Buschow K.H.J. (Ed.) Concise Encyclopedia of Magnetic and Superconducting Materials

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metal alloys the narrow 3d band leads to a certain

degree of localization, which has to be taken into

account. Examples for this latter behavior are most

Mn compounds in particular the Mn containing

Heusler alloys whose ﬁnite temperature magnetic

properties have successfully be described on the basis

of a Heisenberg model (Ku

bler et al. 1983).

See also: Density Fluctuational Theory: Magnetism;

Magnetism in Solids: General Introduction; Phase

Transitions, Landau Theory of; Spin Fluctuations

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Itinerant Electron Systems: Magnetism (Ferromagnetism)

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352

Josephson Junctions: High-T

With the advent of ceramic superconductors, attempts

were very quickly made to translate the techniques

known from classical superconducting electronics

to this new class of materials. In classical supercon-

ductivity, Josephson junctions are generally fabricated

in a multilayer technology, incorporating at least

two superconducting layers (niobium or NbN) and

between them either insulating layers for tunnel junc-

tions (Al

, MgO, AlN, etc.) or normal conducting

layers for proximity effect devices or combinations

thereof for special junction types, e.g., SINIS junc-

tions. For high-T

devices this concept turned out to

be very difﬁcult with the materials preparation

techniques available at that time and with the very

short coherence length of the high-T

superconduc-

tors (HTSs). It was recognized very early that grain

boundaries in HTSs behave like Josephson junctions.

Much research was done on how to prepare grain

boundaries in HTSs in a controlled manner and to

elucidate the relationship between grain boundary

structure and critical current density, j

, for the

supercurrent. This led to the experimental veriﬁcation

of the prediction for a d-wave symmetry of the wave

functions describing the superconducting state in a

HTS. The results also made clear that grain boundary

junctions are unlikely to create the necessary repro-

ducibility needed for superconducting electronic de-

vices. Nevertheless, as a research tool or for devices

with a very small number of junctions like SQUIDs,

the grain boundary junctions are very valuable.

Subsequently a new junction type has been dem-

onstrated, which makes use of the high critical cur-

rent densities in the ab-planes of the HTS and the

epitaxial growth of homologous perovskite materials

onto a ramp, cut into the superconductor under a ﬂat

angle. Even though the fabrication process is more

complicated, the reproducibility and controllability

of these junctions is much better than that of grain

boundary junctions. Circuits of some tens of junc-

tions can be realized with reasonable chance of

success. In various forms, this junction type is the

standard in research laboratories and industry for

circuits with about 10 junctions or more.

The I

product of HTS Josephson junctions

strongly inﬂuences the switching speed and maximum

frequency in digital circuits and oscillators and the

modulation voltage for SQUIDs. Whereas at low tem-

peratures I

products of 30 mV or more were orig-

inally expected for YBaCuO Josephson junctions, the

maximum values reached are about 9 mV. Most junc-

tions, however, only show an I

productofafew

hundred microvolts at their operation temperature. It

is clear that interfaces between electrode and barriers

of the Josephson junctions play an important role. It

has been shown that band bending effects at these in-

terfaces probably play an important role in decreasing

their transparency. There are strong indications that

calcium doping near the interface might decrease the

band bending.

1. Grain Boundary Junctions

The ﬁrst HTS Josephson junctions were based on the

naturally occurring grain boundaries in sintered bulk

materials or in polycrystalline ﬁlms prepared by the

two-step method. It was possible to demonstrate the

Josephson effect and SQUID operation with these

junctions, but a controlled preparation was impossi-

ble. After the epitaxial growth of YBCO on SrTiO

was demonstrated, Dimos et al. (1990) used this

technique to prepare the ﬁrst controlled grain bound-

aries on a SrTiO

bicrystal: two crystals of SrTiO

with different orientation of the crystal axes are

glued together, so that an artiﬁcial grain boundary is

created.

YBCO ﬁlms epitaxially grown on top of the bicrys-

tal have the same orientation as the substrate and

form a grain boundary with the same angle as the

bicrystal at the bicrystal interface (see Fig. 1(a)). By

changing the angle of the bicrystal, grain boundaries

in the YBCO ﬁlms with different angles can be cre-

ated. In this way more complicated grain boundary

structures can also be created such as tri-ray and

multiple parallel structures.

