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NOV 7 1969

NBS TECHNICAL NOTE 381

Some Applications of

the losephson Effect
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NBS TECHNICAL NOTE 381

ISSUED OCTOBER 1969

Nat. Bur. Stand. (U.S.), Tech. Note 381, 63 pages (Oct. 1969)

CODEN: NBTNA

Some Applications of the Josephson Effect

R. A. Kamper, L. O. Mullen, and D. B. Sullivan

Cryogenics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

Final Report on Interagency Order NASA-C-7756-B

National Aeronautics and Space Administration

Lewis Research Center

Cleveland, Ohio

NBS Technical Notes are designed to supplement the Bureau's regular publications program. They provide

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CONTENTS

1 . Introduction

2. The Fabrication of Junctions

2. 1 Niobium Films . 2.2 Niobium-Lead Tunnel Junctions

2. 3 The Mechanism of the Process

2.4 Performance

3. Noise Thermometry

3. 1 Measurement Schemes

3.2 Theoretical Limitations

3. 3 Experimental Tests

4. Possible Contribution of Superconducting Devices to

Nuclear Magnetic Resonance Detection 31

4. 1 Piecemeal Improvements 33

4.2 Magnetometry 35

4. 3 Conclusions 37

5. Overall Conclusions 38

APPENDIX 39

REFERENCES 58

Page

1

2

2

5

7

10

16

20

21

26

111
LIST OF FIGURES

Page

Figure 1. Variation of pressure in the vacuum chamber

during warming of the niobium films at a steady

rate after exposure to oxygen at a temperature

of about 80 K 9

Figure 2. Tracing of the current versus voltage characteristic of a niobium-lead Josephson junction

prepared by this process 11

Figure 3. Constant voltage steps generated by microwave

irradiation at 8. 34 GHz 14

Figure 4. Josephson oscillation of a thin film junction

at 38 MHz 17

Figure 5. Basic circuit for noise thermometry 18

Figure 6. Arrangement for noise thermometry by frequency counting 28

Figure 7. Details of junction, bias resistor, and primary

of output transformer. The gap between the

niobium and brass blocks is exaggerated for

clarity 30

Figure 8. Current versus voltage characteristic of a

thin film Josephson junction 42

Figure 9. Dependence of I c

(fig. 8) on applied magnetic

field. The scales depend upon the geometry

of the junction 43

Figure 10. The quantum interferometer, a) ideal, b) early

practical version (ref. 47) 44

IV
LIST OF FIGURES (Continued)

Page

Figure 11. Current versus voltage characteristic of a

thin film Josephson junction connected to a

circuit with a resonance at frequency

/ = 2eV/h 46

Figure 12. Current versus voltage characteristic of a Josephson junction irradiated at a frequency / = 2eV/h 47

Figure 13. Josephson oscillation. The response of a receiver tuned to 43 MHz is displayed as

a function of DC bias on the Josephson

junction 48

Figure 14. The Clarke null detector 50

Figure 15. The tunneling cryotron 52

Figure 16. Current versus voltage characteristic of the

gate of a tunneling cryotron. The operating

points are marked A and B 53

SOME APPLICATIONS OF THE JOSEPHSON EFFECT

R. A. Kamper, L. O. Mullen, and D. B. Sullivan

We describe techniques for fabricating permanent

Josephson junctions between thin films of niobium and

lead, and for absolute noise thermometry at very low

temperatures using the Josephson effect. We discuss the

possible benefits of applying superconductivity to nuclear

magnetic resonance detection, and review other applications of the Josephson effect.

KeyWords: Josephson effect ; superconductivity; tunnel

junctions; thermometry.

1 . Introduction

This is the final report on work performed on Interagency Order

NASA-C-7756-B, for the Lewis Research Center of the National Aeronautics and Space Administration, with additional funding from the

National Bureau of Standards. It is a sequel to NASA Contractor Report CR 1189 (September, 1968), in which we described our early

studies of the Josephson effect and its applications. In that report we

described the characteristics of Josephson oscillation which we had observed; methods for fabricating Josephson junctions; and designs for,

and early tests of, a picovoltmeter and a noise thermometer for the

millikelvin range. We subsequently chose the fabrication of junctions

and the noise thermometer for further development, and we report the

results of that effort here. We have developed a permanent, rugged

tunnel junction between thin films of niobium and lead, with electrical

characteristics that show great promise for permanent instruments

based on the Josephson effect. We will describe the fabrication and

properties of this type of junction in full detail in this report. We have

investigated the theoretical limitations of noise thermometry with the

Josephson effect, and constructed a practical system for testing in the
millikelvin range. These will also be discussed. An important aspect

of the practical application of superconductivity to electronics is the

search for opportunities in activities that could benefit from improved

instruments. With this in mind, we analyzed the improvement that

could be made in nuclear magnetic resonance detection by the application of superconducting devices. We present this analysis in this report.

Finally, to fill in the background for our work and to indicate other

areas of opportunity, we included as an appendix a review of the Josephson effect and its applications which we prepared for the IEEE Transactions on Instrumentation and Measurement.

2. The Fabrication of Junctions

In our previous report we described several methods we had

tried for fabricating Josephson junctions between thin films of niobium

and lead. We have given further attention to the most successful of

these methods, as well as the problem of protecting the junctions from

deterioration in storage. In this chapter we present the resulting recipe

for making junctions which can survive thermal cycling and storage at

ambient temperature, exposed to the atmosphere, for many months without measurable deterioration. We also comment on the probable mechanism of the process and on the performance of the junctions.

2. 1 Niobium Films

o We prepare our niobium films by evaporation, at a rate of 10A

per second, in a high vacuum (~10"9 Torr, or 1.3x10" N/m ), onto a sapphire substrate maintained at a temperature of 400 °C.

The vacuum system we use is a large stainless steel chamber

equipped with a titanium sublimation pump (with liquid nitrogen cooled

pumping surface), a large (135 liter/ second) ion pump, and a small

roughing system, consisting of a mechanical roughing pump and an oil

vapor diffusion pump, connected to the main vacuum chamber via an

elaborate cold trap. This last is valved off during high vacuum runs.
The working space is surrounded by coils of tubing through which we

circulate liquid nitrogen. Stray niobium vapor condenses on these coils

during (and before) deposition of the films, and assists the other pumps

[21 by absorbing residual gas. We start our runs by thoroughly outgassing all parts of the system, near their highest working temperatures.

The evaporation source is a drop of molten niobium, approximately 1 cm diameter, in a water-cooled copper boat. It is heated by

electron bombardment from a heated loop of tungsten wire. By means

of some carefully placed electrostatic shields, the majority of the electrons are guided to strike the niobium. Stray electrons cause troublesome heating of the parts they strike. A total power of 1 . 2 kW is sufficient to maintain the niobium at a temperature of 3200 K, measured

by optical pyrometry using the melting point of niobium to check the

instrument. At this temperature the niobium evaporates at a rate sufo ficient to deposit 10A of niobium film per second on a substrate 25 cm

away. We developed this evaporation source by adapting a commercial

unit which was unsatisfactory in its original form.

We chose single crystal sapphire substrates for their excellent

thermal conductivity at low temperature. For depositing films we

have a substrate holder equipped with a movable mask and a shutter, as well as means for raising (with a heater) and lowering (with liquid

nitrogen) the temperature, and a thermocouple to measure it. The

complete assembly fits in a 3. 5 era port in the side of the vacuum

chamber.

We usually evaporate the niobium onto substrates at 400 °C. A

lower substrate temperature results in films with low superconducting

[21 transition temperatures. Neugebauer and Ekvall attributed this effect to contamination of the films deposited on cold substrates by residual gases in the vacuum system. They suggested that contamination
is favored by a low temperature and cited evidence to support this

hypothesis. However, it is interesting to note that we obtain similar

results to theirs although we have an initial vacuum four orders of

magnitude lower in pressure and an evaporation rate one order of

magnitude greater. Our films are of better quality (as judged from

their superconducting transition temperatures) than they reported, but

we have to maintain our substrates at a similar temperature to achieve

the best quality. It is possible that variations in the crystal structure

of the deposited films with substrate temperature affect the superconducting transition temperature independently of any contamination.

We have observed with a polarizing microscope that even our

good films have a non-cubic crystal structure with orientation controlled by the substrate.

