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SEMICONDUCTORS AND SEMIMETALS VOLUME 7 Applications and Devices Part B

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SEMICONDUCTORS AND SEMIMETALS Edited by R. K. WILLARDSON BPLL A N D HOWFLL t l E C I H O N I C MATFKIALS DIVISION PASADENA. CALIFORNIA

ALBERT C. BEER BATTELLE MEMORIAL INSTITUTE COLUMBUS LABORATORILS

COLUMBUS. OHIO

VOLUME 7 Applications and Devices Part B

1971

@

ACADEMIC PRESS

New York and London

COPYRIGHT 0 1971, BY ACADEMIC PRESS, WC. ALL RIGHTS RESERVED NO PART OF THIS BOOK MAY BE REPRODUCED IN ANY FORM, BY PHOTOSTAT, MICROFILM, RETRIEVAL SYSTEM, OR ANY OTHER MEANS, WITHOUT WRI7TEN PERMISSION FROM THE PUBLISHERS.

ACADEMIC PRESS, INC.

111 Fifth Avenue, New York, New York 10003

United Kingdom Edition published by ACADEMIC PRESS, INC. (LONDON) LTD. Berkeley Square House, London W1X 6BA

LIBRARY OF CONGRESS CATALOG CARDNUMBER: 65-26048

PRINTED IN THE UNITED STATES OF AMERICA

Contents LISTOF CONTRIBUTORS. . PREFACE . . . . . CONTENTS OF PREVIOUS VOLUMES .

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vii ix xi

DIODES Chapter 7 IMPATT Diodes T. Misawa Introduction . . . . . . , . . Dynamic Negative Resistance in p n Junction in Breakdown . Fundamental Phenomena and Mathematical Formulation . Analysis of Electrical Characteristics . . . . Design Considerations . . . VI. Diode Fabrication . . . . . . . . VII. Observed Electrical Characteristics . . . . . VIII. Conclusions . . . . . . . Appendix A. DC Equations and Numerical Solution . . Appendix B. Small-Signal AC Solution . . . . Appendix C. Addenda to Numerical Analysis of Large-Signal Read Diode . . . . . . Appendix D. Theory of TRAPATT Mode of Operation . List of Symbols . . . . . . 1. 11. 111. IV. V.

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382 442

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463

Operation of

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Chapter 8 Tunnel Diodes H . C . Okean 1. Introduction . . . . . . 11. The Physics of Tunnel Diode Operation . 111. Principles of Tunnel Diode Fabrication . . . . . . IV. Terminal Properties of Tunnel Diodes . V. Experimental Characterization of Tunnel Diodes VI. Tunnel Diode Applications in Sinusoidal Circuits . VII. Tunnel Diode Applications in Pulse and Digital Circuits VIII. Present and Future Role of Tunnel Diodes . . V

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vi

CONTENTS

Chapter 9 Silicon Carbide Junction Devices Robert B. Campbell and Hung-Chi Chang 1. Introduction . . . . . . 11. Silicon Carbide as a Semiconductor Material

DeviceTechniques . Silicon Carbide Power Diodes p-n Junction Detectors . Active Devices . . Irradiation Effects . . Luminescent Diodes . Summary . . . X. Addendum . . .

111. IV. V. VI. VII. VIII. 1X.

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RECTLFIERS Chapter 10 High-Temperature Power Rectifiers of GaAs, - xPx R . E . Enstrorn, H . Kressel, and L. Krassner I. Introduction . . . . . . . 11, High-Temperature Rectifier Design Considerations 111. p-n Junction Formation . . . . . . . . . . IV. Device Fabrication V. Rectifier Test Results . . . . . AUTHQRINDEX . SUBJECTINDEX .

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721

List of Contributors Numbers in parentheses indicate the pages on which the authors' contributions begin.

ROBERT B. CAMPBELL, Westinghouse Astronuclear Laboratory, Pittsburgh, Pennsylvania (625) HUNG-CHICHANG,' Westinghouse Astronuclear Laboratory, Pittsburgh, Pennsylvania (625) R. E. ENSTROM, RCA Laboratories, David Sarnof Research Center, Princeton, New Jersey (687) L. KRASSNER,~ RCA Laboratories, David Sarnof Research Center, Princeton, New Jersey (687) H. KRESSEL, RCA Laboratories, David Sarnofl Research Center, Princeton, New Jersey (687) T. MISAWA,Bell Telephone Laboratories Inc., Murray Hill, New Jersey (371) H. C. OKEAN,Airborne Instruments Laboratory, A Division of CutlerHammer, Inc., Melville, Net43 York (473)

' Present address: National Chiao University, Hsinchu. Taiwan, China Present address: Unitrode Corporation. Watertown. Massachusetts.

vii

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Preface

The extensive research that has been devoted to the physics of semiconductors and semimetals has been very effective in increasing our understanding of the physics of solids in general. This progress was made possible by significant advances in material preparation techniques. The availability of a large number of semiconductors with a wide variety of different and often unique properties enabled the investigators not only to discover new phenomena but to select optimum materials for definitive experimental and theoretical work. In a field growing at such a rapid rate, a sequence of books which provide an integral treatment of the experimental techniques and theoretical developments is a necessity. The books must contain not only the essence of the published literature, but also a considerable amount of new material. The highly specialized nature of each topic makes it imperative that each chapter be written by an authority. For this reason the editors have obtained contributions from a number of such specialists to provide each volume with the required detail and completeness. Much of the information presented relates to basic contributions in the solid state field which will be ofpermanent value. While this sequence of volumes is primarily a reference work covering related major topics, certain chapters will also be useful in graduate study. In addition, a number of the articles concerned with applications of specific phenomena will be of value to workers in various specialized areas of device development . Because of the important contributions which have resulted from studies of the 111-V compounds, the first few volumes of this series have been devoted to the physics of these materials: Volume 1 reviews key features of the 111-V compounds, with special emphasis on band structure, magnetic field phenomena, and plasma effects. Volume 2 emphasizes physical properties, thermal phenomena, magnetic resonances, and photoelectric effects, as well as radiative recombination and stimulated emission. Volume 3 is concerned with optical properties, including lattice effects, intrinsic absorption, free carrier phenomena, and photoelectronic effects. Volume 4 includes thermodynamic properties, phase diagrams, diffusion, hardness, and phenomena in solid solutions as well as the effects of strong electric fields, ix

X

PREFACE

hydrostatic pressure, nuclear irradiation, and nonuniformity of impurity distributions on the electrical and other properties of 111-V compounds. Volume 5 , which is devoted to infrared detectors, is the first of a number of volumes to deal specifically with applications of semiconductor properties. Volume 6 is concerned with injection phenomena in solids, including current injection and filament formation, double injection, internal photoemission, and photoconductor-metal contacts. The present volume is issued in two parts, 7A and 7B, and is concerned with semiconductor devices, including those utilizing bulk negative resistance phenomena as well as effects due to barriers and junctions. Subsequent volumes of Semiconductors and Seminzerals will include further work on infrared detectors and a variety of fundamental phenomena such as lattice dynamics, galvanomagnetic effects, luminescence, nonlinear optical phenomena, and electro-, thermo-, piezo-, and magnetooptical effects. The editors are indebted to the many contributors and their employers who made this series possible. They wish to express their appreciation to the Bell and Howell Company and the Battelle Memorial Institute for providing the facilities and the environment necessary for such an endeavor. Thanks are also due to the U.S. Air Force Offices of Scientific Research and Aerospace Research and the U.S. Navy Office of Naval Research and the Corona Laboratories, whose support has enabled the editors to study many features of compound semiconductors. The assistance of Crystal Phillips, Martha Karl, and Inez Wheldon in handling the numerous details concerning the manuscripts and proofs is gratefully acknowledged. Finally, the editors wish to thank their wives for their patience and understanding. R. K . WILLARDSON ALBERT C. BEER

Semiconductors and Semimetals Volume 1 Physics of 111-V Compounds C . Hifsum, Some Key Features of 111-V Compounds Franco Eassani, Methods of Band Calculations Applicable to IIILV Compounds E. 0. Kane, The k ' p Method V. L. Eonch-Eruevich, Effect of Heavy Doping on the Semiconductor Band Structure Donald Long, Energy Band Structures of Mixed Crystals of 111-V Compounds Laura M . Roth and Petros N . Argyres, Magnetic Quantum Effects S . M . Puri and T. H. G e b d e , Thermomagnetic Effects in the Quantum Region W. M . Becker, Band Characteristics near Principal Minima from Magnetoresistance E. H. Purley, Freeze-Out Effects, Hot Electron Effects, and Submillimeter Photoconductivity in lnSb H . Weiss, Magnetoresistance Betsy Ancker-Johnson, Plasmas in Semiconductors and Semimetals

Volume 2

Physics of 111-V Compounds

M . G. Holland, Thermal Conductivity S. I.Novikova, Thermal Expansion U. Pieshrugen, Heat Capacity and Debye Temperatures G . Giesecke, Lattice Constants J . R . Drubble, Elastic Properties A . U . Mac Rae and G. W . Gobeli. Low Energy Electron Diffraction Studies Robert Lee Mieher, Nuclear Magnetic Resonance Bernard Goldstein, Electron Paramagnetic Resonance T . S . Moss, Photoconduction in 111-V Compounds E. AnronFik andJ. Tauc, Quantum Efficiency of the Internal Photoelectric Effect in lnSb G. W .Goheli and F. G . Allen. Photoelectric Threshold and Work Function P. S. Pmjhun. Nonlinear Optics in I l l - V Compounds M . Gershenzon, Radiative Recombination in the 111-V Compounds Frank Srerrt, Stimulated Emission in Semiconductors

Volume 3 Optical Properties of Ill-V Compounds Mari.in H a s , Lattice Reflection William G. Spitzer, Multiphonon Lattice Absorption D . L . Stierwalt and R. F. Potter, Emittance Studies H. R . Philipp and H . Ehrenreich. Ultraviolet Optical Properties Manuel Cardona, Optical Absorption above the Fundamental Edge Earnest J . Johnson, Absorption near the Fundamental Edge John 0. Dimmock, Introduction to the Theory of Exciton States in Semiconductors E. Lax and J . G. Mauroides, Interband Magnetooptical Effects

xi

xii

CONTENTS OF PREVIOUS VOLUMES

H. Y . Fan, Effects of Free Carriers on the Optical Properties Edward D. Palik and George B. Wright, Free-Camer Magnetooptical Effects Richard H. Bube, Photoelectronic Analysis B. 0. Seraphin and H. E. Bennett, Optical Constants

Volume 4

Physics of 111-V Compounds

N. A. Goryunova, A. S. Borschevskii, and D. N. Tretiakov, Hardness N . N. Sirota, Heats of Formation and Temperatures and Heats of Fusion of Compounds A"'BV Don L. Kendall, Diffusion A . G. Chynoweth, Charge Multiplication Phenomena Robert W . Keyes, The Effects of Hydrostatic Pressure on the Properties of 111-V Semiconductors L. W . Aukerman, Radiation Effects N. A . Goryunova, F. P. Kesamanly, and D. N . Nasledov, Phenomena in Solid Solutions R. T. Bate, Electrical Properties of Nonuniform Crystals

Volume 5 Infrared Detectors Henry Levinstein, Characterization of Infrared Detectors Puuf W . Kruse, Indium Antimonide Photoconductive and Photoelectromagnetic Detectors M . B. Prince, Narrowband Self-Filtering Detectors Ivars Melngailis and T. C. Harman, Single-Crystal Lead-Tin Chalcogenides Donald Long and Joseph L. Schmit, Mercury-Cadmium Telluride and Closely Related Alloys E. H. Putley, The Pyroelectric Detector Norman B. Stevens, Radiation Thermopiles R. J . Keyes and T. M . Quist, Low Level Coherent and Incoherent Detection in the Infrared M . C. Teich, Coherent Detection in the Infrared F. R. Arums, E. W . Sard, B. J . Peyton, and F. P. Pace, Infrared Heterodyne Detection with Gigahertz IF Response H. S. Sommers, Jr., Microwave-Biased Photoconductive Detector Robert Sehr and Ruiner Zuleeg, Imaging and Display

Volume 6 Injection Phenomena Murray A. Lampert and Ronald B. Schilling, Current Injection in Solids: The Regional Approximation Method Richard Williams, Injection by Internal Photoemission Allen M . Barnett, Current Filament Formation R. Baron and J . W . Mayer, Double Injection in Semiconductors W . Ruppel, The Photoconductor-Metal Contact

Volume 7 Applications and Devices: Part A John A. Copeland and Stephen Knight, Applications Utilizing Bulk Negative Resistance F. A. Padovani, The Voltage-Current Characteristic of Metal-Semiconductor Contacts P. L. Hower, W . W . Hooper, B. R. Cairns, R. D. Fairman, and D. A. Tremere, The GaAs FieldEffect Transistor Marvin H. White, MOS Transistors G. R. Antell, Gallium Arsenide Transistors T. L. Tansley, Heterojunction Properties

SEMICONDUCTORS A N D SEMIMETALS VOLUME 7 Applications and Devices Part B

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Diodes

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CHAPTER 7

IMPATT Diodes T. Misawa

. . . . . . . . . . . . . . . . 372 I . INTRODUCTION NEGATIVE RESISTANCE I N pn JUNCTION IN BREAKDOWN . 372 I1. DYNAMIC 1 . Negative AC Power Dissipation . . . . . . . . . . 373 2 . Transif-Time Effect . . . . . . . . . . . . . 374 3 . Saturation of Carrier Drft Velocity . . . . . . . . . 374 4 . Dynamics of Avalanche Multiplication . . . . . . . . 375 5 . Negative Resistance in pn Junction in Breakdown . . . . . 375 PHENOMENA AND MATHEMATICAL FORMULATION . . 371 111. FUNDAMENTAL 6 . Drifr Velocities of Carriers . . . . . . . . . . . 377 7 . Aiialanche Multiplication . . . . . . . . . . . . 377 8 . Governing Equarions . . . . . . . . . . . . . 380 OF ELECTRICAL CHARACTERISTICS . . . . . . . 382 IV . ANALYSIS 9 . Space-Charge L a j w in pn Junctions . . . . . . . . . 382 10. Static Current-Voltage Characteri.stics . . . . . . . . 383 11. Growing Waiw in Arwlunching Electron-Hole Plasma . . . . 390 12. Small-Signal Anal.ysis . . . . . . . . . . . . . 393 13. Large-Signal Anal.v.ri.7 . . . . . . . . . . . . . 411 . . . . . . . . . . . . . 429 V . DESIGNCONSIDERATIONS 14. Scaling Rule fbr liirious Structures . . . . . . . . . 429 IS . Structure Puranzeters . . . . . . . . . . . . . 430 16. Material Parameters . . . . . . . . . . . . . 432 11. Thermal Considerntion . . . . . . . . . . . . 434 . . . . . . . . . . . . . . 442 VI . DIODEFABRICATION I8 . Impurity ProJie . . . . . . . . . . . . . . 442 I9 . Fabrication Techniques . . . . . . . . . . . . 449 CHARACTERISTICS . . . . . . . . 451 VII . OBSERVED ELECTRICAL 20 . Small-Signal Charrrcreristics . . . . . . . . . . . 451 2 I . Oscillator Chnracrerisrics . . . . . . . . . . . . 454 VIII . CoNCLUsloNs . . . . . . . . . . . . . . . . 461 APPENDIX A . DC EQUATIONS A N D NUMERICAL SOLUTION . . . 462 APPENDIX B. SMALLSIGNAL AC SOLUTION . . . . . . . . 463 APPENDIXC . ADDENDA TO NUMERICAL ANALYSIS OF LARGE-SIGNAL OPERATION OF READDIODE . . . . . . . . . . . 464 466 D . THEORY OF TRAPATT MODEOF OPERATION . . . APPENDIX LBT OF SYMBOLS. . . . . . . . . . . . . . . 471

37 1

372

T. MISAWA

1. Introduction When the p n junction diode is reverse-biased, then, practically speaking, current does not flow. However, when the reverse voltage exceeds a certain value, the junction breaks down and current flows with only slight increase of voltage. This breakdown is caused by avalanche multiplication of electrons and holes in the space-charge region of the junction. The p n junction in the avalanche breakdown condition exhibits negative resistance characteristics in the microwave frequency range. This negative resistance can be exploited to generate microwave power and amplify microwave signals. Since the negative resistance is based upon avalanche multiplication and the transit-time effect of carriers, the device has been called the IMPATT (Impact Avalanche Transit-Time) diode. IMPATT oscillators have produced continuous output powers ranging from 5 W at 12 GHz with an efficiency of 9 %,to 37 mW at 106 GHz with an efficiency of 1.6%. Germanium devices have shown an efficiency as high as 15.3% around 6 GHz. The highest frequency of oscillation reported is 341 GHz from a Si unit. Signal amplification has been observed in the above frequency range with reflection-type amplifiers. The idea of utilizing the dynamic property of avalanche multiplication in conjunction with the carrier transit-time effect in the space-charge layer of the p n junction for obtaining a dynamic negative resistance was originally proposed by Read in 1958.' Very little work has been reported in the literature on this type of device until 1965, when Johnston et al. discovered, rather independently of Read's proposal, that microwave oscillation can be obtained from Si pn junction diodes which were structurally quite different from Read's model.' Since this discovery, intensive study has been made on the dynamic characteristics of pn junctions in breakdown. It is believed that the characteristics are fairly well understood theoretically and basic properties of the device have been investigated fairly thoroughly with laboratory units made of such common semiconductors as Si, Ge, and GaAs. in the following, after a brief description of the negative resistance of the pn junction in breakdown, a theoretical study on its electrical characteristics is presented. Then, some design considerations and fabrication techniques of laboratory models are discussed. Finally, the observed characteristics of experimental units are presented.

11. Dynamic Negative Resistance in pn Junction in Breakdown In this part, a simplified explanation will be given of the origin of the dynamic negative resistance in a pn junction in breakdown.

' W. T. Read, Bell. Sysr. Tech. .I37, . 401 (1958). R. L. Johnston, B. C. DeLoach, and B. G . Cohen, Bell Syst. Tech. J . 44,369 (1965)

7. IMPATT

DIODES

373

1. NEGATIVE AC POWERDISSIPATION

When ac voltage is present across a diode with negative-resistance terminal characteristics, ac electric energy is produced within the device. If we look into the inside of the device, electric energy is dissipated in some places within the device and is generuted in other places. However, the net power dissipation has to be negative in order for the diode to exhibit the negative resistance property at the terminals. In this section, we will see how negative power dissipation is possible in a semiconductor. Electric energy is dissipated when an electric current flows in the direction of an electric field. Negative dissipation or generation results only when current flows againsr the field. When current and field change periodically in time, the average dissipation over'one cycle must be negative in order to have negative ac power dissipation. It will be convenient to use the terminology of ac circuit analysis in describing the above situation. The ac power dissipation is positive when the phase difference between ac current and field is less than 90" and negative when the phase difference is more than 90". In a solid, more current flows when there are more carriers and when the velocities of the carriers are larger. The current density is given by

J

=

qno,

(1)

where q is the charge of the carrier, n is the carrier density, and z) the carrier velocity. A change in current caused by a change in field 6 E is given by

6J

=

q(n . 6 z 1

+ v . bn),

(2)

when changes, prefixed with 6, are small. There is a possibility of negative power dissipation when the carrier velocity decreases as the field is increased and/or the carrier number decreases as the field is increased. A good example of the first case is the transferred electron effect in GaAs. This is a microscopic property set by nature which is beyond the control of the engineer. However, the second case of the change in carrier number can be realized in ordinary semiconductors by designing a proper structure. Designability is based on the fact that the change in carrier density or bunching of carriers is fairly indirectly related to electric field. (Actually, only the divergence of the field is connected with the charge of carriers through Poisson's equation.) So it is possible to have a reduction of carrier number with an increase of field. When various quantities change sinusoidally with time, which is expressed in complex form as ejw', Eq. ( 2 ) becomes

J

=

q(n,v

+ o,n),

(3)

where boldface type designates a vector or phasor and the subscript zero implies dc values or time averages. As noted above, v is in phase with E in

374

T.

MISAWA

most semiconductors; therefore, the first term in Eq. (3) contributes to power loss. When n leads or lags the field E by more than 90" and when its contribution to power generation is large enough to overcome the loss due to the v term, the net effect is power generation. The necessary phase difference is obtained by the transit-time effect, which will be discussed in the next section. 2. TRANSIT-TIME EFFECT

Once carrier bunching is produced at a certain place (cathode) in a device in a regularly pulsating way, it flows downstream with a finite transit time. The bunching may decay due to diffusion or the dielectric relaxation effect. When one observes the carrier stream at a certain position, one sees that the phase of the modulated carrier density is determined by the transit time from the cathode to the observing position. When there is an ac field having phase independent of position, at some point downstream, the phase of the ac carrier density lags the field by 90". The phase difference will remain more than 90" over a distance in which the transit angle changes by an additional 180". A negative-resistance device can be made by making the ac power generation in this space larger than the dissipation in the preceding space. A variety of devices may be made according to the choice of cathode and dynamics of carrier transit in the interaction space. In 1954, Shockley proposed two structures which work according to this general m e c h a n i ~ m . ~ Read later proposed the use of an avalanching region as a cathode.' He showed that the avalanche region produces 90" phase delay in itself so that the whole interaction space can contribute to power generation in a very efficient way. This turns out to be a substantial advantage over Shockley's structures. Before discussing the dynamics of avalanche multiplication, we consider an important feature of carrier dynamics in the interaction space. This is the saturation of carrier drift velocity at high fields.

3. SATURATION OF CARRIER DRIFTVELOCITY It was pointed out that an increase in carrier velocity with field contributes to power loss. However, the carrier velocity actually saturates at the high fields that exist in the space-charge region of pn junctions (above -2000 V/cm in the case of electrons in Si). Because of the saturation of velocity, the power loss due to velocity change [the first term in Eq. (3)] is practically zero. When the carrier velocity increases with field, dielectric relaxation tends to smooth out carrier bunching. That is, the extra charge of bunched carriers produces a change in field which, in turn, induces current that acts to reduce the charge. This debunching reduces the magnitude of the power generation in the later part of the passage. However, when the velocity saturates, dielectric relaxation does not take place, because the change in field does not produce W. Shockley, BeNSysi. Tech. J . 33. 799 (1954).

375 a change in current. This makes power generation in the interaction space more efficient. The saturation value of the velocity is referred to as "scattering-limited velocity" in the literature. 4.

DYNAMICS OF

AVALANCHE MULTIPLICATION

The breakdown of the p n junction is caused by avalanche multiplication of electrons and holes.3a As the field becomes high, a charge carrier can obtain enough energy from the field to release a bound electron into the conduction band, thus also creating a hole in the valence band. The probability of this electron-hole pair creation depends upon field strength. When the probability in one passage across the space-charge region approaches unity, a very large number of carriers are produced from one original carrier and a large current starts to flow. This is avalanche breakdown. As the field changes periodically with time around an average value, the generation rate of carriers follows the field change almost instantaneously. However, the carrier number does not change in unison with the field. For example, even when the field has passed a peak value, the carrier number keeps increasing because the carrier generation rate is still above the average value. The total number of carriers peaks and starts to decrease when the field has decreased from the peak to the average value. In other words, the ac variation of the number of carriers lags the generation rate by 90" and the generation rate is in phase with the ac field. From discussions given in the preceding two sections, it is seen that, when the avalanche region is followed by a drift region in which the carrier drifts at scattering-limited velocity, ac power is generated very effectively when the transit angle lies between 0" and 180".

5 . NEGATIVE RESISTANCE IN

pH

JUNCTION IN BREAKDOWN

a. Read Diode

Read showed that the above situation can be realized in the space-charge layer of a pn junction by properly tailoring the impurity distribution. Figure l(a) shows his n'pip' structure and Fig. l(b) presents the field distribution at breakdown. The space-charge region extends over the whole region between the n+ region at left and the p i region at right. In the spacecharge region, the charge of ionized impurities is not neutralized by electrons and holes as is the case in a bulk semiconductor. Therefore, the field profile is determined by the impurity distribution. Avalanche multiplication takes place only near the left end of the spacecharge layer where the field is highest. Electrons generated in the avalanche region immediately enter the H + region and do not play any important role. '"In the narrow pn junction, the tunneling process is responsible for breakdown

376

T. MISAWA

la )

FIG.1. (a) The structure and (b) the field distribution of the Read diode. (After Read.')

Holes drift through the rest of the space-charge layer. The field is maintained high enough so that holes drift at scattering-limited velocity. This structure will show an optimum negative resistance at the frequency where the hole transit time is half a period. b. General Junction Diode In his original analysis, Read neglected the width of the avalanche region as far as transit-time effects are concerned. The only effect of avalanche multiplication was to inject carriers, with 90" phase delay, at the edge of the space-charge layer. This made the physical argument simple and the analysis tractable, but practical realization difficult. In general, in pn junctions, the region where avalanche multiplication takes place can occupy an appreciable fraction of the total space-charge layer and negative resistance of quality comparable to that with the Read structure is obtained. It is found that ac power is also generated in the avalanche region. The transit-time effect in the avalanche region is appreciably different from that in the avalanche-free region. Here, not only do both electrons and holes exist, but also their behavior is closely interrelated due to avalanche multiplication. While dynamics in the avalanche-free region were described by the behavior of the individual carrier, the collective behavior of the electron-hole plasma governs the dynamics in the avalanche region. The power-generating interaction in the avalanche region is closely related to a spontaneous growth of a plane space-charge wave in an infinite, avalanching electron-hole plasma, which will be discussed in Section 14a. It is based upon the delay in avalanche multiplication and the flow of charge carriers downstream at finite speed, just as in the Read diode.

7 . IMPATT

DIODES

311

111. Fundamental Phenomena and Mathematical Formulation In this part, we discuss two fundamental phenomena encountered in the IMPATT diode, avalanche multiplication and velocities of charge carriers, in more detail as a preparation for the detailed analysis given later.

6. DRIFT VELOCITIES OF CARRIERS4 As the electric field is applied, the drift velocity, or the average velocity of the electrons (or holes), increases proportionally to the field strength as long as the field is small. The proportionality constant is called the carrier mobility. Energy obtained from the field is effectively transferred to the lattice through collisions with phonons and the temperature of the electrons is practically that of the lattice. As the field is increased, it turns out that the energy-transfer mechanism is not efficient enough to keep the electron temperature down. As a result, the mobility of the electrons decreases and the drift velocity does not increase with field as fast as it did at lower fields. At still higher fields, the electron can obtain sufficient energy to emit an optical phonon. The electron loses all the energy acquired from the field in emitting an optical phonon. This takes place as soon as the energy of the electron reaches the optical phonon energy. In this condition, the average velocity of the electrons is one-half of the velocity that corresponds to the optical phonon energy and remains the same as the field is increased. The saturation value, which is called scattering-limited velocity, is of the order of lo7 cm/sec in common semiconductors. The experimentally observed relations between velocity and field are shown in Fig. 2 for electrons and holes in Si and Ge.5 The electric field in the junction in breakdown is on the order of several hundred kV/cm. The velocity can be considered constant in most cases. The following simple expression can describe the gross nature of the velocity change : (4) POE/[l + (POElU,)l, where p o is the low-field mobility and 11, the scattering-limited velocity. 1’ =

7. AVALANCHE MULTIPLICATION’ At higher fields, some “lucky” electrons (or holes) can escape the optical phonon scattering discussed in the preceding section and can acquire sufficient energy to create electron-hole pairs. The required energy is on the order of the gap energy between the conduction and valence bands. W . Shockley, Bell Syst. Twh. J . 30. 990 (1951 1. The curves were obtained by T. E. Seidel at Bell Telephone Laboratories from his own measurements and data published by other researchers. A. G . Chynoweth, in “Semiconductors and Semimetals” (R. K. Willardson and A. C. Beer. eds.). Vol. 4,p. 263, Academic Press. New York and London, 1968.

’

378

T. MISAWA

I o7

>

lo5 E (V/cm)

FIG.2. Drift velocities of electrons and holes in Si and Ge as a function of field. Filled circles are for n-type Ge: V, = 6.5 x lo6, p o = 3800; open circles are for p-type Ge: V, = 8.2 x lo6, po = 1800; filled triangles are for n-type Si: V, = 1.0 x lo’, p o = 1400; open triangles are for p-type Si: V, = 1.05 x lo’, po = 480.

FIG.3. Ionization rates of electrons and holes in Ge, Si, and GaAs as a function of field. The dashed line is for the average of a and p in Si used by Read.’ (After Misawa.26)

7. IMPATT

379

DIODES

The probability of pair creation is averaged over all the electrons and is expressed by the ionization rate, which is the probability per unit distance of passage per electron. In terms of the ionization rates of electrons and holes, c1 and /3, the generation rate of carriers is given by

where u, and up are drift velocities of electrons and holes and n and p are electron and hole densities. The ionization rate is a strongly increasing function of the field strength. Figure 3 shows measured values of ionization rate for Si, Ge, and GaAs.' According to Baraff's theory,* the ionization rate depends upon only three material constants: ionization energy, 4, which is about 1.5 times the energy gap, optical phonon energy 4,and effective mean free path for optical phonon scattering A. A universal relation between ionization rate and field is obtained by proper normalization in terms of the above three material constants. Figure 4 shows the relation.6 This relation, especially with its analytical approximation,' is convenient for extrapolating measured values. The following expression also has been used in the literature' : GL

or

P

=

A exp[-(h/E)"],

m

=

1 or 2 .

(6)

The less chance there is of optical phonon scattering, the larger the chance of ionization. The ionization rate increases with the mean free path of the optical phonon scattering. It has been considered that better-quality material has a longer mean free path and, therefore, a larger ionization rate." Optical phonon scattering involves not only emission of the phonon, but also absorption of the phonon. More optical phonons are available for absorption when the temperature is high. Therefore, the ionization rate becomes smaller at higher temperatures because of shorter mean free path. The effective mean free path is related to lattice temperature by'

1 = A. tanh(gr/2kT).

(7) As the number of electrons increases, the effect of collisions between electrons becomes appreciable. In InSb, the generation rate increases faster than relation (5) predicts when the electron density is above 1014/~m3.6 This kind of carrier density is quite common in Si IMPATT diodes. However, it is not known if there is any deviation from (5) in the case of Si. The

' S. M . Sze and G. Gibbons. A p p / . f / 7 ~ . \ . Lett. 8. I I I (1966). G. A. Bardff, Ph.v.r. Rev. 128, 25017 (1962); Chynoweth' gives a convenient summary of this paper. ' C. R. Crowell and S. M . Sze. Appl. f / i j , s . Lett. 9. 242 (1966). l o C. A. Lee, R. A. Logan, R. L. Batdorf. J . J . Kleimdck, and W. Wiegmann, f / i ? s . Rrr. 134, A761 (1964).

380

T. MISAWA

x Ci

Ei /q EX FIG.

4. Baraff’s universal curves for ionization rate as a function of field. (After Chynoweth

ionization rates shown in Fig. 3 were obtained under the condition of very small carrier density.

8. GOVERNING EQUATIONS Changes in electron and hole densities are described by continuity

equations :

+ g U,, , ap/at = - q p ( d ~ , / i i x ) + g - L,,,, an/&

=

q - '(SJ,,/d.u)

-

(9) where g is the generation rate due to avalanche multiplication given in Eq. (5) and U,, and U,, are recombination-generation rates via localized levels (recombination-generation centers) in the forbidden gap.' Suppose there is only one type of recombination-generation center. The number of charged centers N i changes according to the following equation :

'

dNJdt

=

U c p - U,,.

(10)

In most cases, the U terms in Eqs. (8) and (9) are negligible compared with other terms. They will become important only when the space-charge region is depleted of electrons and holes at a certain phase of the oscillation cycle. This occurs when the current through the diode swings to the minimum. The electron and hole currents are composed of drift current and diffusion current, J , = -q~,n + ~ D , ( & I / ~ X ) , ( 1 1) J , = ~ ~ o , P- yD,,(Sp/Sx), (12) where D, and D, are diffusion constants. It is not well established what D, and D, should be in such a high field that drift velocities saturate." However, it may be reasonable to use the Einstein relation13 with a mobility ji defined as ju/El and electron or hole temperature,

D,

=

(kK/q)Lt7

D,

=

(kT,/m,.

The diffusion term is not important at higher fields except when the "wavelength" of carrier bunching is very small, which occurs at very high frequencies. It is important at the edge of the space-charge layer where the field is weak and the Einstein relation has a well-established meaning. Only Poisson's equation has been considered for describing the electric field, E & E / d X = y(N, - N , + N i+ p - n ) , (13) where E is the dielectric constant of the semiconductor and N , and N , are the densities of ionized donors and acceptors. Here, N i q represents the charge of recombination-generation centers rather symbolically. It may be negligible in most cases. 'I

l2

l3

W. Shockley and W. T. Read. Jr.. Phix. R w . 87. 835 (19521. Reasonable definitions of diffusion and its calculation were worked out at relatively low field by D. J. Bartelink and G. Persky, private communication and Appl. Phys. Lett. 16, 191 (1970). See, for example, W. Shockley. "Electrons and Holes i n Semiconductors." p. 300. Van Nostrand, Toronto, New York. and Landon. 19.50.

382

T. MISAWA

TABLE I Values used in normalization Quantity

(a)

(b)

5 Pm 8.5 x 10" cmjsec

10 pn 10' cmjsec 10- l o sec

2.71 GHz 1015/cm 3 1.36 x lo3 A/cm2 7.54 x lo4 V/cm

1.592 GHz

Expression

Length Velocity Time Angular frequency Frequency No. per unit volume Current density Field Voltage Impedance Admittance

36.1 mho/cm2

~

3.7 x lo3A/cm2 3.5 x lo5 Vjcm 350 V 0.0946 ohm-cm2 10.76 mhojcm'

' Used in Section 12d; w is the width of the space-charge region, u is the scattering-limited velocity, 7 is the transit time, unit admittance is the admittance of the space-charge-layer capacitance for a normalized frequency of 0.5. in Sections 12e and 13a; in Section 130. E, is the peak field in the avalanche region.

It is convenient to introduce dimensionless variables by normalizing various quantities in the equations. This facilitates not only manipulation of the equations by eliminating cumbersome coefficients, but also numerical solution of the equations. Table I lists the units for various quantities. Normalization is accomplished by choosing proper units for length, velocity, and carrier density or electric field. Various values will be used for the units in the following as indicated in the table.

IV. Analysis of Electrical Characteristics The equations given in the preceding part are sufficient to describe the behavior of the IMPATT diode, once the impurity profile and environment (circuit) are given. Actually, it is not only possible but also almost practical, with present-day computers, to solve the equations numerically to any desired accuracy. However, meticulously accurate solutions do not necessarily give good perspectives. In this part, we will discuss both simplified, approximate solutions and elaborate, accurate analyses. 9.

SPACE-CHARGE

LAYERIN pn JUNCTIONS

In a p n junction, the transition from p-type to n-type conductivity is very sharp and hence the change in electric potential takes place in a narrow region around the metallurgical junction. This narrow transition region, which is

7. IMPATT

DIODES

383

also called the space-charge region, is almost completely depleted of mobile carriers. Therefore, there is a large field gradient due to the charge of ionized impurities, as described by Poisson‘s equation,

i7EJ2.y

=

N, - N,,

(14)

which is now in normalized form. The situation prevails up to the point where the field determined by (14) drops to zero. Beyond this point, the impurity charge is neutralized by the space charge of the carriers and the field is very low. The description that the space-charge region is completely depleted of carriers, and that elsewhere space charge is completely neutralized, is a good one and simplifies the treatment of the space-charge region. As the reverse bias is applied to the pn junction, the space-charge region widens and the peak field increases to accommodate the increased voltage. As the junction is biased beyond breakdown, current starts to flow. Equation (14) still holds until the current increases so much that the carrier density becomes appreciable compared to impurity densities. However, after the carrier density becomes appreciable, the field profile is not determined by the impurity density only. The situation becomes complicated. In the space-charge region, the field is very high and electrons and holes drift away at scattering-limited velocities into n-type and p-type regions, respectively. The supply of carriers into the region is by thermal generation in the adjacent regions. For example, electrons are generated in the p region. They diffuse toward the edge of the space-charge region and, as soon as they arrive at the edge, they drift down through the space-charge layer to the 12 region. When the field is high enough, electrons produce electron-hole pairs in the passage and current starts to flow. 10. STATIC CURRENT-VOLTAGE CHARACTERISTICS

The static or dc characteristics of the pn junction in breakdown are obtained by setting the time derivatives in the fundamental equations to zero. The diffusion current is not important in the space-charge region where the field is high. The continuity equation for electrons then becomes dJ,Jdx

= ctJ,

+ PJ,,

where it is assumed that the x axis is perpendicular to the junction plane and is from p to n region. By using the fact that the total current J = J , + J , is independent of x, the hole current J , can be eliminated from the above equation, dJ”1d.X

- (X -

B)J,

=

DJ.

A small number of electrons enter the space-charge region from the p-type side and holes from the n-type side. We designate the currents

384

T. MISAWA

associated with them as J,, and J,,. Integration of the above equation with the boundary conditions J,(O) = J,, and J,(w) = J - J , gives

+ M,J,,,

J = M,J,,

(17)

where

M,

=

A

=

(19)

1/(1 - A ) ,

low/3s,’ exp[

(CI -

(20)

/3) dx’

When A approaches unity, the total current becomes very large. The condition of avalanche breakdown is A

=

IOwD { [s,^ exp

(cl

-

D) dx‘]

}

dx = 1

From a symmetry argument, the above equation can be written as

The analytical solution given above is useful only when CI and /3 are known functions of x. This is the case when the current is small and the space charge of the carriers is negligible. The field is then determined solely by the impurity distribution. Then, cl and 3/ are fixed functions of x independent of current. For most of the studies on current multiplication and avalanche breakdown, the assumption of negligible carrier space charge does not impose any serious problem. The above equations have been extensively used in experimental determinations of c( and p from measured M’s or breakdown voltage and in theoretical estimate of breakdown voltage in various structure^.^,' However, when one wants to know current-voltage relations after breakdown, this simplified solution becomes worthless because, at higher currents, the voltage remains the same as the breakdown voltage. Changes in field profile due to carrier space charge have to be taken into account . When the carrier space charge cannot be neglected, the complexity of the problem increases by orders of magnitude. This is because the modified field affects the carrier distribution. Now, neither field nor carrier density can be obtained independently, and the whole problem has to be solved

385

x e -x

erfc ( -1

L2

0

xi

Xe

X

FIG. 5. Silicon “abrupt”-junction diode made on epitaxial layer. C, = 10”/cm3, L , = 1.123 pm, X , = 3 pm,C , = 8 x 1015/ccm3,C,,,, = 1.5 x IOI9/cm3, L , = 0.3743 I‘m, X , = 7.5 pm.

self-consistently. An analytical solution is impossible except for some special cases which are remote from reality.I4--l6 Numerical analysis with a modern computer has been successful in solving the p r ~ b l e m . ” ~Appendix ~* A explains the details of solution. We will discuss the results of such an analysis of two structures. One structure, a diffused “abrupt” junction, has been used often in actual IMPATT diodes, and the other, an idealized pvn diode, is of some interest because of its dc negative-resistance characteristics. The “abrupt” junction is made by diffusing acceptors into a uniformly doped n layer. When the junction is shallow, the field profile is more or less triangular and resembles the ideal abrupt junction. In the actual diode, the junction is made on an epitaxial layer grown on a low-resistivity substrate. The epitaxial layer is made thick enough so that the space-charge layer terminates in front of the substrate. The space-charge layer extends into the substrate at high current density or high temperature. Figure 5 shows the impurity distribution of the silicon abrupt-junction diode to be analyzed. The field and current distribution of the diode are shown in Fig. 6a for six bias currents, 100, 200, 500, 1000, 2000, and 5000A/cm2. The negative charge of electrons partly compensates the positive charge of donors in the epitaxial layer. Because of this, the space-charge region extends further toward the substrate at higher currents. At the highest current, the field

’‘

J. 8. G u m . in “Progress in Semiconductors’. ( A . F. Gibson, ed.). Vol. 2. p. 213. Hcywood,

I”

London. 19.57. Hideharu Egawa. l E E E T,.tr/rs. E / w / ~ ~Dcc>iws J/? ED-13. 754 (1966). B. Hoefflinger. l E E E Eons. Electrori Dci>ic,e.sED-13. 151 (1966). T. Misawa. lEEE Trms. E k t r o n Dczvw.s ED-13. 143 (1966). H.C. Bowers. IEEE f i r m s . Elecrron Deciicrs ED-15. 343 (1968).

386

T. MISAWA

400

I t -

z W LT

IT

0.8 300

2 -1

2 0

E

0.6

\

1

t c

z

L 200

W

LL

0.4

_J 0

w LL

5 u

z

I00

0

0.2 0

W -I

W

0

0

FIG. 6a. Field and current distributions of the Si abrupt junction in Fig. 5. 130

I20

110 v)

IA

0 5

100

90

80

0

1

2

3

4

5

DENSITY IN kA/cm2 sec

CURRENT

FIG.6b. The V-I curves at four temperatures of the Si abrupt junction in Fig. 5.

1.0

400

z W

a 0.8

5 u

300

-I

a 0.6

z -

t0 I\

200

F-

z

LL

0.4

w

a a 3 V

z 0

0.2 a

RATIO

CURRENT

k

V

W

W

0

0

1

2

3

4

5

6

7

8

9

0 10

DISTANCE IN p m

FIG.7a. Field and current distributions of Si pvn diode with a width of 10 pn and v-region doping of N , = 7 x 10'4/cm3.

penetrates into the substrate. This shows up as a sharp change of field near the n-side end. The current distributions shown by dashed lines in Fig. 6a indicate that avalanche multiplication takes place over a region about 1 p wide on the n-type side of the field peak. Since electrons have a larger ionization rate than holes in silicon, the avalanche region is shifted toward the n-type side with respect to the field peak. There, more electrons with the larger ionization rate are present than on the p-type side. The calculated current-voltage characteristics are plotted in Fig. 6b. Curves at various temperatures are obtained by using temperature-dependent ionization rates discussed in Section 7. Since the computation neglects thermal generation of carriers, the curve at the highest temperature (600°K) may not be accurate. The slope of the curves is very close to what is expected from space-charge resistance. l 9 Next, we consider an idealized p\w structure which has a constantly doped v region sandwiched between very highly doped p and n regions. The edges of the space-charge region remain fixed at the edges of the v region after punchthrough, as reverse bias is applied. Figure 7a shows field and current distributions and Fig. 7b shows current-voltage characteristics of a Si diode whose v region is 10 p wide and has a donor density of 7 x 1014/cm3.

''

S. M . Sze and W. Shockley, Bell SW. Twh. J . 46, 839 (1967)

388

T. MISAWA

250 24 0

200

h I 0

I

I

I

I

I

I

I

I

I

2

4

6

8

10

12

14

16

18

20

CURRENT D E N S I T Y IN k A / C m '

FIG. 7b. The V-I curve of the Si pvn diode of Fig. 7a.

In Fig. 7a, we notice that the field profile is profoundly distorted at high current densities where the mobile carrier densities exceed the ionized donor density. From the current distributions shown by the dashed lines, it is seen that avalanche multiplication takes place all over the space-charge region at low currents and it becomes confined at both edges as the field becomes distorted at high currents. It is to be noted that the voltage across the diode decreases as the current is increased. This dc differential negative resistance may deserve more detailed attention and has been the subject of many reports. In order to have a certain amount of current through a pn junction in breakdown, a certain amount of carrier generation is required. The larger the current, the larger is the amount of generation. As the current is increased, the field profile changes due to the charge of added carriers. If this change in field is such that a greater amount of carrier generation is obtained with reduced voltage (which is the integral of the field over the region), a negative resistance results. Generally, the increase in generation rate for a given increase in field is larger at the place where the field is higher. Therefore, negative resistance is obtained when the added charge due to the increased current causes high fields to rise and lower fields to fall. In the space-charge

389

FIG.8. Electric field E and carrier generation rate g before a small increase in current 61, and changes in carrier densities, electric field, and generation rate after the increase in current for (a) negative and (b) positive differential resistance cases. For case (a), J6g dx = 61 and 5 bE d x < 0 ; for case (b), I6g d x = 61 and 6 E d x > 0.

region, the added charge lowers the field in the center and raises it near the ends. This is because more electrons are added near the n-type end and more holes near the p-type end. Therefore, roughly speaking, the differential resistance is likely to be negative when the field profile is upward concave and positive when upward convex. The situation is illustrated in Fig. 8. Actually, the above statement is too crude. The presence of negative resistance has to be determined case by case. Let us consider a special case of constant electric field across the spacecharge region. When electrons and holes have equal ionization rates, the condition of breakdown, Eq. (21), becomes

390

T. MISAWA

When a small change in field 6 E is introduced, the above condition is written as

jOw(dol/dE)6E dx

= 0.

Since the field is constant, da/dE is also constant. Then, the above condition reduces to

IOwdEdx= 6 V = 0. Therefore, the differential resistance is zero. When the ionization rates of electrons and holes are not equal, a similar argument leads to

It has been found with numerical analysis that, when a’/p’ < a//?,the differential resistance is negative, and when cr’//?’ > a//?,it is positive. In the actual diode, the field does not drop vertically as in the above ideal cases. The effect of the charge of added electrons and holes is largest in these low-field regions at the edges. According to the preceding argument, this contributes to the positive resistance. A substantial upward concavity in the center portion is required to obtain negative resistance against the unfavorable effect of the end regions. Sometimes, unequal ionization rates of electrons and holes contribute to more negative resistance, as seen in the above case of constant field. There, negative resistance is obtained even with a flat field profile when conditions are favorable. The unequal ionization rates must contribute to the negative resistance in Fig. 7b of the Si p v n diode. 1 1 . GROWING WAVEIN AVALANCHING ELECTRON-HOLE PLASMA~O

The simplest way to investigate the dynamics of avalanche multiplication is to consider the plane waves in the uniformly avalanching, infinite, electronhole plasma. This is because the infinite size of the actual device introduces additional complexity. We consider the simplest case, namely electrons and holes have equal ionization rates and drift at the same scattering-limited velocity. Diffusion and generation-recombination via localized levels are neglected. Then the fundamental equations become, in normalized form,2oa

i3Eld.x

=

N,

-

NA+p - n,

(24)

+ g n + p),

(25)

anpt = 8 . 1 ~ 8 .

T. Misawa. IEEE Trans. Electron Devices ED-13, 137 (1966).

7. IMPATT

DIODES

+

39 1

aplat

=

- ( S J , / ~ . ~ ) r(n+p),

(26)

J,

=

-n,

(27)

-17.

(28)

J,=

The x axis is in the direction of the electron flow. When the time-varying ac part of various quantities in the above equations is much smaller than the time-independent part, the equations can be linearized for the ac components which vary like ej"". Then, we haveZoa dE/dx = J ,

-

J,,

(29)

+ (a- jw)J,,+ aJ,,

(30)

dJ,/dx

=

a'JE

dJ,/dx

=

-a'JE - aJ,

-

( M - jw)J,,

(31)

where a’ = da/dlEl and J is the total dc current. In the case ofconstant electric field, a and a’are independent of x. Therefore, all the coefficients in Eqs. (29H31) are constant. Then, according to a theorem on linear differential equations,*' the solution is a sum of terms of the form e-jkx with three different values of k. It is found that one of the k's is zero and the other two are the roots of the following dispersion relation:

k2

+ 2a'J

- j 2 t m - w 2 = 0.

(32)

Let us discuss in more detail the wave solutions of Eqs. (293-(31). The dispersion relation (32) is solved for o as jw

=

a

+ (a2-2a'J

- k2)lI2.

(33)

When k is real, we have a spatially sinusoidally varying perturbation. Equation (33) shows that the perturbation grows exponentially with time. When the wavelength is small (large k ) or the current is large, the quantity in the square root sign of Eq. (33) is negative. In this case, the perturbation oscillates in time and propagates in space while its amplitude grows. The time constant for the growth is a.This growth of the periodic carrier bunching is a rather remarkable phenomenon. For, one might think that avalanche multiplication would randomize the regular carrier bunching, especially since electrons and holes created by avalanche move away in the opposite direction. Let us examine in more detail how this growth of bunching or instability is obtained. First, we consider the case when carriers drifting at the scatteringlimited velocity receive a spatial density perturbation. Avalanche multiplication has not yet set in. The perturbation in density, or bunching of carriers, ""The scattering-limited velocity was chosen as unit velocity in the normalization. 2 1 See, for example, I. S. Sokolnikoff and R. M. RedhefTer,"Mathematicsof Physics and Modern Engineering," p. 100. McGraw-Hill, New York, 1958.

