SQUID ’80. Superconducting Quantum Interference Devices and their Applications: Proceedings of the Second International Conference on Superconducting Quantum Devices, Berlin (West), May 6–9, 1980 9783110846621, 9783110080636

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SQUID '80 Superconducting Quantum Interference Devices and their Applications

SQUID '80 Superconducting Quantum Interference Devices and their Applications Proceedings of the Second International Conference on Superconducting Quantum Devices Berlin (West), May 6-9, 1980 Editors H. D. Hahlbohm • H. Lubbig

W G DE

Walter de Gruyter • Berlin • New York 1980

Editors

Hans-Dieter Hahlbohm, Dr. phil. Heinz Lübbig, Dr.-Ing. Physikalisch-Technische Bundesanstalt Institut Berlin Abbestraße 2 - 1 2 D - 1 0 0 0 Berlin 10

CIP-Kurztitelaufnahme der Deutschen Bibliothek

SQUID : superconducting quantum interference devices and their applications / ed. H. D. Hahlbohm ; H. Lübbig. - Berlin ; New York : de Gruyter. NE: Hahlbohm, Hans D. [Hrsg.] 1980. Proceedings of the Second International Conference on Superconducting Quantum Devices : Berlin (West), May 6 - 9 , 1980. - 1980. ISBN 3-11-008063-X NE: International Conference on Superconducting Quantum Devices (02, 1980, Berlin, West)

Library of Congress Cataloging in Publication Data

International Conference on Superconducting Quantum Devices, 2d, Berlin, 1980. SQUID '80, superconducting quantum interference devices and their applications. Bibliography: p. Includes index. 1. Superconducting quantum interference devices - Congresses. I. Hahlbohm, H. D. 1930. II. Lubbig, H., 1932III. Title. TK7872.S8I57 1980 621.39 80-28184 ISBN 3-11-008063-X

© Copyright 1980 by Walter de Gruyter & Co. Berlin 30. All rights reserved, including those of translation into foreign languages. No part of this book may be reproduced in any form - by photoprint, microfilm, or any other means - nor transmitted nor translated into a machine language without written permission form the publisher. Printing: Karl Gerike, Berlin. - Binding: Lüderitz & Bauer, Buchgewerbe GmbH, Berlin. Printed in Germany.

PREFACE In studying the nine invited lectures and the 64 contributed papers collected in this volume, it becomes clear that the IC Squid 80 conference was necessary to draw together the last four years of research and development work in this field. This underlines what we pointed out in the preface of the proceedings of IC SQUID 76 ^ , that "theory and applications in several branches are just at the beginning". The present state, as demonstrated here, shows that this statement still holds true. Impressive examples are the appearance at IC SQUID of novel devices (e.g. long Josephson junctions) and potentially new basic physical processes (e.g. macroscopic quantum tunneling). Nevertheless, the contents of this volume represent significant advance in the field of Superconducting Quantum Interference Devices and their applications. rd A specific feature of IC SQUID 80 was the strong connection with the 3 Workshop on Biomagnetism which was organized simultaneously. For this reason, lectures and papers on SQUID application in Biomagnetism have been 2) excluded here and will be published in a separate volume . In preparing the present volume, a few restrictions proved to be unavoidable. It was impossible to enforce an uniform unit system (in particular the SIS) for the different contributions. Consequently, a comparison of the different results is at times unnecessarily complicated. Furthermore, a comprehensive classification scheme for this field, which could be used as the subject index, has not yet been fully developed. Therefore, we have been forced to make decisions which might be considered in some cases to be rather arbitrary. rd The large extent of this volume together with the proceedings of the 3 Workshop on Biomagnetism reflects the size of both conferences. The delegates, representing 21 countries, included 197 participants. Our thanks go to all of them, and to the authors who have enabled us to produce these volumes. The conference was proposed and encouraged by the European Physical Society.

VI The p u b l i c a t i o n of the proceedings i s a f i n e occasion to acknowledge once more the generous support of the conference by the President of the Deutscher Bundestag, the B e r l i n Senate, the President of the P h y s i k a l i s c h Technische Bundesanstalt, and the Siemens AG. A l s o i t should be emphasized that without the cheerful and active p a r t i c i pation of the members of the I n s t i t u t B e r l i n of the Physikalisch-Technische Bundesanstalt in a l l aspects of the conference a c t i v i t i e s , the meeting would not have been p o s s i b l e . Our thanks go to G. Sauerbrey, the head of the I n s t i t u t B e r l i n , and a l l

i t s members.

We are a l s o g r e a t l y indebted to the l o y a l t y and patient s e c r e t a r i a l a s s i s t a n c e of Frau M. Bieber and Frau A. Lochmann in connection with the organization of t h i s volume. We are grateful to the De Gruyter Publishing Company f o r i t s valuable cooperation in preparing these proceedings.

B e r l i n , September 1980

H.-D. Hahlbohm H. LUbbig

1) Superconducting Quantum Interference Devices and t h e i r A p p l i c a t i o n s , W. de Gruyter, B e r l i n 1977.

2)' Biomagnetism, W. de Gruyter B e r l i n , in press.

CONTENTS

JOSEPHSON JUNCTION PHYSICS Progress in physics of Josephson junctions.

H. LUbbig

1

Non-equilibrium phenomena in Josephson junctions. J. Bindslev Hansen, P.E. Lindelof

29

Study of a spin-glass phase transition by the dc Josephson effect. C. Van Haesendonck, L. Van den dries, Y. Bruynseraede, A. Gilabert..

71

Characterization of non equilibrium superconductivity via the Josephson effect. A. Gilabert, C. Vanneste, P. Sibil lot, D. Ostrowsky

81

Locally lowered tunneling barriers in light-sensitive Josephson junctions.

M. Russo

87

Preparation parameters and characterization of vanadium based Josephson junctions. A. Barone, M. Russo, A. Di Chiara, G. Peluso

95

Measurement of the c o s y -amplitude of niobium point contacts contained in a rf-SQUID.

S.N. Erne, H. Luther, H.J. Scheer

109

An electronic analogue of a high frequency theory of the Josephson effect.

D.G. Jablonski, J.R. Waldram

115

Supercurrent interference patterns and quasiparticle excess currents in Josephson tunnel junctions.

P.W. Epperlein

131

Magnetic field behavior of current steps in long Josephson junctions G. Costabile, A.M. Cucolo, S. Pace, R.D. Parmentier, B. Savo, R. Vaglio

147

Properties of coherent vortex motion in Pb-Nb-Pb ion implant variable thickness bridges.

P. Crozat, G. Vernet, R. Adde

157

VIII The effect of magnetic field on the height of microwave-induced step.

Wei Chong-de, Li Jia-zhang

165

The current-phase relation of superconducting bridges. Yao Xi-Xian

171

Sub-harmonic steps of superconducting bridges. Yao Xi-Xian

173

Effects of microwave radiation on granular Al microbridges. B. Dwir , G. Deutscher

177

JUNCTION AND CIRCUIT NOISE Fluctuations analysis,

J. Clarke

187

Quantum limited ac-biased SQUID magnetometer.

A.P. Long,

R.J. Prance, T.D. Clark, J.E. Mutton, M.W. Potts, A. Widom, F. Goodall

207

On the (¿^-dependence of rf-SQUID noise.

R. Cristiano, S.N. Erne,

H. Luther

211

The plasma resonance in the rf impedance and the wide-band response of a capacitively shunted Josephson junction. T. Poorter, H. Tolner

219

Low frequency noise in small-area tunnel junction dc SQUIDs. M.B. Ketchen, C.C. Tsuei

227

Thermodynamic equilibrium fluctuations generated by a Josephson tunnel junction described by the Werthamer theory.

G. Brunk

237

Quantum versus thermally excited fluxoid transitions in a SQUID ring.

j. Kurkijarvi

247

JUNCTION AND CIRCUIT FABRICATION Junction and circuit fabrication.

L.D. Jackel

257

High reliability Pb-alloy Josephson junctions for integrated circuits.

H.-C. W. Huang, S. Basavaiah, C.J. Kircher, E.P. Harris,

M. Murakami, S. Klepner, J.H. Greiner

297

IX Superconductive tunneling through edge-grown barriers. G. Dousselin, J. Rosenblatt

329

Refractory weak link Josephson devices.

J.H. Claassen,

E.J. Cukauskas, M. Nisenoff

333

Fabrication and characterization of the film parameters in ionimplant Nb bridges with thick Pb banks. Nb weak links for SQUID applications.

P. Crozat, R. Adde R.B. Laibowitz, A.N. Broers,

R.F. Voss, S.I. Raider, J.M. Viggiano Ultra low noise dc SQUIDs.

345

353

R.F. Voss, R.B. Laibowitz, M.B. Ketchen,

A.N. Broers

365

Some properties of Nb£0 5 thermally grown tunnel barriers in Nb-Nb 2 0g-Pb(In) Josephson junctions.

J.C. Villegier, G. Matheron ..

381

Dc SQUIDs fabricated with niobium-niobium tunnel junctions. V.J. de Waal, P. van den Hamer, J.E. Mooij

391

Fabrication and characterization of thermally recyclable submicron niobium-niobium Josephson junctions.

G.M. Daalmans

399

Simple fabrication and characterization of thin-film niobium SQUID's working at 4.2 K.

D. Pascal

417

CRYOGENIC TECHNIQUES Cryogenics for SQUIDs.

J.E. Zimmerman

423

FUNDAMENTALS FOR SQUID APPLICATIONS Fundamentals for SQUID applications.

R.P. Giffard

Signal and noise parameters of SQUID's.

445

V.V. Danilov,

K.K. Likharev, O.V. Snigirev

473

SQUID APPLICATIONS IN LOW FREQUENCY DEVICES Applications of SQUID's to nuclear gyros and magnetometers. R. Adams, S.P. Potts, J.C. Gallop, W.J. Radcliffe

509

X Application of the SQUID magnetometer for optomagnetic investigation.

H. Heidrich, P. Mateew

Optimising the design

519

of thin-film dc SQUID gradiometers.

C.M. Pegrum, G.B. Donaldson

535

The temperature, pressure, and power dependence of stable cryoresistors.

J.C. Macfarlane, H.C. Collins

Measurement of order-parameter aluminium film.

549

variations in a superconducting

J.A. Pals, J. Dobben

Toroidal SQUID with a normal metal filter.

553 T. Fujita

561

Behavior of the dc impedance of an rf-biased resistive SQUID. D. Van Vechten, R.J. Soulen, Jr., R.L. Peterson Input inductance of the rf SQUID in hysteretic mode.

569 S. S. Tinchev

585

Analysis of the reversible magnetization of a rf SQUID containing a weak link with a non-sinusoidal current phase relationship. H. LLibbig

591

Experimental evidence for quantum electrodynamic flux tunneling in SQUID magnetometer.

A.P. Long, R.J. Prance, T.D. Clark, A. Widom,

J.E. Mutton, J. Sacco, M.W. Potts,

G. Megaloudis

599

W.M. Goubau

603

SQUID APPLICATIONS IN GEOPHYSICS

Geophysical applications of SQUIDs.

Use of superconductive magnetic gradiometers for measuring magnetic effects of geophysical origin.

W. Podney

615

The design of dewar systems for geophysical SQUID magnetometers. B.R. Barnard

633

JUNCTION AND SQUID APPLICATIONS IN COMPUTERS AND CRYOELECTRONICS Computers and Cryoelectronics.

T. Van Duzer

651

XI Turn-on delays in single Josephson junction devices. R.L. Peterson

685

Effects of magnetic fields and quasi-particle conductance on transition dynami cs in dc SQUIDs.

E. Ben Jacob, Y. Imry

Direct-coupled four Josephson junctions logic gate.

703

S. Takada,

S. Kosaka, H. Hayakawa

713

Tolerances and gain of asymmetric Josephson junction interferometer for AND gates.

H. Beha

725

Josephson field effect transistors - JOFET's. R.J. Prance, T.D. Clark

735

JUNCTION AND SQUID APPLICATIONS IN MICROWAVE DEVICES RF applications of superconducting tunneling devices. N.F. Pedersen Experimental results of the magnetic coupling.

739

Cui Guang-Ji,

Meng Xiao-Fan, Guo Wei-Xin, Li Jia-Zhang, Dai Yuan-Dong Microwave properties of long Josephson junctions.

763

K. Yoshida,

K. Hamasaki, F. Irie, M. Inoue

769

Microwave induced harmonic and subharmonic steps in the I-V characteristics of current fed Josephson junctions.

Y. Braiman,

E. Ben-Jacob, Y. Imry

783

The singly quasi-degenerate Josephson junction parametric ampflifier. Design guide lines.

O.H. Soerensen

797

Josephson parametric amplifier as a part of a gravity wave detection scheme.

J. Kadlec, W.O. Hamilton

Josephson junction applications in plasma physics.

813 B.T. Ulrich,

M. Tutter

831

Video-detection of mm-wave radiation using SIS Josephson junction. H.J. HartfuB, K.H. Gundlach, J. Kadlec

841

XII MM-wave detection using q u a s i p a r t i c l e tunneling. H.J. HartfuB, K.H. Gundlach

851

Fabrication of small Josephson tunnel junction.

K.H. Gundlach,

M. Zahn, K. Okuyama, H.J. HartfuB

857

Detection of mm-radiation with high current density submicron niobium-niobium Josephson j u n c t i o n s .

G.M. Daalmans, Th. de Graauw,

S. Lidholm, Fr. v. V l i e t

863

Theory of Josephson junction mixers.

G.J. Ehnholm

875

C h a r a c t e r i s t i c s of Josephson junction harmonic mixers with even and odd harmonic numbers.

K. Fujisawa, S. K i t a , Y. Ohmae,

T. H i r o s a k i , K. F u j i i e

889

S I S q u a s i p a r t i c l e mixing with long antenna-coupled a r r a y s . S. Rudner, N.J. Feldman, E. Kollberg, T. Claeson

901

Josephson r a d i a t i o n emitted from a microbridge at 9, 35 and 69 GHz. J. Mygind, N.F. Pedersen, O.H. Soerensen, B. Dueholm, T.F. Finnegan, J. Bindslev Hansen, M.T. Levinsen, P.E. Lindelof Coherent r a d i a t i o n of Josepshon junction a r r a y s .

907 Yuan-Dong Dai,

Y.H. Kao

921

Microwave generation using coherent arrays of Josephson j u n c t i o n s . A.K. J a i n , A.M. Kadin, J.E. Lukens, P. Mankiewich, R.H. Ono, D.B. Schwartz

939

A new integrated microwave SQUID c i r c u i t design. T.F. Finnegan

S.N. Erne, 955

SUMMARY AND CONCLUSIONS Summary and conclusions. Subject Index Author Index

J. Clarke

^61 971 988

LIST OF PARTICIPANTS Adde, R.

I n s t i t u t d'Electronique Fondamentale, Université Paris-Sud, Bat. 220, 91405 Orsay, France

Aittoniemi, K.

Department of Technical Physics, Helsinki University of Technology, SF 02150 ESPOO 15, Finland

Bain, R.R.P.

Department of Applied Physics, John Anderson Building, University of Strathclyde, Glasgow G4 ONG, Great Britain

Barbanera, S.

Laboratorio di Elettronica dello Stato Solido, C.N.R., Via Cineto Romano 42, Roma, Italy

Barnard, B.R.

Cryogenic Consultants Limited, 231 The Vale, Acton, London, W3, Great Britain

Barone, A.

Laboratorio di Cibernetica del CNR, Via Toiano 2, 80072 Arco Felice (Napoli), Italy

Basavaiah, S.

IBM Thomas J. Watson Research Center, P.O.Box 218, Yorktown Heights, New York 10598, USA

Bastuscheck, C.M.

Departments of Psychology and Physics, New York University, 6 Washington Place, New York, New York 10003, USA

Beha, H.

I n s t i t u t für Elektrotechnische Grundlagen der Informatik, Universität Karlsruhe, Hertzstraße 16, 7500 Karlsruhe , Germany

Ben Jacob, E.

Department of Physics and Astronomy, Tel Aviv University, Ramat Aviv, Israel

Bergmann, W.H.

Kraftwerk Union AG, R122, Sperberweg 10/1, 8520 Erlangen, Germany

XIV Bloyet, D.

I.S.M.R.A., Université de Caen, 5 Avenue d'Edimbourg, 14032 Caen-Cedex, France

Boesiger, P.

Institut für biomedizinische Technik, Universität Zürich und ETHZ, Moussonstr. 18 8044 Zürich, Switzerland

Borek, L.

Vacuumschmelze Hanau GmbH, 6450 Hanau, Germany

Brauer, F.

HNO-Forschungstrakt, Klinikum Westend, Spandauer Damm 130, 1000 Berlin 19, Germany

Brenner, D.

Department of Psychology and Physics, New York University, 6 Washington Place, New York, New York 10003, USA

Brunk, G.

Physikalisch-Technische Bundesantalt, Institut Berlin, Abbestraße 2-12, 1000 Berlin 10, Germany

Buchholz, B.

Physikalisch-Technische

Bundesanstalt,

Institut Berlin, Abbestraße 2-12, 1000 Berlin 10, Germany Buck, K.

French-German Research Institute, 12 rue de l'Industrie, 68301 Saint-Louis, France

Buck, W.

Physikalisch-Technische

Bundesanstalt,

Institut Berlin, Abbestraße 2-12, 1000 Berlin 10, Germany Buhrman, R.A.

School of Applied and Engineering Physics, Cornell University, Clark Hall, Ithaca, New York 14853, USA

Calander, N.

Physics Department, Chalmers University of Technology, 41296 Göteborg, Sweden

Ciaassen, J.

Naval Research Laboratory, 4555 Overlook Ave., S.W., Washington, D.C. 20375, USA

XV Clark, T.D.

School of Mathematical

and Physical

Sciences,

University of Sussex, Falmer, Brighton, Sussex, Great Britain Clarke, J.

Department of Physics, University of California, Berkeley, California 94720, USA

Combasson, J.

DRET/SOR

, 26 Boulevard

75996 Paris Aimées Cosme!Ii, C.

Victor,

, France

Istituto di Fisica "G. Marconi", Università Degli Studi Di Roma, Piazzale delle

Scienze,

Roma, Italy Costa Ribeiro, P.

Departemento de Fisica, Pontificia

Universidade

Católica, C.P. 38071 - Rio de Janeiro, Brasil Cristiano, R.

Scuola di Perfezionamento in Scienze e Fisiche dell' Università di 84100 Salerno,

Crozat, P.

Cibernetiche

Salerno,

Italy

Institut d 1 Electronique

Fondamentale,

Fac. des Sciences, Bat. 220, 91405 Orsay, France Crum, D.B.

S.H.E. c/o Klaus Schäfer GmbH, Postfach 488, 6078 Neu-Isenburg, Germany S.H.E. Corporation, 4174 Sorrento Valley Blvd., San Diego, California 92121, USA

Cucolo, A.

Istituto di Fisica, Università di

Salerno,

84100 Salerno, Italy Cui

Guang-Ji

Department of Physics, Peking University, Peking, China

Daalmans, G.M.

Laboratorium voor Technische Technische Hogeschool

Natuurkunde,

Del ft, Postbus 5046,

2600 CA Del ft, The Netherlands Delle Cave, G.

Laboratorio di Cibernetica del Via Toiano 2, 80072 Arco Felice Italy

CNR, (Napoli)

XVI Di Chiara, A.

Istituto di Fisica della Facolta' di Ingegneria, Università di Napoli, P. Tecchio , Napoli , Italy

Donaldson, G.B.

Department of Applied Physics, John Anderson Building, University of Strathclyde, Glasgow G4 ONG, Great Britain

Dubuc

I.S.M.R.A., Université de Caen, 5 Avenue d'Edimbourg, 14032 Caen-Cedex, France

Dueholm, B.

Physics Laboratory I, Technical University of Denmark, 2800 Lyngby, Denmark

Dugnoille, B.

Faculté Polytechnique de Möns, Service de Thermodynamique, Departement Basses Temperatures, Bd. Dolez 31, 7000 Möns, Belgium

Durcansky, G.

Institut für Festkörperforschung, Kernforschungsanlage Jülich, Postfach 365, 5170 Jülich, Germany

Duret, D.

Institut d'Electronique Fondamentale, Université Paris-Sud, Bat. 220, 91405 Orsay, France

Dwir, B.

Department of Physics and Astronomy, Tel Aviv University, Ramat Aviv, Israel

Eghrari, I.R.

Departemente de Fisica, Pontificia Universidade Católica, C.P. 38071- Rio de Janeiro, Brasil

Ehnholm, G.J.

Low Temperature Laboratory, Technical University of Helsinki, SF-02150 Espoo 15, Finland

Epperlein, P.W.

IBM Research Laboratory, Säumerstr. 4, 8803 Rüschlikon, Switzerland

Ernê, S.N.

Physikalisch-Technische Bundesanstalt, Institut Berlin, Abbestraße 2-12, 1000 Berlin 10, Germany

XVII F a r r e l l , D.E.

Department of Medicine, Case Western Reserve University, Cleveland, Ohio 44106, USA

Feldman, M.J.

Physics Department, Chalmers University of Technology, 41296 Göteborg, Sweden

Fenici, R.

Universita' Cattolica Del Sacro Cuore, Servizio Cardiologia - P o l i c l i n i c o "A. Gemelli", Largo Gemelli 8, Roma, Italy

Finnegan, T.F.

Physikalisch-Technische Bundesanstalt, I n s t i t u t Berlin, Abbestraße 2-12, 1000 Berlin 10, Germany

Freedman, A.P.

Division of Pulmonary Diseases, Hahnemann Medical College and Hospital, 230 North Broad Street, 19102 Philadelphia, Pa. , USA

Fujisawa, K.

Department of Electrical Engineering, Faculty of Engineering Science., Osaka University, 1-1 Machikaneyama-cho; Toyonaka, Osaka, Japan

Fujita, T.

Department of Physics, Tohoku-University, Sendai 980, Japan

Ganssen, A.

Siemens AG, Uß Medizinische Meßtechnik, Abt. RKG 2, Henkestraße 127, 8520 Erlangen, Germany

Gassinger, C. Giffard, R.P.

Hölderlinstr. 27, 6000 Frankfurt/M., Germany Physics Department, Stanford University, Stanford, California 94305, USA

Gilabert, A.

Laboratoire de Physique de la Matière Condensée, Universitè de Nice, Pare Valrose , 06034 Nice Cedex, France

Glasl, R.

Physikalisch-Technische Bundesanstalt, I n s t i t u t Berlin, Abbestraße 2-12, 1000 Berlin 10, Germany

Gmelin, E.

Max-Planck-Institut für Festkörperforschung, Heisenbergstraße 1, 7000 Stuttgart 80, Germany

XVIII

Good, J.

Cryogenic Consultants Ltd., Metrostore Building 231 The Vale, London W3 7QS, Great Britain

Goubau, W.

Department of Physics, University of California, Berkeley, Ca 94720, USA

Gramm, K.

Institut of Technology, Solid State, Uppsala University, Studentstaden 7, 75233 Uppsala, Sweden

Grohmann, K.