The superconducting transition temperatures we observe depend upon film thickness, being depressed below the value for bulk

o niobium in films less than 1000A thick. The following table shows the

relationship between film thickness and transition temperature for a reasonably good set of films.

o Film Thickness (A) Transition Temperature (K)

11000 9.2

2200 9.3

1300 8.9

600 8.7

300 7.9

200 6.9

The transition temperature of bulk niobium lies somewhere between

9. 19 IC

3 land 9.46k[4 ^
These films have a mirror-like appearance, even under a microscope with a magnification of a few hundred diameters. They are

attached very firmly to their substrates, and survive soldering of leads,

thermal cycling to low temperatures, abrasion, careless handling,

atmospheric corrosion, etc. They may be removed with hydrofluoric

acid, to which the sapphire substrates are resistant.

In response to a request from the NASA-Lewis Research Center,

we found a technique for separating a niobium film intact from its subo strate. We started by evaporating a layer of copper, about 2000 A thick,

on a sapphire substrate at ambient temperature. We then heated it to

o 400 °C and deposited a film of niobium about 1000 A. thick. After cooling

this structure and removing it from the vacuum chamber, we slowly

immersed it in a 10% solution of nitric acid. Most of the copper dissolved in the acid and the niobium film floated off intact. We collected

it on a perforated metal plate and rinsed it with water containing some

ethyl alcohol to reduce the surface tension, which would otherwise

break the film.

2. 2 Niobium-Lead Tunnel Junctions

In brief, we make our tunnel junctions by exposing cold (80 K)

niobium films to a glow discharge in oxygen, driving off unwanted discharge products with a thermal cycle, and depositing the lead films

over the treated niobium films.

After depositing the niobium films we cool the substrates to

about 80 K by circulating liquid nitrogen in the substrate holder. We

normally maintain this temperature for about one hour before proceding with the next stage. Then, we shut down the pumps and admit

oxygen at a pressure between 5 X 10"3 Torr and 2 X 10~2 Torr (0. 7

to 3N/m ). We maintain a glow discharge in the oxygen gas at 300 V
and about 200mA for a period varying from 200 sec to 220 sec, using

the chamber wall and substrate holder for the negative electrode. We

find that the addition of about 10% nitrogen to the oxygen facilitates control of the discharge.

The exposure time is critical. If it is too short continuous barriers fail to form. Too long an exposure generates a visible frost

which disappears during the subsequent thermal cycling, and the quality

of the junctions then depends very strongly on the temperature reached

during the thermal cycle, making quality control very difficult.

After exposure of the niobium films to the discharge, we restart

the pumps to restore the vacuum. We then heat the niobium films, with

an electric heater in the substrate holder, up to a temperature between

-50 °C and -80 °C, measured with a thermocouple. If the films have

been overexposed to the discharge, they can be restored to a usable

condition at this stage by continuing the heating to a higher temperature.

As soon as the films reach the peak temperature, we cool them to 80 K

by circulating liquid nitrogen, and deposit the lead films by evaporation

from a source similar to the one we use for niobium. Before removing

the junctions from the vacuum we warm them up to ambient temperature

in order to avoid condensing water on them, which attacks the lead films,

Finally, to protect the lead films from atmospheric corrosion,

we coat the junctions with polyimide plastic. We heat them to about

100 °C in air to dry them thoroughly, and paint on a thin layer of the

unpolymerized plastic thinned 10:1 with a thinner provided by the manufacturer. Both the warming and the thinning of the plastic are necessary precautions to avoid destroying the junctions.
We normally attach leads to the films by a soldering technique

invented by Dr. V. D. Arp, of this laboratory. First, we cover the

area of film to be soldered with a thin layer of either an air drying

varnish or polyimide plastic. When this layer is hard, we solder the

leads on with indium. No flux is necessary. The molten indium appears to melt the varnish, forming a good mechanical bond with satisfactory electrical contact. Some care must be taken with lead films

because the indium dissolves the lead. This problem does not arise

with niobium, and we try to arrange our evaporation masks so that we

deposit patches of niobium film under the parts of the lead films where

we intend to solder leads.

2. 3 The Mechanism of the Process

We believe that the barriers in our niobium-lead tunnel junctions

are formed by some active product of the glow discharge, which condenses on the cold niobium films and remains there as an adsorbed

layer which then attacks the lead film after its deposition, forming a barrier of some compound of lead.

The main evidence in support of this hypothesis comes from the

effects of variations in the process. If we use rather a long exposure of

the cold niobium films to the glow discharge, and omit the subsequent

thermal cycle before depositing the lead, the lead film is completely

destroyed on warming, leaving a transparent dielectric layer overlapping the intact niobium film. If we use a normal exposure, and extend

the thermal cycle up to ambient temperature before depositing the lead,

the result is a simple metallic contact between the niobium and lead

films. In contrast, we can heat the complete niobium-lead junctions up

to at least 150°C with impunity. These two observations suggest

strongly that it is the lead alone which reacts to form the barrier. An
additional piece of evidence is that the process is very specific. We

have been unable to make niobium-magnesium tunnel junctions at all

this way, and niobium -aluminum junctions have all been of inferior

quality.

The big unanswered question is the identity of the active species

which condenses on the cold niobium films and subsequently attacks the

lead. In this connection we call attention to figure 1, which shows the

variation of pressure in the vacuum chamber with temperature as the

substrates and niobium films are warmed at a steady rate from 80 K to

ambient temperature. Two curves are shown. The upper curve corresponds to our normal routine for making tunnel junctions using a glow

discharge. The lower curve was observed after exposure to oxygen in

the absence of a glow discharge. The pressure of oxygen during exposure is indicated by the symbol dP(Os).

The most striking features of figure 1 are the multiple peaks of

pressure and the wide difference between the two curves. The weak

presence of the main peaks in the lower curve may be due to the ion

pump, which was running continuously while these curves were being

recorded. It appears that the discharge generates several species of

low vapor pressure which condense on the cold surfaces and then evaporate at different temperatures. An analysis of the composition of the

gas in the vacuum system with a mass spectrograph confirms this impression. We observe prominent components of the mass spectrogram

corresponding to 1 1 distinct molecular species, all of which contribute

to the first large peak in pressure shown in figure 1.

The top six components of that peak (in order of intensity) have

mass/charge ratios: 44(C0 3 ); 28(CO, N 2 ); 16(CH4 ,0); 40(A); 12, 13(C);

18(HsO). The numbers are in atomic units and the most likely chemical assignments are given in parentheses. The ratio of concentrations
TEMPERATURE,

129 154 177

K

238

-7 -6 -5 -4

THERMOCOUPLE emf, mV

Figure 1. Variation of pressure in the vacuum chamber during warming of

the niobium films at a steady rate after exposure to oxygen at a temperature of about 80 K.
of the two isotopes of carbon corresponds to their natural relative

abundance. Together, these six species account for 95% of that first

large peak in figure 1. The second prominent peak in figure 1 contains

contributions from: 18(H 2 0) and 28(CO, Ns), which account for 70% of

the total pressure. Other minor constituents are: 15(CH3), 17(OH),

14(N), 29(? ), 30(NO). In addition, there are faint traces of: 48(0 3 ); 46(N0 3 ); 44(N g O); 38, 36(HCl); 37, 35(d). These last are very reactive gases which may have an influence out of proportion to their

concentration.

Many of the more volatile molecular species we have listed may

have been trapped by less volatile components, such as carbon dioxide,

or generated by decomposition of more complex molecules by ion bombardment within the mass spectrograph. The presence of carbon,

hydrogen, argon, and chlorine in the vacuum chamber must be due

either to impurities in the oxygen or to release from the chamber walls

by the action of the glow discharge. It would be possible to eliminate

them in a bakeable system.

The most likely candidate for the active agent that attacks the

lead films appears to be water. However, we have tried exposing the

niobium films to water vapor without a glow discharge and did not

succeed in producing adequate barriers. The direct action of the glow

discharge appears to be essential.

2. 4 Performance

A common characteristic of junctions fabricated by the technique

discussed in this chapter is their freedom from background current due

to processes other than quantum mechanical tunneling. A tracing of a

typical current vs. voltage characteristic of one of our junctions at 4K

is shown in figure 2. The current that passes at zero voltage depends

10
7

6-

e

5

i- 4-

O 2-

1 1 Nb -Barrier- Pb

Area 1 x 1 mm

4.0 K

(\

___ ^

i

II 2 3

VOLTS , mv

Figure Z. Tracing of the current versus voltage characteristic of a niobium<

lead Josephson junction prepared by this process.