392

T. MISAWA

-

dc E

LARGEST DENSITY

ELECTRON DENSITY

HIGHEST IONIZATION e+ j w t

IONIZATION

FIG.9. Instability in avalanching electron-hole plasma. In the figure, the tildes indicate vectors. (After Misawa.")

does not decay, as discussed in Section 2, because the dielectric relaxation does not take place. (We are neglecting diffusion.) When electrons bunch periodically in space, the bunching moves toward the positive x direction at the scattering-limited velocity without decay. This corresponds to the root with the plus sign in Eq. (33) with tl and a' equal to zero. The situation is illustrated schematically in Fig. 9. An electric field perturbation accompanies this electron density perturbation. As is seen from Poisson's equation, the field lags the electron density by 90". Now, we consider what happens when avalanche multiplication is introduced. Since the dc field is in the negative x direction, the highest field is obtained when the ac field is at the negative peak, as indicated in Fig. 9. We have more generation (or ionization) when there are more electrons and when the field is stronger. Therefore, the largest generation takes place somewhere between the place with the largest density and the place with the highest field. Thus, the generation rate leads the electron density by less than 90". The extra electron density created by the avalanche lags the generation rate by 90". The resulting, modified electron density now leads the field by less than 90" and the

accompanying current lags the field by more than 90" (remember the electron charge is negative). This makes the ac power dissipation negative. The perturbation gets energy from the dc field and grows in amplitude. Holes created by avalanche also form a periodic pattern. It turns out that the pattern is dragged by the electron-density wave and moves in the same direction as the latter, although individual holes moves in the opposite direction. The hole-density wave also lags the field by more than 90". The situation discussed here may be modified appreciably by the presence of the boundary. However, the above instability present in the infinite plasma indicates that a terminal dynamic negative resistance is obtained when we have uniform avalanche in the space-charge region of the pn junction. This case will be discussed in more detail in Section 12d. 12. SMALL-SIGNAL ANALYSIS

It is rather a simple matter to analyze the case when the time-dependent component is much smaller than the dc component, because the relevant equations are linear. In the IMPATT diodes, it has been found that the smallsignal analysis is very useful as a guideline in designing the oscillator diode, although theoretically there is only a rather philosophical relation between small-signal characteristics and oscillator performance. The practical importance of the small-signal analysis is based upon this empirical fact. a. Generai Analysis-N

uinericul Approach

L 7 3 2 2

The analysis to be discussed here assumes that diffusion is negligible in the space-charge region. This will be a reasonable assumption as long as the diffusion length for the transit time is smaller than the wavelength of the space-charge wave in the space-charge region. The equations to be solved are similar to Eqs. (29H31) and are listed in Appendix B. They look more complicated because electrons and holes do not have the same ionization rate and velocity and because field dependences of velocities are taken into account. Extra complexity arises because now coefficients of the equations are not constant. The dc electric field is not constant and J , and J , do not appear in the form of the sum. These dc quantities must be determined beforehand as functions of position. The method of analysis discussed in Section 10 may be used for this purpose, The boundary condition is that the electron current and the hole current are given as J,, and J, at the p-type and the n-type ends, respectively. Another constant that enters the problem is the total current through the diode J . Because of the linear nature of the problem, any quantity, such as electron or hole density, electric field, and so on, is composed of three terms, each of H. K . Gummel and D. L. Scharfetter. Bell. S

j ~ tTuch

J . 45, 1797 (1966)

394

T. MISAWA

600 2 00

500 400 N

N

E

300

0

2 c

100

0

c

E E

200

E

z -

I d

100

0

z

z U

2

0

O

3 D

z

-100

0 0

t

W 0

2 v)

-200 -100

0

10

20

30

FREQUENCY I N GHz

FIG. 10. Small-signal admittance of Si abrupt-junction diode at a bias current of lo00 A/cm2.

which is proportional to J,,, Jps,or J. The voltage across the space-charge region, which is the integral of the field, is not an exception : V

=

I

E dx

=

ZJ

+ Z,,J,, + Z,,J,,

.

(34)

Z, Z,,, and Z,, are the final products of the computation, and therefore depend upon the structure of the diode (impurity profile), material constants, bias condition, and frequency. Ratios of J,, and J, to V are on the order of magnitude of the conductance of the reverse-biased pn junction. Their values are much smaller than l/Zln or l/Z,,. Therefore, the last two terms on the right-hand side of (34) are neglected and Z is the impedance of the spacecharge layer. The ratios Z,,/Z and ZIp/Zare the ac counterpart of the dc multiplication factors M , and M , in Eqs. (1 7H20).The impedances Z,, and Z,, are important in the case when J,, and J, become comparable to J, for example, by photogeneration. Appendix B gives the details of the calculation. Figure 10 shows the calculated admittance, G = 1/Z, of the Si p n abrupt junction at a current density of loo0 A/cmZ, whose dc characteristics were discussed in Section 10. The susceptance is inductive at lower frequencies, goes through a resonance, and approaches the susceptance of the space-

395 CONDUCTANCE

POS. - ----

SUSCEPTANCE

__

NEG.

---_

A = 100 A / c m 2

B = 200

C =

F

D = 1000 A/crn2 E - 2000 F = 5000 I

I

2

I 3

I I 1 I I l l 4 5 678910

I

I

I

2

3

4

I l l 1 1

5 6 789100

FIG. 1 la. Small-signal admittance of Si abrupt-junction diode at various bias currents: frequency versus admittance.

charge-layer capacitance at higher frequencies. The conductance is positive at lower frequencies and turns negative at a frequency that is slightly lower than the resonance frequency mentioned above. The magnitude of the negative conductance peaks at about 16 GHz and then decreases toward higher frequencies. The admittance at various other currents is plotted in Figs. 1la, b. Very roughly speaking, the admittance increases proportionally to the current. It is seen that both the resonance and the cutoff frequencies increase proportionally to the square root of the bias current. For a fixed frequency, the negative conductance initially increases proportionally to current, reaches a peak, then turns over, and finally becomes positive above a certain critical value. This change of sign takes place at higher currents when the frequency is higher. Another important small-signal parameter, which has been found particularly useful in connection with oscillator performance of the diode, is the Q defined as Q = energy stored in diode/energy dissipation per radian

396

T. MISAWA

B

100

G

mho/crn2

FIG.l l b . Small signal admittance of Si abrupt-junction diode at various bias currents.

where E is the dimensionless field (see Table I) when unit ac current flows through the diode and R is the real part of the diode impedance. This is a measure of how effectively ac power is generated in the diode, and indicates the buildup rate of oscillation when the diode is used as an oscillator. A smaller magnitude of the negative Q indicates a better quality of the negative resistance. Figure 12 shows the Q of the diode whose admittance was discussed before. For a given bias current, the magnitude of Q exhibits the minimum at a frequency close to that which gives the maximum magnitude

397 100 8 6

4

A

I

I

I

1

I

l l l l

I

I

1

1

1

1

1

j

FREQUENCY IN GHz

FIG. 12. Small-signal Q of Si abrupt-junction diode as a function of frequency and bias current. Curve: A, 100A/cm2; 3, 200A/cm2: C , 500A/cmZ; D, l kA/cmZ; E, 2kA/cm2: F, 5 kA/cm2. CONDUCTANCE SUSCEPTANCE

01

2

3

4

NEG -

POS

-

5 67891 FREQUENCY IN

--__

2

3

4

5 6 78910

GHz

FIG. I3a. Small-signal admittance and Q of Si pvn diode. Parameter IS bias current. Curve: A, 100A/cm2; B, 200A/cm2; C, 500A/cm2; D, 1 kA/cmZ; E, 2 kA/cm2; F, 5 kA/crnZ; G, 10 kA/cmZ; and H, 20 kA/cm2.

398

T. MISAWA

loo

F -

10

-w >

-

b

5w

l

-

-z 0

r

-

--

0.01 0.I

2

3

4

5 67891

2

I 3

I 4

l l l l l 5 678910

F R E Q U E N C Y IN GHz

FIG. 13b. The Q of the Si pvn diode of Fig. 13a.

of the negative conductance. The optimum frequency goes up with current, again proportionally to its square root. The quality of negative resistance improves as the current is increased, up to a certain current. In this particular diode, the best negative resistance is obtained at about lo00 A/cm2. Above this current, the negative resistance degrades. The optimum frequency of the diode is about 15 GHz. It has been considered that better quality of the small-signal impedance indicates better oscillator performance. A more detailed discussion in this connection will be given in Section 12f. Figure 13a shows the small-signal admittance and Fig. 13b the Q for the pvn diode whose dc characteristics were discussed in Section 10. Because of the presence of dc negative resistance, the conductance remains negative at lower frequencies, in contrast to the case of the abrupt junction. Note that with the space-charge layer width of 10 pm,the transit angle (0 = cowd) is II at about 5 GHz. The susceptance shows similar resonance characteristics as in the abrupt junction. The Q is better at lower frequencies and improves as the bias current is increased. As was the case with dc negative resistance, the low-frequency characteristics are sensitive to slight changes in doping at the edges of the space-charge region. When the doping changes realistically from the heavily doped end regions to the center region, the low-frequency negative conductance tends to disappear, especially at lower currents. However, the characteristics at higher frequencies (around and above the resonance frequency) remain more or less the same.”

7. IMPATT

399

DIODES

The general analysis given above has the merit of being straightforward and exact but gives hardly any insight into what is going on inside the diode. In the following, we discuss a more idealized analysis which sheds more light upon the relation between device structure parameters and characteristics.

6. Drift Regionz3 First, we consider the region where no avalanche multiplication takes place. We assume that electrons (and holes) move at the scattering-limited velocity. Then the injected, bunched electrons flow down the drift region without any debunching. From Eq. (30) with CL = 0, the electron current is given byzoa J, = JnOe-Jwx, (36) where J,, is the injected current at x

E

=

=

0. The associated electric field is

Eo - (J,,/jw)(e-j"" - I),

(37)

where E, is the field at x = 0. The x axis is in the direction of electron flow and the scattering-limited velocity is taken as unit velocity. The important jwE,. By relation here is the one between J,, and total current J = J,, integrating Eq. (37) over the width of the drift region w,, we obtain the following expression for the total current :

+

J = j(O/wd)vd

+ PdJnO

7

(38)

where /?d = (1 - e-jo)/jO, 8 = OW,, (39) and V, is the ac voltage across the region. The first term of (38) is the current through a capacitor whose width is wd. The second term represents a current proportional to the injected electron current. The coefficient is a current transfer factor whose magnitude and phase change according to the transit angle 0 as sketched in Fig. 14. It may be interesting to note that, although the electron current given by (36) rotates all the way around the origin in the phase plane, the current through the region based on the electron current remains in the two lower quadrants of the complex plane. Corresponding to the two current components mentioned above, the equivalent circuit is a parallel connection of a capacitor with a as shown in Fig. 15. width of wd and a current generator PdJnO

c. "Narrow" Avalanche Region--Read's Original Approach1vz3

Analysis of the avalanche region where avalanche multiplication takes place is complicated. Read was able to simplify analysis to a substantial

'' M . Gilden and M . E. Hines, l E E E Tram. Electron Dwrces ED-13, 169 (1966).

400

T. MISAWA

FIG.14.Schematic of complex current transfer factor Bd in the drift region.

degree by the following assumption: the total particle current, i.e., the sum of electron and hole currents, does not change with position although each component is dependent upon position. We know that this is true when the currents do not change with time. However, he assumed that this would remain approximately correct as long as the currents change slowly with time. He claimed that the approximation is good when the avalanche region is narrow and the transit angle through it is small. The merit of this approximation is much more appreciated in large-signal analysis than in small-signal analysis, for the approximation made it possible to solve the all-but-intractable problem. Following Read, we assume that electrons and holes have equal scatteringlimited velocities and ionization rates. We obtain the following continuity equations for electrons and holes20a: aJjat

=

-(a~,jax)

+ MJ,,

+

aJ,pt = ( a ~ , / a x ) G I J ~ ,

(40) (41)

where J o = Jn(x,t ) + J,(x, t ) is independent of x according to the abovementioned approximation. A tractable equation is obtained by adding the -., J

b FIG.15. Equivalent circuit of drift region. Tildes indicate vectors.

401 above two equations, d(J,

+ J,)/dt

=

dJ,/dt

=

[ d ( J , - J,)/dx]

+2d,

Noting that J , is a function o f t only, the above equation is integrated over the avalanche region of width wa, r wa

W,

dJo/dt

=

IJ, -

J,lta + 25, J

tl

dx

0

=2 4

J-1

ctdx - 1 )

+ 25,.

The currents are in normalized units.20aIn (42), it is seen that the dynamics in the avalanche region are represented by a single, ordinary differential equation. Equation (42) can be linearized for small ac parts as follows :

J,

=

(2dJ/jo)EO,

(43)

where 2 is the average of dcc/dE over the avalanche region and 5 is the total dc current. In Read's approximation, a unique, position-independent ac field E, exists in the avalanche region because the displacement current juE,, is also independent of x. Combining the displacement current and the inductive current, the avalanche region is represented by a parallel connection of the following inductor and capacitor,20a -

La = wa/2dJ,

(44)

c, = l / W a .

(45)

The expressions are for unit area. A realization of the Read diode is illustrated in Fig. 16. The impurity distribution in this p + n v n f structure is tailored in such a way that the field in the v region in breakdown is high enough to maintain the electron saturation velocity but low enough to confine avalanche multiplication within the p'n junction region. By properly choosing a value for the avalanche region width, the structure can be analyzed by Eqs. (43),(38), and (39).The equivalent circuit is shown in Fig. 17. Assuming that W, is negligible, Read approximated the total admittance by that of the drift region whose width is equal to the total space-

402

T. MISAWA READ DIODE

P+

n

FIG.16. A p'nvn'

v

n+

Read diode.

FIG.17. Equivalent circuit of Read diode. Tildes indicate vectors.

charge-layer width and obtained the following expression for the admittance20a: 0 2Y Y ( 0 )= u! 1 - e - j o - j 2 y ’ Y - - ( lww -)b),

o2

2

The small-signal admittance calculated from the above expression reproduces most of the behavior of the exact admittance obtained from the numerical analysis shown in Figs. 10 and 11. A major qualitative difference between Read’s approximation and the exact analysis is the fact that in the former both real and imaginary parts of the admittance change sign at a single frequency o,,while in the exact analysis the real part changes sign at lower frequency than the imaginary part. However, Read’s expression will be quite valuable when one wants to have a rough idea about the smallsignal characteristics of a diode whose avalanche region is not wide. Read’s original equation (42) governing the dynamics of the avalanche region can be extended to the case when electrons and holes have different ionization rates and scattering-limited v e l ~ c i t i e s Under . ~ ~ the assumption that the value of the total particle current is independent of position, one obtains the following extended equation :

24

C . A . Lee, R. L. Batdorf, W . Wiegmann. and G. Kaminsky. J . A p p l . P h ~ a 38,2787 . (1967). The particular expression in the following is given by C . A. Lee, in “High Frequency Generation and Amplification Conference Proceedings,” p. 243. Cornell University School of Electrical Engineering, Ithaca. New York, 1968 ( A D 666-582).

404

T. MISAWA

and M , and M , are given by Eqs. (18) and (19) with the integration interval replaced by the avalanche region. The extended equation, Eq. (47), will be useful because silicon, one of the most used semiconductors for the IMPATT diode, has quite different ionization rates for electrons and holes. It is to be noted that, although M and T~ are dependent upon the composition of the primary current, JAs and Jhs, their product, which appears in the first term of (47), is independent of it. When electrons and holes had the same properties, z1 was one-half of the transit time across the avalanche region.

d . “Wide” Avalanche Region-pin Diode When the field is constant, analytical solution of small-signal characteristics is possible even for a “wide” avalanche r e g i ~ n . ~ We ~ . ~discuss ’ the simple case when electrons and holes have equal characteristics except sign of charge.26 The analysis may be applicable to a pin diode. As discussed in Section 11, the small, time-varying parts of the field and particle currents are each composed of three terms as follows:

E

=

C,ejkx

+ C,e-jkx + [ ( ~ c-I j o ) / k 2 ] J , + o)C,e-jkx - (u’J/kZ)J,

(53)

+ o)C,ejkx+ +j(k - c 0 ) ~ ~ e-- (jM ’J/k2)J, ~~

(54)

J, = +j(k - o)C,ejkx - ) j ( k

,

J = -- j ( k

(52)

where k is one of the roots of (32),

k

= (0’ -

2a‘J

+~~wcI)’”,

and C, and C , are constants to be determined by the boundary conditions. We choose CI so that the breakdown condition tlw = 1 is satisfied, i.e., M = 1 when the width of the space-charge region is chosen as unit length for normalization. From the left side, electrons enter the region, giving rise to an electron current JnS.At the right end, the hole current is equal to J,,. These two conditions are sufficient to determine the values of C, and C , . Thus, the impedance of the pin diode can be calculated from the general expression (34).We showed there that actually J,, and J,, are equated to zero. The calculated small-signal admittance of a model diode is shown in Fig. 18. Actually, the admittance of the space-charge layer as a capacitor ( j w / w = j o , with w as unit length) was subtracted. The diode is essentially a 5-pm-wide Si diode, an average value between electron and hole ionization rates having been used. The units of normalization are given in column (a) of Table I. The susceptance is inductive and is almost that of a fixed inductor. 25

26

S. T. Fisher, ZEEE Trans. Electron Devices ED-14, 313 (1967). T. Misawa, ZEEE Trans. Electron Devices ED-14,795 )1967).

LO

.\

-

w

V

z

a Ik

-.

-

-

n

lo-‘ -

W

2

$

10-2

\

I

\

\

I

-ah.

‘\

-\.

-

- REAL - IMAGINARY

N J a

‘\.g.o

\

h\

5 0

a

.I \

I

,.f..2 . f .. **.,CURRENT

o...

-

0.1

----

1

--

0.01

1

I

I

1

I

I

I

1

I

1

1

1

NORMALIZED FREQUENCY

FIG.18. Small-signal admittance of idealized pin diode. (After Misawa.*’)

The arrows in Fig. 18 indicate resonance frequencies where the “inductors” resonate with the space-charge-layer capacitance. The conductance is negative and almost constant over the frequency range shown. It turns out that the low-current, low-frequency approximation of admittance is very good in the current and frequency range investigated.26 The approximation formulae are G, = d J / 5 (55)

La-‘ = 3 d J / w , (56) where w is the width, and is equal to unity in the present normalization because it was chosen as unit length. The expression for the inductance is the same as that for the narrow avalanche region (44) except for the numerical factor.26aThe only new thing here in the wide-region case is the frequencyindependent negative conductance given by (55). Comparing the results obtained above with the admittance of the pvn diode shown in Fig. 13, which was obtained by a numerical method, we see that the simplified analysis can reproduce the essential features of the admittance over an octave of frequency centering on the resonance frequency. At higher currents, the field in the pvn diode becomes distorted because of mobile carrier charge and its admittance behaves differently from that of our pin diode. However, our simplified model still can describe the behavior of a structure that is made to have uniform field at these high currents. 26”Thedifference in the numerical factor was also pointed out by Fisher.”

406

T. MISAWA

n TYPE

p TYPE a = CONST

JPO

DRIFT

AVALANCHE

DRIFT

REGION

REGION

REGION

FIG.19. Simplified model of general IMPATT diode.

e. General Case-IMPATT Diode

A general IMPATT diode whose avalanche region may not be narrow can be analyzed by connecting the drift-region solution of Section 12b with the avalanche-region solution of Section 12d.26 Although this kind of approach may not be good for the meticulous analysis of experimental data, it gives a general idea of how the characteristics of the diode change with structure parameters. Let us consider a general structure shown in Fig. 19 with one constantavalanche region followed by two drift regions which receive electrons on the n-type side and holes on the p-type side. The avalanche-region solution is the same as that in the preceding section. We know the values of electron and hole currents at the boundaries with the drift regions. When the injected particle current is known, the solution in the drift region is obtained from Eqs. (36)and (37). The small-signal admittance and Q are calculated according to the general procedure. By combining the equivalent circuit of the drift region in Fig. 15 with that of the avalanche region explained in the preceding section, we obtain a general equivalent circuit shown in Fig. 20. Each drift region, whose capacitance and current transfer factor are suffixed with n or p according to whether it is located on the n- or p-type side, has a current generator /jdJnO. The JnOis not as simply related to the components in the equivalent circuit of the avalanche region as in the case of the Read diode shown in Fig. 17. In the Read diode, JnOwas a component of current which flows through La. In the present case, it has to be computed from the avalanche-region solution. The results of an analysis along the line explained above will be presented for a series of diodes whose avalanche regions occupy from 10% to 100% of the 10-pm-wide space-charge layer. The avalanche region is located at one end of the space-charge region so that the diode has only one drift region. Pertinent data for the diodes are listed in Table I1 and units for normalization in column (b) of Table I. The diodes are assumed to be Si diodes. For the

7. IMPATT

407

DIODES

FIG.20. Small-signal equivalent circuit of IMPATT diode.

ionization rate, the average value between electrons and holes shown in Fig. 3 is used. The breakdown voltage in the last column in Table I1 is obtained by assuming 100 kV/cm in the drift region. Figure 21 shows admittances of the six diodes at a bias current of 0.0704 or 260 A/cm2. The real part is plotted in Fig. 21(a). As the avalanche region becomes wider, the frequency range over which the conductance is negative increases and its magnitude decreases. Also shown in the figure is the conductance of a Read diode with M , of 0.1 calculated from (46). It is seen that our SIMU-1 behaves almost in the same way. The bias current of 0.0704 was chosen so that the conductance of the Read diode at transit angle n is positive above this value. The imaginary part is shown in Fig. 21(b). Except for the 10% unit, SIMU-1, the behavior is more or less the same as the pin unit, SIMU-6. TABLE I1

Structure No.

Fraction of avalanche region

a

SIMU-1 2

0.1

3 4

0.5

2

2 ;

5 6

0.9 1.o

1.5 1.11 1

1 3

10 3

*’

60 21.98 15.69 12.69 9.61 8.8 I

v (V) 125 162 184

202 229 239

408

T. MISAWA 3

I

J = 0.0704 ( JI) SCALE

2

w

u Z a tu

I

3 0

z

0

u o

n W

N

a

I LL

0

-1

2

-2

-? TRANSIT ANGLE IN RADIANS

FIG.21a. FIG.21. (a) Real and (b) imaginary parts of the admittance of the six structures listed in Table I1 as a function of frequency (transit angle) for bias current of 0.0704, or 260A/cm2. (After Misawa.26)

One of the outstanding dependences of characteristics on avalanche-region width is obtained when the small-signal Q is compared between the structures. Figure 22 shows the small-signal Q of the six structures at five bias currents ranging from 130 A/cm2 to 2090 A/cm2. In the 10% unit, SIMU-1, the Q assumes the best value at the lowest bias current shown for the transit angle of about n. Although not shown, the Q degrades at still lower currents as was the case with the abrupt-junction diode shown in Fig. 12. As the avalanche region widens, the optimum frequency for this bias current decreases and the Q degrades. It is seen that a larger bias current is required for the optimum Q with a wider avalanche region. This bas an important practical implication :as an oscillator, the structure with a narrower avalanche region will reach a “reasonable” efficiency at lower bias currents. This is an advantage for CW operation.

7. IMPATT

409

DIODES

10

4 8 7 w

0

z 6

a

In w 5 0 v)

3

m 4 0

w

2

3

J

a

2

a 2 0

z

I

C

1

-2 0

1

2

I

I

3 4 5 6 7 8 T R A N S I T ANGLE IN RADIANS

I

I

I

9

I

FIG.21h.

,f: Implication of Small-Signal Q with Regard to Oscillator Perfbrmance

Since it is possible to perform extensive analysis of the diode in the smallsignal regime because of its simplicity, it will be very convenient if the largesignal performance of the diode can be predicted from the small-signal analysis. Here, we consider how the small-signal Q may be used as a measure of oscillator performance of the diode.26 The Q was defined in (35)as 271 times the ratio of average ac energy stored in the diode to average energy dissipation per cycle. This can be written as

where W is ac energy stored in the diode and the angular brackets indicate the time average over one cycle. When the diode has a negative resistance, dW/dt is positive and Q is negative. It is seen that the Q is a measure of how

I0 5

100

I 5

9

z 100

I

I

I

1

I

2

3

4

5

1

1

1

1

I

l

l

6

7 8 9 1 0

-- 3

I

3 (0)

4

5

I

6

I

I

I

7 8 9 1 0 1

TRANSIT ANGLE I N RADIANS

1

Ib)

FIG.22. Small-signal Q of the six structures listed in Table I1 as a function of frequency for bias currents (1)-(5): (1) 130, (2) 260, (3) 520, (4) 1040, (5) 2090 A/cmZ.The dashed lines are for negative Q and the solid lines for positive Q.The arrow indicates the resonance frequency.

(After Misawa.26)

F

effectively the stored energy is used to deliver power to the outside world. The smaller is its magnitude, the more effective is the diode. Another way of interpreting the Q is that it is a measure of how rapidly the oscillation builds up. Actually, the oscillator is composed of the diode and a circuit. The buildup rate of the energy of the total system is

( d W / d t ) = (dWd/dt)

+ (dW,/dt)

-w[((wd>/Qd)i((Wc>/QC)l - W ( W ) / Q , (58) where the suffices d and c refer to diode and circuit and quantities without a suffix are for the total system. The ratio between ( W,) and ( W , ) depends upon the individual case. In order for the oscillation to build up, the magnitude of Qd has to be less than Q,( W,)/( W,). This fact also indicates that a smaller magnitude of Qd means a better quality. As oscillation builds up, Qd degrades and a stationary state is obtained. It is very likely that the final amplitude will be large when lQdl is small and oscillation builds up vigorously. In this sense, Qd can be a measure of the final oscillation amplitude. =

13. LARGE-SIGNAL ANALYSIS Information on oscillator performance on the IMPATT diode can be obtained only from the large-signal analysis, no matter how helpful the small-signal analysis is. The large-signal analysis consists in solving fundamental equations given in Section 8 according to time evolution. This makes it necessary to use a numerical approach. Some effort has been done along this line with the help of a computer. The computation is rather bulky because it involves integration both in space and time. On the other hand, in his original analysis, Read was able to perform the space integration analytically with simplifying assumptions and obtained most of the essential features of large-signal operation of the narrowavalanche IMPATT diode.' In the following, first we discuss Read's analysis and then present some results of numerical analysis which have appeared in the literature. a. Read Diode'

In the Read diode, avalanche multiplication takes place in a narrow region at one end of the space-charge region and produces a number of carriers which are injected into the rest of the space-charge region. When the voltage across the space-charge region changes sinusoidally in time, the field in the avalanche region changes more or less in phase with the voltage. The carriers supplied by the avalanche process are appreciable when the avalanche field is above the breakdown field. The carrier injection reaches a peak not when the field peaks, but when the field falls to the breakdown value. The injected

412

T. MISAWA

carriers drift across the space-charge region while the voltage goes through the lower half of the cycle. This timing results in an out-of-phase current through the diode and produces ac energy. The carrier injection process is governed by

:J

(wJ2)(dJo/dt)= J o (

a dx - 1)

+ J,,

(59)

which is Eq. (42). Here, J o is either the electron or hole current which emerges from the avalanche region. It was assumed that time variations are so slow that the sum of electron and hole currents is position-independent as was the case in the quiescent condition. Further, we assume that the effect of the space charge of carriers on the field configuration is negligible. We will consider an example in which the avalanche region is uniformly doped and the field in the region changes linearly from its peak value as shown in Fig. 23. We take the peak value of the field at breakdown as the unit for normalization. When a changes as Em, where rn is a constant,

JoWn

adx

N

E;",

(60)

where E , is the peak field. The result was obtained by extrapolating the linearly changing field to zero and integrating over the whole region [0, 11 as illustrated in Fig. 23. The current thus produced travels down the space-charge region. When the field in the space-charge region is high, the carriers drift at the scatteringlimited velocity and diffusion is negligible. The carrier distribution, and thus

P POSITION

FIG.23. Field in Read diode

X

413

the particle current distribution J ( x , t ) , retains the original shape : J(x, t ) = J,(r - x / u ) ,

or

J ( x , t)

=

Jo(t - x)

161)

in normalized form. To be specific, we consider the case in which holes travel toward the positive x axis. The total current through the diode I is a sum of the hole current J(x, t ) and the displacement current dE(x, t ) / d t : I(t) = J(x,t )

+ dE(x, t y a t ,

where unit diode area was assumed. Integrating the above expression over the space-charge region, we obtain

I

=

I,

+ I,,

where

I,

= ( l / ~ ) / ~ ~ J ( x , i=) d( Ix/ w )

Jo(t - x / u ) d x ,

Jnw

I,

= (l/w) d V / d t

With the normalization given in column h of Table I,

I,

=

dV/dt.

(63)

The first component, I , , is the current induced by moving holes, and the second component, I,, is a capacitive current. Finally, we have to find out how the field in the avalanche region changes with diode current and voltage. From Poisson’s equation (14), the voltage across the diode is given by

where Q is the sum of the charge of ionized impurities Qf and mobile carrier charge, which is equal to J(x, t ) :

414

T. MISAWA

At zero current, the above relation becomes V,

=

E,w

+

JOw

IOx Qr dx’ d x ,

where V, and E, are the breakdown voltage and the peak field at zero current. Therefore, V - V,

=

w(E, - E,)

+

low lxw

J(x’, t) dx’ d x .

Changing the order of integration for the last term, we obtain

Eo(t) = E ,

+ (I/W)

(W

1

- x)J(x, t ) d x

or, with E, and w as units for normalization, Eo(t) = 1

+ V(t)

s,

,

1

-

Vo -

(1 - x)J(x,t)dx,

or, from (61),

E,(t) = 1

+ V ( t )- Vo -

1-

(1 - t

+ t’)J,(t‘)dt‘.

(64)

1

This equation tells us how the peak field in the avalanche region changes with diode voltage and the charge of holes drifting through the space-charge region. Equations (59H64) give relations connecting the field in the avalanche region E , , hole current emerging from the avalanche region J,, the current through the external circuit I = I, + I , , and the diode voltage V. The external circuit determines the relation between V and I . The problem boils down to solving the four equations for the four unknowns. In deriving Eqs. (62) and (64), the avalanche region was treated as if it did not occupy any space in the space-charge region. However, the width of the avalanche region appears in the Eq. (591, which governs the carrier injection process. Anyway, the dynamics in the avalanche region were not treated correctly under the assumption that it does not matter because the avalanche region is thin. Figure 24 shows the behavior of voltage, peak field, avalanche current, and induced external current for a 10-pm-wide diode with an avalanche region whose width is & of the space-charge-layer width. The ionization rate changes with field as E6, i.e., m = 6 in Eq. (60). The diode is biased in such a way that the average current through the diode is 0.1. An ac voltage with an amplitude of 0.19 and a frequency corresponding to a transit angle of n is present across the diode. The structure and the conditions described above are the same as those used by Read in his original estimate of a possible

415 I, = 0.4

0.2

I,

= 2

0 0 J

w_

I-

z

IL

wa

W

a a

a

+ J

3 V

0

>

- 0.2

0

UNIT TIME

FIG.24. Voltage V, peak field E , , avalanche current J,,, and induced external current J , of Read diode with w, = 0.1 at a bias current of 0.1, a frequency of H.

efficiency as high as 30 % (except for the ac voltage, which as 0.2 in his estimate). The curves in Fig. 24 were obtained by numerically solving the fundamental equations (59), (62),and (64) with (60). With the sinusoidal voltage across the diode, the peak field in the avalanche region also changes almost sinusoidally, although it is appreciably modified by the charge of holes which are created by avalanche and are drifting through the space-charge region. This is seen from (64). As the bias current increases, the effect of the mobile carrier charge will be more and more pronounced. The avalanche current J , keeps increasing as long as E , stays above E,, which is unity here, as seen from Eq. (59). Therefore, J , peaks when E , has decreased to 1. Because of the regenerative nature of the avalanche process, this peak is very sharp at this large ac amplitude. This is seen by rewriting (59) as follows : +wa d(ln J,)/dt =

CI

dx

-

1

+

(JJJO).

(65)

416

T. MISAWA

When the right-hand side changes almost sinusoidally, In J o will change in a similar way. However, J , will peak sharply when In J , peaks moderately, especially when its amplitude is large. Since J o peaks sharply, the induced external current will be more or less constant over unit time after J , peaks, as is seen from (62) by replacing Jo(t’) with the &function. This fact is well demonstrated in Fig. 24. Here, I, remains at the constant value while the bunch of holes traverses the spaceregion. If the voltage is at the negative half-cycle while I , is flowing, a highquality negative resistance is obtained. This is the condition we have here. At the present high bias current of 0.1, the existence of the negative resistance hinges upon the fact that holes are very well bunched and the mobile carrier space charge practically does not exist during the positive half-cycle of voltage except for that of carriers being generated. As the amplitude decreases, the space-charge region is not completely depleted of holes and their space charge has an unfavorable effect on E,. At small enough amplitudes, J , peaks before the voltage does and the negative resistance disappears. This is seen from (46) for the small-signal admittance. The above fact shows that the small-signal theory is sometimes powerless in describing oscillator performance. We now consider the spatial distributions of field and holes. At the moment when the voltage peaks, there are hardly any holes ; therefore, the field profile is the same as that at breakdown except that the whole profile is raised by Vpeak - V,. The profile is shown in Fig. 25 as E , . On the other hand, at the moment when Eo assumes the lowest value, there is a large bunch of holes in the middle of the space-charge region. According to (61), the hole distribution looks the same as J o ( t ) in Fig. 24. In the part of the space charge region behind the hole bunch (left side), the field is lowered by lEOmln - 11. The field rises within the hole bunch by lemmx. The field profile at this moment is shown in Fig. 25 as EL.

FIG.25. Schematic of field and current profiles in Read diode. The dashed line is the field at breakdown.

417

In the illustration in Fig. 25, it is depicted that E L ( x )bottoms at the trailing edge of the hole bunch. This happens when the initial field in the drift region at breakdown is equal to IEo,,n - 11, which is about 0.3, or 100 kV/cm in the present case. When this bottoming takes place, holes do not move at the scattering-limited velocity any more. The hole distribution starts to collapse from the rear end. As this tendency continues, at still higher amplitudes, the output power will not increase with amplitude as fast as formerly, and finally starts to decrease. Namely, this field bottoming is the onset of a saturation mechanism which eventually limits the oscillator power. The analysis in this section does not tell how this saturation mechanism works. Another mechanism which limits the oscillation amplitude is avalanche multiplication in the drift region. This takes place when the field becomes excessively high. The electrons and holes produced by this untimely avalanche multiplication upset the current-voltage phase relation. Fortunately, the field peaks when the space-charge region is depleted of carriers. Higher fields will be tolerated in the oscillating condition than in the quiescent condition. Considering these saturation mechanisms, we can conclude that the case shown in Fig. 24 is approaching the final amplitude in reasonable Read diodes, which confirms the present theoretical model. The admittance at w = 7c is shown in Fig. 26 for several bias currents. This was obtained with the same numerical analysis as that used for obtaining the results shown in Fig. 24. The figure shows how the admittance changes as the voltage amplitude increases. The admittance includes the component that is responsible for the capacitive current given in Eq. (63). As the amplitude of ac voltage increases and exceeds a certain value, the shape of J o ( t ) becomes so sharp that the current waveforms remain practically the same. Namely, I,(r) simply switches between zero and twice the average value. Then, the admittance that is responsible for I,(t) decreases inversely proportionally to the voltage amplitude. Since the space-chargelayer capacitance remains the same, the total admittance approaches its value, 7c in the present normalization. This is seen in Fig. 26. When the voltage changes as V, sin of, the admittance (conductance and susceptance) at the fundamental frequency is given by

(2/wV,)[(J0(t) sin or)sin Q

G

=

B

=0

+ ( J o ( t )cos w t ) ( l - cos o)],

+ (2/wVa)[(Jo(r) sin ot)(cos

Q -

1)

+ ( J o ( t ) cos w t ) sin 01,

(66) (67)

where the angular brackets denote time average over one cycle. When Jo(t) is very sharp, it can be approximated as I , . 6(t - t , ) , where I , is the average diode current and 6 is the delta function. The sharp pulse occurs at t = t , . Read showed that, with w = n, t , is given as a function

418

T. MISAWA

3.0

W

0

2

U In

2.5

$ v)

3 v)

- 1.0

- 0.5

2

0

CO N D U C TANC E FIG. 26. Change of admittancz with amplitude of ac voltage V, for four bias currents, 0.01, 0.02,0.05,and 0.1. The dashed line is for a diode with large saturation current. Values obtained from a sharp pulse approximation are shown with crosses for I , = 0.01 and 0.1.

of I , and V , by

sin ntl

=

(Zd/2K) + +mK

(68)

when J o ( t ) is very sharp. In deriving the above equation, Joldx - 1 was expanded as a Taylor series and terms up to ( E , - 1)* were retained. With this approximation, the admittance at o = TC is given by

G

=

(4Zd/nV,)cos or,,

B

=

n

-

(41d/nVa)sin w t , .

(69) (70)

Admittances calculated with the above equations are designated by crosses in Fig. 26 for V , = 0.1, 0.15, and 0.2. It is seen that they are good approximations at large amplitudes.

7. IMPATT

DIODES

419

At lower currents, the admittance due to I,(t) becomes proportionately small. Thus, IGI decreases and B approaches closer to n. This is seen in Fig. 26 and from Eqs. (69) and (70). In other words, the diode impedance at large amplitude increases with the bias current. This is just opposite lo the situation in the small-signal case. Another significant fact is that the ratio of the real part to the imaginary part of the admittance or the impedance also increases with current. These two facts may have some practical importance because in the actual diode a parasitic series resistance is inevitable. The parasitic resistance will outweigh the small negative resistance and absorb a larger fraction of generated ac power when large capacitive current flows. We discussed, in connection with Fig. 24, that the peak field E,, falls earlier than diode voltage V because of the charge of created holes. The effect is larger a t higher current. This makes the phase delay of J o with respect to voltage smaller and deteriorates the phase relation between voltag: and current I,. Read proposed to limit the total carrier charge in the spacecharge region t o less than half the charge CV, that produces the voltage variation. Since the former is I,t, where z is the transit time, which is taken as unity, the above condition becomes 1, <

iv,

in our normalization. Once the admittance is known, the output power is computed as jGVa2. It increases almost linearly with V’. When the initial field in the drift region is 0.3, as assumed before, the field starts to bottom at the amplitudes shown by the arrows in Fig. 26. Above these amplitudes, the output power may not increase with V , as fast as expected from the calculated G. A conserldative estimate of the maximum output power is obtained at the indicated amplitude. It is 0.01 a t a bias current of 0.1. The average diode voltage, obtained from the numerical analysis, is s ?own in Fig. 27 as a function of amplitude for the various bias currents The quiescent voltage goes up with current because of space-charge resistance. As the amplitude increases, the average voltage goes down. This is understood as follows. As noted before, the current waveform is almost independent of amplitude. The same field is required to produce the same current. Therefore, the field preceding the ,Io([)pulse will remain the same even as the amplitude increases. As seen from Fig. 24 or Eq. (64), the field changes with time in the same way as the voltage in this portion of the cycle. Naturally, the average voltage goes down as the amplitude increases as long as its crest is kept the same. Within the same framework as that for the admittance, Read obtained the following expression for voltage change : V - V, ( = E , in Read’s notation) = + I , - ) m K 2 ,

which is again a good approximation as shown in Fig. 27.

(71)

420

T. MISAWA 0.06 1

0

> I >

-0.08 -

\

Id'o.1

\

\

-0.10 -

0

\

I

I

0.I

0.2

\

\

0.25

"0

FIG.27. Change of diode voltage with amplitude of ac voltage V,. The dashed line is for a diode with large saturation current. Values obtained from a sharp pulse approximation are shown with crosses for I , = 0.1.

Assuming that V, = 0.4, which is not unrealistic considering that the drift field is 0.3, the input power at I , = 0.1 and V, = 0.19 is (0.4 - 0.027) x 0.1 = 0.0373. Since the output power was 0.01, the efficiency is 27%. We stated that J , and I , remain more or less the same as the amplitude exceeds a certain value. This is true as long as we plot them in linear scale as in Fig. 24. Actually, the minimum J o decreases exponentially with V, and may become comparable to the saturation current. In the example discussed hitherto, J , was taken as lo-", which is less than 1 pA/cm2, and J , did not fall to this value even at the highest amplitude. (Actually, J , approached to within an order of magnitude of J , . ) Read showed that the minimum J , will be greater than 10- l o if V, is no larger than 2 . 6 ~ In ~ .our example, w, was 0.1. We show results for the case where J, is no longer negligible with a dashed line in Figs. 26 and 27. We chose J , as loF7and w, = 0.05. Since more carriers are available from which J , builds up, J , reaches its peak too early in the cycle. This degrades the phase relation and results in a poor admittance and hence low output power. The average voltage goes down faster with amplitude than before, because the voltage has to remain above V, for less time due to larger initial J,.

So far, the discussion has been restricted to the case in which electrons and holes have equal ionization rate and equal scattering-limited velocity. We mentioned that this limitation can be lifted by using Eq. (47) inslead of (59). It was Lee et a/. who derived this generalized equation (47) and performed a detailed study on the generalized case.24 They reported that the essential features remain unchanged. Although we discussed the characteristics of the Read diode only at w = n, the theory can be used for lower frequencies. Evans was able to show that a closed-form solution is possible when the transit angle is very sma1L2’ He used his approximate solution in analyzing a certain type of Si IMPATT diode which showed oscillation at lower transit angles. h. Numerical Analysis30a

The numerical solution of the IMPATT diode equations is essentially to simulate what takes place in the actual diode. We shall discuss three cases which have appeared in the literature: (1) a Si diode with a relatively narrow avalanche region reported by Scharfetter and Gumme1,28 (2) a Si pvn diode reported by Ward and U d e l ~ o n and , ~ ~( 3 )a Ge diode reported by Johnston et The first two cases deal with moderately-large-amplitude operation of diodes and the third case with very-large-amplitude operation at a relatively low frequency. The analyses used Eq. (6) with experimentally determined parameters for electron and hole ionization rates. Scharfetter and Gummel used a realistic dependence of drift velocities upon field, including the low-field, constant-mobility regime, the high-field, constantvelocity regime, and the transition region between the two. Ward and Udelson assumed a velocity initially increasing linearly with field and at higher fields increasing as E”’. The Scharfetter-Gummel diode is shown in Fig. 28. It is a Si p + n v n f diode with a gradual transition from n to v regions. The figure also shows field profiles and current composition at two different bias currents. From the plot of current composition, it is estimated that the avalanche region occupies about one-fifth of the total space-charge region. The analysis was performed for the case when approximately sinusoidal voltage is present across the diode. Figure 29 summarizes the results at a bias current of 200A/cm2. This current density is relatively small, so that the small-signal admittance has a negative real part around the frequency corresponding to a transit angle of n. As the voltage amplitude increases,

’’ W. J . Evans and G . I. Haddad, IEEE Trrrrrs. E/rc/rfJnDPz3I’w.v ED-16. 78 (1969). ” 29

3o

D. L. Scharfetter and H. K. Gummel. IEEE 7 i t m s . E / P C ~ WDrriczr I? ED-16. 64 (1969). A. L. Ward and B. J. Udelson. I E E E Trons. Elecrron Deuices ED-IS, 847 (1968). R. L. Johnston. D. L. Scharfetter, and D. J . Bartelink. Proc. IEEES6. 161 I (1968). See also Appendices C and D.

T. MISAWA 400 IMPURITY DENSITY

---

- 360

FIELD

- 320

CURRENT

- 280 E

e

n+

I

7 \

/-w

J

- 120

----

w

80

- 40 kl

0

1

2

3

4

5

6

7

8

9

0 10

DISTANCE IN prn

FIG.28. Impurity distribution, field profile, and current composition in a Si ptnvn+ diode analyzed by Scharfetter and Gumrnel. (After Scharfetter and G ~ m m e l . * ~ )

the conductance decreases and the susceptance approaches that of the space-charge-layer capacitance. These features are qualitatively the same as those obtained with a simplified analysis given in the preceding section. The “snapshot” of carrier and field distributions inside the diode is shown in Fig. 30 for a frequency of 12.4 GHz, current density of 200 A/cm2, and efficiency of 12%. Diode voltage and current at each instant when the “snapshot” was taken are shown in the V-I plane in the upper left corner. The plot substantiates what Read described in his original analysis. At time (l), voltage is at a maximum and the carrier density starts to be appreciable in the avalanche region. This corresponds to the case designated by E , in Fig. 25 for the Read diode. One-quarter of a cycle later, at time (2), the charge pulses are fully formed and the first half of the electron bunch has already entered the drift region. This corresponds to time t , in Read’s analysis [see Eq. (68)].The holes disappear quickly into the p + region. At

423 70 60

50 40

30 I20 I10

O0 w

u

30

5 t

80 ?i V

70

2

60

50 40

30 20 10

0 -2 5

-20

-If

- 10

-5

0

C 0 NDU CTA N CE FIG.29. Admittance of the diode in Fig. 28 as a function of frequency and ac voltage amplitude. Equiefficiency lines are also indicated. Current density is 200 A/cm2. (After Scharfetter and Gummel.28)

time (3), the electron bunch is half way into the drift region and the voltage is at its minimum. This corresponds to the case designated by EL in Fig. 25. Another quarter cycle later, the electrons are disappearing and the field in the avalanche region starts to grow above the quiescent value. The amplitude of oscillation is relatively small here. The electron pulse has not yet sharpened as in Fig. 24 and no sign of bottoming of the field at the trailing edge is seen at time (3). Actually, the field is bottoming at the leading edge. The highest theoretical efficiency reported by Scharfetter and Gummel is 18 % at 9.6 GHz with a voltage amplitude of 38 V. The efficiency is still sharply increasing with amplitude at this point.

424

T. MISAWA

x

x

10'5

I. 2

1.0

105

5

c FIELD ELECTRONS HOLES

-

(3)

I I

ni

4

N

5

0.8 E

[1s

w a

Y

3 >

z

>

t

Z

0

0.6

-I

wLL

u a 2

[1s

w

g

c

0 W

0.4

a

_1

w

V

I

0.2

u 0

1

2

3

0

4

5

6

7

8

9

10

DISTANCE IN p m

FIG.30. "Snapshots" of field profile and carrier density distribution at four instants 4 cycle apart. Current density is 200A/cmz, frequency is 12.4GHz. and efficiency is 12%. (After Scharfetter and Gurnme1.28)

According to Read's analysis as presented in the preceding section, the output power keeps increasing with the voltage amplitude, until the field in the drift region bottoms and/or avalanche multiplication starts to take place in the drift region, thus invalidating his approach. Analysis of this super-Read regime is necessary in order to know the true theoretical limit of the oscillation efficiency of the Read-type diode. So far, no report is available on this subject. Ward and Udelson reported in detail on low-frequency oscillation of a Si n+ppf diode with a capacitive load. The particular circuit used is illustrated in Fig. 31. The impurity distribution is shown in Fig. 32. The space-charge cm'. Since region is 2.5 pm wide and the cross-sectional area is 4 x the carrier velocity kept increasing with field, the result may not be quanti-

7. IMPATT

425

DIODES

R E V E R S E VOLTAGE ( V )

100

20

-a

I

L

40

60

80

1

I

I

I

I

1

1100

FIG. 31. Oscillator circuit and obtained oscillation presented as a phase plot. Circles are time markers with an interval of S psec. (After Ward and U d e l ~ o n . ~ ~ )

tatively correct, but it is believed that the qualitative nature of the operation is well represented by their computation. In Fig. 31, instantaneous values of diode current and voltage are plotted. Circles on the I/-I curve are time markers with an interval of 5psec. The whole cycle takes 235psec. The time sequence is in the direction of the arrow. When the diode voltage moves up on the top, flat portion of the cycle, the space-charge region is well depleted of carriers. As the voltage approaches the peak, carriers start to be generated. Figures 32 and 33 show carrier distributions and field profile at several instants when the current goes through the peak. Numbers attached to the curves are times in picoseconds with respect to the moment when the current peaks. At 11 psec before the current peak, the current has just started to flow. The carriers are generated mostly at the right end of the space-charge region, where, although the field is lower than at the left end, more electrons, which have a larger ionization rate, are available. At the moment when the current peaks, both electrons and holes are present throughout the space-charge layer. Because

426

T. MISAWA

0

0.5

1.0

I .5

2.o

2.5

FIG.32. “Snapshots” of electron and hole distributions at five time points: - 1 1 , -4, 0, 5, and 24 psec. The origin of the time scale is the moment when the current peaks. The thin line is for the impurity profile. (After Ward and Udel~on.’~)

of excess holes at the left edge and excess electrons at the right edge, the field profile has a saddle in the middle and voltage is lowered below the value at breakdown. The situation is similar to that in dc condition shown in Fig. 7a. After the current has peaked, the voltage drops down ; generated carriers disappear in the time interval comparable to the carrier transit time. As is seen from Fig. 31, the current flows during a very small fraction of one cycle. Although efficiency for this particular oscillation was not quoted, the authors reported that efficiency as high as 14% was obtained in a similar oscillation. Since the dc V-Z curve was not reported, it is not possible to assess how the negative-resistance characteristics are enhanced in the dynamic condition.