Physikalisch-Technische Bundesanstalt, Institut Berlin, Abbestraße 2-12, 1000 Berlin 10, Germany

Gundlach, K.

Max-Planck-Institut für Physik und Astrophysik, Föhringer Ring 6, 8000 München 40, Germany

Gutmann, P.

Physikalisch-Technische Bundesanstalt, Bundesallee 100, 3300 Braunschweig, Germany

Gross, F.

Institut für Experimentalphysik, Universtität Graz, Universitätsplatz 5, 8010 Graz, Austria

Hah.lbohm, H.-D.

Physikalisch-Technische Bundesanstalt, Institut Berlin, Abbestraße 2-12, 1000 Berlin 10, Germany

Hari, R.

Laboratory of Clinical Neurophysiology, University Hospital of Helsinki, Haartmanink 4, 00290 Helsinki 29, Finland

Hartfuss, H.-J.

Institut für Astrophysik, Max-Planck-Institut für Physik und Astrophysik, Forschungsgelände, 8046 Garching , Germany

Hechtfischer, D.

Physikalisch-Technische Bundesanstalt, Institut Berlin, Abbestraße 2-12, 1000 Berlin 10, Germany

Heiden, C.

Institut für Angewandte Physik, Universität Gießen, Heinrich-Buff-Ring 16, 6300 Gießen, Germany

Hillenbrand, B.

Siemens AG, Forschungslabor FL MET 1, Postfach

32 40, 8520 Erlangen 2, Germany

XIX Hinken, J.

Physikalisch-Technische

Bundesanstalt,

Bundesallee 100, 3300 Braunschweig, Germany H i t z f e l d , M.

Physikalisches I n s t i t u t , Universität

Karlsruhe,

Engesserstraße 7, 7500 Karlsruhe 1, Germany Högstedt, P.

Physics Department, Chalmers U n i v e r s i t y of Technology, 41296 Göteborg, Sweden

Hoenig, H.E.

Physikalisches I n s t i t u t , Universität

Frankfurt,

Robert-Mayer-Str. 2 - 4 , 6000 Frankfurt/M., Germany Hoffmann, A.

Physikalisch-Technische Bundesanstalt,

Institut

B e r l i n , Abbestraße 2 - 1 2 , 1000 B e r l i n 10, Germany Hopf, U.

Begonienstr.10, 8000 München 45

Hübener, R.P.

Experimentelle Physik I I , U n i v e r s i t ä t Tübingen, Morgenstelle 14, 7400 Tübingen 1, Germany

Huiskamp, W.J.

Kamerlingh Onnes Laboratorium, Nieuwsteeg 18, Leiden, The Netherlands

J a b l o n s k i , D.G.

Cavendish Laboratory, U n i v e r s i t y of Cambridge, Madingley Road, Cambridge CB3 OHE, Great B r i t a i n

J a b l o n s k i , H.

S.H.E-. GmbH, Maria-Theresia-Allee 22, 5100 Aachen, Germany

Jackel, L.D.

Bell Laboratories, Room 4D-337, Holmdel, New Jersey 07733, USA

J a k s c h i k , J.

Physikalisch-Technische Bundesanstalt , I n s t i t u t B e r l i n , Abbestraße 2-12, 1000 B e r l i n 10, Germany

Joseph, S.

Physikalisch-Technische Bundesanstalt,

Institut

B e r l i n , Abbestraße 2-12, 1000 B e r l i n 10, Germany J u l i u s , E.

Kernforschungsanlage J ü l i c h , Postfach 1913, 5170 J ü l i c h , Germany

J u t z i , W.

I n s t i t u t für Elektrotechnische Grundlagen

der

Informatik, U n i v e r s i t ä t Karlsruhe, Hertzstr. 7500 Karlsruhe 21, Germany

16,

XX Kadlec, J.

Department of Physics and Astronomy, Louisiana State University, Baton Rouge, LA 70803, USA

Katila, T.

Department of Technical Physics, Helsinki University of Technology, 02150 Espoo 15, Finland

Karp, P.F.

University of Kuopio, P.O. Box 138, 70101 Kuopio 10, Finland

Kelhä, V. 0.

Technical Research Centre of Finland, Metal 1imiehenkuja 8, 02150

Ketchen, M.B.

Espoo 15, Finland

IBM Thomas J. Watson Research Center, P.O. Box 218, Yorktown Heights, New York 10598, USA

Klaudius, A.

Westendstr. 77, 6000 Frankfurt/M. , Germany

Klein, K.-D.

Physikalisch-Technische Bundesanstalt, Institut Berlin, Abbestraße 2-12, 1000 Berlin 10, Germany

Kötzler, J.

Institut fUr Festkörperphysik, Technische Hochschule Darmstadt, 6100 Darmstadt

Krönke, H. Kurkijärvi, J.

Vacuumschmelze Hanau GmbH, 6450 Hanau,

Germany

Department of Technical Physics, Helsinki University of Technology, 02150 Espoo 15, Finland

Laibowitz, R.B.

IBM Thomas J. Watson Research Center, P.O. Box 218, Yorktown Heights, New York 10598, USA

Leifer, M.

Department of Physics, Stanford University, Stanford, California 94305, USA

Lekkala, J.

Biomedical Engineering Laboratory, Department of Electrical Engineering, Tampere University of Technology, 33101 Tampere 10, Finland

Levinsen, M.T.

H.C. 0rsted Institute, Physics Laboratory I, University of Copenhagen , Universitetsparken 5, 2100 Copenhagen 0, Denmark

XXI Lindelof, P.E.

H.C. (Jrsted I n s t i t u t e , Physics Laboratory I , University of Copenhagen,

Universitetsparken 5,

2100 Copenhagen:0, Denmark Long, A. P.

Department of Physics, University of Sussex, Falmer, Brighton,

Lounasmaa, O.V.

Sussex, Great Britain

Low Temperature Laboratory, Helsinki University of Technology, 02150 Espoo 15, Finland

Ludwig, W.

Dornier System, Abt. NTF, Postfach 1360, 7990 Friedrichshafen, Germany

LLibbig, H.

Physikalisch-Technische Bundesanstalt, I n s t i t u t Berlin, Abbestraße 2-12, 1000 Berlin 10, Germany

Luther, H.

Physikalisch-Technische Bundesanstalt, I n s t i t u t Berlin, Abbestraße 2-12, 1000 Berlin 10, Germany

Macfarlane, J.C.

CSIRO Division of Applied Physics, P.O. Box 218, Lindfield NSW 2080, Australia

MacLead, R.

I n s t i t u t für medizinische Physik, Universität Graz, Warrachgasse 27, 8010 Graz, Austria

Malmivuo, J.

Biomedical Engineering Laboratory, Department of Electrical Engineering, Tampere University of Technology, 33101 Tampere 10, Finland

March, J.F.

Physikalisch-Technische Bundesanstalt, I n s t i t u t B e r l i n , Abbestraße 2-12, 1000 Berlin 10, Germany

Martinoli, P.

I n s t i t u t de Physique, Université de Neuchâtel, Rue Breguet 1, 2000 Neuchâtel, Switzerland

Mateew, P.

I n s t i t u t für Festkörperphysik I I I , Technische Universität Berlin, Jebensstr. 1, 1000 Berlin 12, Germany

Matisoo, J.

IBM Thomas J. Watson Research Center, P. 0. Box 218, Yorktown Heights, New York 10598, USA

XXII

Meissner, B.

P a r i s e r S t r . 5, 1000 B e r l i n 15, Germany

Modena, I .

Laboratorio di Elettronica d e l l o Stato Solido del CNR, Via Cineto Romano 42, 00156 Roma, I t a l y

Mooij, J.E.

Laboratorium voor Technische Natuurkunde, Technische Hogeschool D e l f t , Lorentzweg 1, D e l f t , The Netherlands

Mrowinski, D.

HNO-Klinik, Klinikum Westend, Spandauer Damm 130, 1000 B e r l i n 19, Germany

M ü l l e r , K.

Physikalisch-Technische Bundesanstalt,

Institut

B e r l i n , Abbestraße 2-12, 1000 B e r l i n 10, Germany Mutton, J.E.

School of Mathematical and Physical

Sciences,

U n i v e r s i t y of Sussex, Falmer, Brighton, Sussex, Great B r i t a i n Mygind, J.

Physics Department I , B u i l d i n g 309, Technical U n i v e r s i t y of Denmark, 2800 Lyngby, Denmark

Naito, S.

Yokogawa E l e c t r i c Works, 9-32 Naka-Cho 2 Chome, Musashino-Shi, Tokyo 180, Japan

Neighbours, J.R.

ONR London, 223 Old Marylebone Rd., London NW1, Great B r i t a i n

Neubert, D.

Physikalisch-Technische Bundesanstalt,

Institut

B e r l i n , Abbestraße 2-12, 1000 B e r l i n 10, Germany Neumaier, K.

Z e n t r a l i n s t i t u t für Tieftemperaturforschung, Bayerische Akademie der Wissenschaften, Hochschul gelände, 8046 Garching, Germany

Nink, R.

Physikalisch-Technische Bundesanstalt,

Institut

B e r l i n , Abbestraße 2-12, 1000 B e r l i n 10,Germany Ohmichi, H.

National Medical Center H o s p i t a l , C l i n i c a l

Research

I n s t i t u t e , 1, Toyamacho, Shinjuku-ku, Tokyo 162, Japan

XXIII Okada, Y.

Neuromagnetism Laboratory, New York U n i v e r s i t y , 6 Washington Place, New York, New York 10003, USA

Pace, S.

I s t i t u t o di F i s i c a , U n i v e r s i t y of Salerno, Via Vernieri 42, 84100 Salerno,

P a l s , J.A.

Italy

P h i l i p s Research L a b o r a t o r i e s , Eindhoven, The Netherlands

Pascal, D.

I n s t i t u t d ' E l e c t r o n i q u e Fondamentale, Université P a r i s - S u d , Bat. 220, 91405 Orsay, France

Palow, J.

Physikalisch-Technische Bundesanstalt,

Institut

B e r l i n , Abbestraße 2-12, 1000 B e r l i n 10, Germany Parmentier, R.D.

Universita di Salerno, I s t i t u t o di F i s i c a , 84100 Salerno,

Pedersen, N.F.

Italy

Physical Laboratory I , Technical U n i v e r s i t y of Denmark, B u i l d i n g 309,

Pegrum, C.M.

2800 Lyngby, Denmark

Department of Applied P h y s i c s , John Anderson B u i l d i n g , U n i v e r s i t y of Strathclyde, Glasgow G4 ONG, Great B r i t a i n

Peiheng Wu

Cavendish Laboratory, U n i v e r s i t y of Cambridge, Madingly Road, Cambridge CB3 OHE, Great B r i t a i n

Pelizzone, M.

Department de Physique de la Matière Condensée, 32 Bd. d'Yvoy, 1211 Geneve 4, Switzerland

P e r r i n , N.

Laboratoire de Physique de l ' E c o l e Normale Supérieure, 24 rue Lhomond, 75231 Paris Cedex 05, France

Peters, M.J.

Department Technical P h y s i c s , Technical

University

Twente, Postbox 217, Enschede,The Netherlands Peterson, R.L.

National Bureau of Standards, D i v i s i o n 724.03, Boulder, Colorado 80303, USA

Plonsey, R.

Department of Biomedical Engineering, Case Western Reserve U n i v e r s i t y , Cleveland, Ohio 44106, USA

XXIV Podney, W.

Physical Dynamics, Inc. , P.O. Box 556, La Jolla, California 92038, USA

Poorter, T.

Kapteyn Astronomical Institute, Department Space Physics, P.O. Box 800, Groningen, The Netherlands

Potts, M.

School of Mathematical and Physical Sciences, University of Sussex, Falmer, Brighton, Sussex, Great Britain

Prance, R.

School of Mathematical and Physical Sciences, University of Sussex, Falmer, Brighton, Sussex, Great Britain

Prestele, K.

Siemens AG/UB Med/EG 1, Henkestraße 127, 8520 Erlangen, Germany

Robinson, S.E.

Division of Pulmonary Diseases, Hahnemann Medical College and Hospital, 230 N. Broad Street, Philadelphia, PA 19102, USA

Rogali a, H.

Institut für Angewandte Physik, Universität Gießen, Heinrich-Buff-Ring 16, 6300 Gießen, Germany

Romani, G.L.

Laboratorio di Elettronica dello Stato Solido, C.N.R., Via Cineto Romano 42, Roma, Italy

Rose, D.

Institut für Hochfrequenztechnik, Technische Universität Berlin, Einsteinufer 25, 1000 Berlin 10, Germany

Rudner, St.

Physics Department, Chalmers University of Technology, 41296 Göteborg, Sweden

Rushby, H.

School of Mathematical and Physical Sciences, University of Sussex, Falmer, Brighton, Sussex, Great Britain

Russo, M.

Laboratorio di Cibernetica del CNR, Via Toiano 2, 80072 Arco Felice (Napoli), Italy

Sauerbrey, G.

Physikalisch-Technische Bundesanstalt, Institut Berlin, Abbestraße 2-12, 1000 Berlin 10, Germany

XXV Savo, B.

Istituto di Fisica, Università Salerno, 84100 Salerno, Italy

Scheer, H.-J.

Physikalisch-Technische Bundesanstalt, Institut Berlin, Abbestraße 2-12, 1000 Berlin 10, Germany

Schlief, R.G.

Physikalisch-Technische Bundesanstalt, Institut Berlin, Abbestraße 2-12, 1000 Berlin 10, Germany

Schuster, G.

Physikalisch-Technische Bundesanstalt, Institut Berlin, Abbestraße 2-12, 1000 Berlin 10, Germany

Soerensen, O.H.

Physical Laboratory I, Technical University of Denmark, 2800 Lyngby, Denmark

Soler-Mejia, J.L.

Instituto Politecnico Nacional, Mexico City, Mexico

Soulen, R.J., Jr.

Temperature Measurements and Standards Division, Room B-128, Physics Building, National Bureau of Standards, Washington, D.C. 20234, USA

Suhr, H.

Physikalisch-Technische Bundesanstalt, Institut Berlin, Abbestraße 2-12, 1000 Berlin 10, Germany

Stevens, R.

Department of Physics, University of Lancaster, Lancaster

Stroink, G.

LA1 4YB , Great Britain

Department of Physics, Dunn Building, Dalhousie University, Halifax, Nova Scotia, B3H 3J5, Canada

Stuart, C.I.J.M.

Centre for Quantum Field Theory and Complex Systems, P124, Department of Physics, University of Alberta, Edmonton, Alberta T6G 2J1, Canada

Swithenby, S.J.

Physics Discipline, The Open University, Walton Hall, Milton Keynes, MK7 6AA, Great Britain

Takada, S.

Electrotechnical Laboratory, 1-1-4, Umezono, 'Sakura-mura, Niihari-Gun, Ibaraki, Japan

Teppner, U.

Physikalisch-Technische Bundesanstalt, Institut Berlin, Abbestraße 2-12, 1000 Berlin 10, Germany

XXVI Teszner, D.

Hôpital Ambroise Paré, 9 Avenue Charles de Gaulle, 92100 Boulogne, France

Thorn, H.-G.

Kernforschungsanlage Karlsruhe, 7500 Karlsruhe, Germany

Thürley, F.

Physikalisch-Technische Bundesanstalt,

Institut

B e r l i n , Abbestraße 2-12, 1000 B e r l i n 10, Germany Tinchev, S.S.

I n s t i t u t e of E l e c t r o n i c s , Bulgarian Academy of Science, bui. Lenin 72, Sofia 1184, B u l g a r i a

Tripp. J. H.

Department of P h y s i c s , Case I n s t i t u t e of Technology, Case Western Reserve U n i v e r s i t y , Cleveland, Ohio 44106, USA

T r o n t e l j , Z.

Physics Department, U n i v e r s i t y of Ljubljana, 61001 Ljubljana, P.O. Box 543, Yugoslavia

U l r i c h , B.

M a x - P l a n c k - I n s t i t u t für Plasma-Physik, 8046 Garching/München, Germany

V a g l i o , R.

I s t i t u t o di F i s i c a , U n i v e r s i t à di Salerno, Via Vernieri 42, 84100 Salerno,

Vaidya, A.W.

Italy

Central Research L a b o r a t o r i e s , EMI L t d . , Trevor Road, Hayes, Middlesex, Great B r i t a i n

Van Duzer, Th.

Department of E l e c t r i c a l Engineering and Computer Sciences, U n i v e r s i t y of C a l i f o r n i a , Berkeley, C a l i f o r n i a 94720, USA

Van Haesendonck, C.

Laboratorium voor Vaste S t o f - F y s i c a en

Magnetisme,

Katholieke U n i v e r s i t e i t Leuven, Celestijnenlaan 200 D, 3030 Leuven, Belgium Varpula, T.

Department of Technical P h y s i c s , H e l s i n k i

University

of Technology, Otakaari 3A, 02150 Espoo 15, Finland V i l l e g i e r , J.C.

LETI, Commissariat a l ' E n e r g i e Atomique, 85X - 38041 Grenoble, France

XXVII Vollmer, R.

Neurologische Abteilung, Krankenhaus Lainz, Wolkersbergenstraße 1, 1130 Wien, A u s t r i a

Voss, R.F.

IBM Thomas J. Watson Research Center, P.O. Box 218, Yorktown Heights, New York 10598, USA

de Waal, V.J.

Laboratorium voor Technische Natuurkunde, Technische Hogeschool Del f t , Lorentzweg 1, Del f t , The Netherlands

Weber, H.W.

Atominstitut der ö s t e r r e i c h i s c h e n

Universitäten,

SchüttelStraße 115, 1020 Wien, A u s t r i a Wende, B.

Physikalisch-Technische Bundesanstalt,

Institut

B e r l i n , Abbestraße 2r12, 1000 B e r l i n 10, Germany Westerhaus, W.J.

M a x - P l a n c k - I n s t i t u t für

Festkörperforschung,

Heisenbergstraße 1, 7000 Stuttgart 80, Germany Wevers-Henke, J . J .

Department Technical P h y s i c s , Technical

University

Twente, Postbox 217, Enschede, The Netherlands Widom, A.

School of Mathematical and Physical

Sciences,

U n i v e r s i t y of Sussex, Falmer, Brighton, Sussex, Great B r i t a i n Williamson, S.P.

Department of P h y s i c s , New York

University,

4, Washington Place, New York, N.Y. 10003, USA Witt, Th. J.

Bureau International des Poids et Mesures, P a v i l l i o n de B r e t e u i l , 92310 Sevres, France

Wolber, L.

Physikalisch-Technische Bundesanstalt,

Institut

B e r l i n , Abbestraße 2-12, 1000 B e r l i n 10, Germany Wolf, P.

IBM Research Laboratory, Säumerstr. 4, 8803 RLischlikon, Schweiz

Yao X i - X i a n

Department of P h y s i c s , Nanking U n i v e r s i t y , China

Yoshida, K.

Department of E l e c t r o n i c s , Kyushu U n i v e r s i t y , Fukuoka 812, Japan

Zimmerman, J.E.

Cryogenics D i v i s i o n , National Bureau of Standards, Boulder, Colorado 80302, USA

JOSEPHSON JUNCTION PHYSICS

PROGRESS IN PHYSICS OF JOSEPHSON JUNCTIONS

H. LUbbig Physikalisch-Technische Bundesanstalt, I n s t i t u t B e r l i n , Abbestraße 2-12, D-1000 B e r l i n 10, Germany

Introduction The t i t l e encompasses divers categories: "JOSEPHSON j u n c t i o n s " as the real object, " p h y s i c s " in the sense of an unified description of the derived physical properties, and the "progress" in t h i s f i e l d as an indication of the h i s t o r i c a l development, s p e c i f i c a l l y including the extensions and generalizations of the theory o r i g i n a l l y developed by B. D. JOSEPHSON. Concerning JOSEPHSON j u n c t i o n s , f i r s t of a l l one has to account for the d i v e r s i t y of relevant junction configurations: tunnel junctions,

proximity-

effect j u n c t i o n s , and microbridge junctions. All of these types of junctions are u s u a l l y denoted by JOSEPHSON junction

although these structures are

d i f f e r e n t with respect to geometry, material c o n s t i t u e n t s , and the basic physical processes

associated with the phase coherent phenomena which are

observed when a current or a voltage i s applied to the contact. Thus,in t r y i n g to represent the physics of JOSEPHSON junctions in an uniform way while keeping in mind the variety of s t r u c t u r e s , one has to look on the corresponding phenomenological d e s c r i p t i o n s . By considering the microscopic model of each junction type as the postulate and the deduced macroscopic behaviour (the current-phase-relationships

for example) as the corresponding

d e r i v a t i v e , the main question a r i s e s : how to synthesize these derived properties within a s i n g l e concept known as the "JOSEPHSON e f f e c t " . The uniqueness of t h i s term t r i v i a l l y r e s u l t s from the f a c t , that i t defined,

is

s t r i c t l y speaking, by the phase coherence which o r i g i n a t e s

tunnelling process: B.D.JOSEPHSON

in a

considered the tunneling through an

i n s u l a t i n g b a r r i e r in predicting the physical consequences of t h i s coherence.

Squid '80 © 1 9 8 0 Walter de Gruyter & Co., Berlin • New York

2 This was nearly twenty years ago. At present a multitude of non-tunnel-type structures is known, and it is confirmed now that the phase coherent phenomena

due to weakly coupled superconductors are of much more generality

than originally assumed. in

The tunnel junction has an outstanding position

the field of junction types; but the concept of phase-coherent tunnel-

ling plays the role of the classical version of the generalized

JOSEPHSON

effect in the following sense: (i ) it provides a guiding principle in explaining the more multifarious behaviour of weak links; (ii) on the basis of the WERTHAMER theory, it serves as an example of a theoretically well understood junction type; (iii) as a consequence of the fact that in tunnel junctions the electrodes act as reservoirs in thermal equilibrium, the tunneling theory

can be applied to construct a limiting case

for processes distinguishing which are based on

non-equilibrium states

in an essential way. With respect to progress in the physics of JOSEPHSON junctions, it should be recalled that the theory of tunnelling-assisted phase coherence had become clear in a complete and comprehensive manner in the middle of the sixties as a consequence of the work of WERTHAMER, /1/, and LARKIN and OVCHINNIKOV, /2/. With regard to weak links^and microbridges in particular, since the pioneering paper of ASLAMAZOV and LARKIN, /3/, more detailed theoretical investigations have only begun appearing about six years ago and have been mainly focussed on the dynamical non-equilibrium state. Most of the weak link analyses have been based upon the time dependent GINZBURG LANDAU equation (TDGL) for either the gapless case or extended versions. These investigations have

considerably promoted an understan-

ding of the appearance and the properties of continuous phase gradients in weak links.

Simultaneously these models have led to a description of

the discrete phase slip centers which appear in long superconducting filaments; a phenomenon which can be regarded as a limiting process of the JOSEPHSON effect in constriction weak links with direct conduction pathes present /4/. The first comprehensive

description of the applicability of the TDGL to

"one-dimensional structures with electrodes in equilibrium" (ODSEE) is found in a recent extensive review on weak links by LIKHAREV, /5/.