11
very strongly on the orientation of the junction in the Earth's magnetic

field, indicating that it is a true Josephson tunnel current. The part

of the curve at small but finite voltage can be explored either by suppressing the Josephson current with a magnetic field, or by decreasing

the current from a value exceeding the maximum Josephson current. It shows typical quasi-particle tunneling behavior, with a sharp rise near

3mV associated with the energy gaps of the superconductors, followed

by an ohmic response to higher voltage.

We regard a junction as acceptable if the (ohmic) background

current is less than 10% of the tunnel current in the ohmic region of the

curve. The yield of acceptable junctions is about 60% if we include

failures due to obvious causes such as vacuum leaks, malfunction of

pumps, etc. Counting only runs in which we adhere to the specified

conditions, the yield is near 100%. However, it has proven difficult

to control the resistance of the junctions, which is a measure of the

barrier thickness. We have made acceptable junctions with resistances

varying from 0.06O to 100 (for a junction VfL square), measured at 4K

in the ohmic range above 3mV. In general, only junctions with resistance less than about 10 show a Josephson current. Part of the problem is caused by poor thermal contact between the sapphire substrates

and the substrate holder. We notice that junctions sharing a substrate

usually have very similar resistance, which differs from that of junctions on other substrates made in the same run. A solution to this

problem which we are working on is to take advantage of the longevity

of these junctions and build up a library of junctions with graded characteristics.

12
Sets of these coated junctions have survived the following endurance tests, with no detectable deterioration:

1) Storage at ambient temperature, exposed to the atmosphere,

for a period of 4 months. This indicates that the junctions are stable

against diffusion into the films.

2) 400 dips into liquid nitrogen, allowing time for the junctions

to warm up to ambient temperature, while exposed to the atmosphere,

between dips. The frost that forms during this treatment would rapidly

destroy unprotected lead films.

3) Soldering leads on with indium 3 or 4 times.

In test (2) the leads were detached by differential thermal contraction after an average of 50 dips. However, on replacing the leads

we found no detectable deterioration of the junctions. In test (3) there

was a tendency to destroy the lead films by dissolving them in indium,

but the junctions remained intact.

We emphasize that we have not yet tested any of these coated

junctions to destruction. They were all usable after these tests, which

must continue to find the limits of abuse they will survive. However,

they have already demonstrated great promise for application in permanent instruments.

We have observed the expected effect of irradiation, with microwaves at X-band, on the DC characteristics of these junctions (see

appendix). Figure 3 shows a recorder trace of the direct current vs. voltage characteristic demonstrating constant voltage steps at interval

V = h//2e, where h is Planck's constant, / is the microwave frequency,

and e is the electron charge. We also sent a junction to Dr. H. A.

Fowler, at the National Bureau of Standards in Gaithersburg, who re- ported that it would be usable for his purpose of determining the fundamental constant e/h very accurately by relating the voltage interval of

the steps to the NBS standard volt.

13
300 -

200 -

<

m I-2

UJ

or

cco 100

20 40 60

VOLTAGE,/* V

Figure 3. Constant voltage steps generated by microwave irradiation at 8. 34 GHs

14
We have also observed free oscillation of one of these junctions

at 38 MHz, driven by a steady bias voltage of about 8 X 10~8 V. This

frequency is more than two orders of magnitude lower than previously

observed with thin film junctions.

Generation of oscillation at this frequency requires a very small

resistor (~ 10~6Q) connected in parallel with the junction in a low inductance circuit to maintain the bias voltage. We therefore used a sapphire

substrate in the form of a square, 0. 5 cm on each side and 0. 25p thick.

This was placed on one face of a 0. 5 cm cube of brass which functioned

as the bias resistor. Two opposite faces of the block were coated with

lead-tin solder to form superconducting electrodes. The strips of niobium and lead films forming the junction were 0.2/% wide and about

o 1000 A thick. They were connected to the bias resistor and the tuned

output circuit with short lengths (~ \%) of fine tinned copper wire. The

junction, bias resistor, and tuned output transformer (for impedance

matching) were enclosed in a copper screening can with a single layer

solenoid wound outside. This supplied a steady magnetic flux density

in the range from zero to one millitesla. The need for this magnetic

field precluded the use of superconducting screens and made the junction rather susceptible to noise radiated from outside the cryostat (we

did not have a screened enclosure for this work).

The spectrum of oscillations we observed at 38 MHz as we

varied the steady bias voltage was a strong and quasi periodic function

of applied magnetic field. As we varied the field we could generate

one, two, or three quantum transitions, with some regions of field in

which the oscillation appeared to be suppressed. The change in flux

1 density required to make a drastic change in the spectrum of oscillations was of the order of 100 microtesla in any part of the available

range of ± 1000 microtesla. It is natural to associate this behavior

15
with the well known periodic dependence of the DC properties of thin

film Josephson junctions on applied magnetic field (see appendix). The

period one would expect for a junction with dimensions like ours would

indeed be about 100 microtesla. However, the response of the Josephson oscillation to a magnetic field which we observe is rather complex

and hysteretic, probably because of trapped magnetic flux in superconducting parts of the apparatus. The frequency at which we were working was much too low to excite the microwave resonances which are

present in Josephson junctions by virtue of their low phase velocity for

wave propagation.

We show a recorder trace of the Josephson oscillation at 38 MHz

plotted against DC bias in figure 4. The steady magnetic flux density

was about 750 microtesla. The oscillation was nearly sinusoidal. The

second harmonic (at \ bias voltage) is clearly visible but higher harmonics are almost absent. The line width of the oscillation was somewhat dependent on magnetic field and rather broad, of the order of

1 MHz. This will need to be reduced for practical applications of this

oscillation.

3. Noise Thermometry

The principle of the application of the Josephson effect to noise

thermometry is illustrated in figure 5. The Josephson junction is connected by leads of very small inductance (< 10"9 H) to a shunt of small

resistance R ( ~ 10"5Q). A direct current I of the order of 10 mA through

this shunt will maintain a steady bias voltage of the order of 10~7 V across

the junction, driving it to oscillate at a frequency of the order of 50 MHz. •" The frequency / of oscillation is related to the bias voltage V across the

junction by

16
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DC

50 MHz + SIDEBANDS

r*>J I0

?

V + NOISE

JOSEPHSON

JUNCTION

Figure 5. Basic circuit for noise thermometry.

18
h/ = 2eV

or / = V/cpo (1)

where h is Planck's constant, e is the electron charge, and cp = h/2e

is the magnetic flux quantum. The voltage V across the junction is

V = IR + noise (2)

and the fluctuations in V due to noise will be converted into fluctuations

in the frequency /. If the shunt resistance R is small compared with

the resistance of the junction and the impedance of the current supply,

its Johnson noise will dominate the fluctuations in the frequency of

oscillation. These fluctuations will then contain sufficient information

to determine the absolute temperature of the shunt resistor.

In the remainder of this chapter we will describe practical

schemes for thermometry based on this principle and discuss their

theoretical limitations. It appears to be theoretically possible to measure noise temperatures in the millikelvin range. Finally, we will discuss the performance of prototype thermometers.

The essential components of a noise thermometer are a resistor

to generate thermal noise and a preamplifier, with noise temperature less

than the temperature to be measured, and with sufficient gain to generate

a signal detectable by a receiver at ambient temperature. In the arrangement we describe here the Josephson junction fulfills the function of the

f i 7I

preamplifier. A simple analysis 1

' shows that the components of the

noise spectrum which have the greatest effect on the spectrum of the

Josephson oscillation are all at low frequency (< 1 kHz at 4 K, less at

lower temperatures). They create a narrow spectrum of sidebands

close to the center frequency IR/cpo . Thus the Josephson junction

[8] amplifies the noise signal by parametric up-conversion. The oscillation of the junction is the pump, the input frequency is less than 1 kHz,

and the output (idler) frequency is near the oscillation frequency of 30-

19
50 MHz. The maximum theoretical power gain of such an amplifier is

[9] the ratio of output to input frequencies, which is in excess of 10 at 4K

and may be as much as 107 at lower temperatures. With this preamplifier an ordinary radiofrequency communications receiver should suffice for noise measurements.

