Qiu X.G. (Ed.) High Temperature Superconductors

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For the high-T

superconductors (HTS) these models can be adapted, leading to

device parameters scaling with the higher T

. This results in promising properties in

comparison to conventional low-T

(LTS) superconductors (Beasley, 1995). For

example the frequency range is now extended to several THz. On the other hand, the

nature of the high-T

materials results in new aspects like anisotropy of the parameters

with crystal orientation, pairing symmetry (d-wave instead of conventional s-wave),

high penetration depth and small coherence length. An excellent review on weak links

in high critical temperature superconductors is given by Tafuri and Kirtley (2005).

Another physics is related to high-T

cuprate superconductors because they have an

atomically layered structure of superconducting sheets S and S′ separated by insulating

or normal conducting layers with different coupling strengths t and t′, respectively (see

Fig. 8.3). In this way the weak coupling is realized in a periodic stack of Josephson

junctions with atomic dimensions along the crystallographic c-axis. These intrinsic

Josephson junctions can be described by the Josephson or more general weak link

8.3 Intrinsic Josephson junctions within the unit cell of the high-T

superconductor Bi

CaCu

(Yurgens, 2000, Fig.1, Copyright (2000) by

IOP Publishing Ltd). Reprinted with permission from Yurgens A (2000)

‘Intrinsic Josephson junctions: recent developments’, Supercond. Sci.

Technol. 13, R85–R100, Fig.1. Copyright (2000) by IOP Publishing Ltd.

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physics but the small dimensions as well as the series connection of many junctions

gives rise to some special behaviour and parameters (so-called intrinsic Josephson

effects). Modelling of high-T

Josephson junctions has to take into account these

special properties. Thus within the last years many improved, adapted or new models

have been introduced to describe the physics of high-T

Josephson junctions. I

(T) or

(T) have been calculated for d-wave superconductors and different kinds of

coupling barriers, see e.g. Tanaka and Kashiwaya (1997), Golubov and Tafuri (2000),

Yokoyama et al. (2007), and references therein. As one example of the unusual

behaviour, it should be pointed out that the magnetic ﬁeld pattern in the case of a hybrid

junction with one electrode with d-wave symmetry (S

junction) drastically changes,

resulting in a zero critical current without ﬁeld (so called ‘

-junction’), see Fig. 8.4.

8.1.3 Possibilities of applications

There are many applications of Josephson junctions or related weak link devices

in superconducting electronics and measurement science. The superconducting

quantum interference device (SQUID), as the most prominent application, will

be treated in the next chapter. Thus single junction and junction array applications

8.4 Magnetic ﬁeld pattern of a conventional Josephson junction,

eq. [8.2] (dashed line), and a hybrid

-junction of a d-wave high-T

superconductor and an s-wave low-T

superconductor (Tafuri and

Kirtley, 2005, Fig. 19b. Copyright (2005) by IOP Publishing Ltd).

Reprinted with permission from Tafuri F and Kitley JR (2005), ‘Weak

links in high critical temperature superconductors’, Rep. Prog. Phys. 68,

2573–2663, Fig. 19b. Copyright (2005) by IOP Publishing Ltd.

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in other ﬁelds will be discussed here.

The unique properties of Josephson devices offer interesting new systems. The

IV-characteristics (Fig. 8.2) are highly non-linear thus ampliﬁcation and mixing is

possible. In the case of hysteretic junctions, there are two branches of the

characteristic which allow switching between the two states. This can be used for

latching logic and digital circuits. The modulation of the IV-characteristics in an

external magnetic ﬁeld (Fig. 8.4) can be used as magnetic sensor devices similar to

SQUIDs. Photons produce characteristic changes of the IV-characteristics, too – a

broadband video detection results from changes in the characteristics connected to

the adsorbed energy of the radiation. Photon-assisted tunnelling leads to additional

structures in the IV-characteristics and Josephson junctions can be used for photon

detection down to the single-photon limit. If the frequency of the radiation is in the

range of the internal Josephson oscillations (depending on the voltage from MHz

over GHz up to the THz range) there are synchronization effects like Shapiro steps

which can be used for detection, too. Because of the fundamental relation of Eq.