3 The unique aspects of higher-dimensional structures and the influence of dimensionality on the junction's behaviour were brought into focus by DAALMANS, KLAPWIJK, and MOOIJ, and other authors, see /6/. Also in this regard the semiclassical analysis of the heat flow, affecting the high frequency properties of these structures, hensive

should be mentioned.

A compre-

paper discussing these heating effects is that of OCTAVIO,

SKOCPOL and TINKHAM, /7/. A second line of inquiry

arises through basic study of non-equilibrium

processes in superconductors. The displacement of the quasiparticle distribution function from the thermal equilibrium state plays the central role here. Since the excited quasiparticles play the role of the "normal electrons" in the two fluid model of superconductivity, the relaxation of the non-equilibrium distribution of the quasiparticles towards the equilibrium state controls the dynamics of the system, /8/. The electron-phonon collision time is an important parameter of this process. This in particular means that the BOLTZMANN equation for the quasiparticle distribution governs the problem explicitly together with the GINZBURG LANDAU equation, /9/. With respect to microbridges the appearance of excess currents and of a shoulder in the I-V characteristic near the zero voltage

state are affected directly. This has been made clear by the theore-

tical papers of ARTEMENKO, VOLKOV and ZAITZEV, /10/,and more recently of SCHMID, SCHD'N and TINKHAM, /11 /. At this conference an invited paper is devoted to the influence of nonequilibrium

phenomena of this type on the behaviour of JOSEPHSON junc-

tions. It is the intention of the present paper to serve as an introductory overview of various junction types as well as to make a clear distinction between phase coherent phenomena related to thermal equilibrium situations and those related to non-equilibrium states. The paper is organized as follows: A brief review of junction types is sketched including a schematic comparison of geometries and basic physical models. The second and the third parts concerning stationary and non-stationary properties are oriented to the question: to what extent can the classical version of the JOSEPHSON effect serve as a guiding principle or first

4 approximation in describing the various junction types. The conclusion of this work is devoted to the question to what extent do these junction properties influence the macroscopic description of the SQUID from the viewpoint of physics and measurement technique. 1.

Overview on main junction types

In a discussion of junction types, three main geometric classes are to be distinguished:

Sandwich structures, thin-film weak link geometries, and

microbridge configurations with constricted coupling regions, Fig. 1.

SANDWICH STRUCTURES

SIS

S

N S' S SE

:z

THIN FILM STRUCTURES

normal metal

ion implantation

underlay

CONSTRICTION STRUCTURES

~zi

£

r VTB

CTB

Fig.

1

Main junction types

5 The sandwich structures are formed by either an insulating o

oxide barrier

about 20 A thick, or by a normal-conducting, superconducting or semiconducting layer with a typical thickness between 0.1 and 10 pm. In thin film weak links, the weakened zone is achieved by means of a normal conducting underlay or by direct ion implantation. In constriction geometries variable thickness or three-dimensional bridges (VTB) and constant thickness or twodimensional bridges (CTB) are to be distinguished. The span which connects the banks is a few tenth of a pm long. A discussion of the physical processes associated with each structure makes clear the fundamental differences. In SIS sandwiches the phase coherence comes about by tunneling.

In sandwiches with thicker barriers and in thin

film weak link configurations the basic process which connects the states of the electrodes is to be assigned as a proximity effect at the boundaries. Quite another mechanism governs the phase coherence in constriction bridges. Here the lower critical current of the coupling region is caused by the constriction in width (CTB) or in width and thickness (VTB). In this case the order parameter and the phase gradient varies continuously through the coupling region. Therefore, "direct conductivity" is involved in the phase coherence in these structures. For purposes of comparison, the electronic parameters of the SIS tunnel junction are used. In the SIS the product of the critical current, I c , and the normal state r e s i s t a n c e ^ , defines a characteristic voltage: vc = Ic R n . r A j n c c N 2 e

tgh

A m 2 KB T

(1)

which depends on the temperature function of the electrode energy gaps, A

(T),

only. This dependence characterizes the "resistively shunted

junction model" (RSJM) ti " (p C — 2 e

+

for the current

1

tv

R^

2 e

I

p

+

I c siny?

=1,

flowing through the junction.

tHp= 2 e V ,

(2)

6 In the finite voltage state (I

I c ), the influence of capacitive effects

is described by means of the Stewart-Mc Cumber parameter

B

c

= ( 2_e -h

}

!

L

C

r2 c

N

J ^ c = o r j o ^ AlO)

c

R

N

t >

A

* 2A(0)

(3)

As a consequence of the fact that the RSJM involves only one free parameter if the electrode material is specified, B tio of the classical damping time T

c

is proportional to the ra-

and the intrinsic gap response

time X A ( o ) . In the zero voltage

(I -C I c )

state, the junction acts as an "inductan-

ce" and one can use a non-linear inductance coefficient

£ ( 0 ) = — dl

f

Vdt

J

, 2 e

I

¿0

(4)

cosy»

as reference parameter which is an even function of the related magnetic flux in the junction. With these and other closely related parameters, the main features of the different structures can be analyzed. ferent junction structures

Individual properties of the dif-

do not appear however, because of the

approximative structure of the RSJM. To study these one has to analyse the stationary current phase relation (CPR) in a detailed manner, and, for the non-stationary case, to investigate the dynamic resistivity of the structure, /12/.

2.

Common stationary properties of the weak links

2.1 Macroscopic

description of the CPR

For the purpose of an uniform description of the stationary state, some phenomenological properties are first compiled which are common to all of the aforementioned weak-link

structures.

If no average voltage appears across the junction, the system is in the stationary state. The coupling energy

7

F (

f ,

T/T c

)

(5)

necessary to establish this non-dissipative state of phase coherence between the reservoirs in the electrodes, is the important physical quantity: 1) The phase difference - 0, ( T/T

L

0

0

)


Iqp 2 ), which correspond to the flow of COOPER pairs and quasipar-

18

eV/2 A (0)

eV/2A (0)

eV/2A(0) Fig. 4

The four response functions

I a n d

Iqpi> I q p 2

(in units of 2 A (o)/ e R j in dependence of the normalized frequency eV/2 A (o) for various values of the reduced temperature for identical superconductors, /18/. The pairs I j 1 f Ij2 and I ^ I q p 2 s a t i s f y the KRAMERS-KRONIG relation, resp..

t i d e s resp. (In this section HARRIS'S sign convention, /18/, i s applied) The amplitudes

and I ^ , are related to the s i n y - and the cos f -term

resp. and to one another by means of the KRAMERS - KRONIG relation as required by causality. The same is true for the constituents of the quasiparticle current i f one f i r s t substracts the linearly-increasing branch of

19 I

2* This OHMIC branch represents the r e s i s t i v i t y in the normal conducting

state of the system which i s superimposed even i f the state i s superconduct i v e . As a consequence of the equilibrium d i s t r i b u t i o n of the q u a s i p a r t i c les the structure of the d i s p e r s i v e r e l a t i o n s i s characterized by the equilibrium gap only. The current balance equation i s s p l i t into two b a s i c a l l y d i f f e r e n t parts: an instantaneous one , and a second one which represents the transient from the i n i t i a l to the present state. The structure of the current phase r e l a t i o n s h i p I L 3 rized by the following general properties: i ) I L c p J

i s to be charactei s reduced to the

state described by the RSJ model only at the i n i t i a l point of time. Since the RSJ model i s an approximation common to a l l weak l i n k types, no s p e c i f i c properties are involved in t h i s s t a t e ;

i i ) i f an a r b i t r a r y voltage,

(p , i s across the junction the convolution contributes at a l l times;

i i i ) the structure of the continuous functions

finite

completely

involves the frequency dependence of the superconductive components of the c o n s t i t u t i v e current phase r e l a t i o n s h i p . Following t h i s concept we f i n d the c l a s s i c a l JOSEPHSON effect to be i d e n t i f i e d as that type of a time depending nonlinear s e l f - c o u p l i n g process which i s controlled by the s p e c i f i c relaxation functions tA

and

Here the

describe the relaxation between the i n i t i a l state , ip ( - oo ), and

the present s t a t e , ^ ( t ) , which are not n e c e s s a r i l y states of dynamic equilibrium. In a physical context, the relaxation functions balance the s e l f coupling in such a way that the q u a s i p a r t i c l e s d i s t r i b u t i o n s within the electrodes remain in t h e i r thermal equilibrium s t a t e . The functions term and the s i n p

and fA_ are related to the s e l f - c o u p ! i n g of the cosf -term r e s p e c t i v i l y , Eq. (18).

-

Their time dependence i s

shown in F i g . 5 f o r two values of the reduced temperature. The period of /"\+ equals the i n t r i n s i c gap response time

T/T c ). The

point at i n f i n i t e l y long time corresponds to the switch in of the j u n c t i o n ' s perturbance the zero point to the present time in Eq. (18).

20

Fig. 5

Relaxationfunctions for two values of the reduced temperature. ( The origin of the upper curve is shifted by one unit in the vertical direction)

3.2

Observable results

In Fig. 6 the influence of the time dependent self-coupling effect in small tunnel junctions on the(averaged) current voltage characteristic i s indicated. The s o l i d lines in the l e f t

and the middle part of the figure repre-

sents results of an analog-computation involving the retarded integrals, Eq. (18), /19/.

(The DC-current controlled case i s studied and vanishingly

21 low temperature is assumed.]

\\\ \

I ,\ •1 • J\

k

1

Ikji

•«=—

\

\

v— \ V N

v

S>

. \

La 1 cu 1. ____RSJ WERTHAMER TH.

Fig. 6

FDSC : M C D O N A L D ....DATA

ìt al.

Calculated current-vol tage characteristics, and data.

Because of the small value of the STEWART-Mc CUMBER parameter chosen, B c = 0,15, the RSJ model doesn't show any hysteresis, as shown by the dashed lines. The remaining hysteresis, therefore, directly results from the self-coupling terms in Eq. (18).

In the middle part, the lower

threshold, 0( , of the hysteresis is plotted for comparison with the STEWART-Mc CUMBER criterion, /20/. The circles are data, /21/. In the right part of the figure results of various theoretical models (TDGL: time depending

GINZBURG LANDAU Eq., FDSC: frequency dependent self-

coupling) are shown for comparison with data measured on a point contact, 122/. (Further details such as the shape near the gap voltage, V g a p , and the appearance of subharmonic gap structures at the lower threshold of the hysteresis

are not discussed in the present paper.)

22 3.3

General properties of the c l a s s i c a l JOSEPHSON effect

To investigate the general properties of the system, a representation i s introduced which focusses on the essential physical

U

parameters:

9

sin i f )

\ cos ti.

(t) (t)

=

+

0

\

-

The two dimensional state vector

[U.

\

0

2e R, N (

(t)

-

(20)

tu 2e R,,

combines the s t a t i o n a r y components

of the current-phase-functional while the dynamic properties are included in the r e s i s t i v i t y matrix M .

Each of i t s non-vanishing components i s a

l i n e a r superposition of a continuous relaxation function,

(describing

the time dependence of the s e l f - c o u p l i n g ) , and of the DIRAC " " d i s t r i b u t i o n term

(due to the normal state r e s i s t i v i t y ) . The current-phase functional QO I L

0

is positive definite, /23/, as required by the second law of thermodynamics. (This is affected by the internal structure of M independent on the way the junction is incorporated

only, and, therefore, into an external elec-

trical circuit.) The classical version of the JOSEPHSON effect, therefore, is to be characterized completely by ponent,

and ii)

i) the sinusoidal shape of the stationary current com-

the internal structure of the relaxation functions M

Eq.(19), which define the specific nature of the dynamic resistivity in

, -

tunnel junctions. What does the analys is of the classical JOSEPHSON effect indicate regarding a formal description of more complicated junction types? The constitutive current phase relations in any case can be decomposed into two parts, which describe the reversible and the irreversible mode of operation. The various types of reversible current phase relations can be classified uniquely by means of the coupling energy of the stationary phase coherent state of the junction. The irreversible part specifies the nature of the self-coupling mechanism of the components of the stationary the type of dynamic resistivity

CPR, describing in this way

which depends on the thermal equilibrium

properties of the quasiparticles. 4.

Implications for SQUID1s

Finally, the influence of various properties of the weak links themselves on the operation of SQUID's will be discussed briefly. For simplicity only a single junction interferometer is considered.

24 The flux-controlled operation of a weak link is realized in those devices which are coupled inductively to an external circuit. Under stationary conditions ( i.e. I < I Q ), the weak link acts as a"nonlinear inductance" ^6(0)

=

d 0 / dl, cf. Eq. (4). ( Here

I denote the current circulating

in the interferometer and 0 the flux actually enclosed.) Consequently, the interferometer is operated in the inductive (non-hysteretic) mode or in the dissipative (hysteretic) mode depending 2

on wether the energy related to the

macroscopic loop inductance, I L, is smaller or greater than

|

2

| I ,

the energy which is due to the phase coherent state of the junction. Since "£() depends on the critical current and the shape of the CPR, so does the limiting condition between both modes of operation. 4.1

Non-hysteretic mode

In the stationary state the junction is operated reversibly, and, consequently, changes of the states

of the device are specified by Eqs. (15)

and (16) (representing the conditions for dynamic stability respectively;

I

= a

SQUID loop). Since the current

I

equilibrium and for

denotes the flux applied to the

, when multiplied by the mutual in-

ductance, w .describes the nonlinear reaction of the SQUID loop upon the external circuit, the essential

point here is to explain

of the specific nature of the CPR on the current I { ( f )

a

the influence

). This can be

analyzed in a straight-forward way, /24/. The relation between the circulating current and the external flux can be expressed as a FOURIER sinus series CO

I

( 0a)

=

I0

H

"^flp

sin ( n 21T

/ cf>0 ) ;

(23)

n =1 a direct consequence of the odd periodic nature of the stationary CPR. The specific shape function i ( (¿> , T/T ) = ^

i k sin K tp , = 2-r

of the CPR influences the pattern by means of the coefficients

/

1.

MA

Jexc > 0 ,

6f = 0

Jexc = 0,

6f < 0

-v;

Ek

\ l /

3.

Jexc0

\ V V

>

Fig. 3. Representation of a propagating neutral (temperature) imbalance mode in a one-dimensional superconductor. As in Fig. 2 the four pictures are taken a quarter period apart.

38 in the phonon temperature, which of course depends on the thermal conductivity of the superconductor and on the thermal contact to the substrate or to the helium bath. Fig. 3.1 shows the population on the different excitation branches when there is a neutral excitation current or a heat current. Fig. 3.2 shows the dispersion curves when there is a neutral excess of excitations (the gap is small). The series of 4 pictures shows how a propagating temperature mode would look.like in a superconductor in analogy to second sound in 4 superfluid He. So far , such a mode, although a logical twin mode to the charged branch imbalance mode,has not been observed in a superconductor. To sum up this short introduction to non-equilibrium superconductivity we construct a diagram, Fig. 4, which serves the purpose of illustrating the ingredients which go into the description of a superconductor in a non-equilibrium state. As seen the phase part of the condensate wavefunction is coupled to the charge imbalance mode whereas the amplitude of the condensate "wavefunction couples to the neutral imbalance mode. Both types of imbalance exchange energy with the lattice but do not interact directly. The complete set of equations describing the dynamics of the

2

non-equilibrium state of the superconductor is very complicated. However, simplified models, - although often with a very restricted range of validity (such as the time dependent Ginzburg Landau theory) -, are useful for gaining qualitative insight, as we shall soon demonstrate.

The Current-Phase Relation. For an infinitely long wire of superconducting material, which is

so

thin

that spatial variations of the order parameter

can be considered to be one-dimensional, it is easy to solve

39

Fig. 4.

"Non-equilibrium superconductivity condensed into a single picture".

the well-known Ginzburg-Landau equations for the order parameter and the supercurrent density. Generally 0

=

2m ( I 5c ~

2eA)2

^

+

+

^Ul2^

eR , . *dXi|> ,dip*. 4e2,*,^ 1 J. -t- r dx •J - rip-r s =t 2im dx —) ~ m r r

(7> 1

(8)

40 ip

is a macroscopic wave function proportional to the energy

gap but chosen so that the absolute square gives the pair density a 2 g = (Jjq

] i|j| where

= ^n t|Jo

.

a

and

3

are chosen such that

is the amplitude of the equilibrium order

parameter giving the equilibrium pair density. 5 = the Ginzburg-Landau coherence length. If a constant supercurrent density

Jg

^

is

/4ma is forced through the

wire and i'f the superfluid density is assumed constant throughout the wire, then the following simple solution exists"^ 2 n Vs 1 J = en v = en (1 — v s s s so 3 2' s m where

v

(9)

= ^ ^ is the superfluid velocity which is pros zm ax j portional to the phase gradient ^ , and where nsQ is the J

unperturbed superfluid density. As the superfluid velocity

J s i

Fig. 5.

Supercurrent vs. superfluid velocity for an infinitely long one-dimensional superconductor.

41 or the phase gradient increases the supercurrent goes through a maximum (the critical current) and decreases to zero again. This is illustrated in Fig. 5. Efforts have been directed towards entering this negative slope region at low frequencies or at d.c.

but it was soon realized that in order to enter

this region the wire must be part of a small loop with an inductance current

I

L

such that the product of

L

and the critical

of the wire should be smaller than one flux quantum

(LIc < $ ). To-day this is a well-known criterion for a SQUID to be in a non-hysteretic mode. However, it has later been shown that this region is always unstable unless the length of the superconducting region studied is shorter than the Ginzburg12

Landau coherence length.

In fact, when such a long thin

superconductor enters the resistive state it automatically forms resistive centers where the order parameter varies only in a region of the order of the 13 coherence length. This is the so-called phase slip centers. In the situation where the length of the superconducting wire is smaller than the coherence length we have a Josephson junction type structure with a periodic current-phase relation. Such a short piece of superconducting wire must practically speaking be connected to two superconducting reservoirs which are hardly affected by the current in the weak link connecting them. This has been attempted in devices where two superconductors are connected by a weak superconductor, which can be anything between an insulator, a normal metal, a weaker 14 15

superconductor or just a small superconductor (a microbridge). '

Josephson Tunnel Junctions. By far the best understood Josephson junction is the tunnel junction. The reason is that tunnel junctions differ from most other of Jpsephson junctions in three aspects:and the 1) The types critical current density through the barrier

42 normal state conductivity in the barrier are many orders of magnitude smaller than that of the two superconductors.lt is therefore a good approximation to assume that the superconductors are in equilibrium, i.e. unaffected by the current through the barrier. 2) The intrinsic capacitance, C, of the tunnel structure shunts the a.c. Josephson effecit. As a consequence, it is the voltage and not the current which goes into the Josephson equations as the controlled parameter in by far the largest part of the relevant frequency range. For an autonomous Josephson tunnel junction the potentials of the two superconductors are constant. If this was not the case excitations would be injected on the two sides of the barrier and in addition the superconductors would have a perturbed density of state due to the oscillating potential (self-photon-assisted tunnelling). 3) There are no free electrons in the barrier apart from the evanescent tails of the electronic wavefunction of the two superconductors. Thus the barrier region cannot support any non-equilibrium state apart from that which reflects the properties of the electrodes. The current trend in the application of Josephson tunnel junctions is to decrease the capacitance in order to apply these junctions at still higher frequencies. This can be done by making the area of the junction smaller. But since this will also increase the junction resistance, one must at the same time reduce the barrier height or thickness. This in turn increases the supercurrent density through the barrier. If we want to have negligible capacitive shunting at the upper frequency

f m a x ' where we want to use the tunnel junction, then

we must have ¿r > RC

2ir f max

v(10)

'

43 The product of the critical current, I c , and the resistance, R, of the junction is always given by ic R =

g

(ID

Finally, if the supercurrent density increases, flux quantization becomes important. It modulates the properties of the junction over the length scale given by the Josephson penetration depth,

A

. Therefore, the area of the junction must

be smaller than a circle with radius ITAj = ^gp^j ^ O c L

AJ , i.e.

> Junction Area

where A is the London penetration depth and -L critical current density.

(12) J

C

is the

In order to operate a tunnel junction at a high frequency we must therefore have a small capacitor shunting the junction and/or a small junction resistance. The resistance of the junction can be decreased by reducing the oxide thickness slightly since

R

depends on the thickness according to an

exponential law. This does not change the capacitance significantly. However, there is a limit to how small we can make the resistance because the critical current density increases and eventually makes the Josephson penetration depth smaller than the junction. This happens when I c = J c - A r e a ^ ^ s 8[mA] O L

(13)

corresponding to R = 0,lft . If we have achieved this critical current and still want to increase the operating frequency then the capacitance must be decreased, i.e. we must decrease the area of the junction. If we continue to do this then eventually the critical current density will reach its bulk value. This frequency is far up in the terahertz region.

Fig. 6. SEM-picture of a burnt-out indium thin-film microbridge.

Fig. 7. SEM-picture of a typical variable-thickness indium microbridge made by the cross-scratching method using a sharp razor blade.

45 The number of experiments done with Josephson tunnel junctions under these extreme conditions are few. However, it is presumably in this region that non-equilibrium effects will start to play a dominant role in the description of their properties. On the other hand under these conditions it will presumably be difficult to distinguish the properties of tunnel junctions from those of microbridges.

Microbridges. In microbridges there certainly are extreme non-equilibrium effects involved. One which is indeed shared with small area, high current density Josephson tunnel junctions, is shown in Fig. 6. This picture shows the effect of excessive heating on a microbridge. A small calculation will show how this can come about. A typical microbridge is shown in Fig. 7. The crossscratch method"'"^ used in our laboratory yields the geometry shown. The bridge length is typical 0.3 ym, the width 0.5 ym and the thickness 0.3 ym. If such a bridge is biased at a current of 2 mA and a voltage of 1 mV then the heat dissipated per unit volume in the bridge region will amount to a rather 3 impressive number, namely 40 MV/cm . Using a typical value for the heat capacity of the material, we find that the temperature of an isolated microbridge would rise above the critical temperature in 10

sec. But the bridge is well

cooled by the massive background superconductor and its thermal time constant can indeed be as short as 10

sec. However,

short electrical pulses exceeding the typical bias values given above can lead to the damage shown in Fig. 6. Geometry of microbridges: How do we best represent the geometry of a typical microbridge? It has become customary to distinguish between two types of bridges as shown in Fig. 8(a) and (b). One is planar as if it were cut out of a film, the other

46

2DB

(a) 3DB

/ A s S !

d\

V = —1

c*

*

/

/

/

•/

/

/

-

/

/

/

•

/

\

/ / 1

7

'R-

V =

+1

(b)

Fig. 8(a) 8(b). Two and three-dimensional microbridge geometries,

is three-dimensional at the point where a small neck connects the two massive superconductors. In most cases real bridges are intermediate; i.e. with a bridge which is thinner than the background film. These practical realizations are often referred to as variable thickness bridges. In the following we shall develop some ideas which refer to the 3-dimensional bridge, 3DB. However, most of the conclusions apply - with minor modifications - to the 2-dimensional bridges (2DB).

