Although it is possible to increase the capacity by increasing the thickness or length of the REBCO thin film that has asymmetric characteristics, it is also possible that the asymmetry is affected by the self-magnetic field.

In this example, the nanorods were introduced uniformly from the bottom of the thin film to the surface. On the other hand, numerical simulations have confirmed that the asymmetry changes depending on the length of the nanorod. A similar structure can be realized by laminating a layer in which nanorods are not introduced and a layer in which nanorods are introduced. Although the thickness of the thin film is expected to be an important parameter in such a laminated structure, it is expected that asymmetry can be improved by optimizing the internal structure of the thin film.

Since superconducting diodes are expected to be used with applied alternating current, it is also important to evaluate their asymmetric characteristics with respect to alternating current. Furthermore, when actually using superconducting diodes, characteristics with respect to current drive amplitude are also important. Since the asymmetry of the magnetic flux flow resistance as well as the asymmetry of _Ic is taken into consideration in the rectification ratio, it is necessary to evaluate the characteristics for a current exceeding _Ic . It is necessary to appropriately set I _c asymmetry and current capacity for the rated current of superconducting equipment.

[Superconducting device 1: Control of surface roughness]
In many cases, the interface side with the substrate tends to be in a weak superconducting state due to stress due to lattice mismatch between the material constituting the substrate and the superconducting material, and magnetic flux easily enters from the substrate interface. Therefore, the present inventors believe that if the surface of a thin film with a clear boundary between superconductivity and non-superconductivity is made flatter, the asymmetry in potential energy between the surface side and the interface side of the thin film will increase. , we thought that it is possible to increase the asymmetry of the critical current value.

In order to improve the surface flatness of a thin film, the type of substrate, surface roughness of the substrate, crystallinity or crystal orientation, thin film formation method, film thickness, film formation conditions, etc. are adjusted. Although it is possible to form a thin film so that the surface is flat, it is easier and more effective to flatten the surface of the thin film after forming the thin film to manufacture a superconducting device with the desired characteristics. I can do it. In general, the surface roughness of a thin film increases as the film thickness increases, and it is difficult to deposit a large area thin film with a flat surface. However, if the surface is made flat after deposition, Since a superconducting device having good characteristics and having a thick superconducting layer or a large area superconducting layer can be easily manufactured, the superconducting device can be made to have a large current. Furthermore, by flattening the surface of the thin film of a manufactured superconducting device, a superconducting device currently in circulation as a product, a superconducting device in use, etc., the characteristics can be improved.

FIG. 104 schematically shows the configuration of a superconducting device according to an embodiment. The superconducting device 20 includes a superconducting layer 24 formed on a substrate 22 containing a different material from the layer 24 containing a superconducting material (hereinafter also referred to as "superconducting layer 24"). The root mean square roughness of the surface of the superconducting layer 24 is less than a predetermined value. This superconducting device 20 has a first critical current value I _cup in a first current direction and a first current ^direction in a state where a magnetic field having a component in a direction parallel to the surface of the superconducting layer 24 is applied. The second critical current value I _c ^down in the second current direction different from the current direction is different.

The method for manufacturing the superconducting device 20 according to the embodiment includes treating the surface of the superconducting layer 24 formed on the substrate 22 containing a material different from that of the superconducting layer 24 to reduce surface roughness. Contains steps to perform. FIG. 105 schematically shows a method for manufacturing superconducting device 20 according to an embodiment. By performing the treatment to reduce the surface roughness of the superconducting layer 24, the root mean square roughness on the surface of the superconducting layer 24 can be reduced, and a superconducting device 20 with good characteristics can be easily and easily produced. It can be manufactured efficiently.

The superconducting material may be any element, alloy, compound, etc. that can be in a superconducting state. For example, simple elements such as Nb, alloys or compounds such as NbC, MgB ₂ , H ₃ S, LaH _10±x , La-Ba-Cu-O system, Y-Ba-Cu-O system, Bi-Sr-Ca - Copper oxide superconductors such as Cu-O system, Tl-Sr-Ca-Cu-O system, Hg-Sr-Ca-Cu-O system, LaOFeP, LaOFeAS, Sm(O _1-x F _x )FeAs , an iron-based superconductor such as NdFeAs (O _1-x F _x ), an organic superconductor, or the like. The superconducting material may be REBa ₂ Cu ₃ O _y (REBCO: RE is a rare earth element containing Y), and in particular may be SmBa ₂ Cu ₃ O _y (SmBCO) using Sm as RE. .

The critical temperature of the superconducting material may preferably be 50K or higher. In the high temperature region where bulk pinning decreases, the effect of the surface barrier is considered to be more important, so the characteristics of superconducting devices can be improved more effectively. The critical temperature of the superconducting material may be more preferably 77.3K or higher. As a result, the superconducting device can be operated using relatively inexpensive liquid nitrogen, so operating costs and energy consumption can be reduced. The critical temperature of the superconducting material may be 55K or higher, 60K or higher, 65K or higher, 70K or higher, 75K or higher, 80K or higher, 85K or higher, 90K or higher, 95K or higher, or 100K or higher.

Substrate 22 may be a single crystal substrate, a metal substrate with an oriented intermediate layer, or any substrate on which superconducting layer 24 can be formed. The oriented _intermediate layer may be formed of yttria stabilized _zirconia (YSZ), _LaAlO3 (LAO), MgO, _Gd2Zr2O7 (GZO), _CeO2, etc.

The method for forming the superconducting layer 24 is a vapor phase epitaxy (VPE) method such as a physical vapor deposition method (PVD) or a chemical vapor deposition method (CVD). Alternatively, a chemical solution deposition method (CSD) may be used, or any other method may be used. As the PVD method, a sputtering method, a pulsed laser deposition method (PLD), a molecular beam epitaxy method (MBE), or the like may be used.

