Parinov I.A. Microstructure and Properties of High-Temperature Superconductors

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48 1 Superconductors and Superconductivity

To get an idea of how large this force is, let us ﬁnd the current (j) that must

be applied in the direction perpendicular to the vortex in order to produce

the Lorentz force f

. It is known that the Lorentz force per unit length

of a vortex is jΦ

/c (Φ

is the magnetic ﬂux of the vortex, c is the speed of

light in vacuum) [935]. Then, the force applied to the part of the vortex which

actually interacts with the defect is jΦ

d/c.Equatingthistof

, from (1.23),

we obtain

j =

8Φ

ξ. (1.24)

Furthermore, since H

= Φ

√

2πλξ [935], then from (1.24) we obtain

j =

√

2πλ

. (1.25)

It may be shown that j in the last expression is of the same order of

magnitude as the Cooper pair-breaking current [935]. Thus, in order to tear

the vortex oﬀ a spherical void, it is necessary to apply the maximum possible

current for a given superconductor.

The above discussion is also applied to a superconductor, containing tiny

dielectric inclusions. It also remains valid (at least by the order of magnitude)

for normal metal inclusions, provided the size of the inclusions is larger than

ξ. The restriction is caused by the proximity eﬀect,

which is essential only at

distances of the order of the coherence length ξ from the interface. Therefore,

the various types of inclusions present eﬀective pinning centers in supercon-

ductors. This property is widely used in technical applications, when large

critical currents and magnetic ﬁelds act.

As eﬀective pining centers in superconductors we also note dislocations,

dislocation walls, grain boundaries and interfaces between diﬀerent supercon-

ductors. The above analysis of vortex-defect interactions forms the basis for

interpretation of eﬀects caused by the so-called columnar defects [713], pro-

duced in high-temperature superconductors by irradiation. In this case, the

normal cylindrical amorphous regions are formed in the superconductor. The

nuclear tracks represent themselves as cylindrical regions with diameter being

only 5–10 nm, that is, of the order of the coherence length ξ.Aswehavejust

seen, cavities of such sizes are eﬀective pinning centers. This is one of the

very few possibilities for producing artiﬁcial defects of sizes comparable with

the coherence length in HTSC. In given materials, the coherence length is so

short that any metallurgical methods used to produce pinning centers, such as

precipitates or grain boundaries, have small eﬀect, due to the disproportional

size of defects, or not applicable at all, due to the brittleness of the material.

If thin layer of a superconductor is brought in contact with layer of a normal metal,

then pairs of electrons with summary zero impulse, formed in the superconductor

will stretch on both layers. Proximity eﬀect depends on the interface nature and

the relative thickness of both layers.

1.7 Weak Links of Josephson Type 49

Each defect is capable of trapping approximately one vortex. Hence the

optimum pinning eﬃciency can be expected at magnetic ﬁelds, for which the

vortex lattice period is less than the average distance between the amorphous

tracks. When the Lorentz force

caused by the applied ﬁeld becomes greater

than an interaction force with defect or inhomogeneity, then a displacement

of vortex ﬂux leads to energy dissipation and initiation of ﬁnite electrical

resistance. This state of vortex structure is called the resistive state.

As may be expected, vortex moving caused by the Lorentz force and cor-

responding resistance to magnetic ﬂux strongly depend on three unique prop-

erties of HTSC, namely high critical temperature, small coherence length and

layered anisotropic structure. Combining the above features strongly facili-

tates vortex moving and destroys superconductivity. Due to this, the resistive

transition essentially expands in magnetic ﬁeld. This is one from causes, stimu-

lating tremendous eﬀorts of material scientists directed to change of the HTSC

manufacture technology with aim to decrease the vortex moving, making more

active the magnetic ﬂux pinning. Obviously, this problem will be complicated

with the discovery of superconductors, possessing even greater temperatures

of transition into superconducting state.

Composition features and modern

manufacture techniques for basic HTSC systems will be considered in Chap. 2.

1.7 Weak Links of Josephson Type

In 1962, Josephson published a theoretical paper [500] predicting the existence

of two remarkable eﬀects. One was supposed to ﬁnd them in superconducting

tunnel junctions. The basic idea of the ﬁrst eﬀect was that a tunnel transition

should be able to sustain a superconducting (i.e., zero-voltage) current. The

critical value of this current was predicted to depend on the external magnetic

ﬁeld in a very unusual way. If the current exceeds the critical value, which

is a characteristic of a particular junction, the junction begins to generate

high-frequency electromagnetic waves. This phenomenon was called second

Josephson eﬀect.