47

V = V0eitp/2

V = W0e'^2

x 1

2

1

2

Fig. 9. The ODSEE model.

A theoretical treatment of a 3DB starts with the GinzburgLandau equations. One of the problems with the Ginzburg-Landau equations is to choose the correct boundary conditions. So far the most popular model of a microbridge has been to consider a one dimensional bridge with length

&

connecting two massive

superconductors in which the properties are unaffected by the 17 behaviour of the bridge. The reason for this choice is that the mathematics become simple. This so-called ODSEE

model

(One Dimensional Superconductor with Electrodes in Equilibrium) is illustrated in Fig. 9. This model attains its justification from a simple argument based on the Ginzburg-Landau theory, which we shall now persue. G-L theory for a small 3DB:

Neglecting external as well as

selfinduced magnetic fields the Ginzburg-Landau equations can be written 2 £22 Vn 2 Y =

j

s

=

+ 2m

(14) V 2 (1'*^ - f^f*) o

(15)

48

c|)0

V = -

Fig. 10. The three-dimensional microbridge geometry used in our perturbation calculation.

A simple theory for the Josephson effect in constrictions can be formed by considering a 3DB much smaller than the temperature dependent coherence length, £, and by arguing that in JJ

this case the terms on the left hand side of eq. (14) dominate."1 It is therefore sufficient to solve (14*) together with the boundary condition on the surface of the superconductor VlY = 0

(16)

where the gradient is projected perpendicular to the superconductor-insulator boundary. The equations (14) and (16) have their precise analogue in the equations for the electrical potential in a current-carrying (Ohmic) metal. The solution can therefore be written as a linear combination of such an

49 electric potential (not forgetting that shall use a normalized potential

¥

is complex). We

v , which has the value -1

far to the left and +1 far to the right, as indicated in Fig. 10. If the order parameter has the values ¥

f

a

r

¥

and

to the left and far to the right respectively,

then the order parameter can be written as the following function of

v * = Ito(l-v)e"i

(

1

_ |

V

I

)

D

=

V

v(r) N(0)lwr

2

(41)

vol

We see, as before, that unless we introduce a cut-off in the charge imbalance at some distance from the bridge, the

inte-

grated charge imbalance becomes infinite.This cut-off

length

is given by For

V>>RIc

the charge imbalance diffusion length AQ = v f , / t Q t 0 • the RSJ-model predicts that the Josephson

tion is sinusoidal with frequency RIc

w =

2 TT

c

—

oscilla-

i amplitude

. The normal current and the supercurrent oscillate in

antiphase with the current amplitude I

an£

I

. Roughly a charge

is injected during each period. If this is not

to supply the integrated charge imbalance the low frequency

limit is

IT

2

(eq.

sufficient

(41)), which in

eRI N(0)owA , then A must c -J v v start to decrease with frequency. This changeover frequency, to0/is

57 (0rt = u

2 z± e R N (o)wA q t Q

(42)

We might also include a discussion of the neutral imbalance, which decays with a characteristic time T_ and over hj v t t a characteristic length A = j / e 0 . Again,evidently, by far the largest part of the energy stored in this non-equilibrium is outside the bridge, out to a distance of

.

The

ratio of non-equilibrium excitations of this type inside 2 2 (i.e. within w) and outside the bridge is w /A .

Current Control and the Excess Current in Microbridges. We shall now deal with the implications of current control rather than voltage control in microbridges. There can be no doubt that a microbridge of the type we consider here looks into an external impedance which is much larger than its own resistance which is normally of the order of 0.1 i2. This statement can of course be violated at singular frequencies, i.e. at d.c. or at selected resonances, but we shall here attempt a description of microbridges covering all frequencies. Let us start by considering a series of I-V characteristics (IVC) for a typical microbridge taken at various temperatures, Fig. 12. A number of features are apparent. When the critical current is exceeded there is an excess supercurrent on top of the normal current at all voltages. As the temperature is decreased the excess current at low voltages develops into a 24 25 "shoulder" structure or a "blimp" . ' We shall now focus our interest on this excess current, in particular the shoulder. Let us start with the simple resistively shunted Josephson junction model (RSJ-model), with current control. The current is a sum of two contributions: a supercurrent with a sinusoidal current-phase relation and an Ohmic current for which the voltage is locked to the time derivative

58

In microbridge

21/5/80 TCK1

Film thickness: 1.0pm R n = 15 [ m Q ]

3.37 340 3.43

J

I

VOLTAGE < V >

Fig. 12.

L

J

I

L

10[pV/div]

Experimental I-V characteristics taken at different temperatures for a well-cooled variable thickness indium microbridge.

59 of the phase. The prediction based on that model is shown in Fig. 13. As seen this model already predicts an excess current. This is connected with the non-linear variation of the phase or voltage with time. We have already seen that introducing a relaxation time into the TDGL-model with voltage control gives an excess current (cfr. eq. 32). Is it possible that this excess current adds to the one which is a result of the RSJ model? The answer is no. We shall now attempt to explain why. A phenomenological relaxation theory. We shall use a theory which introduces a relaxation mechanism into the RSJ model by assuming that the bottleneck for the oscillation frequency is the variation in the superfluid density in the bridge region

26

In the middle of the bridge we have according to equation (24) so

(1 + cos (t) )

(43)

which varies in time. However, this variation is hampered by a finite relaxation rate

1/T , where

T

is an unspecified

relaxation time. As demonstrated above,the critical current is proportional to the equilibrium density of the superfluid. For simplicity we shall let any deviation from the equilibrium

Voltage versus time for different bias

points

JULJUX Fig. 13. Analog computer simulation of the resistively shunted junction modfel( with current control). The waveform of the ac voltage across the junction is shown for a number of bias values on the hyberbolic dc I-V characteristic .

60 Is-ns0 sirup

AIS

AIS

O

1

^

^

^

^

-t

Fig. 14. Relaxation effect in the voltage controlled case. This picture shows qualitatively how a relaxation time delay of the superfluid density (broken line) may lead to an enhanced forward supercurrent. The two lower curves represent suitable spatial averages of the perturbed superfluid density^* , and of the extra supercurrent, Al

//K

W V x ,t

Fig. 15. Relaxation effect in the current controlled case. Similarly to Fig. 14 this picture shows qualitatively the extra supercurrent, Al , that results from a relaxation time delay of the superfluid density. Again the two lower curves represent suitable spatial averages of the perturbed superfluid density, n* , and of the extra supercurrlnt, Al . The waveforms are drawn for /RI = o,12 .

61 density, eq. (43), determine the value of the maximum critical current, although a suitable spatial average would be more appropriate. If under this condition we introduce a parameter Y n

which is the perturbed

density

n*

normalized to

s Y

=

irs

the total current in the model can be written 1

where

y

= Y I c sin*

+

^

M

(44)

must be determined from a relaxation equation dt

= n i + Yy sin T G the classical temperature independent spin-flip scattering of the Abrikosov-Gorkov (4) theory. Below T g the spin freezing starts and the spin-flip life time monotonically increases with decreasing temperature, because "inelastic" spin-flip scattering becomes less probable at lower temperature. Contrary to the ferromagnetic order, the spin-glass order allows at T = 0 K a finite "elastic" spinflip scattering. The spin-flip scattering

1/T g ) as it was

calculated by Grest et al. is shown as a function of temperature in fig. 1 (curveEA). In a second approach Grest et al. (3) use the cluster mean field theory developed by Soukoulis and Levin (5). According to this theory, the spins already gather at T > T_ in weakly ij coupled clusters; below T^,these clusters are gradually blocked in random directions so that there is again a complete freezing of the spins at T = 0 K. This model not only explains the broad maximum observed in the specific heat, but it predicts also a cusp in the susceptibility at T . Unfortunately, calculations of T g based on this cluster theory are very complicated and become nearly impossible for large cluster size. An approximative calculation of T g as a function of temperature for clusters containing only two impurities

was also perfor-

med by Grest et al. The result is shown in fig. 1 (curveC/"IF) and should be valid for very dilute alloys assuming the Kondo

73 effect is very weak. Using the Abrikosov-Gorkov

(4) theory for the scattering of

superconducting electrons by magnetic impurities, Grest et al. (3) conclude that the temperature dependence of t s is immediately reflected in the superconducting order. This is in clear contradiction with the theoretical results of Sadovskii and Skryabin (6). These authors claim that, within the EdwardsAnderson approach, the increase of T compensated by a decrease of t s

below T is exactly S (j due to local magnetic fields

built up by the spin system. It is clear that in that case the curve for the "cluster approach" (fig. 1, curve CMFjmust also be modified: the important reduction of the scattering

A

1.50 1.25

CO

tr 1.00 z •D > 0.75

0.4

cr < cr

1

t= 0.50 m cr < 0.25

$

0

0

_L 0.5

0.8 1.2 T/ TG

EA

_L JL 1.0 1.5 T/TG

2.0 1

Fig. 1. Temperature dependence of the inverse spin-flip scattering time 1/T as calculated by Grest et S al. (3). E.A.: Edwards-Anderson approach; C.M.F. "Cluster Mean Field" approximation. The insert shows 1/Ts deduced from the experiments of Schuller et al. (7).

74 rate (1/T ) will mainly be compensated by the influence of local magnetic fields.

B. Experiment A first experimental indication of a possible phase transition in superconducting spin-glasses was recently obtained from one electron tunneling measurements performed by Schuller et al. (7) on AgMn alloys. They observed an anomalous behaviour of the zero bias conductivity in Al-A^C^-AgMn/Pb proximity junctions around T^ of the thin AgMn film. According to the theory of Abrikosov and Gorkov (4), this anomaly corresponds to a 5 % step-like decrease in the spin-flip scattering rate when the temperature is lowered from 1.2 T^ down to 0.8 T G (see insert in fig. 1). According to the calculation of Grest et al. (3), the variation of T

S

above T_ indicates the existence of spin clusters, CJ

while the constant value of T s at lower temperature is consistent with the compensation of the spin-glass effect by local magnetic fields as predicted by Sadovskii and Skryabin (6). Unfortunately, the interpretation of the one electron tunneling experiments involves large errors. Indeed, due to the rather high impurity concentration that is needed to have a well defined spin-glass effect, the AgMn/Pb sandwiches show a pronounced gapless behaviour. Hence, the absolute variation of the zero bias conductivity around T„ caused by a small change in the spin-flip scattering rate is hard to detect. Recently, Niemeyer and von Minnigerode (8) have measured the critical current in Pb-AgMn-Pb sandwiches as a function of the Mn concentration. They also observed an anomalous behaviour of the coherence length in the AgMn film around the freezing temperature of the AgMn layer. As in the case of the Schuller et al. (7) experiment, the interpretation of the experimental data depends on elaborate calculations using a theoretical

75 model. It seems therefore necessary to develop a more sensitive and direct detection method of the superconducting order which can also be used in the gapless regime.

Josephson Tunneling in Spin-Glasses We propose to study the spin-glass phase transition by measuring the variation of the dc Josephson current in a S'-I-SX Josephson junction. The electrode S' is supposed to be a BCS superconductor (with transition temperature T

Lb

,), while the

SX electrode is a superconductor containing magnetic impurities X so that SX shows a spin-glass behaviour below a fixed temperature T^. The maximum dc Josephson current in such a junction is given by (9): eRI„ M =

A S ,(T) 2k_T Z B ^ ,.2 , _2 2. 1/2 n (Ac, (T) + Ti in ) o ri

C

E dE E + A 2

2

Re

[(u 2 -!) 1 / 2 (1)

In this formula R is the tunneling resistance, e is the electron charge, ?iwc is the energy cut-off introduced by BCS, Ag,(T) is the BCS order parameter of the electrode S' and Tiu) = (2n + l)irk_T where n = 0, + 1 , + 2, ... For a superconn c — — ductor containing magnetic impurities, the complex ratio u = (oisx and A g x are the renormalised energy and order parameter for SX) is given in the first Born approximation by the implicit equation (10) uaP£ = E + ir SX

u

(u-l)1/Z

(2)

T is the Abrikosov-Gorkov pair breaking parameter (%1/T ) and r^V» Ag X is the BCS order parameter given by the usual self-consistency condition:

76

r/As(0)

Fig. 2. Reduced Josephson current RI M /RI M (c -»- 0) and energy gap fi_x/Ag(0) versus reduced pair breaking r/S~(07.

77 ftlW c O

dE Re

1

(3)

In order to calculate the Josephson current we must fix a value for the pair breaking parameter and determine the complex ratio u from eq. (2) and eq. (3). The self-consistent solution is then inserted into eq. (1) from which I M is calculated . The variation of the Josephson current and energy gap at T = 1.5 K as a function of the pair breaking parameter is given in fig. 2. Since the impurity concentration is high in a spin-glass system, tunneling experiments can only be performed in the gapless regime where r/A g (0) > 0.40; A g (0) is the order parameter of the SX electrode at T = 0 K in the limit of zero impurity concentration. The insert in fig.2

clearly shows that

for such a strong pair breaking the Josepshon current can still detect small variations in r. Fig. 3 shows the variation of the Josephson current versus temperature for two impurity concentrations corresponding to

r/A

s

(0)

=

0.450

(a) and

r/A

g

(0)

=

0.486

(b) so that the

SX electrode is gapless in both cases. The corresponding temperature dependence of the pair breaking parameter around T_ that was used to calculate RI„ is shown in the insert of G M fig. 3. The shape of the variation of r around T corresponds Vj to the results of Schuller et al. (7). For (a) the step height is about 5 %, while for (b) their is a variation of about 1.5 % around T„. For all the calculations we took A„(0) b o= A„,(0). It is clear that even a small change in the spin-flip scattering rate gives a pronounced effect in the temperature dependence of the Josephson current. On the other hand, a change of 5 % in T gives only an absolute variation of 0.5 % in the zero bias conductivity as measured by Schuller et al. (see fig. 2 in ref. 7).

78

Fig. 3. Variation of the reduced Josephson current RI M /A S .(0) with the reduced temperature T/T , The insert shows the variation of the reduce! pair breaking parameter r/A„(0) with T/T , as used for the calculation of the Josephson current.

79

Fig. 4. Variation of [RIM/Ag.(0)] with T/T cs .. In the absence of a spin-glass effect the behaviour of [RIm]^ near T c s x is approximatively linear (dashed line).

In the absence of a spin-glass effect one expects near 2

the superconducting transition a linear behaviour of I M versus T(T/T LOA c v > 0.8, where T__ v is the transition temperature of the LDA2 alloy SX). In fig. 4 the I M ( T ) curves, corresponding to the spin-glass transitions considered above, deviate markedly from this linear behaviour.

Conclusion In this paper an analysis has been made of the possible influence of the spin-glass order upon superconductivity. The existing theoretical models describing this interaction are

80 not only very approximative but also in contradiction with each other. Experimentally, a small anomaly in the superconducting order has been observed around T_ Cj but the interpretation of these results is very difficult and based on a theoretical model. To overcome these difficulties, we propose to use the Josephson effect as a very sensitive tool to detect a possible phase transition in a spin-glass at T G - Moreover, the Josephson current enables to detect any further variation of the spin-flip scattering below T ij.

Acknowledgement We are much indebted to the Belgian Interuniversitair Instituut voor Kernwetenschappen for financial support.

References 1. Mydosh, J.A.: Amorphous Magnetism II, edited by Levy, R.A. and Hasegawa, R., Plenum, New York 1977. 2. Edwards, S.F., Anderson, P.W.: J. Phys. F5, 965 (1975); Fischer, K.H.: Phys. Rev..Lett. 34, 1438 (1975). 3. Grest, G.S., Levin, K., Nass, M.J.: Phys. Rev. B21, 1219 (1980). 4. Abrikosov, A.A. , Gorkov, L.P.: Sov. Phys. JETP ]_2, 1243 (1961) . 5. Soukoulis, C.M., Levin, K. : Phys. Rev. Lett. 39, 581 (1977). 6. Sadovskii, M.V., Skryabin, Y.N.: Phys. Stat. Sol.(b) 95, 59 (1979) . 7. Schuller, Y. , Orbach, R. , Chaikin, P.M.: Phys. Rev. Lett. 4_1 , 1413 (1978) . 8. Niemeyer, J., von Minnigerode, G.: Z. Phys. B36, 57 (1979). 9. Nam, S.B.: Phys. Rev. j_56, 470 (1967). 10. Skalski, S., Betbeder-Matibet, O., Weiss, P.R.: Phys. Rev. 136,A1500 (1964).

CHARACTERIZATION OP NON EQUILIBRIUM SUPERCONDUCTIVITY VIA THE JOSEPHSON EFFECT

A. Gilabert, C. Vanneste, P. Sibillot and D. Ostrowsky Laboratoire de Physique de la Matière Condensée Université de Nice Parc Valrose 06034 Nice Cédex FRANCE

Introduction A number of theoretical models have been proposed to describe the properties of non-equilibrium superconductors with the two most popular being the so -called y*and T*models (1),(2). Comparisons between these theories and experiments based on the use of superconducting tunnel junctions have been made and while a general agreement has been found, a number of important points such as the existence of a first order transition predicted by the u model have not been clearly elucidated. In this paper we propose the use of the Josephson effect as a finer probe of these models.

Results We consider a Josephson tunnel junction made of two superconducting electrodes with energy gap AJ and A 2 . One of these electrodes ( A 2 ) may be driven away from equilibrium. The nonequilibrium state is characterized by a normalized excess quasiparticle number n = (N - NT)/4N(O)A0 defined as the departure of the number density N of quasiparticles from the equilibrium number density N^, at the temperature T. N(o) is the single spin density of states at the Fermi level and A0 the energy gap at OK.

Squid '80 © 1980 Walter de Gruyter & Co., Berlin • New York

82 The maximum dc Josephson current IM

(T -,n) A x ^

IM

(o;o)

This relation states that

(T)

Aj (o)

(T;w) is calculated by : A 2 (T;») A2

(1)

(o;o)

(T;n) is proportionnal to the

product of the energy gaps on each side of the barrier of the junction and can describe the Josephson current, as calculated by Ambegaokar and Baratoff (3), to better than

10%.

In the u* model, the quasiparticles are in thermal

equilibrium

with the phonons at the lattice temperature but with their distribution displaced by an effective chemical potential u*. Using this model Owen and Scalapino

(1) obtained the varia-

tion of the reduced energy gap as a function of temperature for various values of n and predicted that a first order transition to the normal state would appear at a critical value n c . Introducing in equation 1 these variations of A 2

(n;T) we

obtain the temperature dependence of Xjv[ (fig.l). Of course, the Josephson current shows the first order transition

: for

a given excess quasiparticle number, a junction will be driven from Josephson tunneling to single particle tunneling above a critical temperature. It will be interesting to see if the Josephson current shows such a transition for several reasons

: a calculation of Chang and Scalapino

(4) indicates

that the u* model may not be adequate to describe non equilibrium superconductors since at low temperature

(T/T c

< 0.7)

a density instability is energetically more favorable than a normal-superconductor phase transition and at high temperature, the quasiparticle recombination time is no longer much larger than the quasiparticle thermalization time. However first order transitions in non-equilibrium superconductors have been reported using single electron tunneling experiments

(5)>(6).

The advantage of using the dc Josephson effect rather than single electron tunneling is experimental

: I M is well deter-

mined even near T c while the energy gap (or the differential conductance at zero bias) determined from current voltage cha-

83 racteristics is more affected by thermal smearing. In the T* model (2), the quasiparticles and the phonons with energy greater than 2A (T ) remain in both thermal and chemical equilibrium at an effective temperature T* greater than the considered temperature T. There is no first order transition. In this model, Parker obtained the variations of T versus the quasiparticle number and versus the optical photon injection power. Using these relations, we have calculated, the temperature dependence of

IJVJ

(T;«)/Ijy¡(o;o) for a given

excess quasiparticle number (dashed line in fig.l). This behaviour is different from the y

model, at high temperatures

and for high injection levels. Pig.(2) shows the variations of the supercurrent versus normalized optical power P.P C is the optical power above which the superconductor becomes normal. In fig. (2), a comparison is made with a simple heating (dashed line). In simple heating, the quasiparticles and phonons of all energies are thermali-

*

*

zed with an effective temperature t = t / t c given by (2) : (t*4 - t**)/(l - t 4 ) = P/rP

. The difference between the modic fied heating model and the simple heating is very pronounced at low temperature or for high optical power injection. In conclusion, we propose to use the Josephson current Ijy[ as a probe for testing non equilibrium superconductivity and we have outlined why this should provide a more detailed description of the non equilibrium state.

References 1. C.S. Owen and D.J. Scalapino : Phys.Rev.Lett.28;1559 (1972) 2. W.H. Parker : Phys.Rev.B.12;3667 (1975) 3. V. Ambegaokar and A. Baratoff : Phys.Rev•Lett.10;486

84 (1963) and 10., 104 (1963) J.J. Chang and D.J. Scalapino : Phys . Rev . B ._10; 4047 (1974) 5. J. Puchs, P.W. Epperlein,M. Welte and W. Eisenmerger : Phys.Rev.Lett.38;919 (1977) 6. I. Iguchi : Journal of Low Temp.Phys.¿1;605 ( 1978)

85

t/tc Fig.l

: Temperature dependence of the Josephson current for different excess quasiparticle number. ( — ) p model. ( )T model.

86

l ( T ; P / P c ) / I (0 j 0)

Pig.2

: J o s e p h s o n c u r r e n t v e r s u s o p t i c a l p o w e r for two ratures. ( ) T m o d e l . ( ) Simple h e a t i n g .

tempe-

LOCALLY LOWERED TUNNELING BARRIERS JOSEPHSON

M.

IN

LIGHT-SENSITIVE

JUNCTIONS

Russo

Istituto di C i b e r n e t i c a del C o n s i g l i o N a z i o n a l e d e l l e 80072 A r c o F e l i c e , Italy.

Ricerche

S i n c e 1968 J o s e p h s o n j u n c t i o n s e m p l o y i n g a p h o t o c o n d u c t i n g film a s neling b a r r i e r have been realized

(1) .

tun-

T h i s k i n d of s t r u c t u r e , k n o w n a s

light-sensitive junction, has been widely investigated p a y i n g particular attention to s a m p l e s h a v i n g a c a d m i u m s u l p h i d e b a r r i e r

(2-4) .

T h e e x p e r i m e n t a l data a v a i l a b l e o n these j u n c t i o n s s h o w the r e l e v a n t r o l e p l a y e d o n the t u n n e l i n g b e h a v i o r b y the material c h o s e n for the s u p e r c o n ducting electrodes.

In fact, the b a r r i e r p a r a m e t e r s

(height and shape)

are

s t r o n g l y affected b y the s p e c i f i c s e m i c o n d u c t o r / m e t a l c o n t a c t s . I n the c o n text of the p r e s e n t w o r k , a m o n g o t h e r p r o p e r t i e s ,

it is of r e l e v a n t i n t e r e s t

the m a x i m u m s e m i c o n d u c t o r film t h i c k n e s s , s , w h i c h a l l o w s the o b s e r v a t i o n of d c J o s e p h s o n c u r r e n t b e f o r e

(after)

i l l u m i n a t i o n . D e p e n d i n g o n the s u p e r -

c o n d u c t i n g e l e c t r o d e s e m p l o y e d , the t y p i c a l t h i c k n e s s v a l u e s a r e : junctions

s ^ 50-H00

s — 500 (1000) A .