7. IMPATT

427

DIODES

500

c

0 E

400

\

>

f 0 -I

W

300

0

[t

l-

0

W

-I

w 200

100

0

0.5

1.0 1.5 DISTANCE ( p m )

2 .o

2.5

FIG.33. “Snapshots” of the field profle at the same five time points as in Fig. 32. (After Ward and Udel~on.’~)

The small-signal negative resistance of the pin-type diode extends well into lower frequencies even without dc negative resistance. Since the diode reactance is inductive there, an oscillation with a capacitive load similar to that considered here should be possible without requiring dc negative resistance. Johnston et al. analyzed the performance of a Ge diode at such a low frequency that a small-signal negative resistance does not exist.30 The diode is of the abrupt-junction type like the one shown in Figs. 5 and 6 except for a slight penetration of the space-charge region into the highly doped region of the substrate. The space-charge region is about 5 pm wide and the breakdown voltage is 60 V. The analysis was performed in conjunction with observed high-efficiency (up to 43 04)oscillations at very small transit angles. Figure 34 shows “snapshots” of carrier density and field distributions together with instantaneous values of current and voltage at the moment

428

T. MISAWA

‘1I p =

FIELD

OO

v

ELECTRONS ---- HOLES

0

L32

FIG.34. “Snapshots” of field and carrier density distributions in a Ge diode for a fundamental frequency of 3 GHz. Scale limits: 0-1.75 x 10’6/cm3 for carrier densities, (t2.5 x los V/cm for the field, 0-8 ,urn for the distance, 0-100 V for the voltage, and CL-7000A/cmz for the current. (After Johnston et a1.”)

when the “snapshot” was taken. Note that current and voltage waveforms contain higher harmonics. These higher harmonics invoke effects which were responsible for higher-frequency oscillation and eventually make the low-frequency oscillation possible. The oscillation frequency is 3 GHz. Because of very large carrier densities at phase (c),the field in the avalanche region is drastically modified in contrast to the first case discussed in Fig. 30. An even more drastic effect is seen in phase (d), where the field bottoms over a wide region in the center and electrons and holes are “trapped.” This makes it possible for the diode to carry a large current at small voltage. It has been found that the efficiency of oscillation is very critically dependent upon the waveform of the oscillations. This may have been expected because

7. IMPATT

DIODES

429

higher harmonics were responsible for the very existence of the oscillation. A theoretical efficiency up to 25 04 has been reported in this type of oscillation,30b,30c V. Design Considerations

In this part, we discuss general design considerations which will be useful in actual fabrication of the device. More specific problems will be discussed in the next part. 14. SCALING RULEFOR VARIOUS

We have seen that the fundamental equations which govern the dynamics of the IMPATT diode can be normalized in terms of the material and structure parameters of the device. This fact indicates that one solution is applicable to a variety of devices with different material and structure parameters. For different devices, one just chooses different units for normalization. The scaling rule to be discussed here enables us to obtain characteristics of a new diode, which can be a scaled-down version or made of a different material, from the characteristics of the original diode. We consider the case in which characteristics are calculated by a simplified method discussed in Section 12e. Suppose we have an admittance plot as a function of frequency and bias current. In the plot, all quantities are dimensional, i.e., not normalized. Since bias current J appears in equations in combination with M’ as U’J, the normalized M'J is invariant. Keeping this fact in mind, we obtain the multiplication factors given in Table 111 for TABLE 111 Quantity Frequency

Multiplying factor WI _ v2 _

W2

c,

Impedance Current' a When CL oc Eb,where E is the field in the avalanche region, al’/a2’ = E,w,/E,w,.

'ObThis efficiency was obtained in a computer simulation of an experimental case in which 33% was observed. Private communication from Scharfetter. 30cW.J. Evans and D. L. Scharfetter, I E E E Trans. Electron Deuices ED-17, 397 (1970).

430

T. MISAWA

converting the plot for the original diode of width wl,scattering-limited velocity u l , dielectric constant and field derivative of ionization rate a l ' , to that for the diode with w 2 ,u2, E ~ and , tlz'. Values on coordinate axes or given as parameters that are not dimensionless but dimensional are to be multiplied by the appropriate factors for the conversion. For example, we scale down a diode with an avalanche region occupying one-third of the total space-charge region by a factor of two. The proportion of the avalanche region is kept constant and the material is the same. Then, all the values on the frequency axis have to be multiplied by two; for example, change 5 GHz to 10 GHz. All the values on the admittance axis are multiplied by a factor of four. Since the field in the avalanche region increases very little with the halving of the space-charge region, the values designating bias currents are multiplied by a factor of slightly more than two. Although the above multiplying rule applies exactly only to the simplified small-signal analysis given in Section 12e, the rule will be approximately correct for more accurate results obtained by the numerical method. Furthermore, the idea of converting normalization units is useful even for largesignal analysis. 15. STRUCTURE PARAMETERS

a. Width of Space-Charge Region The scaling rule discussed in the preceding section gives us information on the effects of changing the width of the space-charge region. Since the operation of the IMPATT diode is based upon transit-time effects, the operating frequency is inversely proportional to the transit time. Let us consider the case in which the width is halved in order to double the operating frequency. The case was discussed in the preceding section. By applying the scaling rule to the Q versus frequency plot, such as the one in Fig. 12, it is concluded that the same quality of negative resistance is obtained at a frequency twice as high, as intended. However, a bias current slightly more than twice as large is required to obtain this, and the impedance level will be only one-quarter of the original one. By further reducing the width of the space-charge region, a still higher operating frequency is obtained. However, this process cannot be continued indefinitely. In addition to the practical difficulty of handling too low an impedance, the tunneling current, which becomes a dominant breakdown process in narrow junctions, degrades the quality of the negative resistance.' In the tunneling process, the current changes simultaneously with the field. The important time delay cannot be obtained with tunneling as is possible with avalanche. So far, the highest frequency reported was obtained with a

431

E

C

FIG. 35. Changing avalanche-region width with doping level in the n region in a p + n n + structure.

432

T. MISAWA

Si junction diode with a 360-A wide space-charge layer.31 The frequency was 341 GHz. In this diode, the peak field was estimated as high as 2500 kV/cm. This field is considered to be high enough that most of the current is carried by the tunneling process.32 b. Width of Avalanche Region

The small-signal analysis given in Section 12r showed that, at a low bias current density, the diode with a narrower avalanche region has a negative resistance of better quality. This indicates that a diode with a narrower avalanche region is preferable as a CW oscillator. Figure 35 shows how the avalanche region becomes narrower in the p+nn+ structure as the doping level is increased in the n region. The narrowest avalanche region is obtained with the highest doping level, designated as (3). In order to reduce further the avalanche-region width, a more elaborate, hyperabrupt structure as in the Read diode is required. As the avalanche region becomes too narrow, tunneling again begins. This is more of a problem with higher-frequency diodes, which have narrower space-charge layers. Another objection to the too-narrow avalanche region comes from the adverse effect of saturation current at large amplitude, which was discussed in Section 13a. Thermally generated carriers swamp the space-charge layer at the ebbing phase of the cycle and deteriorate what would otherwise be a high efficiency. Some authors consider a wider avalanche region necessary for high-power capability and high efficiency.28 16. MATERIAL PARAMETERS

Effects of material constants will be considered here mostly based upon the scaling rule given in Section 14. a. Ionization Rate

The most straightforward effect of the ionization rate appears in the breakdown voltage. Materials with larger ionization rates, like Ge, result in lower breakdown voltage. This is an advantage when the amplitude of voltage swing is appreciably smaller than the breakdown voltage, because it reduces the necessary input power for operation. The field derivative of the ionization rate a’ is also important, for the small-signal characteristics depend upon a’J, where J is bias current. With larger CI‘, the same Q is obtained at smaller bias current. This is favorable for CW operation of the diode. Figure 36 shows a’ as a function of c1 for four common semiconductors, Ge, Si, GaAs, and Gap. The rate x’ is about two ”

L. S. Bowman and C. A. Burrus, IEEE Trons. Elrcrron DiwieeJ ED-14. 41 1 (1967). J. L. Moll, “Physics of Semiconductors,” p. 239. McGraw-Hill, New York. 1964.

433 2

I-

-

5 0

-

>

U W

n W

v \

0.1 -

d

U

v'

iS’

0.011

I

(ELECTRON)

I

I

I

I l l

I

I

l

l

IONIZATION RATE PER cm

FIG. 36. Plots of a' (After Misawa.z6)

=

da/dE as a function of ionization rate

a

for Ge, Si, GaAs, and Gap.

times larger in Ge than in Si. This indicates that a Ge diode will work better at a low bias current than a Si diode. b. Currier Velocity As the scattering-limited velocity of the charge carrier increases, say by a factor of two, the operating frequency goes up proportionately, but the impedance level is halved and twice as much bias current is required. However, in most of the common materials, like Ge, Si, or GaAs, almost the same scattering-limited velocity, on the order of lo7 cm/sec. has been observed. It seems that there is not much choice as far as this variable is concerned. c. Dielectric' Constant

With a larger dielectric constant, the impedance level will be inversely proportionally lower for the same operating frequency and a proportionally larger bias current will be required. The larger dielectric constant of G e is a disadvantage.

434

T. MISAWA

d. Material Choice-Ge, Si,and GaAs From the preceding arguments, Ge seems to be the best material among the three listed above. However, its thermal property compares unfavorably with that of Si. Thermal conductivity is about 30 % that of Si and its smaller energy gap tends to lead to a thermal runaway condition at a lower temperature. Gallium arsenide has even a smaller thermal conductivity than Ge, but otherwise its properties are comparable to those of Si. Because of its band structure, the tunneling process takes place more easily in GaAs than in Ge or Si3*This makes GaAs less suitable for high-frequency diodes, which have necessarily high field. Silicon has reasonable material properties and, in addition, as far as material preparation and processing are concerned, it is the best-developed material. It has been observed that Ge and GaAs diodes have superior noise characteristics.

17. THERMAL CONSIDERATION Part of the input power to the diode is converted into microwave energy, but the rest of it is wasted and simply heats the diode. When the diode temperature reaches a certain point, a thermal runaway condition sets in, namely a certain spot in the diode area becomes hotter and starts to draw more current than the rest of it, thus inducing further temperature rise at the spot. Finally, the melting point is reached and the diode is destroyed. In order to obtain proper operation of the diode, a reasonable current density must be achieved before this burnout takes place. Heat is primarily generated in the space-charge region where the field is high. It travels through the semiconductor body and the metal support (stud) to be dispersed into the environment. In the following, we discuss first the thermal resistance (i.e., the temperature rise per unit power dissipation) of the diode, assuming uniform heat generation over the junction area. With this uniform heat generation, it is found that temperature is not uniform over the junction. Since the current through the space-charge layer is dependent not only on voltage but also on temperature, as discussed in Section 10, current cannot flow uniformly, and thus heat generation is nonuniform. In the latter half of this section, a more elaborate analysis will be presented in which the current distribution is not assumed to be uniform, but is determined in a self-consistent way. Since the microwave characteristics are dependent upon current density, it is important to know the current distribution across the junction.

435 a UNIFORM HEAT FLUX f

b r THERMAL CONDUCTIVITY

FIG.37. Uniform heat flux incident over a circular area on a large heat sink.

a. Junction Temperature When the diode is made in such a way that the junction is very close to the heat sink, most of the temperature rise is inside the heat sink, not in the semiconductor. We shall obtain the temperature distribution in a heat sink whose dimensions are considered very large compared to the diode diameter.32aWe consider the case in which a uniform heat flux f is incident over a circle with radius a on the surface of an infinite solid with thermal conductivity K, as shown in Fig. 37. The temperature rise AT above the ambient is given by AT(r, z ) = ( ~ ' u / K )

e-"J,(lZ~)J,(~a)(d~/lZ),

(72)

where J , and J , are Bessel functions.34 The coordinate system is explained in Fig. 37. It is assumed that adiabatic conditions prevail over r > u. The temperature distribution on the surface of the heat sink is obtained by putting z = 0 in Eq. (72) as follows :

""The case in which the size of the heat sink is small was discussed by Kennedy.33 3 3 D. P. Kennedy, J. Appl. Phys. 31, 1490 (1960).

436

T. MISAWA

0.6 0

0.2

0.4 0.6 DISTANCE FROM CENTER

0.0

1.0

RADIUS

FIG.38. Temperature distribution in the case of uniform heat flux given by Eq. (73). (After Gibbons and Mi~awa.~')

where E and K are the complete elliptic integrals of the first and second kind.34a Temperature is highest at the center of the diode and gradually falls off to 63% (2/n)of the center temperature at the edge as illustrated in Fig. 38. The highest temperature in the circular area, r < a, is given by

AT(0,O)

Omaxna2f,

Om,, = l / n a ~ ,

(74)

where 0 is the corresponding thermal resistance. The thermal resistance for the average temperature is34 @,,

= 8/3n2aY ~ (3.7ffK)-'.

(75)

It is to be noted that when a uniform temperature is assumed over the area r < a the thermal resistance is equal

0

=

1/4a~.

(76)

H. S. Carslaw and J. C. Jaeger, "Conduction of Heat in Solids". p. 216. Oxford Univ. Press (Clarendon),London and New York, 1959. 34"Theseparticular expressions came to the author's attention through Hein's 35 V. L. Hein, unpublished work.

34

7

Si

0.8

Ti

0.16

AU

3.0

Ni

0.71

W/cm

-x 0.02 prn

RS

Rt

m

Rg

0.2 p m

Rn

FIG. 39. Cylindrical section between junction and heat sink, which is composed of Si and several layers of metals. The thickness and thermal conductivity of each layer are indicated. (After Swan er a[.36)

The important feature of this “spreading” thermal resistance is the fact that it is inversely proportional to the diode radius. This makes it possible to have larger flux density, therefore large current density for a given temperature rise, by reducing the junction area. As discussed before, greater and greater current density is required for higher-frequency diodes, and this may be achieved by reducing the junction area. The above tendency does not continue indefinitely, for, with smaller area, the thermal resistance of the cylindrical section between the junction and the heat sink, which is inversely proportional to area, instead of radius, becomes important. Figure 39 shows an example of a structure with a copper heat sink and cylindrical section, which is composed of Si and several layers of metals,36 Calculated thermal resistances of various sections and their total R, are plotted in Fig. 40 as a function of diode area. The crossover between spreading resistance R , and cylindrical resistance occurs at 5 x cm2 in this particular case. Of course, the crossover point can be lowered by thinning the cylindrical section. Swan has proposed using Type 11 diamond, which has five times the room-temperature conductivity of copper, as heat sink.37 Figure 40 also contains curves for the diamond heat sink. Another way of improving thermal resistance is to use a junction geometry with a small linear dimension, such as a stripe or annular shape. .” C. B. Swan. T. Misawa. and L. Marinaccio. f E E E Trcrrzs. Elwtrort Dw;w.s ED-14, S84 (1967).

’’ C. B. Swan, Proc. IEEE 55, 1617 (1967).

T. MISAWA

0. * DIODE AREA (ern')

FIG.40. Thermal resistances of the structure shown in Fig. 39. (After Swan et

Figure 41 compares the annular geometry with the solid circular one with equal area.38 By using a ring whose width is of the diameter, an improvement of a factor of two is obtained. The curve was obtained by superimposing two solutions of the form of Eq. (73). Some improvements in oscillator performance were observed in Si diodes with ring geometries.38a b. Current Distribution3'

We have seen above that when uniform flux or current density goes through the diode the center part of the diode is hottest. On the other hand, we know that as temperature goes up the diode voltage increases for a given current. Since the voltage across the junction is constant over the diode area under most conditions, the current tends to concentrate in the cooler portion of the diode. This will make the temperature distribution more uniform. G . Gibbons and T. Misawa. Solid Store Electron. 11. 1007 (1968).

38aL. P. Marinaccio, Proc. ZEEE 56. 1588 (1968).

INNER RADIUS OF RING WIDTH OF RING

FIG.41. Improvement in thermal resistance of ring structure relative to solid diode versus the radius-to-width ratio of the ring. Comparison is on an equal-area basis. (After Gibbons and M i ~ a w a . ~ ’ )

Let us consider the simplest case in which voltage goes up linearly with temperature and also with current. The characteristics are illustrated in Fig. 42. The relation is expressed by J = G[V-

(vo + p791,

(77)

where G is the incremental conductance after breakdown, which is assumed to be independent of V and T ; V, is the breakdown voltage at zero temperature, which is most conveniently chosen as room temperature, and p is its temperature coefficient. The particular values of the parameters used for Fig. 42 are appropriate for a Si abrupt-junction diode for X band (8.2-12.4 GHz) reported by Misawa.” The boundary conditions are now

G V ( V - Vo),

/?’=GI/P

39

for

r
T. Misawa, IEEE Trans. Electron Devices ED-14, 580 (1968).

440

T. MISAWA

v (VOLTS) FIG. 42. Relations between junction voltage and current density. Area is 1.1 x cm’. Dashed lines are for an isothermal relation and the solid line for the case when the diode temperature goes up with current. (After Gibbons and M i ~ a w a . ~ ~ )

The only difference from the constant-flux case is the presence of term BIT in the first equation. When dimensionless temperature and length are introduced with a unit temperature offbullc and a unit length of a, Eq. (78) becomes

aT/az

=

1-p

7;

where all quantities, including p’ are normalized. Since the differential equation V2T = 0 does not have any parameter, the only parameter in the whole problem is dimensionless p’, which is equal to a$/rc in the dirnensional expression. This fact indicates that, once a set of solutions is obtained for various values of dimensionless p, it can be used for cases with many different values of K , a, V,, p, G, and V.

7. IMPATT

5 -CURRENT DENSITY ---TEMPERATURE

INPUT POWER = 17 5 W EFF RAD = 6 O p

100

00

60

40

441

DIODES

20

0

20

40

DISTANCE

( pm)

60

00

0

FIG.43. Temperature and current distribution across a ring structure and a solid structure with equal area and equal input power. Temperature-dependent input heat flux is assumed. (After Gibbons and M i ~ a w a . ~ ' )

Figure 43 shows temperature and current distributions over a 60-pmradius diode. They are obtained by a numerical method with boundary conditions (78). The diode has the temperature-dependent characteristics given in Fig. 42 and is placed on a copper heat sink. Temperature and current density are normalized in terms of their values at the center. The curves are for an input power of 17.5 W, which is near the burnout point of the diode. The relative temperature at the edge is about 0.8, which means that temperature uniformity has improved by a factor of two over the case of uniform heat flux. With this temperature variation, the current changes by more than 100% from center to edge. It has now been found that, when the input power is increased for a given diode, or when the radius is increased with average current density kept constant, the relative temperature distribution becomes more uniform. However, since the temperature itself goes up with these changes, the relative current distribution becomes less uniform. This situation may be seen from Eq. (77). Figure 43 also shows current and temperature distributions in a ring diode with the same area and input power as the solid circular one. We can see an appreciable improvement in the uniformity of current distribution.

442

T. MISAWA

VI. Diode Fabrication In this part, we first discuss, in some detail, the structures of various types of diodes which have appeared in the literature. Then, an example of the diode fabrication process is presented. 18. IMPURITY

PROFILE

By tailoring the impurity profile, we can change the width and position of the avalanche region in the space-charge region. We will discuss various types of diode thus obtained. a. Read Diode

The Read diode is obtained by inserting an “intrinsic” region at the end of the space-charge region of a conventional pn junction.’ Actually, the “intrinsic” region is a very lightly doped region of either n or p type. The width of the space-charge region is tailored so that the carrier transit angle is approximately equal to n at the operating frequency. It is understood that the “intrinsic” region occupies most of the space-charge region. The important requirement is to keep the field in the “intrinsic” region at breakdown high enough to ensure the scattering-limited velocity for carriers but low enough to prevent avalanche multiplication. Some design data are available in the literature when the “original” pn junction is of the abrupt type as in the example shown in Fig. 44. Gibbons and Sze4’ defined the avalanche region as the region of high field over which M , given in (19) is equal to 20, i.e., the avalanche region width w, satisfies the following equation : A(w,) =

Jowa

p [ exp

(tl -

1

p) dx’ d x

=

0.95,

where the origin of the x axis is the position of the highest field. The computed avalanche-region width for Ge and Si is plotted in Fig. 45. For example, for a 0.5-pm-wide avalanche region in a Si diode, an impurity concentration of 2.1 x 1016/cm3is required. Another important design parameter is the peak field at breakdown. It is shown in Fig. 46, not only for the abrupt junction, but also for the onesided linear-graded j ~ n c t i o n . ~For ’ the above example of a 0.5-pm-wide avalanche region in the Si diode, the peak field is 470 kV/cm. Figure 47 shows that the space-charge-layer width of the abrupt junction with an impurity concentration of 2.1 x 10’6/cm3 is 1.5pm. From this information, the field profile is constructed as illustrated in Fig. 44. When it is decided that the field in the drift region is 100 kV/cm, the n region should be 1.2 pm wide. 40

G. Gibbons and S. M. Sze, Solid State Electron. 11, 225 (1968).

7. IMPATT

443

DIODES

2.I xi016 c m - 3

IMPURITY DISTRIBUTION

1

I

1

;

I

I

3

4

I I I

FIG.44. A p+nvn+ Read diode with abrupt junction. Values are for a 10-GHz Si unit

When this avalanche region is to be used in a 10-GHz diode, the total spacecharge region is 0.5 x lo7 cm/sec x 10- GHz- ' = 5 pm. The breakdown voltage of the diode will be 72 V. In order to obtain a reasonable field in the drift region, it is important to control accurately the total number of impurities in the avalanche region, more precisely in the n region in the case of the p + n v n + structure. According to Gauss's theorem, the field drop across the n region is proportional to the total number of impurities. In the above example of a Si, 10-GHz diode, the field dropped from the peak value of 470 kV/cm to 100 kV/cm. If the total

444

T. MISAWA 10

E

i

I

k

5 z 0 Vl

W

K

I

W

r V z a 1 a 1

a

1017

1016

IMPURITY DENSITY

PER cm3

FIG.45. Avalanche-region width in Ge and Si abrupt junctions. (After Gibbons and Sze.4')

impurity content is 20% too large, the field in the drift region is almost zero, a catastrophic result. Several Read diodes have been reported in the literature. Lee et aL4' made a low-frequency unit which has a very wide space-charge region (180 pm) and relatively thin avalanche region (6 pm). The structure is shown in Fig. 48. The theory indicates that this wide structure works at very small current density. Great pains were reported to have been taken in order to suppress microplasma effects which are usually present at low current levels in a conventional pn junction. The n + p section of their n+pnp+ structure was made by a double diffusion technique, i.e., by first diffusing deep a low concentration of acceptors and then diffusing shallow a high concentration of donors. The microwave Read diode was first reported by DeLoach and J ~ h n s t o n . ~ ' The diode oscillated at about 5GHz in CW mode. The diode was a Si p + n v n + unit and was made by the double diffusion technique. Figure 49 shows the impurity profile determined by the measured capacitance versus 4'

42

C. A. Lee, R. L. Batdorf, W. Wiegmann, and G. Kaminsky, Appl. Phys. Lett. 6.89 (1965). B. C. DeLoach and R. L. Johnston. IEEE Trom. Electron Derrces ED-13, 181 (1966).

7. IMPATT

445

DIODES

IMPURITY G R A D I E N T (ATOMS/Cm4 1

8X

lo5

1020

102'

1022

loz3

7 c

F

1014

1015 1016 IMPURITY CONC. (ATOMS/cm3)

loJ7

FIG.46. Peak field at breakdown in Ge and Si abrupt and one-sided linear-graded junctions. (After Gibbons and S Z ~ . ~ ' )

voltage relation and Fig. 50 is the theoretical field profile of the diode obtained by the method discussed in Section 10. Another method of making the hyperabrupt structure, which was used by Johnston, is to introduce the ti layer while growing the epitaxial According to Cicolella, there is not much difference in oscillator performance between the two ~tructures."~ The operating frequency of all the reported Read diodes ranges from several hundred M H z to about 10 GHz. b. Abrupt-Junction

The abrupt junction is a structure in which one can get a narrow avalanche region rather simply. As discussed in Section 15b a narrow avalanche region is advantageous for CW operation of the diode. According to results reported in the literature, the abrupt-junction diode outperforms the Read diode. 43

44

R. L. Johnston and J . G. Josenhans. Pmc. l E E E 54. 412 (1966): R. L. Johnston. private communication. D. F. Cicolella, private communication, 1967.

446

T. MlSAWA BREAKDOWN VOLTAGE IN V

E =l

G a w >

4 w W

[L

a

I 0 I

W

0

a v, LL

0

I

6 3 loi4

1015

10’6

10”

BASE IMPURITY DENSITY PER cm3

FIG.47. Breakdown voltage and space-charge layer width at breakdown of Ge, Si, and GaAs abrupt junctions. (After M i ~ a w a . ~ ~ )

FIG.48. Schematic cross section of Si npnp Read structure with guard ring. (After Lee et a[?’)

7. IMPATT

447

DIODES

Pm

FIG.49. Impurity distributions for a Si microwave Read diode. (After DeLoach and Johnston.4z) 390 360 -

330 -

300

-

-.2 4 0 E

270-

0

r

g

9

2

210180-

150I20 90 -

60 30 -

0

1

0

1

1

1

1

2

1

3

1

1

4

1

5

1

1

6

,

I

7

I

I

8

I

9

I

I

1

I

I

0

I

1

1

FIG. 50. Calculated field distribution for the Read diode shown in Fig. 49. (After DeLoach and Johnston.42)

448

T. MISAWA

A reasonably abrupt junction can be made by diffusion when the junction depth is less than the space-charge-layer width. We showed the computed field profile in Fig. 6 for a Si diode with a junction depth of 3 pm and a spacecharge-layer width of about 4 pm.It is almost triangular. The relations for the ideal abrupt junction connecting impurity density, space-charge-layer width, and breakdown voltage, shown in Fig. 47, are good guides in designing. Since the space-charge-region width is determined solely by the impurity density, this must be controlled accurately. It has been found to be very important to adjust the diffusion depth so that there is no high-resistivity, unswept region left between the spacecharge region and the low-resistivity substrate of the epitaxial layer."5 However, if the junction is located too close to the substrate, a pin-like field profile, such as the one designated by (2) in Fig. 35, results. The fraction of the space-charge layer that the avalanche region occupies will be larger. Because of its simplicity, it is practical to build the diode with a spacecharge region as thin as 0.2 pm for CW operation above ~ O O G H ZA. ~ ~ smoother field profile in this "abrupt"-junction diode may be an advantage in this high-frequency range because one can avoid the unfavorable tunneling process which would take place more easily when a thinner avalanche region is used as in the Read diode. Reported CW operation of this type of diode extends almost continuously ~ ~ are ~ mostly ~ - ~ Si~units ~ but Ge from 5 GHz to above 100 G H z . ~ They diodes also were made for the 5-10GHz range.48 The same Ge unit also showed high-efficiency (about 40 %) oscillations at lower frequencies : at 3 GHz in pulse ~ p e r a t i o n ~ and ' . ~ ~at 450 MHz in CW ~ p e r a t i o n . ~ ' c. Linear-Graded Junction Diode

In many of the early works, the diode with the linear-graded junction was used ~ i d e l y .This ~ , ~type ~ of diode is obtained when the diffusion depth is greater than in the abrupt-junction diode. The diode has a relatively wide avalanche region in the middle of the space-charge region. In this way, both electrons and holes contribute to ac energy generation. In contrast, in the two types of diode discussed in the preceding sections, only one kind of carrier plays a dominant role because the avalanche region is located at the edge. S. R. Kovel and G . Gibbons, Proc. IEEE55, 2066 (1967). T. Misawa, Proc. I E E E 56,234 (1968). 4 7 C. B. Swan, T. Misawa, and C. H. Bricker, PFOC.f E E E 5 5 . 1747 (1968). 47aD.F. Cicolella. private communication. 1967. 48 R. L. Rulison, G. Gibbons, and J. G . Josenhans, Proc. IEEE 55,223 (1967). 49 An efficiency of 40% was observed by Johnston up to 5 GHz, private communication, 1969. D. E. Iglesias and W. J. Evans, Proc. IEEE56, 1610 (1968). 45

46

Burrus and Bowman’’.s1 made a wide variety of Si diodes of this type with relatively low breakdown voltages on heavily doped “plain” (nonepitaxial) wafers. With this simple structure, they were able to obtain oscillation ranging from 15 GHz to 341 GHz in pulse operation. The work established the high-frequency capability of the IMPATT device.

d. pin Diode Here, the pin diode includes any diode in which the field is more or less constant over most of the space-charge region. The diodes designated (1) and (2) in Fig. 35 belong to this category. The ‘ 7 region” of the diode may have quite a large impurity concentration and still the diode can be considered a pin diode. This type of diode is made by lowering the doping in the epitaxial layer of the abrupt-junction diode. Since the structure has an inherently small series resistance and does not require stringent control of the epitaxial layer resistivity, the pin diode is the easiest to make while still showing decent oscillator performance. As discussed in Section 15b, the low-current performance is inferior to structures with narrower avalanche region. Silicon p f n n + diodes that worked in the 3-12GHz range have been These diodes had about a 2-pm-wide i region whose resistivity ranged from 0.7 ohm-cm to more than 30 ohm-cm. Similar diodes, but with a wider i region, were made by Prager et a1.54,5sThese diodes gave oscillations of several hundred MHz with efficiencies as high as 6004 in pulse operation. 19. FABRICATION

TECHNIQUES

In this section, diode fabrication techniques will be discussed by presenting fabrication steps used by Misawa and Marinaccio in making Si pvn diodes53 and Si abrupt-junction diodes.39Although there is much room for improvement, the process proved to be satisfactory for experimental purposes. The Si diodes were made on epitaxial layers grown on a thick substrate. In this way, we can use a much thicker wafer than necessary, to ease handling during processing. C . A . Burrus, Proc. IEEE 53. 1256 (1965). T. Misawa, IEEE Trans. Elerfron Decires ED-17. 299 (1970). T. Misawa and L. P. Marinaccio. Bell SI,.F/. Trcli. J . 45, 98Y (1966). 5 4 H. J. Prager, K. K . N . Chang. and S. Weisbrod. Prac. lEEE5.5. 586 (1967). ” H. J. Prager, K . K. N. Chang. and S. Weisbrod. Pro(.. First Bienttitrl (‘omell Conl. En,?. Appl. Electron. Phenomena, p. 266 (1967). 5‘

52

’’

450

T. MISAWA n+ SUBSTRATE

n EPITAXIAL LAYER

BORON DIFFUSION 3 p m DEEP

U (EVAPORATED AND PLATED 1

i (EVAPORATED)

BONDING AND TAILORING JUNCTION S I Z E

COPPER

FIG.51. Processing steps used for Si “abrupt”-junction diode.

The process steps to be discussed are explained in Fig. 51. The first step is to grow an epitaxial layer on a low-resistivity substrate. The active region will be made in the epitaxial layer. The substrate is utilized as a mechanical support during handling of the wafer and it does nothing but harm as far as electrical characteristics are concerned. In the Si abrupt junction, the substrate resistivity was on the order of 0.005 ohm-cm and the epitaxial layer

was 7.7 pm thick with a donor density of 7 x 1015~ m - A~ conventional . method of hydrogen reduction of SiCI, was used.56 The next step is to form a junction by acceptor diffusion. In the case of the Si diodes, open-tube boron diffusion was used. The surface concentration was kept at a relatively low level, o n the order of cm-3. There is an indication that lower surface concentration tends to give Iess microplasma effect." However, with too low a surface concentration, it is difficult to make a good ohmic contact. The diffusion depth was 3pm in the examples we are discussing. A nonpenetrating type of ohmic contact was achieved by evaporating a followed by an evaporated thin layer of Ti, which serves as an adhe~ive,~' gold layer. The gold layer was then reinforced by plating for the convenience of later handling. Gold dots were then formed on both sides by the KPR5'" technique. The dots on both sides of the slice are aligned as shown in Fig. 51 and serve as etching masks in the process of separating pellets. The pelietization was achieved by etching from both sides as indicated by the dotted lines. The pellet is bonded on a gold-plated copper stud by thermocompression bonding.58 It is advantageous from a thermal standpoint to mount the junction side down as shown in Fig. 51. For any practical application, a hermetically sealed encapsulation will be necessary for reliability, especially when the diode is of a mesa type as explained here. Figure 52 illustrates the encapsulation for the Si diodes. The old-fashioned mesa diode explained above is not the only way to achieve proper operation of the IMPATT diode. A planar structure is usable once edge problems are solved, Schottky-barrier diodes have also shown o s c i l l a t i ~ n . ~ ~ ~ ~ ~ "

VII. Observed Electrical Characteristics In this part, we list some of the observed electrical characteristics of IMPATT diodes which have appeared in the literature. Small-signal characteristics are discussed first, and then oscillator characteristics are presented. 20. SMALL-SIGNAL CHARACTERISTICS Since small-signal characterization of the diode is rather simple, the comparison of theoretical results with observed characteristics is useful in "' H. C. Theuerer. J. J. Kleimack. H . H. Loar. and H . Christensen. Proc. IRE48, 1642 (1960). 57 K. D. Smith, H. K. Gummel. J~ D. Bode. D 8.Cuttriss, R . J. Nielsen. and W. Rosenzweig. Bell. S w t . Tech. J . 42, 1765 (1961). 57"KodakPhoto Resist, a product of Eastman Kodak Co. 5 8 H . Christensen. Be/! Lob. Rec 36. 127 (1958). 5 9 J. C. trvin. IEEE Tmns. Eletrron Dcuiccs ED-13. 208 (1966). 5 va S. M. Sze, M. P. Lepselter, and R. W. MacDonald, Solid Siaie Elccrron. 12, 107 (1969).

452

T. MISAWA

FIG.52. Microwave package.

establishing the appropriateness of our present understanding of the IMPATT diode. A rather detailed report was published by Josenhans and Misawa on the small-signal characteristics of a Si pvn diode.60 The diode is of the pin type discussed in Section 9d and the space-charge region is 1.8 pm wide, of which the avalanche region occupies more than 60 % . 5 2 The particular diode whose cm2. characteristics are presented has a cross-sectional area of 3.1 x Figure 53 shows, on the Smith chart, the change of the diode admittance with frequency at a bias current of 15 m A or 500 A/cm2. The Smith chart is an extended one in which any point outside the unit reflection circle represents a negative real part.60a The unit admittance is 20mmho. The real part is negative and almost constant over the frequency range studied. The imaginary part changes from inductive to capacitative near 9 GHz. Note that the transit angle is about 1 rad at this frequency. It is characteristic of the pin diode that the negative resistance extends well below the resonance frequency as discussed in Section 12d. " J.

G. Josenhans and T. Misawa, IEEE Tmns. Electron Devices ED-13, 206 (1966). 60"Rememberthat the Smith chart is a plot on the S plane of the admittance Y by a transformation of S = [l - ( Y / Y o ) ] / [ l+ (Y/Yo)],where Yo is the unit for normalization. The imaginary axis on the Y plane becomes the circle for unit reflection. The right and the left halves on the Y plane transform into the inside and the outside of the circle on the S plane.

453

1.15 mA

FIG.53. Variation of diode admittance as a function of frequency at a bias current of 15 mA for a Si p v n diode, plotted on extended Smith chart. Conductance is negative over the frequency range investigated. (After Josenhans and Misawa6')

The diode conductance at various frequencies is plotted as a function of bias current in Fig. 54. The negative conductance is proportional to the bias current at low currents. The conductance then bends over and finally turns positive at high currents. The low-current characteristics correspond to the frequency-independent negative conductance around the resonance frequency shown in Fig. 18. The bendover of the conductance is a result of positive resistance characteristics at low frequency. The observed behavior of the diode admittance is exactly what is expected from a pin diode. Comparison was made with theoretical calculations obtained from a numerical analysis of the structure. It was found that agreement was excellent. Although no quantitative comparison between theory and measurement was reported, Johnston and Josenhans found that with their Read diode the real and imaginary parts of the admittance change sign at the same frequency as is expected from a narrow-avalanche-region diode.43

454

T. MISAWA

+ 0.5

-

3

0

IT

E

E w

v

o

0

z a

L 3

n 2

0 0

w n

p -0.5D

-I .(

0

10

5

15

BIAS CURRENT (mA)

FIG.54. Variation of conductance as a function of bias current at five frequencies for the same diode as the one in Fig. 53. (After Josenhans and Misawa.6')

Val'd-Perlov et al. also measured the small-signal impedance of a G e diode.61 Their impedance behaved more or less Read-like, which suggests that the diode has a rather narrow avalanche region. They reported that good agreement was obtained between calculated and measured values.

2 1. OSCILLATOR CHARACTERISTICS It seems that the main application of the IMPATT diode is as a microwave oscillator. Here, we will discuss some representative characteristics of IMPATT-diode oscillators. Figure 55 shows output power and efficiency of a Si Read diode as functions of input power.43 The diode has a 10-pm-wide space-charge region. Although details of the structure are not available, it is believed that the avalanche region occupies about & of the total space-charge region. The diode was operated CW at about 5 GHz. The efficiency reaches the highest V. M. Val'd-Perlov, A. V. Krasilov, and A. S. Tager, Radiotekhn. i Elektron 11, 2008 (1966) [English Transl.: Radio Eng. Electron. Phys. 11, 1764 (196611.

455

I

5

O

i

POWER IN ( W )

FIG.55. Read-diode oscillator output power and efficiency versus input power. Frequency is about 5 GHz. (After Johnston and J ~ s e n h a n s . ~ ~ )

value of 5 % at a relatively low input power and remains more or less constant at higher input power. The pin diode is the other extreme of the whole family of IMPATT diodes. Plots of output power and efficiency as functions of input power are shown in Fig. 56 for a Si pvn diode.s3 The diode was operated CW at about 12 GHz. The diode was made by diffusing boron about 3 pm deep on a 5-pm-thick, n-type epitaxial layer. The resistivity of the epitaxial layer was high SO that the I’ region was mostly swept out at a relatively low voltage. Figure 57 shows the field profile of a diode similar to the one used in the above oscillation m e a ~ u r e r n e n t The . ~ ~ profile was obtained from the measured voltage dependence of the space-charge-layer capacitance. The oscillation efficiency of this pvn diode keeps increasing up to the highest possible input power, at which the current density was about 2 kA/cm2. This is in sharp contrast to the case of the Read diode. A similar plot for a Si “abrupt” junction is shown in Fig. 58.39 The diode was operated CW at about 12 GHz. The structure of the diode is similar to that shown in Figs. 5 and 6. In this diode, the efficiency flattens out just prior to burnout, a situation between the two extremes discussed above. The highest current density was 1100 A/cmZ.

456

T. MISAWA 2.8 2.6 2.4 2.2 2.0 I .8 -I

1.6 0

II: i.4

:

z 1.2

6 z

w

LO 0 LL LL

0.8

w

0.6 0.4 0.2 0

FIG. 56. Output power and efficiency versus input power for a Si pvn diode. Frequency f = 12.04GHz. (After Misawa and M a r i n a ~ c i o . ~ ~ )

Efficiencies of Ge abrupt-junction diodes operated in the 5-10-GHz range also exhibited similar characteristics4* but with higher values than Si units, in agreement with considerations presented in Section 16d.The highest efficiency observed is 15.3%.62 The behavior of the oscillation efficiency for the three types of diode given above confirms the trend predicted from the calculated small-signal Q . It was discussed in Section 12e that the diode with a narrower avalanche region exhibits a better Q at a low bias current. Indeed, the Read diode, which has the narrowest avalanche region, exhibited high efficiency at low bias currents, b2

D. E. Iglesias, Proc. IEEE 55, 2065 (1967); private communication, 1967.

457

WIDTH IN pm

FIG.57. Measured field profile in the space-charge region of a Si pvn diode similar to the one in Fig. 56.

- 12.60 N

I

2

12.40

6 w

,“

12.20 12.00 1000

I

t

8001

20007 - I P, 0

A

- N0.70

0

d

- N0.59

4. ._EFF

-

POWER IN WATTS

FIG.58. Output power, efficiency, and oscillation frequency versus input power for Si “abrupt”junction diode. (After M i ~ a w a . ~ ’ )

458

T. MISAWA

whereas the efficiency of the pvn diode, which has the widest avalanche region, was still sharply increasing at the highest possible bias current. In between, the efficiency of the abrupt-junction diode flattened out at the highest current. High-frequency oscillations were obtained in diodes with low breakdown voltages, in which most of the current is considered to be carried by tunneling, not by avalanche multiplication. Although tunneling does not produce the extra phase delay at the cathode that existed in the case of the avalanche process, it seems that the transit-time effect is favorable enough to lead to oscillation. Bowman and Burrus31 reported oscillation from a Si lineargraded junction diode at frequencies as high as 341 GHz. The breakdown voltage of the diode is 6 V. The width of the junction is 360A, and the estimated highest field is 2500 kV/cm, which is well into the range where the tunneling process dominates. By assuming a scattering-limited velocity of lo7cm/sec, the transit angle is only 0.07 rad in this oscillation. This small transit angle is in disagreement with our present understanding because the absence of phase delay in tunneling would seem to require an even higher transit angle than in the case of avalanche. Okabe and Nishizawa reported oscillations around 150 GHz from a GaAs diode with a breakdown voltage as low as 4.9 V.63 Since in GaAs direct tunneling (without participation of phonons) is possible, the tunneling process is more dominant in this GaAs diode than in the above Si diode. “Spurious” oscillations were observed in IMPA’IT diodes in the frequency range where a small-signal negative resistance does not exist.2 It was reported that, when an oscillation exists at frequency f o , oscillations at fi and f2 are possible in such a way that f l + f2 = fo .42 This is a parametric effect based upon nonlinearities of the oscillations. In a study of the frequency conversion characteristics of the oscillating diode, Evans and Haddad showed that negative resistance is possible atfl 0rf2, depending upon circuit conditions, in the presence of an oscillation at fo , where-f, f f2 = f o .27 Very large efficiency has been obtained at lower frequencies (decimeterwave range) from diodes oscillating at small transit angles. Prager et al. observed an efficiency of 60% at 775 MHz with a Si p + n n + diode.55 The diode is one of a group of diodes that showed similar characteristics. The diode typically had a 12-pm-wide space-charge layer which was swept out at about half the breakdown voltage, which ranged from 165 to 185 V. The resistivity of the n region was 4-6 ohm-cm. The bias current was on the order of 1000 A/cm2. The large efficiency was characteristically accompanied by a large drop in the diode voltage, sometimes as low as half the breakdown voltage. 63

T. Okabe and J. Nishizawa. Bulk Oscillation by Tunnel Injection. 1968 IEEE Electron Devices Meeting, October 23-25, 1968.

7. IMPATT

459

DIODES

10 FREQUENCY (GHz)

100 200

FIG.59. Compilation of observed oscillation efficiencies at various frequencies. A : Johnston . ~:~M i ~ a w a D . ~: ~Swan.’(’ E: Swan er al?’ and J ~ s e n h a n s B: . ~ ~Misawa and M a r i n a ~ c i o C F : Igle~ias.~’ G : M i ~ a w aH. ~: Marinaccio.65 ~ I : Prager et ~ 1 J : Johnston . ~ ~ et u1.” K : Iglesias and Evans.50 L : Snapp et Dotted circle surrounding point indicates pulse operation. Otherwise, CW operation.

The above diode is more or less of a pin type. Similar behavior was also observed with abrupt-junction diodes, both of Ge30*50and of Si.64 Oscillation efficiencies as high as 45 were obtained between 0.4 and 4 GHz from Ge and Si diodes similar to those discussed in the beginning of this section. In both diodes, it has been found that tuning at higher harmonics is very important. Figure 59 summarizes oscillation efficiencies reported in both CW and pulse operations. There is a distinct trend of decreasing efficiency towards higher frequency. C. A . Snapp, L. A. Stark, and B. Hoefflinger. Performance and Theory of Avalanche Resonance Pumped Impatt Oscillators, 1968 IEEE Electron Devices Meeting. October 23-25. 1968. O S L. P. Marinaccio. private communication, 1968. ” C. B. Swan, private communication, 1968. 64

460

T. MISAWA

OUTPUT

DIELECTRIC SLUG T E F L O N SUPPORT

1

L

PAC K A G ED DIODE

FIG.60a. Coaxial oscillator circuit with double-slug tuner. BY PASS CAPACITOR

SLIDE SCREW TUNER

\ SLIDING PISTON

WAFER'

L I

TO CONVERTER

RAISED COSINE TAPER FROM 0.050" TO 0.400" HEIGHT BY 0.900 W I D T H

FIG.60b. Reduced-height waveguide oscillator circuit. (After DeLoach and Johnston?')

Figure 60a-c illustrates representative oscillator circuits. Figure 60a is a coaxial circuit with a double-slug tuner.52 The diode is mounted at the end of a coaxial line, usually with a characteristic impedance of 50 ohms. When the length of the slug is one-fourth of the wavelength and its relative dielectric constant is E, the double-slug tuner can convert into the matched load any impedance whose reflection coefficient is less than E ~ For. convenience, ~ ~ the 67

T. Moreno, "Microwave Transmission Design Data," p. 108. Dover, New York, 1948.

461 I\\

I

/+

BIAS CAPACITOR

FIG.60c. Waveguide oscillator circuit with local resonator around diode. (After M i ~ a w a . ~ ~ )

metal sleeve contacting the outside conductor has generally been used. The reduced outside diameter of the slug section of the coaxial line has the same effect as the dielectric slug. It has been found that this coaxial circuit is more versatile than the waveguide circuit to be discussed below. Arrangements with more than two slugs were used for the high-efficiency, low-transit-angle In this way, it is possible to tune rather oscillation discussed independently for the fundamental and the harmonic frequencies. The reduced height Figure 60b is a reduced-height waveguide facilitates the matching of the diode, which usually has an impedance lower than that of the full-height waveguide. Matching to the waveguide impedance becomes easier when a resonant structure is formed directly around the diode. In the circuit shown in Fig. 60c, the resonance is achieved by a local radial transmission line.46 In the frequency range above 50 GHz, a conical structure sometimes worked better than the flat structure shown in Fig. 60c. This circuit is a simplified version of the circuit originally developed by Swan, which has a coaxial arrangement to further facilitate matching6'

VIII. Conclusions In the decade or so since Read published his classic paper, the scope of the IMPATT device family has grown far beyond his original conception. What we have now is not a mere solid-state version of the vacuum-tube transit-time

'' Electrical Design News, p. 100. June 10. 1968.

462

T. MISAWA

device. The distributed nature of carrier generation, the existence of two types of charge carrier, and the feedback effect of the charge of generated carriers upon generation has contributed to the diversity of structure and operation of the device. In contrast to this rather phenomenal diversification of the device, the oscillation performance of the IMPATT diode is far behind Read's original prediction. His estimate of 30% efficiency has never been achieved except in the low-frequency range of decimeter waves. At the higher end of the frequency spectrum over which IMPATT diodes have operated, the dimensions of the device are so small that the validity of the fundamental equations used for the analysis becomes doubtful. In addition, the current density is very high, for example, about 100 kA/cm2 in 100-GHz CW Si diodes. It is conceivable that at this high carrier density the ionization rate can be different from that observed at very low current density. Although oscillation was observed well into the submillimeter-wave range, the presence of unfavorable tunneling processes and low impedance levels seems to confine the practical range of device operation to the millimeter-wave range and below. Appendix A. DC Equations and Numerical Solution The fundamental equations in normalized form are

+ p - n, &/at = ( a J J a x ) + av,n + pv,p, ap/at = (aJ,/ax) + av,n + pu,p,

aE/ax

=N D

- N,

J, = vnn, J,=

-V PP

(79)

(80) (8 1)

(82) 5

(83)

where v,, and up are absolute values of the electron and hole velocities, and the positive direction of the x axis is from p- to n-type regions. The dc equations are obtained by setting the time derivatives to zero. Since the total dc current J = J , J , is constant, we obtain, by eliminating J, from Eqs. (79) and (80),

+

+ UP ' ) J , + N , - (J/u,), d J J d x = (a- B)J, + B J , dE/dx

=

(v,'

(84) (85)

where N , = N D - N A . The boundary conditions are: J , = J,, and E = E, at the p-side end of the space-charge region, i.e., at x = x i , and J , = J - J,, and E = E , at the n-side end, i.e., at x = xf. Here, E , is the critical field for

velocity saturation; Nf is a known function of x ; and u,, up and a, p are known functions of E . They can be doping-dependent if it is desirable. Since the boundaries of the space-charge region are not yet known, the numerical integration is started with a tentative value of x i and given J,, and E, . The integration is terminated when IEl becomes smaller than E, . At the terminated point x = xf, J , is not generally equal to J - J p s . It is too large when xiis chosen too far out in the p region, and too small when x iis too close to the metallurgical junction. The integration is repeated by changing x i until J,, satisfies the boundary condition. Actually, the succeeding value of xi is chosen to be the bisecting point of the last two values of xi which sandwich the as-yet-unknown correct value of x i . When x i approaches the correct value, the final value of x i is obtained by interpolation. The J,, and J , are usually taken as zero. It has been found that it is more economical to start integration at the less-doped side. When the width of the space-charge layer is given in the problem, as in the case of the pvn diode of Section 10, the value of field at one end is used as the parameter of iteration. Modification of the above method to this case is obvious.