3. 1 Measurement Schemes

We will discuss two approaches to the measurement of Johnson

noise using the Josephson effect, which we will call by the names

spectrum analysis and frequency counting.

Spectrum analysis requires a narrow band receiver to explore

the long-term average of the spectrum of sidebands near the Josephson

oscillation frequency. The quantity measured is the linewidth A/, which

is the frequency interval between the two points at which the spectral

density is one half of its peak value at the unperturbed frequency IR/cp • Assuming that the only significant source of broadening is Johnson noise

from the shunt resistor R, the mean square fluctuation in voltage V^

across the junction is given by

V

2 = n

4kTR.d/ (3)

where k is Boltzman's constant, T is the absolute temperature, and d/

is an interval of frequency. Application of standard FM theory to the

corresponding fluctuation in frequency yields a formula for the observed

linewidth bf\

10*

A/ = 4TrkTR/cpc or

A/ = (4.03 X 107 )RT . (4)

We will discuss the experimental verification of this formula in section

3.3.

20
We have given most of our attention to the alternative approach,

frequency counting. A signal derived from the Josephson oscillation is

amplified and used to drive a frequency counter, which repeatedly counts

the number of cycles in a fixed gate time T. Fluctuations in the frequency then appear directly as fluctuations in the count. A convenient

measure of these fluctuations is the variance, or mean square deviation

o~ . If the only noise present is white, thermal noise generated by the

resistance R, then

a

2 = (/- ff = 2kTR/Tcpo3

or

JS I / A v , 1 ^6 cT = (6.4 X 1(f) RT/t. (5)

This approach to noise measurement has the advantages that it is easy

to automate the recording of data and to discriminate against spurious

sources of noise, such as flicker noise, with anomalous power spectra.

In both these schemes of thermometry the measured quantity is

related to the absolute temperature by an expression containing fundamental constants and easily measured quantities only. In principle no

calibration is required.

3. 2 Theoretical Limitations

In this section we discuss the fundamental theoretical limitations

on the range and accuracy of noise thermometry with the Josephson

effect.

First, let us discuss the validity of the Nyquist formula, equation (3), on which equations (4) and (5) are based. This formula is

based on Boltzmann statistics, whereas the photons involved in the generation of noise should properly be described with Bose statistics. The

21
difference is only significant at very low temperatures, such that

h/>kT

or

//T £20GHz/K. (6)

[7] We have shown that the components of the noise spectrum which have

the major effect on the Josephson oscillation are those at frequencies

of the order of the linewidth A/ (equation 4) or less. A comparison of

equation (4) with the limit given in equation (6) shows that Boltzman

statistics, and hence the Nyquist formula, should be an excellent approx

imation at any temperature.

Next we consider the current supply to maintain the constant

bias voltage on the shunt resistor R. In its simplest form this would

consist of a battery with an emf of a few volts in series with a resistor

R , of the order of 103

Q,, at ambient temperature T . Neglecting the

battery, the effective noise temperature Tn

of the combination of R and

R in parallel is

Tn

= (RT + R T)/(R + R ). (7)

The contribution to Tn from the resistor R at ambient temperature is

RT /(R + R ). If R = 10 _5Qand R = 103

fi, then this amounts to 3 X 10 _6 K,

which is clearly negligible. The question of noise contributed by the

battery has been investigated by Knott. He tested several different

dry cells and found the noise that they generated in the frequency range

3

of interest was comparable with Johnson noise on a resistor of 10 Q at

ambient temperature. Thus the combination of battery and resistor

would be a satisfactory power supply for noise thermometry down into

the microkelvin range.

22
The ultimate low temperature limit to the Josephson noise thermometer will most likely be set by the noise temperature of the junction

itself. This has been analyzed by several authors, most completely and recently by Stephen. ' We will summarize his conclusions briefly.

A perfect junction transmits current by tunneling of Cooper pairs

and by tunneling of quasi particles. The respective contributions of

these two processes to the total current depend upon voltage and temperature. The significant differences so far as noise is concerned are

in the quantities I/V, 51/3 V, and the double charge per particle carried

by Cooper pairs. At high temperatures, when kT > eV, both processes

generate Johnson noise appropriate to the temperature and some suitably defined effective resistance (equation 3). At very low temperatures

(kT <^ eV) they only generate shot noise. This is similar to Johnson

noise at an effective temperature Te ff, where

Teff^eV/k

or

Teff «h//2k (8)

where / is the frequency of Josephson oscillation. If / = 40 MHz, then

Te££«i 10" K. Thus the lowest effective noise temperature attainable

with an isolated Josephson junction oscillating at 40 MHz is of the order

of one millikelvin. However, in the circuit proposed for thermometry,

the shunt resistor would damp the noise emf generated by the junction.

The effective noise temperature of the combination would be given by

an expression of the same form as equation (7), with a suitably defined

effective resistance for the junction. Inspection of equation (7) shows

that it would be possible to measure temperatures below T e ff with a very small shunt resistance.

23
In addition to the two tunneling processes we have discussed,

real junctions can transmit some current by ohmic leakage through the

barrier. This would presumably generate Johnson noise. It can be

considered as part of the shunt conductance with no further complication of the problem.

Thus the fundamental limitations to noise thermometry with the

Josephson effect that we are aware of would permit its use in the temperature range from about 10"3 K up to the critical temperatures of conveniently available superconductors, near 10K. However, a real system is subject to noise from sources other than those considered by

Stephen. There are external sources such as radio stations, atmospheric and galactic noise, etc, which can be eliminated with a screened

enclosure. There are also strange noise-generating processes within

the junction which can only be eliminated by patient development.

So far we have discussed fundamental limitations which are common to measurements by both spectrum analysis and frequency counting.

We will now discuss some points which are peculiar to frequency counting.

First, random error. A simple analysis shows that the rms

scatter At on the value T of a noise temperature measured by the frequency counting method is

AT = TV2/n (8)

where n is the number of measurements of frequency used to compute

the variance of the fluctuations. This is a purely random error arising

from the statistics of measuring a fluctuating quantity.

A frequency counter also introduces a systematic error, which

arises because it only counts complete cycles. Thus the measured frequency is always an integral multiple of T"1

, where T is the gate time.

24
If a counter is set to measure a signal with an arbitrary frequency /,

then its reading will switch randomly between the two integral multiples

of T _1 bracketing /. Let us denote these quantities So and (/o + T~ ). Assuming that there is no phase correlation between the signal and the

time base of the counter, then a fraction 1 - (/ - So) T of the .readings

will be /o and a fraction (/ - /o )t will be (/o + t" ). Thus the mean

value of a large number of readings is just equal to /. However, this

also introduces an extra fluctuation in the measured frequency. The

variance cr of this extra fluctuation is

°

;

2 = (/ - /o)T

_1 -(/-/ ) 2

. (10)

In practice, / will fluctuate also, so we should average ®r over all

values of (/ - /o) between zero and T" . Doing this, we find the mean

p variance o of the extra fluctuations introduced by the counter is c a

2 = (6t 2

) -1

. (11)

c

The variance of the total observed fluctuations will then be the sum of

o" (equation 5) and a (equation 11). The effect is to introduce a shift

c

6 T in the measured temperature, where

6T = T (a 2 /a 2

) c or 6T = cpo2 /(12 kRT). (12)

It is a trivial matter to correct measured temperatures for this effect,

but the extra fluctuation increases the random scatter of the measurements and will ultimately limit the resolution of temperature when 5T

exceeds T. Thus the minimum resolvable temperature T . , taking n mm

readings with a counter of gate time t, is

25
Tmin mm = 6TV2/n

or 2 /TT~

rmm "l2kRT (i3)

or

Tmin = 3.5 X 10-8 (RTyn) _1

.

Thus a fairly long gate time is desirable for measuring very low temperatures. With R = 10~5Qand T = 1 second, millikelvin resolution could

be obtained in a run of a few minutes.

The conclusion, then, is that none of the fundamental theoretical

limitations on this type of thermometry, which we have been able to

find, would preclude its convenient use at temperatures down to one

millikelvin, or its use at even lower temperatures with some extra

precautions.