The electrical transport through such a grain

boundary shows Josephson behavior, which can be

described by an RSJ model with some capacitive

loading. The normal resistance and the critical cur-

rent density of the grain boundary junction depend

on the grain boundary angle (see Fig. 1(b)).

Whereas the electrical transport can be described

by simple models, the magnetic ﬁeld dependence of

the critical current density is complicated and shows

only a vague resemblance to the Fraunhofer pattern

found for classical Josephson junctions. This be-

havior was for long attributed to inhomogeneities in

the grain boundary. Subsequent work has shown

instead that the magnetic ﬁeld dependence can be

explained by a d-wave symmetry of the wave function

describing the state of the superconductor.

The local structure of the grain boundary leads to

locally back-ﬂowing currents and thus to a mixture

of positive and negative current densities along the

junction. Simulations assuming d-wave symmetry

yield good agreement with measured results for

the magnetic ﬁeld dependence. In contrast to the

well-known ﬂux lines containing F

¼h/2e, ﬂux lines

353

containing F

/2 can spontaneously occur at interfac-

es. Tsuei and Kirtley (2000) predicted the d-wave

symmetry and showed experimentally using a tricrys-

tal grain boundary ring structure (see Fig. 2) that the

predicted ﬂux lines with half-integer ﬂux quanta exist.

In this geometry two of the three junctions are

normal Josephson junctions, the third is a Josephson

p-junction, in which an additional phase shift of p

occurs owing to the symmetry of the d-wave function:

J ¼ J

sinjðnormal Josephson junctionÞ

J ¼ J

sinj þ p ¼J

sinjðJosephson p-junctionÞ

The Josephson p-junction is unique to HTSs. It can

simplify the design of superconducting electronics

circuits and it opens opportunities for new applica-

tions, e.g., qubits for quantum computing.

In addition to the bicrystal method, a number of

other methods exist for creating artiﬁcial grain

boundaries. The two principal ones are seed layer

junctions and step edge junctions (Fig. 3). Seed layer

junctions make use of the fact that some oxide layers

grow on top of each other epitaxially, but rotated in

their crystal axes by a certain angle owing to a mis-

match of the lattice parameters. The complicated

grain boundary structures result in poor Josephson

behavior and bad reproducibility. Step edge junctions

in contrast can yield junctions of high quality,

although this technique is also not very reproducible.

Figure 2

Experimental conﬁguration for the p-ring tricrystal

experiment of Tsui and Kirtley (2000).

Figure 1

(a) Bicrystal grain boundary Josephson junction; (b)

dependence of the critical current density on the grain

boundary angle.

Figure 3

(a) Seed layer and (b) step edge Josephson junctions.

354

Josephson Junctions: High-T

For fabrication one has to prepare a step on a

substrate surface, which is either done by etching

away part of the substrate or by locally adding

(homo)epitaxially a layer on top of the substrate. Step

height and angle are critical. Deposition of a thin ﬁlm

of a HTS on top results in the formation of grain

boundaries at the top and the bottom edge of the step.

A step edge Josephson junction thus consists of two

series-connected closely coupled Josephson junctions.

In general some roughening owing to the etching or

lithographic process occurs along the step resulting

in complicated grain boundary structures along the

edge. For a small number of Josephson junctions next

to each other as needed in SQUID applications, these

junctions are quite similar in general. High-quality

step edge junctions have successfully been fabricated

and incorporated in SQUID structures.

2. Josephson Junctions with Artiﬁcial Barriers

Two advantages of classical planar Josephson junc-

tions are the ability to fabricate it anywhere on a

substrate and to change its transport properties in a

controlled way, e.g., engineer the composition of the

barrier down to the atomic level by thin-ﬁlm depo-

sition techniques. For high-T

Josephson junctions

one would also like to adjust the barrier transparency

and its height and fabricate the junction in places

where it would be needed from circuit design re-

quirements and not vice versa. In this sense planar

high-T

Josephson junctions would be ideal. Not only

is the circuit design and layout well known from

classical superconductivity, but also barrier material

and barrier thickness could be varied or even complex

barrier structures realized.

