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few exceptions. During the measurement of I–V

characteristics, the sample is surrounded with m-metal

or niobium cans to minimize the inﬂuence of external

magnetic ﬁelds, e.g., the terrestrial magnetic ﬁeld. An

I–V characteristic measured for a Nb/AlO

/Nb junc-

tion at 4.2 K is shown in Fig. 3. Like this example, at

4.2 K Nb/AlO

/Nb junctions typically show high-

quality tunneling characteristics with a well-deﬁned

gap and very small subgap leakage currents.

The gap voltage, V

, which is deﬁned as the voltage

at which the slope of the I–V curve becomes a max-

imum, is 2.9 mV for the junction in Fig. 3, very close

to the theoretical value (3.0 mV) calculated for a

Josephson tunnel junction with niobium base and

counter electrodes. This means that the supercon-

ducting properties in the base and counterelectrodes

of the junction are as good as that for bulk niobium.

The relative amplitude of leakage currents for a

Josephson tunnel junction can be evaluated by a ratio

of a static resistance measured below V

(typically

at a voltage near half of V

) and a static resistance

measured above V

(typically at a voltage more than

twice V

The former is called the subgap resistance, R

and

the latter the normal resistance, R

. Nb/AlO

/Nb

junctions typically have R

values exceeding 10

unless their critical current density is extremely high.

The specific capacitance, C

, i.e., a capacitance per

unit area, for a Josephson tunnel junction is an im-

portant parameter in the design of SQUIDs, SIS

mixers, etc. C

values for Nb/AlO

/Nb junctions have

been estimated from measurement of Fiske modes for

junctions (van der Zant et al. 1994) and measurement

of resonant voltages for SQUIDs (Maezawa et al.

1995).

1.3 Stability

The stability of Nb/AlO

/Nb junctions against ther-

mal cycling, aging at room temperature, and anneal-

ing at an elevated temperature has been examined. In

Figure 2

Fabrication process of a Nb/AlO

/Nb junction.

Figure 3

I–V characteristic for a Nb/AlO

/Nb junction at 4.2 K

(vertical axis: 1 mA per division; horizontal axis: 1 mV

per division).

360

Josephson Junctions: Low-T

one study (Gates et al. 1984) 400 Nb/AlO

/Nb junc-

tions were cycled 4880 times between room temper-

ature and 6 K, resulting in no failures due to shorts

and no change in the average critical currents. The

same junctions were then aged in a nitrogen atmos-

phere at room temperature for two months, resulting

in no change in the average critical currents. Finally,

the junctions were annealed at 100 1C for 2 h in a

helium atmosphere, again resulting in no change in

the average critical currents. A ﬁnite change (reduc-

tion) in the critical currents was observed after the

junctions had been annealed at 150 1C.

2. NbN Josephson Junctions

2.1 Fabrication

Fabrication of Josephson junctions with NbN ﬁlms

as base and counter electrodes was ﬁrst reported by

Shinoki et al. (1981). Reactively sputter-deposited

NbN ﬁlms were used as electrodes and amorphous

silicon (a-Si) ﬁlms that had been produced by glow

discharge decomposition of silane (5% SiH

and 95%

argon) as tunnel barriers. The NbN/a-Si/NbN junc-

tions showed good tunneling characteristics with

small subgap leakage currents. However, their gap

voltages remained at 4.2 mV, much lower than the

theoretical gap voltage (46 mV) for a Josephson

tunnel junction with NbN base and counter elec-

trodes. Improvement of the gap voltage for NbN

junctions was made by Shoji et al. (1985) by intro-

ducing very thin MgO ﬁlms (o1 nm) as tunnel bar-

riers and a ‘‘whole-wafer’’ process to the junction

fabrication. MgO is employed as a barrier material

for NbN junctions since it has the same structure (B1:

f.c.c., NaCl type) as NbN and a lattice parameter

close to that of NbN. Wang et al. (1997) reported

NbN junctions with reactively sputter-deposited al-

uminum nitride (AlN) barriers had gap voltages as

large as those for NbN/MgO/NbN junctions. AlN

also has B1 structure and a lattice parameter close to

that of NbN.