3. 3 Experimental Tests

The linewidth of Josephson oscillation at frequencies of 30 MHz

and below has been measured by A. H. Silver and J. E. Zimmerman,

[17] of the Ford Scientific Laboratory, and published jointly with one of us. They found that equation (4) described the observed relationship between

linewidth and R and T, to within the experimental error (about 5%), in

the range 1. 7 X 10"lofi< R <2. 6 X 10"5

Q; 1.4K < T < 8K. At the time of

making these measurements, these authors did not know the exact numerical coefficient of equation (4). This result demonstrates the feasibility of thermometry in the temperature range above 1.4K as well as

the feasibility of observing the narrower linewidths required for thermometry at lower temperatures.

26
We have constructed a prototype thermometer based on frequency

counting. The layout is shown in figure 6. The signal from the oscillating Josephson junction is coupled by a tuned transformer and coaxial

line into a communications receiver. In the receiver the signal is

amplified and mixed with another signal from a tunable local oscillator

(L.O. ) to generate a signal at an intermediate frequency near 455 kHz.

This intermediate frequency is measured directly with a frequency

counter and recorded on paper tape. We have a simple computer program to compute the variance of the fluctuations in the frequencies re- corded on the tape and hence the noise temperature. This program corrects the data for the extra fluctuations introduced by the counter, which

we discussed in section 3.2.

In analyzing white noise, care must be exercised to discriminate

against other sources of noise, such as flicker noise, which have an

anomalously large part of their spectral distribution at very low frequencies (the power spectrum for flicker noise is proportional to /

"

). These will always interfere with measurements requiring long periods

of time. Methods of analyzing and handling flicker noise have been developed by Barnes and Allen. Following them, and the suggestions

of Dr. D. Halford of this laboratory, we have arranged our computer

program to calculate the variance o from the formula

° =K/i-/j)

3

(14)

where /j and/: are two successive measured frequencies. The advantage

of equation (14) over equation (5) is that (14) is only sensitive to fluctuations with period comparable to the interval between successive measurements or less, whereas (5) is sensitive to fluctuations with period

up to the total length of time required to take all the data. It is also

27
4-> oo

>^oa

0)u

>^u

+->

<u

CO

r-Hoo

CDs

bfl

PIuu<

SO

CDh

bfl

28
helpful to use as short a gate time T as possible, since this increases

the sensitivity of the variance o to white noise. The dependence of a on T for noise sources with other commonly found power spectra is

weaker. As a check on the frequency spectrum of the observed fluctuations, our computer program also calculates a from equation (14)

taking measurements with double and quadruple intervals. That is, as well as taking j = i + 1, it takes j = i + 2 and j. = i + 4. If we are observing pure white noise, this leaves the value of a unchanged apart

from random scatter. If there is a component with a different power

spectrum, then these three values of o will differ significantly.

The layout we use for the oscillating junction and shunt resistor

is shown in figure 7. It incorporates some suggestions made to us by

Dr. J. E. Zimmerman of the Ford Scientific Laboratory. The junction

is formed between the etched tip of the Nb-Zr wire and the niobium

block when the whole structure is compressed by the 0-80 screw. The

brass block functions as the shunt resistor. The layer of lead-tin

solder is ,1 tinned" onto its surface and pressed against the niobium block

when the assembly is bolted together, forming a superconducting joint

of high critical current. The coupling hole forms the single turn primary of the output transformer. The secondary is a 15 -turn coil wound

inside the coupling hole and tuned to 30 MHz with a 500 pF capacitor.

The dominating RF impedance in the primary circuit is the junction

itself.

This system functions at 4K. By patient manipulation of the

adjusting screw it is possible to obtain stable Josephson oscillation and

record a realistic noise temperature. However, the junction does have

a strong tendency to generate multiple quantum transitions which mix

with signals from the receiver to generate a complex spectrum of

spurious resonances which are noisier than the desired oscillation.

29
<H

LU2 K . . 2

LU

—

CO

O

O "3

(T

Q

UJ

N

\— LU < oc _J —

Q- £ 1 ^

q:

n

LU

Q_ -Q

0- Z OO * D COUNTE FLATH Q _J < O

CDO

LU CO

u

<D£u

u

u o >+-l m CO

ti T3

ctf CD u

+->

+-> n3

+-> !hcuGO

CtO

a «J o X

<+H CD o co >N

•r-l

fc CO n5 X a oo • H ,—1

Oh

£i

CO TJ CO

fl

ril «t U _ rQ U X!

4-> fl CO ni • l-l en p

CD 3 M •iH ,0

CO

O

nj •iH • H rt X!

CD

rt 5 o a

-l-> CD u 0) 3

•r"J (U O

£1ft • CO i—i

03 >>

IS CU Jj

CD

r^ 43

Q

H o

CD3

bO

•r-l

30
We are experimenting with buffer amplifiers to try to cure this problem.

We have mounted the junction in an experimental He - He4 dilution refrigerator built by Dr. R. Radebaugh and Dr . J. D. Siegwarth of this

laboratory. This refrigerator is capable of providing a continuous

operating temperature of 0.02K for tests of thermometry. Some minor

troubles remain to be eliminated before we test noise thermometry with

the Josephson effect at this temperature.

4. Possible Contribution of Superconducting Devices to

Nuclear Magnetic Resonance Detection

Nuclear Magnetic Resonance (NMR) is the resonant interaction of a radio-frequency field with the Larmor precession of the magnetic moments of atomic nuclei in a steady magnetic field. Its intensity, spectral

distribution, and transient response give information about the multipole

moments of nuclei, their isotopic abundance, and their interaction with

their immediate surroundings. Interesting information about the solid

and liquid states can be inferred from this. Our purpose here is to consider possible ways to improve the sensitivity of detection of this phenomenon by the application of superconductivity.

After a brief sketch of the essential features of NMR as they affect

detection schemes, we will discuss the relative merits of piecemeal improvements to the systems in current use and the possibility of using a

flux quantum magnetometer. We will express all quantities in S. I. units.

It is convenient to represent the combined magnetic behavior of

all the nuclei in a specimen in terms of the complex magnetic suscepti-

[20]

bility X introduced by Bloch . This is a tensor whose components

are functions of frequency. At zero frequency it is usually more or less

isotropic and is just the contribution Xo of the nuclei to the static magnetic

susceptibility of the specimen. If the nuclei are temporarily disturbed,

31
this longitudinal magnetization relaxes back to equilibrium in a characteristic time Ti . The other important components of Xoccur in the plane

transverse to the steady magnetic field at frequencies near the resonant

frequency w . There is a component X i n phase with an applied RF field

and a component X in quadrature. The transverse magnetization relaxes

to the steady state with a characteristic time T 2 . If Xo is the peak value

of X > observed with a small RF field exactly on resonance, then

Xo = 2Xo V^o T S . (15)

In a complicated system with several resonances, each contributes an

amount given b> equation (15) to Xo •

In present-day schemes for detecting NMR, the specimen is placed

in the tank coil of a resonant LC circuit. The resonant frequency of the

circuit is then perturbed by X > while X contributes to the absorption of

power and hence influences the Q factor when the Larmor frequency is

brought into coincidence with the resonant frequency of the circuit. Both

[21] these effects may be detected with an RF bridge with a sensitive receiver . The sensitivity of a bridge to small changes in X and X increases as the

RF level is increased, but a limit is set by the degrading of all components of susceptibility at high levels due to saturation of the resonance.

At the optimum RF level Xo . X > and X are all reduced to half their

equilibrium values. The minimum detectable equilibrium value of X

[22] under this condition is then

it X32FkT A Y

2 T 1 T 3 -li

where F is the noise figure and A the bandwidth of the receiver, T is the

ambient temperature, U and T] are the volume and the filling factor of the

tank coil, and w = yHo , where Ho is the steady field causing Larmor precession at frequency cu . Achievement of this theoretical sensitivity in

practice requires great stability of the oscillator and bridge components

32
in order to avoid microphonic noise. This makes it necessary to search

for resonances by varying the magnetic field while keeping the frequency

constant. This problem can be avoided by making the tuned circuit part

[ 23, 24]

of an oscillator operating at a low level. Variations in Q then

cause variations in the level of oscillation which can be observed with a receiver. The ultimate sensitivity of this arrangement is given by an

expression similar to equation (16). In practice it is difficult to achieve

a good overall noise figure F over a wide range of RF levels because of

the need to operate the active components in non-linear parts of their

*[25j characteristics. However, an optimum noise figure of 2 has been

[23] reported in the literature. Equation (16) represents the performance

with which any improved detection system must compete.