Soon after their discovery, both eﬀects obtained experimental conﬁrma-

tion [968, 1167]. Moreover, it soon became clear that the Josephson eﬀects

exist not only in tunnel junctions, but also in other kinds of the so-called

weak links, in particular, short sections of superconducting circuits, where

the critical current is substantially suppressed [630,631,1004]. So, initiating

weak superconductivity is based on the quantum nature of the superconduct-

ing state that assumes the existence of condensate of the Cooper pairs. This

means that all electron pairs in the superconducting state occupy the same

In general case, the Lorentz forces can be initiated as transport current, as screen-

ing currents caused by sample magnetization.

Nevertheless, it is not obligatory that superconductors with transition tempera-

tures near to room temperature will possess oxide structure.

50 1 Superconductors and Superconductivity

quantum level and are described by a single wave function, common to all of

them. Their behavior is mutually conditioned and they are coherent.

Consider two bulk superconductors having the same temperature and com-

pletely isolated from each other. The behavior of the superconducting elec-

trons in each of them is subjected to own wave function, when they are in the

superconducting state. Then, because the temperatures and the materials of

the superconductors are identical, the amplitudes of the wave functions must

also be the same. However, the phases, in this case, are arbitrary. This situa-

tion remains as long as the superconductors are isolated from each other. Let

us establish a weak contact between them, that is, the contact that is weak

enough so as not to change radically the electron states of the two super-

conductors, but suﬃcient to initiate a perturbation. In this case, a new wave

function is formed that is general for the joint superconductor, which can be

considered as a result of interference between the wave functions of both its

pieces. Therefore, phase coherence is a direct result of establishing the weak

link.

The weak links (Josephson junctions, JJs) can be classiﬁed in the following

way:

(1) Devices without concentration of current such as tunnel junctions of the

“superconductor–insulator–superconductor” type (S–I–S) (Fig. 1.18a). The

thickness of an insulating layer, as a rule, is about 1–2 nm, and the critical

current density is in the order of 10

A/cm

, that is, much less than the

critical current density of the bulk superconductor, in particular, exceed-

ing 10

A/cm

at 77 K and 0 T in Y(RE)BCO melt-processed samples.

(2) Layered structure of the “superconductor–normal metal–superconductor”

type (S–N–S). It involves the normal layer with thickness of ∼ 1 μm

(Fig. 1.18b). The wave functions of the superconducting electrons pen-

etrate the normal metal due to the proximity eﬀect. In the region of their

overlap, the wave functions interfere, establishing phase coherence between

bulk superconductors. If the amplitude of the superconducting wave func-

tion in the weak link is small, then the critical current is also small.

(3) Layered structures where a normal layer between two superconductors is

replaced by a doped semiconductor or another superconductor with a small

critical current density. For example, if a narrow superconducting ﬁlm is

covered by thin ﬁlm of a normal metal (Fig. 1.18c), then the amplitude of

the superconducting electron wave function in the ﬁlm is reduced, where

the ﬁlm contacts with normal metal, due to proximity eﬀect. This causes

local decrease of the critical current density, that is, weak link formation.

(4) Devices with concentration of current. The critical current density in the

weak link is the same as in the bulk, but the absolute value of the critical

current is much less. A superconducting ﬁlm with a short narrow con-

striction (Dayem bridge) falls into this category, provided the size of the

High-quality tunnel Josephson junctions, made of niobium with a barrier layer of

aluminum oxide, attain the critical current density of ∼ 10

− 10

A/cm

1.7 Weak Links of Josephson Type 51

ISS

∼2 nm ∼1 μm

(a) (b) (c)

∼ξ

YBaCuO

(d) (e) (f )

Fig. 1.18. Diﬀerent types of weak links: (a) tunnel junction (S–I–S); (b) sandwich

structure (S–N–S); (c) normal ﬁlm (N) causes local suppression of the order param-

eter of superconducting ﬁlm (S); (d)Dayembridge;(e) bridge of variable thickness

(longitudinal cross-section); (f) grain-boundary junction

constriction is of the order of the coherence length, ξ (see Fig. 1.18d).