2.2 Electrical Characteristics

An I–V characteristic measured for a NbN/MgO/NbN

junction at 4.2 K is shown in Fig. 4. Like this example,

NbN/MgO/NbN junctions typically show good I–V

characteristics at 4.2 K with gap voltages greater than

5 mV and small subgap leakage currents. This is the

same as for the case of NbN/AlN/NbN junctions. The

values for NbN/MgO/NbN and NbN/AlN/NbN

junctions are roughly twice those for Nb/AlO

/Nb

junctions, but are still smaller than the theoretical V

value for all-NbN junctions. The reduction of exper-

imental V

values from the theoretical value mainly

arises from lower superconducting energy gaps in

counter electrodes than in base electrodes. The relative

amplitude of leakage currents for NbN/MgO/NbN

and NbN/AlN/NbN junctions depends strongly on

their critical current density. For example, NbN/MgO/

NbN junctions with J

o1kAcm

2

typically have

410, while junctions with J

41kAcm

2

have

o10. A theoretical explanation for the reduc-

tion of R

values with increase in critical current

density has not been given. C

values for NbN/MgO/

NbN and NbN/AlN/NbN junctions have been esti-

mated from measurement of Fiske modes (Shoji et al.

1985) and measurement of resonant voltages for

SQUIDs (Wang et al. 1997), respectively.

Critical currents for a NbN/MgO/NbN junction

measured at 2 K and higher temperatures are plotted in

Fig. 5. As can be seen, owing to high superconducting

Figure 4

I–V characteristic for a NbN/MgO/NbN junction at

4.2 K (vertical axis: 0.2 mA per division; horizontal axis:

2 mV per division).

Figure 5

Temperature dependence of critical current for a NbN/

MgO/NbN junction.

361

Josephson Junctions: Low-T

critical temperature (14–17 K) in NbN electrodes, crit-

ical currents of NbN Josephson junctions at 10 K are

more than 60% of those at 4.2 K. This has stimulated

development of Josephson devices that are operated at

10 K with a compact closed-cycle refrigeration system.

2.3 Stability

As is the case for Nb/AlO

/Nb junctions, Josephson

junctions having NbN electrodes show extremely

high stability with respect to thermal cycling and

storage in air. Furthermore, because NbN is less

chemically active, Josephson junctions with NbN

electrodes can withstand a higher processing temper-

ature than those with niobium electrodes.

3. Summary

Fabrication of high-quality Josephson junctions with

sputter-deposited niobium ﬁlms or reactively sputter-

deposited NbN ﬁlms as electrodes has been achieved

by the use of barrier materials ﬁt to the electrodes and

the introduction of a ‘‘whole-wafer’’ process. In the

case of Josephson junctions with niobium electrodes,

aluminum is employed as a barrier material since it

shows suitable wetting on a fresh surface of niobium.

Because of the afﬁnity of aluminum to niobium, an

aluminum layer deposited on a niobium electrode

covers the surface of the electrode well, resulting in

the formation of a uniform and pinhole-free tunnel

barrier by thermal oxidation of the aluminum layer.

The introduction of a ‘‘whole-wafer’’ process enables

junctions to be fabricated with good run-to-run re-

producibility. In the case of Josephson junctions with

NbN electrodes, high-quality tunneling characteris-

tics with gap voltages greater than 5 mV and small

subgap leakage currents have been achieved by the

use of very thin MgO or AlN ﬁlms as tunnel barriers.

Both materials have the same structure as NbN and

lattice parameters close to that of NbN, which must

be the origin of the improved junction characteristics.