[8.4], a voltage standard can be realized using the direct relation between external

frequency and voltage across the junction. The use of large junction arrays allows

exact voltages, up to 10 V as well as digital standards and a.c. voltage standards,

see Hamilton (2000). Because the Josephson oscillations are strongly connected to

the applied voltage, a tuneable frequency source can be realized. Especially in the

THz range, this offers new ways of compact radiation sources in contrast to

extended laser systems. To enhance the power of radiation instead of single

junctions, synchronized arrays of many junctions have to be used.

The dynamics of Josephson junctions can be used for many digital electronics

applications. Rapid single ﬂux quantum (RSFQ) logic is based on the equivalence

of a voltage pulse and a single ﬂux quantum. In contrast to the latched logic, the

switching times are very small and the dissipated power is very low. Thus SFQ or

RSFQ circuits will bring out many applications in superconducting electronics,

see ter Brake et al. (2006).

For each application, the main important parameters of the junctions have to be

realized in adapted technologies within small margins. For large junction arrays this

requires a small spread of single junction parameters like I

and R

. Stability of the

parameters on temperature during operation and on long time scales (ageing) have to

be realized. In the case of the high-T

Josephson junction, this situation is even more

complex and has to include a lot of additional requirements. For example, the high-T

materials often use adapted single crystalline substrates with high dielectric constants

resulting in decreased r.f. properties and parasitic capacitances. The small coherence

lengths result in problems of weak link dimensions and possible junction types,

including multilayer systems. On the other hand, the intrinsic nature of the high-T

materials offers new ways like the intrinsic Josephson junctions and phase-sensitive

junctions with new properties. For example, with the

-junctions a new digital logic

family can be installed, e.g. Ortlepp et al. (2007) and references therein.

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8.2 Types of high-T

Josephson junctions

8.2.1 Overview

The general veriﬁcation of the Josephson effects for high-T

superconductors was

ﬁrst realized by point contracts and break junctions. It was shown that even if

there are some differences to conventional superconductors, Josephson effects

can be observed which can be qualitatively described by the usual models,

especially with the same ﬂux quantum. Meanwhile there are many types of thin

ﬁlm Josephson junctions using different coupling mechanisms:

• grain boundary junctions,

• artiﬁcial barrier junctions,

• modiﬁed microbridges,

• intrinsic Josephson junctions,

• hybrid junctions.

8.2.2 Grain boundary junctions

The ﬁrst group of junctions uses the special property of the high-T

cuprates that,

because of the very small coherence length of a grain boundary in the thin ﬁlm,

acts as a weak link or Josephson junction. This strong spatially reduction of

superconductivity can be artiﬁcially induced in an epitaxial thin ﬁlm. Thus a

junction can be placed in a superconducting line by induction of a grain boundary.

This can be done by modiﬁcation of the substrate or an additional thin ﬁlm layer

of a non-superconducting material. Most popular but quite expensive is the use of

bicrystal substrates where a single crystal substrate is cut and after some polishing

coupled again with a ﬁxed disorder of the crystal orientation of both parts. There

are different possibilities of disorientation depending on the tilt direction and

grain boundary angle. The standard bicrystal substrate uses a well installed angle

between the a- or b-axis, while c-axis of both parts is parallel. The resulting

junction is determined by this grain boundary angle. An asymmetric or a symmetric

case can be realized (Fig. 8.5). It was shown that the dependence of the critical

current density on that angle covers a wide range (Fig. 8.6), and can be reproduced

with good accurancy, see Gross et al. (1990), Hilgenkamp and Mannhart (2002),

Gross (2005), and Mannhart (2006). This leads to commercial standards of

symmetric and asymmetric bicrystal substrates with, e.g., 24 and 36 degrees for a

lot of materials like SrTiO

, LaAlO

, NdGaO

, sapphire (Al

), MgO, Si, etc.

Other kinds of bicrystal junctions can be realized if there is a tilt with respect to

the ab-planes or c-axis of both parts of the crystal. Because of the anisotropy and

the d-wave symmetry in the high-T

materials, such substrates can be used to

realize junctions with different superconducting phase coupling.

Another way of inducing a well-deﬁned grain boundary in the growing high-T

ﬁlm is a step-edge in the substrate. It was shown that for angles larger than

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8.5 Two types of bicrystal junctions with (a) asymmetric and (b)

symmetric grain boundaries (Tafuri and Kirtley, 2005, Fig. 23, Copyright

(2005) by IOP Publishing Ltd.). Reprinted with permission from

Tafuri F and Kitley JR (2005), ‘Weak links in high critical temperature

superconductors’, Rep. Prog. Phys. 68, 2573–2663, Fig. 23. Copyright

(2005) by IOP Publishing Ltd.