Another example is a bridge of variable thickness, such that the thickness

of the basic ﬁlm is hundreds of nanometers, at the same time, the thickness

of the bridge itself is only several tens of nanometers (Fig. 1.18e).

(5) Grain boundary (or bicrystal) transition. It is a typical one for high-

temperature superconductors (Fig. 1.18f). Due to the extremely short

coherence length in HTSC (ξ ∼ 1 nm), defects in their crystalline struc-

ture can act as weak links. The best-controlled defects can be produced

between two regions of an epitaxial high- temperature ﬁlm with various

crystal orientations (grain boundaries). The critical current density of such

a weak link can be varied, changing the misorientation angle between two

crystallites.

HTSC Josephson junctions can also be classiﬁed into the following three

classes [355]:

– junctions without interfaces, in which the weak coupling is achieved by

locally degrading the superconducting properties of a HTSC thin-ﬁlm

microbridges by focused electron or ion beam irradiation;

52 1 Superconductors and Superconductivity

– junctions with intrinsic barriers or interfaces formed, for example, using

the intercrystalline boundaries of diﬀerent crystallographic orientations;

– junctions with extrinsic interfaces, in fabrication of which artiﬁcial barriers

from normal metals and insulators are used.

From the standpoint of the damage and material strength problem, the last

two classes of the Josephson junctions display most interest. HTSC JJs with

extrinsic interfaces are prepared by using the ﬁlm technology, and they them-

selves present multi-layered structures (hetero-structures) with rectilinear and

inclined interfaces. There are diﬀerent technological possibilities, which are

discussed in detail in the following two chapters, for increasing superconduct-

ing properties of these systems. For example, an overdoping by calcium of

intergranular boundaries in multi-layered structures and YBCO super-lattices

permits to signiﬁcantly increase J

at all temperatures up to T

, but also at

magnetic ﬁelds up to 3 T [174].

Composition Features and HTSC

Preparation Techniques

Microstructure, strength and other HTSC properties are deﬁned by the

existence of numerous components. This circumstance supposes diﬀerent

chemical, physical and mechanical inﬂuences during numerous technological

operations to prepare ﬁnal sample from initial powders. Super-sensitiveness

of HTSC ﬁnal properties to the technical conditions, their manufacture and

to composition features, and also numerous eﬀects have determined various

ways of the oxide superconductor preparation. HTSC samples in the forms of

ﬁlms at the mono- and polycrystalline substrates, coated conductors, tapes

and superconducting bulks are the most interesting for applications. Their

preparation techniques are considered in this chapter.

2.1 YBCO Films and Coated Conductors

In general, in order to synthesize HTSC ﬁlms (as YBCO family as another

ones) in situ and ex situ methods are used. In the ﬁrst case, the ﬁlm crystal-

lization takes place directly during their deposition and an epitaxial growth

occurs under corresponding conditions. In the second case, the ﬁlms are de-

posited initially under low temperature, that is insuﬃcient to form necessary

crystalline structure, and then the ﬁlms are sintered in O

atmosphere that

leads to the crystallization of the necessary phase (e.g., this sintering tem-

perature is equal to 900–950

◦

C for YBCO ﬁlms). Most one-stage methods

are realized under thermal treatment that is much more lower compared with

two-stage methods. The high-temperature annealing forms large crystallites

and rough surfaces, deﬁning small critical current density. Therefore, the in

situ methods have advantages initially. According to the preparation methods

and the deposition of HTSC components on a substrate, there are physical

methods of deposition, including all possible evaporations and scatterings, and

also the chemical methods of precipitation.

Methods of vacuum co-evaporation. These assume simultaneous or succes-

sive (layer-by-layer) co-precipitation of HTSC components evaporated from

54 2 Composition Features and HTSC Preparation Techniques

diﬀerent sources by using, for example, electron beam guns or resistive

evaporators. The ﬁlms, prepared by this technique, yield their superconduc-

tive properties to the samples, manufactured by methods of laser evaporation

or magnetron scattering. Methods of vacuum co-evaporation are used in two-

stage synthesis, when the structure of ﬁlms, scattered in ﬁrst stage has no

principle consideration, as also the oxygen contents in them.