See also: Josephson Junctions: High-T

Bibliography

Gates J V, Washington M A, Gurvitch M 1984 Critical current

uniformity and stability of Nb/Al–oxide–Nb Josephson junc-

tions. J. Appl. Phys. 55, 1419–21

Gurvitch M, Washington M A, Huggins H A 1983 High quality

refractory Josephson tunnel junctions utilizing thin alumi-

num layers. Appl. Phys. Lett. 42, 472–4

Huggins H A, Gurvitch M 1985 Preparation and characteristics

of Nb/Al–oxide–Nb tunnel junctions. J. Appl. Phys. 57,

2103–9

Kroger H, Smith L N, Jillie D W 1981 Selective niobium an-

odization process for fabricating Josephson tunnel junctions.

Appl. Phys. Lett. 39, 280–2

Kuroda K, Yuda M 1988 Niobium-stress inﬂuence on

Nb/Al-oxide/Nb Josephson junctions. J. Appl. Phys. 63,

2352–7

Maezawa M, Aoyagi M, Nakagawa H, Kurosawa I 1995 Spe-

cific capacitance of Nb/AlO

/Nb Josephson junctions with

critical current densities in the range of 0.1–18 kA/cm

. Appl.

Phys. Lett. 66, 2134–6

Miller R E, Mallison W H, Kleinsasser A W, Delin K A,

Macedo E M 1993 Niobium trilayer Josephson tunnel junc-

tions with ultrahigh critical current densities. Appl. Phys.

Lett. 63, 1423–5

Shinoki F, Shoji A, Kosaka S, Takada S, Hayakawa H 1981

Niobium nitride Josephson tunnel junctions with oxidized

amorphous silicon barriers. Appl. Phys. Lett. 38, 285–6

Shoji A, Aoyagi M, Kosaka S, Shinoki F, Hayakawa H 1985

Niobium nitride Josephson tunnel junctions with magnesium

oxide barriers. Appl. Phys. Lett. 46, 1098–100

Van der Zant H S J, Receveur R A M, Orlando T P 1994 One-

dimensional parallel Josephson junction arrays as a tool for

diagnostics. Appl. Phys. Lett. 65, 2102–4

Wang Z, Uzawa Y, Kawakami A 1997 High critical current

density NbN/AlN/NbN tunnel junctions for submillimeter

wave SIS mixers. IEEE Trans. Appl. Supercond. 7, 2797–800

A. Shoji

Electrotechnical Laboratory, Tsukuba, Japan

Josephson Voltage Standard

The electronic system of a macroscopic superconduc-

tor is characterized by the formation of electron

pairs, so-called Cooper pairs (Bardeen et al. 1947),

which carry d.c. currents without these being dissi-

pated. The Cooper pair system of two separated su-

perconductors can be described by two independent

single macroscopic order parameters c

1,2

7exp(ij

1,2

), the time evolution of which is

expressed by the Schro

dinger equation @c

1,2

/@t ¼

(i/_)E

1,2

. E

1,2

are the energies of the Cooper pair

systems and 7c

1,2

7 ¼(n

1,2

)

1/2

denotes the Cooper pair

densities n

1,2

. In 1962 Josephson described the phe-

nomenon of Cooper pair transport between two

weakly coupled superconductors by two equations:

¼ I

sin j and VðtÞ¼ð_=2eÞdj=dt

The ﬁrst Josephson equation denotes the supercon-

ducting d.c. Cooper pair current across the barrier

dependent on the phase difference j

j

¼j of the

order parameters of the two weakly coupled super-

conductors: a Josephson junction. I

is the maximum

possible supercurrent. The second equation shows that

the voltage across a Josephson junction is propor-

tional to the time derivative of the phase difference

(see Josephson Junctions: Low-T

, Josephson Junctions:

High-T

). If the Josephson junction is biased by a

constant voltage, V(t) in the second Josephson equa-

tion is replaced by the constant value V. Integrating

362

Josephson Voltage Standard

the equation and introducing the result j ¼j

(2e/_)Vt into the current equation, one obtains

I ¼I

sin(ot þj

), which describes an alternating

supercurrent with frequency f ¼o/2p ¼2e/V.The

Josephson junction is a high-frequency oscillator that

converts a frequency into a voltage: V ¼(h/2e)f ¼j

The parameter j

denotes the ﬂux quantum. The

d.c. voltage across a Josephson junction is the rate of

ﬂux quanta transferred across the junction. If the

Josephson oscillator is phase locked to an external

microwave oscillator with a well-known frequency,

, constant voltage steps appear at V

¼nj

(n ¼1, 2, 3 y) in the nonlinear d.c. characteristic of

the junction (Shapiro 1963). For the nth harmonic the

current range, DI

, over which the junction oscillator

is phase locked to the external oscillator is described

by DI

¼2I

(2eV

/_o

7, where V

is the radio-

frequency (RF) voltage amplitude across the junc-

tion. The precision of the voltage steps is determined

only by the uncertainty of f

, which can be kept

smaller than 10

11

by means of modern frequency

standards like atomic cesium clocks. This makes the

voltage steps ideal reference voltages for standard

voltage measurements. The maximum step voltage

(e.g., V

E145 mV for f

¼70 GHz) is limited by the

energy gap voltage of the superconducting electrodes

(e.g., 2.5 mV for niobium).

In contrast to the ideal Josephson contact de-

scribed above, a real junction is a parallel connection

of the external current source I(t) ¼I

þI

sin o

the junction normal-state resistance R

, the junction

capacitance C, and the ideal Josephson inductance

I ¼I

sin j. If the currents are distributed homogene-

ously across the junction area A, this circuit is de-

scribed by

þ I

sin o

t ¼ I

sin j þ VðtÞ=R

þ CdVðtÞ=dt

(Stewart 1968, McCumber 1969, Kautz 1981). With

V(t) ¼(_/2e)dj/dt, i

¼I

, i

¼I

, O ¼_o

/2eI

¼_t/2eI

,andb ¼2eI

C/_, one obtains a

dimensionless differential equation for a damped

driven oscillator:

j=dt

þ dj=dt þ sin j ¼ i

þ i

sinðOt

where b

1/2

is the quality factor for the LC Josephson

resonator and characterizes the damping of the Jose-

phson oscillator.

Large values of R

and C lead to low junction damp-

ing and thus to a hysteresis in the d.c. characteristic.

Particularly, superconductor–insulator–superconductor

(SIS) tunnel junctions provide very low damping

and a strong hysteresis in the d.c. characteristic

(Fig. 1(a)). Moreover, in this case, the quasiparticle

branch of the d.c. characteristic more or less follows

the voltage axis at nearly zero current for voltages

smaller than the gap voltage. Therefore, the constant

voltage steps may cross the voltage axis with the

effect that reference voltages are generated without

any current ﬂowing across the junctions (Fig. 1(b)).

The zero current steps generally are multivalued:

up to about seven deﬁned voltage steps per junction

for f

¼70 GHz. Other junction types made of super-

conductor–normal metal–superconductor (SNS)

sandwiches or superconductor–insulator–normal

metal–insulator–superconductor (SINIS) sandwiches

(Maezawa and Shoji 1997, Sugiyama et al. 1997,

Kupriyanov et al. 1999) show much higher damp-

ing and thus no hysteresis in the d.c. characteristic

(Fig. 1(c)).

There is only one reference voltage step at a certain

bias current (Fig. 1(d)), which makes the reference

voltage single valued but also results in an arbitrarily

lower maximum output reference voltage per single

junction at a given frequency. Typical junction data

are given in Table 1.