In order to improve the surface flatness when forming the superconducting layer 24, it is preferable to select a substrate 22 and a crystal growth method that can epitaxially grow a superconducting material on the substrate 22. Any substrate 22 and film formation method may be selected as long as the surface can be sufficiently flattened by a treatment to reduce the thickness. Superconducting materials may be formed into forms other than thin films. Superconducting device 20 may have layers other than substrate 22 and superconducting layer 24.

Treatments for reducing surface roughness include dry etching that does not use liquid chemicals, wet etching that uses liquid chemicals, polishing treatments such as chemical mechanical polishing (CMP), and chemical methods such as ion milling. Alternatively, any treatment that can physically reduce surface roughness may be used. In particular, reactive ion etching, which is an example of dry etching, is suitable. In order to avoid deteriorating the superconducting properties of the superconducting device, it is desirable that the process be performed in a manner and under conditions that do not cause cracks or the like in the superconducting layer during the process.

As mentioned above, the asymmetry in the critical current value of the superconducting device 20 is thought to be caused by the asymmetry in potential energy between the interface side and the surface side. The time or intensity at which the root mean square roughness becomes less than a predetermined value such that the surface barrier at the surface of the superconducting layer 24 is larger than the surface barrier at the interface between the substrate 22 on which the superconducting layer 24 is formed and the superconducting layer 24. It is desirable that it be executed in Furthermore, it is desirable that the treatment be performed for a time or at an intensity that increases the difference between the surface barrier at the interface and the surface barrier at the surface. For example, the surface barrier at the interface is generally reduced due to lattice stress caused by the difference in crystal structure between the substrate material and the superconducting layer material. It is desirable to carry out the treatment for a time or intensity such that the root mean square roughness of the surface of 24 is reduced. Thereby, a superconducting device 20 with good characteristics can be manufactured.

The treatment for reducing surface roughness depends on the type of the substrate 22, the orientation or crystallinity of crystals on the surface of the substrate 22, the method for forming the superconducting layer 24, the orientation or crystallinity of the superconducting material in the superconducting layer 24, It may be performed for a time or with an intensity that further depends on the degree of lattice mismatch between the substrate 22 and the superconducting layer 24, or the type, number, volume, or density of the microstructures introduced inside the superconducting layer 24. The type of substrate 22, the orientation or crystallinity of crystals on the surface of substrate 22, and the degree of lattice mismatch between substrate 22 and superconducting layer 24 can be factors that affect the surface barrier on the interface side. The formation method of the superconducting layer 24, the orientation or crystallinity of the superconducting material in the superconducting layer 24, the type, number, volume, or density of the microstructure introduced inside the superconducting layer 24 are determined by the root mean square of the surface side. The square root roughness, and therefore the surface barrier, can be a factor that affects the surface barrier. Furthermore, the type, number, volume, or density of the microstructures introduced into the superconducting layer 24 can be factors that affect superconducting properties due to bulk pinning or the like. The type, time, intensity, etc. of treatment for reducing surface roughness may be determined by further considering these factors. Thereby, a superconducting device 20 with good characteristics can be manufactured.

The treatment for reducing surface roughness may be performed such that the root mean square roughness on the surface of superconducting layer 24 is less than a predetermined value. As mentioned above, in many cases, the flatter the surface, the greater the asymmetry of the surface barrier (potential energy) with the interface. Device 20 can be manufactured. The root mean square roughness δR on the surface of the superconducting layer 24 after treatment is, for example, less than 90 nm, less than 80 nm, less than 70 nm, less than 60 nm, less than 55 nm, less than 50 nm, less than 45 nm, less than 40 nm, less than 35 nm, less than 30 nm, It may be less than 25 nm, less than 20 nm, less than 15 nm, less than 10 nm, or less than 5 nm.

The superconducting device 20 according to the embodiment includes a superconducting layer 24 formed on a substrate 22, and has a surface barrier (or potential energy) at the interface between the substrate 22 and the superconducting layer 24 and a surface of the superconducting layer 24. The surface barrier (or potential energy) at This superconducting device 20 has a characteristic that the critical current value is highly asymmetric. Thereby, for example, the rectification rate when used as a rectifier can be improved.

In this superconducting device 20, it is desirable that the root mean square roughness on the surface of the superconducting layer is less than a predetermined value. Thereby, a superconducting device with good characteristics can be manufactured. The root mean square roughness δR on the surface of the superconducting layer 24 may be within the above-mentioned value range, for example.

In this superconducting device 20, in a state where a magnetic field having a component in a direction parallel to the surface of the superconducting layer 24 is applied, the first critical current value in the first current direction is different from the first current direction. Preferably, the second critical current values in the second current direction are different. Thereby, the rectification efficiency can be improved when this superconducting device 20 is used as a rectifier.

The asymmetry of the critical current value expressed as the ratio between the difference between the first critical current value and the second critical current value and the average of the first critical current value and the second critical current value is 22% or more. It may be. The asymmetry of the critical current value is more preferably 23% or more, 24% or more, 25% or more, 30% or more, 35% or more, 40% or more, 45% or more, 50% or more, 55% or more, 60%. Above, it may be 65% or more, 70% or more, 75% or more, or 80% or more. Thereby, the rectification efficiency can be further improved when this superconducting device 20 is used as a rectifier.

The direction of the magnetic field applied to the superconducting device 20 only needs to have a component in a direction horizontal to the surface of the superconducting layer 24; in short, it must be perpendicular to the surface of the superconducting layer 24. good. The angle θ between the direction of the magnetic field and the direction perpendicular to the surface of the superconducting layer 24 may be 0°<θ≦90°. θ is more preferably 90°, 89.5° or more, 89° or more, 88° or more, 87° or more, 86° or more, 85° or more, 80° or more, 75° or more, 70° or more, 65° The angle may be 60° or more, 55° or more, 50° or more, or 45° or more.