(200) A , in P b - l n

s »

in P b - P b

300 (400) A , a n d in I n - l n

T h e s e data s h o w how the o b s e r v a b i l i t y of

dc

Joseph-

s o n c u r r e n t t h r o u g h " t h i c k " b a r r i e r films is related to the p e c u l i a r ties of I n - C d S i n t e r f a c e s .

proper-

T h i s c i r c u m s t a n c e is p r o b a b l y d u e to a s l i g h t

i n t e r d i f f u s i o n b e t w e e n i n d i u m a n d c a d m i u m s u l p h i d e l e a d i n g to a stable o h m i c contact (5) .

M o r e o v e r a better m e c h a n i c a l s t a b i l i t y of t h i s

ductor/metal contact w i t h r e s p e c t to o t h e r i n t e r f a c e s w i t h soft

semicon-

superconduc-

tors has been o b s e r v e d . U n f o r t u n a t e l y , the a d v a n t a g e s c o n n e c t e d to. the u s e of i n d i u m e l e c t r o d e s a r e p a r t i a l l y r e d u c e d b y the low critical, t e m p e r a t u r e of s u c h (T

C

= T

= 3 . 4 K ) a n d the small e n e r g y g a p

C In

by indium.

However,

(A/e

s i n c e the electrical p r o p e r t i e s

Squid '80 © 1980 Walter de Gruyter & Co., Berlin • New York

structures

= 0 , 5 3 mV)

exhibited

(the b u i l t in potential

88 b a r r i e r ) at the metal/semiconductor interface a r e still p r e s e r v e d for a v e r y thin metal film a n d the s u p e c o n d u c t i n g p r o p e r t i e s are extended into a normal metal o v e r a long distance ( h u n d r e d s of A n g s t r o m s ) v i a p r o x i m i t y effect ( 6 ) , it is p o s s i b l e to couple the s u p e r c o n d u c t i n g b e h a v i o r of a h i g h T c s u p e r c o n d u c t o r to the electrical b e h a v i o r of an I n / C d S contact.

A

schema-

tic d r a w i n g of a t u n n e l i n g s t r u c t u r e h a v i n g s u c h a b e h a v i o r is s h o w n in Fig.

1 w h e r e lead is u s e d as h i g h T" c s u p e r c o n d u c t o r .

In s u c h a s t r u c -

ture the thin i n d i u m layer p r o v i d e s a l o w e r i n g of the t u n n e l i n g b a r r i e r o n one s i d e of the s a n d w i c h leading to a t u n n e l i n g b a r r i e r as in a P b - C d S - l n junction.

H o w e v e r , s i n c e the In film is b a c k e d b y a thick Pb l a y e r , its

s u p e r c o n d u c t i n g p r o p e r t i e s a r e i n d u c e d b y lead; in p a r t i c u l a r , for a s u i t able choice of the t h i c k n e s s e s , the g a p s t r u c t u r e and the critical

tempera-

ture e x h i b i t e d b y the whole s t r u c t u r e a r e v e r y close to the v a l u e s of a Pb-CdS-Pb

junction.

Pb - CdS-In - Pb Fig. 7 - Schematic drawing of a light-sensitive having a thin indium interiayer for the towering tunneling barrier.

junction of the

Before g i v i n g a s h o r t account of the junction fabrication p r o c e d u r e ,

the

choice of lead a n d i n d i u m a s s u p e r p o s e d films d e s e r v e s some comments. In fact, it is well k n o w n the s t r o n g tendency of i n d i u m to form a l l o y s with soft metals. T h i s c i r c u m s t a n c e leads t o - p r o b l e m s of stability of the junction characteristics.

N e v e r t h e l e s s a P b - l n electrode has been c h o s e n , at this

stage of the r e s e a r c h , both for some technological opportunities a s well a s for the k n o w l e d g e of the interface b e h a v i o r with cadmium s u l p h i d e . W o r k is in p r o g r e s s to realize samples e m p l o y i n g a N b / l n electrode.

89 T h e junctions are realized b y conventional thin film deposition t e c h n i q u e s . T h e sample have a lead b a s e - l a y e r , a cadmium s u l p h i d e film a s b a r r i e r a n d a counterelectrode made b y a thin i n d i u m film b a c k e d b y a thick lead l a y e r . T h e metals have an initial p u r i t y of 99.999%, the C d S is p o w d e r i n g the same p u r i t y . T h e film a r e deposited at a p r e s s u r e in the 10

hav-

6

Torr

r a n g e from c u r r e n t heated Mo boats onto 7059 C o r n i n g g l a s s s u b s t r a t e s held at room temperature. T h e film geometry is selected b y e v a p o r a t i n g t h r o u g h stencil m a s k s .

T h e whole p r o c e s s is realized without b r e a k i n g the v a c u u m .

Details about the p r e p a r a t i o n p r o c e d u r e are reported in Ref. 4

but for the

top electrode made b y two s u b s e q u e n t e v a p o r a t i o n s of i n d i u m a n d lead. T o obtain a completely " p r o x i m i z e d " i n d i u m l a y e r , t h i c k n e s s v a l u e s of about 6

o

3000 A a n d 300 A for lead and i n d i u m film r e s p e c t i v e l y h a v e been adopted. In the following it shall be p r e s e n t e d p r e l i m i n a r y measurements

concerning

a n application of this fabrication technique. T o obtain junctions e x h i b i t i n g a spatial modulation of the s u p e r c u r r e n t , a local l o w e r i n g of the b a r r i e r a c h i e v e d b y p l a y i n g on the i n d i u m film g e o m e t r y .

c u r r e n t d e n s i t y is obtained b y r e a l i z i n g top electrodes made b y spots b a c k e d b y the lead film. point of view

is

T h e modulation of the indium

In this c o n f i g u r a t i o n , from the electrical

(the built in potential b a r r i e r ) , the s t r u c t u r e , e x h i b i t i n g a

critical temperature near that of lead, c o n s i s t s of a parallel of a P b - C d S - P b a n d a P b - C d S - l n junction.

S i n c e the occurrence- (before illumination) of o

d c J o s e p h s o n effect is o b s e r v e d u p to a C d S film t h i c k n e s s of 50-5-100 A in a P b - P b s t r u c t u r e , a n d u p to 300 A in a P b - l n j u n c t i o n s , the choice of the semiconductor t h i c k n e s s

( *

300 A ) a l l o w s the s u p e r c u r r e n t to flow

t h r o u g h the b a r r i e r film in the P b - l n r e g i o n o n l y .

Junctions having

such

a feature h a v e been realized. T h e actual c o n f i g u r a t i o n s a r e s k e t c h e d in Fig.

2.

O n each substrate three junctions of a c r o s s type geometry h a v e been r e a 2

lized ( L x W

= 0 . 4 x 0 . 5 mm ) , each junction h a v i n g either one o r two

i n d i u m spots

(about 130 ^.m in d i a m e t e r ) , together with a P b - P b test j u n c -

tion. T h e junctions realized b y the above p r o c e d u r e h a v e been m e a s u r e d at temp e r a t u r e s below 4.2 K . T h e c u r r e n t - v o l t a g e c h a r a c t e r i s t i c s and the m a g n e tic field dependence of the z e r o - v o l t a g e c u r r e n t h a v e been c o n s i d e r e d .

90

. Pb In . CdS - Pb

'//////////////s//.

a.

SINGLE

JUNCTION

7//////////////J. 7/yS '/////////s///''''-

b.

DOUBLE

( 3000 Â ) (300 A> (300 A) (3000 A )

Pb In CdS Pb

JUNCTION

Fig. 2 - Tunnel junction structures. On the right it is shown a schematic cross-section of the junctions. The current can flow either directly between the two lead films or through the indium layer. Due to the behavior of Pb/CdS and In/CdS interfaces and the relative thicknesses of the films, the current through the indium dominates and it is possible to observe a "localized" dc Joseph son effect. Before i l l u m i n a t i o n , at 4.2 K , all the j u n c t i o n s e x h i b i t a tunnel c h a r a c t e r i s tic w i t h a clear s t r u c t u r e at V = 2 A p b / e quasi-particles branch. test j u n c t i o n ;

and a s l i g h t non l i n e a r i t y in the

In F i g . 3 it is shown the behavior of a Pb-CdS-Pb

it is w o r t h n o t i n g that, on this sample, the zero-voltage c u r -

r e n t is completely absent due to the semiconductor b a r r i e r t h i c k n e s s .

More-

o v e r , for the f i l m thickness r e p o r t e d , it is not possible to l i g h t induce Josephson c u r r e n t in the test j u n c t i o n s for a l i g h t / d a r k c o n d u c t i v i t y

ratio

2

up to 7 • 10

(this being not a l i m i t i n g value b u t j u s t the highest v a r i a t i o n

reached in the present experiments) . On the c o n t r a r y , in d a r k c o n d i t i o n s , j u n c t i o n s characterized b y the p r e sence of either one o r two i n d i u m spot show a zero-voltage c u r r e n t .

This

circumstance guarantees both the enhancement of the P b - l n c r i t i c a l temper a t u r e and the o c c u r r e n c e of a s u p e r c u r r e n t t u n n e l i n g path t h r o u g h the

V (2

mV/div)

Fig. 3 - Current-voltage characteristic of a Pb-CdS-Pb test junction, in zero externa! magnetic field, at 2.2K and before illumination. The test samples, prepared together with Pb-CdS-ln/Pb structures, are characterized by the complete absence of zerovoltage current. indium l a y e r . In Fig. 4 it is shown a typical l - V characteristic of a structure having two indium spots ("double junction" configuration, see Fig.

2b).

By comparison with the test junction, a rough estimate of the tunneling 3 conductivity of the P b - l n and Pb region gives a 10 time higher value for the spots.

V O L T A G E ( l mV / d i v )

Fig. 4 - Current-voltage characteristics, before illumination, of a Pb-CdS-ln/Pb sample having the top electrode geometry shown in Fig. 2b; on the left side it is shown the l-V characteristic at ¿t.2K, on the right side the zero-voltage current at 2. IK. The ratio between the tunneling conductivity of this junction and of the test one is about IS.

92 In F i g . 5 a r e reported experimental data c o n c e r n i n g the dependence of the zero voltage c u r r e n t on the external magnetic field for a " d o u b l e " junction s t r u c t u r e . T h e measurements are performed o n a sample at 4.2 K , before i l l u mination. In the f i g u r e it is c l e a r l y s h o w n the o c c u r r e n c e of both interferencial a n d diffractive b e h a v i o r s , the latter is due to the not n e g l i g i b l e p h y s i c a l d i m e n s i o n s of the indium spots with respect to the whole junction.

Fig. 5 - Magnetic field dependence of the zero voltage current in a "double" junction structure before illumination, T = U.2K. To show the double modulation a solid curve through the experimental points is also drown. Although an explanation of this behavior is intuitive on the basis of two localized barrier lowering, nevertheless, an accurate theoretical fitting of the experimental data is not possible by a simple step-like current density profile (7).

A rather p u r e interferencial b e h a v i o r is e x h i b i t e d b y " d o u b l e " junction s t r u c t u r e s after illumination. In fact, due to the t h i c k n e s s of the top lead electrode ( w h i c h s h a d e s the l i g h t - s e n s i t i v e b a r r i e r ) the illumination o c c u r s o n l y at the junction e d g e s . In this case the light e n h a n c e d J o s e p h s o n c u r rent is localized in a small r e g i o n of the indium s p o t s . M o r e o v e r , for a suitable cadmium s u l p h i d e b a r r i e r t h i c k n e s s

o

( — 400 A ) , the zero voltage

93 c u r r e n t is entirely l i g h t - i n d u c e d , a n d , as c o n s e q u e n c e , a s h a r p p e a k i n g occurs. In F i g . 6 it is s h o w n the magnetic field dependence of the l i g h t - i n d u c e d J o s e p h s o n c u r r e n t in s u c h a type of s t r u c t u r e .

It is w o r t h noting that,as

expected, the dependence does not show a diffractive b e h a v i o r at all.

Sî

W i 05 4 0 05 D O 30 Q

d

X co W 05 X ir

2

•

°

m •S

•

•

10

I 4

I

CONTROL

I 6

I

CURRENT (mA)

Fig. 6 - Magnetic field dependence of the light-induced Josephson current in a "double" junction structure, T - t.2K. The junction is illuminated by an electronic flash through a light pipe in contact with the sample substrate. T h e author is grateful to S . Piantedosi, C . S a l i n a s and C . S a l v i a for their technical a s s i s t a n c e .

T h i s r e s e a r c h is s u p p o r t e d in part b y the C o n s i g l i o

Nazionale delle R i c e r c h e u n d e r the Progetto Finalizzato S u p e r c o n d u t t i v i t à .

References 1.

G i a e v e r , I.: P h y s . R e v . Lett. 20, 128 (1968).

2.

Barone, A . , Rissman, P., Russo, M.:

3.

B a r o n e , A . , R u s s o , M . , V a g l i o , R . : A I P C o n f . P r o c . 44, 340

R e v . P h y s . A p p i . 9, 73

(1974). (1978).

94 4.

A n d r e o z z i , F . , B a r o n e , A . , Paterno, G . , Russo, M . , V a g l i o , R . : P h y s . Rev. B18, 6035 (1978), and references r e p o r t e d t h e r e i n .

5.

Barone, A . ,

6.

Cilabert, A . : therein.

Russo, M . :

P h y s . L e t t . A49, 45 ( 1 9 7 4 ) .

7.

B a r o n e , A . , P a t e r n o , G . , Russo, M . , V a g l i o , R . : Solidi 41a, 393 (1977) .

A n n . P h y s . 2, 203 (1977), and references Phys.

reported Status

P R E P A R A T I O N P A R A M E T E R S A N D C H A R A C T E R I Z A T I O N OF V A N A D I U M BASED JOSEPHSON A . Barone, M.

JUNCTIONS

Russo

Istituto di Cibernetica del C N R , 80072 A r c o Felice, A . Di C h i a r a , C .

Italy.

Peluso

Istituto di F i s i c a della Facoltà di I n g e g n e r i a , U n i v e r s i t à di Napoli Napoli, Italy.

Introduction In spite of the e n o r m o u s amount of w o r k devoted to J o s e p h s o n

structures

of v a r i o u s c o n f i g u r a t i o n s a n d e m p l o y i n g different materials, there a r e still some open q u e s t i o n s c o n c e r n i n g the p o s s i b i l i t i e s offered b y v a n a d i u m electrodes for tunnel j u n c t i o n s . T h e aim of this paper is to d i s c u s s some aspects of the p r e p a r a t i o n p r o c e d u r e a n d experimental b e h a v i o r of v a n a d i u m b a s e d junctions also in the f r a m e w o r k of the e x i s t i n g

literature.

T h e v a n a d i u m films u s e d in this w o r k a r e realized b y electron g u n d e p o s i tion and e x h i b i t good s u p e r c o n d u c t i n g p r o p e r t i e s . Both, native o x i d e a n d artificial

(cadmium s u l p h i d e )

layers, are considered as tunneling

barrier.

Experimental data c o n c e r n i n g the characterization of the whole junction a r e g i v e n a l s o b y i n v e s t i g a t i n g the effect of external p a r a m e t e r s , s u c h a s a p p l i e d magnetic field a n d light e x p o s u r e , on the J o s e p h s o n c u r r e n t . T h e availability of both v a n a d i u m o x i d e a n d cadmium s u l p h i d e b a r r i e r samples can remove those ambiguities in the interpretation of the b e h a v i o r of v a n a d i u m junctions w h i c h are inherent to v a n a d i u m o x i d e s .

Moreover,

v a n a d i u m , a s h a r d metal, allows quite stable junctions a n d seems to offer some a d v a n t a g e s o v e r n i o b i u m in the fabrication of longlife

light-sensitive

junctions. In section two details of the junction p r e p a r a t i o n p r o c e d u r e a r e g i v e n , a n d

Squid '80 © 1 9 8 0 Walter de Gruyter & Co., Berlin • N e w York

96 properties of vanadium films a r e discussed as well as those of cadmium sulphide and oxide b a r r i e r s .

In the t h i r d section a r e reported various e x p e r i -

mental results on junctions, including measurements on the dependence of the critical c u r r e n t upon the external magnetic field and other data which allow a rather complete characterization of the samples. Whenever is possible it is attempted to give a more exhaustive picture of the topic providing comparison with data available from the literature.

2. Junction Preparation Although good results have been reached by various authors, the p r e p a r a tion procedure of vanadium based junctions cannot be considered so firmly established as it is for the widely employed niobium technology.

Therefore

some attention has been devoted to the main preparation steps which are compared with the fabrication procedure usually described in other w o r k s .

2a) Vanadium layer.

It is well known the important rôle played by the

enclosure of gases in transition metal films (niobium, vanadium and tantalum) on parameters characterizing both the normal and superconducting states.

T h e r e f o r e , d u r i n g the vanadium film preparation, the deposition

parameters, such as vacuum conditions, evaporation rate and substrate temperature, (1920

V

C),

require a careful control.

Due to the high melting point

the most commonly used deposition technique of vanadium films

is the electron gun evaporation, although other possibilities have been e x plored ( 1 , 2 ) .

The typical vacuum conditions and the relatively low depo-

sition rates usually realized, impose the use of substrates held at high temperature (up to 300 ° C ) to decrease the sticking coefficient for oxygen and nitrogen.

The most significant parameters for the preparation of v a -

nadium layers a r e reported in Table 1 which summarizes data available from the literature on superconducting tunneling. In the present experiments the film contamination is kept low only by o p e r ating at v e r y low pressuré avoiding substrate heating. initial purity by Alfa Inorganics)

Vanadium

(99.9%

is evaporated by means of a 2kW elec-

97

• .-H

.in. o.

A. O

•è

a E ai 4J 6 O o M

C/5 o< «< O

O o

cO

O O — iOi

r-» O — i i

CS

•I' oM C

00 1 o r-1 1 O

o m sr • ai J= l-l O *J M ( A J £(30 C Q 4-1 < ai 6 h -> C •H i «H Xi J*-> rH 41 >

o 1 — < i1 (— < >

.û eu

o > >

>%

X

1 /-s >> C M 06 rH TD O §

1 ctí r-* TD 0 C ¿A (¡i 0) O « -o « -O o A3 A3 m co

9«

• a> « •H o

rH• 0»M ma •o m 4J m a C rH 4) 4J m ijw 0) c e J: C 4) C0 O O 0) U v M 4) B 3 m e y (afc 2 > 3 R ) a n d ¿AuPbg = Q > 6 5 M 3

A

meV (at 4.2 K), t£ u voltages

Pb 3

= 5.6 K (13).

The current jumps at the

V = 2.6 mV and 1.95 mV are due to single-particle

tunneling by pair-breaking processes, and correspond to struc-

143 |[mA],dV/dl[arb.units]

0.5 4 ®

©

(

aof I v [ m v ] ®

©

Figure 7 - I-V characteristic and differential resistance dV/dl vs. V of an In/Au/Pb(M2)-oxide-Pb/Au/Pb(M3) tunnel junction at 2.3 K. The current scale has been expanded as indicated. ® = 2A P b /3e, @ = 2A Pb /2e, (3) = (AMO + A„" P b 3 )/e, M2 M3 © = (A M2 + APb-phase )/e . Pb-pha s e tures expected at eV = A M 2 + A M 3

2A

Pb

and eV = A M 2 +

AuPb3^ A s Fig. 7 shows, no structure at eV = A... due M2 M3 M3 to single-particle tunneling of thermally-excited quasiparticles was observed.

However, the interesting fact is that the

current step structures located at

V = 1.3 mV and 0.85 mV can

definitely be attributed to MT in this case, too (Table 3), and correspond to structures at eV = 2A P b /m for

m = 2 and

m = 3, respectively [see Eq. (2)]. Table 3 - Experimental and calculated SGS values Experimental

Multiparticle tunneling

Selfcoupling.

6I2 (2A Pb /2e) 6I1 (2A Pb /e)

0.017

0.031

SI 3 (2A Pb /3e) 6I1 (2A Pb /e)

< 0.0012

0.0017

maximum values, calculated for 2-(2m $) 1 ^ 2 -t/ti

0.18

0.

144 Measurements of the temperature dependence of the two-particle current steps (m = 2) resulted in a smearing of the steps with increasing temperature in the range 2.3 K < T < 4.2 K, but their heights remained practically unchanged within the measuring accuracy.

According to a simple theoretical argument,

a reduction of the two-particle tunneling with increasing temperature is expected, however, due to a decreasing finalstate phase space for two-particle processes.

More experi-

mental information on this topic and on the two-particle current as a quasiparticle injection current can be found in Refs. 14 and 15.

5.

Discussion and Conclusion

The side-lobe spread observed in the interference patterns of Au/Pb/In-base electrode Josephson junctions is positively correlated with the heights of subharmonic gap structure current steps.

The steps are caused exclusively only by multiparticle

tunneling processes.

In particular, in asymmetric junctions

we observed the current step located at the larger gap voltage to be the higher one, and found the odd-m SGS at eV = (A„„ + Hi A M3 >/m for m = 3. From the ruling out of the self-coupling, we conclude that our symmetric and asymmetric Pb-alloy junctions were free of metallic shorts. The definite explanation of the origin of the SGS within the MT model indicates a defective junction oxide structure, and that m a y b e a random distribution of Pb- and In-oxide spots with extremely different tunneling probabilities (or say, supercurrent densities).

This conclusion is supported by the

value of about 200 for the ratio between the areas of Pb and In oxides calculated with experimental data on the basis of the MT model (4.2.1).

Assuming an average grain size of about

145 0.2 pm, we evaluated for the average distance between In-oxide spots approximately 5 ym, which is in the order of the Josephson penetration depth, a characteristic length for the supercurrent interference effect.

In this case, an influence

on the interference pattern may be possible, and a correlation between the strength of side-lobe abnormalities and the height of subharmonic gap structure current steps can be expected. The present paper was performed within the IBM Josephson project.

Helpful discussions with Drs. A. Baratoff, D.F. Moore

and P. Wolf are gratefully acknowledged.

In particular, I

should like to thank Dr. (Mrs.) P. Mukhopadhyay from the Indian Institute of Technology, Bombay, for supplying detailed information on her model on multiparticle tunneling.

Thanks

are due to the Technology Group for fabricating the samples, and to W. Bucher for his expertise in doing the experiments.