60 degrees there are well-pronounced grain boundaries at both ends of the

substrate step induced in the high-T

ﬁlm during deposition (Fig. 8.7). Depending

on step angle and substrate material as well as technology, one or two junctions

will be established. There was some discussion and investigation of the crystal

structure concerning the question of whether the lower or upper step-edge

determines the junction with the lower critical current dominating the

IV-characteristics of the whole contact. In general the existence of two junctions

in series causes problems in the dynamics and the stability of the system, see

Seidel et al. (1995). Thus one tries to make both junctions very different in their

critical current. Another way is to avoid a second junction, as is done for MgO

step-edges by Foley et al. (1999) where only the upper junction exists, while at

the lower end of the step-edge there is a smooth growth of the ﬁlm.

A general advantage of the step-edge junctions in comparison to bicrystal

junctions is that they can be placed anywhere on a ﬂat, quite cheap substrate. By

etching the step into a thin ﬁlm of an insulating material with crystallographic

parameters allowing growth of the high-T

material in the top layer, the junctions

can be placed in higher levels of multi-layered devices, too.

The third possibility, to produce an artiﬁcial grain boundary in the high-T

ﬁlm,

is the so-called biepitaxial junction (Fig. 8.8). A seed layer partially covers the

substrate and the material of the seed layer induces another orientation of the ﬁlm

growth in comparison to the uncovered regions of the substrate. The disadvantage

of this type of junction is that often there is only a ﬁxed angle between the two

ﬁlm parts of 45 degrees, which is not optimal with respect to critical current (see

Fig. 8.6). A placement of the junction anywhere on the substrate is an advantage,

including multi-layer technology. Thus a junction can be realized very easily in

the upper layers of a thin ﬁlm system.

The grain boundary junctions offer an excellent standard technology for many

applications. Even if the nature of the barrier and the coupling mechanism is still

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under discussion, see for example Hilgenkamp and Mannhart (2002) and

references therein, they give a high reproducibility and good performance like a

high I

product.

8.2.3 Artiﬁcial barrier junctions

This kind of Josephson junction uses an artiﬁcial barrier layer between the

superconductors and various geometries (Fig. 8.9). Depending on the nature of the

barrier material (insulating, semiconducting, normal conducting, superconducting

8.6 Critical Josephson current density on grain boundary angle at 4.2 K

of different bicrystal junctions, reproduced from Mannhart, 2006, Fig. 4

a and b; for details see comments therein. Reprinted with permission

from Mannhart J (2006), ‘Properties of grain boundaries in high-T

superconductors – Notes on a recent presentation’, Physica C 450,

152–155, Fig. 4 a and b, Copyright (2006) by Elsevier Science Ltd.

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8.7 Step-edge junction with two grain boundaries induced in the HTS

ﬁlm (shown schematically). C = c-axis direction of the crystals.

8.8 Biepitaxial junction types (shown schematically): (a) classically,

(b) MgO-based and (c) CeO-based out-of-plane type (Tafuri and Kirtley,

2005, Fig. 24, Copyright (2005) by IOP Publishing Ltd). Reprinted with

permission from Tafuri F and Kitley JR (2005), ‘Weak links in high

critical temperature superconductors’, Rep. Prog. Phys. 68, 2573–2663,

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with depressed T

, geometrical constriction, etc.) the thickness and the transport

mechanism can vary in a wide range. Insulating barriers have to be in the order of

0.1 nm because of the very low quantum mechanical tunnelling probability. While

this SIS type in planar geometry (sandwich, Fig. 8.9a), with insulating metal

oxides is the standard junction in LTS circuits (e.g. Nb-NbO

-Pb or Nb-Al-

AlO

-Nb), the requirements of HTS technology lead to additional problems. The

insulating barrier has to grow epitaxially in layered SIS junctions in sandwich or

ramp-edge geometry, and even for a very thin barrier shorts have to be avoided.