The magnitude of the magnetic field applied to the superconducting device 20 is less than 2T, less than 1T, less than 0.9T, less than 0.8T, less than 0.7T, less than 0.6T, less than 0.5T, less than 0.4T, 0 It may be less than .3T, less than 0.2T, less than 0.1T, or less than 0.05T. As shown in the examples described later, the superconducting device 20 according to the embodiment has a maximum asymmetry in the critical current value when a magnetic field of about 0.2 T is applied, so it is possible to use a relatively inexpensive material such as a neodymium magnet. It can be operated using permanent magnets. Thereby, the cost of manufacturing and operating the superconducting device 20 can be reduced.

[Example: Control of surface roughness]
The details of the research conducted by the present inventors regarding the above-mentioned superconducting device will be described in detail below.

In this example, REBa ₂ Cu ₃ O _y (REBCO: RE is a rare earth element containing Y) was used as a superconducting material. REBCO high-temperature superconductor is a material that can be used at inexpensive liquid nitrogen temperatures, has high superconductivity, and is expected to be put into practical use. A REBCO thin film with improved I _c asymmetry was obtained by flattening the surface of the REBCO thin film by etching it. Specifically, reactive ion etching (RIE), which is one of the dry etching methods, was selected as the etching method, and SmBa ₂ Cu ₃ O _y (SmBCO) fabricated on a LaAlO ₃ (LAO) substrate was used. By subjecting the thin film to RIE, a thin film with improved I _c asymmetry was obtained.

[Preparation of SmBCO thin film]
In this example, a SmBCO thin film was fabricated on an LAO substrate using a pulsed laser deposition (PLD) method. A Nd:YAG laser was used as the laser.

[Surface processing by RIE]
In this example, as a method of reducing the surface roughness of the SmBCO thin film and flattening it, surface processing was performed by RIE. RIE is classified as dry etching, which is a processing method using gas using plasma. RIE is a highly accurate anisotropic etching process using physical sputtering using ions and chemical reaction using reactive gas, and is often used in the production of semiconductor devices. FIG. 106 shows a schematic diagram of the parallel plate type RIE used in this example. The physical etching principle of RIE is as follows. Two parallel plate electrodes 4 and 10 are placed in a vacuum container 3, and a sample 9 is placed on one side. The sample side of the electrode (cathode electrode 10) is connected to a high frequency power source 12, and the other side (anode electrode 4) is at ground potential 5. After the gas in the vacuum container 3 is evacuated through the exhaust port 2 and evacuated, an etching gas (in this embodiment, a mixed gas of CF ₄ and O ₂ ) is introduced into the vacuum container 3 through the inflow port 1 . By applying a high frequency voltage between the parallel plate electrodes, the etching gas in the chamber is dissociated into ions and radicals by electron collision, and the ions 8 and electrons 6 form a plasma state 7. Since the mobility of electrons 6 is much greater than that of ions 8, the plasma potential becomes positive. Further, when the cathode electrode 10 is positive, the electrons 6 are accelerated toward the electrode and negative charges are accumulated. When the cathode electrode 10 is negative, the positive ions 8 are accelerated toward the electrode, but their mobility is low, so the amount of accumulation is extremely small. Further, since the blocking capacitor 11 insulates the cathode electrode 10 and the high-frequency power source 12, the electrons 6 accumulated in the electrode are not discharged, and the cathode electrode 10 has a negative potential. Therefore, an ion sheath is formed between the plasma and the cathode electrode, resulting in a potential difference. This is called the sheath potential. Since the ion sheath is formed perpendicular to the sample 9, the ions 8 accelerated by the sheath potential impact the sample 9 perpendicularly, causing anisotropic etching.

[Surface structure observation]
FIG. 107 shows changes in the AFM image of the sample surface due to RIE. RIE was performed on the surface of the sample at various times and intensities, and AFM images before and after the RIE were observed. Dynamic force mode (DFM) of an atomic force microscope (AFM), which is a type of scanning probe microscope, was used to observe the surface structure of the thin film. The AFM used in this example was SPI3800 manufactured by SII nano technology. The probe is attached to the tip of the cantilever, and in AFM, the probe is constantly brought into contact with the sample surface with a small force, and the probe is attached so that the force is constant, that is, the amount of deflection of the cantilever is constant. Surface information is obtained by horizontally operating the piezoelectric element while controlling the distance between the surface and the sample. An optical lever method is used to detect the amount of deflection. The reflected light from the semiconductor laser irradiated on the back surface of the cantilever is guided to a four-part photodiode in the photodetector. Since the reflection angle of the laser changes due to the deflection of the cantilever, the center position of the laser hitting the four-split photodiode shifts and the voltage difference between the photodiodes changes. By detecting this, the displacement of the cantilever is measured. DFM is one of the measurement modes of AFM, in which a piezoelectric element vibrates a cantilever at about the resonant frequency, a probe is brought close to the sample surface, and a laser beam is applied to the back of the cantilever so that the vibration amplitude is constant. , surface information can be obtained by detecting changes in amplitude due to atomic forces with a photodetector. DFM is suitable for measuring soft samples or samples with adsorption force that are difficult to measure with contact-type AFM. In this example, the surface roughness δR was evaluated using the analysis results of the root mean square roughness based on the surface information of a square area of 10 μm on a side. Under any conditions, the flatness of the sample plane was improved by RIE.

[Change in surface roughness due to RIE]
FIG. 108 shows the change (ΔRMS) in the root mean square roughness δR of the surface before and after etching. For three samples subjected to RIE at various times and intensities, changes in δR were evaluated from analysis results of AFM images observed before and after RIE. In all samples, it was shown that RIE reduced the root mean square roughness of the surface and improved the surface flatness.