1. Conventional SIS Voltage Standard

Figure 1 shows that a single Josephson junction gen-

erates reference voltages not much higher than about

1 mV. Early voltage standards on the basis of a single

junction, together with a conventional voltage divider,

provided an output voltage of 1 V with an uncertainty

of about 5 10

8

V (Kose 1974). The accuracy of

these instruments was ﬁnally limited by the complex

calibration procedure for the voltage divider. Further

improvement could therefore be achieved only by

an increase in the Josephson reference voltage from a

few millivolts to values of 1 V or more by means of

large series arrays of Josephson junctions. To realize

such a series array voltage standard, the use of

underdamped SIS tunnel junctions has been suggest-

ed (Levinsen et al. 1977), because for zero current

steps it would not be necessary to have a small junc-

tion parameter spread. In the zero current mode a

parasitic series resistance would not create errors and

the maximum output reference voltage of about 1 mV

per junction in the case of niobium electrodes would

limit the junction number to a technologically ac-

ceptable value (about 1000 junctions for 1 V). In ad-

dition, a large number of quantized voltages between

zero and the maximum output voltage for convenient

nonlinearity or voltage ratio measurements can be

adjusted.

To operate successfully such a series array of un-

derdamped tunnel junctions, two problems must be

solved.

(i) The single junction is a nonlinear, under-

damped oscillator that has to be coupled to the exter-

nal oscillator without creating chaos (for an overview

see Kautz 1996). To reach the goal of a stable

phase lock with the external oscillator, the reso-

nance frequency of the Josephson oscillator,

¼(2eI

/_C)

1/2

, should be kept lower than the

frequency of the external drive, o

. Moreover, the

363

Josephson Vol tage Standard

distribution of the phase difference across the junc-

tion area should be homogeneous. These restrictions

lead to a limitation of the critical current and thus

to a ﬁnite current width of the step. With an external

drive frequency of f

¼70 GHz, a sufﬁcient step

width and a stable phase lock are obtained for critical

currents of about 150 mA and junction areas of

about 20 mm 50 mm in the case of Nb–Al

–Nb

junctions.

(ii) As the stable phase lock of the junctions to the

external microwave is also dependent on the incident

microwave power, the array must be integrated into a

microwave circuit that homogeneously distributes the

microwave power to all junctions (Niemeyer et al.

1984, 1985). The series array is therefore arranged as

a part of a periodic low-impedance (5 O) supercon-

ducting microstripline. In the case of the SIS junction

array, the RF currents are mainly capacitive and the

impedance mismatch between the stripline impedance

and R

is large. This prevents an effective RF power

dissipation in a single junction of the array. As only a

very small fraction of the RF power is transferred to

the single junction, the distribution of the power

along the stripline is homogeneous enough to inte-

grate up to about 3500 junctions into a continuous

stripline. For larger arrays the stripline conﬁguration

is divided into four or eight parallel microwave paths

that are terminated by matched loads and sepa-

rated by d.c. blocks from the RF distribution net-

work (cf. Fig. 2).

This RF design has proved so effective that it can

be applied to circuits with up to 2 10

junctions and

output voltages of more than 10 V (Hamilton et al.

Figure 1

d.c. characteristic of (a) Nb–Al

–Nb tunnel junction (vertical: 1 mV per division; horizontal: 0.125 mA per

division); (b) Nb–Al

–Nb tunnel junction under 70 GHz microwave radiation (vertical: 1 mV per division;

horizontal: 0.125 mA per division); (c) Nb–PdAu–Nb junction (vertical: 20 mV per division; horizontal: 0.4 mA per

division); (d) Nb–PdAu–Nb junction under 10 GHz microwave radiation (vertical: 20 mV per division; horizontal:

0.4 mA per division).

Table 1

Typical junction parameters for SIS, SNS, and SINIS

junctions.

Parameter SIS SNS SINIS

-01

1mV 20mV 100 mV

/2p 70 GHz 10 GHz 70 GHz

100 O 0.003 O 0.1 mO

1

0.06 O -N 0.06 O

A 20 mm 50 mm2mm 2 mm20mm 50 mm

364

Josephson Voltage Standard

1989). Further increases in the circuit reliability can

be achieved by the wafer technology on the basis of

Nb–Al

–Nb (Gurvitch et al. 1983, Niemeyer et al.