2.1 Planar Junctions

HTSs are strongly anisotropic with significantly high-

er critical current densities in the Cu–O ab-planes

than for transport along the c-axis. The quasi two-

dimensional behavior leads to the possibility of build-

ing junctions by layer-by-layer engineering, choosing

layer compositions that enable epitaxial growth on

one side that modify the transport properties from

superconducting to normal conducting or insulating

behavior over a length scale of one or very few per-

ovskite building blocks on the other side.

Such work requires extreme growth control of the

materials and is practically only possible in oxide-

MBE machines or pulsed laser deposition systems

with similar controls. Bozovic and Eckstein (1997)

have done pioneering work especially by applying

MBE to the growth of bismuth compounds and to

the modiﬁcation of transport properties in the c-axis

direction (see Fig. 4). Even though the critical current

densities are still quite low, MBE seems to be the way

towards a reproducible fabrication of large numbers

of high-T

Josephson junctions.

The fabrication of planar Josephson junctions has

been tried in a number of ways. Attempts to isolate

natural tunnel junctions from bismuth compounds

(transport in the c-axis direction) have been success-

ful. These junctions show interesting characteristics,

but have only little practical impact. Attempts to

make use of the c-axis coupling in YBaCuO or to

grow sandwich structures on a-axis-oriented YBa-

CuO results in irreproducible Josephson junction

behavior, with very unrealistic decay length for the

transport through the structures. Sandwich junctions

on 103-oriented YBaCuO have shown some success,

these junctions showing reproducibility comparable

to other high-T

Josephson junctions.

2.2 Ramp-type Josephson Junctions

Ramp-type Josephson junctions form the basis for

most applications in which 10 or more junctions are

needed. They are based on the idea that the barrier

Figure 4

Layer-by-layer engineering of bismuth compounds for

HTS Josephson junctions: (a) cross-section through a

sandwich; (b) I–V characteristics of the resulting

Josephson junction.

355

Josephson Junctions: High-T

for Josephson operation should separate the CuO

planes capable of carrying high current densities and

transporting the supercurrents to the barrier. A sche-

matic cross-section is depicted in Fig. 5(a). The most

critical step is the cut through the base sandwich un-

der a ﬂat angle without destroying the surface of the

ramp for subsequent epitaxial growth of the barrier

and counter-electrode. Depending on the type of

Figure 5

(a) Schematic and (b) magnetic ﬁeld dependence and

I–V characteristics of a typical ramp-type junction.

Figure 6

Dependence of (a) normal state conductance and

(b) critical current density on the barrier thickness for

gallium-doped PrBaCuO for different doping levels.

specific resistance with lines of constant I

product.

356

Josephson Junctions: High-T

barrier and thickness, the critical current density and

the normal resistance of the junction can be adjusted.

The most promising barrier for operation at 77 K is

cobalt-doped YBaCuO. Also ‘‘interface engineered’’

junctions have received a lot of attention because of

their slightly better reproducibility. For operation

at temperatures below 50 K, e.g., for digital applica-

tions, PrBaCuO barriers are very attractive. With this

barrier material the critical current density and

the normal resistance can be adjusted independently

(see Fig. 6(a))—the critical current density via the

thickness of the barrier and the normal resistance via

the amount of gallium doping, which enhances the

specific resistance with increasing gallium content.

2.3 High-T

–Low-T

Junctions

In an effort to combine high-T

and low-T

junctions

on the same chip, high critical current density tran-

sitions between high-T

and low-T

superconductors

have been developed in the form of ramp-type junc-

tions with YBaCuO base electrode, gold barrier, and

niobium counter-electrode. These junctions show ex-

cellent Josephson characteristics (see Figs. 7(a) and

(b)) with little parameter spread. In addition, these

junctions can be prepared on ramps with an orien-

tation in different crystallographic directions, thus

yielding junctions with 0- to p-junction characteris-

tics. Such junctions combine the reproducibility of

the low-T

junctions with the high I

product and

the unique d-wave characteristics of HTSs.