Laser evaporation. This is highly eﬀective in the HTSC thin-ﬁlm deposi-

tion. This method is simple in realization, demonstrates high rate of deposition

and permits contact with small targets. Its main advantage is the evapora-

tion, equally well, of all chemical elements contained in the target [521]. The

ﬁlms, having the same quality as the targets, may be prepared in the target

evaporation under concrete conditions. The distance between target and sub-

strate and also the oxygen pressure are the important technical parameters.

Their right selection allows, on one hand, non- overheating of the growing

ﬁlm by energy of plasma, evaporated by laser, and accompanying formation

of very big grains, but, on the other hand, to state an energetic regime that is

necessary for ﬁlm growth at perhaps very low temperatures of substrate. The

high energy of the components deposited and existence in the laser ﬂame of

monatomic and ionized oxygen permit the preparation of HTSC thin ﬁlms in

one stage. In this case, the ﬁlms are mono-crystalline or possess high texture

with c-axis orientation (the c-axis is perpendicular to the substrate plane).

The main disadvantages of the laser evaporation are the following: (i) small

region in which stoichiometric ﬁlms could be deposited, (ii) heterogeneity of

their thickness and (iii) surface roughness. By using the radiation methods

in ﬁlm preparation, the interesting dependences may be stated, for example,

between the degree of a-axis orientation of YBCO ﬁlm,

the substrate tem-

perature and the material, and also the deposition rate. These dependences

for the ion beam sputtering method in deposition of CeO

buﬀer layer are

presented in Figs. 2.1 and 2.2. Obviously, by using the sapphire substrate in

the preparation of the a-axis-oriented YBCO thin ﬁlm higher rates of depo-

sition are necessary. Moreover, ﬁlm surfaces with smaller roughness are ob-

tained on sapphire compared with SrTiO

, deﬁning its better superconducting

properties.

Magnetron scattering. This permits to obtain in one stage YBCO ﬁlms,

not yielding their superconducting properties to the samples, deposited by the

laser evaporation method. Moreover, they have more homogeneous thickness

and higher smoothness of surface. As at the laser evaporation, the plasma

formation at magnetron scattering creates high-energetic atoms and ions that

Due to the high anisotropy of HTSC, ﬁlms with c-axis orientation only have good

transport and screening properties. At the same time, ﬁlms with a-axis orien-

tation, possessing greater coherence length in direction that is perpendicular to

the surface and distinguished by high smoothness, could be convenient to pre-

pare qualitative HTSC Josephson junctions, consisting of successively deposited

“HTSC-normal metal” (or “dielectric–HTSC”) layers. Films demonstrating mixed

orientation are not desirable in all cases.

2.1 YBCO Films and Coated Conductors 55

1.0

0.5

0.0

600 700

Substrate Temperature (°C)

Degree of a-axis Orientation

650

Fig. 2.1. Dependence of degree of a-axis orientation of YBCO ﬁlm upon the sub-

strate temperature. Solid line (a) indicates deposition rate of 20

A/min on sapphire;

(b) for 10

A/min; (c)for5

A/min. Dashed line (d)isfor5

A/min on SrTiO

[486]

permit to obtain HTSC ﬁlms in one stage at not high temperatures. Here,

the distance of “target–substrate” is also important. At small distance and

insuﬃcient pressure of environment, the substrate is subjected to intensive

bombardment by the negative ions of oxygen that fracture the structure of

growing ﬁlm and its stoichiometry. In order to solve this problem, the set

approaches are used [175], including the protection of the substrate from the

bombardment of energetic ions and its location at optimum distance from

gas-discharge plasma to ensure high rate of deposition and successive growth

of the ﬁlm at the maximum low temperatures.

In situ YBCO thin ﬁlms prepared by out-axis magnetron scattering and

possessing optimum electric properties have demonstrated T

=92Kand

=7× 10

A/cm

;andT

=89KandJ

=2× 10

A/cm

at optimum

smoothness of surface [222,223].

Chemical precipitation from vaporous phase of metal-organic compounds.

The core of the method is the transportation of metallic components in the

form of steams of the volatile metal-organic compounds in a reactor, a mixing

with gaseous oxidizer, decomposition of the steams and condensation of the

oxide ﬁlm on substrate. This method permits to obtain HTSC thin ﬁlms pos-

sessing parameters, which are compared with samples prepared by the physical

The varieties of impulse laser deposition, used to obtain YBCO ﬁlms and coated

conductors with high texture on the diﬀerent mono- and polycrystalline substrates

with and without buﬀer layers, permit to reach the critical current density J

2.4MA/cm

at 77 K and zero magnetic ﬁeld [271].