[Change in critical current value due to RIE]
FIG. 109 shows changes in current-voltage characteristics of the thin film before and after etching. Comparing before RIE (□) and after RIE (○), I _c ^down is almost the same, but the absolute value is slightly smaller after RIE, and I _c ^up is clearly It was bigger after RIE. Therefore, it was shown that the asymmetry of the critical current value was improved by RIE. For reference, current-voltage characteristics (●) are shown when a magnetic field in a direction perpendicular to the surface is applied to the sample after RIE. When a magnetic field perpendicular to the surface is applied, the positive and negative critical current values are approximately equal even after RIE is performed.

[Magnetic field dependence of asymmetry of critical current value]
FIG. 110 shows the magnetic field dependence of the asymmetry of the critical current value. In the sample before RIE, the asymmetry of the critical current value reached its maximum around 0.1T, but in the sample after RIE, the asymmetry of the critical current value reached its maximum around 0.05T. became. By performing RIE, the asymmetry of the critical current value increases and the strength of the magnetic field at which the asymmetry of the critical current value becomes maximum decreases. The value of "asymmetry of critical current value" in the present disclosure may be the peak value of the magnetic field dependence of the asymmetry of critical current value.

[Etching time dependence of asymmetry of critical current value]
FIG. 111 shows the etching time dependence of the maximum value of the asymmetry of the critical current value. By performing RIE on the surface of the sample for 60 minutes, the asymmetry of the critical current value was improved to about 50%. When RIE was performed for 120 minutes, the asymmetry of the critical current value decreased, but this is considered to be because the critical temperature T _c of the sample had decreased to near the measurement temperature.

From the above results, it was confirmed that in the SmBCO thin film subjected to RIE processing, the I _c asymmetry was improved due to the formation of an asymmetric surface barrier accompanying the improvement in surface flatness (or reduction in surface roughness).

As described above, according to the technique of the present embodiment, I _c asymmetry can be expressed and improved by reducing the surface roughness (surface processing) of the superconducting layer of a superconducting device. Further, by increasing the thickness and length of the asymmetric superconducting layer, it is possible to increase the current capacity, which is important for realizing a superconducting diode.

[Superconducting device 2: Introduction of nanorods]
In the above Example 2, by introducing BaMO ₃ (BMO: M=metal) during vapor phase growth of the REBCO thin film, bulk pinning due to defects inside the REBCO thin film is alleviated and I _c asymmetry is improved. It has been shown that it is possible.

Therefore, the superconducting device according to the embodiment includes a superconducting layer formed on a substrate containing a material different from a layer containing a superconducting material (hereinafter also referred to as "superconducting layer"), includes microstructures formed of materials different from superconducting materials. The material forming the microstructure may be BaMO ₃ (BMO: M=metal). M may be, for example, Zr, Sn, Hf, etc. BMO may be introduced during epitaxial growth of the superconducting layer. The BMO may form nanorods parallel to the c-axis of the superconducting layer. The diameter of the nanorods within the superconducting layer may be as large as twice the coherence length ξ _ab . The amount of the material forming the microstructure introduced into the superconducting layer may be 2 to 4% by volume, more preferably 2.1% or more, 2.2% or more, 2.3% or more. , 2.4% or more, 2.5% or more, 2.6% or more, 2.8% or more, 2.9% or more, 3.0% or more, but less than 3.9%, less than 3.8%, It may be less than 3.7%, less than 3.6%, less than 3.5%, less than 3.4%, less than 3.3%, less than 3.2%, and less than 3.1%. The amount of the material forming the microstructure introduced into the superconducting layer may be 3 to 12% in substance amount ratio, more preferably 3% or more, 4% or more, 5% or more, 6% or more, 7% or more, 8% or more, 9% or more, 10% or more, 11% or more but less than 12%, less than 11%, less than 10%, less than 9%, less than 8%, less than 7%, less than 6%, 5 % or less than 4%. As shown in FIG. 103, the superconducting layer may have a laminated structure including a plurality of layers, and the content of the material forming the microstructure may differ from layer to layer. The content of the material forming the microstructure may be varied in a gradient manner in the plurality of layers. The content of the material forming the microstructure may be greater in the layer near the surface than in the layer near the interface with the substrate.

A method for manufacturing a superconducting device according to an embodiment includes a step of forming a superconducting layer containing a superconducting material on a substrate containing a material different from the superconducting layer, and in the step of forming the superconducting layer, superconducting A microstructure made of a material different from the superconducting material is introduced into the layer. The superconducting layer may be formed by epitaxial growth, and the material forming the microstructure may be added to the superconducting material during epitaxial growth of the superconducting layer. The amount of the material forming the microstructure introduced into the superconducting layer may be 2 to 4% by volume, more preferably 2.1% or more, 2.2% or more, 2.3% or more. , 2.4% or more, 2.5% or more, 2.6% or more, 2.8% or more, 2.9% or more, 3.0% or more, but less than 3.9%, less than 3.8%, It may be less than 3.7%, less than 3.6%, less than 3.5%, less than 3.4%, less than 3.3%, less than 3.2%, and less than 3.1%. The amount of the material forming the microstructure introduced into the superconducting layer may be 3 to 12% in substance amount ratio, more preferably 3% or more, 4% or more, 5% or more, 6% or more, 7% or more, 8% or more, 9% or more, 10% or more, 11% or more but less than 12%, less than 11%, less than 10%, less than 9%, less than 8%, less than 7%, less than 6%, 5 % or less than 4%. The step of forming the superconducting layer may include the step of forming a laminated structure including a plurality of layers, and the content of the material forming the microstructure may differ from layer to layer. The content of the material forming the microstructure may be varied in a gradient manner in the plurality of layers. The content of the material forming the microstructure may be greater in the layer near the surface than in the layer near the interface with the substrate.