Appendix B. Small-Signal AC Solution Equations for small ac part, which varies as ejW’with time, are obtained from (79H83)by replacing the time derivative with jw and by retaining only the terms linear in the ac parts. The total current, which is again constant, is now composed of electron and hole currents and displacement current, j = jn + j p + jwE

in dimensionless form. Eliminating ri,

(86)

Is, I, we, obtain ,

where the tilde indicates ac part and quantities without it are dc values. The prime means derivative with respect to field. The equations are solved in the space-charge region determined in the dc solution with the boundary at the p-side end and j p = j, at the n-side end. condition that J , = .ins Since the equations are linear, this boundary-value problem is converted to the “initial”-value problem.

464

T. MISAWA

Because of the linearity of the problem, the solution is a superposition of three components :

S'", which gives the diode impedance, is obtained with j = 1, j,, = j p s= 0 ; S(2)with J = J,, = 0, j n s= 1; and S(3) with = jfls = 0, j p s= 1. -

I

Appendix C. Addenda to Numerical Analysis of Large-Signal Operation of Read Diode As discussed in Section 13a, Read was able to obtain considerable insight into the large-signal operation of his proposed structure by simplifying the analysis to a tractable form. He even estimated a possible ultimate efficiency. However, he had to make various simplifying assumptions. It is interesting to see quantitatively the kind of error to which these assumptions lead. Computer simulations on Si diodes69 revealed that his estimate of efficiency is surprisingly accurate even though there are appreciable errors in some details. Figure 6169ashows waveforms obtained by computer simulation for current and voltage and snapshots of field and carrier distributions a t four instants of time. The computation is for the 5 pm wide unit of Fig. 44, whose avalance region width is nominally 0.5 pm. The frequency is 10 GHz, and the bias current density of about 500A/cm2 is so high that a small-signal negative resistance does not exist. The current waveform is again, as in Fig. 24, for that component which is induced in the external circuit by moving carriers, i.e., I , defined in an equation preceding Eq. (62). As the diode voltage goes through the peak and comes back to the vicinity of the breakdown voltage at moment (3), the electron bunch has completely formed. In contrast to the result of the Read-type analysis of Fig. 24, the current is at its peak at this moment instead of one-half the peak. In addition, the holes which are created at the same time also contribute to the current. As the voltage bottoms at moment (4), the field at the trailing edge of the electron bunch becomes very low and electrons there move at lower speeds. This results in a dip in the current waveform. This slowing down of trailing electrons and diffusion both broaden the electron bunch. As a result, the switching-of€ of the current is not so sharp as in Read's case of Fig. 24. All these effects contribute to the sawtooth-like shape of the current waveform. Fourier analysis of the waveform shows that the ratios of ac to dc components and the power factor are VJV, = 0.55, la/ld = 1.02, and cos cp = -0.91, which gives an efficiency of 25.4 %. T. Misawa, Solid State Electron. 13, 1369 (1970). byaT,Misawa. Solid State Electrons.. to be published

6y

I .6 N

12

5

1.0

4

>

I=

120

0.8

cn

a--

z

I

: 0.6

I I

I-

I

04 LL

I

LT

2

-

EFFICIENCY ~ 2 5 . % 4

1.4

Fi ‘

i

0.2

I

1

:2) ,

C

I

3)

(4)

,

20

40

0 100

80

60

TIME IN psec

(a)

V

0

0

5r m

0

POS IT I0N (b)

FIG.61. Computed current and voltage waveforms (a) and snapshots of carrier and field distributions (b) in Si Read diode. (After Misawa.6q”)

466

T. MISAWA

As the voltage amplitude becomes slightly larger, an appreciable amount of electrons is left behind the moving bunch in the drift region because of the excessive slowing down and eventual reversal of the field. It has been found that the Read mode of operation suddenly ceases to work and efficiency will drop very abruptly beyond this amplitude. It is possible to manipulate the voltage waveform by adding harmonics to increase the fundamental amplitude while keeping the peak value the same. The largest effciency thus computed was 28.3 %. It was found in computer simulation that there is a large concentration of electrons present at the left-hand end of the space charge region because of the proximity of the huge electron bunch and nonzero diffusion.69 This results in electron injection into the adjacent p region. Subsequent release of these stored minority carriers into the depleted avalanche region leads to a premature buildup of carriers in the following cycle and to eventual The storage decrease in efficiency because of a deteriorated phase relati~n.~' of minority carriers can be avoided by using a Schottky barrier, for metal cannot store minority carriers. The result shown in Fig. 61 is for such an improved Read diode. Temperature has been found to have a profound effect on the efficiency of the Read diode."'" In the case of the p n junction diode, the increase of the critical field for velocity saturation (due to lowered mobility) and the increased background carrier densities (due to increased intrinsic carrier density) reduced the efficiency at 600°K to 9 %. In the case of the Pt-silicide Schottky barrier diode, the increased emission current was found to be a main factor, and efficiency was reduced to 3.8 % a t 600°K. +

Appendix D. Theory of TRAPATT Mode of Operation Nearly ideal dynamic negative resistance is obtained in the diode with a trapezoidal field profile under certain circumstance^.^ 1.72 The current and voltage waveforms for this case are illustrated in Fig. 62. The period of the oscillation is an order of magnitude larger than the carrier transit time. It is apparent that a very special circuit is required to realize this current-voltage relation. Theoretical efficiencies from 50 to 60 % are claimed in this mode of ~ p e r a t i o n , ~which is labeled TRAPATT for TRApped Plasma Avalanche Triggered Transit.72 The following description of the TRAPATT operation ~ ~ evolved from the by Clorfeine et aL7 and DeLoach and S ~ h a r f e t t e rhas computer simulation of an experimental o b ~ e r v a t i o n . ~ ~ Misawa, Solid State Electron. 13,1363 (1970). A. S. Clorfehe, R. J. Ikola, and L. S. Napoli, RCA Rev. 30, 397 (1969). B. C. DeLoach, Jr., and D. L. Scharfetter, I E E E Trans. Electron Devices ED-17.9 (1970).

" T.

72

7. IMPATT

DIODES

467

(b)

FIG.62. Voltage and current waveforms for TRAPATT mode (a) and (b), respectively. The square wave for current shown by the dotted line is used in the theory. The solid line shows approximation including up to the fifth harmonics. (After Clorfeine et

Figure 63(a) illustrates field profiles in depleted n’pp’ diode. When a constant current J is applied through the depleted space-charge region, the field increases at a constant rate to accommodate the current, dE/& = J / E , (90) as shown in Fig. 63ta). The field profile is slanted as described by Poisson’s equation

d E l d x = - qN,/E. (91) Now let us define a critical field E,, above which avalanche multiplication is appreciable. We see that the point on the field profile where the field is equal to E , moves to the right at a phase velocity u,. By making the Lagrangian time deri~ative’~ equal to zero, d- E_ - - + d E- - = aE o dx dt at dx dt ’ 73

M. Chodorow and C. Susskind, “Fundamentals of Microwave Electronics,” p. 284. McGrawHill, New York, 1964.

468

T. MISAWA

I

1

FIG.63. Propagation of field profile in the absence of mobile carriers (a) and field profile in the presence of the avalanche shock front (b).

the phase velocity is given by

When the field is higher than E,, avalanche multiplication is appreciable. Created electrons and holes will change the simple situation depicted by Eq. (91)and hence the phase velocity given by Eq. (92). However, an interesting situation arises when the value of the constant current is large enough to make the phase velocity larger than the scattering-limited velocity (J > qv,N,). Under this condition, created holes cannot overtake the fast moving point of the critical field, or the avalanche shock front.74This means that the field profile to the right of the shock front remains undisturbed, and hence u, stays constant. Behind this shock front, created electrons move away promptly to the left and created holes follow the shock front. The excess charge of the holes over that of the electrons is large enough to make the field turn around and

'' D. J. Bartelink and D. L. Scharfetter, Appl. Phys. Lett. 14,320 (1969).

469

+ -

+ ++In t+t+ttt

HOLE ELECTRON

-F I E L D

++ -

+++

+++tttt

FIG.64.Avalanche shock front in computer simulation. (After Scharfette~.’~)

drop to a very small value at which the electrons and holes do not attain the scattering-limited velocity. The field profile which thus ensues is illustrated in Fig. 63(b). As the avalanche shock front moves through the space charge region, a large concentration of electrons and holes is left in the wake. The diode voltage goes down at the same time as the low-field region spreads out. The situation is illustrated in Fig. 62(a). The voltage changes from B to C . This phase of the passage of the avalanche shock front is seen in Fig. 64 which is obtained by computor ~ i m u l a t i o n . ~ ~ After the space charge region is filled with the plasma, the constant current acts to extract electrons and holes. The sequence of following events is illustrated in Fig. 65 and the corresponding diode voltages are shown in Fig. 62(a). The situation of Fig. 34(d) occurs during this period of plasma extraction. When the plasma is completely extracted at point G, the current goes down to zero and the voltage remains the same for the next half-cycle. Then the sequence repeats. In order to realize the described current-voltage relation, a very special load impedance is required up to several higher harmonics. A computer 75

D. L. Scharfetter, Bell Syst. Tech. J . 49, 799 (1970).

470

T. MISAWA

FIG.65. Carrier and field profiles during plasma extraction period. (C), (D),etc., correspond to the moments labeled on the voltage curve in Fig. 62(a).(After Clorfeine ef a/.”)

simulation by Evans and Scharfetter30bdemonstrated that a coaxial system with several slugs properly placed gives something similar to the waveforms of Fig. 62 and an efficiency of 25 %. Actually it is from this very computer simulations that the theory discussed here was deduced. The above-presented discussion can provide a simple design theory. First, the width of the space-charge region is such that the transit time is about one

order of magnitude smaller than the oscillation period. Second, the field at the right-hand end should be near one-half of the left-end value. This dictates the proper impurity density. Finally, in order to keep u, reasonably higher than v,, the bias current should be about two times qv,/N,.

List of Symbols Radius of the circular area over which heat flux is incident Area of diode Avalanche-region capacitance Diffusion constants of electrons and holes Electric field strength Peak field in avalanche region at breakdown Field at the moment when diode voltage is highest Field at the moment when J o ( t ) assumes the minimum value Critical field for carrier velocity saturation Peak field in avalanche region Electric field in avalanche region Ionization energy for electron-hole pair creation Optical phonon energy Heat flux density Generation rate of electron-hole pairs by avalanche multiplication per unit volume Conductance, dc incremental conductance in breakdown Conductance of avalanche region of pin diode Current in external circuit due to space-charge-layer capacitance Bias current of diode Current in external circuit induced by moving charge in space-charge region

J-r

Current density, total dc current density Electron and hole current densities, respectively J,,, J,,, J , Currents due to electrons and holes entering the space-charge layer from adjacent regions, and their sum, respectively ac current due t o electrons injected a t the end of drift region Total particle current in the avalanche region Boltzmann's constant Inductance of inductor in equivalent circuit of avalanche region Multiplication factors of electron and hole currents due to avalanche, respectively Carrier density, electron density Densities of ionized acceptors and donors Density difference, equal to N , - NA Density of charged recombination-generation center Hole density Charge of carrier, magnitude of electronic charge Charge density Charge of ionized impurities Radial variable in cylindrical coordinates Thermal resistance Time Time when J o ( t ) peaks in Read diode

T. MISAWA

Lattice temperature Electron and hole temperatures Capture rates of electrons and holes, respectively, by generation-recombination centers per unit volume Velocity of charge carrier Electron and hole velocities, respectively Scattering-limited velocity Diode voltage Amplitude of ac voltage across diode Diode voltage at breakdown Width of space-charge region Width of avalanche region Width of drift region Axial variable in cylindrical coordinate

GREEK LETTERS Ionization rate of electrons, or of charge carriers Field derivative of a Ionization rate of holes, temperature coefficient of breakdown voltage Current transfer factor through drift region Prefix for small increment Dielectric constant Transit angle through drift region Thermal resistance Thermal conductivity Optical-phonon-scattering mean free path of electrons and its zero-temperature value, respectively “dc” mobilities of electrons and holes, defined as (u/El Low-field mobility Thermal conductivities of copper and diamond Angular frequency

CHAPTER 8

Tunnel Diodes H . C . Okean

I . INTRODUCTION . . . . . . . . . . . . . . I1 . THEPHYSICSOF TUNNELDIODEOPERATION . . . . . I . Semiconductor Energ?.-Eund Strui~ture . . . . . . 2 . p-n Junction Theorj . . . . . . . . . . . . . . 3 . Theory of Quantum-Mechanical Tunneling . . . . . . . 4. Deriiiation of Tunnel Diode I-V Characteristic . . . . . . 111. PRINCIPLES OF TUNNEL DIODE FABRICATION . . . . . . . 5 . Formation of the Tunneling Junction . . . . . . . . . 6 . Fabrierition of the Or.er.all Tunnel Diode . . . . . . . . 7 . Inherent Liniitationa on Tunnel Diode Operution . . . . . IV . TERMINAL PROPERTIES OF TUNNEL DIODES . . . . . . . . 8. DC Current-Voltuge Cl7tir.ocrrristic . . . . . . . . . 9 . Properties o/' Tunnel Diode Equiiialent Circuit . . . . . . 10. Terminul Stability of Tunnel Diodes . . . . . . . . . CHARACTERIZATION OF TUNNEL DIODES. . . . v . EXPERIMEN~AL 1 1 . General Approuch to Tunnel Diode Charcicterization . . . . 12. Lm.- Frequent?. Meusur.rinent.~ . . . . . . . . . . 13. Microwaiw Measurt~inrnts. . . . . . . . . . . . I4. Results of E.vperimentu1 Churrrcter.i:atirin . . . . . . . . . . VI . TUNNELDIODEAPPLICATIONS IN SINUSOIDAL CIRCUITS . 15 . Tunnel Diode Amplifiers . . . . . . . . . . . . 16. Tunnel Diode 0sciNtrtor.c . . . . . . . . . . . . 17. Tunnel Diode Conwrter.c- . . . . . . . . . . . . I8 . Tunnel Diode Detectors . . . . . . . . I9 . Miscellaneous Sinusoidtil Tunnel Diode App1ictrtion.s VII . TUNNELDIODEAPPLICATIONS I N PULSEA N D DIGITAL CIRCLJITS . . 20 . Gwwrul Properties of Tunnel Diodrr in Digitul Circuits . . . 21 . Digital Circuit Functions Perfbrnied bj. Tunnel Diodes . . . . VIII . PRESENTAND FUTURE ROLEOF TUNNEL DIODES. . . . . . 22. Circuit CupuhilitiPs of’Tunnel Diodes Conipurad with Other. Dei.ices 23 . Role of Integrated Cireuit Technology in Possible Tunnel Diode App'plicutiom . . . . . . . . . . . . . . . 24. Conclusions . . . . . . . . . . . . . . . .

473

474 475 475 483 491 498 501 501 505 510 515 515 517 528 534 534 537 539 542 543 543 560 573 584 598 602 602 611 616 616 621 622

474

H. C . OKEAN

I. Introduction The tunnel diode is one of the more significant solid-state electronic devices to have made its appearance in the last decade. It evolved directly from the discovery by Esaki in 1958 that electron tunneling in a narrow, heavily doped p n junction could result in a voltage-controlled negativeresistance device. Immediate importance was attached to the tunnel diode due to its potential as a simple, yet extremely versatile multifunction electronic device. Its potential versatility arose from its simultaneous possession of a highly nonlinear, multivalued current-voltage characteristic, including a region of differential negative resistance, and an extremely high-frequency and/or high-speed capability owing to the low values of parasitics associated with the tunneling p-n junction. In particular, the differential negative-resistance property of the tunnel diode led to its possible utilization in sinusoidal oscillators and amplifiers, the large current-voltage nonlinearity to possible use in converters and detectors, and the multivalued nature of the current-voltage characteristics to use in various types of pulse, digital, switching, and logic circuits. In addition, the potential high-frequency, high-speed capability of the tunnel diode predicted sinusoidal operation in the microwave range to frequencies as high as K band and digital operation at subnanosecond switching speeds. Finally, the broadband character of some of the tunnel diode properties led to proposals of simultaneous multifunctional operation using a single tunnel diode, such as in a self-oscillating frequency converter, including rf preamplification and i.f. postamplification. Whereas many of the possible applications attributed to the tunnel diode upon its discovery have been to a certain extent realized in practice, more widespread utilizations have been limited by restrictions imposed by the basic parameters of the tunnel diode. It will be the main purpose of this chapter to describe the various applications of the tunnel diode in terms of the limitations imposed in each case by these fundamental parameters. In order to accomplish this, the chapter will consist of parts on the physics of tunnel diode operation, the principles of tunnel diode fabrication, the terminal properties of tunnel diodes, the experimental determination of basic tunnel diode parameters, sinusoidal tunnel diode applications such as in amplifiers, oscillators, converters, and detectors, pulse and digital tunnel diode applications, and finally, on an assessment of the present and future roles of tunnel diodes in electronics. While the scope of the chapter appears wide, excessive detail with respect to specific circuits, specific physical realizations, and specific performance formulations will be avoided in favor of more generalized circuit configurations and more fundamental performance limitations for each tunnel diode application. This will more clearly

8.

TUNNEL DIODES

475

demonstrate the central role of the tunnel diode device parameters in determining the ultimate limitations characterizing all tunnel diode applications. 11. The Physics of Tunnel Diode Operation

1 . SEMICONDUCTOR ENERGY-BAND STRUCTURE a. Qualitative Description

The tunnel diode is essentially a heavily doped p~ junction semiconductor device in which quantum-mechanical tunneling of electrons takes place. This in turn gives rise to the unique shape of the tunnel diode voltagexurrent characteristic. In order to gain a qualitative and quantitative understanding of the physics of tunnel diode operation, this section will begin with a brief recapitulation of p-n junction theory. A more general approach is taken than in most past treatments’-” in order to incorporate more accurately the heavily doped junction into the theory. The p-n junction, as is well known,’-’’ consists of an internal interface within a semiconductor sample between two oppositely doped semiconductor regions. To begin with, an intrinsic (pure) semiconductor composed of a Group IV material such as germanium (Ge) and silicon (Si) or a Group III-V compound such as gallium arsenide (GaAs) and gallium antimonide (GaSb) possesses a very low concentration of free carriers and therefore a L. Esaki, Phys. Rev. 109. 603 (1958). L. E. Dickens, unpublished work. 1962. W. F. Chow, “Principles of Tunnel Diode Circuits.” Wiley, New York. 1964. W. H. Card, C. 0. Harbourt, G. M. Glasford. and R. P. Nanavati, unpublished work. 1961. ’ F. D. Shepherd, Jr.. A. C. Yang, and V. Vickers, unpublished work, 1963.

‘ W. Franz, in “Handbuch der Physik” (S. Flugge, ed.), Vol. 17. Springer, Berlin, 1956. ’ L. V. Keldysh, Zh. Eksp. T e o r . Fiz. 33.994 (1957); 34, 962 (1958) [English Transl.: Sot.. Phys.J E T P 6, 763 (1958): 7. 665 (1958)l. E. 0. Kane, J . A p p l . Phys. 32.81 (19611. Y. Takeuti and H. Funada, J . Phys. So(,. Japan 20. 1854 (1965). I ” J. B. Krieger, Ann. Phys. 36. 1 (1966). I V. 1. Fistul and N. Z. Shvarts. Usp. Fiz. N a u k . 77. 109 (1962)[English Transl.: Sou. Phys.-Usp. 5, 430 (1 962)]. 12 J. 0. Scanlan, “Analysis and Synthesis of Tunnel Diode Circuits.” Wiley, New York, 1966. l 3 A. J. Decker, “Solid State Physics.“ Prentice-Hall, Englewood Cliffs, New Jersey, 1957. l 4 w. Shockley, ‘‘ Electrons and Holes in Semiconductors.” Van Nostrand, Princeton. New Jersey, 1950. l 5 J. L. Moll, “Physics of Semiconductors.” McGraw-Hill, New York, 1964. I6 E. Spenke, “Electronic Semiconductors.” McGraw-Hill, New York, 1958. I ’ R. P. Nanavati, “An Introduction to Semiconductor Electronics.” McGraw-Hill. New York, 1963.

476

H. C. OKEAN

very low conductivity. However, the conductivity of the semiconductor may be significantly increased by the controlled substitution for intrinsic atoms ) or within the sample of a given concentration to 1019~ m - of~ n-type p-type impurity atoms. Donor or n-type impurity atoms (Group V atoms such as phosphorus or arsenic) each contribute an additional free electron to the semiconductor, whereas acceptor or p-type impurity atoms (Group 111 atoms such as gallium or aluminum) each contribute a single electron vacancy or “hole” to the crystal lattice. The shifting and refilling of these vacancies, that is, the motion of these holes through the lattice, is equivalent to a current flow of particles of positive mass and charge of magnitude approximately equal to that of an electron. Therefore, both n-type and p-type doped semiconductors possess more free carriers and hence higher conductivity in proportion to the doping level than in the intrinsic case. The quantum-mechanical tunneling phenomenon’-’’ is best explained ’ ~ ~free ~ ~and in terms of the energy-band description of a p-n j ~ n c t i o n . The bound electrons associated with each atom in a given intrinsic or doped semiconductor lattice possess a spectrum of available energy levels as determined by the solution of Schrodinger’s wave equation in the lattice under the constraint of the Pauli exclusion principle. In each case, the energy spectrum consists of two principal continuous allowed energy bands, an upper (conduction) band, and a lower (valence) band, separated by a forbidden band of energy gap E,, as shown in Fig. 1. In an intrinsic semiconductor, the majority of electrons are low-energy, bound electrons occupying states in the valence band, whereas there are few high-energy, free electrons and, by implication, few “free” holes occupying states in the conduction and valence bands, respectively. (The presence of each conduction-band electron implies that of a valence-band hole.) In n- and p-type doped semiconductors, however, there exist narrow, allowed auxiliary donor and acceptor energy bands, located within the forbidden band, immediately below the conduction band and above the valence band, respectively. The total number of available energy states in the donor and acceptor bands is equal to the total number of impurity atoms in n- and p-type doped semiconductors, respectively. However, since the majority of the electrons and holes contributed by donor and acceptor impurities, respectively, are free carriers, occupying the conduction and valence bands, respectively, the auxiliary donor and acceptor states are primarily filled by free holes (ionized donors) and electrons (ionized acceptors), respectively. (The presence of a free donor electron in the conduction band implies that R. L. Sprouli, “Modern Physics.” Wiley, New York, 1956. V. L. Bonch-Bruevich, Radiotekhn. i Elektron. 5. 2033 (1960) [English transl.: Radio Eng. Electron. (USSR)5,238 (1961)l. 2 o S. M. Sze, “Physics of Semiconductor Devices.” Wiley, New York, 1969. l9

8.

> a

I-

DONOR LEVELS

0 W

z W

411

TUNNEL DIODES

'

Eg

FORBIDDEN BAND

E"

I VALENCE B A N D

-a 1

FIG.1. Semiconductor energy-band structure.

of a free hole in the auxiliary donor band, whereas the presence of a free acceptor hole in the valence band implies that ofa free electron in the auxiliary acceptor band.) In fact, the majority of free electrons in the conduction band of an n-type semiconductor and free holes in the valence band of a p-type semiconductor are contributed by the impurity atoms rather than the host semiconductor. The width of the auxiliary energy bands in a doped semiconductor increases with the impurity doping level. For lightly doped semiconductors ( zlOI5 impurity atoms/cm3), it narrows to a discrete energy level, whereas for heavily (degenerately) doped semiconductors (over 10" impurity atoms/ cm3), the auxiliary band overlaps the adjacent main energy band, as is the case in the tunnel diode. h. Quantitatioe Fortnulation of' Encjrgy-Band Configuration For a more quantitative description of the energy-band structure of a given doped s e m i c o n d ~ c t o r , 'we ~ ~consider ~ the energy spectrum of freecarrier densities in each of the allowed energy bands. In particular, let the free-carrier concentrations in the conduction, valence, donor, and acceptor bands in the incremental energy-level range E to E + d E be given by N,(E), N,(E), "@), and N,(E), respectively. Then the total concentrations of free conduction-band electrons n, free valence-band holes p , ionized donor impurities n d + (n-type semiconductor) and ionized acceptor impurities n,-

478

H. C . OKEAN

@-type semiconductor) are expressible as: (la)

s_, E"

P =

s-

(Ib)

/-

(W

m

m

=

J-, Sv(E)g(E)d E , E"

N,(E) d E =

a, Nd(E)

dE =

s-

Sd(E)g(E)

dE,

m

W

na- = J-m N , ( E ) d E

o,

=

S,(E)f(E)dE.

(14

a,

Here, E, and E , are the lower and upper levels of the conduction and valence bands, respectively, S,(E), S,(E), Sd(E), and Sa(E) are the densities, between E and E dE, of the available carrier states per unit volume in the conduction, valence, donor, and acceptor bands, respectively, and f ( E ) is the Fermi-Dirac distribution function, that is, the probability that an available energy state E is occupied by an electron. The Fermi function is given simply by

+

f ( E ) = 1 - g ( E ) = (1

+ exp[(E - E , ) / k T ] } - ' ,

(2)

where T is the absolute temperature, k is Boltzmann's constant, and E, is the Fermi level [the value of E at whichf(i) = 0.51. The Fermi .level E, is a function of the impurity level and is obtained by solution of the equation on the free-carrier concentrations, which expresses the condition for space-charge neutrality, as will be shown shortly. The density-of-states functions S,(E) and S,(E), based on a simplified quantum-mechanical are given by

where m,* and inp* are the effective masses of a conduction-band electron and a valence-band hole, respectively, h is Planck's constant, and U,(E) and U,(E) are empirical functions which satisfy the more exact quantummechanical requirements that, in the limit as (El approaches infinity, S, and S, become zero, and which become unity near band edges E,, E,. Although the donor and acceptor bands in lightly or moderately doped semiconductors are assumed in many treatments to narrow to discrete energy levels Ed0 and Eao, more general analyses yield finite-width densityof-states functions Sd(E) and S,(E) which are generally quite complicated.

8.

479

TUNNEL DIODES

However, they may be conveniently represented by a proposed phenomenological model by which one may account for the increasing width of the donor and acceptor bands as the donor and acceptor impurity levels in n- and p-type semiconductors, respectively, are increased. As suggested by qualitative and quantitative treatment in the heavily doped c a ~ e , ~9*+ 2~n *wel arbitrarily represent Sd(E)and S,(E) by Gaussian functions : exp[-an2(E -

= nd(an/&)

Sd(E)

7

(4)

Sa(E) = na(ap/J;t)exp[-ap2(E - ~ a 0 ) ’ 1 >

where Ed0 and E,, are the mean energy levels defining the donor and acceptor energy bands, respectively, an and ap are inversely proportional to the width of these bands, and nd and n, are the total concentrations of donor and acceptor impurity atoms, respectively, since

j

j

m

(l/nd)

a,

Sd(E) d E

S,(E) RE

= ( l/?la)

=

1.

-m

-OD

In particular, if AEd and AE, are the “quarter-amplitude’’ widths of the distributions Sd(E) and S,(E) such that Sd(Ed’)

=

Sd(Ed, f. AEd) = 0.25Sd(Edo),

S,(E,’)

=

S,(E,, & AE,)

=

O.25S,(Ea0),

(5)

then an =

2.36kT/AEd,

up = 2.36kT/AEa,

(6)

where AEd and AE, are themselves complicated functions of nd and n,, respectively. Note that (l/nd)

r+

ra+

Sd(E)d E z ( l/na)

S,(E) dE z 0.90,

E. -

Ed-

so that 90% of the total donor and acceptor states are included in the “quarter-amplitude” widths of the donor and acceptor bands. In the limit of light doping, widths AEd and AE, approach zero, and lim S,(E)

=

nd 6(E - Ed,),

lim S,(E)

=

n, 6(E - E,,),

AEd-O

AE,-0

(7)

where 6(x) is the Dirac delta function. Therefore, the proposed models for Sd(E) and S,(E) yield, in the limit of light doping, the familiar discrete donor and acceptor energy distributions used in most theoretical models for doped

480

H. C . OKEAN

semic~nductors,’~-”in which all nd and n, available energy states are concentrated at energy levels Ed, and EaO,respectively. The more general models for Sd(E) and S,(E) proposed here in Eq. (4), however, should be more useful under degenerate doping. The superposition of the functions S,(E), SJE), Sd(E), S,(E), f ( E ) , N,(E), N,(E), Nd(E), and N,(E) on the energy-band configurations of arbitrarily doped n-type and p-type semiconductors is shown in Fig. 2. Substituting the various density-of-state functions of Eqs. (3), (4), and ( 6 ) and the Fermi functions of Eq. (2) into the total carrier concentrations of Eq. (l), we may express the latter in the form:

where q

=

qdO

(E - E,)/kT,

= (EdO -

Aqd C,

=

=

qf

=

Ec)/kT,

AEJkT,

47~(2rn,*/h’)~/~, c

(E, - E , ) / k T ,

Vao

q‘

=

= (Eao - Ec)/kT,

Aq,

=

AEJkT,

d =

2.36kT/&

C,

=

AE,,

(E, - E ) / k T , qg

E$kT,

4n(2m,*/h2)3i2, C,

=

2.36kT/& AE,.

c. Requirements on Doping Levels The formulations crucial to doped semiconductor theory and hence to p n junction theory are those that relate the Fermi level E, (or qf) to the

doping levels n,, or n,. These relationships arise from the conditions for space-charge neutrality, which in turn are given by n=p+nd+,

n+n,-=p

(9)

for n-type and p-type semiconductors, respectively. Substitution of Eq. (8) in Eq. (9) yields the desired dependence of qr on nd or n,. The resulting relationships are quite complicated but are of particular importance in the physics of tunnel diodes, since they yield the required impurity levels for degenerate doping, which in turn is required for quantum-mechanical

8.

481

TUNNEL DIODES

CONDUCTION BAND

I

/

7

VAL€NC€ BAND

Nv

I

1.0 DENSITY

OF

STATES

05 f(E)+

0

FERMI FUNCTIONS

FIG.2. Density of states, Fermi functions, and free-carrier densities for arbitrarily doped n-type (solid lines) and p-type (dashed lines) semiconductors.

tunneling, as defined by the conditions’-’’

for n-type and p-type semiconductors, respectively. A general closed-fom solution of Eqs. (8) and (9) for qf in terms of nd or n, is not readily obtainable. However, approximate solutions for nd or II, in terms of qr may be obtained for the extremes of light and degenerate doping

482

H. C. OKEAN

which are somewhat more general than the light-doping solutions presented in the past.’-17 In particular, for light doping, it is assumed that qf < 0, vg vf > 0, exp(vf - v ) << 1, exp(q, + Vf + q’) >> 1, and A v d % Aqa % 0, whereas for degenerate doping, qf > 0, exp(qf - q ) >> 1, and fly],, AQ, > 0. Then, using the integral relationship

+

W

exp[Kx - a’(x - x0)’] dx = exp[Kxo

(a/&)

+ (Kz/4az)]

in Eqs. (4), (6), and (8), we obtain, for both extremes,

where u = 0 and 1 for light and degenerate doping, respectively. Substituting Eq. (11) in (9), we obtain the solutions, under both extremes, for the required doping levels nd and n,: nd

%

31.5(m,*3 / 2 / h 3exp ) qf[l

+ exp(?f - VdO)]

+ ~)(rn,*/m,*)~~’exp( - qg - 2qf)]exp( -0.045 n, x 31.5(m,*3/2/h3)exp qf[l + exp(qao - qf)l x [l - (1

x [(l

+ ~ ) ( m , * / m , * ) ~exp( ~’ -qg

-

Aqd2),

(12)

2qf) - 11 exp( -0.045 AqaZ),

for n- and p-type semiconductors, respectively, where qg + 2qf > 0 ( p > n) for an n-type semiconductor, qg + 217, < 0 ( p < n )for a p-type semiconductor, and u = 0 and 1 for a lightly and degenerately doped semiconductor, respectively. The solutions for the degenerately doped case differ from those obtained for the lightly doped approximation primarily in the dependence on the impurity-band-widening terms Aqd and Aq,. These terms are themselves generally complicated functions of nd and n,, respectively, thereby resulting in the equations (12) being complicated transcendental equations in nd and n,. However, for the relatively weak dependence on Aq, and Aq, exhibited in Eq. (121, we may choose values for Aqd and Aqa that yield typical degenerately doped band structures, that is, AVd

%

-4vld0,

&a

x 4(qg

+

VaO).

(13)

8.

483

TUNNEL DIODES

The primary effect of the nonzero impurity bandwidths, as indicated in Eq. (12), is to reduce the impurity concentration required to produce a given qf relative to that predicted by the light-doping theory. As an example, widths of the order presented above result in a reduction in required impurity level in room-temperature germanium (qdO -0.4) of about 10% compared with the light-doping approximation presented in the curves due to Dickens.’.’’ The solution of Eq. (12) forms the basis for the specification of suitable semiconductor material for use in tunnel diode fabrication. 2. p-n JUNCTION THEORY n. Energy-Bond Structure

The energy-band configuration peculiar to the p n junctionZoaformed at the interface of a p-type and an n-type semiconductor region results from the requirement that, under thermal equilibrium (zero bias), the Fermi levels E,, and E,, in both regions must be at the same absolute energy level E,. This yields p n junction energy-band structures of the type shown in Fig. 3(a) for a lightly doped junction and in Fig. 3(b) for a degenerately doped junction. In both cases, it is seen that the junction consists of three regions, an n-type, a p-type, and a transition region. The fundamental difference between the band structures in these two cases is that, in the degenerately doped junction, the conditions E,, > E,,, E,, < E,, result in the existence of free electrons in the conduction band of the n-type region which are at the same absolute energy level as free empty states, i.e., holes, in the valence band of the p-type region. Since these regions are separated only by a thin forbidden region, it will be shown that there exists a finite probability that n-region free electrons will “tunnel” across the barrier to occupy p-region available states. The requirement that E,, = E,,, = E f , together with the double layer of charge created by the existence of an excess of free holes (net bound negative charge) in the p-type region and of an excess of free electrons (net bound positive charge) in the n-type region, creates a contact potential VOnp,defined in terms of zero bias (V, = 0) quantities as

vonp= RE,,

-

E,,,)/el”b = 0

=

W”, - Evn)/eIvh= 0

3

(14)

which sweeps the transition region free of carriers, where e is the magnitude of electronic charge. Hence, the transition region is known as the depletion layer. Examination of Fig. 3 shows that Vo,,

=

+ AEfp + Eg),

20‘Quantities in the p- and n-type regions will be given p and n subscripts, respectively.

(1.5)

484

H. C. OKEAN I

n REGION

I I TRANSITION I REGION I

p REGION

DISTANCE

(a)

I

I

€CP Etn, E -

- -

Ec;p E O ,

& n €2 ~

w

z

Ein

E""

I I

, n REGION

I

I I

TRANSITION I REGION I I

p REGION

I

FIG.3. Zero-bias energy-band structure of semiconductor p-n junction. (a) Lightly doped semiconductor; (b) degenerately doped semiconductor.

where A E f n = E,, - E,, and A E f , = E,, - E,, remain constant under nonzero bias. We now consider the case where an external bias voltage vh is applied across the r n junction (p region positive for V, > 0), as shown in Fig. 4. This requires that the energy levels E , and E f , be displaced according to the requirement E,, - E f , = eV,. The resulting energy-level configurations for both forward ( v h > 0) and reverse bias (Vh < 0) are shown for degenerately doped junctions in Fig. 4(a, b), respectively. In each case, the width of the depletion layer varies with the applied bias,

8.

485

TUNNEL DIODES

,

v b = Vpn >

0 CP

Eip 00

‘E,p Efp w

n REGION

I

I

I

I I

I

p REGION

DISTANCE

(a)

,

,

. . .-- - . .

.

,

DISTANCE

(b) FIG. 4. Energy-band structure of arbitrarily biased, degenerately doped pn junction. (a) Forward-biased junction ; (b) reverse-biased junction.

and is given by wd

= { [&(

‘Onp

-

1/,)/2ne1

(nap

+ ndn)/napndn}Y.

(16)

For the usual abrupt p-n junction, y = i,whereas for a graded junction, y = and for a general junction profile, 3 < y < f. The small values of w d , corresponding [Eq. (16)] to large values of nd and n,, indicate the possibility of electron “tunneling” in the degenerately doped case. In order to treat this tunneling phenomenon in more detail, we must now characterize the current flow in a p-n junction.

t,

b. Current Flow in the p n Junction The current flow across a general p-n junction consists of the following

486

H. C . OKEAN

components (Fig. 4)

+

where I , = Id,,, I d p n - I,,,, - I,, is the normal p-n junction current, I , = I,,, - I,,, is the net tunneling current, I,,,, is the conduction current from the p to the n region of electrons generated (by thermal electron-hole is the conduction creation) in the p region under the field I/, - Vonp,lgnp current from the n to the p region of holes generated in the n region, Idnpis the diffusion current from the n to the p region due to excess electrons diffusing out of the n region, I d p n is the diffusion current from the p to the n region due to excess holes diffusing out of the p region, I,,, is the tunneling current due to valence- and impurity-band electrons in the p region “tunneling” into available states in the n region, as will be described shortly, and I,,, is the tunneling current due to conduction- and impurity-band electrons in the n region tunneling into available states in the p region. The direction of conventional (positive carrier) current flow is chosen as that from the p to the n region, thereby justifying the negative components of Eq. (17). The normal net current flow I , in a lightly or moderately doped p-n junction has been treated exten~ively’~-’~ and hence will be stated here without further derivation. It is given by

where A is the cross-sectional area of the junction; p , and n, are the hole and electron concentrations in the n-type and p-type regions, respectively, as formulated in Eq. (8); and Dn,D, and T,, T, are the diffusion constants and minority carrier lifetimes of electrons and holes, respectively. The net current I, is a minority-carrier current, which exhibits the familiar exponential I-I/ characteristicZobof a rectifying junction. The tunneling current I , is the component of current of primary interest here and hence will now be treated in some detail. c. Formulation of Tunneling Current

The phenomenon of quantum-mechanical tunneling arises from the existence of a nonzero probability that an electron at energy level E on one side of a p-n junction can tunnel across the transition region to a vacant available ’ObA negative, sharply increasing avalanche current occurs at the Zener breakdown voltage &A < 0, which is well out of the bias range of interest for tunneling, and hence is not con-

sidered here.

8.

487

TUNNEL DIODES

electron energy state at energy level E on the other side of the junction. Quantum-mechanical tunneling may be described quantitatively as follows. Let dl,,, be the incremental component of electron current flow due to electrons between energy levels E and E + dE in the n region tunneling across the transition region into available vacant electron states at energies E to E + dE in the p region. Then dl,,ipmay be expressed as (19) XoASn(E),f~(E)P,p(E)Sp(E) 11 - &(Ell d E , where Pnp(E)is the current transmission probability (in C/sec) of a single electron at energy E in the n region tunneling across the transition region into the p region, S ( E ) is a generalized density-of-states function, becoming S,(E), S,(E), S,(E), or S,(E) and zero in the valence, conduction, impurity, and forbidden bands, respectively,f(E) is given by Eq. (2), A is the crosssectional area of the junction, and x0 is a lattice constant (in cm) to be defined subsequently. Similarly, the incremental component of electron current flow due to electrons between energy levels E’ and E’ dE‘ in the p region tunneling into the n region, is given by dItnp =

+

dltpn = x~A~~(E).~~(E )P,,(E [)S,(E 1 - J,(E’)] ) dE’ . (20) The fundamental requirement on the energy-band structure of a p-n junction in order for tunneling current to flow is, as is apparent upon examination of Eqs. (19) and (20), that there exists a range of energies E for which S,(E) and S , ( E ) are simultaneously nonzero. This condition in turn can only be satisfied if(see Fig. 4) there exists a range of bias voltages Vb = (Ef, - Ef,)/e such that E& > E i , , that is, such that the essential bottom of the donor band and the essential top of the acceptor band in the n and p regions, respectively, overlap. This condition, based on the finite-width impurity-band model [Eq. (4)], neglecting impurity-band “tailing states,” that is, the 5 % of the donor states having E < E i , and the 5 of the acceptor states having E > E&, is more general than the condition for tunneling E,, > E,, obtained for the usual discrete impurity-level approximation and will therefore help explain such:phenomena as band-edge tailing and excess current. The requirement for tunneling then may be written as Vb

< (l/e)[(Efri

-

Edn) + ( E & - E f p ) l ,

(21a)

which, again, is more general than that obtained under the discrete-impuritylevel assumption, Vb < (l/e)[(Efn - ‘ c n ) + (Evp - ‘fp)] (2 1 b) ’

Examination of Figs. 3 and 4 shows that, for lightly and moderately doped junctions, Eq. (21a) requires a large negative Vb, usually exceeding the reverse breakdown potential. However, in the case of a heavily doped junction (Fig. 4). the upper threshold potential for tunneling is positive. In fact,

488

H. C . OKEAN

Ecn lx w

5

LEVELS

Evn I

fl REGION

I

I

I I

I I

P REGION

DISTANCE

FIG.5. Schematic representation of tunneling processes for excess current. A, B, C : Tunneling mechanisms via “deep” impurity sites (traps).

the usual definitive condition for positive bias tunneling is the familiar degeneracy condition of Eq. (lo), that is,

In addition to the dominant interband tunneling process characterized by Eqs. (19)-(21), an additional component of tunneling current has been proposed by Yajima and Esaki” and by Chynoweth et a1.,22 by way of explanation of the “excess” current exhibited by tunnel diodes in the bias region between those regions characteristic of normal tunneling (Eqs. (19)-(21)] and minority-carrier injection [Eq. (18)l.The proposed mechanism for this additional tunneling process is that conduction-band electrons in the n region at energy levels E > E,, tunnel partially across the forbidden gap, then lose energy due to interaction with “deep” impurity levels Ei in the forbidden band, and finally tunnel, at energy level Ei, into the p-region valence band. Several m e c h a n i ~ r n s ~for ~ this - ~ ~interaction-induced tunneling are shown schematically in Fig. 5, with the most probable one involving interaction with “deep” impurity levels and loss of energy in the n region prior to tunneling into the p-region valence band. The origin of these deep impurity levels or “traps” is believed to be lattice dislocations, surrounded by precipitated material. ” ” 23

T. Yajima and L. Esaki, J . Phys. SOC.Japan 13, 1281 (1958). A. G. Chynoweth, W. L. Feldman, and R. A. Logan, Phys. Rev. 121,684(1961). R. P. Nanavati and C. A. De Andrade, Proc. I E E E 52, 869 (1964).

8. TUNNEL

489

DIODES

The magnitude of the interaction tunneling current I , arising from this mechanism may be expressed as 2 2 : 1,

(22)

xo'An,P,,

=

where n, is the total density of the "deep" impurity states at energy level Ei (Fig. 5), P, is the probability (in C/sec) of a single electron tunneling from the impurity states to the p-region valence band, A is the junction area, and xo' is a constant having dimensions of length. The quantitative expression for P, presented in the next section yields an exp(KT/,) dependence for I,. The validity of the above contribution to the excess current has been demonstrated in numerous experiments with Ge, GaAs, and Si tunnel The total tunneling current is obtained from Eqs. (17), (19), (20), and (22) upon integration over the appropriate energy range as P

where it is assumed without loss of generality that P,,(E)

%

P,,(E)

= P(E).

For finite-width impurity bands, we have S,(E) = S,,(E) ,+ Sd,(E) and S,(E) = S,,(E) S,,(E), so that I , may be divided into five components:

+

I, = Ill +

1,2

+ I , , + It4 + I , .

Taking the limits of integration as the regions of overlap of the individual terms in S,,(E)S,(E), the components of tunneling current become

J

EVP

111

=

XoA

S,,JE)S,,(E)[.f,(E)

-

f,(E)IP(E) d E ,

EC,

m

It2

=

6..

S,,,(E)S,,(E)P(E)[f,(E) - f,(E)] d E ,

XOA

JJ-

EVP

It3 = x O A

Sdn(E)Svp(E)P(E)

[fn(E)- f p ( E ) ] d E

7

dE

2

(24)

00

m

It4 = X O A

I,

=

sd,(E)s,p(E)P(E)[,fn(E)

-

00

Xo'An,P,.

Note that in the case of the discrete-impurity-level model, It2, I , , , and Zt4 vanish, leaving (Il1 I,) as the total tunneling current. The terms lI2, I , , , It4 represent tunneling between impurity and conduction and valence states and

+

490

H. C . OKEAN

directly between impurity states, and therefore, as has been stated qualit a t i ~ e l y , 1920 ~ * ~ *contribute both to normal and excess tunneling current. A qualitative derivation of the dependence of tunneling current I , and total current I, on bias voltage V, is obtained by graphically integrating Eq. (24) at several representative positive and negative values of V, under the approximation P(E) x const, as shown in Fig. 6(a-e). The resulting graphical dependence of I , and I , on Vb, obtained using Eqs. (17) and (18), is shown in Fig. 6(f). Referring to Fig. 6, the behavior of I , with V, may be summarized as follows :

1. For V, < 0, as IVbl increases,f,(E) < f,(E), and both I ! : ) = dI,,/dE and (Evp- Ecn)increase without limit. Hence, I l l , I,, and 1, increase negatively without limit, as seen at points I and I1 of Fig. 6(f). The contributions of Zl2, Its, It4, and I, are negligible.

FIG.6. Qualitative derivation of tunnel diode current-voltage characteristic. (a) Vb = V,, < 0; (b) Vb = V,,, < 0; (c) V, = V,,,, = 0: (d) V, = V,,, > 0: (e) V, = V,, > 0 ; (f) Ib-Vbcharacteristic, I i : ' = d I , J d E , k = 1,2,....

8.

491

TUNNEL DIODES

2. At V, = O,fp(E)= ,f,(E), so that I , = 1, = 0 (point 111). 3. As Vb > 0 increases, f,(E) - j p ( E ) > 0 and I!;), If:), and I$) increase, whereas 1::' and (Evp- E,,,) decrease toward zero. Hence, I t l , I,, and I,, exhibit a maximum at some V, = V, and begin to decrease with larger V, > V,, as seen at points IV and V. 4. As V, increases such that E,, < E,,, 1::' = 0, but I!:), I!:), I::’, and ,f,(E) - &(E) increase sufficiently so that I , remains small but nonzero over a wide excursion of V, before eventually dropping to zero, as seen at points VI and VII. However, I, and I , , both exponential in Vb, begin to contribute at these points, so that I, never drops to zero but exhibits a valley at Ib,,,in = I, before increasing rapidly as I , goes into the forward conduction region. The current Ib,,,in is often referred to as the excess current and, as stated previously, is attributed qualitatively' 1.'9-22 to conduction and valence band-edge tailing, tunneling between impurity states, electron-hole recombination in the forbidden band, and electron interaction with photons, phonons, etc., during tunneling. However, the phenomenological Gaussian impurity-band model employed here provides a quantitative explanation for the existence of the band-edge tailing component of Ib,,,in in terms of the tunneling current components / , 2 , I,,, and It4. The determination of I , requires an evaluation of the tunneling probability P(E), which will now be derived from a consideration of the quantummechanical tunneling process.

3. THEORYOF QUANTUM-MECHANICAL TUNNELING a. Wave-Particle Duality und the Schrodinger Equation The phenomenon of quantum-mechanical tunneling'-'* arises from the wave-like nature of charged particles as characterized by Schrodinger's equation, and is exhibited by the nonzero probability that a particle can penetrate a potential barrier exceeding its own energy. Although detailed treatments of the three-dimensional quantum-mechanical tunneling process in actuality, the tunnel in a degenerate pn junction have been diode junction has a one-dimensional carrier, charge, and field distribution with a uniform cross section. Therefore, a one-dimensional model adequately represents the physical situation and will be employed here. The basic postulates of quantum p h y s i ~ s ' ~ ascribe .'~ a wave nature to every particle, and therefore to a prospective tunneling electron. The resulting wave-particle is therefore characterized by the following parameters : (a) momentum p, (b) kinetic energy E, = p2/2m*, (c) effective electron mass m,,*= (3’E,/2p2)-

',

492

H. C . OKEAN

(d) wavelength A = h/p (e) wavenumber k,

=

2nh/p,

k = 24A = p / h = (2m,,*EK)'"/h,

(f) phase velocity c, (g) total energy in potential energy field E ,

+

E = E, E K , (h) momentum (vector) p = pup, (i) wavenumber (vector) k = ku,, ( j ) the unit vector characterizing the momentum direction up. The intensity of the wave-particle t,b as a function of position, assuming that the sinusoidal time dependence exp[J2n(c/,l)t] is separated out, is characterized by the well-known three-dimensional Schrodinger equation,

+ (8n2m,*/h2)(E- E,)t,b(r) = 0 ,

V'$(r)

(26)

where r is a three-dimensional position vector. The Schrodinger equation, alternatively expressed as

+ k2$(r) = 0 ,

V2$(r)

with

k = k(r),

(27)

possesses solutions, under a constant potential field EPo,of the form

$(r)

=

- + B exp(-,jk

A exp(jk r)

*

r) ,

(28)

where, from Eq. (25),

k

=

const

=

[2m,*(E - Ep,,)]1'2/h.