References 1. Meyer, E., Pottel, R.: Physikalische Grundlagen der Hochfrequenztechnik, Vieweg & Sohn, Braunschweig, W. Germany, 1969, p. 65. There exists a formal analogy between the dc-Josephson interference effects and diffraction phenomena in the propagation of electromagnetic waves. Methods to suppress side-lobe maxima are discussed here. 2. Broom, R.F., Kotyczka, W. , Moser, A.: IBM J. Res. Develop. 24, 178-187 (1980). 3. Wilkins, J.W.: Tunneling Phenomena in Solids, Plenum, New York, 1969, 333-352. 4. Hasselberg, L.-E., Levinsen, M.T., Samuelsen, M.R.: Phys. Rev. B 9, 3757-3765 (1974). 5. R.F. Broom's computer program for calculating static interference patterns of shaped in-line junctions has been supplemented with routines for multi-polygon shapes and arbitrary, one-dimensional supercurrent density profiles. All experimental curves originally existed as oscillogram records.

146 6. See, e.g., Barone, A., Paterno, G., Russo, M., Vaglio, R.: phys. status solidi (a) 41, 393-401 (1977). 7. The 6 values were supplied by P. Wolf. 8. Barnes, L.J.: Phys. Rev. 184 , 434-446

(1969).

9. Mukhopadhyay, P.: J. Phys. F.: Metal Phys. 9, 903-915 (1979). ' 10. Broom, R.F., Mohr, Th.O.: Thin Solid Films 47, 249-259 (1977) . 11. Aspen, F., Goldman, A.M.: Cryogenics vol? 721-722 (1976). 12. Gundlach, K.H., Kadlec, J.: Appi. Phys. Lett. 21_, 4 29432 (1975) . 13. Basavaiah, S., Lahiri, S.K.: J. Appi. Phys. 4_5, 27732774 (1974). 14. Epperlein, P.W., Lassmann, K., Eisenmenger, W.: Z. Phys. B 31, 277-384 (1978) . 15. Epperlein, P.W., Eisenmenger, W.: Z. Phys. B 32, 167174 (1979) .

M A G N E T I C FIELD B E H A V I O R O F C U R R E N T STEPS IN LONG

JOSEPHSON

JUNCTIONS

G. C o s t a b i l e , A. M. C u c o l o , S. P a c e , R. D. B. Savo, and R. V a g l i o Istituto di F i s i c a , U n i v e r s i t à di 1 - 8 4 1 0 0 S a l e r n o , Italy

Parmentier,

Salerno

Introduction

The z e r o - f i e l d steps, or dc c u r r e n t s i n g u l a r i t i e s , rent-voltage characteristics

in the cur-

of long J o s e p h s o n tunnel

first r e p o r t e d by C h e n et al.

(1), c o n t i n u e to a t t r a c t

junctions, research

interest b o t h b e c a u s e their study can p r o v i d e f u n d a m e n t a l f o r m a t i o n on the d y n a m i c s of fluxons

in such j u n c t i o n s

b e c a u s e t h e y are a c c o m p a n i e d by the

e m i s s i o n of m i c r o w a v e

iation from the j u n c t i o n , w h i c h m a y be e x p l o i t a b l e o s c i l l a t o r appli c a t i o n s understanding

(3)•

in-

(2)

and rad-

in p r a c t i c a l

A l t h o u g h at least a f i r s t - o r d e r

of the u n d e r l y i n g theory has now b e e n a c h i e v e d

(4),

e x p e r i m e n t a l d a t a , e s s e n t i a l b o t h for the r e f i n e m e n t of the

ex-

isting t h e o r y and for the d e s i g n of a p r a c t i c a l

con-

tinue to be r e l a t i v e l y scarce.

The p u r p o s e of this p a p e r is to

r e p o r t some e x p e r i m e n t a l o b s e r v a t i o n s h a v i o r of the steps in j u n c t i o n s and to o f f e r a q u a l i t a t i v e

of the m a g n e t i c field b e -

f a b r i c a t e d in our

Laboratory

e x p l a n a t i o n for this b e h a v i o r .

s u r e m e n t s have b e e n m a d e b o t h for v e r y long s l i g h t l y long

oscillator,

(L >> A^) and for

(L > A ) j u n c t i o n s w i t h a v i e w t o w a r d

our r e s u l t s w i t h those of other w o r k e r s

Squid '80 © 1980 Walter de Gruyter & Co., Berlin • New York

(5).

Mea-

comparing

148 Experimental Details

Since our fabrication procedure for Nb-Pb junctions has been described in detail elsewhere tial features here.

(6,7), we report only the essen-

The Nb base layer is deposited by rf sput-

tering onto chemically cleaned Corning 7059 glass substrates to a thickness of 300-400 nm.

The Nb geometry is defined by photo-

lithography with an acid etch process.

After a chemical and

sputter cleaning of the Nb surface, the tunnel barrier is formed by thermal oxidation in air.

The Pb counterelectrode is depos-

ited by vacuum evaporation to a thickness of 400-500 nm., and its geometry is defined by a second photoresist-acid etch process.

This simple procedure gives quite adequate results since

the Nb film is impervious to the Pb-etchant. The junctions studied were of overlap geometry, i.e., with the bias current introduced in the direction perpendicular to the long dimension of the junction.

This permits considering as a

first approximation that the bias current is distributed uniformly along the junction (8,9) and corresponds to the theoretical model studied in (4). Measurements effected were of the height (in current) and the position (in voltage) of the current steps as a function of the magnetic field applied in the direction perpendicular to the long dimension of the junction.

A controlled field was applied

by means of a long solenoid surrounding the junction within the cryostat.

External fields were screened by means of a high-

permeability shield surrounding the junction and the solenoid within the cryostat.

All measurements were performed at 4.2 K.

149 Results

Fig. 1 shows the current-voltage characteristic for a junction measuring 850 x 20 ym. L/X

= J

54 A/cm.

14 2

For this junction, the normalized length

, the maximum zero-voltage current density J

, and the normal tunneling resistance R

°

= 0 . 1 0 fi.

Fig. 1 - Current-voltage characteristic of a very long junction showing zero-field current steps.

The current steps in Fig. 1 were measured point by point in zero field with a voltage resolution of better than 1 yV.

The under-

lying quasiparticle characteristic was measured by suppressing the other structures with a strong magnetic field.

150 Fig. 2 shows the f i e l d d e p e n d e n c e of the step h e i g h t s lowest o r d e r c u r r e n t steps of Fig. 1. of the first three c u r r e n t steps

for the

We note that the

(I 1 >

is

behavior

essentially

the same as that of the z e r o - v o l t a g e J o s e p h s o n c u r r e n t

(I ).

Fig. 2 - M a g n e t i c f i e l d d e p e n d e n c e of the z e r o - v o l t a g e J o s e p h s o n c u r r e n t (I ) and the first four c u r r e n t step h e i g h t s (I -I ) for ?he v e r y long j u n c t i o n of Fig. 1. 1 4 We b e l i e v e that this fact can be u n d e r s t o o d in terms of the fluxon propagation mechanism responsible

for the c u r r e n t

steps,

as e v i d e n c e d , for e x a m p l e , in studies u s i n g a m e c h a n i c a l

analog

of the long J o s e p h s o n j u n c t i o n

(10):

The l e n g t h of p e n e t r a t i o n

of a m a g n e t i c field into a j u n c t i o n is of the order of A^ at e a c h end,

T h u s , for a v e r y long j u n c t i o n , w h e n the n u m b e r

of

o s c i l l a t i n g fluxons is small, these spend m u c h of their time the a b s e n c e of field.

A c c o r d i n g l y , as a r o u g h

approximation,

in

151 the field d e p e n d e n c e of the a v e r a g e dc c u r r e n t c a r r i e d by the j u n c t i o n in the p r e s e n c e of fluxons is e s s e n t i a l l y that

observe

in the static case, and the p r e s e n c e of fluxons gives rise

only

to a lowering of the m a x i m u m v a l u e s , since the c o n t r i b u t i o n each f l u x o n to the a v e r a g e total c u r r e n t is e s s e n t i a l l y

of

zero.

Fig. 3 shows the f i e l d d e p e n d e n c e of the step h e i g h t s for the two lowest o r d e r c u r r e n t steps in a j u n c t i o n m e a s u r i n g 1000 x 2 120 pm. a n d for w h i c h L/X = 2.1 , J = 0 . 8 6 A / c m . , and R J o ' NN 1.4 fl. A l t h o u g h the p h y s i c a l l e n g t h of this j u n c t i o n is larger

Fig. 3 - M a g n e t i c f i e l d d e p e n d e n c e of the z e r o - v o l t a g e J o s e p h s o n c u r r e n t (I ) and the first two c u r r e n t step h e i g h t s (I , I ) for a s l i g h t l y long j u n c t i o n .

t h a n that of the j u n c t i o n of Figs. 1 and 2, its

normalized

l e n g t h is s m a l l e r due to the m u c h lower c u r r e n t d e n s i t y . a g a i n we note that the b e h a v i o r of the c u r r e n t steps

(I

is quite s i m i l a r to that of the z e r o - v o l t a g e J o s e p h s o n (I ) e v e n t h o u g h the simple e x p l a n a t i o n of this fact

Once and I

current

given

152 above for the v e r y long j u n c t i o n is c e r t a i n l y less for a s l i g h t l y long

applicable

junction.

The g e n e r a l forms of the curves of Figs. 2 a n d 3 are in e s s e n tial a g r e e m e n t w i t h s i m i l a r r e s u l t s r e p o r t e d by R a j e e v a k u m a r al.

(5).

In c o n t r a s t w i t h these a u t h o r s , h o w e v e r , we have

observed a dramatic difference

in the c u r r e n t - v o l t a g e

the c u r r e n t steps for s l i g h t l y long and v e r y long

et

not

forms

of

junctions.

The c u r r e n t steps in a s l i g h t l y long j u n c t i o n do t e n d to be m o r e b r u s q u e l y v e r t i c a l than those s h o w n in Fig. 1, but the t i o n b e t w e e n the two cases seems to be g r a d u a l and

continuous.

We b e l i e v e , a c c o r d i n g l y , that b a s i c a l l y the same f l u x o n t i o n m e c h a n i s m is r e s p o n s i b l e of all

transi-

propaga-

for the c u r r e n t steps in j u n c t i o n s

lengths.

In a d d i t i o n to m o d u l a t i n g the h e i g h t s of the c u r r e n t steps, a p p l i e d m a g n e t i c f i e l d s l i g h t l y m o d i f i e s their v o l t a g e and, in some c a s e s , i n t r o d u c e s q u a l i t a t i v e l y new T h e s e facts are i l l u s t r a t e d in Figs. 4 and 5.

an

positions

structure.

Fig. 4 shows

the

f o r m of the same c u r r e n t step for three d i f f e r e n t v a l u e s of the field.

The d a t a were t a k e n p o i n t b y p o i n t w i t h a v o l t a g e

reso-

l u t i o n of 0 . 1 pV on the first c u r r e n t step of a j u n c t i o n m e a s u r 2

ing 500 x 60 ym. and for w h i c h L/A^ = 2.2 and R

= 1-4 n.

, Jq =

3.7 A / c m . ,

The m a g n e t i c f i e l d i n d u c e s the g r o w t h of a

structure, which behaves

in a m a n n e r s i m i l a r to a Fiske

at the foot of the c u r r e n t step p r e s e n t

in zero field.

step, The

a c t e r i s t i c shows a h y s t e r e s i s , as i n d i c a t e d in the f i g u r e , variations

of the bias c u r r e n t .

M e a s u r e m e n t s at this level

charwith of

r e s o l u t i o n show also a slight but c o n t i n u o u s v o l t a g e

variation

of the step w i t h field.

demonstrat-

This e f f e c t is m o s t c l e a r l y

ed b y b i a s i n g the j u n c t i o n at a c o n s t a n t c u r r e n t on a c u r r e n t

153

Fig. 4 - M a g n e t i c field i n d u c e d s t r u c t u r e in the c u r r e n t step of a s l i g h t l y long j u n c t i o n .

first

step and m e a s u r i n g the f i e l d d e p e n d e n c e of the f r e q u e n c y of the r a d i a t i o n e m i t t e d b y the j u n c t i o n .

Fig. 5 shows the r e s u l t

s u c h a m e a s u r e m e n t c a r r i e d out at L y n g b y w i t h the

collaboration

of the J o s e p h s o n j u n t i o n group of the T e c h n i c a l U n i v e r s i t y D e n m a r k on- a j u n c t i o n h a v i n g p a r a m e t e r s almost identical those of the j u n c t i o n of Fig. 4.

at 10.2 GHz.

the m i d d l e of the first c u r r e n t step

of

to

The j u n c t i o n p a r a m e t e r s

c h o s e n to have the base f r e q u e n c y a s s o c i a t e d w i t h a bias at a p p r o x i m a t e l y

of

were point

(V = 42 yV)

We n o t e that the form of this f i e l d v a r i a t i o n

v e r y s i m i l a r to that s h o w n in Fig. 6 of the c o m p u t e r r e s u l t s of Erne and P a r m e n t i e r

simulation

(3), a n d we note in p a s s i n g

this e f f e c t c o u l d e v i d e n t l y offer an i n t e r e s t i n g

is

that

possibility

for a fine tuning m e c h a n i s m in a m i c r o w a v e o s c i l l a t o r

application.

154

B

Fig. 5 - M a g n e t i c f i e l d i n d u c e d f r e q u e n c y tuning e f f e c t in a s l i g h t l y long j u n c t i o n b i a s e d on the first c u r r e n t step.

(Gauss)

(voltage) current-

Comments

The p r e s e n t p a p e r is i n t e n d e d to p r o v i d e some initial m e n t a l d a t a n e c e s s a r y for a d e e p e r u n d e r s t a n d i n g of long J o s e p h s o n j u n c t i o n s .

experi-

of the

We b e l i e v e that f l u x o n

dynamics

propagation

can be s a i d to be firmly e s t a b l i s h e d as the b a s i c m e c h a n i s m d e r l y i n g the o b s e r v e d p h e n o m e n a .

However,

it is e q u a l l y

un-

clear

that m u c h w o r k remains to be done to c l a r i f y the d e t a i l s of this mechanism, particularly applications.

in the c o n t e x t of p r a c t i c a l

studies,

ana-

log and d i g i t a l s i m u l a t i o n , and e x p e r i m e n t a l m e a s u r e m e n t s

will

probably constitute

this

end.

A j u d i c i o u s m i x t u r e of a n a l y t i c a l

oscillator

the m o s t e f f e c t i v e p r o g r a m to a c h i e v e

155 Acknowledgements

We thank B. G r o z e a , G. P e r n a , ami F. V i c i n a n z a for e x p e r t nical assistance.

We are g r a t e f u l

tech-

to the L y n g b y group for

m i c r o w a v e m e a s u r e m e n t s r e p o r t e d in Fig. 5.

This w o r k was

the sup-

p o r t e d in p a r t by the G r u p p o N a z i o n a l e di S t r u t t u r a d e l l a M a t e r i a and in p a r t by the P r o g e t t o F i n a l i z z a t o of the C o n s i g l i o N a z i o n a l e delle

"Superconduttività"

Ricerche.

References

1. C h e n , J. T., F i n n e g a n , T. F., L a n g e n b e r g , D. N.: 55, 4 1 3 - 4 2 0 (1971).

Physica

2. P a r m e n t i e r , R. D., C o s t a b i l e , G.: R o c k y M o u n t a i n J. M a t h . 8, 117-124 (1978). 3. E r n é , S. N., P a r m e n t i e r , R. D.: J. A p p i . Phys.

(in p r e s s ) .

4. P a r m e n t i e r , R. D.: in S o l i t o n s in A c t i o n , K. L o n n g r e n a n d A. Scott, eds. (Academic P r e s s , N e w Y o r k , 1978), pp. 173199. 5. R a j e e v a k u m a r , T . V . , P r z y b y s z , J . X., C h e n , J . T . , D. N.: p r e p r i n t (1979).

Langenberg,

6. C o s t a b i l e , G., C u c o l o , A. M . , F e d u l l o , V. , P a c e , S., P a r m e n tier, R. D., Savo, B., V a g l i o , R.: Internal R e p o r t 87/77, Istituto di F i s i c a d e l l ' U n i v e r s i t à di Salerno (1977). 7. L a c q u a n i t i , V . , M a r u l l o , G., V a g l i o , R.: ics M A G - 1 5 , 593-594 (1979).

IEEE T r a n s .

8. J o h n s o n , W. J., B a r o n e , A.: J. A p p i . Phys. 41, (1970).

Magnet-

2958-2960

9. B a r o n e , A . , J o h n s o n , W. J., V a g l i o , R.: J. A p p i . Phys. £ 6 , 3 6 2 8 - 3 6 3 2 (1975). 10. C i r i l l o , M.: G r a d u a t i o n t h e s i s , P h y s i c s degree p r o g r a m , U n i v e r s i t y of S a l e r n o , O c t o b e r 1979 (in Italian).

PROPERTIES OF COHERENT VORTEX MOTION IN Pb-Nb-Pb ION IMPLANT VARIABLE THICKNESS BRIDGES.

P. Crozat, G. Vernet and R. Adde Institut d'Electronique Fondamentale, Bât. 220, Université de Paris XI, 91405 ORSAY (France).

The values of the coherence length £ and of the effective penetration depth >-e££ relative to microbridge

dimensions

(geometrical dimensions of bridge, relative thickness of bridge and banks) are crucial to obtain vortex motion in a single row

^ . There has been several experimental studies of micro2-5 bridges to investigate situations where motion occurs We report here on the dc and microwave properties of variable thickness ion implant Pb-Nb-Pb bridges which present

characte-

ristic feature of coherent vortex motion. These results follow from a choice of particular microbridge parameters ^ which altogether constitute favorable conditions to have one row of vortices in the central part of the bridge

: a/ Large Pb bank

thickness D (500-800 nm) > Xp^ such that vortices are strongly repelled by the banks, b/ The implantation of the Nb bridge brings film uniformity compared to the coherent length

(inho-

mogeneities due to defects = 5 nm), a large increase of (4001) and resistance

(2001) while

drops only very slightly

(10-151). c/ As a consequence of b/bridges with micrometric dimensions are much smaller than * e £ £ . Therefore a single row of vortices is strongly repelled by both banks. A detailed description of the technology and film characterization of these bridges is given elsewhere ^ . The

implanted

Nb bridge thickness is 30-42 nm, their width is .5-4 pm, their length 0.8-4-5 um. The parameters of the bridges

Squid '80 © 1980 Walter de Gruyter & Co., Berlin • New York

considered

158 here are g i v e n in T a b l e Table

1.

I.

Bridge

d

d0

L

W

Tc

Rn

nm

nm

pm

pn

K

n

^(O) A

Co)

124 B2

33

BOO

1,2

1,2

6,8

7

8,,5

110 C2

33

BDD

4,5

1,8

6,6

15

8,,5

750

143 A1

33

80D

0,8

2

6,2

4,5

7,,5

1200

-1/2 S(t) = 5(o) C1 -1 ]

750

x .„(t:) = X ..Co) (1-t)"1 eff eff

Figure 1 represents a typical IV characteristic for a short bridge (1-2)jm) which presents two main parts. At high voltages (> 200 ;JV), the VIC is well 3/2 interpreted by the depairing model with a critical current I 2 = I 0 0~t) Moreover the value of I

fits the depairing G-L expression using the micro-

bridge parameters of Table 1. The low voltage part of the VIC is given for several characteristic cases in Figs 1, 2, 3 and 6. We have compared its main properties with the two principal models related to microbridges in the vortex regime

1,7

We

have found a qualitative agreement with the work of Aslamazov and Larkin

159

Figure

2.

Figure

L o w p a r t of the Bridge.

I-V c a r a c t e r i s t i c

3.

of a 4.5 u m

Long

The first section of the VIC appears typically at a reduced temperature t ^ 0.95 for a 2 pm wide bridge. The determination of the precise (1-t)= temperature dependence of I

is made difficult since it cannot be measured

up to T . Therefore the experimental value of = lies in the range l and f* is a constant to be determined by (4). For short bridges the following inequality is satisfied

Squid '80 © 1 9 8 0 Walter de Gruyter & Co., Berlin • New York

172

•i

I * to

»

t*- x f

+

r.zr'

(6)

so that C-f

*

($)(/>*-

*/>*+

*

J

( 7

)

Substituting (7) into (4) and (5), the integrals are easily calculated to yield '

/

--J

v

.

RT, .

...

(8)

•

The current can be found from (8) by iteration, since

(9) I.

Here after we shall limit our discussion to the first order approximation. Through iteration, (8) and (9) become f t - I

? : ( ' - & ] * {

I-

f¿ ( ' - ¿ ' " ¿ f i r / - * ) - - ! ? ] ! * }

(10)

Taking sines and cosines of both sides of (11) gives H r . ' a - f r ] * cosf

- ,-j t K c - e r f t e c s ? * g

i r . ' c - r°>)V-»« X

r

( 1 2 )

(13)

^

®he quantities />/ and ( f.V» -fcVjcan again be found by iteration from (12). /•=

After substituting the results, (10) becomes I

4-H*s i a z hz. f 1503. (1975). 2. Vystavkin, A.N. et al.: Revue fliys. Appl. 79 (1974). 3. Levinsen, M.T., Ulrich, B.T.: IEEE Trans. Mag. MAG-V1., 807 (1975).

EFFECTS OF MICROWAVE RADIATION ON GRANULAR A£ MICROBRIDGES* B. Dwir and G. Deutscher Department of Physics and Astronomy Tel Aviv University, Ramat Aviv, I s r a e l .

Introduction Microbridges of several geometries and dimensions were fabricated from granular h i thin films of different r e s i s & i t i e s .

In response to micro-

wave radiation, both Shapiro-steps and enhancement of the critical current and Tc were observed in variable-thickness bridges.

In uniform

(Dayem)bridges, heating overwhelmed the quantum effects and neither of the above

effects were pbserved.

Micro bridge Fabrication Granular As, films were prepared by evaporating hi in an oxygen atmosphere (press. 3 x 10"^ Torr) onto room temperature glass substrates. Dayem microbridges were fabricated by photolithographic masking and etching.

Their dimensions were 2.5 x 7.5 ym (WxL) and 0.6 x 1.2 um and

their thickness 1000 A . Variable-thickness bridges (VTB) were made by evaporating a dual-layer structure: 1000 A of pure Al on top of the granular material.

At f i r s t

a uniform bridge was fabricated with the above-mentioned technique. Then, the pure A i layer was etched away only in the bridge area, leaving a thin (1000 A ) granular bridge between thicker (2000 A ) banks.

This

construction not only provided better cooling of the bridge i t s e l f , but also decreased heating of the banks by the microwaves, as well. *

Supported in part by The I s r a e l i Research Council for Research and

Development and The Karlsruhe Nuclear Research Center

Squid ' 8 0 © 1 9 8 0 Walter de Gruyter & Co., Berlin • New Y o r k

178 Electrical Measurement Setup The voltage across the microbridges was measured differentially by a PAR 113 preamplifier and recorded vs. current.

To avoid ground loops,

the driving current was supplied by a battery-powered, opto-isolated current source.

The bridge was inside a superconductive shield and

the whole measuring system was magnetically (y-metal) shielded.

The

residual magnetic f i e l d in the v i c i n i t y of the bridge was less than 4 mG

, and the total equivalent noise at the bridge was less than

3 nV//Hz. Microwave radiation at 10 and 30 GHz was coupled to the microbridges

by

a waveguide, variable attenuators in the waveguide permitting measurements at different microwave power levels.