Other features may be the same as those of the superconducting device 1 or the method of manufacturing the superconducting device 1 described above.

[Superconducting device 3: Introduction of Seed layer]
In order to generate asymmetry in the critical current in a high-temperature superconducting thin film, it is necessary to make it difficult for magnetic flux quanta to penetrate into the superconducting thin film (surface barrier) to be asymmetrical. The above examples demonstrate that the crystal lattice mismatch between the substrate and the thin film and the roughness of the thin film surface promote the penetration of magnetic flux quanta and reduce the surface barrier. In Example 4 above, the surface barrier at the substrate interface is further strengthened by reducing the crystal lattice mismatch between the substrate and the thin film, thereby realizing a state in which magnetic flux quanta more easily penetrate from the thin film surface. developed a method. Specifically, by fabricating PrBa ₂ Cu ₃ O _y , which is not superconducting but has a lattice constant close to that of high-temperature superconductivity, on a substrate, and fabricating an SMBCO thin film as a superconducting layer on top of it, magnetic flux can be removed from the surface of the thin film. This created a situation where it was easy for the attackers to invade. This direction is different from the conventional asymmetry that assumes invasion from the substrate side, so it is expressed as negative asymmetry in FIG. 101 and the like.

In this method, since the surface barrier at the interface between the substrate and the thin film is large, it is expected that the asymmetry will be enhanced by emphasizing the unevenness on the surface side of the thin film. That is, in FIG. 101, if the surface of the superconducting layer is flattened by RIE or the like and δR is decreased, the asymmetry of the critical current value changes in the positive direction, but if δR of the surface of the superconducting layer is increased, the critical current value changes. It is thought that the asymmetry changes in the negative direction. Therefore, when using an LAO substrate with a relatively large degree of lattice mismatch with SmBCO forming the superconducting layer, the asymmetry of the critical current value is improved by reducing δR on the surface of the superconducting layer, and the SmBCO When a PrBCO layer having a relatively small lattice mismatch with the superconducting layer is fabricated on a substrate, it is considered that the asymmetry of the critical current value is improved by increasing δR on the surface of the superconducting layer. As methods for increasing δR, it is expected that methods such as anisotropic etching such as dry etching, wet etching, nanoimprinting to transfer nanostructures, and ion implanter doping elements near the surface are expected to be effective. .

In the future, the use of metal substrates with alignment layers will be essential in the mass production of superconducting diodes. This is because it is used for producing high-temperature superconducting tape wires and has excellent productivity. In the metal substrate with alignment layer, _CeO2 with a lattice mismatch of 0.64% is located on top. Therefore, in order to convert this metal substrate with an alignment layer into a superconducting diode, it is necessary to sandwich a material with low lattice mismatch between the high temperature superconductor such as PrBa ₂ Cu ₃ O _y to create a negative asymmetry ( It is desirable to realize a structure in which magnetic flux easily penetrates from the thin film surface.

Therefore, the superconducting device according to the embodiment includes a superconducting layer formed on a substrate containing a material different from a layer containing a superconducting material (hereinafter also referred to as "superconducting layer"), and The degree of lattice mismatch between the material constituting the interface with the conductive layer and the superconducting material constituting the interface with the substrate of the superconducting layer is less than the first predetermined value, and the root mean square roughness on the surface of the superconducting layer is less than the first predetermined value. is greater than or equal to the second predetermined value. The first predetermined value is, for example, less than 1.0%, less than 0.9%, less than 0.8%, less than 0.7%, less than 0.6%, less than 0.5%, less than 0.4%. , less than 0.3%, or less than 0.2%. The second predetermined value is, for example, 10 nm or more, 20 nm or more, 30 nm or more, 40 nm or more, 50 nm or more, 60 nm or more, 70 nm or more, 80 nm or more, 90 nm or more, 100 nm or more, 150 nm or more, 200 nm or more, 250 nm or more, 300 nm or more. , 400 nm or more, 450 nm or more, 500 nm or more, 600 nm or more, 700 nm or more, 800 nm or more, or 900 nm or more. The substrate may include, as an uppermost layer in contact with the superconducting layer, an intermediate layer made of a material having a lattice mismatch with the superconducting material that is less than a first predetermined value. The superconducting material may be any superconducting material such as a rare earth copper oxide superconductor, and the material constituting the substrate or the intermediate layer has a degree of lattice mismatch with the superconducting material that is less than the first predetermined value. It may be any material.

A method for manufacturing a superconducting device according to an embodiment includes a method for increasing surface roughness of a layer containing a superconducting material formed on a substrate containing a material different from the layer containing the superconducting material. The method includes a step of performing processing. The treatment may be dry etching that is anisotropic etching, wet etching, nanoimprint that transfers a nanostructure, ion implanter that dopes elements near the surface, or the like. The treatment may be performed such that the root mean square roughness on the surface of the superconducting layer is equal to or greater than a second predetermined value. The method for manufacturing a superconducting device includes the step of forming a layer containing a superconducting material on a substrate in which at least the uppermost layer is made of a material whose lattice mismatch with the superconducting material is less than a first predetermined value. But that's fine. A method for manufacturing a superconducting device includes forming an intermediate layer on a substrate including a material having a lattice mismatch degree of less than a first predetermined value with the superconducting material, and including the superconducting material on the intermediate layer. The method may include forming a layer.

A method for manufacturing a superconducting device according to an embodiment includes a method for manufacturing a superconducting device, in which an interface with a superconducting layer of a substrate is formed on a surface of a layer containing a superconducting material formed on a substrate containing a material different from the layer containing the superconducting material. If the degree of lattice mismatch between the material constituting the superconducting material and the superconducting material constituting the interface between the superconducting layer and the substrate is less than a first predetermined value, performing a treatment to increase the surface roughness, If the degree of lattice mismatch between the material forming the interface between the substrate and the superconducting layer and the superconducting material forming the interface between the superconducting layer and the substrate is greater than or equal to a first predetermined value, the surface roughness is reduced. The method further includes a step of executing processing for causing the problem.