Therefore, the wave-particle is seen to exhibit the behavior of a propagating wave (k real) in regions for which E > EPo and of a rapidly attenuated "below-cutoff" wave (k is imaginary and B = 0 for physical realizability) in regions for which E < EPo.The latter case is clearly the one that governs a particle penetrating a constant-potential barrier. The physically significant quantity derivable from the wave-particle intensity $(r) is the probability function @ that the wave-particle is within a given volume U , as given by @ =

1"

$(r)$*(r) dU d 1,

(29)

where the asterisk indicates complex conjugate and @ must be unity for U representing all space. Clearly, Eqs. (28) and (29) suggest that a particle has a nonzero probability of penetrating a constant-potential barrier, thus forming the basis for the more general phenomenon of quantum-mechanical tunneling.

8.

493

TUNNEL DIODES

In the more general case of a position-dependent potential-energy field Ep(r),Eq. (27) becomes a three-dimensional nonlinear differential equation which forms the basis for the more detailed treatments of quantum-mechanical However, at this point, we postulate a uniform crosssectional geometry, resulting in the following one-dimensional model :

+

( d 2 J / / d x 2 ) [k(x)j2J/= (d2J//dxz)+ (8nZm,*/hZ)[E - E & X ) ] $ ( X )= 0 , (30)

where x is measured in the direction of positive (n-to-p) current flow. b. Electron Tunneling through u Potential Burrier

We now consider the problem of an electron at energy E tunneling through an arbitrary potential barrier E,(x) > E (0 < x < I,) as shown in Fig. 7(a).

DI S T A N C E

(a)

xxDISTANCE

I

I

0 x0 I STA NC E

X+

I

L

FIG.7. Electron tunneling through potential-energy barriers. (a) General barrier; (b) general barrier with transition regions; (c) barrier in a p-n junction.

494

H. C. OKEAN

The application of Eq. (30) to this problem results in an extremely difficult nonlinear differential equation. However, under the condition of slowly , ~ the ~,~~ varying E,(x), we may employ the WKB a p p r o x i m a t i ~ n ' ~to solution of Eq. (30), as given by

where rn denotes the region I, 11, or 111 bounded by x < 0,O 6 x Q L, and x > L, respectively, and A,(x) and B,(x) are obtained by invoking continuity at the boundaries. The validity of the WKB approximation for the purposes of this treatment has been verified by the more exact threedimensional solutions due to Kane,* Keldysh,' and Krieger," and by the one-dimensional, phenomenological approach due to Scanlan.' The specific mathematical requirements for the validity of the WKB approximation are24

over 0 < x < L. Equation (32) implies that the slope laE,/axl must be small compared to IE - E,(x)l, particularly at the barrier interfaces between regions I and I1 and between I1 and 111. If this is not satisfied, the WKB solutions are not valid at the interfaces, and separate representations of E,(x) are required within auxiliary interface regions IV and V, as shown in Fig. 7(b). For an exact solution of Eq. (30) in regions IV and V, a piecewise linear representation of E,(x) of the form E,(x) z E T c(x - xi) (Fig. 7b) may be utilized, yielding an exact Bessel function solution to Eq. (30). These results may then be used to match $,(x) = (c/,+’(x) at the various boundary interfaces, thereby yielding the required A,(x) and B,(x). The probability of an electron tunneling through the potential barrier E,(x) is given by the ratio

4

=

I$l,l(X

=

L)/$,(x = 0)l2.

(33)

However, the requirement for physical continuity requires that, at the barrier boundaries, = at x = 0 and $Ill = $I, at x = L. Therefore, the tunneling probability becomes

4=l 24

~ l l ~ ~ ~ / ~ , l ~ ~ ~ l z ~

D. Bohm, "Quantum Theory." Prentice-Hall, Englewood Cliffs, New Jersey, 1951.

(34)

8.

495

TUNNEL DIODES

c . Degenerate p n Junction Tunneling Probability The potential barrier E,(x) relevant to the degenerate p-n junction band structure (Figs. 3 and 4) is the one across the forbidden band gap between the overlapping p valence band and n conducti-on band, and is hence of triangular shape, as shown in Fig. 7(c). Specifically, E,(x) is given by E,(x)

=

E,

E,(x)

=

E

O>x>L,

+ eFx,

0<x Q L,

(35)

where F is the depletion layer field E,/eL = (Vonp- Vb)/w, (Fig. 4). The WKB solution corresponding to the above potential barrier is obtained by substituting Eq. (35) in Eq. (31) in region rn = 11, and invoking the continuity condition at x = 0, L, thereby resulting in

Then, upon substitution of the above in Eq. (34), we obtain the WKB tunneling probability22

4

=

exp{ - ~ 8 [ ( 2 r n n * ) ” 2 / h e ~ ] E,~ ’ 2 )

(37)

where 0 z 1 and where the depletion-layer field F is obtainable from Eq. (16) as =

(I/onp

-

Vb)/wd

= (I/Onp -

112 /u’d,

(38a)

where the width constant Wd is defined as -

wd =

+

[&(nap n d n ) / 2 ~ e n , p n d n ] 1 1 2 .

(38W

The tunneling transmission probability factor (C/sec) of an electron current penetrating the forbidden band is given by

P(E) = P

=

( 2 x o e 2 / h i d )Vonp ( - Vb)’/’ exp[ - c~M;~E,3’~/2( Vonp-

(39)

where a = $ ( 2 ~ 1 , * ) ” ~ /and h e xo is a lattice constant to be defined. Note that, for the triangular potential barrier model, 4 and hence P are independent of E. A virtually identical result is obtained under the assumption of a parabolic potential barrier,20 with the exception that the constant c( is reduced by a factor 0.59. In a similar manner, the probability factor P, (C/sec) for tunneling via “deep” impurity states has been derived2’TZ2to be P, = (2x0’e2/hGd) ( Vonp- Vb)‘’’ exp[ - @ , c ~ , G ~ eVonp ~ ~ ~-( Vb)],

where 0, z 1, a, z $(2rn,*)”2/he, and xg) is a lattice constant.

(40)

496

H. C . OKEAN

d. Energy-Momentum Conservation during Tunneling To examine further the validity of the WKB approximation for the determination of P ( E ) ,we must examine the energy-momentum dependence of the pn junction band edges relevant to the tunneling process. We start by considering the solutions of the wave equation (30) for a conductionor valence-band electron in a semiconductor lattice structure. Following Scanlan,12 the presence of a nonzero periodic potential E,(u) due to the lattice results in one-dimensional solutions of Eq. (30) in the space variable u having the form $(u) = U,(u) exp(jk,u),where the V,(u) are Bloch functions characterized by periodicity in the lattice spacing xo, that is, IU,(u)( = Iuk(u k nxo)l with n = 0 , 1 , 2 , .. . . The resulting energy-momentum dependence E(p) of the conductionand valence-band electrons is no longer the simple parabolic relationship implied by Eq. (25) in the absence of a lattice potential, but rather has the more general form W

E(p) =

1 al(p

- PO)',

- nh/xo

< P d nh/xo,

i= 0

where E(po) is an energy extremum (valence-band maximum or conductionband minimum) and E( - p) = E(p). The periodicity of the Bloch functions then imply a periodicity in p of t-2nxh/xo, yielding the well-known Brillouin zones and forbidden gaps as shown in Fig. 8(a). However, if we now replace p by the reduced momentum p, = p +_ (2nnh/x,), the Brillouin zone structure of Fig. 8(a) telescopes into the momentum-space representation of the semiconductor energy-band structure, shown in Fig. 8(b). In a tunneling p n junction, most of the tunneling electrons travel between n-region conduction-band minimum-energy states and p-region valenceband maximum-energy states, as shown symbolically in energy-momentum space in Fig. 9. The tunneling electron must conserve energy and momentum, thereby giving rise to two types of tunneling; direct tunneling, for which the conduction- and valence-band energy extrema occur at the same value of momentum (Fig. 9a), or indirect tunneling, in which the extrema occur at different momenta pOc and pov (Fig. 9b). In the latter case, momentum must be conserved by some external means such as phonon scattering during the tunneling process (Fig. 9b). In calculations of the tunneling probability for a given semiconductor, direct tunneling usually predominates and the perturbation introduced by the much less probable indirect tunneling process is relatively sma11.7~8*'2~20 In the light of the above remarks, we now examine the validity of the WKB approximation for the calculation of the tunneling probability [Eq. (37)] with respect to a more exact treatment. In particular, the calculation

8.

TUNNEL DIODES

MOMENTUM

p OR p,

la)

E,

-=

0

(P)

?TT

XO

REDUCED MOMENTUM

p,

(b) FIG.8. Energy-band structure in momentum space for an electron in a periodic lattice. Brillouin zone structure; (b) reduced momentum energy-band structure. (After Scanlan.I2)

of P for three-dimensional direct tunneling by Kane' modifies Eq. (37) by the factor

K,

=

(n2/9) exp[ -h(kY2

+kz2)@JWF]

(41)

and modifies the exponential multiplier 6 to be 3x/16 rather than unity. Here, hk, and hk, are the generally small perpendicular components of momentum, so that K , does not greatly alter the WKB solution. A calculation of the indirect tunneling probability modifies Eq. (37) by the factor

498

H . C . OKEAN

I

1

- ENERGY

DIRECT TUNNELING : A p = 0

MOMENTUM - p

(0) E - ENERGY Ec(P)

,

, M’INDIRECT

,

Po,

TUNNELING : A P = pot- pOv LOST DURING PROCESS

Po,

MOMENTUM p

(b) FIG.9. Energy-momentum space for tunneling p-n junction. (a) Direct tunneling; (b) indirect tunneling (Si).

where f ( T ) = l/[exp(hv/kT) - 11, v is the phonon frequency, and E,, is a phonon scattering matrix element having the dimensions of energy. This calculation also replaces Eg312 by ( E g +_ hv)3i2in the exponent multiplier of Eq. (37). For applicable semiconductor materials, K , 10-3K,, so that the probability of indirect tunneling is quite small compared to that of direct tunneling. Therefore, it may be concluded that the WKB approximation for the calculation of the tunneling probability is sufficiently accurate for the purposes of this treatment.

-

4. DERIVATION OF TUNNELDIODE I-V CHARACTERISTIC Having calculated the tunneling probability P(E)and shown it to be essentially independent of E [Eq. (39)], we may now integrate Eq. (24) to obtain the tunneling current as a function of applied bias voltage. Therefore, the

8.

242

In a Less accurate approximation,'' 1, sinh(q,/2)[1

499

TUNNEL DIODES

-

f. at ij

=

-qb/2 is evaluated as

+ C O S ~ ( V ~ / ~C) tanh(@) ]

for qb >> 1

500

H . C . OKEAN

where

I,

=

0.39~oAPa,upkT;

pz

=

l.8{[apnap(l

q,

=

(eV,,,

-

p l = 0.82n,pn,,ap~,/apa,(kT)2 ;

+ 1.05q,,)/~~’zka,T]+ [anndn(1 + 1.05~&,)/G,!~ZkapT]} ; E,/kT); K ii ’. n 2u -p

1 -

ai = 21/2m:3/2n(k~)1/2h-3

(i

=

/ a-T

9

n or p ) ,

and where P is given by Eq. (39), and u(x) is the unit step function u ( x ) = 1 and 0 for x 2 0 and x < 0, respectively. Equation (44) represents the theoretical tunnel diode current-voltage (Ib, Vb) characteristic, as shown with its conduction-to-valence band and conduction-to-impurity-band tunneling and diffusion components of current in Fig. 10 for a representativez5 tunnel diode. The superposition of an experimentalz5 I-V characteristic for this diode on Fig. 10 indicates a relatively close quantitative agreement with theory, particularly with respect to excess current (largely due to the inclusion of the Gaussian donor and acceptor band and “deep” impurity-site tunneling current contributions). The particular parameters of interest which characterize the currentvoltage characteristic are the peak current point (Ip,V,), the valley current point ( I v , K),and the “inflection point” of maximum negative conductance magnitude (IM, VM)as shown in Fig. 10. These parameters are obtained from the total current [Eq. (44)] as follows : Vp = V, at which

dl,,/dab x (d/dqb)[(qT - qb)’ tanh(qb/4)] = 0 ; (45a)

K = Vb

(d/dub)(Itl + I,

at which

VM = Vb(min) at which I,

=

vb =

+ I , ) = 0;

(45b)

d21,,/dqbZ = 0 ;

(454

M;

(4 5 4

(kT/e)qb = [25T(“K)/29oo]vb (MI/).

(454

I,(V,)

+ I,( V,),

(T

=

p, v,

or

Solution of the above relationships yields :

K

(mv)

25[T(“K)/2900i [?T - (1/210)(1J0 exp IT + KxlxO exp(Kx~T)l

Vp (mV) x 50[T (“K)/290”]sinh-’(qT/6),

7

(46)

VM (mV) x 50[T(“K)/290”] In{qT[l + (9~/16)]}. It may be seen from Fig. 10 that, typically, I , , >> It2, It3, It4, I,, and I, for Vb 5 0.5y, so that the current parameters may be expressed as

’’ L.D.Armstrong, Microwave J . 5, 99 (1962).

8.

I,

= l o { [ ( I J o / z o )exp q T

501

TUNNEL DIODES

+ ( K x I x o / I o ) ~ X P ( K ~ V+(IJo/Io)(~XP T)I~ V V

+ ( ~ x o / ~ O ) e x P ( ~+x ~P 2, ) + Pl exP[-K1(?,0 + T i 0 - r1J21). Typically, for a high-quality diode, I , > 101,. In addition, the maximum negative-conductance magnitude of the tunnel diode occurs at VMand is given for large Ip/I, by (48) These fundamental properties of the current-voltage characteristic of the tunnel diode pn junction will be often referred to in later sections, where tunnel diode circuit performance is related to fundamental device parameters. Previous calculations have been made of the peak7 and excessz2 currents under somewhat more restrictive assumptions. For example, the peak tunneling current obtained under a O”K solution of the tunneling integrals’ GM %

(e/kT)ldlt/dqblVM (210qTe/kT)[FM(qT)l l”.

where ii = napnd,,/(nap+ ndn). Further use will be made of these results when considering the material properties of tunnel diodes for various circuit applications. 111. Principles of Tunnel Diode Fabrication

5. FORMATION OF THE TUNNELING JUNCTION a. Applicable Semiconductor Materials The semiconductor materials in which quantum-mechanical tunneling has been observed include the semiconducting Group IV elements and Group III-V compounds having the relevant physical parameters’-’ 2 ~ 2 5 - 3 3 listed in Table I. 26

27

28 29

30

3’

32 33

W. J. Bertram, Jr., C. Dunn, and M. R. Barber, in “Microwave Tunnel Diode Devices and Their Circuit Applications” (H. A. Watson, ed.). McGraw-Hill, New York, 1968. K. K. N. Chang, “Parametric and Tunnel Diodes.” Prentice-Hall, Englewood Cliffs, New Jersey, 1964. G. M. Glasford, R. L. Anderson, and R. P. Nanavati, unpublished work. 1964. N. Holonyak and I. A. Lesk, Proc. I R E 48,1405 (1960). H. S. Sommers, Jr., Proc. I R E 47, 1201 (19S9). H. R. Lowry, J. Giorgis, E. Gottlieb, and R. C. Weischedel, “Tunnel Diode Manual .”General Electric Company, Liverpool, New York (1961 ). C. A. Burrus, Proc. IRE 50, 16x9 (1962). C. A. Burrus, J . Appl. Phys.32. 1031 (1961).

502

H. C. OKEAN TABLE I

PHYSICAL PARAMETERS OF TUNNEL DIODE MATERIALS Semiconductors" Ge Si Suitable doping agents: Donor Sb, As As Acceptor Ga, A1 Al, B Representative impurity 4 x 1019 2 x 1020 concentration (cm-') Forbidden-band 1.11 0.67 E, energy gap (eV) Relative dielectric 11.7 16.4 constant 4EO Impurity ionization energy (eV) E , - Edo 0.01 &o - Ev 0.01 1.1 Relative effective mas? m,*/m0 0.55 0.37 mp*lmo 1300 Mobility (cm2/v-sec) pn 3900 500 1800 PP

GaAs Sn Cd, Zn

GaSb Te, Sn Cd

lnSb Te Cd

5 x

I

2 x 10''

1019

x

10'9

1.35

0.70

0.18

11.1

14.0

15.9

0.0 127 0.0127 0.034

0.0097 0.0097 0.047

0.0097 0.0097 0.021

5000

4000 850

73000 1250

400

"All parameters evaluated at 290"K, except at 77°K for InSb. mo is the mass of the electron.

The ranges of physical parameters that are most appropriate to the realization of a high-quality, high-frequency tunnel diode are : (1) A small band gap E , for high peak current and large power-handling capability. However, E , must be sufficiently large at a given temperature to prevent the flow of intrinsic-carrier current. For this reason, InSb must be operated well below room temperature, say at T = 77°K. (2) A high doping level for low series resistance. (3) A low carrier effective mass for low series resistance and low excess current.

The materials used in the fabrication of high-quality, high-frequency, room-temperature tunnel diodes are Ge, GaSb, and GaAs, with InSb and Si precluded because of the overly low forbidden band gap exhibited by InSb and the high effective carrier mass and resulting high excess current exhibited by Si. In addition, GaAs tunnel diodes had in the past presented a reliability problem,'* which, however, is now believed to be under control. The tabulated physical parameters of the various semiconductor materials used in tunnel diode fabrication strongly influence the electrical parameters of the resulting tunnel diodes and thereby determine which semiconductor material is most appropriate for a given tunnel diode application, as will be described in succeeding sections.

8.

TUNNEL DIODES

503

The most suitable doping agents, which provide the required donor and acceptor impurity concentrations, are also listed in Table I for each of the semiconductor materials under consideration. The manner in which these impurities are physically introduced in the semiconductor will be described in the following section. b. Methods of Junction Formation

A tunneling p - n junction is basically formed by introducing at a localized small area on a heavily doped ( l o L 9or l O ” ~ m - ~n-type ) or p-type semiconductor wafer a small “dot” consisting of or containing an acceptor or donor impurity, respectively. The impurity dot usually consists of a metallic alloy containing the metallic or nonmetallic impurity element. A list of commonly used alloys’ containing the appropriate donor and acceptor impurity element‘s is provided in Table 11. TABLE 11

IMPURITY ALLOYSUSEDI N TUNNELDIODE JUNCTION FORMATION Impurity element Ga Al, B Sb As

Commonly used alloy InGa, SnGa AIB PbSb SnAs

The realization of high-frequency, high-speed tunnel diodes requires that the area of the tunneling p n junction be extremely small ( < cm’), thus making the junction-forming process quite critical and limiting the number of applicable processes. In particular, a junction-forming process is used in which the impurity dot is fused to the semiconductor wafer at the desired junction location by alloying, diffusion, or solution growth. The most common junction-forming processes’ 1,26*32-42 utilizing these techniques for introduction of the C. A. Burrus, Proc. I R E 49, 626 (1961). R. N. Hall, Proc. IRE 40,1512 (1952). 3 6 M. J. Coupland, C. Hilsum, and R . J . Sherwell, Solid State Electron. 5,405 (1962) 3 7 H. C. Okean, Dig. 1966 IEEE G - M T T Int. Symp., Palo Alto, p. 135 (1966). H. C. Okean, IEEE Trans. Microwave Theory Tech. MTT-15,613 (1967) 3 9 G. Gibbons and R. E. Davis, Proc. IEEE 54. 814 (1966). 40 A. Lueck, W. Schultz, and A. Marmiani, Microwaoe J . 9, No. 7,49 (1966). 4 ’ S. S. Im,J. H. Butler, and D. A. Chance, IBM J . Res. Deoelop. 8, 527 (1964). 4 2 H. Hornung and D. Zook, Solid State Elecrron. 9, 7 (1966). 34 35

’*

504

H. C . OKEAN

I

JUNCTION VOLTAGE

Vb

FIG.10. Representative theoretical and measured tunnel diode current-voltage characteristic.

impurity “dot” are the “ball-alloy’’ process,’ the “pulse-bond’’ pointcontacting p r o ~ e s s , ~ ~and - ~the ~ ,~ ~l a~ n, a~ r~~ process. ~-~* In the ball-alloy process, the impurity dot is alloyed to the degenerately doped semiconductor wafer in a furnace at a temperature TA (=500°C) sufficiently high to melt the alloy dot and the adjacent semiconductor material to form an ideal solution of alloy in semiconductor. The solution of impurity in semiconductor or impurity-containing alloy in semiconductor must contribute an essentially equal impurity concentration to that of the opposite type contained in the semiconductor wafer. In actual practice, the alloying process is contained for a length of time AT( 1 min) at T A and, for enhancement of the alloyed impurity concentration, is then cooled rapidly (in seconds to minutes) to room temperature, thus forming the pn junction. The maximum alloying time A z M A X is that which keeps the length ALD over which alloyed impurities diffuse into the semiconductor (with diffusion coefficient DA)less than 0.1L (L is the junction width), with AT,,, given by

-

After cooling ofthe alloyed dot, it is contacted electrically to permit monitoring of the dc 1-V characteristic. Then, the resulting pn junction is reduced in diameter by etching until the desired level of peak current is obtained. The resulting pedestal-like junction configuration is then strengthened mechanically with epoxy prior to diode encapsulation.

8.

TUNNEL DIODES

505

The advantages of the ball-alloy process include its tight control of peak current (junction impedance level) and its adaptability to automation, whereas its disadvantages include variability of junction properties if environmental controls are not strictly adhered to, and the fragility and relatively high parasitic content (discussed in next section) of the junction configuration. The pulse-bond point-contacting process involves the location of a pointed metallic ribbon at a point on the surface of a degenerately doped semiconductor wafer, the strengthening of the resulting point contact with a drop of epoxy, and the formation of the pn junction by passing a voltage pulse ( - 1 V for = 10 psec) through the ribbon and wafer. The resulting p-n junction is very low in parasitic content. thereby lending itself to the fabrication of a very-high-frequency diode.j2-j4 However, the process does not permit the tight control of junction area that the ball-alloy etching allows. The most recently developed tunneling junction-fabrication process and that most compatible with the burgeoning microelectronic integrated-circuit technology is the planar process. Here, the semiconductor surface to be processed is masked off, with only the desired junction area exposed. The desired impurity element or impurity alloy is then alloyed, diffused, or grown into the semiconductor through the window in the mask, yielding the desired planar p n junction. It is only recently3’ that sufficiently small-area planar junctions have been obtained for the realization of high-frequency tunnel diodes. This process holds most future promise, however, particularly with respect to integrated-circuit tunnel-diode application^.^^^^^^^^

6. FABRICATION OF THE

OVERALL

TUNNELDIODE

a. Overall Diode Configuration and Equivalent Circuit Following the formation of the tunneling pn junction, the remaining steps in the fabrication of the tunnel diode include the attachment of an electrical contact to the semiconductor wafer and the impurity dot, which constitute the two halves of the p-n junction, and either the encapsulation of the contacted p-n junction in a diode package for general use or the mechanical strengthening of the unencapsulated junction for ultimate permanent attachment to a specific circuit. Of the various junction types described, the ball-alloy junction is usually employed in an encapsulated structure, whereas the point-contact and planar junction are more adaptable to an unencapsulated diode. The functional representation of the completed tunnel diode is presented in Fig. 1 l(a), showing the junction, contacts, and encapsulation or strengthening. This functional representation provides a clear indication of the origin of the electrical parasitics associated with the tunnel diode junction. These

506

H . C . OKEAN METALLIC CONTACT TUNNELING p-n JUNCTION INSULATING ,MATERIAL FOR MECHANICAL RIGIDITY

SEMICONDUCTOR WAFER METALLIC CONTACT

(b) FIG. 11. Functional representation of tunnel diode. (a) Representation of construction; (b) small-signal equivalent circuit.

parasitics, represented in the small-signal tunnel diode equivalent circuit shown in Fig. 1 l(b), include the voltage-dependent junction capacitance Cj( Vb) across the depletion layer of the p-n junction, the series resistance R , , representing the ohmic losses in the semiconductor wafer and the contacts, the series inductance L, due to current flow through the contacting leads, and parallel capacitance C , across the contacts through the insulating encapsulation or strengthening medium. The junction resistance Rj( Vb) is the inverse slope at v b of the tunnel diode I-V characteristic. Of these parasitics, Cj and R, are internal elements associated with the p-n junction and the semiconductor bulk, whereas L, and Cp are external elements associated with the contacting and encapsulation geometry and the surrounding circuit environment. The dependence of the internal parasitic element values on the physical parameters of the tunnel diode will now b e demonstrated. The junction capacitance C,( Vb) across the depletion width w d is approximated, using Eq. (16), from nondegenerate p-n junction theory12-15 as cj(Vb)

2 &A/Wd

ZZ A{[napndn/(nap

+ ndn)12zee/(vOnp

-

Vb)

(50)

for the abrupt p-n junction typical of tunnel diodes. [For the graded p-n junction, the voltage dependence is proportional to ( Vonp - Vb)- I?] This approximation is valid” for V, < Vb < kVonp,where k % 0.54.75.

8.

507

TUNNEL DIODES

For V, % Vonp, Eq. (50)must be modified by a multiplicative constant, whereas for 0 d vb d V,, C j reaches a minimum for v b = V, and then increases monotonically as Vb decreases further toward zero. These departures from Eq. (50) are due to the extra charges in the depletion layer of a degenerate p n junction contributed by tunneling electrons in the forbidden gap and by free conduction-band electrons and free valence-band holes in the energy states E,, d E d E v p . The tunnel diode series resistance is expressible in terms of the length L, of semiconductor bulk between the junction and the semiconductor contact by

where p B is the resistivity of the degeneratively doped semiconductor bulk, A B ( x ) is the (generally variable) cross-sectional area of the bulk, and R, is the total contact resistance. For geometries in which the uniform bulk region adjacent to the junction dominates R , , the latter becomes

R,

(52)

(LB/A)PB.

The incremental junction resistance Rj(Vb) may be expressed in the form Rj(Vb)

[dJb/dvb];,’

K(Vh)/A?

so that the time constant of the tunneling junction, given by

lRj(vb)lcj(Vb)

+

(53) is independent of junction area, but is, at a given Vb, exclusively a function of the material parameters. The same is approximately true for the resistance ratio I’,= R,/JRj(Vb)I. The influence on tunnel-diode circuit performance of the semiconductor material dependence of the “internal” tunnel diode parasitics, leading to an optimum choice of material for a given tunnel diode application, will be dealt with in later sections. Tj =

IK(Vh)l[2neen,,ndn/(V~np

-

Vb)(nap

ndn)11’2

3

b. Possible Tunnel Diode Geometries

Having described the general configuration of a tunnel diode (Fig. ll), we now provide examples of physical realizations of encapsulated and unencapsulated tunnel diodes as presented in Figs. 12 and 13, respectively. The most common encapsulated tunnel diode geometry is the cylindrical pill shown in Fig. 12(a). Here, a ball-alloy junction is formed 43

W. Getsinger, I E E E Trans. Microwave Theory Tech. MTT-14, 58 (1966).

508

H. C . OKEAN

METALLIC TOP CONTACT METALLIC RIBBON

BALL -ALLOY JUNCTION

CERAMIC STANDOFF

SEMI CONDUCTOR WAFER METALLIC BOTTOM CONTACT

(a)

EPOXY FILLER SEMICONDUCTOR WAFER CONTACT

(b)

INSULAT I NG DEPOSITION

EVA P 0RAT ED CONTACT

SEMICONDUCTOR WAFER

PLANAR JUNCTION

(C)

FIG. 12. Encapsulated tunnel diode geometries (a) Ball-alloy junction, (b) point-contact junction, (c) planar junction.

on the top surface of the semiconductor wafer, which in turn is mounted on a metallic contact stud. The upper half of the junction is contacted by a thin metallic ribbon or a wire mesh which connects to the upper contact stud. The package is held together by ceramic spacers which separate the two studs. A similar encapsulated tunnel diode geometry may be used in conjunction with a point-contact junction44 and a planar junction4' as shown in Figs. 12(b) and 12(c), respectively. The most common realizations of unencapsulated tunnel diodes are those formed directly on a waveguide element for use at high microwave frequencies or those having a geometry compatible with integrated-circuit technology. 44

R. J. Taylor and C. R. Westgate, Dig. I968 IEEE G - M T T Int. Symp., Defroit, p. 179 (1968).

8. TUNNEL EPOXY

509

DIODES

M E T A L L I C WHISKER (CONTACTS WAVEGUIDE WALL)

suppoR<

EPOXY SUPPORT

SEMICONDUCTOR JUNCT AT PO CONTA

KOVAR BEAM LEAD

-I JUNCTION AT POINT CONTACT

POST

(a1

AU

(b)

BEAM LEADS-

METALLIC BALL

\

n

AP - B CONTACT

\

";+

/

n-Si SUBST RATE

n++ DIFFUSE:D LAYER

SOLDER

n/

GLASS

I

p++\ (REGROWN)

/

TUNNELING JUNCT'oN

\

\ n-TYPE Ge

p-TYPE EPITAXIAL GoAs LAYER

FIG. 13. Unencapsulated tunnel diode geometries. (a) Point-contact diode on waveguide post. (b) Point-contact beam-lead diode. (c) Planar beam-lead diode. (d) Planar monolithic ~ )planar diode. (After Im el a/.") diode. (After Hornung and Z o ~ k . "(e)

For example, an unencapsulated point-contact tunnel diode may be fabricated directly on a metallic post for insertion in a waveguide mount32-34 as shown in Fig. 13(a). On the other hand, integrated-circuit techniques that utilize planar strip-line circuits on ceramic or semiconductor substrates would most easily accommodate an unencapsulated tunnel diode that employs beam-lead g e ~ m e t r y ' ~ . ~(for ' - ~easy ~ strip-line series mounting) in

510

H. C . OKEAN

the “hybrid” integrated-circuit approach, or that is fabricated directly in the semiconductor substrate in the “monolithic” integrated-circui t approach. An example of a beam-lead point-contact diode utilizing an epoxy-strengthened PbSb point contact on edge of a 2 x 4 x 4 mil p-type Ge ~ a f e r ~ ’ . ~ ’ is shown in Fig. 13(b). The beam leads are provided by the PbSb ribbon containing the point contact and a Kovar ribbon bonded to the bottom of the Ge wafer. A planar beam-lead tunnel diode39 having a 0.1 mil2 SnAs film dot junction and a 6 mil2 SnAs film dot ohmic contact alloyed to the bottom face of a 5 x 5 x 2 mil p-type Ge wafer is shown in Fig. 13(c).Beam leads making contact at each of the film dots are bonded to the bottom face of the Ge wafer. A monolithic, planar tunnel diode c ~ n f i g u r a t i o nconsisting ~~ of an AI-B impurity dot alloyed through an n++ Si layer diffused onto an n-Si substrate is shown in Fig. 13(d). The p-n junction is formed by the narrow ring between the n + + layer and the p + + region created by the impurity dot. Thin-film contacts to the impurity dot and the n++ layer are deposited on the substrate. Finally, an unencapsulated GaAs tunnel diode configuration4’ useful in integrated-circuit applications is shown in Fig. 13(e).

7 . INHERENT LIMITATIONS ON TUNNEL DIODEOPERATION a. Temperature Limitations It is clear from examination of Eqs. (18) and (44) that the total tunnel diode current is a relatively strong function of temperature. In particular, the temperature dependence of tunnel diode operation is best characterized by the temperature dependence of the key parameters P, V,, I , , V,, I , , and GM which describe the current-voltage characteristics. Referring to Eqs. (38)-(40) and (43H48), these parameters may be written as functions of temperature as follows. Noting that the temperature dependence of band gap E , may be - B(t - l)], where t = T/Toand To is room r e p r e ~ e n t e d ~as. ~E ,~ = , ~Ego[l ~ temperature (“K), we then have %‘ = ( b O / t ) { l PO

vp = v&

+ [P(t - l)EgO/(evOnp

exp{[EdB/(vOnp -

vb)”21(f

sinh-’((rlTo/W { 1 +

Y‘ = V , O { 2

- exP[Koq,oB(t

(zpO/t)exp([GdP/vOnp Iv GM

IvO

-

[P(t -

9

I)}

(544 (54b)

5

l)Ego/(cvonp- 40)l))/sinh- ‘ ( v ~ T o / ~ ) (54c)

- 1)E,o/kvOnp - -wlL

(54d)

50)”21(t

(544

exp{[K,O?TOBE,,/(evOnp

-

= 6 4 0 eXPKwdB/(vo”,, - vM)”21(t

-

EgO)](f

l)), - I)],

- 1)).

(540 (54d

8 . TUNNEL

511

DIODES

Examination of the functional dependence upon r of Eqs. (54cH54g) indicates that (a) I , either increases or decreases with increasing temperature, depending upon whether the exponential factor is large (heavy doping) or small (light doping), respectively; (b) V, decreases slightly with temperature ; (c) I , increases and V , decreases significantly with temperature; and (d) GM decreases slightly with temperature. Experimental data on the temperature dependence of these parameters which qualitatively verify Eq. (54) are presented in Fig. 14(a). 2 .o I

I

/

W

,/

(3

2

/'

$ Lz

0 t-

z

w

u a 3 u

1.c 'V

W

>

I=

4 W

0.5 Ge DIODE

'PO3

PO I

' 'pol

' ’PO2

u

C

I

I

I

I

-80 -60 -40 -20

I

I

1

I

I

0

20

40

60

80

I

100

TEMPERATURE, 'C

(a 1 PERTURBATIONS DUE TO PHONON- ASSISTED TUNNELING INDIVIDUAL PHONON CONTRl8UTlONS

PEAK DUE TO TUNNELING VIA "DEEP" IMPURITY

b' PHONON ENERGIES

(b)

FIG. 14. Temperature effects on tunnel diode current-voltage characteristic. (a) Variation of peak and valley parameters with temperature; (b) perturbations observed at liquid helium temperature. (- -) VJVpo; (-) I p / l p o ; (- - -) Zv/Ivo; (- - -) Vp/Vv0-

512

H. C. OKEAN

In addition, the behavior of the tunnel diode I-I/ characteristics a t liquidhelium temperature (- 4°K)’ exhibits perturbations which provide insight as to the nature of various tunneling mechanisms. In particular, sharp indentations in the low, forward current-voltage region [Fig. 14(b)] are indicative of phonon-assisted (indirect) tunneling, with the voltage positions of the indentations corresponding exactly to the energies of the phonons. Furthermore, the existence of additional current peaks in the excess current region of the current-voltage characteristic indicate the presence of deep “trap” impurity energy states in the forbidden band, with the voltage positions of the peaks corresponding to the energy levels of these states. As many as five such peaks have been exhibited in a phosphorus-doped Ge diode. These deep impurity levels, as shown previously, are responsible for the exponential excess current component of I,.

’

b. Radiation The general effect of the bombardment of a semiconductor by high-energy radiation3322in the form of electrons, neutrons, and gamma rays is the displacement of crystal atoms from their lattice positions, thereby creating electron vacancies and making the net impurity concentration of the semiconductor more p-type, and introducing energy levels in the forbidden band due to these atom dislocations. The perturbations on the electrical properties of a tunnel diode corresponding t o these physical effects are, for high doping levels, primarily the decrease in the minority-carrier lifetimes [Eq. (18)] and the increase in the concentrations n, of forbidden-band electron “traps” due to dislocations. These perturbations in turn result in increases in the diffusion and excess components I , and I , of tunnel diode current with increasing radiation, with the primary increase being that of I , . The relatively high doping levels ndnand napon either side of the tunneling junction are perturbed less rapidly with increasing radiation than are I , and I , . Therefore, the portion of the I-I/ characteristic in which the predominant current flow is due to interband quantum-mechanical tunneling, as characterized by parameters I , and V,, is relatively unaffected by radiation. However, the “valley” parameters I, and V , and, to a lesser extent, the maximum negative conductance G M are strongly affected by radiation. This has been shown experimentally2’ by irradiating a Si tunnel diode with 800-keV electrons, resulting in the series of I-I/ characteristics taken at the different stages of irradiation shown in Fig. 15. These curves show the strong increase in I , and decrease in V , and G M with increasing radiation, finally reaching the point where the drastic increase in I , swamps out the quantum-mechanical tunneling current, thus causing the negative conductance region to disappear. This may be shown quantitatively by expressing the density of “trap”

8.

TUNNEL DIODES

513

impurity states nx in terms of the incident radiation by

where d) is the radiation flux (particles/sec) and t, is the bombardment time. Substitution of Eq. (55) in Eqs. (44H48) yields the dependence of V , and I , on 4tBthat is exhibited experimentally in Fig. 15. Although the valley region and ultimately the negative-resistance region of the tunnel diode I-V characteristic are affected considerably by extremes of radiation, the overall effect of a given amount of radiation on a tunnel diode is not as marked as that on a conventional semiconductor junction device, since the operation of the latter is governed by minority-carrier current flow rather than quantum-mechanical tunneling.

FORWARD BIAS, V

FIG.15. Current-voltage characteristic of Si tunnel diode during various stages of high-energy electron irradiation. (After Chynoweth et a/.”) Here, n is the stage of bombardment prior to the recording of the I-V characteristic.

514 c.

H. C. OKEAN

Maximum Power-Handling Capability

The maximum power-handling capability of a tunnel diode is characterized, as in any other semiconductor device, by its burnout energy level, which in turn is related to its thermal proper tie^.^^,^^ The most important thermal parameters are the thermal resistance rT (in “C/W) and thermal time constant zT. The tunneling p-n junction has thermal properties similar to a pointcontact metal-to-semiconductor j ~ n c t i o n in ~ ~that . ~ most ~ of the incident electrical energy is dissipated in the immediate vicinity of the junction. Therefore, for a circular junction of radius a, zT is expressible as46 zT

=

n2a2/8K

( 56)

~

where K is the thermal diffusitivity at the junction region equal t o the ratio of thermal conductivity to unit-volume thermal capacitance. The burnout capability of a tunnel diode in the presence of a pulse of peak power W, and duration z is a function of the critical junction temperature T,(“C)above which the resulting change in diode performance is intolerable. It is obtained by considering the temperature rise ATp (“C) in the presence of the puke, as given by46 ATp = rTWp[l - exp( - z/zT)].

(57)

For short pulses (z << zT), the total pulse energy W,T is the factor governing burnout, leading to an energy burnout rating EBO in ergs. The latter is derived by setting ATp = T, - To in Eq. (57), under the approximation exp( - z/zT) x 1 - (z/zT). Therefore, EBO

(joules) = ( W,z),.,

=

( T , - T o ) ~ T / joules. ~T

(58)

For long pulses or CW (7 >> zT), the steady-state power burnout rating PBO of the diode is the quantity of interest, and is obtained from Eq. (57) as

PBO

=

(W,),,,

=

( T , - TO)/rTwatts.

For a train of N repetitive pulses of duration cumulative temperature rise is given by ATN

=

r,NWp[l

-

5

(59)

and repetition period zR, the

exp(-z/rT)] exp[(z -

zR)/TT].

(60)

For long pulse repetition periods (7R - z >> zT), the factor exp[(? - zfR)/zT] in Eq. (60) approaches zero, so that the cumulative N-pulse temperature rise ATN never exceeds the corresponding single-pulse temperature rise ATp except for extremely large N ( N -+ E ) . In this case, therefore, cumulative 45 46

D. P. Kennedy, J . Appl. Phys. 31. 1490 (1960). H. C. Torrey and C . A. Whitmer, “Crystal Rectifiers,” McGraw-Hill, New York, 1948.

8.

515

TUNNEL DIODES

pulse burnout will not occur for realistic values of N provided ATp is below the single-pulse burnout limit, which is now the governing factor. On the other hand, for relatively short pulse repetition periods (z, - z = zT), it is conceivable that, even if the energy of a single pulse, Wpz, is not sufficient to produce burnout, the cumulative temperature rise due to N such pulses - To and result in delayed burnout even for relatively small might exceed values of N . In this case, the N-pulse burnout is not a problem for zR >> zT, in which case the single-pulse burnout limit [Eq. (5S)l applies. However, for zR 5 zT, an N-pulse burnout limit is obtainable from Eq. (60) as

(PBO),

=

"Wp)max

=

{(T,- T,)exp[(t, - z)/zT[1 - exp(-r/zT)]

(61)

watts.

Typical burnout limits for tunnel diodes are given by

EBO

=1

erg,

(PBO),,

= 50

mW

d. Frequency Limits on Tunnciling The quantum-mechanical tunneling process is extremely fast, having an upper frequency limitt-12 estimated at well above 1000 GHz. Therefore, the incremental junction conductance obtained from the tunnel diode current-voltage characteristic will be essentially constant from dc to 1000 GHz for Vb within the range that tunneling current is predominant ( v b < Vv). Accordingly, the upper frequency limits are imposed by the diode parasitics [Fig. 1 I@)], not by the tunneling process.

IV. Terminal Properties of Tunnel Diodes 8. DC CURRENT-VOLTAGE CHARACTERISTIC

a. Transcendental Approximutions to Evuct Current- Voltage Characteristic The total current-voltage characteristic of the tunnel diode as derived from basic physical considerations and presented in Eq. (44)may be expressed reasonably accurately in the form 1,

%

[c,(VT - Vb)'U(

V, -

Vb)

+ C,] tanh C3 + c, exp c, Vb

Vb $- c 6

3

(62)

where u(x) is the unit step function and VT = Vonp- (E,/e). The terms in tanh c,Vb represent the quantum-mechanical tunneling current and dominate I, for Vb 5 Vv/2, whereas the excess and diffusion current terms C,expC,Vb and c6 become more important in the region of the valley (V, = V,)and beyond. Therefore, for the low-voltage and negative-resistance region of the I-V characteristic relevant to virtually all tunnel diode applications, that is, 0 < Vb < V,, the following normalized modifications of Eq. (62)

516

H. C . OKEAN

provide reasonable fits to experimental data in this region2.*2,47p49 ib %

c,(l - ub)2u(l -

i, z

c l ’ u b exp( - C2’ub)

ib

z C,

t‘b)

tanhcZcb+ cjt’b,

(634

+ c3‘[exp(c4’i~J- I ] , + C2 sin(?, In ub + C4),

(63b) (63c)

where ib = i b / I p and ub = Vb/v,, the constants ( c ,,c2,c 3 ) ,(cl’, c2‘,cj’, c4’), and (CI, E , , C,, ii4) are chosen such that ib = 1 at ub = up and ib = i, at rb = 1, and where I,, I,, V,, and V, are obtained from experimental data.

b. Polynomial Representations of’ I-V Characreristics The transcendental representations of the tunnel diode current-voltage characteristic are most useful whenever a closed-form solution to a particular tunnel diode problem is sought. However, if a computer-generated numerical solution is desired, a more useful representation of 1, is as an Nth-order polynomial in V,, that is, N

The crudest polynomial fit utilizes the small-argument approximation of Eq. (63), resulting ib % KL’b(1

-

t’b)’U(l

-

ub)

+ cl’b,

(65)

which reduces to Eq. (64) for N = 3 and is really only useful for. Vp < v b d V,. An alternative third-degree approximation is centered at the I-V inflection point I,, V, and takes the form51 Ib

- IM ZZ - GMM(V~ - VM)[ 1 - ~[(VI, - V,)/(V,

Gj(Vbf

- G M ( ~-

[(vb

-

VM)/(~M - v p r 1 2 ~ .

-

VP)l2},

(66a) (6W

This approximation provides a symmetrical, parabolic incremental negative conductance centered about G, at V,, I , and is therefore only valid in the region V, 5 v b S 2VM - Vp. In general, it has been f o ~ n d ’ that ~ . ~a ~reasonably accurate fit of the I-V characteristic requires at least a fourth-order polynomial [Eq. (64)], with errors of less than 5 % and 2 % of I , arising from N = 7 and N = 9 polynomial representations of Ge and GaAs diodes, respectively. However, 47

48 49 5”

51

K. Tarnay, Proe. IRE 50,202 (1962). A. Ferendici and W. H. KO, Pror. I R E 50, 1852 (1962). M. P. Beddows, Proc. I E E (London) 111, 67 (1964). T. P. Brody and R . H. Boyer, Solid Stare Ekctron. 2,209 (19611. F. Sterzer and D. E. Nelson, Pror. IRE 49. 744 (1961).

8.

517

TUNNEL DIODES

a useful fifth-order approximation is based on the quartic conductance model, (674 Gj(vb) 2 9 . 4 5 G , ( V b - V,)(Vb - vv)3/(vv - vP)" and is given by 12y5'

I,

2 1,

+ [(Ip

-

Iv)(K - vb)4(4vb

+

vv

-

5vp)/(vv

-

vp)'],

(67b)

where G M = 2.12[(1, - l v ) / ( v v -

Vp)]

=

)G,)

at

vb

= VM = ( K

+ 3vp)/4.

The choice as to the particular approximation of the 1-V characteristic to be used depends on the nature of the particular problem under consideration, keeping in mind that, in all cases, the incremental junction conductance in the presence of series resistance R , is given by Gj

Z

(dlb/dvb)[l

-

RS(dlb/dvb)]-'= l / R j .

(68)

The derivation of Eq. (68) stems from the fact that dlb/dT/,, the slope of the dc 1-I/ characteristic at a given v b , represents an incremental terminal conductance which is the reciprocal of R , + R,, the series combination of incremental junction resistance R, and spreading resistance R,. The terms Gj(Vh) and R,:'(Vb) will be used interchangeably in the remainder of the chapter to represent the incremental slope of the 1-V characteristic.

9.

PROPERTIES OF

TUNNELDIODE EQUIVALENT CIRCUIT

a. Important Parameters 91 Cirruir Model

The small-signal tunnel diode equivalent circuit presented in Fig. 1I(b) is expanded52a to include equivalent mean-square noise generators (lN2),, and ( ViS)av in Fig. 16. Here, (IN2),, is the shot-noise current arising from the randomness of electron motion associated with the total dc current flow and ( ViS)av is the thermal noise generated in the ohmic resistance R,, as given, respectively, by (1,2),, = 2elbNBN

and

( V ~ S ) ~=, 4kTBNR,,

(69)

where BN is the "noise bandwidth" in hertz and 1 b N is the equivalent dc shot-noise current arising from I , at a given v b . It is seen in theory and has been verified experimentallys3 that, since (ZN2)av is the sum of the meanflowing square noise currents generated by the separate components of

'*

J. A. Narud and C. S. Meyer, I E E E Truns. Circuit Theory CT-10.526 (1963). ""The validity of this circuit model and the relative independence of frequency of its parameters has been demonstrated from dc through the microwave range. s 3 B. G. King and G. E. Sharpe, I E E E Trans. EIectron Devices ED-11. 273 (1964).

518

H . C . OKEAN

Z d = I/Y,

z;= I / Y i

FIG.16. Small-signal equivalent circuit of actively biased tunnel diodes.

from the n to p and p to n halves of the junction, and since f b is the difference of these components, f b n will generally be slightly larger than f b at a given V,. In particular, for an idealized tunnel diode junction,53

However, it has been found, over the useful negative-conductance range of Vb, that % 1, is valid with very small error. The small-signal, steady-state terminal immittance of the tunnel diode, as obtained in the negative-resistance region under sinusoidal excitation at angular frequency w, is described in the domain of real frequency w in terms of four characteristic frequencies, the resistance cutoff frequency w R , the series and parallel self-resonant frequencies w, and cob, and the junction frequency wj. The latter is defined simply as w j = lGjl/Cj, whereas wR and w, are defined in terms of the internal small-signal impedance z d ' of the tunnel diode (Fig. 16),which is given by

where Y, = RJR, 1, = L$R2C, w j = I/RC, C = Cj(Vb),and R = l/(Gj( for G j < 0 in the region of interest (V, ,< Vb < K), and where C j and Gjare functions of V,, as expressed in Eqs. (50) and (68), respectively. Noting that, for a useful active device, r, < 1 and Rd' < 0 over 0 < w < w R , where wR is defined as the resistive cutoff frequency above which Rd' ceases to be negative, then OR

=

wj[(l/rs) -

(72)

8.

519

TUNNEL DIODES

Furthermore, w , is that w > 0 at which X,’ = 0, as given by w, = (Oj[(1/ls) -

111’2.