The tunnelling probability can be drastically enhanced using semiconducting or

normal conducting barriers. But in this case the direct conductivity, Andreev

reﬂexion or hopping mechanisms dominate the transport through the barrier and

determine the Josephson coupling. For epitaxial growth in multilayer systems,

perovskite-like materials such as doped YBaCuO, PrBaCuO and NdCeCuO are

used. Even for such materials the problems with homogeneity, multi-layer epitaxy,

barrier thickness control and reproducibility are hard to solve, so the interfaces

play an important role.

An interesting way to reduce the problems leads to trench bilayer junctions

where the coupling barrier is deposited ﬁrst, (Fig. 8.9b). The epitaxially grown

superconductor ﬁlm on top of this barrier layer has to be cut by electron lithography.

8.9 Some types of planar artiﬁcial barrier junctions (shown

schematically): (a) sandwich, (b) trench in bilayer, (c) SNS trench-

bridge type. B = barrier, S = superconductor, N = normal conductor.

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The resulting trench has to be in the order of 100 nm to realize a proximity effect-

based coupling via the base layer. To avoid the problems with multilayer epitaxy,

a trench in a single HTS layer can be ﬁlled with normal metal (Au or Ag) resulting

in an SNS bridge junction (Fig. 8.9c). But the trench width below 200 nm, as well

as the interface problems between the HTS and the normal metal, lead to problems,

too. The ﬁrst problem can be avoided with a step in the substrate, the buffer layer

or the insulating interface layer. One version is shown in Fig. 8.10a, the so-called

SNS step-edge junction (Dilorio et al., 1993, 1995).

The deposition of the normal metal and the HTS layer is realized with different

angles of incidence. These junctions show reduced I

-products because of the

normal shunt between large parts of the superconducting ﬁlm and the normal

metal. The I

-product can be enhanced up to 10 mV by etching away these

shunts (Rosenthal et al., 1993), see Fig. 8.10b. Another version uses additional

insulating layers on top of the superconductor before etching the trench that leads

to capacitive shunts, (Fig. 8.10c). A widely used type with a good reproducibility

is the so-called ramp-type or ramp-edge junction, see Fig. 8.11. Here the barrier is

placed at the etched ramp of a superconductor/insulator double layer. As barrier

materials, normal metals, semiconductors or insulators can be used if they grow

epitaxially or do not strongly disturb the growth of the superconducting counter-

electrode. An interesting version uses no artiﬁcially deposited material as barrier,

8.10 Different SNS step-edge junctions (shown schematically):

(a) shunted, (b) without shunt (after etching), (c) capacitively shunted.

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Josephson junctions 331

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but uses the disturbed interface at the etched ramp. This ‘natural’ barrier depends

on the etching process but is easy to realize and offers a high reproducibility

(‘interface-engineered barriers’).

Problems in barrier junction technology result from shorts and inhomogeneities as

well as from the strong inﬂuence of the intrinsic transport mechanism of the barrier

materials on the noise properties of these junctions, e.g. Sarnelli and Testa (2002).

8.2.4 Modiﬁed microbridges

This kind of junction uses artiﬁcially induced weak links in superconducting

microbridges. The modiﬁcation of the superconducting material can be done by

electron, ion or proton beams if the diameter of the beam is clearly below 100 nm

(Fig. 8.12). Directly written focussed e-beam (FEBI) junctions show an excellent

Josephson behaviour but often have a low stability over time because the

modiﬁcation is self-annealing at room temperature. By additional annealing

processes these problems can be solved (Pauza et al., 1997). The modiﬁcation

with ions as a focussed beam as well as through masks with slit width below

150 nm are very stable over time. But besides complex dependencies on

preparation parameters, there are often problems with a very restricted range of

working temperature or with ﬂux-ﬂow coupling instead of Josephson behaviour.

Modiﬁed microbridges can also be obtained if in the bridge region a scratch or a

small etch trench is induced in the substrate before superconducting ﬁlm is

deposited. Another type uses diffusion of material into the bridge region in a small

part of the bridge. If it is technologically possible to prepare the active part of the

bridge with geometrical dimensions in the order of the coherence length of the

superconductor, the traditional concept of nanobridges works (Fig. 8.13a). For

high-T

materials, the very small coherence length results in additional

requirements on the technology. If the nanobridges do not show typical ﬂux-ﬂow

behaviour it can be assumed that besides the geometrical dimensions (Fig. 8.13b

8.11 Ramp-type junction (shown schematically). There exist different

variations where the barrier layer is restricted to parts like the edge

only.

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