1989, Mu

ller et al. 1997).

Since 1990 the Josephson constant, K

J90

Z 2e/h, has

been ofﬁcially deﬁned as a practical unit to the value

of 483597.9 GHzV

1

for the reproduction of the unit

of volts. This value was chosen as close as possible to

the SI value but is not identical to it because an in-

strument as precise as a Josephson series array volt-

age standard does not exist. Only direct comparisons

between Josephson voltage standards may allow one

to deﬁne their practical precision, which normally is

limited by the room temperature zero instrument and

the drift of the thermal e.m.f. differences in the volt-

age leads. Key comparisons of the PTB standard with

that of the BIPM reveal uncertainties of 5 10

11

related to 10 V.

2. Programmable Voltage Standards

In the case of the conventional SIS voltage standard,

the use of zero-current voltage steps implies a difﬁcult

stability problem: as the reference voltages complete-

ly overlap the system does not automatically return

to the adjusted voltage if the phase lock is lost owing

to an external disturbance. Readjustment of the

standard is time consuming and thus prevents rapid

programmable selection of certain reference voltages.

Especially, the synthesis of a.c. voltages for D/A

conversion with fundamental precision seems to be

Figure 2

(a) Design of a 10 V SINIS array with 69 120 Nb–Al

–Al–Al

–Al

–Nb junctions. Chip size: 28 mm 10.5 mm.

(b) d.c. characteristic of the array without and with 70 GHz microwave radiation.

365

Josephson Vol tage Standard

impossible. Therefore, using highly damped junctions

(cf. Fig. 1(c) and (d)) in series arrays to avoid the

reference voltage being multivalued has been sug-

gested (Hamilton et al. 1995). If such an array is bi-

ased on a constant voltage step, it will remain at the

adjusted value even if the phase lock is lost for a short

moment. Besides zero voltage, an individual junction

contributes an exactly deﬁned number of constant

voltage steps to the total reference voltage: in modern

designs the steps are 7V

. In this case, an array of N

junctions provides only one reference voltage: NV

To adjust rapidly any voltage between zero and NV

new circuit designs have been suggested, which are

described below.

2.1 Binary Arrays

For the rapid selection of d.c. reference voltages it has

been suggested to divide an array of highly damped

Josephson junctions into a series of binary sections

that allow the reference voltage to be deﬁned by

combining a certain fraction of the binary sections in

such a way that the desired reference voltage is ob-

tained (Benz et al. 1997). Binary divided SNS arrays

of 32768 Nb–PdAu–Nb junctions have been success-

fully operated at 16 GHz and generate RF-induced

reference voltages of 1 V. As the junction capacitance

approaches zero (Table 1), the RF currents are resis-

tive. The array is part of a coplanar stripline conﬁg-

uration of eight parallel lines, with a line impedance

of about 50 O, so that a large impedance mismatch

between junctions and stripline allows homogeneous

microwave coupling to all junctions.

The small product of I

of 10–40 mV is tolerable

for voltage standards with relatively low drive fre-

quencies and maximum output voltages not larger

than 1 V. But it would be advantageous to increase

to values that would make possible drive fre-

quencies of 70 GHz and thus a reduction of the junc-

tion number for a given maximum output voltage.