Clearly, if I, 9 r, or L J R C R , = /,< I , then ox3 oiR and vice versa, the implications of which will be examined shortly. Furthermore, examination of Eqs. (71) and (73) indicates that, for 1, < 1, 2,’ appears capacitive for o below Q, and inductive for w above it, whereas for 1, 3 1, z d ’ is inductive over all frequencies and no series self-resonance exists. is expressible in terms of the terminal admittance Yd of the Finally, tunnel diode (Fig. 16), which is given by

+ jBd = ( l i z d ’ ) f j w c , , & = [Rd’/(Rb2+ X;’)] + j { Q C , - [X,j‘/(RL2+ xb2)]).

Yd = Gd

(74)

In particular, wb is the frequency of parallel resonance of C, with inductive that is, the frequency w > 0 for which Bd = 0, as given by

zd’,

wb

E wj

(I

+ c,(l

-

I,)

+ {[l + c,(l

- /,)I2

+ 41,C,p2)

24c,

where cp = C,/C. Clearly, cob >, (ox, otherwise a parallel resonance would not be possible. Further insight into the importance of the various circuit parameters is obtained by examining the Smith chart loci,54 described as functions of normalized frequency wiwR by the real and imaginary parts of z d ’ and Y i [= Yd - j w C , ] in the complex reflection-coefficient plane over the active range of the tunnel diode (0 d w d wR) as shown in Fig. 17 for a family of values of 1, and for a typically small value of r s . It is seen from these curves that several modes of small tunnel diode equivalent circuit behavior are po~sible,’~ and these are enumerated in Table 111 with respect to the behavior of Yd‘(,jw) [= Gd’(w) jBd’(co)]over 0 d w < O J ~ .These modes of behavior of Y i are particularly relevant to bandpass sinusoidal tunnel diode operation about some coo below series self-resonant frequency 0,.In particular, the reactive diode parasitics C, L,, and C, may be individually resonated at wo by external reactive elements L’, C,‘, and Lp’, respectively, resulting in a triple-tuned negative-resistance model for a tunnel diode, as shown in Fig. 18(a). However, for I, d 0.5, and coo 5 OSw,, or for I, 5 1 . 5 ~and ~ wo 5 0.25wR, the diode terminal immittance may be approximated by (Fig. 17) a parallel - G d O C, d O circuit which may be resonated at wo by a parallel inductor L,’-thus resulting in the parallel-tuned model of Fig. 18(b).

+

s4 55

P. H . Smith, Microwave J . 8. 83 (1965). H.C. Okean, l E E E Trans. Microwcwe Theory Tech. MTT-14,323 (1966)

520

H. C . OKEAN

FIG.17. Normalized loci in reflection coefficient plane of tunnel diode internal impedance and admittance functions Z,‘(jw/w,) and yd’(jo/wR)over 0 < w/oR < 1 for typical resistance ratior, = 0.05.(0)w/wR = O ; ( X ) W / O , = O.5;(O)w/wR = 1.0.

In addition, if r, < 1, < 1, proper choice of L, and C , yields the seriestuned approximation for Yd = Yd’ jwC, as shown in Fig. 18(c).However, parallel-tuned operation is usually more advantageous for sinusoidal tunnel diode applications, making the realization of a small ls in a tunnel diode quite desirable. Finally, the two noise generators in Fig. 16 may be combined, using Norton’s theorem, to yield a total terminal noise current ( I & ) a v as shown in Fig. 19(a) and given by

+

where t d is the diode equivalent excess noise temperature ratio, cr t = TIT’, = 290”K, and KN = I b N R (expressed in mV).

= w/w,,

8.

52 1

TUNNEL DIODES

TABLE I l l MODESOF TUNNELDIODESMALL-SIGNAL IMMITTANCE BEHAVIOR

Range of 1,

Mode

Behavior of B,'(tu) as 0 < 0) --t (OR

Behavior of ICd'((u)l as 0 < (I)--t (J>R

~

0

1

< I,

,< 0.5~~ Decreases monotonically

I, z 0 3 , 2

0.5,< I , < r s

3

I,

=

4

rr

< I,

5 6

toward zero Flat to 0 50,. then decreases monotonically to zero

-

Increases slightly more rapidly than wC,' Increa3es slightly more rapidly than wCd'

Increases to" lG,lM at wM and decreases to Lero Increases to Y as w 2 i d R ,then decreases abruptly to zero

Increases more rapidly than'

Same as mode 2

Increases to maximum at w < wM, decreases through zero at tox 2 w Mto minimum at w > w,, then approaches zero as w --t wR

1
Same as mode 2

DecreaTes to minimum, then approaches zero as OJ + (uR

I, 2 2

Same as mode I

Same as mode 5

rs

<1

IGdlM = maximum value of ~C,((IJ)~, occurring at C,' = [dB,'/dw], = ".

(0

WC,'

Increases to x as o Y w R ,then decreases abruptly through zero to - Y at (uR

= toM.

The dominant term in this expression is the shot-noise constant = I,$, which may be considered a noise figure of merit for the tunnel diode. A function of the bias voltage as well as the semiconductor material, K N may be approximated over the active range of the tunnel diode, using Eqs. (66) and (70), by K N

where K N M = l M / G M , KN(v b ) = I ~ NV b() l R j ( Vb)l % I,( v b ) l R j ( Vb)]. In accord% I,, K N may be determined ance with the active-region approximation graphically at Vb, > V, from the current-voltage characteristic, as shown in Fig. 19(b). Equation (77) indicates that KN(vb) exhibits a broad minimum K N , , i n at some vb, > vM,which in turn corresponds to an approximate minimum in ( I ~ , ) , , [Eq. (76)]. The minimum noise bias vb, and the corresponding minimum noise constant K N , , i n may be determined by differentiating Eq. (77) with respect to v b , setting the resulting expression equal to zero, solving for v b = vb,, and substituting the result in Eq. (77). Under

522

H. C. OKEAN

FIG. 18. Equivalent circuits of tuned tunnel diodes. (a) Individually resonated parasitics; L I C l = L,C, = L,L, = 1/oo2.(b) Parallel-tuned model; ls < 1.5rs; GdO= G/(l - rJ[l (l,/rs)(wOz/wRz)]; Cdo 2: C, (CGdo/G); L,' = l/wo2Cdo. (c) Series-tuned model: L , C , = L,C2 = l/ooz; 2r, c Is < I .

+

the approximation (V, - VM)2 << 3( Vp - VM)2, the resulting values are V,, KN,min

K N M (-~ (1 - [(VM - V p ) / K ~2~} ]1 / 2 1, *KNM(l

+{

2 112 - LvM

-

Vp)/KNMI

)

1.

(78)

of the series resistance R, as embodied The degrading effect on td (or in the parameters r, and cr in Eq. (76) is relatively small for a reasonable quality tunnel diode, for which r, and << 1. In fact, the small reduction in t , obtained by choosing a tunnel diode of sufficient quality so that r, 5 0.05 and wR > 40, (a2< 0.0625) is usually offset by the increase in diode cost and in difficulties in circuit implementation introduced by such a choice. Finally, Eq. (76) indicates that the dominant shot-noise contribution to t d is independent of temperature, so that t , cannot be reduced by physical cooling of the tunnel diode.

8.

523

TUNNEL DIODES

"bo

(b) FIG.19. Noise model of tunnel diode. (a) Terminal noise equivalent circuit; (b) graphic determination of noise constant KN(Vbo) at active region bias Vbo .

b. ModiJications of Equivalent Circuit Model at Lurge Signal Levels The voltage dependence of the incremental small-signal junction quantities Gj(Vb) and Cj(Vb) requires that they be modified under large-signal conditions. In particular, if the voltage across the diode junction due to an incident CW signal of frequency oo is given by V, coswot, then the total voltage across the junction I/=is given by v b V, cos mojot, where v,, v,, . . , V,, . . . are the amplitudes of the harmonics of V, cos o,t generated by the nonlinear quantities Gj( Vb), Cj( Vb).We may therefore define'' amplitudedependent large-signal quantities Gj, and Cj, at fundamental frequency oo in terms of the Fourier integrals

+ I:=,

Gjl

=

(1/2n) Jo2K

Gj(5,)

d(w),

524

H . C. OKEAN

ej,

The amplitude dependence of Gj, and is seen more explicitly by substituting in Eq. (79) the expressions for Cj(YT)and Gj(V,,) obtainable from Eqs. (50),(66), and (67) under the reasonably realistic assumption that the combination of tunnel diode and external circuit parameters imposes a short-circuit constraint on all of the higher harmonic components of yT, that is, V2 = V, = . * .= 0. The resulting expressions for Gj, and C j l i n terms of fractional conductance and capacitance distortion parameters 6Gj, and SCj, are

[quartic Gj(V,)],

(80b) (80c)

with the latter determined following a power-series expansion of Cj(Vb)in

Kn" - . . ~-

Vh.

It is immediately seen in Eqs. (80a) and (80c) that the quadratic model of Gj, decreases in magnitude and increases with increasing V , , whereas the quartic model of Gj, [Eq. (80b)l decreases in magnitude, remains relatively constant, or increases to some maximum and then decreases in magnitude with increasing V, , depending upon whether ub = ( V , - Vb)/( V , - V,j is greater than, equal to, or less than 0.5, respectively. For ub < 0.5, the maximum positive value of dGj, is 31 - 2q,)2/ub(l - t'b), occurring at V,/(V, - V,) = [2ub(l - 2 ~ , ) ] ' ' ~In . addition, Gj, is considerably more amplitude-dependent than Cj,, since

cjl

Vonp -

vb

>>

v~ - V,,

Vb -

V,,

and

I vb

- Vl,

.

In fact, the amplitude dependence of Cj, is often negligible, so that cj1(&, V,) can usually be approximated by Cj(Vb). The relationship of V, to more realistic circuit parameter values, i.e., output CW power, input CW power, etc., depends on the particular tunnel diode circuit application. However, it may be generally stated that, under any application, tunnel diodes having the largest Vonp,V,, and V, will exhibit the least large-signal performance perturbation. Finally, two characteristic ratios which are important in certain largesignal applications are the switching figure of merit lp/Cj(V,) and the peakto-valley ratio lp/Iv.

8.

TUNNEL DIODES

525

c. Dependence upon Physical Diode Parameters The parameters which characterize the tunnel diode equivalent circuit, as formulated in the preceding subsections, may each be expressed in terms of the physical properties of the diode as presented in preceding sections. First of all, “internal” parameters associated with the junction itself and with the bulk semiconductor material adjacent to the junction are evaluated at a convenient reference operating point, that is, the current-voltage inflection point (I,, V M GM). , The resulting “internal” inflection-point parameters, GM, CjM, R,, and KNMare obtainable from Eqs. (44HS2) and (77), and are expressed as

where k,, k,, and k, are physical constants independent of semiconductor material and geometry, and fi = napndn/(nap+ ndn) is the “average” doping level of the junction. These results are similar to but somewhat more detailed than those derived by Shepherd et ~ 1 . ~ The external parasitics L, and C, are primarily dependent upon the encapsulation or contacting geometry of the tunnel diode and on the geometry of its external environment rather than on its junction parameters. Therefore, as the limiting values of L, or C, as the geometry we define and Cp,min external to the tunnel diode is reduced to the point where the external environment contributes no electrical or magnetic stored energy. The characteristic frequencies describing the small-signal tunnel diode equivalent circuit may be expressed to a good approximation in terms of the physical parameters of the diode, using Eqs. (71k(73), (7S), and (81), as

526

H. C . OKEAN

@R,max

@,,ma,

N

%

Wb,max %

where, as stated in Eqs. (15), (44), and (46), VOnp

=

(l/e)[Eg

+ (kT/e)qTl;

vM =

(kT/e)ln{qTL1+ (qT/16)l}?

qT z In[ndnnap(mp*mn*)-3’2].

In addition, the large-signal characteristic ratios Ip/Cjvand Ip/I, may be expressed in terms of semiconductor material parameters, using Eqs. (44), (46), and (81), and assuming that the excess current due to deep impurity levels (I,) dominates the valley current,

The above equations (81) and (82)indicate that tunnel diode high-frequency ~ ~ ~ increases , with increasing doping level ( i i ) and capability ( w ~ ,wRSmax) decreasing effective mass (m,*, m,*), energy gap ( E J , and dielectric constant (E). The large-signal, high-speed capability of the tunnel diode, characterized in Eq. (83) by ratios lp/Cjvand Zp/Iv,is dependent on the above material ~and ,o ~ ~ with , ~ ~ Ip/Iv ~~ ~ also, being parameters in a similar manner as w enhanced by decreasing “deep” impurity concentration n,. The resonance frequencies and created by the parasitics L, and C, are primarily influenced by device geometry but also increase with decreasing m,*, mp*, and E. Finally, it is seen in Eqs. (46) and (80H82) that an improvement in tunnel diode low-noise capability (a decrease in KNM)requires a

8.

527

TUNNEL DIODES

decrease in qT, whereas an improvement in large-signal linearity (a decrease in 6Gj, and 6Cj1) requires an increase in qT. Thus, contradictory requirements on the material for low doping and high effective mass and vice versa must be satisfied for best low-noise performance and large-signal capability respectively. Therefore, the choice of semiconductor material depends on the particular tunnel diode application, as will be illustrated in the following sections.

d. Numerical Values of Tunnel Diode Terminal Quantities Representative numerical value^^*^^' 1 , 5 5 of the key terminal quantities characterizing the tunnel diode are summarized in Table IV for those semiconductor materials applicable to tunnel diode fabrication, based upon the formulations of Eqs. (80H86) and the material parameters listed in TABLE IV

TYPICAL VALUES OF TUNNEL DIODETERMINAL QUANTITIES Range of values for given type of semiconductor Parameters

Si

Ge

40-70 90- 120 250-350 10-15 2-10 5-10 25-50 10-20 I540 80-100 120-170 5&80 1-1.6

500 290 1-200

80-100 100-130 400-500 3-5 < 0.5 1-2 5 10-20 15 4 0 150-170 120-150 15&170 3-3.4 650 290

0.1-100

0.02-0.2 0.05-0.15 (unencapsulated) &O. 1 (unencapsulated)

GaAs

90- 120 200-300 450-600 10-20 2-10 5-10 20-40 1 0-20 15-40 120-150 300-370 80-120 1.62.4 850 290 1-50 0.2-100 0.05-0.4 0.2-2.0 (encapsulated) 0.24.5 (encapsulated)

GaSb

30-50 60-80 180-250 15-20 0.5-5 5-10 15-30 10-20 15-10 5Q-80 80- 120 3s55 0.7-1 .I 550 290 30-70 0.2-5 0.04-0.2

lnSb

7-10

300 77

" T,, is the maximum temperature at which the negative-resistance region appears (tunneling current is not masked by diffusion current). T,, is the useful operating temperature.

528

H. C . OKEAN

Table I. Also included in Table IV is the maximum temperature at which the tunneling current sufficiently dominates the diffusion current (I,) to yield a useful negative-resistance characteristic. It is seen in Table IV that (a) the various voltage quantities are approximately related by V, x 6Vp, V, x 2Vp,K N M zz $Vp, and x Vp; (b) the lowest values of parasitics L, and C, realizable in an encapsulated diode are about 0.2 nH and 0.2 pF, respectively; in an unencapsulated diode, Ls,minx 0.1 nH and Cp,min approaches 0; (c) Ge tunnel diodes have the highest frequency capability; (d) GaSb tunnel diodes have the lowest noise output ; (e) GaAs tunnel diodes have the largest characteristics voltages V,, VM, V , and hence the highest power-handling capability ; (f) GaAs tunnel diodes also have the largest characteristic ratios I $ I , and Ip/Cj, associated with fast switching capability ;(e) Si tunnel diodes have relatively inferior characteristics in all categories ;and (f) InSb tunnel diodes are not useful at room temperature and only become competitive with other tunnel diodes when operated under considerable cooling. Accordingly, it will be shown in more detail in following sections, that GaSb and Ge tunnel diodes are most useful in low-level, low-noise amplifiers and detectors, and GaAs diodes in highlevel amplifiers, CW oscillators, and digital circuits. 10. TERMINAL STABILITY OF TUNNEL DIODES a. Fundamental Stability Criteria

One of the most formidable problems encountered in the various applications of tunnel diodes is the strong tendency, under improper circuit conditions, toward terminal instability. The latter arises from the incremental negative-resistance property of the tunnel diode and is defined as the onset of periodic oscillations (at fundamental frequency 0 < o < w R )or of dc bias point switching occurring when the tunnel diode is biased in its negativeresistance region under a given external terminating circuit. The maintenance of terminal stability, that is, freedom from self-excited oscillations and switching, requires the satisfaction of stringent stability criteria on the external circuit immittance (impedance or admittance) presented at the tunnel diode terminals. The criteria governing the stability of a tunnel diode are stated in terms of the impedance 2, or admittance Y, presented to the terminals of a passively terminated tunnel diode. It is assumed that the diode is biased at an operating point Vbo, I , , in the negative-resistance region of its characteristic, as shown in Fig. 20(a), at time t = 0, such that the operating point is not necessarily stable. The criteria for stability arise from the physical requirement that the incremental current through or voltage across the tunnel diode in response to an incremental impulse function (at t = 0) of applied voltage

8.

529

TUNNEL DIODES

or current, respectively, decays as a function of time to zero in the steady state. The 1-V characteristic of a tunnel diode exhibiting an oscillatory instability has a discontinuous, highly distorted segment in the active region [Fig. 20(b)]due to rectified oscillatory current, whereas that due to a switching instability has a missing segment within the active region [Fig. 2O(c)]. This

LOAD LINE FOR OC RESISTANCE Rb < R M - R,

0

V

bo

"b

FIG. 20. Representative tunnel diode current-voltage characteristic.(a) Stable tunnel diode :

(b) oscillating tunnel diode; (c)switching tunnel diode.

530

H . C . OKEAN

distinctive behavior in the I-V characteristic provides a useful experimental indication of the presence of a tunnel diode instability in a given circuit. The quantitative stability criteria are expressed in the domain of complex frequency s = 0 jo,in terms of the total loop impedance Z,(s) = Z,(s) Z,(s) or the total node admittance YN(s)= Yd(s)+ Y,(s) at the tunnel diode terminals. The fundamental stability conditions on immittance functions Z1(s)= Nl(s)/Dl(s)and YN(s)= NN(s)/DN(s) is that Zl(s)and Y,(s) [Nl(s)and NN(s)]have no zeros in complex frequency s, such that Re(s) >, 0, this being the frequency domain equivalent of the requirement for decaying timedomain responses in current and voltage. A more detailed description of the behavior of the passively terminated tunnel diode is obtainable in terms of the nature of the roots s, = cr, + jo, (rn = 1,2,3,. . . ,n) of Zl(s)or YN(s).The various modes of behavior, both unstable and stable, are summarized in Table V, and are valid for other twoterminal dc-biased negative-resistance devices' 2,55*s6as well as the tunnel diode.

+

+

TABLE V BEHAVIOROF PASSIVELY TERMINATED TUNNEL DIODEIN TERMS OF IMMITTANCE FUNCTION ROOTS ~~

Nature of roots (s,

=

u,

+ jw,)

Circuit behavior

( I ) om < 0, all m = 1,2,.. . , n

Stable

(2) om= 0, w, > 0, m = mi

Constant-amplitude sinusoidal oscillation at frequency wml

(3) om> 0, w, > 0, m = m 1

Increasing-amplitude sinusoidal oscillation at w m I ,becoming a steady-state oscillation at om,(with Cmi = 0 and Gm, determined by large-signal diode parameters) or a periodic, nonsinusoidal oscillation of fundamental frequency G,,

(4) urn> 0,w, = 0, m = rn,

Switching of bias to new operating point, or relaxation oscillation between two operating points

(5)

u, > 0, w, > 0,m

=

m,,m 2 , . . .

Simultaneous oscillation at wml, o m 2.,. .

Since the tunnel diode parameters Gj and Cj are functions of KO,the conditions for stability must be investigated at each V,, within the negativeresistance region. For many diode applications, the concept of absolute ~ . ~has ' been stability over the entire range of V,, is of i r n p o r t a n ~ e . ~ It 56

57

G . Martinelli, Proc. I E E E 53, 1265 (1965). R. Aron, Calif. Inst. of Technol., Tech. Rep. 15 August 1960.

8.

TUNNEL DIODES

531

s h o ~ n ~that ~ , stability ’ ~ at V,, = V, generally implies stability at all Vbo, so that all stability criteria become absolute stability criteria under the conditions Gj( Vbo) = G,, Cj( Vbo) = Cj(V,).

b. Specific Stability Criteria The basic conditions for stability expressed in Table V lead to specific criteria 12.5 5.5 8-63 for (a) the establishment of a stable d c operating point, (b) short- and open-circuit stability, (c) stability under a given passive termination, (d) ultimate stability, that is, potential stability under at least one passive terminating immittance, and (e) the onset and sustenance of sinusoidal oscillations, as summarized in Table VI in terms of the basic tunnel diode equivalent circuit parameters. These criteria are established by setting the appropriate conditions (Table V) on the roots ,s of Z,(.s) or or YN(s), as obtained by direct solution or by use of the Routh-Hurwitz criterion,64 the Nyquist criterion,6s or the real-immittance-function criterion.’ The specific tunnel diode stability criteria presented in Table VI not only significantly restrict the external circuit design in any given application, but also establish the following criteria regarding the optimum combination of tunnel diode device and material parameters. First of all, the short-circuit stability criterion (aR< cox) does not directly apply to the more realistic case of a tunnel diode terminated by an arbitrary passive imrnittance, but it does provide a measure of potential tunnel diode stability under a wide range of arbitrary terminating immittances in terms of the basic diode parameters. Secondly, for tunnel diodes that are not shortcircuit stable (/, 3 rs), the behavior of Yd(.ju)for various values of Is/rs (Fig. 17) indicates that, for 1 6 IS/rs6 3, the additional stability criterion (6) is generally automatically satisfied for all Y,(jo) in the small interval ( o , , w b ) containing ox, near which (-dB,/dw) and lGdl >> 0. For further increases in ( / J r S )> 3, the range of realizable Y,(jo) capable of satisfying criterion (6) becomes progressively more restrictive, virtually disappearing

’’ I. T. Frisch, Proc. I E E E 52. 922 ( I 964). D. C. Youla and L. 1. Smilen, Proc. / R E 49, 1206 (1961). C. S. Kim and A. Brandli, I E E E Trans. Circuit Theory CT-8,416 (1961 ). 1. Hefni and W. C. Barnes, I E E E T r u m Microwwe Theory Tech. MTT-l5,427 (1967). 6 2 M. E. Hines, Bell Sysr. Tech. J . 39.477 (1960). B. T. Henoch and Y . Kvaerna, Stanford Univ. Electron. Lab., Tech. Rep. 213-2, August 1962. 6 4 E. A. Guillemin, “The Mathematics of Circuit Analysis.” Wiley (Technology Press), New York. 1949. O 5 H. W. Bode, “Network Analysis and Feedback Amplifier Design.” Van Nostrand, Princeton, New Jersey, 1945.

5y

’’

‘’

532

H. C. OKEAN

TABLE VI

TUNNEL DIODESTABILITY CRITERIA

Circuit condition

Terminating immittance -

1. Bias circuit stability62

Z , = R,

2. Short-circuit stability

Z,

=0

3. Open-circuit stability

Y,

=0

4. Arbitrary terminating

impedances5 (including C, in Zgl)

+ jwL,

2,' = R,'(w)

Z,'

=

Criteria on circuit elements"

Z,/(l

+ jX,Ym)

+ jwC,Z,)

5. Arbitrary terminating admittance55 (Is < r,)

Y, = G,(w) + j B , ( o )

6 . Arbitrary terminating admittances5( I , > rs)

YE = G,(w) + jB,(w)

7. Condition for potential stability under at least one passive ter~nination~~ (including Cp)

Z,', Y,'

8. Condition for onset sinusoidal oscillations" at w o

Y, = G,(u>) + jB,(w)

9. Condition for sustenance of steadystate sinusoidal oscillations at G o

Y,

= G,(w)

+ jB,(w)

"For absolute stability, choose R = l/C, and Cj(Vb)= Cj(V,) in 1-7: (0)= criterion for prevention of unwanted oscillation ; (SW) = criterion for establishment of stable operating point (no switching), which requires that dc load line of circuit intersect the tunnel diode current-voltage characteristic only at the desired negative-resistance operating point [Fig. 20(a)].

8.

533

TUNNEL DIODES

for I , > 1. Finally, the ultimate limitation (7) shows that the tunnel diode cannot be stabilized with any realizable passive termination if 1, 3 3/(1 + r,). Therefore, the most important requirement on tunnel diode device design from a stability standpoint is that 1, be below some upper stability bound 1 < I, < 3. This emphasizes the desirability of realizing a low L,, or, for a fixed L, and oj,it limits the maximum useful negative-conductance level (GM)max to ls,maJcojLs, which in practice falls between 0.05 and 0.2 mhos. c. Basic Principles of Tunnel Diode Stabilization

The methods of external circuit design employed to stabilize a tunnel diode against the onset of undesired sinusoidal or relaxation oscillations vary but somewhat with the particular tunnel diode application,' 2955361~63,66*67

FIG.21. Typical tunnel diode biasing and stabilizing networks. (a) Series bias feed network; (b) parallel bias feed network ; (c) series-connected stabilizing network; (d) parallel-connected stabilizing network.

certain fundamental techniques are common to all applications. These include the electrical isolation of sections of external circuitry which operate in widely separate frequency ranges, and the use of resistively loaded selective stabilizing networks. The first technique'2$62employs low-pass or bandpass filtering to couple specific portions of the external circuit to the tunnel diode within specific frequency ranges and to strongly decouple them at all other frequencies. 66

J. Hamasaki, I E E E Trans. Mirrowmv Theory Tech. MTT-13. 213 (19651. Trans. Microwaue Theory Tech. MT"-15, 554 (1967).

'' B. A. Miller, T. P. Miles, and D. C . Cox, I E E E

534

H. C. OKEAN

Typical is the use of low-pass filtering in the form of rf chokes and bypass condensers to couple the bias voltage source to the tunnel diode at dc and decouple it at high frequencies. Two commonly used dc biasing arrangements which satisfy the conditions for bias circuit stability are shown in Fig. 21, a series bias feed employing a bypass condenser and inductive dc in Fig. 21(a), and a parallel bias feed using an rf choke and dc blocking capacitor in Fig. 21(b). Similar bandpass filtering techniques are used to separate critical circuits in each multifrequency tunnel diode applications as frequency converters. The second general approach involves the use of resistively terminated band rejection filters55,63*66,67 which resistively load the tunnel diode at all frequencies outside the frequency range of interest and provide only a small, lossless perturbation within the band of interest. Simple series- and parallelconnected stabilizing networks, which should be connected as physically and electrically close to the tunnel diode junction as possible, are shown in Figs. 21(c) and (d), respectively.

V. Experimental Characterizationof Tunnel Diodes 1 1. GENERAL APPROACHTO TUNNELDIODECHARACTERIZATION

The various terminal parameters of tunnel diodes as described in the preceding section may be determined experimentally using low-frequency and microwave measuring techniques. Most of the significant parameters such as the I-I/ characteristic, Cj(Vb),R , , and K , can be measured at low frequencies. However, the predominance of high-frequency sinusoidal and high-speed digital tunnel diode applications requires that the diodes be characterized at microwave frequencies for the following reasons. First of all, the contribution of the tunnel diode parasitics L, and C, to measurable tunnel diode behavior is most strong at microwave frequencies. In addition, the microwave properties of the geometry of the tunnel diode and its immediate mounting environment introduce43 additional parasitic reactances and impedance transformations within the accessible terminals of the tunnel diode, which influence the effective values, at these frequencies, of conventional equivalent circuit parameters, with respect to not only parasitics L, and C,, but, to a lesser extent, semiconductor parameters Gj, Cj, and R , . Finally, a unique requirement on tunnel diode measurements introduced by the negative-resistance property of the tunnel diode is that the latter must be stable in its measurement circuit, in accordance with the stability criteria stated in the preceding section. This requires that the tunnel diode be characterized in a microwave mounting fixture that presents a wellcontrolled, preferably resistive immittance characteristic to the tunnel diode

8.

535

TUNNEL DIODES PARA L LE L- C 0 NN ECT E D D IS K STAB I L I ZI NG,RESISTOR

PILL-TYPE TUNNEL DIODE

BEAM LEAD, UNENCAPSULATED TUNNEL DIODE

1

CONTACT AREA

TO CONNECTOR

SUBSTRATE GROUND PLANE

TAPERED TRANSMISSION L I N E TRANSFORMER

REDUCED-HEIGHT WAV EGU IDE

TUNNEL DIODE (C 1

FIG. 22. Tunnel diode mounting configurations. (a) Coaxial mount; (b) microstrip mount; (c) waveguide mount.

over its entire active frequency range when inserted in the measurement circuit. Depending upon the type of measurement to be made, several mounting configurations may be used in microwave transmission media most compatible with the geometry of the tunnel diode under test or most representative of that intended for the given tunnel diode application. These include a mount with a microwave stabilizing resistor adjacent to the tunnel diode for low-frequency measurements, or a mounting fixture at the end of

536

H. C. OKEAN MICROWAVE TD MOUNT VARIABLE DC VOLTAGE-

VI

VARIABLE AUDIO OR PULSE VOLTAGE \

TO VOLTMETER, OR TO HORIZONTAL SCOPE AND

’

STABILIZING

RESISTOR\ 1

TO VOLTMETER, OR T O V E R T I C A L SCOPE AND RECORDER INPUTS

vE RECORDER I N P U T S

(a)

MOUNTED TD VARIABLE DC VOLTAGE BRIDGE

I-TPRECISION RsD{ STANDARDS

RF SIGNAL G EN E RAT0 R MOUNTED

?i;cs~

VARIABLE DC VOLTAGE

L& I

TD

SLOTTED L I N E

I I 1.----I

B I A S TEE

LOCAL OSCILLATOR

FIG.23. Measurement circuits for tunnel diode characterization. (a) Resistance bridge for I-V curve tracer and series resistance measurement ; (b) capacitance measurement circuit ; (c) microwave reflection measurement circuit.

or across a constant or ultra-broadband, tapered characteristic impedance transmission line for microwave reflection or transmission measurements, as shown in Fig. 22(a-c), respectively. The applicability of these mounts to particular tunnel diode measurements will be discussed in the following sections.

8.

TUNNEL DIODES

537

12. LOW-FREQUENCY MEASUREMENTS a. Measurement of Current-Voltage Characteristic The first measurement usually made in the characterization of a tunnel diode is that of its current-voltage characteristic. This is most frequently including the tunnel diode, mounted in conaccompanied by junction with a stabilizing resistor [Fig. 22(a)], as one of the arms of a resistive bridge, as shown in Fig. 23a). The bridge is first balanced with the mount including the stabilizing resistor in position by adjusting the variable resistor R, for a zero indication on voltmeter 4. The tunnel diode is then inserted in the mount, unbalancing the bridge such that the voltmeters V, and V, yield the tunnel diode I-V characteristic with Vb 2 V, and I , 2 SV, ( S is a scale factor). A versatile circuit utilizing this bridge provides both a dc and a full-wave rectified 60-cycle input voltage to the bridge and presents the metered voltages VEand V, to the vertical and horizontal deflection plates of an oscilloscope and to an X - Y recorder. This circuit therefore doubles as a curve tracer, a point-by-point I-V indicator, and an all-purpose dc bias supply for the tunnel diode. The recorded I-V trace provided by this circuit also yields the incremental negative conductance G j (I/b) and the shot-noise constant KN(V,,) as functions of bias, as given by Eqs. (68) and (77). The incremental junction conductance Gj( V,,,) may be measured more directly in the circuit of Fig. 23(a) by superimposing on the dc input V,,, a small (less than 10 mV peak-to-peak) audio signal. The resulting peak-topeak ac components AVE and A 4on V, and V, as read on the oscilloscope or on ac voltmeters yields Gj( Vbo) directly as

’,’’ ’-”

Gj(60)

[ ( 1 / s ) ( A v E / A V , ) -R J 1 .

(84)

h. Measurement qf Series Resistunce

The series resistance of the tunnel diode [mounted as in Fig. 22(a)] may also be measured3.’ in a modification of the resistance-bridge measuring circuit of Fig. 23(a), in which a small (less than 10 mV) audio sinusoidal or pulse voltage is superimposed on the dc bias V’,. The latter must be set in a high-current region of the I-V characteristic in order to minimize the contribution of Rj(Vb).Since measurements in the forward region (Vb > V , ) are perturbed by minority-carrier injection and hence conductivity modulation of the semiconductor bulk, vb is usually set in the high-current reverse region, 1 3 7 1 . 7 2

68 6y

J. A. Narud and T. A. Fype, Elrcfronic,s 34. 74 (1961). C. D. Todd. Rev. Sci. Insrrutn. 32. 338 (1961 ).

G. E. Fox. Solid Srnre Design 3, 27 ( 1962). E. L. Bonin and J. R. Baird, Pioc. / R E 49. 1679 (1961). ” R. J . Wilfinger and B. A. Zolotar. Riw. Sci. Instrum. 33, 693 (1962). O

”

538

H. C. OKEAN

at I , zz -501, to -2001,. Under this condition, the measured incremental resistance is of the form337’

+ (K/lzbl)?

(85) where AZ, and Av, are extracted from the incremental voltages AVE and A& read on the oscilloscope or voltmeters at the outputs of the initially balanced bridge. If these measurements are repeated a t several values of I , , v b in this range, Rsmay be extrapolated from a plot of R,,,,( V,) versus I ; in the asymptote as becomes infinite. R r n d V b ) = [A1b/Avbl;,’

Rs

c. Measurement of Shot-Noise Constant The shot-noise constant KN = IbN(Vb)\Rj(vb)l is usually measured in the active region by extracting it from the measured Z- V characteristic as shown in Fig. 19(b) under the approximation I , , zz 1,. However, measurements have been made53*73to verify the proposed bias dependence of i b N [Eq. (70)] and thereby to test the validity of the above approximation by directly measuring the output noise power level of actively biased Ge, GaSb, GaAs, and Si tunnel diodes as functions of bias and frequency. These measurements utilized a tunnel diode mounted in conjunction with a shunt stabilizing resistor [Fig. 22(a)] connected in parallel with the input circuit of a low-noise H F preamplifier. Careful precautions were taken to ensure the absence of tunnel diode oscillations, as ascertained by monitoring the Z-V characteristic and the output spectrum of the tunnel diode. One set of measurements, by King and S h a r ~ e extracted ,~~ the measured equivalent shot-noise current zbN( vb) from the output noise power of the preamplifier measured with and without a noise diode connected across the input terminals of the amplifier. The other, by Giblin,73 obtains lbN(i$) by comparing the output noise voltage of the preamplifier at tunnel diode bias V , to that at zero bias. The results of these measurement^^^.^^ indicate that, at frequencies below 1 MHz, the measured IbN(Vb) is considerably larger than its theoretical counterpart of Eq. (70), due primarily to l / f noise. However, at frequencies in the 30-MHz range, the measured i b N exhibits approximately the predicted dependence on Vb expressed in Eq. (70), so that in the active region the approximation I,, x 1, appears valid and, for most applications, is therefore sufficiently accurate in the determination of KN. d. Measurement of Junction Cupacitance

Low-frequency measurement of the tunnel-diode junction capacitance Cj(V,) is usually performed on a standard VHF or H F admittance 73

R. A. Giblin, Elect. Eng. 36, 766 (1964).

8. TUNNEL DIODES

539

bridge.3,11 . 6 9 . 7 4 F or measurements in the active bias region, a coaxial tunnel-diode mount is usually used which incorporates a shunt stabilizing resistor (Fig. 22a). However, for minimum measurement error due to stabilizing and diode junction conductances, measurement of Cj at v b z V, 6 is preferred, in which case the stabilizing resistor is not required. A typical capacitance-bridge measurement circuit shown in Fig. 23(b), utilizes a small H F or VHF voltage ( z1-5 mV rms at 1-100 MHz) superimposed upon the dc bias in order to ensure an incremental measurement of Cj(Vb). The measurement consists in balancing the bridge with the stabilized diode mount in the unknown branch, and rebalancing it with an essentially nonreactive resistance standard and a known capacitance standard in place of the diode mount. The difference in capacitance indicated on the capacitance standard for the two balance conditions is the terminal capacitance of the diode, from which c j ( v b ) may be extracted. Case capacity C,may be obtained from a similar measurement on an open-junction tunnel diode with identical geometry. The use of precision external standards minimizes errors due to parasitic reactances. The diode resistance values used in the extraction of c j ( v b ) from measured data are obtained prior t o this measurement as described in the preceding sections. The measurement frequency is chosen to minimize errors due to these resistances and to the series inductance.

+

13. MICROWAVE MEASUREMENTS a.

Rejection Measurements

Microwave reflection measurements are usually used to determine the microwave equivalent-circuit parameters of a tunnel diode mounted at the end of a transmission line, although characterization in other diode mounting orientations is also p ~ s s i b l e . ~Th ~ e, ~reflection ~ - ~ ~ measurement consists in the determination of the microwave immittance of a suitably biased tunnel diode imbedded in a one-port mount by means of a measurement of its voltage reflection coefficient. This is usually accomplished by a standard slotted-line measurement technique,78 in which determination is made of the minimum position and amplitude (VSWR) of the voltage standing-wave pattern established on a slotted section terminated at one end by the mounted tunnel diode. In a representative measurement ~ i r ~ ~ i[Fig. t ~2 3~ ~, ,~ ~ - ~ the microwave test signal is applied to the loosely coupled slotted-line probe and the output end of the slotted line is connected through an isolator to a 74 75

h ’ 77

D. E. Thomas, IEEE Trans.Electron Derices ED-IQ,278 (1963). H . Fukui, Dig. 1961 In!. S d i d State Circuirs Con6 Philadelphia, Pennsyfuaniu, 1V. I6 (1961). C. S. K i m and C. W. Lee, Microwaces 3. 18 (1964). J. W. Bandler. f E E E Trans.EIectron Dei%-es ED-15, 275 (1968). E. L. Ginzton, "Microwave Measurements.'' McGraw-Hill, New York, 1957.

540

H . C . OKEAN

highly sensitive microwave receiver. This ensures that the rf signal power incident on the tunnel diode will be below 1 pW and that the resultant peakto-peak rf voltage across the tunnel diode junction will be less than 10 mV, thereby permitting a valid small-signal measurement. The presence of the output isolator ensures that the mounted tunnel diode will be terminated essentially in the resistive characteristic impedance of the measurement system over a broad frequency range, thereby aiding in tunnel diode stabilization. The small-signal immittance of the mounted tunnel diode is obtained from the measured reflection data at a given frequency, following a determination, based on a priori knowledge or on a reflectometer measurement, as to whether the measured reflection coefficient magnitude is greater or less than unity at this frequency. The latter requirement is due to the exhibition of reflection coefficient magnitudes greater than unity by the tunnel diode input immittance at frequencies at which its real part is negative. This is in contrast to the more familiar case of passive components, for which input reflection coefficients cannot exceed unity. However, the slotted-line measurement of VSWR cannot distinguish between positive and negative real parts of measured in input immittance, hence the required prior determination. Repetition of this measurement over a range of microwave frequencies yields a locus of the measured immittance at the accessible terminals of the tunnel diode mount, from which may be extracted some or all of the small-signal equivalent circuit parameters, depending on the tunnel diode bias and the complexity of the mount. In particular, measurements made with the tunnel diode biased on the valley o r positive-slope regions of its current-voltage characteristic may utilize a simple mounting fixture in which the tunnel diode is connected at the end of a transmission line (or waveguide) having the same characteristic impedance Z , and geometry as that of the measuring system. However, for diodes biased in the active region, this fixture can only be used when the nominal R M characterizing the diode is greater than Z,. Otherwise, stability requirements dictate the use of either a mount with a taper that transforms Z , to Z,, < R , over a wide frequency range [Fig. 22(b)] or a mount that includes a stabilizing resistor [Fig. 22(a)]. The small-signal tunnel diode equivalent circuit may be characterized completely in a given microwave frequency range by obtaining the measured immittance loci under several conditions of tunnel diode bias. I n each case, the measured terminal immittance loci of the tunnel diode proper are obtained by subtracting the immittance contributions of the mount itself, due to its stabilizing resistor, impedance transformers, and/or reactive parasitics from the original immittance data. The measured data equivalent-circuit parameter values may be conveniently extracted from the measured immittance loci using the following

8.

TUNNEL DIODES

541

sequence of immittance measurements: (a) measurement of C , using an open-junction tunnel diode ; (b) measurement of L, and R , with the tunnel diode reverse-biased at several current points in the range - 101, t o - 501,, evaluating R , = R,,,, in the asymptote as approaches infinity (under this condition, the junction contribution is essentially shorted out) ; or, alternatively, measurement of L,, R , , and Cj(Vb) at valley bias V, [Gj(Vv) % 01; (c) measurement of Gj(Vb) and Cj(Vb) under active bias (V, < Vb < Vv), accomplished by removing measured values of C,, L,, and R , from measured terminal immittance [Eqs. (71) and (7411. It is noted that the above measurement procedure is useful only when the tunnel diode is mounted at the end of a transmission line or when the immittance corrections due to the mount contributions are relatively simple. If these conditions are not satisfied, two other approaches to tunnel diode characterization at microwave frequencies may be utilized, the transmission measurement and the oscillating diode measurement, as will now be described.

6. Transmission Measurements The microwave transmission measurement, originally proposed by De L o a ~ h 'to ~ characterize microwave varactors, is a convenient method of determining the values of the parasitics associated with a tunnel diode mounted in shunt across a transmission line. It consists essentially in measuring the small-signal insertion-loss-frequency characteristic, in a conventional low-level transmission-loss measurement circuit, of a symmetric section of uniform or tapered transmission line across the central plane of symmetry of which is mounted a valley-biased tunnel diode. The small-signal equivalent circuit of the valley-biased diode, including the effect of mounting parasitics, may be represented near diode self-resonance w , [Eq. (73)] by a series R,'-L,'-C' circuit parallel-connected across the transmission line. Therefore, the overall structure approximates that of a single-section band-rejection filter having a single-peaked maximum in insertion loss centered at ooz ox(K).The equivalent parameters Rs', L,', and C', approximating the valleybiased tunnel diode transformed by the mounting parasitics, are directly obtainable from the center frequency oo,peak insertion loss LM,and halfpeak loss bandwidth AOJof the single-peaked insertion loss characteristic using the relationships

The actual small-signal diode parasitics R , , L,, and Cj(V,) may then be extracted from the measured values R,', Ls', and C' after prior evaluation of the mount parasitics.

'' B. C. De Loach, I E E E Trans. Microwave 7heory Tech. MTT-12, 15 (1964)

542

H . C . OKEAN

c. Measurements on Oscilluring Tunnel Diobe

An alternative method’ of determining the equivalent series inductance of the tunnel diode at microwave frequencies utilizes a simple, lightly coupled cavity-type tunnel diode oscillator model in which the external impedance a t the diode terminals is 2, z R g + joL,. The physical geometry of the variable-dimension, below-resonance (inductive) cavity is chosen to simulate the tunnel diode mounting geometry of interest in the inductance evaluation. The tunnel diode is biased sufficiently into the active region such that a weak sinusoidal oscillation at LO,,, is barely maintained, corresponding to the conditions

the latter determining the required degree of cavity coupling to the measurement circuit. The measurement procedure consists in determining Q,,,for several values of L, corresponding to several settings of the variable cavity dimension, << 13 adjusted keeping vb fixed. Then, for light coupling [(R, + Rg)[Gj(Vb)l such that Eq. (87) is satisfied, a plot of measured COG: versus L, will fall essentially on a straight line, which extrapolates to L, = - L , at coo;: = 0. 14. RESULTSOF EXPERIMENTAL CHARACTERIZATION The numerous measurements made of the terminal properties of tunnel diodes,3. 1 1,s 5,68-17 while usually applicable to particular tunnel diode geometries in particular mounting environments, lead to the following general conclusions regarding the equivalent circuit parameters : ( 1 ) The incremental junction conductance Gj( V,) measured at microwave frequencies (through X band) is essentially the same as that extracted from the low-frequency [-I/ characteristic, so that Gj may be considered independent of frequency. (2) The incremental junction capacitance Cj( I/,) measured at microwave frequencies agrees with that obtained via low-frequency bridge measurement, so that Cjmay be considered independent of frequency. (3) The series resistance R, exhibits a weak frequency dependence which may be approximated by R,

R,o(l

+ +fz),

0

W. B. Hauer, I R E Trans. Electron Devices ED-8, 470 (1961).

(88)

8.

543

TUNNEL DIODES

where 6 z 0.014.03 G H z - ~andj, , is the resistive cutoff frequency. This is cpnsistent with the “low-frequency approximation” of the skin effect in circular conductor^.^^.^^ (4)The series inductance L, for a given diode geometry is a strong function of the mounting environment, sometimes varying by a factor as high as 3 : 1 for different external geometries. The minimun inductance LF,min for a given diode geometry (Table IV) occurs when the mount geometry and diode geometry are completely compatible. The same remarks hold, to a lesser extent, for the parallel capacitance C,.

VI. Tunnel Diode Applications in Sinusoidal Circuits

15. TUNNEL DIODEAMPLIFIERS a. Single-Stage Tunnel Diode AmpliJer Configurations

The incremental negative resistance, extremely high-frequency capability, low junction parasitics, and low excess noise temperature ratio characterizing the tunnel diode make it well suited for use as the active element in low-level microwave amplifiers. Specifically, the incremental negative resistance of a tunnel diode biased into its active region (V’ < V, < V,) and embedded in a suitable external circuit results in power amplification of a small rf signal superimposed on the dc bias voltage. This is immediately seen by considering the voltage reflection coefficient r at the interface of an actively biased tunnel diode and its passive terminating network, defined in terms of diode and network input admittances Yd and Y,and of complex frequency as12,55

r(s)

IYg(-

s,

- yd(s)l/[yg(s)

+ yd(s)].

(89)

At real frequencies s = jo,the ratio of rf power carried by a normalized electromagnetic voltage wave b ( j o ) reflected from the tunnel diode to that by the wave a(@) incident upon the tunnel diode is given

where a ( j o ) and b(jco) are approximately normalized to some reference resistance Ro and have the dimensions of (power)’’2. Clearly, Ir(jw)12 > 1 at all frequencies for which G d ( W ) < 0 (0 < w < wR) for the tunnel diode, indicating useful stable reflection amplification of the incident wave, provided that the terminated tunnel diode is stable, e.g., Y,(s) + Yd(s)has no zeros in s having Re(s) 3 0 (Table VI), and that the terminating network contains some means of separating the incident and L. E. Dickens, f E E E Trans. Microwave Tbrory Tecb.MTT-15, 101 (1967).

544

H. C . OKEAN

reflected waves a(jw)and b(jw)and coupling them through external “input” and “output” ports to a source and load, respectively. Accordingly, many single-stage tunnel-diode amplifier configurations are possib~e,3,11,12,26,38,55,62,63,66,6 7.82-94 particularly at rf and microwave frequencies, each utilizing one or more tunnel diodes in the general configuration shown in Fig. 24(a). Here, an ( N + 2)-port-coupling network provides separate access ports for an rf input signal (source port), and rf output signal (load port) and N tunnel-diode circuits (amplifier ports). The N tunnel diodes interact to yield a single source-to-load gain mechanism (rather than N cascaded gain mechanisms), thus maintaining the single-stage character of the configuration. Each tunnel diode circuit consists of a mounted tunnel diode (or a multiple array of tunnel diodes) coupled through a series of functional networks. In general, for bandpass operation about rf or microwave frequency w o , these networks may include reactive tuning element s, broadbanding resonators, a stabilizing network [Figs. 21(c) and (d)], a bias feed network [Figs. 21(a) and (b)], and an impedance transformer, as shown for a representative configuration in Fig. 24(b). The three most common and most useful tunnel diode amplifier configurations are the circulator-coupled reflection amplifier, the hybrid-isolatorcoupled reflection amplifier, and the isolatorTcoupledtransmission amplifier, shown schematically in Fig. 25(a-c), respectively. Each of these tunnel diode amplifier configurations exhibit a nominally unilateral input-to-output power gain characteristic and input and output impedance characteristics that are nominally “matched” to resistive source and load impedances RG and R,, respectively. These properties arise from the unique nonreciprocal and/or signal-separation properties of circulators, isolators, and hybrid junctions as Ascoupling networks for negative-resistance amplifiers.2~ 2*55*57~59382*83

’’ R. D. Gallagher, Microwave J . 8-62 (1965). P. Kolk, Microwaves 4, 16 (1965). R. Steinhoff and F. Sterzer, RCA Rev. 25, 54 (1964). J. W. Bandler, I E E E Trans. Microwave Theory Tech. MTT-13, 814 (1965). 8 6 E. W. Sard, in “Proceedings of the Symposium on Active Networks and Feedback Systems,” p. 319. Wiley (Interscience). New York, 1960. ” J. H. Lepoff, Microwaves 3 , 3 8 (1964). R. C. Havens, Microwave J . 9, No. 5,49 (1966). 8 9 C. A. Burrus and R. Trambarulo. Proc. IRE 49, 1075 (1961). 90 J. J. Sie. Proc. IRE 48, 321 (1960). 9 1 R. M. Kurzrok, Proc. IRE 50,226 (1962). 92 E. G. Neilsen, P r o f . IRE 48, 1903 (1960). 93 M. E. Pedinoff, IRE Trans. Microwaue Theory Tech. MTT-9. 557 (1961). 94 J. 0. Scanlan, Electron-Tech. 39, 321 (1962). 83

84

’’

8. TUNNEL

545

DIODES

ACTIVELY -BIASED TUNNEL DIODE

RF SOURCE MPLlFlER COUPLING NETWOR

(a 1

S T A B I LIZ IN G

RESONATORS wO

TUNNEL DIODE 0

IMPEDANCE TRANSFORMER

W

TUNING ELEMENT

L PF DC BIAS FEED NETWORK

FIG. 24. General single-stage tunnel diode amplifier configuration. (a) Overall amplifier; (b) tunnel diode circuit.

suming “ideal” circulators, isolators, and hybrids in order to formulate the amplifier performance limitations imposed solely by the tunnel diode device parameters, the basic amplifier input-output parameters may be expressed as follows: %(w)= insertion power gain z $oIrA(,jw)

O(w) = insertion phase z arg[rA(jw)

+ mi2,

+ m],

(914

(91 b)

546

H. C. OKEAN

p,

9 CIRCUIT

SOURCE

~

-

4

RL

TD CIRCUIT

-

LOAD

C IRCUL A T 0 R

JUNCTION

1

ISOLATOR

I

Y

I

,.