Other features may be the same as the above superconducting device 1 or 2 or the method for manufacturing superconducting device 1 or 2.

(Second embodiment)
As a second embodiment of the present disclosure, a power supply device using the superconducting device according to the first embodiment and a superconducting device using the power supply device will be described. In the following description, a superconducting magnet system, which is an example of a superconducting device, will be mainly described, but the technology of this embodiment can be applied to any superconducting device using a superconductor.

FIG. 112 shows the configuration of a superconducting magnet system. A conventional superconducting magnet system 90 shown in FIG. 112(a) includes a DC power supply 91, a coil 92, and a cooling device 94. The coil 92 is formed by winding an electric wire made of a superconductor, and generates a magnetic field when a DC current supplied from the DC power supply 91 flows through the electric wire. A closed loop circuit may be formed using wires made of superconductors. In this case, the persistent current switch 95 switches to persistent current mode. The cooling device 94 may be, for example, a Dewar bottle into which liquid helium or liquid nitrogen is introduced.

The superconducting magnet system 90 can generate a strong magnetic field by using a superconductor that has zero electrical resistance and is capable of passing a large current for the coil 92. The application of superconducting magnets to strong magnetic fields can improve the performance of various devices such as magnetic resonance imaging (MRI) devices, nuclear magnetic resonance (NMR) devices, and accelerators. As the properties of superconducting wires improve, the magnetic fields of these devices are increasing, and the development of new high-field devices such as fusion power generation devices and superconducting power storage devices is expected.

However, most of the superconducting materials currently in practical use are low-temperature superconductors such as Nb-Ti and Nb ₃ Sn, which require liquid He, an expensive refrigerant, for cooling. Therefore, operating costs are a major issue for current superconducting magnets. Therefore, the development of magnets using high-temperature superconductors that can be used at liquid nitrogen temperatures is expected. The advantage of high-temperature superconducting magnets is that they can be operated by cooling using liquid nitrogen, an inexpensive refrigerant, or a refrigerator, so the cost required for cooling can be reduced.

On the other hand, the main factors of the cooling load of the superconducting magnet system 90 are heat generation due to the resistance of the current lead 93 and connection resistance of the coil connection part, and heat conduction from the outside to the inside of the cooling device 94 via the current lead 93. This is heat intrusion, and nearly 90% of the cooling load is caused by heat intrusion from the current leads 93. In addition, as the magnetic field increases, it is necessary to increase the current supplied to the magnet, and the diameter of the current lead 93 with a large current capacity needs to be increased. The larger the lead diameter is, the greater the heat intrusion due to heat conduction via the current lead 93, and therefore a higher cooling capacity is required.

For example, when assuming a conduction-cooled current lead 93, consider the cooling load due to heat intrusion into the cooling device 94 at a room temperature of 300K to 77K. The thermal balance equation in the minute section dx in the length direction of the current lead at the rated current I is:
becomes. κ(T) is the thermal conductivity of the current lead with respect to temperature T, A is the cross-sectional area, and ρ(T) is the resistivity. The first term on the left side is a conduction heat term, and the second term is a heat generation term. Assuming copper current leads and assuming that the thermal conductivity is constant from room temperature 300K to 77K, from the Wiedemann-Franz law κ(T)ρ(T)=L ₀ T, ρ(T)=L ₀ T/k becomes. Using this to solve the above equation, we find that the heat intrusion at the low temperature end is
The relationship between A and L that minimizes , and the Q (=Q _min ) at that time is,
Therefore, the heat penetration Q _min when the current lead 93 is optimized is proportional to the current value I. Considering that T _H =300K, T _L =77K, and that the current leads 93 are a pair, the heat penetration is approximately 90 W/kA. Therefore, improvements to power supply circuits have been proposed to reduce cooling costs due to heat intrusion.

In the superconducting magnet system 90, a large DC current is supplied from outside the cooling device 94. On the other hand, as a method of suppressing heat intrusion, the following two methods can be considered, for example. The first method is to provide a power source inside the cooling device 94. As a power source, a magnetic flux pump can be used. However, although excitation of the magnet by a magnetic flux pump that does not use the current lead 93 can greatly suppress heat intrusion and heat generation, there is a problem that the excitation speed is slow because the output voltage is small. Therefore, it is difficult to supply current using only a magnetic flux pump. Another method for suppressing heat intrusion is to supply a small current from an external power source and convert it into a large current by a transformer inside the cooling device 94. By supplying a small AC current from an external power source and converting it into a large DC current inside the cooling device 94, the current lead 93 can be made thinner and heat intrusion can be suppressed.

In this embodiment, in order to further suppress heat intrusion, current is supplied to the coil 92 using non-contact power supply technology. FIG. 112(b) shows the configuration of a superconducting magnet system 50 according to the second embodiment. The superconducting magnet system 50 includes a power supply device 30, a power supply device 40, a cooling device 52, and a coil 92.

The power supply device 30 includes an AC power supply 31 and a power supply unit 32 for supplying AC power supplied from the AC power supply 31 to the power supply device 40 in a non-contact manner. The power feeding unit 32 may be powered by a non-radiation type contactless power feeding method such as a magnetic field coupling type, an electric field coupling type, or an evanescent wave type, or a radiation type non-contact power feeding method such as a laser type, a microwave type, or an ultrasonic type. Power may be supplied by a contact power supply method, or by any other non-contact power supply method.