The temperature was stabilized

electronically to better than 0.2 mK, and varied between 1.5 and 2.3 K.

Effects on Various Bridges 3/2 The c r i t i c a l current of Dayem bridges varies as (1 - T/Tc) seen from f i g . l .

as can be

I t agrees with the Ginzburg-Landau theory for dirty

superconductors near T c (see also r e f . l ) .

The c r i t i c a l temperatures were

2.213K and 2.260K for p=100 and 1000 u« - cm respectively. 5 6 The 2 extrapolated c r i t i c a l current density at T = 0 i s 5.10 and 10 A/cm . The effect of microwave radiation on I c can be seen in f i g . 2 , which shows typical I - V curves of the microbridges at different microwave power levels.

To investigate the p o s s i b i l i t y of heating effects as the main

cause for the decrease in ¡ c with increasing microwave power, use i s made of the relation between I and T from f i g . l . The change in temperature of the sample ,caused by microwave power P radiated on it, i s taken as: 4 4 Tg = T^ + aP where T^ i s the Helium-bath temperature and a an (unknown) constant (see ref.2). I (T) = I (0) (1-T/T )

When we put Tg = ( T ^ + a P ) ^ in the relation 3/2

, we obtain:

179 To confirm t h i s formula, we p l o t ( f i g . 3 ) the function . I (T ,P),2/3v4 T c (1 - (j ^ ' '

against

Puw(I c (0) and T c are known from f i g . l ) .

The l i n e a r r e l a t i o n can be seen c l e a r l y , which shows that the decrease i n I

i s due to heating by microwave power.

The heating was strong enough

to suppress any microwave induced steps, as can be seen from f i g . 2 . In the VTBs, heating was not so s t r o n g , and enhancement o f I An example o f the enhancement i s seen in f i g . 4 , where I a g a i n s t microwave power P.

was observed.

i s plotted

The c r i t i c a l current increases with increas-

ing power to a maximim, then decreases quickly to zero.

A graph of the

value of the maximum I

(as a function o f microwave power), I , for c rt /^ cm d i f f e r e n t temperatures, i s shown i f f i g . 5 , where I , as well as 2/3 I are plotted a g a i n s t T. Again there i s a l i n e a r dependence, and the c r i t i c a l current density at T=0 (extrapolated 1 .) i s around 5.10

C

O

A/cm .

From f i g . 5 , T c can be found to be 2.030K, and the microwave r a d i a t i o n seems to increase T

to 2.05 K (1%). The maximum enhancement of T c c which was observed was about 2%. Those orders of magnitude agree with previous measurement o f T frequency used (10 GHZ)

enhancement i n pure

As. films ( r e f . 2 ) .

The

was high enough to break p a i r s , since the

measurements were done near T .

Higher frequency (30 GH z ), which was

l a r g e r than A ( T ) , did not cause any enhancement i n I .

A l l these

r e s u l t s are with q u a l i t a t i v e agreement with nonequilibrium q u a s i p a r t i c l e e x c i t a t i o n theories

(ref.3).

Microwave-induced steps were present in the I - V c h a r a c t e r i s t i c s

(fig.6).

They were however, limited to the v i c i n i t y of T c and to low microwave powers.

At low temperatures the I - V c h a r a c t e r i s t i c s became h y s t e r e t i c

and no steps could be observed.

The step height i s plotted against

microwave power for several temperature in f i g . 7 .

There i s q u a l i t a t i v e

agreement with theory ( r e f . 4 ) , although exact comparison with Besselfunctions i s hard to make. while the gap A(T) ^ 20yV to the gap.

The I c R n product was about 40yV at T=2.02, and the radiation frequency (10 GHz) comparable

180 References 1.

G. Deutscher, Rev. De Phys. App. 8,127 (73).

2.

J.A. Pals and J. Dobben, P.R. B. 20,935 (79).

3.

J . J . Chang and D.J. Scapalino, J . Low Temp. Phys., 29,477(77).

4.

E. Ben-Jacob, U. Braiman and J. Imry, to be published.

181

182

M) Fig. 2:

I-V c h a r a c t e r i s t i c s of Dayem bridge f o r various microwave powers.

183

Fig. 3:

Change in I

of Dayem bridges as a function of microwave

power.

184

185

Fig. 5:

I

and I

o f VTB as

f u n c t i o n o f temperature.

Fig. 7: Step height as function of microwave power for various temperatures.

JUNCTION AND CIRCUIT NOISE

FLUCTUATIONS

John

ANALYSIS

Clarke

D e p a r t m e n t of P h y s i c s , U n i v e r s i t y of C a l i f o r n i a , B e r k e l e y , and M a t e r i a l s and M o l e c u l a r R e s e a r c h D i v i s i o n , L a w r e n c e B e r k e l e y Laboratory, Berkeley, California 94720

I.

Introduction

This

paper

tions, rf

briefly

and

the

SQUIDS.

tively

as

first

these discuss

resistive in w h i c h the

SQUID,

for

II.

We are

junctions

arising

from

junction

treatment

only

a

juncdc

the RSJ

should

is a p p r o p r i a t e , in w h i c h

and

in

model.

noise

the limit

and

resisbut

and m i c r o b r i d g e s by

Nyquist

in

el R / k „ T ^ l o B

for

capacitance,

can be a p p r o x i m a t e d

the limit

limit

and

compared of

frequency

Noise

in

consider produced

theory

is used

the r e s u l t s

are

The q u a n t u m

limit

the p r e d i c t e d

importance low

to

valid

zero

of

el

O

in

so We

the

R/kT>fiu, Eq. (5) reduces to Eq. (3), while in the D limit k T

includes

=

tank

in

(15)

.

preamplifier

T

,

substantially

are

circuit

and

o

4 / 3

\

the

voltage 17-19

T

u ^ / 2 tt , i s

a as

2

co rf

B

steps

across

the

shown

e(a)/lHz

lifier

the

of

2 , r k

the

defines

bath temperature. .s7,18,20,21

where

in

frequency,

measured

If

o > 7

tilts

SQUID.

can

Webb"'"*' f i r s t

between

density

acteristic

it

and

SQUID,

uncertainty

transitions

spectral

noise

a

rf

be

S ^

aiong

SQUID

calculation

Kurki jarvi

The

the

a

=

of

S^i')/2L 9

the to

preampe ^ / l H z

do

197

Equation

(18)

demonstrates

that

for

fixed

a and

( e f f )

T

the (e f f )

^ noise

energy

tends

to

increase

importance amplifier only

does

when

the

bution

scales

of is the

of

the

tank

in

to

the

to

characterize

a

SQUID,

flux

list It

II is

lists

of

be

the

noted

where

K

the

input

circuit.

is

circuit,

noise

for

The

noise

energy

a

with

cooled

cooled device SQUID than

the

was (v),

limited on

the

the

predicted.

tend

input

'

to

preNot

decrease

the

coil

in

is

contri-

is

coupled

necessary

Amplifier by

the

turn

Thus,

SQUID

are

just

to

and to

produces

there

circuit,

of

six

be

rf

as

tank

induce

a

voltage

current

and

for

dc

the

uncorrelated.

noise

is

energy

energy more

the

be

and

model.

this

exhaustive. divided

the

by

SQUID

referred

to

and the

characterization

(iv) The

noise

became

noise.

seems noted,

to

be

is

in

good

advantage

demonstrated.

preamplifier

should

been

thus

useful

(iii)

clearly

hand,

has

between

is

again

than

of

purposes.

(i), of

SQUIDS;

rather

coefficient

a much

other It

relative the

temperature.

addition,

assumed

noise

intrinsic

by

'

representative

SQUIDS

the

an

which

usually

predictions

'vO.lK,

'

input

practical

of

in

the

whether

SQUIDS

be

is

on

T^

insignificant.

when

circuit. the

are

preamplifier

to

in

The

most

general,

temperature but,

'

SQUID

coupling

and

the

ment

the

that

the

In

bath

downconverted

performance

to

K^,

input

are

rf

practice,

detailed noise analysis 1 8 ly 2 2 2 3 24

input

they

intended

should

in

the

becomes

SQUID,

circuit.

sources

Performance

Table

a more

the

although

noise

in

largely

or

cooled,

dc

noise

in

noise

is

circuit

the

depends

temperature

the

noise

source

SQUID,

of

current

voltage

B.

case

rf

real

noise

room

increased.

terms

preamplifier

As

circuit

is

two

preamplifier

the

However,

as

the at

as

When

of

using

(iii)

was

negligible, The

and

sensitivity

substantially

however,

that

agree-

the

the of

higher value

198

•a N 01 3S ^ >1 3 Z5 co m -e- Ml cn a; O g iH

O m

•a o ra H T) U -H -ri -H M-l M M 1 -O T> COG •H U *H í O H 4J -H ^ B O

•H -H

oCM 1 JH B o ra rH c c CM •H 3 ra rH 4-1 ra MH •1-1 r—1 4-1 O "O ,1 p. C I—I C ra -H •H a) •H 4J O .C C C O C U 4J C o P. O 0 O 4-1 3 -H 4J 4-1 /-s •H •H > •ri •H •w'

4J c •H O p.

r^ CM 4-1 a) O H ra o u « c 1 O CM O

'—*

1>

—'

00 IN 4-1 C rH

•u ra ra 4-1 o Vi T3 B ra4-1 -rl •H 4-1 C O O c CU IH P. o 1 o o 0) 4-1 >4

•H >

•—'

199 of a listed was not given in ref. earlier for

27, but was

paper on the same SQUID by

this discrepancy

(vi) w e r e operated

the same group.

are not clear.

at X - b a n d .

At

taken from The

F i n a l l y , devices

these frequencies,

an reasons

(ii) and the model

is certainly

invalid, and one cannot make any c o m p a r i s o n s

tween

and

theory

improve

experiment,

significantly and

It is a p p a r e n t

that by using

amplifiers

energy

of

the use of cooled and

It is possible the 400MHz at

V.

1/f

(i).

can

device

that one could

resistance

of

more

around

by

going

complicated

improve on

a great

increase

frequency

one

the in

could

However,

the m o d e l , one would

>300i2, implying

to use a tunnel

noise

straight-

GaAs-FET p r e a m p l i f i e r .

in the range of validity be necessary

on the

sensitivity

considerably

(say) 3GHz, at which

and/or

At frequencies

is relatively

SQUIDS without

to use a cooled

require a junction probably

rf frequencies

One does gain

the system becomes

cost by working to remain

SQUID

GaAs-FETS

inexpensive.

expensive.

still hope

higher

toroidal

forward

sensitivityof

of the X-band

one can improve substantially

400MHz,

and

that one

Giffard.

the 20MHz

to 10GHz, but

it seems unlikely

on the p e r f o r m a n c e 28

of H o l l e n h o r s t

cooled

but

be-

that it would

junction.

Noise

Relatively

little attention

devices

developed

serious

limitation

has been paid

recently.

to 1/f noise

In fact, 1/f noise may

on the low frequency

performance

in

the

become a of

SQUIDS.

29 Clarke and Hawkins biased

resistively

spectral

density

measured shunted

the voltage noise

tunnel junctions

at frequencies

between

and

about

in

current-

found

a 1/f

0.1Hz and a few

10's of Hz. The noise at lower frequencies was not 2 The spectral density was proportional to (3V/3I ) , oi that the noise involved 1/f f l u c t u a t i o n s in I , and

measured. indicating ^ to (dl /dT) ,

200 suggesting

that

temperature

the critical

fluctuations.

the spectral

densities

current

With

for

fluctuations

arose

these a s s u m p t i o n s ,

the voltage

one

fluctuations

from finds

to be

given

by29 3Acvf \ d T )

\3I

w h e r e A is the junction area, and

c^ is the heat capacity

unit area

of junction with a thickness

coherence

lengths of

is not likely

equal

the two s u p e r c o n d u c t o r s .

to be valid

the spectral density

of

down

to very

flatten out as the frequency

fluctuations

is lowered.

sion should

give at least a rough

frequencies

above

(say) 0.1Hz.

However,

lower bound

In a dc SQUID,

will produce both a v o l t a g e and a circulating however,

the c o n t r i b u t i o n

overall v o l t a g e noise it.

We can adapt

of

Equation

low f r e q u e n c i e s

the temperature

of a

to the sum of

the

(19) because

must

this

expres-

of the noise this noise current

at source

noise;

the latter

is relatively

(with V ^0) to the

is shown together with the input VSWR of the GaAs FETAmp versus GaAs varactor voltage on the FETAmp input matching circuit.

We observe that

below 3K and = 1

x

6

decreases rapidly as 1g a t h is reduced

/

lo

The corresponding intrinsic energy We attribute the temperature

(i.e. ) to the

onset of fluxoid tunnelling

in the SQUID ring (4). For an unlocking probability of 10 7(5) the maximum measured slew rate attained in this system was 3.8 x 106$o/sec. at a modulation frequency of 3 MHz (T Bath 4.2K). -Although external noise plays a part in unlocking such

209

Figure 1

10.0 f -


few degrees) above 3 MHz, leading to relatively large error fluxes being fed back into the SQUID ring (5).

With some modest improvement in summer

bandwidth we expect to attain a fully-locked slew rate > 6 x 10 6 $ o /sec in our UHF magnetometer. Hie system noise at 1.8K appears to be set by noise from the room temperature electronics and external, particularly low frequency (< 1 kHz) external noise.

It seems likely that with (i) lower noise second stage

UHF amplification (ii) more reverse isolation between the tank circuit and the room temperature electronics and (iii) better electromagnetic shielding, energy sensitivities ^ h x 1 J/Hz. could be achieved.

References 1.

Long, A.P., Clark, T.D. and Prance, R.J.: Rev. Sci. Instrum. 51 (1), 0085 (1980).

2.

Kurkijarvi, J.: Phys. Rev. B^, 832 (1972).

3.

Jackel, L.D. and Buhrman, R.A. : J. Low Temp. Phys. 19_, 201 (1975).

4.

Prance, R.J., Long, A.P., Clark, T.D., Widom, A., Mutton, J.E., Sacco, J.E., Potts, M.W. and Megaloudis, G.: "Evidence for Quantised Energy Levels in an AC-biased SQUID Magnetometer, submitted to Physical Review Letters.

5.

Brunet-Brunol, D., Pascal, D. and Duret, D.: J. Appl. Phys. 50(1), 521 (1979) .

ON THE 0 nr -DEPENDENCE OF RF-SQUID NOISE

R. C r i s t i a n o * , S.N. Erne and H. Luther Physikalisch-Technische Bundesanstalt, I n s t i t u t B e r l i n , AbbestraBe 2-12, D-1000 B e r l i n 10, Germany

Abstract The 0 D £-dependence of noise in the RF-SQUID i s investigated by a n a l y t i c and numeric c a l c u l a t i o n s and by experiments on a Nb-point contact SQUID. The r e s u l t s lead to c r i t e r i a for optimum signal to noise r a t i o in the SQUID and to complications in the treatment of the spectral power d i s t r i bution of the noise. Introduction Until now work on SQUID noise only has involved c a l c u l a t i o n s of the noise amplitude of elementary sources and t h e i r dependence on various parameters of the SQUID /1-4/. However, in experiments on Nb-point contact RFSQUIDs working in the non hysteretic

DIFFERENT

ARBITRARY S C A L E S

regime we have observed, that the amplitude of the noise in the tank c i r c u i t voltage Vj depends on the applied DC magnetic f l u x

too.

Q u a l i t a t i v e l y t h i s experimental behaviour may be v i s u a l i z e d by the example shown in Fig. 1, where the amplitude V-j. of the tank c i r c u i t v o l tage and the RMS-value (? of the noise voltage superimposed on V^. are plotted versus 0 n r . To study

cDDC

-lOrt

FIG. 1

*Present address: Scuola Di Perfezionamento In Scienze Cibernetiche E Fisiche D e l l ' Università Di Salerno -

Squid '80 © 1980 Walter de Gruyter & Co., Berlin • New York

Italy

212 this dependence and to analyze its consequences for the operation of the RF-SQUID are the aims of this paper. Theory The two intrinsic noise sources considered here are the dissipative part of the current through the weak link and the dissipation in the tank circuit. We can represent the first of these two noise contributions by an additional stochastic flux superimposed on the unperturbed DC-flux and the second one by fluctuations of the RF-current in the tank circuit. Both lead to a random

variation of the actual SQUID output signal around its determiA

nistic (i.e. noise free) value V T . Due to the nonlinear relationship Vy(0Q£, I^p) (whereby I^p is the RF-bias current amplitude) the amplitude A V-p of these fluctuations will depend on the SQUID working point. This can be qualitatively seen from the shape of the functions V-j-CIRp) shown in Fig. 2 for two values of f DC' Expanding in differential form the output voltage function w ~ V-p (I R p> 0 D C ) around the deterministic working point we obtain RFO' DCO

0>n/2

FIG.2

Z|VT

=

9 VT 3i„

where in general A I R p and

A IRF

3V 3(t>DC

AK

are related to the amplitude of the

fluctuations in the tank circuit and in the SQUID loop respectively. A

'SV-TX'A

can be defined as the sensitivity Sn[- to the tank circuit noise RF to the dc-flux noise. B c a s the sensitivity S ^

and

213 The following theoretical analysis is based on the framework of the general theory of the non hysteretic SQUID /5/. In a first step we calculate S R p and S

-

2 P' ± H = 2c + V()

(2)

V(0) = ¿ « D - * x ) 2 - i c ^ 0 3 2 7 1

(3)

where the dissipative normal current term has been left out as it is difficult to incorporate in a Hamiltonian formalism. Apart from a number of qualitative remarks we will neglect this potentially all important term in the present analysis. In Eqs. (2-3), C is the capacitance and i

the critical cur-

rent of thé Josephson junction, L the inductance of the SQUID ring and o = h/2e = 2.07 x 1 0 - 1 5 V . The solutions of Eqs. (2-3) are the eigenfunctions of H in • in the potential of Eq. (3) in some given external flux . The interesting quantity in the context of fluxoid transitions is the lifetime of the flux in the metastable valley of V() for just below the critical

at which that particular

valley is no more a minimum of V(). In the quantum case the WKB method gives wave functions part of which are essentially localized in the metastable hollow. It is clear that the lowest of these localized states is roughly the harmonic oscillator ground state in the small valley. The third order polynomial in (J) 2iri 3®

,



r* -62¥A*x]

(4)

c

o

is an excellent approximation to the potential V( =

ai o Mo to "O

CTI m

>

ai o

CM CM UD

00 OO

ai •i—

— ,IO > -

1—1 1—1 ai IO t—

so

•p •r— C 1—1 XJ c IO 1/1 e o -(->

IO 3 a. o a. ai DE IO co

3

•n /L. On Tt o the other hand, a thinner weak link permits operation over a m u c h wider temperature range since the critical current saturates at low temperatures.

Weak links w i t h a wide oper-

ating range in temperature generally have T c < 1 0 K . illustrates a series of rf current-voltage taken at 20 MHz for a SQUID with a T

~5K.

Figure 5

characteristics This particular

device responds to external flux down to approximately 3.5K below w h i c h the response degrades.

Figure 6 illustrates

the range of behavior of the critical current and SQUID operation as functions of temperature for several samples. is p l o t t e d only for the region of SQUID operation.

Data

Note that

341

Fig. 5. Similar to Fig. 4, for a device with a thinner w e a k link. Curve (e) in Fig. 6 shows the temperature dependence of its critical current. for lower values of the critical current the curves are linear in temperature w i t h a small exponential tail.

Some of these

devices have b e e n measured b o t h at 20 MHz and 10 GHz and found to exhibit a Josephson critical current temperature dependence over m o s t of their range of operation (18).

The

noise properties of these devices are b e i n g characterized by measuring the fractional step rise parameter "a" of Jackel and Buhrman (19) and found to b e intrinsic over some portion o f the range of operation.

The details of these measurements

will be reported elsewhere. In our own experience using NbN, an important criterion for success seems to entail a granular film structure.

Recent

experiments (20) o n such films in high magnetic fields indicate t h a t classical vortex flow is totally absent.

Apparently

the vortices are strongly pinned, and the development of

342

Fig. 6. The temperature dependence of the critical current, in units of /L, for several rf SQUIDs using granular NbN weak links. voltage across a film is by some mechanism other than vortex motion.

W e may speculate that the criterion for good Joseph-

son behavior is strong vortex pinning in the weak link.

This

limit has not, to our knowledge, b e e n addressed theoretically to date.

In granular hi films the pinning forces are weak,

presumably because the characteristic grain size is small compared to the coherence length (21).

The grain size of

our N b N films, o n the other hand, is of the same order as The concept of a vortex becomes somewhat tenuous in this case. To the extent that such a concept remains valid, it is plausible that pinning forces m i g h t be quite high in these granular films.

A n alternative way to think about the granular

N b N devices is in terms of some sort of synchronization of

343 Josephson tunnelling currents between individual grains. Such concepts could not, however, be extended to cover the instances mentioned above of Josephson behavior in nongranular systems. In conclusion, there are strong indications that nearly "ideal" Josephson performance can be obtained in weak links made from low coherence length materials.

This raises

exciting prospects for the use of these materials in devices, in view of their obvious superiority in ruggedness and stability to the soft superconductors.

The possibility of

making useful devices which operate at temperatures achievable with simple-closed cycle refrigerators cannot be discounted . The authors wish to acknowledge useful and stimulating conversations with S. Wolf and D. Gubser.

REFERENCES 1.

Likharev, K.K.: Rev. Mod. Phys. 51, 101-159 (1979).

2.

Laibowitz, R.B., Broers, A.N., Yeh, J.T.C., Viggiano, J.M.: Appl. Phys. Lett. 35, 891-893 (1979).

3.

Likharev, K.K.: Sov. Phys. JETP 34, 906-912 (1972).

4.

Aslamazov, L.G., Larkin, A.I.:

5.

Boone, B.G., Arrington, C.H.III, Wang, L., Deaver, B.S.:

6.

Gubankov, V.N., Koshelets, V.P., Ovsyannikov, G.A.:

Sov. Phys. JETP 41,

381-386 (1975). IEEE Trans. Mag. MAG-13, 735-738 (1977). Sov. Phys. JETP 44, 181-186 (1976). 7.

Crozat, P., Vernet, G., Adde, R.: this conference.

8.

Golovashkin, A.I., Lykov, A.N.:

Sov. Phys. JETP 47,

110-115 (1978). 9.

Kuriki, S., Gundlach, K.H.: J. Appl. Phys. 50, 3514-3517 (1979).

344 10.

Harris, E.P., Laibowitz, R.B.: IEEE Trans. Mag. MAG-13, 724-730 (1977).

11.

Falco, C.M.: private communication.

12.

Gu, J., Cha, W., Gamo, K., Namba, S.: J. Appl. Phys. 50, 6437-6442 (1979).

13.

Rachford, F.J., Wolf, S.A., Hirvonen, J.K., Kennedy, J., Nisenoff, M.:

14.

IEEE Trans. Mag. MAG-13, 875-878 (1977).