2.4 Electron Beam and Ion Beam Josephson

Junctions

Oxygen-deﬁcient or structurally damaged regions of

HTSs have a lower T

or become normally conduct-

ing or even insulating. Such damage can be intro-

duced locally by high-energy bombardment with

electrons or with ions. In this way a Josephson junc-

tion can be ‘‘written’’ into a thin ﬁlm of YBaCuO.

The resulting junctions show good nonhysteretic

Josephson behavior. For electron beam writing, elec-

tron microscopes with an acceleration voltage of

about 400 keV are needed; for ion beam writing, fo-

cused ion beam (FIB) etchers are applied with an

acceleration voltage of about 30 keV. Quite high

radiation doses are needed to prepare the barrier, so

that the writing speed is quite low. In addition, the

junction parameters cannot easily be modiﬁed. Nev-

ertheless, electron beam and FIB writing is attrac-

tive for the prototyping of simple superconducting

circuits but cannot be considered as a production-

type technique.

3. Conclusion

The availability of reliable and reproducible high-T

Josephson junctions depends strongly on advances in

materials research in the area of perovskites and the

reﬁned control of the deposition of these materials,

both for composition and structure. The techniques

for the preparation of high-T

Josephson junctions

are sufﬁcient for small electronics circuits with about

10–50 Josephson junctions. For applications with a

larger number of junctions, the knowledge of fabri-

cation and understanding of these materials has to be

improved significantly in order to reach the required

reproducibility.

See also: Josephson Junctions: Low-T

Bibliography

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of YBa

7x

/YBa

2.79

0.21

7x

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7x

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junctions. Appl. Phys. Lett. 65, 904–6

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transport properties of grain boundaries in YBa

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entation dependence of grain-boundary critical currents in

YBa

7d

bicrystals. Phys. Rev. Lett. 61, 219–22

Figure 7

YBaCuO/Au/Nb ramp-type junction: (a) cross-section;

(b) I–V characteristics.

357

Josephson Junctions: High-T

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trolled preparation of all high-T

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University of Twente, Enschede, The Netherlands

Josephson Junctions: Low-T

In the ﬁeld of superconducting electronics, Josephson

junctions with electrodes made of niobium thin ﬁlms

¼9.0–9.3 K) or niobium nitride (NbN) thin ﬁlms

¼14–17 K) play an important role. For example,

Josephson junctions with niobium thin ﬁlms as elec-

trodes and very thin aluminum oxide layers as bar-

riers (Nb/AlO

/Nb junctions) are widely used for

implementing practical superconducting devices,

e.g., superconducting quantum interference devices

(SQUIDs) for biomedical applications (see SQUIDs:

Biomedical Applications), superconductor–insulator–

superconductor (SIS) mixers for radio astronomy,

and Josephson junction devices for voltage standards

(see Josephson Voltage Standard). Also, Nb/AlO

/Nb

junctions are used for demonstrating the performance

of various digital and analog circuits that are oper-

ated based on Josephson effects. This is because

Nb/AlO

/Nb junctions are extremely stable with re-

spect to thermal cycling and storage in air, have high-

quality tunneling characteristics, and can be fabricated

with good run-to-run reproducibility. Josephson

junctions with NbN thin ﬁlms as electrodes are used

for fabricating superconducting devices with unique

performance, e.g., an SIS mixer having low noise tem-

peratures at a frequency range over 700 GHz and an

analog-to-digital converter operated at 10 K.

This article describes the fabrication, electrical

characteristics, and stability of Nb/AlO

/Nb junc-

tions and NbN Josephson junctions.

1. Nb/AlO

/Nb Junctions

1.1 Fabrication

The ﬁrst successful fabrication of Nb/AlO

/Nb junc-

tions was reported by Gurvitch et al . (1983), followed

by a large number of reports on the characterization

of junctions and the development of technologies for

fabricating junctions with high yield, high uniformity,

and high reproducibility. The adoption of aluminum

as a barrier material for Josephson junctions with

niobium electrodes was motivated by the fact that

aluminum shows a suitable wettability on fresh sur-

faces of niobium. Because of the afﬁnity of aluminum

to niobium, an aluminum layer deposited on a nio-

bium base electrode well covers the surface of the

electrode even when the thickness of the overlayer is

very small (o10 nm). This enables the formation of a

uniform and pinhole-free tunnel barrier by thermally

oxidizing an aluminum layer on a niobium electrode,

resulting in the fabrication of a high-quality junction.