>

TD CIRCUIT

LOAD

RL

* 01

(b)

CIRCUIT

SOURCE

D

-

ISOLATOR

-

ISOLATOR

-

ISOLATOR (Cf

FIG. 25. RF and microwave tunnel diode amplifier configurations. (a) Circulator-coupled reflection amplifier;(b) hybrid-isolator-coupledreflection amplifier; (c) isolator-coupled transmission amplifier.

8.

547

TUNNEL DIODES

where rA(jO) =

[yg*(;w)

- yA(jw)l/[yg(jO)

+ yA(jw)l

and YA(j w ) are the input reflection coefficient and admittance of the tunnel diode circuit, as given by I r A l > 1, Re YA < 0, in the amplification band. The quantity Y,(;w) is the input admittance at the amplifier port of the coupling network, as presented to the tunnel diode circuit (Fig. 25), and the asterisk is used to denote the complex conjugate. Furthermore, it follows that $ o = 1,

m=O,

for reflection amplifiers ;

m = 1, for transmission amplifiers. $, = RGRL/(RG + R,)', The amplifier insertion parameter usually of primary interest is the insertion gain 29, although in certain amplifier applications, the phase 8 is also of importance. The relative advantages of each of these three configurations, as dealt with previously in the literature,' 2 * 8 3 * 9 s . 9 6and as touched upon in the following sections, are qualitatively that the circulator-coupled reflection configuration uses the smallest number of components and has the lowest potential noise capability, the hybrid-isolator-coupled reflection configuration has, with the advent of multioctave hybrids and isolators, the greatest bandwidth capability, and the isolator-coupled configuration in some cases lends itself to the simplest physical embodiment. The particular aspects of tunnel diode amplifier realization and performance, power-handling capability, and stabilization will be discussed with reference to these three single-stage amplifier configurations in the following sections. b. Tunnel Diode Amplifier Gain and Bandwidth Capabilities

Tunnel diodes are usually operated well below their serious self-resonant frequency [Eq. (73)] in bandpass amplifier applications. Therefore, either parallel or series inductive tuning of the tunnel diode is required to resonate its capacitive reactance at the amplifier center frequency oo,which results, to a good approximation, in the small-signal equivalent circuit models of Fig. 18(b, c), which are valid about a reasonable passband centered at coo. As stated previously, the parallel-tuned approach has the advantages of easier stabilization, less sensitivity to diode parameter variations, and generally broader bandwidth capability, and is accordingly used more frequently in practical tunnel diode amplifier realizations. Therefore, particularly since tunnel diodes with sufficiently low series inductance are readily 95

96

A. C. Macpherson, I E E E Trans. Circuit Theory CT-11, 136 (1964). P.C. J . Hill, Pruc. I E E (Lundon) 112, 15 (1965).

548

H. C. OKEAN

obtainable, the parallel-tuned configuration is preferable and will be considered exclusively for the remainder of the section on sinusoidal tunnel diode applications. The midband insertion power gain of a tunnel diode amplifier stage of either the circulator of hybrid-coupled reflection type or the isolator-coupled transmission type [Fig. 25(aHc)] is given by %w,)

90

= rl/o(rAo

+ mI2,

where

with $, the nominal midband coupling network input impedance level at amplifier port(s) of coupling mechanism, equal to R , for circulator- and hybrid-isolator-coupled reflection amplifiers, and equal t o RGRJ(RG + RL) for the isolator-coupled transmission amplifier ;n2 is the midband impedance transformation ratio from coupling network to diode terminals [Fig. 24(b)] ; and RdOis the midband negative terminal resistance magnitude of a paralleltuned tunnel diode [Fig. 18(b)], Rdo

= R(1 - rJ[1

-

(4wO2/rsuR2)].

It is immediately seen that, unlike conventional amplifiers utilizing twoport active elements such as transistors and vacuum tubes, tunnel diode reflection and transmission amplifiers (and other negative-resistance amplifiers) can have unlimited midband gain, approaching infinity and the onset of oscillation at coo as n2Rgoapproaches & ., Passband stability requires (Table VI) that R,, > n2Rgofor a parallel-tuned diode. In addition, Eq. (92) shows that, at a given value of Ti,, the midband gain of the transmission amplifier is reduced with respect to that of the reflection amplifier by a factor $, = R,RJ(R, RL) 5 0.25, which attains its maximum value of 0.25 at RG = RL. Finally, high midband gain in a tunnel diode amplifier is achieved only at the expense of reduced bandwidth, as will be shown in the following paragraph. The bandwidth capability of a bandpass tunnel diode amplifier may be formulated, without loss of generality, by assuming that in the amplifier passband the tunnel diode circuit of Fig. 24(b) is representable by a ladder network of N alternate parallel and series bandpass resonators interposed between the negative diode terminal resistance - Rd, and the transformed coupling network impedance n2Rgo,as shown in Fig. 26(a). The bandpass resonators are formulated to include the passband reactance contributions of the parallel-tuned tunnel diode, of the essentially reactive passband stabilizing network representation, of the impedance transformer, and of the coupling mechanism input immittance. In addition, we utilize the generally

+

8.

II

'

PARALLELTUNED I TUNNEL

I

549

TUNNEL DIODES

I I I

N A D

I I Rdo Q 2 7

OR

N EVEN

---+

1 I

2 'A0

1 Q@doq

n2

N =m

I

/

/"'

I

FIG.26. Characteristics of broadband tunnel diode amplifiers. (a) Passband model of tunnel diode circuit for Nth-order broadbanding; 7 = ( w / o o )- ( w o / w ) ;QdO= W ~ R , , C (b) ~ ~Nth. order, maximally flat reflection gain characteristics.

most desirable bandpass gain-frequency characteristic for rf and microwave amplifier application, the Nth-order, maximally flat (Butterworth) gain c h a r a c t e r i ~ t i c , ’ ~for * ~ ~which ~ ~ ~ ~ IrA(jo)12 ~~ has the form [Fig. 26(b)]

where N is the "order" of the maximally flat gain response, and v] is the bandpass frequency variable equal to (w/wo)- (wo/w). For Nth-order, maximally flat gain, the a-power [Fig. 26(b)] amplifier assuming bandwidth (3 = ~ 5 9<~go)may be expressed as follows,1z~55~57~59 that the diode reactance, rather than that of the stabilizing network, impedance transformer, or coupling mechanism, is the bandwidth-limiting

550

H. C . OKEAN

e1emenP

or

(94b)

+

where Q,, = ooR,,Cdo z (oo/oj)(l cp), rn = 0 and 1, and $, = 1 and (RGRL)1’2/(RG+ RL) 5 0.25 for reflection and transmission amplifiers, respectively. For N = 1, the familiar single-peaked gain response [Fig. 26(b)] is obtained, which, for high gain (go>> I), exhibits the following voltage gainhalf-power (c( = 0.5) bandwidth product :

On the other hand, the ultimate in amplifier bandwidth is obtained with and ideally flat gain characteristic [Fig. 26(b)] [ 9 ( w )= 9, over B,, centered at f,, and g(o)2 $, otherwise], which results from the maximally flat response in the limit as N becomes infinite. The bandwidth B, ofthis response is given by

+

B , z oj/2{1n[(~0/$0)”2 m ] }(1 + cp). Similar results, exhibiting a slightly broader bandwidth capability, are obtained from an equiripple (Chebychev) gain-frequency response. 12955s7,59 The selectivities of the broadbanding resonators Q 2 , Q 3 , . . . , QN [Fig. 26(a)] required to realize an Nth-order, maximally flat (or equiripple) gain characteristic, given Q1 = Q,,, have been derived as functions of Tio in the literature on filter and negative-resistanceamplifier synthesis, 2 s 5 s 7 s 5 ) , 9 7 - 1 O 3 These results, however, require that, if a stabilizing network is employed, it be of the series-connected type [Fig. 21(c)],for, if the parallel-connected type [Fig. 21(d)] is used across C,,, a bandwidth degradation of Q,9/(Qdo Qst) occurs. Here, Q,, = oOCstRdO is the stabilizing network selectivity required

+

E. S. K u h and J. D. Patterson, Proc. I R E 49, 1043 (1961). Y. T. Chan and E. S. Kuh, I E E E Trans. Circuit Theory CT-13, 6 (1966). y 9 L. Weinberg and P. Slepian, I E E E Trans. Circuit Theory CT-7, 88 (1960). l o o R. Levy, Proc. I E E (London) 111, 1099 (1964). l o ’ W. J. Getsinger, I E E E Trans. Microwave Theory Tech. MTT-11,486 (1963). J. 0. Scanlan and J. T. Lim, I E E E Trans. Microwave Theory Tech. MTT-12, 504 (1964). ‘ 0 3 J. 0. Scanlan and J. T. Lim, I E E E Trans. Microwave Theory Tech. MTT-13, 827 (1965).

97

98

8.

55 I

TUNNEL DIODES

for the stabilizing conductance to exceed GdO = RT:, thereby passivating the tunnel diode outside its “stability bandwidth.”’ 03a These results assume the parallel-tuned model [Fig. 18(b)] of the tunnel diode, therefore requiring that parasitic inductance L, be sufficiently low that I , 5 2r,. If this is not the case, either the series-tuned model [Fig. 18(c)] may be used, resulting in a bandwidth degradation of about $, or the more exact triple-tuned model [Fig. 18(a)] may be used, placing stringent limitat i o n ~ ’ ’on ~ L, and C, in order to satisfy the broadbanding requirements on Q 2 and Q 3 [Fig. 26(a)]. Equations (94H96) immediately indicate that, at a given midband gain level go,the bandwidth capability of a transmission amplifier is inferior to that of the corresponding reflection amplifier by a factor ranging between 5 0.5 in the single-tuned case ( N = 1 ) and

Jl/o

+

In~o’’2{ln[(~o/$o)”2I ] ) - ’

5 (1 + 1.4/lng0)-’

in the ideally flat case ( N = cx;). Furthermore, it is seen that the bandwidth capability of a tunnel diode amplifier of any degree of broadbanding and at a specified midband gain level go varies linearly with the tunnel diode junction frequency, that is, B, z K w j . Therefore, Eq. (82a) indicates that the bandwidth capability of a tunnel diode amplifier increases with increasing tunnel diode doping level, and decreasing diode effective carrier mass, energy gap, and dielectric constant. The tunnel diodes having the highest potential amplifier bandwidth capability (Table IV) are hence those of GaSb, Ge, and GaAs, with representative maximum gain-bandwidth products being

g?2(Bl)o.55

+ cp)l&

GHz,

(974

[(%/$o) (dB)IB, = [lo l ~ g i o ( % ‘ $ ~ ) l B5 % 135/(1 + cP) dB-GHz, (97b) for the single-tuned and ideally flat gain characteristics, respectively. Typical bounds on single-tuned and ideally flat half-power bandwidths at 10 dB reflection gain (ria = 10) and cp % 0.5 are 1.0GHz and 9.0GHz. These numbers far exceed the theoretical maximum bandwidth capabilities of other microwave negative-resistance amplifying devices. The measured bandwidth capabilities of practical tunnel diode amplifier realizations55,63,66.67,82-94 generally fall considerably short of the corresponding theoretical limitations imposed by the tunnel diode [Eqs. (94H97)] in that the frequency dependence of the coupling mechanism and impedance transformer often becomes the bandwidth-limiting element,” typically reducing the above values by a factor of two to four. Io3”The“stability bandwidth” of the tunnel diode, centered at w,,, is the band over which the external circuit immittance presented to the tunnel diode (excluding the stabilizing network) is sufficiently well controlled to satisfy the stability criteria. Outside this band, the stabilizing network contributes G,, > IG,I. thereby making Re Y, > 0 and passivating the diode.

552

H. C . OKEAN

c. Amplijer Noise Performance

One of the most useful characteristics of a bandpass tunnel diode amplifier, particularly at microwave frequencies, is its relatively good noise performance. The usual measure of amplifier noise performance is the noise figure F , definedlo4 as the ratio of total noise power PNT in a bandwidth E N about some frequency o at the output terminals of the amplifier to that portion of PNTa t these terminals due to noise power k'l,'BN(k is Boltzmann's constant) generated in the matched resistive input termination R , a t temperature = 290°K. Hence, F may be expressed as

F PNT/kTBNY(O). (98) The noise figure of each of the three types of single-stage tunnel diode amplifier under consideration [Fig. 25(a-c)] may be ~ b t a i n e d ~ ~by' cal~ ~ ~ ~ * ' ~ ~ d a t i n g the noise output power PNd absorbed in load resistance R , [Fig. 24(a)] due to the tunnel diode terminal noise current generator (I;,)*" [Eq. 76)] shown in Fig. 19(a), and by then substituting it in F

=

I

+ [PNd/kTBN%(o)].

(99)

The resulting expressions for the single-stage tunnel diode amplifier noise figure are given, neglecting losses in the coupling mechanism and in the tunnel diode circuit, for each of the three amplifier types by FA =

1 + { I - [l/y(W)l)fd>

(100)

where, in the case of the isolator-coupled transmission amplifier, equivalent load conductance G L is chosen for a midband output match'05" [GL = GG - (Gdo/n2)]and where td is the equivalent excess noise temperature ratio of the tunnel diode [Eq. (7611. In each case, for high-gain operation with a high-quality tunnel diode [%(w) >> 1, rs,o/wR << 11, the noise figure reduces to FA = 1 + 0.020KN (mV).

(101)

Therefore, F A is primarily a function of shot-noise constant K N = I,R (mv), so that, for low-noise operation at a specified gain level, the tunnel diode A. Adler, R. S. Engelbrecht, S. W. Harrison, H. A. Haus, M. T Lebenbaum, and W. W. Mumford, Proc. I E E E 51, 435 (1963). B. C. DeLoach, IRE Trans. Electron Detlices ED-9, 366 (1962). Lo5"Thischoice of G, eliminates the contribution to PNdof noise generated in G, (that is, in the load isolator) and re-reflected back into G, due to a power mismatch when G, # GG (Gdo/n2). Thus, this choice of G, minimizes FA as a function of G,.. In the circulator- and hybrid-coupled reflection amplifier, the noise generated in the equivalent Ioad termination is always nominally "matched" to the amplifier output and therefore does not contribute to PNdor FA. '04

8.

553

TUNNEL DIODES

should be biased at its minimum noise point V,, [Eq. (78)]. In addition, it is clear from Eqs. (76) and (100) that only negligible reduction in F is obtained by physically cooling ( t << 1) the amplifier. A more accurate description of the noise performance of a tunnel diode amplifier used as the preamplifier for an rf or microwave receiver is given by the overall receiver noise figure F R , expressed as f'R

= FA

+ [(F'

-

l)/g(~)l,

(102)

where F' is the noise figure of the post-receiver, that is, the portion of the receiver following the tunnel diode amplifier, and Y(w) is the amplifier gain. Examination of FR makes it clear that any reduction in FA obtained by operation at low gain [Eq. (loo)] would be more than offset by an increase in the post-receiver contribution (F' - l)/g(w). The theoretical value of noise figure obtainable in a high-gain tunnel diode amplifier utilizing a high-quality (a,r, << 1) tunnel diode and a low-loss coupling mechanism is, as indicated by Eq. (101) and Table IV, primarily a function of the tunnel diode semiconductor material. Representative theoretical values obtained at the minimum bias voltage are given in Table VII. TABLE VII

Semiconductor material

FA(dB) = 10 log,, FA

GaSb Ge GaAs Si

2.8 3.6

4.8 6.25

Therefore, it is clear that the lowest-noise amplifiers are obtained using GaSb tunnel diodes. However, noise performance almost as low is obtained using Ge diodes, which are more readily available and, as will be shown, have superior power-handling capability. In practical microwave tunnel diode amplifiers, the measured FA(dB) is typically larger by 1.61.5 dB than the values stated above, with typical increases of 0.3 dB, 0.2 dB, and 0.5-1.0 dB due to nonzero r, and a, to coupling mechanism losses, and to tunnel diode circuit losses, respectively. The overall noise figure F R of microwave receivers utilizing these amplifiers is typically larger by a n additional 0.14.5 dB due to F'. d. Large-Signal Handling Capabilities of Tunnel Diode Arnpl@ers

The description of tunnel diode amplifier performance presented in the preceding sections assumes linear small-signal operation, as implied by the

554

H. C. OKEAN

incremental,small-signal equivalent circuits of Fig. 18. However, the presence of a nonnegligibletotal rf voltage amplitude V, across the tunnel diode junction perturbs the incremental values of junction negative conductance Gj(Vb) and, to a lesser extent, junction capacitance Cj(Vb),as indicated in Eq. (80). These signal-leveldependent perturbations in turn result in largesignal, amplitude-dependent perturbations AY(o) and AO(w) on the smallsignal amplifier gain and phase-shift characteristics g(o)and O(o),respectively. In particular, using a total-differential sensitivity analysis5 and assuming the capacitance perturbation is negligible (6Cj, % 0), as is usually the case in practice, the maximum gain and phase perturbations, occurring at midband and the band edges, respectively, may be approximated by l O l o g ~ ~ A%~4.34(rA0 ( ~ ~ ) - ( l / r A O ) ] 6Gjl dB,

IAB(wi)l

2 8 * 7 [ r ~+ 0 (l/rAO)]l~~jl!

(103)

f 104)

d%,

where the fractional large-signal junction conductance perturbation 6Gjl(Vl, Vb) is defined in Eq. (80). Equation (104) also defines the incremental gain and phase sensitivity to arbitrary changes in G j , or, replacing 6Gjl by wo6Cj1, to arbitrary changes in Cj. The measure of the large-signal capability of tunnel diode amplifiers of most general interest’2*66*’06 is the midband output saturation level, that is, the amplifier output rf power level Po, corresponding to a prescribed amount of compression Ago (dB) (usually - 1 dB) of the small-signal midband gain. This is evaluated by determining the variation of midband gain with rf input signal level Pi, as formulated by substituting the quartic large-signal representation of 6Gj, [Eq. (80b)l in Eq. (103) and expressing rf junction voltage amplitude V, in terms of Pi,, under the approximation Ii3GjlI << 1, as VI

N

((2Pin/G~)(l- rs~)([(g~/lCl~)~’~ -I- m12 -

(105)

9

where rsM= RsGM and $o and m are defined in Eq. (91). The resulting variation of gowith Pi, follows that of Gj, with V,, as described in the interpretation of Eq. (80b), that is, (a) godecreases monotonically with Pi,(gain compression) for & < 0.5(Vy Vp); (b) 3oremains relatively constant with Pi,, then decreases as P i for V, = 0.5(Vv V,); and (c) go increases with Pi, to some maximum (gain expansion), then decreases with further increases in Pi, for V, > 0.5(Vv V,). Clearly, the large-signal gain behavior of a tunnel diode amplifier is significantly dependent on bias voltage v,, with = 0.5(Vv v,) = 2VM - vP (or zib = 0.5)106a being the optimum bias for maximum undistorted output power. (This agrees with a previous calculation, on a simpler Gj(Vb)rnodel,by Hamasaki.66)

+

+

+

+

06

A. Leber and H. C. Okean, Wesron 68 Tech. Papers, Session 5, paper 2, p. 1 (1968). is defined after Eq. (106).

8.

555

TUNNEL DIODES

The midband output saturation level Pas for 1 dB gain compression is then given, using Eqs. (Sob), (103), and (104), by

(106)

where Ub = (v,- Vb)/(V, - V,); p d = (v,- V,)’Gp,q/(l - r s M ) . This expression shows that, for a given normalized bias voltage level ub = 0.5, the large-signal capability of a tunnel diode amplifier varies directly with the squared voltage swing (V, - V,)’ of the active region of the diode current-voltage characteristic and with G,, the maximum diode negative conductance magnitude. Similar dependence on (V, - vp)2G, is exhibited by other measures of the large-signal capability of tunnel diode amplifiers, such as phase distortion, AM-to-PM conversion, harmonic distortion, and intermodulation level. l o 6 Representative values of Pd and Po6,which indicate the relative large-signal capabilities of the various tunnel diode semiconductor materials, and which = 10, are obtained under the typical parameter values 2)b = i,G, = 0.02, I‘io $o = 1 (reflection amplifier) are shown in Table VIII. This tabulation shows TABLE VllI

Material

GaSb Ge Si GaAs

- 3.0

+ 1.0 +4.1 + 5.5

- 20 - 16.3 - 13 - 12

that, of the various tunnel diode semiconductor materials, GaAs tunneldiodes exhibit the highest gain saturation level when used in tunnel diode amplifiers, followed by Ge and GaSb diodes in decreasing 4-dB steps. In addition, Eq. (106) shows that the amplifier gain-saturation level increases directly with increasing tunnel diode G, , the usable upper bound of which is determined by stability (Table VI) and amplifier realizability conditions as (GM)max% 2R,Cj/L,. For existing encapsulated tunnel diodes (Table IV), (G&,ax % 0.0350.07 mhos, resulting in a potential 2-5 dB improvement in Po, as compared with the above values. However, the use of unencapsulated tunnel diodes in an integrated amplifier3*increases (GM)max to 0.07-0.14 mhos and increases this potential improvement in Po, to 5-8 dB.

556

H. C. OKEAN

(a 1

(b)

FIG.27. Push-pull tunnel diodes. (a) Circuit configuration ; (b) composite current-voltage characteristic. (After Leber and Okean.lo6)

The signal-handling capability of a single-diode, single-stage tunnel diode amplifier may be improved by replacing the single tunnel diode by an array of multiple tunnel diodes. The simplest multidiode configuration is the push. which two identical diodes, connected in parallel pull configuration,'06-'08 in at rf, are biased with opposite polarities in such a fashion as to produce a composite diode current-voltage characteristic which exhibits a wider bias range of linear behavior than a single diode (Fig. 27). It has been shown that the maximum improvement in gain saturation level provided by a push-pull tunnel diode amplifier stage is 3dB as compared with one with a single identical diode operated at the same bias voltage and at the same gain (accomplished by changing transformer ratio n, Fig. 24). A further improvement in signal-handling capability is theoretically obtainable by using an M x M series-parallel array of identical tunnel diodes (Fig. 28). For an even distribution of dc bias voltage and current between series- and parallel-connected diodes, respectively, the composite currentvoltage characteristic of the array has M times the voltage and current range of the active region than that of a single diode, and therefore exhibits the same negative-resistance level as a single diode. Therefore, a tunnel diode amplifier utilizing the M x M array has, in theory, M 2 times the power-handling capability of the single-diode amplifier. It has not been possible to demonstrate this improvement experimentally, due to the difficulties encountered in obtaining identical diodes, in distributing the dc bias equally between diodes, and in suppressing internal modes of spurious oscillation within the lo'

C. W. Lee, Dig. 1967 I n ( . Solid Srafe Circuirs, Con/. X, 102 (1967). L. E. Dickens, IEEE Trans. Microwme Theory Tech. MTT-9, 361 (1961).

8. 'TUNNEL DIODES

557

FIG.28. An M x A4 series-parallel tunnel diode array. (a) Circuit configuration; (b) composite current-voltage characteristic. (After Leber and Okean.'")

array. However, the possibility of a microminiature integrated-circuit realization of such an array, with self-contained bias distribution and stabilizing networks and batch-fabricated unencapsulated tunnel diodes, may make its use feasible in practice. e. Multistage Amplijiers The theory of single-stage tunnel diode amplifiers may be extended to include cascaded, mutually isolated, or interacting multistage amplifiers of various types. The primary advantages in utilization of a multistage tunnel diode amplifier as opposed to a single-stage amplifier of the same overall power gain are the potential improvements in bandwidth and in sensitivity to element variations. The disadvantages of the multistage approach include the incurrence of a slight degradation in noise performance and in the ease of stabilization, and the use of more tunnel diodes, more circuit elements, and more dc power. The various types of tunnel diode amplifier that may be classed as multistage include : (1) a cascade of M identical, mutually isolated single-stage amplifiers of the types described in Fig. 25, either synchronously- or staggertuned in center frequency ; (2) a cascade of M different, mutually isolated single-stageamplifiers, which combine the performance advantages of several single-stage types, such as low-noise (GaSb) input stages and high-power ; (3) an iterated network consisting of M tunnel (GaAs) output diodes embedded in repetitive sections of actual or artificial transmission line, thus constituting an iterated traveling-wave amplifier ;(4) a distributed, bilateral, traveling-wave amplifier formed by utilization of a distributed, electrically long tunnel diode junction. The bandwidth, sensitivity (to element variations), and noise-figure cap= goM as abilities of a cascade of M identical stages of total gain gT0

558

H. C . OKEAN

compared with those of a single-stage amplifier of gain gT0, are BNM/PN1

z

[(q,qN- i)/(r:r

- i)](21/M- i)1'2N z M

as N

-,co (107a)

(for Nth-order, maximally flat gain),

(F*M

- 1)/(FA1 - 1) = (1 90

=

-

??;:)/(I

- 9 p f )> 1 ;

+ mI2.

$o(rAo

(107c)

It follows from Eqs. (107aH107c) that there exists a maximum M (usually

3-6) beyond which cascading becomes disadvantageous. The advantages ofcascading low-noise input stages and high-power output

stage^*^,'^^ follow directly from Eqs. (101) and (106) and Table IV, from which it may be shown that a two-stage, 20-dB tunnel diode amplifier utilizing GaSb and GaAs diodes in the first and second stages, respectively, can simultaneously achieve a noise figure of 3 dB and an output saturation level (for less than 1-dB gain compression) of - 12 dBm. The extremely broadband small-signal negative-resistance characteristic of the tunnel diode has led to several proposals for the incorporation of many identical tunnel diodes in iterated, artificial-transmission-line type of traveling-wave amplifier structures.' 1,62.109,1 l o Such traveling-wave amplifiers should, in theory, make maximum use of the tunnel diode by absorbing parasitics (Cj, L,, C,) in a frequency-independent transmission-line structure. Equivalent circuit representations of two possible iterated tunnel diode amplifiers are presented in Fig. 29(a, b). The theoretical bandwidth of each of these traveling wave amplifiers is from dc to somef,, which may be expressed as f H = min(fc

9

(108)

where f , is the cutoff frequency of the inherently low-pass artificial transmission line and CI < 1 is the fraction of active bandwidthf, of the tunnel diode for which Gd Gdo Z Const ( a Z! 0.5). The ultimate in a true distributed traveling-wave tunnel diode amplifier is obtained by the use of a distributed large-area tunnel diode junction." 1 9 1 l 2 lo9

'lo

’I1

l2

N. F. Moody and A. G. Wacker, Proc. IRE 49, 835 (1961). C. A. Skalski, Proc. IRE 48, 1909 (1960). W. W. Anderson and M. E. Hines, Dig. 1960 Int. Solid State Circuits Conf.111, 12 (1960). A. C. Scott, IRE Trans. Electron Devices ED-9,417 (1962).

8.

559

TUNNEL DIODES

A R T I F I C I A L TRANSMISSION L I N E SECTIONS

(a 1

TD N

m

DC BLOCK

GL

DISTRIBUTED p - n JUNCTION

METALLIC PARALLEL-PLANE CONDUCTORS

DlSTR I BUTED SEMICONDUCTOR

(C) FIG.29. Distributed tunnel diode amplifiers. (a, b) Iterated, artificial transmission-line amplifiers: (a) TD: -Gdi = -G. i = 1.2.. ... N : Cdi = iCi &C,+,), C,, = 0. 9,z GL/Gol = 1 + (NGIG,,); Goj = ( C j / L j ) I i 2j , = 1,2,.. . ,N. (b)f, = l/[2n(LC)"2]; go = 2 N : T D : -G di - 2G,, i = 1,. . . , N - 1 : GdN = - G o : Cdi= C/2; C,, = C. (c) Traveling wave amplifier utilizing distributed p-n junction. (After Anderson and Hines.' '

+

Although this amplifier has an extremely high gain-bandwidth capability, it exhibits bilateral gain, and therefore is prone to instability. However, if distributed nonreciprocal, magnetized ferrite material is introduced in a composite structure" [Fig. 29(c)J,unilateral gain is obtained. The iterated and distributed traveling-wave tunnel diode amplifiers described in Fig. 29(a-c) do not find wide practical use, due to the difficulty of physical realization of the structures and of the maintenance of constant resistive source and load impedances over comparable bandwidths.

560

H. C. OKEAN

f: Examples of Practical Tunnel Diode Amplifiers The current state of the art in practical tunnel diode amplifier realizations in the UHF through Ku band (0.5-18 GHz) microwave frequency3 8,55,63,66,67,82-94,106,113,114 range includes amplifiers that have exhibited octave bandwidths, noise figures as low as 3.0 dB, and unsaturated output power levels as high as -5dBm. A representative summary of measured tunnel diode amplifier performance capabilities is provided in Table IX. 16. TUNNEL DIODE OSCILLATORS a. General Oscillator Conjiguration

The tunnel diode, by virtue of its incremental negative resistance, may be used as the active element in a simple sinusoidal oscillator, particularly at rf and microwave frequencies. The basic oscillator configuration is dictated by the circuit requirements imposed by the conditions for the inception and sustenance of sinusoidal oscillations, as formulated in Table VI. The overall schematic and the rf equivalent circuit of a general tunnel diode oscillator are presented in Fig. 30(a,b), respectively. The most general oscillator circuit is a one-port network consisting of a mounted tunnel diode (or array of tunnel diodes) coupled to a resonant cavity tuned to the desired frequency of oscillation,an additional reactive element to resonate the tunnel diode parasitics at the desired frequency of oscillation, a low-pass, rf-isolated dc bias feed network, an impedance transformer to transform the rf load impedance to a level required at the diode terminals to sustain oscillations, an rf isolator between the transformer and the external rf load impedance to prevent variations in the latter from affecting the oscillator performance characteristics, and a stabilizing network for suppressing other spurious out-of-band oscillations while not affecting the desired oscillation. The overall role of these functional circuit components is to ensure that the diode and transformed load impedances yd(jo) and G ( j o )satisfy the criteria for oscillation (Table VI) exclusively at the desired frequency of oscillation fo . In addition, the high-selectivity resonant cavity serves to stabilize the frequency of oscillation against short- and long-term variations in tunnel-diode and other circuit parameters. b. Frequency of Oscillation

A tunnel diode may theoretically act as a source of fundamental sinusoidal oscillations at any frequencyf, from dc up to its resistive cutoff frequency 113

'

l4

L. N. Tolopko, Electron. N e w s April (1968). Product Survey, Microwaves 4, 32 (1965).

TABLE IX REPRESENTATIVE MEASURED PERFORMANCE CHARACTERISTICS OF CURRENT TUNNELDIODEAMPLIFIERS ~

TY Pea H/R C/R C/R CIR C/R C/RC,d C/R C/R C/R C/Rc C/R C/R C/R C/R

No. of stages

(GHz)

2

0.7

1

1.3

2 2 2

2.8 3.0 3.35 3.95 3.95 6.0 5.65 6.0

I 1

2 1

I 2 1 1

1

'C/R : Circulator-coupled

fo

10 9.5 16

18.5

Diode material Ge GaSb GaAs Ge Ge Ge Ge Ge GaSb Ge Ge GaSb Ge Ge

4 (dB)

(A%,: (dB)

17

~

18

1.o

19 18 22 II 12 18 17 16 18 19 16

-

16

3.0 0.4

0

(fvO.5

(GH4

(dB)