Gubser, D.U., Wolf, S.A., Francavilla, T.L., Feldman, J.L.: Inhomogeneous Superconductors-1979, AIP Conf. Proc. No. 58 (American Institute of Physics, N.Y., 1980), pp. 159-168.

15.

Ciaassen, J.H.: to be published in Appl. Phys. Lett., May, 1980.

16.

Russer, P.: J. Appl. Phys. 43, 2008-2010 (1972).

17.

Ciaassen, J.H., Richards, P.L.: J. Appl. Phys. 49, 4117-4129 (1978).

18.

Rachford, F.J., Cukauskas, E.J.: Appl. Phys. Lett. 35,

19.

Jackel, L.D., Buhrman, R.A., J. Low Temp. Phys. 19,

881-884 (1979). 201-246 (1975). 20.

Gubser, D.U., Wolf, S.A.:

proc. of Conf. on Ordering in

Two Dimensions, May 28-30, 1980. 21.

Abeles, B.: Applied Solid State Science, Vol. 6, ed. Raymond Wolfe (Academic Press, N.Y., 1976), pp. 73-78.

FABRICATION AND CHARACTERIZATION OF THE FILM PARAMETERS IN ION-IMPLANT Nb BRIDGES WITH THICK Pb BANKS

P. C r o z a t

a n d R.

Adde

Institut d'Electronique Fondamentale, Paris XI, 91405 ORSAY (France).

We present

fabrication

superconducting micrometric and have

techniques

thick

Pb b a n k s . W e d e s c r i b e

in detail

rization using

the

line

Nb

with

the

evolu-

conditions.

and their

First

Then we

caracte-

test films. We finally

of t y p i c a l

Pb-Nb-Pb

main

implantation

quantitatively

implantation effects

superconducting

dis-

bridges.

fabrication : are e v a p o r a t e d w i t h e - b e a m

q u e o n h e a t e d Si s u b s t r a t e s Torr). The

resulting

ion

of t h e f a b r i c a t i o n t e c h n i q u e s .

T h i n 35 n m t h i c k N b f i l m s (= 1 0 " 8

of t h e

of Nb b r i d g e s

w i t h the e x p e r i m e n t a l

the m a i n p a r a m e t e r s

Microbridge

Université

and m e a s u r e m e n t s

and electronic parameters

we give a short account

cuss

220,

d i m e n s i o n s w h i c h are w e a k e n e d by

t i o n of t h e p a r a m e t e r s analyze

Bât.

films

(400°C)

are

in a c l e a n h i g h

fine grained

techni-

vacuum

( g r a i n s i z e = 20 nm)

i n a g o o d d e g r e e of b r i d g e u n i f o r m i t y . A n a r r o w

(0.S to

4 urn w i d e , u p to

100 u m l o n g )

is p r o t e c t e d 1

resist using microscope the p r o t e c t e d a r e a , Nb cal e t c h i n g . T h e n t h e fined with AZ

projection

l e n g t h of the b r i d g e

1350 S h i p l e y r e s i s t

'

c l e a n i n s i t u the N b s u r f a c e

(%.0.8

(thickness

Backsputtering

just prior

(500 to 800

Squid '80 © 1980 Walter de Gruyter & Co., Berlin • New York

nm).

with

2

. E x c e p t in

is r e m o v e d b y p l a s m a e t c h i n g

in surface before d e v e l o p m e n t . t h i c k Pb e l e c t r o d e s

lithography

Nb

or pm)

= 1 pm) is u s e d

chemiis

de-

hardened to

to t h e d e p o s i t i o n

of

346 The technique of hardened surface resist presents two important advantages

: a/ it insures good inverse profile of the 3 resist leading to adequate separation between the lead films deposited on the Nb film, and on top of the resist, even for thick lead films

(800-1000 nm); b/ resist surface hardening

protects the resist against polymerisation during the processes of back sputtering and Pb film deposition which The large thickness of the Pb electrodes

follow.

(500-800 nm) compared

to the Nb film and the good acoustic match of Pb with Nb ^ insures that the non linear properties are well limited to the bridge area. This result is important since it appeared tly that acoustic matching of superconducting usual substrates

recen-

films to the

(glass, Sapphire, Silicon) is rather poor

Ion implantation and superconducting

4

film properties:

Ion implantation is performed simultaneously on microbridges and test films. In Pb-Nb-Pb bridges with thick banks, the latter are acting as a mask during implantation, without modification of the bank properties.

Implantation in the Nb test

films are operated through metal masks with a geometry

adapted

to the measurement of T , p and H ^ f t ) . Our previous study of implantation in superconducting Nb films had shown the importance of the created defects on the weakening of superconductivity ^ . More precisely, we have shown ^ recently that in implanted Nb films the lowering of T c and the increase of p are proportional and vary as the square root of the energy deposited

in the lattice. As implantation of some species may

produce secondary effects

(chemical for implanted

oxygen,

magnetic for implanted rare-earths), we have selected here argon implantation which creates only defects in Nb. We have performed multiple implantations

in order to obtain relatively

uniform profiles adapted to Nb films with thickness between 30 and 45 nm. They are characterized by

: Argon

ion energy :

347 70 keV, 20 keV; relative dose

: 0.75, 0.25.

Measurements of T c and p in Nb films prior to

implantation

indicate that there is no clear correlation between films deposited under different conditions, i.e. for small variations of T c

(8.5 - 8.8°K), large uncorrelated variations of

the mean free path are observed

(

between 8 and 4 nm). On the

other side, the evolution of the normalized (1-T ./T

parameters

•), Ap = p• - p ., and to a lesser extent £.(t)/e

appear very well correlated 1 for argon implantation).

in implanted Nb films

.(t)

(see Fig.

It must be noted that correlation

in the evolution of the different film parameters also occurs under film modifications due to processing annealing, backsputtering

(e.g.

temperature

...). A typical result is represen-

ted in Fig. 1 (squares) and shows film evolution under proces15 2 sing equivalent to a fluence of 10 ions/cm .

Ap

Ap

jufl.cm 1 -Tc,i/Tc,ni

0 IONS/CM2

Figure 1 : evolution of T , p and 5 m

implanted Nb 15 13 15 test films for fluences between 3.10 and 6.10 / 2 ions/cm .

348 Besides the one half power dependence of ¿ T c with energy deposited in the lattice, the results in Fig. 1 are

characterized

by the proportionality between AT c and Ap on one side, and a very weak variation

of

( t ) / g ( t ) . This latter result ap-

appears surprising at first sight since it is often assumed in the litterature that g s h o u l d drop strongly under

implantation.

The correlated decrease of T

and increase of p we have obserc ved in Nb films is a characteristic of materials with a high T c associated to a high density of states N(Ep). It has been observed in implanted A15 alloys that the above effects

corres-

pond to a decrease of N(Ep). We have developped a quantitative analysis to interpret the evolution of the electronic and 7

superconducting properties of Nb implanted films

. We have

shown that the decrease of T c is essentially related to a decrease of the electron-phonon coupling coefficient A. The latter is well interpreted by a decrease of N(Ep) proportional to X(1+A) (our experimental results verify the assumption of g Varma and Dynes ). 3"

2.5-

2

1.5-

0.9

"•8

T

c.l'T c ,ni

Figure 2 : Evolution of g

0.7

versus T

0.6

0.5

degradation.

349 Considering the evolution of

> we have in a first

step calculated the variation of C Q = (0 .1 8 H

v p > ) / (n k g T c )

normalized to its non implanted value as a function of T ./T • r cr c m We obtain with a 10-20°s p r e c i s i o n . s t r o n g l y increases with implantation

(Fig. 2) due to the decrease of T , the in-

crease of Vp, and the slight decrease of the strong

coupling

coefficient n • Then the Table 1 shows with some typical examples that the ratio

(t)/£ n i(t) has only small variations

Nb films since the increase of the decrease of the mean free path

for

is grossly compensated by . Table 1 also shows the

calculated evolution of the penetration depth A(o) and of the effective penetration depth * e f £ = 2x 2 /d

(d = film

thickness).

The above results show in conclusion that implantation of thin Nb films allows to obtain easily a 50% decrease of T with c ' corresponding for

increases of 3001 for the resistivity and 4001

while the variation of the coherence length is only

10-15% .

Pb-Nb-Pb microbridge characteristics : Table II - gives the parameters of several bridges

realized

and measured as indicated above, which allow some comment. The bridge lengths and widths are much larger than S(t) as soon as t < 0 . 9 9 but they are much smaller than * e £ £ in a wide range of temperature, and the bridge operates in the vortex regime. The large thickness of the banks favors a strong repulsion of the vortices from the shores. Moreover the bridge film presents a great uniformity

(large density of defects =5 nm in implanted

Nb films) . Then for short bridges compared

to * e £ £ the situa-

tion is favorable to have vortices moving in a single row. A detailed analysis of the VI characteristic and the bridge behaviour under microwave irradiation is given elsewhere.

350 TABLE

I. Calculated values

Experimental values Fluences . ? ions/crrr

_ . . Tc,i/Tc,ni

1015

0,86

2.10

15

0,77

2.10

15

0,79

6.10 1 5

0,74

TABLE

. p./p . l ni

.

. r ., £.[t)/£ .t £ ./£ . Z./Z .(t) X __ ./A _ . oi ^oni l ni effi effni l ni

r

1,5

0,97

1,32

G,9B

2

2,6

0,87

1,59

0,B75

4

2,1

0,92

1,53

0,92

3,2

2,6

0,85

1,70

0,87

4,5

II. L

w

nm

B nm

)jm

jjm

143 A2

33

800

0.8

2

2.10 15

6.2

4.5

141 A1

33

800

0.8

1

6.10 15

5.4

9.5

124 B1

33

800

2

1.2

101b

6.9

8.4

Bridge

Bridge

d

Z nm

d

5

n

A [0)

0 ions/9

S(t)

nm

nm

[0,95) nm

T K

R

c

N N

\ eff(t)

(0,80) t:0.95 nm um

0.80 um

X

GL

mA

143 A2

1.3

50

140

50

14

60

6

5

141 A1

1

75

170

56

16

75

7.5

1 .3

124 B1

2.5

36

95

60

17

28

2.8

5.8

References 1. P a l m e r , D . W . (1 9 7 3 ) .

and Decker,

S.K.:

Rev.

Sei.

Inst.,44,1621

351 2. Pascal D. (private

communication)

3. Hughes M., Babolat M. and Tigreat P., Proc. Int. Conf. on microlithography, p. 81, 21-24 juin 1977, Paris. 4. Kaplan S.B. : J. Low Temp. Phys. 37.» 343

(1 979)

5. Crozat P., Adde R. Chaumont J., Bernas H., and Zenatti D., in Applications of ions beams to Metals, Edited by S.T. Picraux, Plenum Press NY (1974). 6. Crozat P., Bernas H., Chaumont J. and Adde R. 7. Crozat P., Thèse Doctorat d'Etat, Université 1980 (unpublished)

(unpublished) Paris-Sud,

8. Dynes R.C. and Varma C.M., J. Phys. F 6, L 215

(1976).

NB WEAK LINKS FOR SQUID APPLICATIONS

R.B. Laibowitz, A.N. Broers, R.F. Voss, S.I. Raider and J.M. Viggiano IBM Thomas J. Watson Research Center Yorktown Heights, NY 10598 USA

INTRODUCTION Ultra low noise thin film DC SQUIDs have been constructed with Josephson elements consisting of either all-Nb tunnel junctions or very narrow variable thickness bridges (nanobridges).

Tunnel junctions consisting of a Nb base

electrode with a Pb-alloy counter electrode have also been studied.

These

SQUIDs are very small in size with tunnel junctions typically 1 fim by 1 /¿m and nanobridges 0.25 fim long, 50 nm wide and 30 nm thick.

Junctions as small as

0.3/im x 0.3/im and bridges as short as 0.12jum have also been fabricated.

The

use of Nb thin films, particularly in the case of the tunnel junction SQUID, has led to increased ruggedness and resistance to failure during temperature cycling. Special substrates designed for transmission electron microscopy ( T E M ) are used for the bridge SQUIDs.

TUNNEL JUNCTIONS 1,2

The tunnel junction SQUIDs

were made on Si wafers with about 20 to 25

independent sections (chips) per wafer. Junction size a n d / o r loop area could be varied on a single wafer and the individual chips, a few square mm in size, were then diced for mounting and subsequent low temperature studies.

On the same

chip a variety of single junctions were also fabricated and their properties were also studied.

A typical micrograph of these tunnel junctions is shown in Figure

Squid '80 © 1980 Walter de Gruyter & Co., Berlin • New York

354 1. Complete SQUID pictures are included in the companion paper by R. Voss et al 3 . The Nb was deposited from an e-gun heated source at a rate of 1 to 3 nm/sec and a pressure during evaporation < 0 . 1 microTorr.

The junction cross section

consisted of a Nb base electrode 140 nm thick, a plasma grown niobium

oxide

4

tunnel barrier and a Nb counter electrode about 230 nm thick . also contains an extensive list of references to Nb technology.

Reference 4 The Nb films

generally had a T c of about 9.1 K with an occasional low value of about 8.9K. The slightly lower T c did not have any obvious effect on the junction characteristics.

In general, high quality ( e.g.

low excess current ) characteristics were

not needed for satisfactory operation of the SQUIDs. plasma cleaned

The base electrode was

through the resist layer which defines the counter electrode

pattern in an Ar discharge with 400 V rf at a pressure of 4 mTorr. Oxygen was then admitted into the chamber and a low voltage plasma ( 160 to 200 V ) established at about 3 mTorr using 4 a mixture of 5 % oxygen and Ar to produce the tunnel barrier. Previous work showed that an oxidation time of about 2 min. at a pressure of 40 mTorr would produce junctions with a current density of 2

about 100 A / c m . In our present work at the lower pressures oxidation times of up to 60 min. have been used to obtain similar current densities. Although this increased time is

expected, the small junction size, as defined by the narrow

canyon in the resist material, may also influence the oxidation time in that the surface of the resist will compete with the tunnel barrier for the available oxygen. After completion of this step the system was pumped to a low pressure and the counter electrode was deposited. teristic is shown in Figure 2.

An example of a junction IV charac-

Also shown in the figure is the effect on the

junction of microwave radiation at a frequency of about 145 gHz.

In this

particular case the junction had a dipole antenna connected to it to enhance the coupling . Electron-beam lithography was used exclusively to pattern these circuits. Standard PMMA resist, either in a single layer or as a double layer with a copolymer 5 ,

355

Figure 1. Scanning electron micrographs of the all Nb tunnel junctions at 1 /¿m linewidths. The upper picture also shows the Pd-Si shunt resistor pattern.

356

2 Figure 2. The I-V characteristics for a 1 /¿m all Nb tunnel junction at 4.2K. (a) without microwaves; (b) with 145 G H z microwaves applied.

357 was spun onto the wafers

1 /im thick). The pattern was then exposed in the

resist by a computer controlled electron beam system and lift-off was used to complete the definition of the metal lines. The high intrinsic stress involved in the Nb metallization often resulted in some resist failure limiting the yield. The e-beam lithography could easily pattern junctions 0.5 /im x 0.5 nm with smaller dimensions possible although at a lower yield. However, junctions with areas of 2

about 0.5 to 5 /tin were typically made. The junction area could be varied on the wafer. Initial results on the current density as a function of junction

area 2

showed that area scaling did not extend to the smaller junctions, i.e. ljum smaller. The small junctions had greater current densities than expected.

or

Back

sputtering from the resist walls onto the junction area during oxidation and the subsequent limiting of the growth of the tunnel barrier is a possible mechanism for the higher current density in the smaller junctions. Also, as discussed above, the competition of the resist walls with the tunnel barrier for the available oxygen may result in thinner tunnel barriers. Initially it was thought that the lower quality junctions could be self or internally shunted to produce hysteresis free characteristics.

SQUID operation was ob-

served in these self shunted circuits but for low noise operation the complete elimination of hysteresis was necessary.

To accomplish this, a shunting resistor

was added to the SQUID circuit as seen in Fig. 1. Another level of lithography and a metallurgy compatible with the Nb deposition was then required. This was 6 7

achieved with a Pd-Si resistor ' . Typically, 20 nm of Pd was deposited on a Si wafer in the desired shunt pattern. The wafer would then be annealed for about 0.5 hr at 250C to form the Pd 2 Si. Resistivity values from 40 to 80 nS2-cm were generally achieved.

The results of the SQUID measurements are contained in

the companion paper in this issue.

NANOBRIDGES

358 The basic fabrication process and many of the properties of the variable thickg ness N b nanobridges have been published previously

( see also the references

cited in Reference 8) and will only be summarized here. The substrate on which the nanobridge and the nanobridge SQUIDs were constructed consisted of very thin membranes of Si 3 N 4 . These membranes covered mm sized holes in Si chips, producing windows.

A schematic view of such a sample is shown in Figure 3

along with a micrograph of a completed bridge SQUID. This type of substrate is transparent to electrons and permits detailed T E M studies of the fine lines or nanobridges. In addition use of such a substrate virtually eliminates the possibility of loss of resolution due to back scattered electrons.

Thus, in the S T E M

system, the fine lines could be both fabricated and their structure studied. A pad or contact pattern ( ~ 80 nm thick) was first established on the window substrate using standard e-beam lithography.

In this configuration the length of

the bridge is determined by the pad separation. Bridges as short as .12 ;u,m have been made.

Much shorter bridges could be made using the high resolution

lithographic techniques discussed below. A f t e r the Nb pads were fabricated, the samples were sputter cleaned and a « 30 nm blanket film of N b was then 9

deposited. The grain size in this film was about 15 nm . It is from this film that the nanobridges are formed.

To define the pattern this film is exposed to the

electron beam of the STEM.

A contamination layer (carbon) is built up where

the beam is incident on the film.

With this protective contamination layer in

place the entire sample is then ion milled in an Ar beam.

The 30 nm of N b is

removed everywhere except where the contamination protects the Nb, completing the structure.

Lead wires were then ultrasonically bonded to the pads far

f r o m the windows. The samples made in this way were capable of surviving several cycles to liquid helium temperature. An example of a nanobridge micrograph and IV curves with and without 36 Ghz microwaves applied is shown in Figure 4. The microwave induced steps as seen in the figure are useful for studying the resistively shunted junction model for bridges and frequencies as high as w 150Ghz have been used in these investiga-

359

a

b

Figure 3. (a) Schematic diagram of the sample and its substrate showing the very thin windows and the variable thickness geometry. Figure 3. (b) Scanning electron micrograph of a N b nanobridge SQUID sample. The high cone-like structures at the end of each nanostripe are cones of contamination resulting from the electron beam holding at that point before each scan.

360

Figure 4. (a) Transmission electron micrograph of a Nb nanobridge. (b) IV curve without microwaves applied, (c) IV characteristic with 3 6 G H z applied.

361

Nb

1.5

•

x

> I.O B o: o

. X X

o o X* X.

0.5 X

• x

3

o X • „

5

».

x

»g°c 7

TEMPERATURE(K)

Figure 5. ICR versus temperature for three bridges. Resistance values are 30S2 for the full circles, 45S2 for the x and 44S2 for open circles.

362 tions. This work will be reported on in a later paper. The ac Josephson effect is also useful for identifying bridges with good Josephson properties.

An earlier g

study of the structure of the IV characteristics with phase slip centers estimate of the quasiparticle diffusion length for

led to an

Nb films of 90 nm and a

quasiparticle inelastic relaxation time of about 18 ps. These results are in good agreement with earlier theoretical estimates 1 0 .

The typical dependence of the

bridge critical current on temperature is shown in Figure 5. The increase of the critical current with decreasing temperature can result in a device with no hysteresis at 4.2K yet extensive hysteresis at lower temperatures.

This effect

limits the useful range of the nanobridge SQUIDs. An intrinsic energy sensitivity of about 3h ( h is Planck's constant) which is the lowest ever reported for any SQUID has been observed in these bridge SQUIDS. The superconducting transition of these bridges appears to be that of a granular superconductor with a 9 two part transition , i.e. a high T c 0 at which the grains become superconducting and a lower T c below which long range superconductivity is established.

Inter-

granular Josephson coupling is believed to be a possible mechanism for this effect. Future work is planned to study these effects and to optimize bridge size so that hysteresis free operation is obtained at the desired current density.

ACKNOWLEDGEMENTS

The authors gratefully acknowledge many helpful discussions with C. Chi, J. Harper, J. Cuomo, W. Molzen, W. Grobman and E. Alessandrini.

The electron

beam lithography (Vectorscan system) efforts of W. Grobman, T. Donohue and J. Powers is also acknowledged as is the technical expertise of J. Speidell, G. Waters and J. Kuran.

REFERENCES

363 1.

R.F. Voss, R.B.

Laibowitz, S.I. Raider, W.D. Grobman, J. Clarke, Bull.

Am. Phys. Soc., 24, 265 (1979). 2.

R.F. Voss, R.B. Laibowitz, S.I.Raider and J.Clarke, J. Appl. Phys., 51, 2306 (1980)

3.

R.F. Voss,R.B. Laibowitz, M. Ketchen and A.N. Broers, this conference

4.

R.F. Broom, R. B. Laibowitz, Th. O. Mohr and W. Walter,IBM J. Res. Dev., 24, 212 (1980).

5. M. Hatzakis, J. Vac. Sei. Techn., 16, 1984 (1979). 6. C. J. Kircher, Solid State Elec., 14, 507 (1971). 7. U. Koester, K.N. Tu and P.S. Ho, Appl. Phys. Lett., 31, 634 (1979). 8.

R.B. Laibowitz, A.N. Broers, J.T.C. Yeh and J.M. Viggiano, Appl. Phys. 35, 891 (1979).

9.

R.B. Laibowitz, A.N. Broers, B.R. Patton and D. Stroud, AIP Conf.

58,

278 (1980). 10.

S.B. Kaplan, C.C. Chi,J.J. Chang, S. Jafarey and D.J. Scalapino, Phys. Rev. B, 14, 4854 (1976).

ULTRA LOW NOISE DC SQUIDS

R. F. Voss, R. B. Laibowitz, M. B. Ketchen, and A. N. Broers IBM Thomas J. Watson Research Center Yorktown Heights, NY 10598

USA

Introduction

Three different Josephson weak link technologies have been used to successfully fabricate ultra low noise dc SQUIDs: (1) all-Nb tunnel junctions using electronbeam lithography to define minimum linewidths < 1 /¿m; (2) Pb alloy tunnel junctions using photolithography to define minimum linewidths « 2.5 nm; and (3) Nb weak links (nanobridges) formed from electron-beam

contamination

lithography with minimum linewidths < 30 nm. New techniques were developed which, for the first time, directly record SQUID voltage noise and small signal flux sensitivity as a function of both current and flux bias.

In this paper, de-

tailed measurements on the three types of SQUIDs will be presented that dem2

onstrate that the intrinsic energy resolution n / 2 L (

(i0)

io

Figure 4. Characteristics of Nb 1/im tunnel junction SQUID at 1.6K with I b of 3.7 fiA.

370 I dV/d | with the peak near