4. 1 Piecemeal Improvements

Looking at the formula in equation (16) for the sensitivity of the

NMR detectors currently in use, it is obvious that some improvements

can be made simply by replacing various components with superconducting

versions.

Turning first to the factor FkTo in equation (16), there is scope

for a superconducting preamplifier, such as a parametric up-converter

f ? 61

or a linear cryotron amplifier , to gain an order of magnitude by

operating at a low effective temperature. This has been achieved by

Silver and Zimmerman using the Josephson effect. Their device

suffers from the limitation that it only operates with a very low RF level,

so that its performance would fall short of the optimum expressed by

equation (16) except when the relaxation times t x and t 2 are long. The

advantage of low temperature operation has also been obtained with field

r 28

1

F 29] effect transistors by Miyoshi and Cotts, and by Alderman.

The limitation is that the effective value of To is controlled by all

the lossy components in the input circuit, including the tank circuit and

33
specimen. Thus if the specimen accounts for a significant part of the

damping of the tank circuit it too must be cooled. In general, this has

the effect of increasing the components of susceptibility, but also increases the relaxation time Ti . It may not always be desirable to work

with a cold specimen, and if not the attainable effective noise temperature

is limited.

Another obvious application of superconductivity is in raising the

Q of the tank circuit. This has been investigated by Persyn, Victor, and

Rollwitz, who operated a system at 0.95 MHz with a superconducting

tank circuit. Because of their choice of superconductor and layout (lead

coated copper wires), they were restricted to work at flux densities less

than 20 millitesla. They observed a considerable improvement in sensitivity over a non- superconducting system working at the same low field.

However, the factor ou in equation (16) requires us to consider flux densities approaching 1 tesla. Further development is required on high-Q

circuits at these high fields. Once again, the limit to attainable performance maybe set by loss in the specimen.

The presence of superconducting material will cause a distortion

of the magnetic field at the specimen, and it is important to preserve the

homogeneity of the field to avoid broadening the resonance. In order to

operate in a high field, the tank coil would be made of a type II superconductor, whose magnetic effect in a transverse field can be represented by a large diamagnetic susceptibility. Field distortion would be

caused by unsuitable geometry of the coil or by variations in its effective

magnetic susceptibility due to uneven flux pinning. The simplest geometry

to use would be a thin film of superconductor deposited on an insulating

cylinder with a narrow helical scratch to form it into an inductive coil.

If we approximate this geometry by an infinitely long cylinder of radius

r coated with a film of susceptibility Xand thickness d, then a uniform

34
transverse field H outside the cylinder would generate a uniform field

H inside, where

H = H (l +Xd/r)-\ (17)

In this expression, X cannot exceed H /H , where H is the thermodyc c namic critical field of the superconductor. Variations in X must be less

than X itself. It would be perfectly feasible to use a film 1000 A thick,

with r of the order of 1 cm. Field distortion should therefore be below

the part per million level.

4. 2 Magne tome try

There are reported in the literature several very sensitive super-

[31] conducting magnetometers. Some of these operate by modulation of

the inductance of a circuit carrying a persistent current, thereby gener-

[ 32, 33] ating an alternating voltage proportional to the magnetic flux, while

others are essentially flux-quantum counters which depend on the proper-

[ 34, 35] ties of multiple Josephson junctions and can be sensitive to changes

f 361

in magnetic flux of 10

l quanta. Recently Mercereau reported a reliable, engineered version of a magnetometer based on flux quantization

capable of detecting changes in flux density of 10" tesla.

The scheme of NMR detection we propose to analyze is one in

which the change in flux density 6B, resulting from the change in static

nuclear susceptibility Xo induced by NMR, is detected with a supercon-

[33] ducting magnetometer. This was first suggested by Pierce. The

crucial practical problem in this scheme would be supplying the RF field

to induce NMR without interferring with the very sensitive magnetometer.

This might be accomplished simply by avoiding the modulation frequency

in the inductance modulated magnetometers if the readout system were

sufficiently linear to avoid excessive mixing. Other possible schemes would

[33] supply RF power in pulses, or as ultrasonic phonons when the nuclei

under study possess quadrupole moments. Another problem is that the

35
steady magnetic field must be stable to 10" tesla. This can only be

accomplished with superconductors, and it precludes sweeping or modulating the magnetic field. These problems are not trivial, and the purpose of this analysis is to discover if they are worth attacking.

In order to compare this system with detection by power absorption, let us assume that sufficient RF field is applied to saturate the

resonance to the extent of halving Xo from its equilibrium value. This

corresponds to the optimum RF level for detecting x'and X • The change

in magnetic flux density 6B corresponding to the minimum detectable NMR

signal given by equation (16) is then

6B = J Mo Xo Ho

32 FkToAi^oTi

L T]Uu>oQt s (18)

A superconducting magnetometer can only compete in sensitivity with

the present-day RF spectrometers mentioned in our introduction if the

quantity 6B given by equation (18) exceeds 10" tesla. For a numerical

comparison, let us take U = 1 cm3

, 7] = 1, Q = 100, A= 1 Hz, ou = 10 MHz.

This flatters RF spectrometers at ambient temperature by a factor greater

than unity but less than 10. Substituting these numbers into equation (18)

we find

6B m 5 X 10" 15 /t 1 /t 3 . (19)

Thus if T\ = t 2 , as often happens in liquids for example, the best sensitivity obtainable with a superconducting magnetometer is approximately

equal to that of a good RF bridge or marginal oscillator operating at

ambient temperature. Clearly there would be no reward for the considerable effort of development. However, if t x » t 2 the superconducting

magnetometer would begin to show some advantage. This condition is

often observed in solids, particularly at low temperatures.

36
There are other unusual circumstances when the superconducting

magnetometer would be advantageous: for example, Pierce's magnetom-

[33]

eter was designed for a non-destructive readout of the orientation of

the spins of a polarized sample of He in a nuclear gyro. There was no

problem with sensitivity because of the metastable polarization of the

spins.

4. 3 Conclusions

It appears that using a cold input circuit (possibly including a superconducting preamplifier) and a superconducting high-Q tank circuit

can each raise the sensitivity of an otherwise conventional NMR detector

by an order of magnitude if the specimen permits. The impressive sensitivity of superconducting magnetometers gives an advantage to NMR

detection only in unusual circumstances, such as very long Tj.

This last statement appears surprising unless one understands

how large the flux quantum is compared with other fundamental quantities.

In order to change the magnetic flux linking a cylinder 1 cm long, of

arbitrary cross section area, by one flux quantum it would be necessary

to flip approximately 10 nuclear spins within its volume. One's respect

for NMR as a sensitive probe of matter is enhanced by this reflection.

37
5. Overall Conclusions

In this report we have given a recipe for fabricating permanent

niobium-lead Josephson junctions and a design for a millikelvin noise

thermometer which is presently in the prototype testing stage. Both of

these appear to be real contributions to the practical application of the

Josephson effect. An examination of the possibility of applying superconductivity to NMR detection revealed a less promising situation.

38
APPENDIX

A Review of the Josephson Effect

Prepared for the IEEE Transactions on Instrumentation

and Measurement

The original discovery of the Josephson effect followed the classic

pattern which is optimistically described in many textbooks of elementary science but quite rarely encountered in real life. It is a very striking

manifestation of quantum mechanics on an unusually large scale, which

[ 37-39]

was originally predicted theoretically by B. D. Josephson in 1962.

He published his theory under the cautious title "Possible New Effects in

Superconductive Tunneling," and it was quickly challenged by several other

eminent theorists. There was a vigorous debate until the first experimental

observation of the effect by Anderson and Rowell the following year.

In view of the controversy they, too, used cautious words and reported

the "Probable Observation of the Josephson Superconducting Tunnel

Effect. " With the accumulation of more experimental evidence the doubts

evaporated, and published statements became bolder. Since then there

has been an exciting period of invention of devices, based on the Josephson

effect, which promise to revolutionize many aspects of electronics. The

purpose of this article is to sketch the main features of the effect itself

and to describe some of these applications.

The Josephson effect occurs at a Josephson junction, which is a weak electrical contact between two pieces of superconducting metal. We

will discuss Josephson junctions and their highly non-linear electrical

characteristics in the following section. Thereafter we will describe

briefly some devices, based on these characteristics, which range in

state of development from early concepts to well engineered instruments.