Large products of I

are obtained in series arrays

of Nb–Al

–Al–Al

–Nb SINIS junction (Schulze

et al. 1998). Here the transparency of the junction

barriers can be adjusted over a wide range by the

fabrication parameters. This allows SINIS arrays

to be operated over a frequency range of at least

10–100 GHz. Typical junction parameters are listed

in Table 1. An 8192-junction array divided into bi-

nary subarrays is, therefore, large enough to reach a

maximum output voltage of 1 V. Moreover, the mi-

crowave supply to the conventional voltage standard

can be used for this type of programmable voltage

standard. Direct comparisons of the 1 V output volt-

ages of SIS and SINIS arrays show no deviation

within a standard uncertainty of 1.6 10

10

(Behr

et al. 1999). Rapid calibration of Zener references

has been realized with a standard deviation of less

than 10 nV. With a two-array system fully automated

calibrations of the ratio of a 1 O/10 O resistive voltage

divider have been performed with an uncertainty of

ﬁve parts in 10

(Behr et al. 2000). A 7492-junction

SINIS array has been used to determine the fast re-

verse d.c. to d.c. transfer difference of a multijunction

thermal converter (Funck et al. 2000).

The SINIS arrays are integrated into a low-imped-

ance microstripline comparable to that for the SIS

arrays. However, in contrast to the SIS junctions, an

arbitrary part of dissipative RF current here ﬂows

over the junction resistance because R

is comparable

to the stripline impedance. This impedance matching

allows RF power from the individual junction oscil-

lator to be transferred to the stripline to an amount

large enough for the phase locking of adjacent junc-

tions. If the junction number is large enough, the ar-

ray will act as a coherent microwave oscillator whose

output power is added to the RF power of the exter-

nal oscillator that is locked to the ﬁrst junctions in the

array (Schulze et al. 1999). It is, therefore, possible to

generate constant voltage steps in very long arrays,

although the attenuation of the stripline is rather high

(about 0.05 dB per stripline period or 1 dB mm

1

As a result of the microwave contribution from the

active stripline, the microwave power required to

generate a certain reference voltage is about 10 times

smaller than that needed to reach comparable output

voltages by means of a conventional SIS array with

much fewer junctions. The coherent operation of the

SINIS array makes it possible to generate maximum

reference voltages of 10 V with a 69120-junction array

under 70 GHz radiation with an RF power of less

than 1 mW at the circuit antenna (Fig. 2) (Schulze

et al. 2000, Kohlmann et al. 2000).

The binary arrays described reach a minimum

switching time between different reference voltages of

about 1 ms. This makes them ideal programmable d.c.

quantum voltmeters. However, while array sections

are switched from the step voltage to zero voltage,

undeﬁned voltage states of the transients between the

voltage steps contribute to the reference voltage. This

makes it difﬁcult to achieve an accuracy sufﬁcient for

synthesizing fast a.c. voltages.

2.2 Digital-to-Analog Converter

To overcome the difﬁculties with the switching tran-

sients in the case of binary arrays, it has been sug-

gested using an RF pulse drive instead of a sinusoidal

microwave drive, which allows the reference voltage

to be adjusted by controlling the repetition rate of the

drive over a wide range (Benz and Hamilton 1996,

Benz et al. 1998). By the restriction to single polarity

pulses the system generates unipolar waveforms only.

A unipolar 23.4 MHz sine wave with a peak-to-peak

amplitude of 4.3 mV with an error of ﬁve parts in 10

has been veriﬁed in experiments (Benz et al. 1998).

Bipolar waveforms can be synthesized by biasing of

366

Josephson Voltage Standard

an array of overdamped junctions with a signal com-

posed of a conventional sinusoidal drive and a two-

level broadband digital code. This allows a controlled

sequence of negative and positive pulses to be gen-

erated. Reference voltages between NV

and þNV

are obtained by time averaging of periodic sequences

of pulses with an appropriate number and polarity

(Benz et al. 1999). A synthesis of a sine wave with an

amplitude of 718 mV at 5 kHz has been veriﬁed. All

pulse-driven D/A converters need a perfect broad-

band transmission line without dispersion for fast

signal propagation. In practice this is very difﬁcult to

achieve for large arrays with an output voltage am-

plitude of 1 V or more.

In principle, the use of rapid single-ﬂux quantum

(RSFQ) voltage multipliers would overcome the dif-

ﬁculties with the broadband transmission lines of the

pulse-driven systems (Semenov 1993, Semenov et al.