The power supply device 40 includes a power receiving section 41 that receives AC power supplied from a power feeding section in a non-contact manner, and a converting section 42 that converts the AC power received by the power receiving section 41 into DC power. The power reception unit 41 may be configured with a transformer capable of boosting the power supplied by the power supply unit 32. The converter 42 includes the superconducting device of the first embodiment. That is, the converter 42 rectifies AC power into DC power using a superconducting device whose critical current value differs depending on the direction in which current flows as a rectifying element. The electric wire connecting the power receiving section 41 and the converting section 42 and the coil 92 may be formed of a superconducting material. In this case, the power supply device 40 and the coil 92 may constitute a closed loop circuit made of superconducting material. Thereby, once AC power is supplied from the power supply device 30, a persistent current can be caused to flow in the closed loop circuit, so that energy consumption can be reduced. Further, since the power source and the coil 92 are not connected by the current lead 93, there is no need to disconnect the power source and the coil 92 after supplying current to the coil 92, or to provide a persistent current switch 95. Thereby, the energy consumption of the superconducting device can be reduced with a simpler circuit configuration.

The cooling device 52 has a temperature lower than the critical temperature of the superconducting material constituting the superconducting device used in the converting section 42 and lower than the critical temperature of the superconducting material forming the closed loop circuit including the coil 92 and the power receiving section 41. Cool the power supply 40 and coil 92 to a low temperature. The cooling device 52 may be a Dewar bottle into which liquid helium or liquid nitrogen is introduced, or may be a refrigerator that cools the inside using a heat pump or the like. In the cooling device 52, the converting section 42 may be located within the refrigerant, and the power receiving section 41, electric wires, etc. may be located outside the refrigerant.

FIG. 113 shows an example of the configuration of the converter 42. The converter 42 uses the superconducting device according to the embodiment described above as the superconducting rectifier 44. The converter 42 may be a bridge rectifier circuit using four superconducting rectifying elements 44 as shown in FIG. 113(a), or a bridge rectifying circuit using two superconducting rectifying elements 44 as shown in FIG. A full-wave rectifier circuit using conduction rectifier 44 may also be used. The converter 42 may also be constructed by replacing the semiconductor diode of any known rectifier circuit with a superconducting rectifier 44.

FIG. 114 shows the current resistance characteristics of the superconducting rectifying element 44. The resistance value of the superconducting rectifying element 44 is zero when the current value is between the critical current values Icdown and Icup. When the current value exceeds the critical current value, it transitions to a normal conduction state and resistance occurs. The current-voltage characteristics of the superconducting rectifying element 44 are as shown in FIG.

According to the power supply device 40 of this embodiment, it is possible to suppress heat intrusion through the current leads, and therefore it is possible to reduce the energy consumption required to cool the superconducting material. Furthermore, since a rectifying element made of a superconducting material is used as a rectifying element for converting AC power received without contact into DC power, energy consumption can be further reduced.

The present disclosure has been described above based on examples. Those skilled in the art will understand that this example is merely an example, and that various modifications can be made to the combinations of these components and processing processes, and that such modifications are also within the scope of the present disclosure. .

An aspect of the present disclosure is a power supply device. This power supply device includes a power receiving section that receives AC power supplied from a power feeding section in a non-contact manner, and a conversion section that converts the AC power received by the power receiving section into DC power. It includes a superconducting device whose critical current value differs depending on the direction. According to this aspect, the energy consumption of the power supply device can be reduced.

A superconducting device includes a layer containing a superconducting material formed on a substrate containing a material different from the layer containing the superconducting material, and the root mean square roughness at the interface between the substrate and the layer is less than a predetermined value. There may be. According to this aspect, the characteristics of the superconducting device can be improved, so the rectification rate in the power supply device can be reduced.

The device further includes a magnetic field generator for applying a magnetic field having a component in a direction parallel to the surface of the layer to the superconducting device, and in a state where the magnetic field is applied, the first critical current value in the first current direction and the first critical current value in the first current direction. The second critical current value in a second current direction different from the first current direction may be different. According to this aspect, the characteristics of the superconducting device can be improved, so the rectification rate in the power supply device can be reduced.

The asymmetry of the critical current value expressed by the ratio of the difference between the first critical current value and the second critical current value to the average of the first critical current value and the second critical current value is 22% or more. There may be. According to this aspect, the characteristics of the superconducting device can be improved, so the rectification rate in the power supply device can be reduced.

The layer may include microstructures formed of a material different from the superconducting material. According to this aspect, the characteristics of the superconducting device can be improved, so the rectification rate in the power supply device can be reduced.

Another aspect of the disclosure is a superconducting device. This superconducting device consists of one of the above power supplies, an electric wire made of a superconducting material for passing a direct current converted by the converter of the power supply, and a superconducting device included in the superconducting device of the power supply. and a cooling section that cools the conductive material and the superconducting material forming the wire to a temperature lower than their critical temperatures. According to this aspect, the energy consumption of the superconducting device can be reduced.

The power supply device and the electric wire may form a closed loop circuit made of superconducting material. According to this aspect, the energy consumption of the superconducting device can be further reduced.

1 Inflow port, 2 Exhaust port, 3 Vacuum vessel, 4 Anode electrode, 5 Ground potential, 6 Electron, 7 Plasma, 8 Ion, 9 Sample, 10 Cathode electrode, 11 Blocking capacitor, 12 High frequency power source, 20 Superconducting device, 22 Substrate, 24 Superconducting layer, 30 Power feeding device, 31 AC power supply, 32 Power feeding section, 40 Power supply device, 41 Power receiving section, 42 Conversion section, 44 Superconducting rectifying element, 50 Superconducting magnet system, 52 Cooling device, 90 Superconducting Magnet system, 91 DC power supply, 92 Coil, 93 Current lead, 94 Cooling device, 95 Persistent current switch.