56 2 Composition Features and HTSC Preparation Techniques

300 nm

10 µm

300 nm

(a)

(b)

Fig. 2.2. Atomic force microscopy images of YBCO ﬁlms deposited on (a)SrTiO

and (b) sapphire substrate with CeO

buﬀer layers. Sputter conditions for the ﬁlms

are identical [331]

methods of deposition. The comparative advantages of the method considered

to last ones are the following: (i) a possibility to obtain homogeneous ﬁlms

on details with non-plane conﬁguration and possessing a great area; (ii) more

high rates of precipitation under conditions of high quality; (iii) a ﬂexibility

of process at the preliminary stage of technological regime due to the smooth

change of the vaporous phase composition.

The following techniques are as the most widespread ones:

– preparation of ﬁlms and coated conductors (CC) with two-axes texture by

using the ion-beam-assisted-deposition (IBAD) [464,1151];

– preparation of ﬁlms and coated conductors by using the rolling-assisted

biaxially textured substrates (RABITS) [336,337,769,1181];

2.1 YBCO Films and Coated Conductors 57

– preparation of two-axes ordered buﬀer layers by using the inclined

substrate-pulsed laser deposition (ISPLD) [395];

– preparation of thin ﬁlms by the magnetron sputtering [1042];

– preparation of buﬀer layers by the electron beam evaporation [680], laser

ablation [646,893], ion beam sputtering [331,486] and rf-sputtering [147,

632,701];

– preparation of thick epitaxially grown ﬁlms by the liquid phase epitaxy

(LPE) [1155];

– preparation of ﬁlms by the electrophoretic deposition [704];

– preparation of buﬀer layers by the surface oxidation epitaxy (SOE) [678];

– preparation of coated conductors by using the metal-organics decomposi-

tion (MOD) [985];

– preparation of thick ﬁlms on the base of precursor ﬁlms by the metal-

organic Chemical vapour deposition (MOCVD) [253].

As substrates in various techniques, the Ni-based alloys (Inconel, Hastelloy,

Ni-Cr, Ni-V, etc.), metals (Ni, Ag, Zr), oxides (Al

,SrTiO

,NdGaO

LaAlO

,MgO,PrO

) and non-metals (Si, glass) have been used. As buﬀer

layers YSZ, CeO

,MgO,SrTiO

,ZrO

,BaZrO

and NiO have been used.

As it has been noted, the critical current could be enhanced due to the

formation of artiﬁcial defects in the sample, playing role of the magnetic ﬂux

pinning centers. With this aim, the defects with linear sizes, l,whichare

near to the superconducting coherence length (e.g., l = 2–4 nm in Y-123

at T<77 K), and density of order of (H/2) × 10

−2

,whereH is in

Tesla, are the best of all. This high density of defects with nanometer sizes

is reached with diﬃculty at the stage of sample fabrication; therefore the

ionic irradiation is usually used for this goal. In [399], a method has been

proposed for fabrication of Y-123 ﬁlms, consisting of non-superconducting Y-

211 particles with l ∼ 8 nm, density of which was larger than 10

−2

.This

method consists of alternative deposition of the Y-123 and Y-211 layers, and

further formation of the Y-211 “islands” (because of mismatches of the lattice

periods of (2–7)% for Y-123 and Y-211 phases). In this case, the thickness of

Y-123 layers and Y-211 layers was equal to ∼ 10 and ∼ 1 nm, respectively,

but Y-211 nanoparticles were distributed uniformly into Y-123 matrix. These

ﬁlms have much more larger current density, compared to Y-123 ﬁlms without

defects, moreover, one decreases much more slower at the enhancement of

magnetic ﬁeld.

From the view of material strength, the main aim is to select neigh-

boring layers with like thermal and crystallographic properties, and also

to prevent chemical reaction between them. It is necessary to note, that

the critical current density of the ﬁlm on polycrystalline substrate dimin-

ishes considerably at the existence of high-angle intergranular boundaries

[206], causing the problem of weak links. Therefore, for tape applications,

it is very important to prepare ﬁlms with highly in-plane aligned crystalline

structure, that is, to form the ordered structure not only along the c-axis,

but along the a-direction. As a rule, thick YBCO-coated conductors are