1997, Sasaki et al. 1999). These complex digital cir-

cuits amplify the voltage with integer gain by mul-

tiplication of SFQ pulses. An RSFQ D/A converter

contains a certain number of voltage multipliers in

series connection that are independently controlled

by the generation of a train of pulses with a repetition

rate proportional to the input code. With a 2500-

junction circuit an output voltage of 5 mV has been

veriﬁed. Higher voltages can basically be achieved by

hybrid integration of such circuits.

See also: Electrodynamics of Superconductors: Flux

Properties; Electrodynamics of Superconductors:

Weakly Coupled; Metrology: Superconducting

Cryogenic Current Comparators

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Josephson Voltage Standard

Kerr Microscopy

Kerr microscopy allows the imaging of magnetic do-

mains and magnetization processes in an optical po-

larization microscope. The method is based on the

magnetooptical Kerr effect, i.e., the rotation of plane

polarized light in dependence of the magnetization

direction on reﬂection from a nontransparent sample.

In this article some fundamentals and possibilities

of Kerr microscopy will be presented. Examples of

domain images obtained by the method from a va-

riety of materials can be found in Magnets, Soft and

Hard: Domains. For a comparison with other imag-

ing techniques (see Magnetic Materials: Transmission

Electron Microscopy and Magnetic Force Micro-

scopy). A comprehensive review on domain imaging

with emphasis on Kerr microscopy is given by Hubert

and Scha

fer (1998) where also an extended bibliog-

raphy can be found.

1. Kerr Microscope

Domain observations with a lateral resolution down

to the limit of optical microscopy (about 300 nm)

are possible in a conventional polarizing microscope

(Fig. 1). The domain contrast is optimized by the

rotation of an analyzer and compensator. The aper-

ture diaphragm, controlling the illumination, has to

be adjustable so that the angle and plane of incidence

can be chosen, allowing optimization of the Kerr sen-

sitivity to in- or out-of-plane magnetization conﬁgu-

rations (see Sect. 2). The application of ﬁelds up to 1 T

is possible using an electromagnet with proper pole-

tip geometry. The often weak domain contrasts re-

quire image processing for enhancement (see Sect. 3).

2. Kerr Effect and Contrast

For the Kerr effect the magnetooptical interaction

between light and magnetization m is phenomeno-

logically described by a dielectric law

D ¼ eðE þ iQm  EÞð1Þ

in which a displacement vector D, representing the

magnetooptically generated light amplitude, is con-

nected to the electric vector E of the illuminating

plane light wave (e is the dielectric constant and Q is a

complex material constant). Accordingly, the Kerr

effect is linear in magnetization.

The cross-product in Eqn. (1) reveals the gyroelec-

tric nature of the Kerr effect. Its symmetry can be

derived by using the concept of a Lorentz force

(m E) acting on light-agitated electrons (Fig. 2(a)).

The Lorentz motion v

Lor

(parallel to D) creates a

Figure 1

The essential components of a Kerr microscope. The

inset shows the diffraction plane of the microscope

where the illumination diaphragm can be viewed and

adjusted. To obtain best contrast conditions the

illumination should be restricted to the zone of

maximum extinction that is cross-shaped at crossed

polarizers due to depolarization effects. For

perpendicular incidence an aperture iris has to be

centered, while for oblique incidence an off-centered slit

aperture is preferred.

Figure 2

(a) Schematic diagram of the (longitudinal) Kerr effect.

The interaction of the incident light E-vector with the

magnetization m generates the ‘‘Lorentz velocity’’v

Lor

The regularly reﬂected amplitude N is modiﬁed by the

magnetization-dependent amplitude K, leading to a

rotation of the E-vector in reﬂection by a small angle

; (b) the analyzer should be set at the angle b4j

achieve optimum contrast conditions.

369