In general, these devices are well adapted to handling very small signals

39
with a very low noise level. Many of them have a very wide dynamic

range. Often their calibration can be related directly to fundamental

constants, making absolute measurements possible. Since the Josephson

effect requires superconductivity, all these devices must operate at a very low temperature, usually provided by a bath of liquid helium.

Josephson Junctions

There are several practical ways to make the weak electrical

contacts required by the Josephson effect. An ideal junction might consist of two superconductors separated by a vacuum gap about 10 A (10~ cm)

wide and perhaps a square millimeter in area. Electrons would cross

[39 41]

this gap by the quantum mechanical tunnel effect. The nearest

practical approach consists of a strip of thin film of one superconductor

deposited on an insulating substrate such as glass, quartz, or sapphire.

Its surface is covered with an insulating barrier of the desired thickness

(usually by oxidation of the metal), and then a strip of thin film of the

second superconductor is deposited across the first to complete the

junction. The barrier does not need to be an insulator. A layer of normal

[42] metal such as copper, about 10, 000 A thick, will work instead. Another

approach is to use a continuous strip of superconducting thin film with a

[43]

very narrow constriction (a few micrometers wide). The electrical

characteristics of this microbridge structure differ from those of crossed

film junctions, but the similarities are sufficient for many practical purposes. An intermediate approach is to press a slender point on one

[6] superconductor lightly against the other to form a point contact junction.

It is not quite clear whether a surface layer formed by atmospheric corrosion forms an insulating barrier, or if the narrow contact area functions

as a microbridge. However, point contacts have the great advantage that

they can be adjusted while in operation and they work very well. The

more permanent structures such as crossed film junctions and microbridges have the compensating advantage of greater mechanical stability.

40
Superconductors commonly used to make Josephson junctions are

lead, tin, indium, niobium, tantalum, etc. It is not important whether

the same or two different superconductors are used to form a junction.

The electrical characteristics of these junctions depend on how

[ 44 } 45] they are made, but one feature they all have in common is the ability

to pass a limited current (in the range from a few pA to a few mA) without

any voltage appearing. A somewhat idealized I-V curve for a crossed

film junction is shown in figure 8. If the current passing through the

junction exceeds I (fig. 8) a voltage appears and there is often an unstable

region of negative dynamic resistance. There is a characteristic voltage

of the order of a millivolt, determined by the energy gaps of the superconductors, at which the current rises sharply before settling down to

an ohmic response at high voltage. Microbridges differ from crossed

film junctions mainly by the absence of the low current region at intermediate voltage.

The magnitude of I is very sensitive to a magnetic field applied

c in the plane of the junction. Figure 9 shows a plot of I versus magnetic

flux density for an ideal crossed film junction. Similar curves have been

[46] observed in the laboratory. The vertical scale depends critically on the

thickness of the insulating barrier, while the horizontal scale is controlled

by the width of the junction and the properties (penetration depths) of the

superconductors. The periodicity is caused by quantum interference

between electrons crossing different parts of the barrier. It is analogous

to optical diffraction at a narrow slit. The analogue of optical interference

between two slits can be created by connecting two Josephson junctions in

parallel in a superconducting circuit as shown in figure 10. The curve

shown in figure 9 then becomes the envelope of an interference pattern

of much shorter period. This period corresponds to the quantum of

magnetic flux h/2e «si 2 X 10" Weber, (h is Planck's constant and e is

41
Z

UJ

a:O

VOLTAGE

Figure 8. Current versus voltage characteristic of a thin film Josephson junction.

42
w&Oo

COz

UJQX

BJ

a) r—I

03U

UJ

(D AH

T3

.—1

0) -^mU

-i

j-> cd

05

O

•r-H e P

T5 ti CD 3 ^

•'

—i

r—ia,

a,

CD 5 aj mo

>>

s u

00 -(-> a) 00 a

•rH m o

CD&J0

u

n <a m £ o

+j

CD e

(Ja

CD o

X! T3 a a

CD CD Oh A <D CD Q T3

CD

r-l

43
(a)

t

Tin Films

(b)

Formvar

Insulator

Quartz Substrate

Tin Oxide

Josephson Junction

Figure 10. The quantum interferometer, a) ideal, b) early practical version

(ref. 47).

44
the electron charge. ) Each minimum in the interference pattern occurs

when a whole number of magnetic flux quanta link the superconducting

[47]

loop. This arrangement has become known as a quantum interferometer.

It has obvious applications to magnetometry and other arts.

If a resonant circuit is connected to a Josephson junction a peak

appears in the direct current vs. voltage characteristic as shown in

figure 11. The voltage V at which the peak appears is related to the resonant frequency / of the circuit by h/ = ZeV. This corresponds to approximately 484 MHz per |W.

If a radio frequency or microwave signal is addressed to the junction,

the direct current vs. voltage relationship becomes profoundly modified

as shown in figure 12. It develops a series of steps at equal intervals of

voltage.

by h/ = 2eV.

[49]

voltage. Once again the voltage interval V is related to the frequency

Finally, if a receiver is connected to the junction, a coherent os-

[ 49 50] dilation ' can be detected at the same frequency /= 2eV/h. The

waveform is usually non-sinusoidal, so harmonics of this frequency can

also be detected at sub -multiples of the fundamental voltage. These are

illustrated by an actual recorder chart shown in figure 13. The receiver

was tuned to 43 MHz and the odd signal shape was a result of lock-in

detection. This oscillation is a quantum mechanical effect. A pair of

electrons with charge 2e falls through a potential drop V, and the energy

2eV which they gain is radiated away as a quantum h/. Frequencies

[51] [52] ranging from a fraction of 1 Hz to 10 GHz have been observed.

Applications of the Josephson Effect

With some exercise of ingenuity it is possible to devise sensors of

almost anything known to man using the Josephson effect, and most of

them would probably perform rather well. We will restrict our discussion

to devices which at least exist in prototype form.

45
UJ

O

Ir "

VOLTAGE

Figure 11. Current versus voltage characteristic of a thin film Josephson

junction connected to a circuit with a resonance at frequency

/ = 2eV/h.

46
UJ

a:

<rID

V VOLTAGE

Figure 12. Current versus voltage characteristic of a Josephson junction

irradiated at a frequency / = 2eV/h.

47
ZHl/M £fr IV 1VN9IS JO 3AUVAIH3Q

48
Perhaps the most obvious application of the Josephson effect is to

magnetometry. The quantum interferometer (fig. 10) is clearly a very

sensitive sensor of magnetic field. The most advanced magnetometer to

[36] date was described recently by Mercereau. It is based on a variation

of the quantum interferometer using a superconducting ring with only one

microbridge. By coupling this structure inductively to a resonant L-C

circuit it is possible to measure its impedance at 30 MHz. This turns

out to be a periodic function of both steady and RF magnetic fields, the

period corresponding to the flux quantum. Mercereau described a well

engineered instrument capable of detecting changes in steady magnetic flux

of 10 quanta. Because of the macroscopic nature of the quantization in

the superconducting state the philosophical problems this appears to raise

can be resolved.

A sensor of magnetic field can also sense electric current, and

[53] Clarke has made this the basis for a very sensitive null detector,

illustrated in figure 14. The device consists of a short length of superconducting niobium wire with a blob of superconducting lead-tin solder

frozen onto it. The solder does not wet the niobium because of the presence of an oxide layer. Once in many attempts a pair of Josephson

junctions are formed, probably at the ends of the solder blob. They then

form a quantum interferometer which is sensitive to the circumferential

magnetic field due to the current in the niobium wire. Clarke reports

that this device can detect 10" A. Because of the very small inductance

of the niobium wire, this current would build up in one second if driven

by a voltage of 10" V. The device is therefore a very sensitive detector

of a voltage null in a low impedance circuit. By connecting the ends of

the niobium wire together, this device can be made into a magnetometer.

A change in magnetic flux linking the loop Would be opposed by a persistent

induced current, which would be sensed by the quantum interferometer.

The minimum detectable change in magnetic flux density is once again

49

lO" 14 tesla[

35]
/

INTERFEROMETER

TERMINALS

SOLID BLOB

NIOBIUM WIRE

CONNECTION FOR

MAGNETOMETER _ o

Figure 14. The Clarke null detector.

50
Both the magnetometers we have mentioned are only sensitive to

changes in magnetic field. They require special precautions to set the

zero for absolute measurements.