However, there exist several causes that induce dete-

rioration of junction characteristics. For example,

Huggins and Gurvitch (1985) emphasized that heat

sinking of the substrate to a water-cooled table dur-

ing the junction preparation is crucial for obtaining a

high yield of high-quality samples. Experimental re-

sults suggest that without heat sinking of the subst-

rate, diffusion of oxygen atoms in the barrier into

the electrodes occurs by elevation of the substrate

temperature during the deposition of the counter

electrodes. Kuroda and Yuda (1988) have claimed

that relaxation of stress in sputter-deposited niobium

ﬁlms with etching of the ﬁlms causes deformation of

the electrodes, resulting in large leakage currents in

junctions.

Fabrication of Nb/AlO

/Nb junctions is generally

carried out in a sputtering system with a stainless

steel chamber (or chambers), a water-cooled subst-

rate holder (or holders), sputtering targets of niobium

and aluminum, and a vacuum pump (or pumps)

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Josephson Junctions: Low-T

(see Fig. 1). A wafer (usually a single crystal of sil-

icon) with a mirror polished surface is set on the

substrate holder (the turntable in Fig. 1) with a good

thermal contact. After ﬁlling the chamber with re-

search-purity argon up to a pressure of 1–2 Pa, a

niobium ﬁlm (100–200 nm) is deposited on the wafer

by sputtering the niobium target. A very thin alumi-

num layer (5–10 nm) is then deposited on top of the

niobium ﬁlm by sputtering the aluminum target. The

formation of a tunnel barrier is achieved by oxidizing

the aluminum layer in a static atmosphere of pure

oxygen. The pressure of oxygen gas and oxidation

time are set so as to obtain a targeted critical current

density, J

, for the junctions (Miller et al. 1993). After

ﬁnishing the formation of a tunnel barrier, a niobium

ﬁlm (100–200 nm) for the counter electrodes of the

junctions is deposited in an argon atmosphere, re-

sulting in the formation of a junction sandwich on the

wafer (Fig. 2(a)).

Definition of individual junctions from the junc-

tion sandwich is performed using photolithography

and etching techniques. After taking the wafer out

of the sputtering system, the wafer is covered with a

photoresist pattern that deﬁnes the base electrodes of

the junctions. Multilayers unprotected by the photo-

resist pattern are then removed by wet etching or

dry etching (Fig. 2(b)). The definition of individual

junctions is performed by trimming the counter nio-

bium ﬁlm in a reactive gas using another photoresist

pattern as a mask (Fig. 2(c)). Next, an insulation ﬁlm

(usually a sputtered SiO

ﬁlm) is deposited onto the

sample to protect the exposed surface of the base

electrodes (Fig. 2(d)). Via holes for making contacts

to junctions are then fabricated by locally etching the

insulation ﬁlm in a reactive gas (Fig. 2(e)). Finally,

wiring electrodes are fabricated by depositing a nio-

bium ﬁlm on the sample and trimming with a reactive

gas (Fig. 2(f )).

The process used for fabricating Nb/AlO

/Nb

junctions is called a ‘‘whole-wafer’’ process because

a junction sandwich is formed on the whole surface of

a wafer prior to the lithographic processes. The ad-

vantage of the ‘‘whole-wafer’’ process is that all wet

processes are excluded from the formation of the

junction sandwich, enabling fabrication of junctions

with good run-to-run reproducibility. The concept of

the ‘‘whole-wafer’’ process was ﬁrst demonstrated by

Kroger et al. (1981) in the fabrication of Nb/Si:H/Nb

junctions.

1.2 Electrical Characteristics

Measurement of current–voltage (I–V) characteristics

for Nb/AlO

/Nb junctions is, in general, carried out

while immersing the sample in liquid helium since all

devices fabricated using Nb/AlO

/Nb junctions are

operated at liquid helium temperature (4.2 K), with a

Figure 1

Schematic of a sputtering system used for fabricating Nb/AlO

/Nb junctions.

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Josephson Junctions: Low-T