Claims (24)

a power receiving unit that receives AC power supplied from the power feeding unit in a contactless manner;
a conversion unit that converts the AC power received by the power receiving unit into DC power;
Equipped with
The converting section is a power supply device including a superconducting device whose critical current value differs depending on the direction in which current flows. The superconducting device includes a layer containing a superconducting material formed on a substrate containing a different material from the layer containing the superconducting material,
The power supply device according to claim 1, wherein the root mean square roughness at the interface between the substrate and the layer is less than a predetermined value. further comprising a magnetic field generation unit for applying a magnetic field having a component in a direction parallel to the surface of the layer to the superconducting device,
3. In a state where the magnetic field is applied, a first critical current value in the first current direction and a second critical current value in a second current direction different from the first current direction are different. power supply. The asymmetry of the critical current value is expressed by the difference between the first critical current value and the second critical current value and the ratio of the average of the first critical current value and the second critical current value. The power supply device according to claim 3, wherein the ratio is 22% or more. 5. The power supply device according to claim 2, wherein the layer includes a fine structure formed of a material different from the superconducting material. A power supply device according to any one of claims 1 to 5,
an electric wire formed of a superconducting material and for flowing a direct current converted by the converter of the power supply device;
a cooling unit that cools the superconducting material included in the superconducting device of the power supply device and the superconducting material forming the electric wire to a temperature lower than their critical temperature;
A superconducting device equipped with The superconducting device according to claim 6, wherein the power supply device and the electric wire constitute a closed loop circuit made of a superconducting material. A layer containing the superconducting material formed on a substrate containing a different material from the layer containing the superconducting material,
The layer containing the superconducting material includes a microstructure formed of a material different from the superconducting material,
A superconducting device, wherein the amount of the material forming the microstructure introduced into the layer containing the superconducting material is 3 to 12% in terms of substance amount ratio. The superconducting device according to claim 8, wherein the material forming the microstructure is _BaMO3 (M=metal). The layer containing the superconducting material has a laminated structure including a plurality of layers,
10. The superconducting device according to claim 8, wherein the amount of the material forming the microstructure introduced into the layer containing the superconducting material differs for each of the plurality of layers. 10. The amount of the material forming the microstructure introduced into the layer containing the superconducting material is larger in the layer near the surface of the layer containing the superconducting material than in the layer near the interface with the substrate. Superconducting device described in. forming a layer containing the superconducting material on a substrate containing a different material from the layer containing the superconducting material;
In the step of forming the layer containing the superconducting material, a fine structure formed of a material different from the superconducting material is introduced into the layer containing the superconducting material,
The method for manufacturing a superconducting device, wherein the amount of the material forming the microstructure introduced into the layer containing the superconducting material is 3 to 12% in terms of material amount ratio. The layer containing the superconducting material is formed by epitaxial growth,
13. The method of manufacturing a superconducting device according to claim 12, wherein the material forming the microstructure is added to the superconducting material during epitaxial growth of a layer containing the superconducting material. The method for manufacturing a superconducting device according to claim 12 or 13, wherein the material forming the microstructure is BaMO ₃ (M=metal). The layer containing the superconducting material has a laminated structure including a plurality of layers,
15. The method for manufacturing a superconducting device according to claim 12, wherein the amount of the material forming the microstructure introduced into the layer containing the superconducting material differs for each of the plurality of layers. 15. The amount of the material forming the microstructure introduced into the layer containing the superconducting material is greater in the layer near the surface of the layer containing the superconducting material than in the layer near the interface with the substrate. A method for manufacturing a superconducting device according to. A layer containing the superconducting material formed on a substrate containing a different material from the layer containing the superconducting material,
The degree of lattice mismatch between the material constituting the interface of the substrate with the layer containing the superconducting material and the superconducting material constituting the interface of the layer containing the superconducting material with the substrate is a first degree of mismatch. is less than a predetermined value,
A superconducting device, wherein the root mean square roughness of the surface of the layer containing the superconducting material is equal to or greater than a second predetermined value. 18. The substrate includes an intermediate layer made of a material having a lattice mismatch degree of less than the first predetermined value with the superconducting material as an uppermost layer in contact with the layer containing the superconducting material. The superconducting device described. A superconducting device comprising: performing a treatment to increase surface roughness on a surface of a layer containing a superconducting material formed on a substrate containing a material different from the layer containing the superconducting material. Production method. 20. The method according to claim 19, further comprising the step of forming a layer containing the superconducting material on a substrate in which at least the uppermost layer is made of a material having a lattice mismatch with the superconducting material that is less than a first predetermined value. A method for manufacturing superconducting devices. forming on the substrate an intermediate layer containing a material whose lattice mismatch with the superconducting material is less than a first predetermined value;
20. The method of manufacturing a superconducting device according to claim 19, further comprising the step of forming a layer containing the superconducting material on the intermediate layer. 22. The method of manufacturing a superconducting device according to claim 19, wherein the treatment for increasing surface roughness is anisotropic etching, wet etching, nanoimprint, or ion implanter. 23. Any one of claims 19 to 22, wherein the treatment for increasing the surface roughness is performed such that the root mean square roughness on the surface of the layer containing the superconducting material is equal to or greater than a second predetermined value. A method of manufacturing the superconducting device described. A material constituting an interface between the layer containing the superconducting material of the substrate and the layer containing the superconducting material formed on the surface of the layer containing the superconducting material formed on the substrate containing a material different from the layer containing the superconducting material. If the degree of lattice mismatch between the layer containing the superconducting material and the superconducting material constituting the interface with the substrate is less than a first predetermined value, performing a process to increase surface roughness; A method for manufacturing a superconducting device, comprising the step of performing a process for reducing surface roughness when the degree of lattice mismatch is equal to or greater than the first predetermined value.

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