[54] Meservey has suggested that by careful attention to geometry

it would be possible to construct a sort of absolute ammeter, using a quantum interferometer to relate the ampere to the flux quantum.

Another application of the sensitivity of the Josephson effect to

[55] magnetic field is Matisoo's tunneling cryotron. In this device the

[ 56, 57]

gate strip of a thin film cryotron is replaced by a thin film

Josephson junction. An insulated control strip is laid across the junction

(fig. 15). When a current is passed through the control strip it generates

a magnetic field which affects the maximum supercurrent I which the

junction can pass as shown in figure 9. The I-V characteristic of the

gate is illustrated in figure 16. If it is biased to the operating point A

(fig. 16), a small pulse of current in the control strip can depress I below

the operating current and cause the device to switch to the operating point

B at a voltage of the order of a millivolt.

This device was designed for a computer element. Its advantage

over the original thin film cryotron is its high resistance in the switched

state, which permits very fast switching. A switching time of 10"'

seconds has been achieved for diverting current from one branch of a network to another.

Turning now to the Josephson oscillation, it too can be used to mea-

[51]

sure very low voltage. The record is held by Silver and Zimmerman,

who indirectly observed the oscillation of a Josephson junction at 0. 2 Hz,

corresponding to a DC bias voltage of 4 X 10" volts. They used the

junction both as oscillator and mixer, to mix the very feeble signal from

the self-oscillation with a much stronger one at 30 MHz. The resulting

amplification by parametric up-conversion was sufficient to make it observable.

51
UJ

aou+Jou

bfl a•l-l 1—1

<U 2

IT)

60

fn

52
UJ

a:

crO

VOLTAGE

Figure 16. Current versus voltage characteristic of the gate of a tunneling cryotron. The operating points are marked A and B,

53
Another interesting achievement of these experimenters was to

set up a very sensitive RF circuit to observe the influence of a passive

[ 27] resonant circuit on the I-V characteristic of a Josephson junction

(fig. 11). They were able to sense the presence of various resonant

structures, including a sample of powdered cobalt inductively coupled to

the circuit. They detected the nuclear magnetic resonance of Co at

218 MHz, showing that their instrument has potential as an RF spectrometer. Its distinctive feature in this respect is its very low level of

excitation, which would be an advantage with a specimen with a very long

relaxation time.

The current and voltage in an ideal Josephson junction at zero

temperature would be related by

§ = (2eV/M-d2

- I3

)*

at c

when I ^ I s and this approximately represents the behavior of a real

Josephson junction in experimentally accessible conditions. This relationship makes a Josephson junction an extremely efficient and broad band

r coi

RF mixer, with the additional feature that applying a DC bias adds the

self-oscillation of the junction to the mix. The time dependence of the

I-V relationship generates this and other unique properties not shared by

classical non-linear mixers. We have already mentioned a demonstration

of this effect at 0. 2 Hz. At the other extreme, Kose, McDonald, Evenson,

[591 and Wells have observed the mixing of signals from an HCN laser

near 900 GHz by a Josephson junction.

The steps in the I-V characteristic of a Josephson junction under

the influence of an RF signal are actually another manifestation of this

mixing effect, with one of the resultant signals at zero frequency. Parker,

Taylor, and Langenberg have measured the relationship between

applied frequency / and voltage interval V for these steps to an accuracy

54
of a few parts per million. Assuming that the relationship truly is h/ = 2eV, they used their results to derive a new value for the fine structure

constant a = e /#c. This resolved an old discrepancy between the calculated and measured values of the hyperfine splitting of the hydrogen atom.

It will probably have a significant impact on the accepted values of the

fundamental constants.

They found the measured relationship between frequency and voltage

to be independent of temperature within their experimental error. More

[42] recently Clarke showed that this relationship is the same to one part

p in 10 in junctions made of lead, tin, and indium. This has raised the

interesting possibility of ultimately using the Josephson effect to replace

[62] electrochemical cells to maintain the standard volt, and there appear

to be many potential advantages in doing so. Another application related to RF mixing is the detection of radir / -d i ation. Grimes, Richards, and Shapiro have shown that when a point

contact Josephson junction is biased to suitable operating point, it becomes

a sensitive detector of long wavelength radiation. The usable range covers

the radio and microwave regions of the spectrum, down to a short wavelength limit of a few hundred micrometers. Taking a detected bandwidth

of 1 Hz, the minimum detectable signal is 10" watts in a system sensitive to the whole spectrum or 10 watts with a narrow band filter. In

p addition to this great sensitivity, the response time is very short (10"

seconds), permitting high frequency chopping of the incident signal to

discriminate against background radiation.

Finally, noise thermometery. Since the frequency of an oscillating

Josephson junction is determined by the bias voltage, it follows that fluctuations in the voltage due to thermal noise will cause fluctuations in frequency. Measurement of these frequency fluctuations can therefore form

[7] the basis of a new scheme of absolute thermometry. Once again, the

55
Josephson junction acts as a parametric up-converter which amplifies

the very feeble noise voltage, generated by a resistor at a low temperature, to a high enough level to detect with a receiver at ambient temperature.

One technique to measure the frequency fluctuations is to use some

kind of spectrum analyzer to measure the linewidth A/ of the oscillation.

TM. . . K

[10] This is given by

A/ = l6-rre

2 kTR/h2

assuming that the only source of noise is a resistor R at a temperature T

connected in parallel with the junction. The quantity k is Boltzmann's

[17]

constant. This relationship has been checked experimentally in the

range 2 K < T < 8 K, and 1.7 X 10~ 10 n < R < 2. 6 X 10" 5 P. Another technique to measure the frequency fluctuations is directly

with a frequency counter. Under the same assumptions as before the variance ((/ - (/)) ) of fluctuations in repeated measurements of the frequency / with a counter with gate time t would be

<(/ . </>)

2

) = 8e 2 kTR/ih2

.

Advantages of this technique are its facility for automation and the possibility of analyzing the statistics of the observed fluctuations to eliminate

other sources of noise, such as flicker noise, with a different frequency

[19] spectrum.

The interesting question is the low temperature limit of this scheme

of thermometry. Assuming that extraneous sources of noise can be eliminated, the fundamental limit is set by photon shot noise generated by the

[15] Josephson junction. This sets a lower limit of eV/k to the effective

noise temperature of the junction. For a junction oscillating at 40 MHz

this effective temperature would be 10~ 3 K. It would be possible to measure lower temperatures if the resistor R were small compared to the

56
resistance of the junction. Thus the possibility exists of measuring

absolute noise temperatures in the millikelvin range.

Looking back over the devices we have discussed, it appears that a Josephson junction is almost a universal sensor. This is a source of

embarrassment when designing an experiment to measure a single quantity,

but the rewards of perseverence are great.

57
References

1. R. A. Kamper, L. O. Mullen, and D. B. Sullivan, Superconducting

Thin Films, NASA Contractor Report CR 1189 (1968).

2. C. A. Neugebauer and R. A. Ekvall, Vapor-deposited superconductive films of Nb, Ta, and V, J. Appl. Phys. 35_, 547-553 (1964).

3. B. W. Maxfield and W. L. McLean, Superconducting penetration

depth of niobium, Phys. Rev. 139, A1515-1521 ( 1965).

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5. J. C. Swihart, Field solution for a thin -film superconducting strip

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7. R. A. Kamper, Millidegree noise thermometry, Symposium on the

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simple magnetic field meter, Rev. Sci. Instr. 21_, 219-225(1950).

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59
25. D. H. Howling, Signal and noise characteristics of the PKW marginal

oscillator spectrometer, Rev. Sci. Instr. 36, 660-667 (1965); Signal

and noise characteristics of the Robinson nuclear absorption circuit,

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28. D. S. Miyoshi and R. M. Cotts, Helium cooled RF preamplifier

for use in NMR, Rev. Sci. Instr. 39, 1881-1884(1968).

29. D. W. Alderman, Nuclear Magnetic Resonance Study of KCl:Li"'"

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30. G. A. Persyn, J. M. Victor, and W. L. Rollwitz, High-Sensitivity

Nuclear Magnetic Resonance for the Quantitative Analysis of Body

Fluids (USAF School of Aerospace Medicine Report SAM-TR -67-70,

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60
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(Abstract only).

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61
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and submillimeter wave radiation, Proc. IEEE 54, 560-575 (1966).

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62
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/ ~ GPO 854 - 206

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