0.5 0.26 0.5 2.0 0.5

5.0 3.6 6.0 5.0 5.0

0.1W . 4

0.5

~

3.0 ~

4.0

0.5

0 3

0.44 4.0

-

0.2 5.0

4 -

~~~~~~~~~

F(Jo)

1.o

4.8-7.1 4.5

5.5 4.3 5.1 5.5 4.5 6.0 7.0

reflection amplifier stages ; H/R : hybrid-isolator-coupled reflection amplifier stages.

(A9)ppdenotes peak-to-peak passband ripple. Integrated circuit amplifier using unencapsulated tunnel diode and thin-film tunnel diode circuit. Parameter distribution for 85 amplifiers.

Pdfo) (dBm)

- 21 - 17 -9 - 18 - 18 - 1 8 t o -27 - 22 - 18 - 25 -

- 18 - 24 - 27 - 29

Ref. 114

66 114

106, 113, 114 113 38

Po 4 C

z

z

r

114

0

106, 113, 1 I4

8

114

v1

38 106, 113, 114 114

I14 1I4

z

562

H. C. OKEAN

fR [Eq. (72)], although interaction of these oscillations with the highly nonlinear tunnel diode current-voltage characteristic can result in the generation of harmonics'2.115offo (nf,) greater than fR. In most tunnel diode o s ~ i l l a t o r s , ~ ~ " ~ ' ~ ~the ~ ~initial ~ ~ ~ and steady-state frequencies of oscillation (f, and f,)are established either by a series or parallel inductance which resonates the capacitive diode reactance and/or a high-selectivity series or parallel resonator with center frequency only slightly perturbed by the diode reactance (Fig. 30). However, the configuration utilizing the parallel-tuning inductance and the parallel resonator is preferred due to its greater ability to suppress voltages at harmonics offo at the tunnel diode junction. In each case, the initial frequency of oscillation fo is influenced by the small-signal tunnel diode parameters Cj(V,), Gj( Vb), whereas the steady-state oscillation frequencyfa is a function of the large-signal tunnel diode parameters Cj, , G j l . Therefore, the latter is somewhat dependent upon the amplitude of the rf oscillation voltage, as will be derived in the next section, although this dependence is minimized by the use of a high-selectivity external cavity (Fig. 30). The latter, if electronically variable in frequency, also facilitates electronic tuning of the frequency of oscillation.' 25-129 13'15-131

c. Output Power of Tunnel Diode Oscillator

A calculation of the rf power PLdelivered to the load resistance RL by the oscillating (at Go) tunnel diode generally requires solution of the nonlinear voltage node differential equation at the tunnel diode junction under a specified voltage dependence of the junction conductance, neglecting

G. R. S. Serophim and I. M. Stephenson, Proc. I E E E 54, 1167 (1966). F. Sterzer, Advan. Microwaves 2, 1 (1967). D. T. Young, C. A. Burrus, and R. C. Shaw, Proc. I E E E 52, 1260 (1964). I L 8 C. A. Burrus and R. Trambarulo, Proc. IRE 48, 1776 (1960). ’I9 F. Sterzer, Microwaue J . 11, No. 2, 67 (1968). IZ0 K. Mano and H. Kimura, Rep. Res. Inst. Elect. Comm. (Japan) 15, 101 (1964). A. Presser and A. E. Roswell, Proc. IRE 51,224 (1963). D. R. Persson, Radio Elect. Eng. (London)31, 241 (1966). I Z 3 L. E. Coerver, l E E E Trans. Circuit Theory CT-12, 138 (1965). C. C. Hoffins and T. K . Ishii, I E E E Trans. Microwave Theory T e c h . M m - 1 2 , 176 (1964). W. L. Shelton and W. L. Frederick, Microwaue J . 5, 192 (1962). G. Thompson, Proc. IEEE 53, 535 (1965). D. H. Hornbostel, Proc. IEEE 53, 1751 (1965). M. M. Fortgang and H. J. Hindin, Proc. I E E E 52,419 (1964). M. L. Wright, Proc. I E E E 52, 442 (1964). 1 3 0 D. Cawsey, Proc. I E E (London) 113,943 (1966). 1 3 ' A. C. Scott, IEEE Trans. Circuit Theory CT-10, 53 (1963).

IL5

$ 1 ,I( 8.

BIAS FEED NETWORK

563

TUNNEL DIODES

-

/i"" IMPEDANCE TRANSFORMER

STABILIZING NETWORK

RESONATOR

1I : n

C

OR

iS,

OR

ISOLATOR 0

0

(a 1

FIG. 30. Tunnel diode oscillator representations. (a) General overall circuit configuration. (b) RF equivalent circuit: = ( w / O o ) (w,/w).

-

that of Cj. However, this calculation may be greatly simplified in the parallel-tuned tunnel diode oscillator circuit model (Fig. 30) by the usually valid approximation that the total time-varying junction voltage u j ( t ) consists entirely of the dc bias and fundamental sinusoidal oscillatory components, that is, that the harmonics of the oscillation are essentially short-circuited. Hence, u j ( t ) is expressible as uj(t)

z V, +

V, sin Got.

(10%

The rf output power PL is then calculated by determining the steady-state amplitude V, under which rf power balance occurs, that is, where Po, the that absorbed average power per cycle delivered by the oscillation, equals Pg’, in Gg',the total passive conductance presented to the tunnel diode junction. Therefore, utilizing the general oscillator circuit model of Fig. 30, the power

564

H. C. OKEAN

balance condition is expressible as

where icj(t), the current flowing through the nonlinear, negative junction conductance Gj(Vb), is characterized as some GMF(uj(t))x G,F(Vb +Vl sin Got)[Eqs. (62H68)I.The primary step” in the calculation of PLis the solution of Eq. (1 10)for V, . As a consequence of Eq. (1lo), the average largesignal fundamental negative junction conductance G,,( Vb, V,) satisfies the steady-state oscillation condition

at Go, for which B,’(G,) = 0, Assuming that the external oscillator components, including reactances, resonators, bias feeds, transformers, stabilizing networks, and isolators, are essentially lossless at Go,the power output PLof the tunnel diode oscillator is reduced by the power dissipated in the tunnel diode series resistance R,. Examination of the general circuit model of Fig. 30 shows that PLmay be expressed as

PL= RLpg‘/(RL 4- n2R,) =

-

gRsGM[l + ( 6 0 ~ ~ ~ 1 / g ~ G ~ ~ ) ] } . (112)

The determination of PL,therefore, is accomplished by the solution of Eq. (110) for V, , the calculation of Gj,and Cj, [Eq. (SO)] at that V, ,and the substitution of these quantities in Eq. (112). The resulting pL(vb) is then maximized with respect to Vb and g by obtaining the appropriate solution to aPJag = 0 and W J d V , = 0, yielding PLSmax of the form

where F,, and WR1 are the large-signal quantities [Eq. (SO)] ?,I

0

=

~ = 1

RJGjiI = R$GM; (gGM/Cjl)[(l/Fsl) -

C.1 1

2 1

C;

lll”;

and where constant kp depends upon the particular functional form of Ib( V,) but is always in the range 0.1-0.2. In particular, kp is tabulated as a function and in Table X, where qj is the junction of Ib(vb), along with q j , dc-to-rf conversion efficiency. The overall dc-to-rf conversion efficiency qL

Fop,

8.

565

TUNNEL DIODES

TABLE X OPTIMUM OUTPUT CHARACTERISTICS OF TUNNEL DIODE OSCILLATORS

Ib

GM

0.341 (V" - VP)/2 0.186

*( vv

0.5

-

VP]( 1, -

v, + v,

v, - v, i H v, -i1 2 3 V" -

1

I, - I, I, - I,

I,

.)'

+ 41,

0.47

is given by

The functional dependence of PL,max is further elucidated by the fact that

I, - I, is itself a function of the diode maximum negative-conductance level GM,expressible as Ip - I

=

kv(vv -

vp)GM

(115)

3

where k , is presented for each of the diode I,( V,) models in Table X. In addition, the frequency factor [l - (6&/6R1)*]indicates that PL,max has the inverse-square frequency dependence exhibited by all oscillators utilizing p n junction or other transit-time-limited devices' 32 and that the maximum frequency offundamental oscillation is115 (O0)max

=

(ORl)max

(GM/C)[(l/GMRs)

-

1]"2.

B. C. De Loach, Dig. 1966 IEEE G - M T T h r . Symp., P u b Alto, p. 28 (1966)

(1 16)

566

H. C . OKEAN

Therefore, it is seen that the resulting PL,maxr given from Eqs. (1 13) and (115) as

-

- ?s1)I1

- (GO/GRl)zl?

3/16,

vM/vpZ

(1 17) is determined primarily by the active voltage excursion (V,, - Vp), representative of a particular semiconductor material, the maximum diode negativeconductance level GM consistent with realizable circuit operation, and the proximity of oscillation frequency Go to resistive cutoff frequency uR1x g112~R,max. In particular, for typical oscillator diodes in the cubic I,V, representation (Table X), PL,max

Fsl Z

kpkv(vv

vp)zGM(l

gR,GM 5 0.25,

VJV, z 5,

k,

ldlpx 0.5,

=

2,

lv/lp x 0.05,

so that PL,max is generally of the order of

For maximum-power microwave operation, G M 5 0.2 mhos [as dictated by out-of-band stability considerations (Table VI)], so that, for the various tunnel diode semiconductor materials (Table IV), Po 5 2.1

mW

for GaAs diodes,

Po 5 0.6

mW

for Ge diodes,

Po 5 0.23 mW

(119)

for GaSb diodes.

Therefore, GaAs tunnel diodes are most frequently used in tunnel diode oscillators. To avoid excessive degradation in output power capability due to the frequency dependence of PL,max, a given oscillator frequency Go requires the Under choice of a tunnel diode of sufficientquality such that OR12 these conditions, conversion efficiencies qL of better than 25 % should be realizable.

duo.

d. Frequency Tunability

Due to the extremely broadband nature of the tunnel diode terminal negative conductance, the frequency tunability of a tunnel diode oscillator is usually determined by the range of adjustment of the external reactive element@)used to resonate the tunnel diode, as shown in Fig. 30. Some degree of tunability is provided by adjustment of the tunnel diode bias voltage, due to (a) the variation of Cj, with bias [Eq. (~OC)], (b) the variation with bias of the large-signal terminal series reactance of the tunnel diode

8.

TUNNEL DIODES

567

under series tuning, due primarily to the bias dependence of the diode largesignal negative conductance Gj, [Eq. (SO)], and (c) the bias dependence of diode admittance perturbations introduced by the existence of a nonzero second-harmonic voltage across the diode.'231 3 3 Such bias-voltage tunability is undesirable, however, due to the large variations in junction negative-conductance level Gj and hence in rf output power PL over the range of bias variation. Therefore, the degree of tunability of practical tunnel diode oscillators, as provided by mechanically or electrically adjustable external reactive elements (Fig. 30), is determined by the degree of adjustability of these elements. In practice,' 25-129 variable external inductors may be realized as mechanically adjustable or electronically tunable (variablepermeability), ferrite-loaded, short-circuited transmission lines, variable capacitors as mechanically adjustable, capacitively loaded below-resonance cavities, or electronically tunable varactors, and tunable resonators as mechanically adjustable, high-Q cavities or as electronically tunable ferrite resonators. Practical bounds on the tuning range are set by either the upper and lower cutoff frequencies of the stabilizing network, or by the bias circuit cutoff frequency on the low end and the diode resistive cutoff or self-resonant frequency on the high end. Therefore, the maximum practical range of tunability of tunnel diode oscillator^'^^-^^^ is about one octave. e. Frequency and Amplitude Stability

The frequency and amplitude stability of a tunnel diode oscillator, that is, the variation in the oscillator frequency and power output with time, may be divided into two categories, the short-term stability due to oscillator noisemodulation of the steady-state frequency and amplitude, and the long-term stability due to variations in the diode and external oscillator circuit elements brought about by variations in bias voltage, temperature, etc. The short-term frequency and amplitude stability of a tunnel diode oscillator are commonly expressed' 34 as the rms frequency deviation (Af)rms(om) and the rms single-sideband noise-to-carrier ratio (R/C)AM,respectively, each given as a function of om, the frequency separation from the nominal oscillator carrier frequency 0,.Each of these parameters is in turn, a strong function of the diode excess noise temperature ratio t , [Eq. (76)] and the loaded selectivity Q T (Fig. 30) of the total oscillator cavity, and are given by'33

'33 134

K . Tarnay, Proc. I R E 51, 384 (1963). J . Josenhans, Proc. I E E E 54, 1478 (1966).

568

H. C . OKEAN

-

where B , is the noise-measurement bandwidth lo3 Hz. Representative values of and (N/C)AM for tunnel diode oscillators using GaAs, Ge, and GaSb tunnel diodes are given in Table XI for typical diode operating parameters, r, x 0.1, Oo/wR % 0.5, and for To = 6 GHz, B, z lo3 Hz, QT z 100, and PLobtained from Eq. (1 19). These values have been essentially verified in practice.12’ TABLE XI

GaAs Ge GaSb

3.5 2.2

1.6

5.8 8.7 11.6

- 147 - 144

- 141

It is apparent from Table XI that tunnel diode oscillators exhibit favorable short-term stability (oscillator noise) characteristics in comparison to other free-running microwave solid-state sources,’34-1 38 with AM and FM noise levels at least an order of magnitude below those of bulk-effect and avalanche oscillators and comparable to those of transistor oscillatorvaractor-multiplier chains. Furthermore, although GaSb diodes exhibit the lowest excess noise temperature ratio, GaAs diodes exhibit the lowest AM and FM short-term oscillator instability, due to their higher signal power level. Therefore, GaAs tunnel diodes are favored for oscillator application due to both their high output power capability and their superior shortterm stability. Still further improvement in the short-tern frequency stability of a tunnel diode oscillator may be obtained by phase-locking it to a frequency-stable, lower-power reference o s ~ i l l a t o r .38~ Alternatively, ~ ~ * ~ ~ ~ ~ the ~ frequency stability of a higher-power oscillator may be improved by phase-locking it with a tunnel diode oscillator, thus indicating an area of particular usefulness of a tunnel diode oscillator. The long-term frequency and amplitude stability of a tunnel diode oscillator under incremental changes in tunnel diode bias voltage and temperature 135 ‘36

13’

J. G . Ondria and J. C. Collinet, Dig. 1968 Int. Solid State Circuits Conf. XI, 82 (1968). C. L. Cuccia and A. Savarin, Dig. 1968 I E E E G - M T T h i t . Svmp., Detroit, p. 99 (1968). E. F. Scherer, Dig. 1968 C-MTT I n t . Symp., Detroif (19681. H. Fukui, Proc. I E E E 54, 1475 (1966).

8. TUNNEL

569

DIODES

may be formulated in a fractional total-differential basis as follows :

where PL % PL,max, at which aPL/dVb, aPL/ag % 0 ;

(l/Cj') dcj'/dvb

%

O.S/(Vo,,p - vb)

%

0.005/mV;

(i/cjl) aCj,/az- [o.5/(v0,, Vb)] a v O n p / za ~5 x %

[l/(I, - I , ) ] d(Z, - I,)/dT [l/( V, - V,)] d( V,

-

V,)/dT

-

%

-0.001

%

- 0.0005

to to

10-~/0c;

+O.O05/OC; -

0.002/OC;

and, depending upon the external tuning mechanisms, (l/Cex,)dCe,,/2 T % 10- to 10-3/OC.Typical values of long-term frequency stability obtainable under reasonably controlled dc bias and temperature (AOo/Oo AT)

%

3 x 10-6/"c; (AGo/Go AVb) % 2 x 10-6/mV.

The long-term stability may be further improved by using a well-regulated thermistor-compensated bias network.38

j : Stabilization against Spurious Oscillations For a tunnel diode oscillating strongly at Go, the conditions on the diode and transformed load admittances Yd(jw) and Y,(jw)for no spurious oscillations at w # ooare expressible in terms of Table VI with the provision that the unperturbed small-signal diode admittance Yd(jo) be replaced by yd(jo), the small-signal diode admittance as perturbed'" by the presence of a strong oscillation at Go. The primary perturbation on Yd(jo) introduced by this oscillation is that the small-signal junction conductance Gj(V,) is distorted,I2' due to the familiar oscillation-induced distortion of the diode I-V characteristic, as shown in Fig. 20(b). The resulting distorted Gj(I/b) = djb/dl/, shown in Fig. 31 typically has two widely separated negative peaks - GMi and - G M , at Vb, and Vb2 in the negative-conductance region of the I-V characteristic, with a negative-conductance minimum at v b % VM (Vb1 < VM < Vb2) and with G,, and G M 2 often greater than the unperturbed GM = lGj( VM)l. Therefore, the perturbed small-signal tunnel diode equivalent circuit, containing -G, Cj(Vb),R , , L,, and C,, as before, must be utilized in order to formulate E, which in turn establishes the out-of-band requirements on F. Sterrer, RCA Rei?.23, 396 (1962)

570

H. C . OKEAN

P' lb’

2 b ’

VV

DC BIAS VOLTAGE, Vb

FIG.31. Incremental junction conductance-voltage characteristic of stable and oscillating tunnel diode.

x(jo)(Table VI) and thereby often dictates the use of an out-of-band stabilizing network. If V, = vb,,,, (chosen to maximize P , at Go,Table X) is near Vb2, then these requirements become quite stringent compared to the true small-signal case (such as in amplifiers), since, in the presence of the oscillation at Go,the perturbed small-signal cutoff frequency WR2 and negative-conductance magnitude G , , evaluated at Vb2, can be considerably larger than their nominal small-signal counterparts w, and G M . Note that, if inadequate stabilization is employed, a fundamental oscillation may exist at a frequency above the nominal diode resistive cutoff (CORM < wo' < 0 R 2 ) but only in the presence of a strong oscillation at Go < oRM. This phenomenon provides one possible explanation for observed above-cutofffrequency tunnel diode oscillations.140 g. Multiple and Distributed Tunnel Diode Oscillators

Several possible approaches to increasing the somewhat limited output power capabilities of tunnel diode oscillators include the use of multiplediode arrays or distributed diode structures in a single oscillator stage12,111,112*131 and the use of a summed output of multiple oscillator stages in a self-locking power-combining configuration. 38 As in the case of tunnel diode amplifiers, a tunnel diode oscillator126 employing two diodes in series, in parallel, or in a push-pull configuration (Fig. 27) or utilizing an M x M series-parallel array of identical diodes (Fig. 28) can theoretically provide, respectively, two, four, and M 2 times the power output of a similar single-diode oscillator.1z6 However, as mentioned previously, these multiple-diode arrays are difficult to stabilize against unwanted intra-array modes of spurious oscillation. ld0

T. K. Ishii and C. C. Hoffins, Proc. I R E 51, 485 (1963).

8.

571

TUNNEL DIODES

The use of an iterated or distributed tunnel diode structure has been p r ~ p o s e d ~ ~ ~ " as ' ~a" means ~ ~ ' ~to~ increase the output power capability of a tunnel diode oscillator. Two oscillator configurations are considered, one using an iterated tunnel diode structure consisting of a large number of discrete tunnel diodes equally spaced along a nominally quarter-wave length of transmission line, as shown in Fig. 32(a),and one using a distributed tunneling pn junction between parallel ground planes, thus forming a nominally quarter-wave distributed tunnel diode transmission line [Fig. 32(b)]. The equivalent circuits of these two oscillator structures are representable by Fig. 32(c). DC BIAS Rb

;

I I

I

I

2

i

I 3

9-1

-_-

I

a

I I LOAD

RL

DISTRIBUTED

DC BIAS

TUNNELING JUNCTION LOAD

€bb

RL

NE LINE

(b) A

2 dx -

1 - dx

--- -

--

-(C )

dx = I FOR ITERATED STRUCTURE

FIG. 32 Iterated and distributed tunnel diode oscillators (a) Iterated ladder distributed structure, (c) equivalent circuit

structure. (b)

572

H. C . OKEAN

A unified a n a l y ~ i s ’ ~ of * ’ these ~ ~ oscillator configurations is presented in terms of quantities f, is,i s E, , E p , and --g(vb, q,),which are defined per unit length for the distributed structure of physical length a [Fig. 32(b)] and per diode section for the a-diode iterated structure [Fig. 32(a)]. The analysis utilizes the following basic relationships :

(a) R F junction and transmission-line voltages are given, under “high-Q” approximation (w >> t/Q,by uj,(x, t ) = q,(x) sin w t ;

ul(x, t ) = V,(x) sin ot,

(123a)

where x is the distance (or number of diodes) along the transmission line. (b) Utilizing cubic I-V approximation (Table X), the fundamentalfrequency large-signal negative-conductance parameter is given by 8,(x)

(123b)

= t(vb){l - [ v , 1 ( X ) / ~ 0 l 2 ) .

where vo = 2[(21/, - Vb - v,)(vb - Vp)]1 2. (c) The squared rf voltage amplitude Vf,(x) is given by

(d) For RL sufficiently large,

where 1

+jot + joEp]] ‘I2, + (i +-8, J o l , ) ( - g , +jot)

or, under “high-Q” approximation, with 8, z 8,

(e) Frequency of oscillation occurs at Pa x 4 2 .

(123e) -

(f) The maximum oscillation output power FL = PL,max is obtained by solution, for FL,of

under the maximization condition aFL/aRL= 0.

8. TUNNEL

573

DIODES

The output power and frequency of the distributed and iterated oscillators, obtained from the analysis outlined above under the “high-Q” approximation, are given by12,131

To z PL,max %

0.25/[u2i(t

+ 2,) + (n2/4)?,2]”’,

(1 24a)

(1 - ff)[l - ((%O/dR)’]vO2ga/12,

(124b)

at RL,oP,% 4/ga, where

dR= @/t)[(l/Pg) - 1]’12;

(!$!)[@,/(t + t,)]<< a 2 / n 2 .

(124c)

Comparison of these results with corresponding parameters fo, PL,max, and R,,,,, for a; single-stage, discrete diode oscillator (with G = ga, C = ?a, R, = Pa, L , = l,a, and C , = t,a) indicates that PL,max

= PL,max

7

70 = (n/2).fo

9

~L,opt

2~L,opt.

(125)

Thus, the distributed and iterated oscillators exhibit a slightly superior powerfrequency capability at a higher optimum load resistance than their discrete oscillator counterpart, but usually not sufficient to outweigh the simplicity of the latter. Finally, the output power-frequency capability of a tunnel diode oscillator may be increased significantly by utilizing a composite oscillator consisting of N single-stage oscillators interconnected by means of an appropriate power-combining scheme.138It has been d e r n o n ~ t r a t e d that ’ ~ ~ the rf output level of the composite oscillator can be as high as about 0.85N times that of each of the individual stages. In addition, the interconnection of the individual oscillators provides a measure of self-phase locking of the composite output, thereby improving the short-term frequency stability of the composite oscillator.

h. Examples of Microwave Tunnel Diode Oscillators The current state of the in tunnel diode oscillators includes frequency of oscillation as high as 108 GHz, rf power outputs as high as 13 mW/diode, octave tunability ranges, and long-term frequency stability of better than k0.05% (over combined temperature and bias voltage excursions of +5WC and +20%, respectively). A summary of representative measured performance capabilities of practical tunnel diode oscillators is presented in Table XII. ’

17. TUNNEL DIODECONVERTERS a. Frequency Conversion Mechunisms in Tunnel Diodes

The highly nonlinear, broad band incremental negative conductance and the low excess noise temperature associated with the tunnel diode

574

H. C . OKEAN TABLE XI1

REPRESENTATIVE MEASURED PERFORMANCE CHARACTERISTICS OF CURRENT TUNNELDIODE OSCILLATORS Diode type Number of diodes Configuration Frequency (GHz) Power output (mW) Tuning Tunability (GHz) Efficiency, 1 0 0 (~%)~ Diode maximum negative-conductance level (mhos) Reference

GaAs 4 2x2 array 0.8 10 Varactor 0.61.0 50

GaAs 2 Series

GaAs 2 Parallel

GaAs

GaAs

1

1 -

-

1.5 1.5 Varactor 1.0-2.0 50

1.55 26

60

7 1.o YIG 5-10 25

2.1 50 0.5 0.2 Varactor 1.8-4.0 40

0.15 126

0.2 126

0.5 121

0.1 127

128

-

GaAs 1

~

-

0.015 117

make it a potentially attractive element for use as either a self-oscillating or externally pumped, low-loss or positive-gain microwave down-converter (mixer).3.1 1,12,14 1-148 The basic frequency conversion mechanism used in a tunnel diode mixer is provided by the nonlinear conductive current-voltage characteristic i = f ( u ) of the tunnel diode junction, assuming that the nonlinearity contributed by the voltage-dependentjunction capacitance C,(u)is negligible over the voltage range of operation. In particular, if the total voltage u(t) applied across the tunnel diode junction consists of a dc bias component V,, a sinusoidal “signal” component u,(t) = V,cos(o,t + O,), and a sinusoidal “pump” or “local oscillator” component uo(t) = Vocos(coot + do), then the total current through the diode junction conductance i(t) will in general contain terms in cos(mw, f no, +.),:O A general frequency converter results from the design of the external circuit to extract power at a particular output frequency lmows k nowo(. The tunnel diode frequency converter, however, is most suited and used almost exclusively as a linear small-signal down-converter for application K. K. N . Chang, G. H. Heilmeier, and H. J. Prager, Proc. IRE 48, 854 (1960). R. A. Puce], Solid State Electron. 3, 167 (1961). 1 4 3 D. I. Breitzer, Proc. IRE 48, 935 (1960). ’ 4 4 C. S. Kim, IRE Trans. Electron Deuices ED-8, 394(1961). ‘ 4 5 L. E. Dickens and C. R. Gneiting, IRE Trans. Microwave Theory Tech.MTT-9,99 (1961). 1 4 6 W. A. Gambling and S. B. Mallick, Proc. IEE (London) 112, 131 1 (1965). 14 M. R. Barber, IEEE Trans. Microwave Theory Tech. MTT-13, 663 (1965). 14 J. Reindel, Microwaue J . 4, 92 (1961). 14

14

8.

575

TUNNEL DIODES

in superheterodyne receiving systems. The linear down-converter is characterized by an "intermediate" (if.) output frequency oi = ,01 - coo/, an image frequency wk = 20, - w,, and by the restriction that junction voltage levels at a,, mi, and other conversion frequencies all be much smaller than the local oscillator voltage level V,. In a bandpass mixer, o S , mi, and ok are each situated in passbands centered at w s 0 ,wio, and w k o ,respectively. The small-signal frequency conversion mechanism is best formulated of the time-varying diode using conventional mixer t h e ~ r y ~ " . ' ~ ' -In' ~terms ' junction conductance gj(t), obtained by superposition of a sinusoidal local oscillator voltage v,(t) = V, cos w,f on the static diode conductance-voltage characteristic G,(v) = dl(u)/dv at a particular dc bias Vb. The resulting gj(t) = Gj(Vb + V, cos w o t )is obtainable with Vb chosen either in the positive (Vb < V,) or negative (V, < Vb < V,) conductance region of Gj(Vb). The latter choice provides possible self-generation of v,(t) at the tunnel diode junction as well as potential frequency conversion with gain. Analytically, gj (t)may be expressed in terms of a known G,( Vb V, cos wet) by means of the following Fourier series expansion : '

+

x

+2

g j ( t ) = Gj,

Gj,cosnoot, n= 1

where Gjn = (1/27r)

Jo2n

Gj(v b

f

Vo COS mot) COS n a 0 t d(wot).

As an example, the Fourier coefficients corresponding to the parabolic and quartic tunnel diode conductance-voltage characteristics [Eqs. (66) and (67)] are listed in Table XIII. TABLE XIII FOURIER CONDUCTANCE COEFFICIENTS OF PUMPED TUNNEL DIODEJUNCTION CONDUCTANCE^ Conductance characteristic coefficient

1

-G

-

vJ1

VM

+GMV"2

0 0

Gj"

(ti

0

= 5.6,. . .)

Vo

VJCVM

b ’

'bMVM

Here,

I;

= V,

+ V, cos wOt

-9.45GM

(u

-

V,,( V"

(V, -

- v)3

v,,"

vbz- $Vo2] -9.45GM[6VO2(Vo2- V, + 2Vb2) - Vb3(1 - V,)]

2GMV0Vb

Gj,

G,,

-

lvM-

-GM[1

G,O Gj 1 Gj,

v -

M[

-

vp)

9.45G,(3VO3(1 - 4Vb) + Vb*V0[3 - 4r0)] 9.45G,[4Vo4 - 3VbVO2(1- 2Vb)] 9.45GMVn3(1- 4V,) 9.45GMVO4 0 4VOAV" - VP) vv

- vb)/(Vv

- vp)

576

H. C. OKEAN

Conventional nonlinear conductive mixer theory46 yields a compact frequency-domain model of the pumped junction conductance gj(t)in terms of the coefficients G,, under the assumption that the external immittance terminating gj(t)is essentially a short circuit at all conversion frequencies Imo, k noo[except those utilized in normal down-converter operation, that is, w,, oo, oi* = &(a,- oo),and image frequency ok = 20, - w, . Under these conditions, the currents through and voltages across gj(t)at the above frequencies are related by the following matrix equation :

where, for the “noninverting” case (0, - oo= mi+ > 0),

zi+ = zi,

K+

&,

=

and for the “inverting” case (w,, - o,= wi- > 0), Ii- = zi*,

&-

=

K*

(the asterisk denotes complex conjugate). This matrix relationship, therefore, provides a three-frequency circuit model for the frequency conversion process in the pumped nonlinear tunnel diode conductance, as will be utilized in the circuit description of overall mixer performance to be presented in the following sections. b. Basic Tunnel Diode Converter Circuit Conjiguration

The most general representation of a tunnel diode converter is that of a five-port network, terminated in the rf signal input, the rf local oscillator input, the i.f. output, the image termination, and the tunnel diode itself, as shown in Fig. 33(a). This model is simplified in the case of a self-oscillating converter, in which the external local oscillator generator is replaced by a reactive termination. The fundamental stability (or oscillation) conditions on Y, the admittance terminating gj(t),may be expressed as follows, using Table VI : (a) For self-oscillating mode, G(o0) = (Gjol; G(o) > lGj,l

B(o0) = 0 ;

[dB(o)/dw],, > 0 ,

at all o # oo for which B(w) = 0 .

(128a)

(b) For externally pumped mode, G(w) > lGjol

at all o for which B ( o ) = 0 .

(128b)

8.

577

TUNNEL DIODES

IF OUTPUT IMAGE TERMINATION SIGNAL INPUT

R GS

zLo

LOCAL OSCILLATOR IN PUT

CONVERTER

T

vLo WO

T TD

(a 1

LOCAL OSCILLATOR IN PUT ISOLATOR IMPEDANCE TRANSFORMER

BROADBAND1NG NW

SIGNAL INPUT

TD

vGS

DC BIAS INPUT

TRANSFORME

I F OUTPUT Li

FIG.33. General tunnel diode converter configurations. (a) Five-port network representation ; VLo = 0,ZLo = j X , , for self-oscillating mixer, (b) Series-connected transmission configuration ; L,,, Lt0, are signal, LO, and i.f. tuning inductors, Z , is image terminating impedance, and 2, is the parallel stabilizing and harmonic suppression impedance.

578

H. C. OKEAN

These conditions and the previously discussed frequency-separation requirements on the mixer suggest, without loss of generality, the use of a transmission-type circuit configuration in which the diode, the signal input network, the local oscillator input network (or reactive termination), the i.f. output network, and the image terminating reactance are all connected in series with one another, as shown in Fig. 33(b). The signal, i.f., and, where applicable, the local oscillator two-port coupling networks are shown, in the most genera1case, to include reactive tuning and broadbanding sections, impedance transformers, and isolators, although simpler coupling networks are often used in practice. The signal and i.f. isolators are particularly important because, under a range of dc bias and local oscillator drive, the converter proper can present a negative input and/or output conductance. DC bias is also provided through a series-connected low-pass filter, and an optional shunt admittance branch connected across the tunnel diode terminals may include provisions for stabilization, and for short-circuit terminations for higher conversion products. A simplified equivalent circuit model of a tunnel diode mixer, which is valid without loss of generality in the passbands of the signal frequency w s , the local oscillator frequency w o , and the i.f. frequency wi, is presented in Fig. 34(a). Here, the signal frequency input circuit, the i.f. output circuit, and the local oscillator input or terminating circuit are each represented as single-tuned,parallel R-L-C circuits in series with each other and with the tunnel diode. These circuits each have properly transformed conductance levels G G , Go, and G,, and sufficiently high, properly chosen resonator selectivitiesto satisfy,in conjunction with the diode parasitics, the admittance requirements at the diode junction conductance at os0, oio,w,, and oo. These requirements and the resulting performance parameters of the mixer are best formulated in terms of the pumped conductance conversion matrix [Eq. (127)] by a three-frequency pumped equivalent circuit, including noise generators, at the plane of gj(t), as shown in Fig. 34(b). In this circuit, the frequency separation properties of the circuit reactances are utilized along with transformation of the tunnel diode parasitics to satisfy the following conditions on Y(jw), the overall admittance “seen” by gj(t), in the passband of a,,mi, and wk:

= G,(1 + jQnJ X ( j d = [Y(jw)lm, % Gi(1 + j Q i V i )

(129a)

y S ( j 4 = [Y(j41ms

(129b)

7

yk(jok)

whereG,

N,

%

[Y(jo)Im,

GG,Gi = G L , Q sN, w,,(C ?1

L,

=

= (4WlO)

+ CG)/G,,

- (oro/oJ

[l/o:o(c+ C,)] - L,,

( 129c)

jQkVk)

Gk(l

Qi

x oio(C

1 = s, i, k

+

+ CL)/G,,and

9

L, x [Wi”O(C CL)IP - L,.

8.

579

TUNNEL DIODES

- ,, Lo

SIGNAL INPUT

-

T

co-

GG

LG

\

4. ( t ) 1

A

cL

7ECG

c

=CP

Cry A

FIG.34. Passband equivalent circuits of tunnel diode converter. (a) Series-connected transmission configuration with parallel-tuned external ports; ws0 % [L,(C + C, + C , ) ] - ' / * . wo z [L,(C + C , + C , ) ] - ' / * ,wL z [LL(C+ C , + CL)]-'iz. (b) Three-frequency circuit model at time-varying junction conductance; 1;’ = 4 - w,C, &(jwl)= [Y(jw)],=,,,, 1 = S, I, k.

This model assumes that the conditions on Y ( j w )are satisfied for optimum V, for given performance criteria under either self-oscillation or external pumping, as expressible in terms of the circuit of Fig. 34(a) as Y(j4

%5

Got1

+ i Q o [ ( d w o )- b 0 / 4 1 )

I

Qo = o*Co/Go

1

where, for external oscillator, Go

[(2pO/Vt,opJ

-

GjO(V0,opJI

> IGjoI

for Gjo < 0 :

where Po is the available oscillator power; and for self-oscillation, Go x

.

IGjd~0,opJl

1130)

580

H. C . OKEAN

c. Mixer Gain-Bandwidth Capabilities Specific gain, bandwidth, and stability formulations have been obtained 12.14 1-148 for the configuration of Fig. 34(b) under the following two standard conditions on image-frequency termination yk that are most often encountered in practice : (a) Short-circuited image termination (SCI) : lBkl >> 1x13 I XI, Gk, IGjil

=

9

0,192

3

so that V, = 0 in Eq. (127). (b) Broadband signal-image termination (BBI) : WkO

since qk x -qs

= o,,>> oio

and

yk

= (ok/oko) - (oko/wk) under

= G,U

- jQ,a,),

these conditions.

The gain, bandwidth, and stability formulations for each of these two cases are summarized as follows for both self-oscillating and externally pumped tunnel diode mixers : (a) Midband conversion gain :

K O = K(co,,, oio)= 4G,GiIV,(2/(1G(2 =

4GsGiGil/[(Gi

+ Gjo)(Gs + Gj, + 6Gj2)

-

(1

+ 6)G;J2.

(131a)

Clearly, K O can be > 1 and, for G,, < 0, it can be made arbitrarily large. (b) Half-power bandwidth (a,fixed) :

B=

+

TCK$~[(G, Gj,

(GsGi)’” IGjlI + 6Gj2)(C + C,) + (Gi + Gjo)(C + C,)]

.

(131b)

(c) Stability conditions at w s 0 ,wio (131c) (d) Conditions for positive conversion gain ( K O> 1) :

Gjo < 0 ;

Gjo

+ 6Gj2 < 0;

or where 6 = 0 for SCI and 6 or negative.

=

1 for BBI terminations, and Gjo can be positive

8.

581

TUNNEL DIODES

It is seen that conversion gain may be obtained even with v b in the positive-conductance region (Gjo > 0), depending on choice of Gjo, Gjl, and G,, and hence (Table XIII), over a range of local oscillator drive Vo. The gain mechanism for Gjo < 0 may be viewed as rf and i.f. amplification preceding and following the mixing proper. Under high-gain conditions, the optimum half-power bandwidth is expressible as

as obtained under “symmetrical loading” :

x [(I Gi,opt % Gs,opt

+ 6)’”IGjll

-

+ 6)l”~lKA’2]’’z

GjJ)’”/(l

-

Gjo - cSGjz,

+ 6Gjz

Note that B,,, resembles the bandwidth limitation of a single-tuned tunnel diode amplifier, modified by the multiplicative factor (IGj II - Gjo)/ IGjol. Accordingly, improvements in mixer bandwidth capability of the same order as that obtainable in amplifiers can be realized by introducing broadbanding resonators in the signal input and i.f. output circuits. Conductance coefficients G,,, G j , , and G,, are strong functions of dc bias V, and local oscillator voltage Vo (Table XIII), so that v b and V, may be chosen to optimize B,,, consistent with specified gain and with a desired input and output conductance and stability margin, as well as to optimize may then be used noise performance. The resulting values of and Vo,opt to determine the effective internal or external local oscillator loading Go [Eq. (130)l. The optimum modes of operation depend strongly on noise performance, as will be discussed in the next section. d. Mixer Noise Performance

The noise performance of a tunnel diode mixer, as derived from more IS formulated in terms of the timegeneral mixer noise theory,1z.46*’41-147 dependence of the equivalent tunnel diode shot-noise current ibN(t) under the influence of the local oscillator voltage V, cos mot. In particular, ibN(t) may be expressed in a Fourier series expansion as ’

ibN(t) =

+ vocosoot)COth[(e/kT)(I/, + Vocosoot)],

(134a) (134b)

582

H. C . OKEAN

where 2n IbNm

ibN(t) cos moot d(oOt),

= (1/2n)[ 0

Jgj(t) dl/,

ibN(t)

+ 10

for

vb

2

&,

and where gj(t) is given in Table XIII. The total mean-square output noise voltage Eiacross Gi = G,, including the dominant contribution due to ibN(t) and the smaller contribution due to the thermal noise voltage = 4kTBNR, generated in R, at wso,oio,and o k o , is expressible in the f ~ r m ' ~ , ' ~ ~

GR

vi&

= 4kTBN

i

lHi112[GN0

1 = s,i,k

+ GjO(Gl/GjO)2rs0 + (010/oRO)2(1

- rsO)l

+ [Hii(Hi*, + H Q ) + (Hz(His + Hik)lGN1 f (HisH$

+ H%ik)GNZ}

(1 35)

7

where GN, = f?lbNl/2kT,1 = 0,1,2; rs0 = R,Gjo; wR0= (Gjo/C)[(l/rso)- 1]''2; T i s the physical temperature of the tunnel diode; and Hii,Hi,, and Hik are elements of the augmented impedance matrix Hsi

~

His

Hii

Hik

Hks

Hki

Hkk

[ ~ s s

s

]

=

[K + Gjo

Gj1

6Gj2

Gj,

+ Gjo

6Gj,

6Gj2

SGj,

6(&

I

+ Gjo)

where 6 = 0 and 1 for the SCI and BBI terminations, respectively. Therefore, the mixer single-channel noise figure (signal in signal channel, noise in signal and image channels) at resonance, defined as

F =1

+ (GiGi/k290BNKo),

is given, neglecting circuit losses, and relegating the contribution of noise generated in Gi to that of the i f . amplifier following the mixer, by the expression

8.

583

TUNNEL DIODES

Calculations indi~ate'~*'~""'that F = Fmin OCCUrS a t &, % Vbm [Eq. (78)] in the negative-conductance region of Gj(Vb), in two possible modes of operation,'"' a high-pump mode (large V,; K O 5 1) and a low-pump mode (V, -+ 0; K O >> 1). In either case, Fminmay be expressed as Fmin

1

+ [(I + ~)KT/~~OI[(G,O/IG~OI) + rso + ( o ~ O / O R O ) ' ( ~

-

'so)]

3

(137)

where K x 1 in the low-pump mode ( G j , , Gj2 x 0) and rc(Gj0, G j l , Cj2) 5 2 in the high-pump mode. Examination of Eq. (137) indicates that Fminis degraded by about 1.6 (2 dB) for operation with the BBI rather than the SCI termination, and for operation in the high-pump versus the low-pump mode. The degradation terms due to R, are similar to those contained in the amplifier noise figure formulation. In the low-pump mode, Fminapproaches that of a high-gain transmission amplifier, as is expected since the mixer gain mechanism in this case is primarily rf amplification at ws0prior to the mixing process. Representative calculated values of Fminin these various modes of operation are given in Table XIV. TABLE XIV

Low-pump mode Semiconductor material

GaSb Ge GaAs

High-pump mode

SCI

BBI

SCI

BBI

2.9 3.1 5.0

4.6 5.7 1.25

4.6 5.7 1.25

6.8 8.0 9.8

Therefore, as in the amplifier case, the use of GaSb tunnel diodes provides the lowest noise capability. e. Comparison of Modes of Mixer Operation Of the two modes of tunnel diode mixer operation'47 described in the preceding sections, it is seen that the low-pump mode exhibits superior gainbandwidth product and noise performance, and requires less local oscillator power Po. However, operation in the small-pump mode is extremely critical to variations in bias voltage, local oscillator drive level, and source impedance. In addition, the dynamic range of a tunnel diode mixer, characterized by the 1-dB gain compression input level PinTs x Po, is much lower in the smallpump mode (Po = - 60 dBm) than in the large-pump mode (Po % - 10 dBm),

584

H. C. OKEAN

the former being even poorer than tunnel diode amplifiers of similar gain level and the latter being comparable with conventional varistor mixers. Taking all of these factors into accwnt, it would seem that the SCIterminated, high-pump mode of tunnel diode mixer operation is the most desirable. The low noise figure of the SCI-terminated, low-pump modemixer can more profitably be obtained by using a separate low-noise tunnel diode amplifier prior to a high-pump mode tunnel diode mixer.

f: Examples of Microwave Tunnel Diode Mixers While not as many practical microwave tunnel diode mixers have been constructed as have amplifiers and oscillators, several experimental models14'-I4* have been fabricated to verify the theory summarized in the preceding sections, and several practical models' l 4 are available commercially. The state of the art on tunnel diode mixers is summarized in Table XV.

18. TUNNEL DIODEDETECTORS a. Detection Mechanism in Tunnel Diodes

The nonlinear current-voltage characteristic of the tunnel diode makes possible its as a low-level envelope detector at rf and microwave carrier frequencies, in a similar manner to conventional pointcontact crystal diodes or hot carrier diodes. In particular, the curvature of the current-voltage characteristic of the tunnel diode junction conductance at a particular dc bias point results in rectification of a small rf or microwave sinusoidal voltage superimposed on the dc bias voltage across the junction, yielding a component of dc rectified junction current which is dependent upon the amplitude of the incident sinusoid. Quantitatively, this detection mechanism is derived,' 5 1 , 1 5 2 under the small-signal assumption, from a truncated Taylor series expansion of the current-voltage characteristic I = f(Vb + V, sin wt) about the dc bias point Vb in terms of a small sinusoidal voltage V,, sin wt, with V, << v b . The rf carrier envelope V, can be constant (CW) or it can itself be a modulated time function Vo(t),such as a sinusoidally modulated envelope V, + V,, cos w,t (w, << w ) or a pulse-modulated envelope of pulse duration z and pulse repetition period T~ (z,zR >> 1/04. The series expansion of I is given by ''7149-153

I 2 f(Vb)

+ V,[dj( V)/dV],, sin w t + )Vo2[d2f(V)/dV2],,sin2cot + . . . (138a)

14’ 15’

'" 15* 153

C. A. Burrus, I E E E Trans. Microwave Theorv Tech. MTT-11,357 (1963). T. H. Oxley and F. Hilsden, Radio Elect. Eng. (London)31, 181 (1966). R. B. Mouw and F. M. Schumacher, Microwaue J . 9 (I), 27 (1966). W. F. Gabriel, I E E E Trans. Microwaue Theory Tech. MTT-15, 538 (1967). P. E. Chaseand K. K. N. Chang, I E E E Trans. Microwave Theory Tech. MTT-11,560(1963).

TABLE XV

MEASUREDPERFORMANCE CHARACTERISTICS OF EXPERIMENTAL TUNNELDIODEMIXERS

Reference Signal frequency (GHz) Local oscillator frequency (GHz) Output frequency (MHz) Diode material Pump mode Local oscillator power (dBm) Image termination Midband conversion gain (dB) Half-power bandwidth (MHz) Midband single-channel noise figure Input level for 1 dB gain compression (dBm) ~~

'I

SO denotes self-oscillating mixer.

141 0.2 1 0.24

145 1.z 1.17

147 1.35

30 GaAs Large

30 Ge Large - 13 SCI 26 2.0 3.0

30 GaSb Large

SCI 23 0.15 2.8

147 1.35

148 2.0-3.0 2.0-3.0

-7 SCI < I

30 GaSb Small - 60

10 Ge SO"

SCI

BBI

>> 1

-

4.9

4.3

-6

- 60

-

12.0

114 4.0-8.0 4.0-8.0

1 I4 12.0- 18.0

P)

12.cL18.0

C

100 Ge Large - 13 BBI 6.0

100

P

8.5

Ge Large -11.5 BBI 9.0 11.0

+

z z

8 0

e!

586

H. C . OKEAN

or I z I, + I , sinwt - I,cos2wt

+ I,,

(138b)

where I b is the dc bias current, equal tof(Vb); I , is the fundamental current amplitude, equal to VoGj(Vb); I, is the second-harmonic current amplitude, equal to VoZGj’(Vb)/4; I , is the rectified dc current, equal to VozGj’(Vb);and Gj’(Vb) = [dGj(V)/dVlv,, and is directly obtainable from the given Gj(Vb) characteristic, as seen in the case of the parabolic [Eq. (66)] and quartic [Eq. (67)] Gj(Vb), for which Gj’(Vb) 2 ~ G MVb( - VM)/(VM - V,)’

(139a)

and Gj’(Vb) 2 37.8G~(Vb-

&)(K

- &)2/(Vv - V,)“,

(139b)

respectively. Examination of Eq. (139) indicates that Gj’ < 0 for Vb < VM; Gj’ = 0 at VM; Gj’ > 0 for Vb > VM;and that IGj’l is maximum at Vb = 0. Similar conclusions hold for higher-order polynomial representations of Gj( Vb). The detection mechanism consists essentially of the utilization of appropriate means of frequency separation to obtain a detected output voltage which, as in other detector diodes, is proportional to I,. The tunnel diode has a higher potential rectification sensitivity in terms of I , than other detector diodes due to (a) the possibility of operation in the negative-conductance region of the I-V characteristic [Gj( Vb) < 01, thereby providing rf amplification prior to detection, (b) the possibility of operation near peak voltage V,, a point of high curvature [large lGj’(Vb)l],and (c) the possibility of operation at zero bias, at which Gj(Vb) >> 0, being compatible with representative rf source impedance levels, thereby providing maximum passive rf power transfer. These properties will be described in detail in the following sections. Finally, tunnel diodes used for envelope detection are often referred to as backward diodes, to distinguish them from conventional detector diodes in which the voltage polarity on the p n junction for high conduction is reversed, or from conventional tunnel diodes, compared to which the tunnel detector diode has a considerably lower peak current, maximum negative conductance, and peak-to-valley ratio. b. Detector Input-Output Characteristics

A general circuit model of a series-connected tunnel diode detector, shown in Fig. 35(a), includes arbitrary bandpass or low-pass coupling network N A and low pass coupling network Nv between the series-connected tunnel diode and the rf source and the video load, respectively. These networks

DC, VIDEO GROUND RETURN

RF SOURCE

W

3

TRANSFORMED RF SOURCE

\RF BROADBANDING

VIDEO / BROADBANDING

TRANSFORMED VIDEO LOAD

FIG.35. Tunnel diode detector representations. (a) General transmission configuration ; N , and Nv are rf and video broadbanding and stabilizing networks; nA2 and nV2 are rf and video impedance transformation ratios. (b) Two-frequency equivalent circuit; RF broadbanding-BPF: LA,= 1/oo2(C CJ, Ci, = l / c ~ , ~ L , , ., . . ; LPF: CAI= rf choke, C;, = L,, = . . . = (o.

+

01

3

588

H. C. OKEAN

provide frequency isolation between the source and load and shape the frequency dependence of the overall detection response. The detection mechanism is contained explicitly in the two-frequency, small-signal equivalent circuit of the detector, including noise sources, presented in Fig. 35(b).Under small-signal, square-law operation, I , is proportional to the available power PAfrom the rf source, that is, 11,1 = PPA,where /l is defined as the short-circuit current sensitivity and may be in terms of the circuit model of Fig. 35(b) as ( 140a)

where p’ applies for Gj > 0 ( l r A I 2 < I) and p- applies for Gj < 0 ( I r A I 2 2 1) ; rs = RsGj ; and QJR =

For the special case,

UGjI/C)t(1/IrsI)(1 + rsN1’2-

= Vp, Gj = 0, and

Vb

lrAI2

5 1 (due to RJ,

lGj’(h)l I1 - lrA(jw)121/2Rsw2c2.

P(O)

The parameter lGj’(Vb)1/2Gj(Vh)of significance for Eqs. (66), (67), and (139) by IGj’)/2Gj=

IVM

-

cv, + v, + 2Kl)(v, - V,)

(140b) Vh

# V, is given from

Gj(Vb),

for quadratic for quartic

Gj(V,).

(141a) (141b)

The input-output parameters of the detector model of Fig. 35 are given in terms of p(w) as follows: Net video current sensitivity : BL = I L P A

( 142a)

= ffv(w)P(4.

Net video voltage sensitivity ; YL

=

(142b)

vL/PA =

Net detector power-conversion gain : K L

=

PJpA = P L 2 R L = IHv(w)12B2pA

9

( 142c)

where H,(w) = lZL/lr) is the current transfer function of low-pass video filter Nv, and Rv = (1 + R,Gj)/Gj is the diode video resistance.

8.

TUNNEL DIODES

589

Examination of Eqs. (139H142) indicates that : (a) IGj'J and, hence, /I exhibit a sharp null at Vb = VM.However, a convenient bias point in the active region is at V, = Vb- = 21/M - V,. (b) K , varies linearly with PA,due to the square-law detection process. (c) The rf and video frequency dependence of transfer characteristics /IL, yL, and K , are fixed by the design of coupling networks N A and N , for specific IrA(jw)12 and H,(o) under the constraints imposed on r, by the tunnel diode parasitics and on H , by the parasitics associated with the video post-detection circuitry. The design of N A and N , utilizes standard passive filter or negative-resistance amplifier theory.55,57,59,99,'oo (d) For bias in the active region (Gj, R, < 0), the stability criterion of particularly in the rf and video Eq. (128) must be satisfied over all o d oR, passbands, for which the conditions ( R , R,)lGjl < I and RL < lRvl must be satisfied. Stabilization techniques and auxiliary stabiiizing networks similar to those presented in Fig. 21 may be utilized to satisfy this criterion. In addition, the use of a nonreciprocal device, e.g., an isolator, at the rf input is desirable. (e) The three most useful modes of detector operation are zero bias << l), peak bias operation (Vb = V,, Gj = 0, operation (V' % 0, Gj > 0, IrA12 I r A 1 2 < I), and active bias operation (v, < vb < v,; Gj < 0 ; 1rAl2 > 1).

+

The magnitudes and bandwidths associated with the rf and video transfer characteristics B(o)and H,(w) may be formulated without loss of generality by assuming that (1) N , is designed for mth-order, maximally flat low-pass behavior in HV2(o),(2) N , is designed for nth-order, maximally flat low-pass or bandpass behavior in /I(w)for the zero- or active-bias modes of operation, (3) N , consists of a direct connection (excluding dc ground return, etc.) of R, to the diode in the peak bias mode. This results in first-order, high-pass behavior in [I - IrA(jw)12],thereby compensating for the w - 2 dependence and yielding a first-order, low-pass, maximally flat of /I[1 - IrA(jo)l2]-' behavior in /I(w). The resulting formulations of detection sensitivity, rf bandwidth, and video bandwidth for the three bias modes of operation are summarized in Table XVI, along with limiting values of sensitivity magnitudes for each of the three widely used tunnel diode semiconductor materials. The results of Table XVI may be summarized as follows: (a) Values of midband, matched (tAo = l), short-circuit current sensitivity

/Iounder passive bias conditions (Vb Q V,) are of the order of 10mA/mW, which equals or exceeds that achievable with conventional envelope detector diodes, whereas, under active bias conditions (Vb > V,), Po can be made arbitrarily large by appropriate choice of R , for large values of rf transmission

H. C. OKEAN

Ultimate limit (BAm) of BAmas n

+

m

r,, = (R, - R J ( R , + RL)

where

B,, = cr-urrent

Representative" parameters for R,GM % 0.1, and materials GaSb Ge Gash at bias voltage Gj, Gj' utilize Eqs. (67) and (1391; f A O = 1 for center frequency. " P o in mA/mW. a

..

...

video bandwidth of H , Bob

RVGM

15 10 5

0.38 0.40 0.41 kb =

vb

< V,,

0

w = ( w / w o )-

Bob

131fso

8.4r2,, 4.2t:, Vb =

RVGM

Bob

RVGM

1.9 - 1.94 - 1.94

9.7 6 3

w

-

vb- = 2v,

-

vp

(wo/w) for bandpass and w / o o for low-pass

CQ

2

Vb

=

v,

ItA(jw)i2,where wo

Po is the rf

2Z 3

r 0

s V

w

592

H. C. OKEAN

-

gain t i o . In particular, values of Po 2000 mA/mW, feasible with reasonable values of t i o 100, are more than two orders of magnitude better than obtainable with conventional detector diodes. (b) Assuming that transformed source impedance R, may be freely chosen for a specified t i o , Po is seen, at a given V,, to be independent of diode impedance level GM, but to increase with decreasing active voltage swing (V, - V,). Since the latter is a function of the diode semiconductor material, GaSb detector diodes yield the largest Po, followed in decreasing order by Ge and GaAs diodes. (c) For a given functional dependence Cj(V,), the diode video resistance at a given Vb is essentially independent of diode material but is inversely proportional to GM. Zero bias video resistances of 250 ohms, readily obtainable in typical detector tunnel diodes ( G M E 0.01 mho), are an order of magnitude less than those obtained in conventional detector diodes, thus making for easier rf and video matching and, as will be demonstrated, better noise performance. (d) Values of video current transfer function Hvo approaching unity under passive bias and arbitrarily large under active bias render the previous remarks on Po also applicable to overall detector transfer functions P,, yL , and K , [Eq. (142)l. (e) Half-power, low-pass or bandpass rf bandwidths for fl( jco), obtainable under active bias, are comparable with those obtainable with similarly broadband reflection-type tunnel diode amplifiers of gain IrA12 [Eq. (94)]; those obtained at zero bias are of the order of Gj(0)/n(C + C,) 5 2-10 GHz, and those obtained under matched peak-bias operation are of the order of (471R,C)- 6 5-25 GHz. (f) The low-pass, half-power video bandwidth Bv of IHv(jo)12, and hence of PL, y,, and K L , is primarily a function of the transformed input time constant R L C L of the post-detection circuitry, which is typically of the order of 10-1000 times C/lGjl. Therefore, B, will be of the order of 5 MHz to 2 GHz, thus determining the upper bound on the frequency of readily detectable sinusoidal envelope modulation (fm < B,) and the lower bound on achievable envelope pulse rise time (T O.5/Bv). The above results lead to the preliminary conclusion that tunnel diode detector operation in the zero-bias mode combines moderately high sensitivity, wideband operation with relative ease of rf and video matching and general circuit simplicity. Active bias operation can yield extremely high detection sensitivity, but at the cost of reduced bandwidth and increased circuit complexity required for stabilization and nonreciprocal isolation, and is extremely critical with respect to circuit adjustments. (Active-bias operation results in a circuit that functions as an rf amplifier, a detector, and a video amplifier in cascade.) Peak bias operation yields extremely high

-

-

8.

TUNNEL DIODES

593

bandwidth at slightly reduced detection sensitivity, but requires more difficult rf and video matching. A further comparison of the relative advantages of these three modes of detector operation requires an examination of the detector noise performance as presented in the next section. c. Detector Noise Performance

The noise performance of a square-law envelope detector such as the tunnel diode detector cannot be meaningfully characterized in terms of rf-to-video noise figure as in a linear converter, due to the power-level dependence of rf-to-video power transfer [Eq. (142c)l and the resulting suppression of rf input noise arising from the square-law detection process. Therefore, the meaningful sources of noise in an envelope detector originate in the video passband and are therefore best characterized by the detector tangential signal sensitivity 4 , defined as the input power level at which a specified video signal-to-noise ratio U , is obtained across G,, where

and where (I&)av is the total video mean-square short-circuit noise current. By convention, Uv is chosen as 2.5 to define the tangential sensitivity, whereas the input power P, at which Uv = 1 is referred to as the minimum detectable signal. The significant sources of video noise which define tangential sensitivity P, include the shot-noise contribution of the tunnel diode junction, the thermal noise contribution of R, and of the equivalent video load GL, and the equivalent excess noise contribution of the post-detection amplifier under input termination R,, characterized by input noise temperature TPA.The flicker (l/f) noise contribution of the tunnel diode may be neglected’’ 1 , 1 5 z over the useful portion of the video passband ( f > 1 kHz) for Vb < V,, thus representing an important advantage of tunnel diode detectors over their conventional counterparts. Utilizing the equivalent circuit of Fig. 35(b), is given by

where BVN is the effective video noise bandwidth, T the ambient temperature, and G N = efbN/2kTwith I,, given by Eq. (70), or

GN = [5800/T (“K)]zb~0th{[5800/T(“K)]Vb (volts))

594

H. C . OKEAN

Tangential sensitivity P, is then obtained from Eqs. (142a),(143), and ( 1 4 4 ) at Uv = 2.5, yielding =

5(kTBVNGNT)1’2/P0

(145)

9

where G,T

= [(GN

+ rsGj)/(I + rJ2I + G d 1 + (TiA/T)I.

The lower the value of P,, the more sensitive the detector. Equation ( 1 4 5 ) may be formulated in terms of the “figure of merit” M of the tunnel diode, which is a measure of the quality of an envelope detector diode and which is defined within the video passband in conjunction with a noiseless video amplifier as

where G,‘

= (GN

+ rsGj)/(I + r,)’ .

(This definition is somewhat more general than that used for conventional detector diodes, in which G N = G, and GN’ = Gv, thus yielding a meaningless result at Gj = 0.) Therefore, P, may be expressed as fl(pw) = 3.16

X

1 0 - 4 { [ B ~(HZ)](GNT/GN))~’~/[M ~

(147)

Representative values of M and PIfor each of the three modes of detector operation and for each of the three diode materials are given in Table XVII TABLE XVII“ Value of parameter for: Parameter

Vb

GaSb

M (W- *)

0

260

VP

1 20

4 (dBm)

b‘

4300

0

- 59.1

VP Vb -

- 55.8 -71.3

Ge 128 67 2300 -56.1 - 53.3 - 68.6

GaAS 63 27 820

- 53 -49.3 - 64.1

Here, GM = 0.0025 mho; GNT% G,’; tio= 10 at Vb- and 1 at = 1 MHz; &- = 2VM - Vp.

& = 0, Vp; B,,

8 . TUNNEL

DIODES

595

based on calculations using Table XVI, Eqs. (144H147), and Eqs. (67) and (70) for GN', under the limiting assumption of a negligible video amplifier noise contribution ( G N T z G"). Table XVII shows that: (a) At a given operating point and impedance level, GaSb tunnel diodes make the most sensitive detectors from a signal-to-noise standpoint (lowest P,, highest M ) , followed in decreasing 3-dB steps by Ge and GaAs diodes. The superiority of GaSb diodes is due to both their higher conductance curvature and hence higher current sensitivity and to their lower noise contribution GN'. (b) The maximum tangential sensitivity (lowest P,) for a given material and impedance level is obtained under active bias conditions, typically at V,- = 2vM - V,, due both to the increase by t i o > 1 in current sensitivity provided by the rf preamplification, and to the slightly lower noise contribution G,' obtained under active bias. The improvement in tangential sensitivity (and M ) under active bias is at least by t i o > 1, whereas, under passive bias, the tangential sensitivity at peak bias is about 3 dB poorer than that at zero bias. (c) The tangential sensitivity (and M ) for a given material and bias point is inversely proportional to G M , assuming rf matching to a desired tio. The values of tangential sensitivity presented here for tunnel diode detectors are generally superior by 3-20dB to those exhibited under similar conditions by conventional diode detectors, whereas the values of M are at worst comparable and at best superior by an order of magnitude. d. Dynamic Range

The tunnel diode detector is basically a small-signal device, with deviation from square-law operation occurring at large signal levels due to higherorder terms in the series expansion of Eq. (1 38a). The first higher-order term to perturb the rectified current is the fourth-order term ( VO4/24)[d4f( V ) / dV4Ivb sin4 wr ,

(148)

which, using Eqs. (138H1401, yields a large-signal to small-signal current sensitivity ratio

Equation (149) indicates that the detector undergoes compression of current sensitivity with increasing power levels, leading to eventual limiting. In particular, the input power level at which 1-dB current-sensitivity

5%

H . C. OKEAN

compression occurs is given by p y

15.6GM(Vb

-

VM)2(Vv

- Vb)3/(Vv

-

Vp)4003

(1 50)

where the following values of P, are obtained under the conditions of Eq. (148): For V, = 0, P, = - 9, - 5.7, + 0.3 dBm for GaSb, Ge, GaAs diodes ; V, = V,, P, = - 15.3, - 11.9, - 5.9 dBm for GaSb, Ge, GaAs diodes; v b = 2VM - v,, P, = - 35.5, - 32.4, -26.4 dBm for GaSb, Ge, GaAs diodes. It is apparent from Eq. (150)that the zero bias mode of detector operation offers the best large-signal-handling capability, whereas the high-sensitivity active mode of operation offers the poorest. Furthermore, as in the case of amplifiers, at a given detector bias, GaAs tunnel diodes exhibit the highest input saturation level, followed in decreasing order by G e and GaSb diodes. e . Comparison of Modes of Tunnel Diode Detector Operation

Comparison of the performance parameters of tunnel diode detectors operated in the zero, peak, and active bias modes and utilizing GaSb, Ge, and GaAs tunnel diodes, as presented in the preceding sections, leads to the conclusion that the zero bias mode is preferred for high-sensitivity, lownoise, wideband, high-dynamic-range operation. Ultra-high-sensitivity, lownoise operation is obtainable in the active bias mode, in which the diode provides the combined functions of rf and video amplification and square-law detection. However, in this case, bandwidth and signal-handling capabilities are reduced to values comparable to those obtained in tunnel diode amplifiers. In general, the results obtained in the active mode are similar to those exhibited by conventional detectors preceded by tunnel diode preamplifiers. Finally, as in the case of amplifiers, GaSb diodes provide the lowest-noise, highest-sensitivity detection and GaAs diodes the largest signal-handling capability, with Ge diodes offering a judicious compromise between these aspects of performance.

5 Examples of Microwave Tunnel Diode Detectors Many tunnel diode detectors have been fabricated in the rf and microwave frequency ranges. The state of the art in practical tunnel diode detectors44,114,149-153 is summarized in Table XVIII, in which it is seen '

that detectors operated in the zero bias mode have achieved tangential sensitivities better than -60 dBm from U H F through X band (1-MHz video bandwidth) and as high as - 55 dBm at 35 GHz. In addition, tangential sensitivities as high as - 75 to - 80 dBm have been achieved over frequency bands in the 3-7-GHz range (B, = 1 MHz, Ge diode) under active bias conditions. The wide rf bandwidth capability of the tunnel diode detector has been verified in practice, with half-power, low-pass bandwidths of greater than 10 GHz and bandpass bandwidths of better than 5 : 1 obtained

TABLE XVIII

MEASURED PERFORMANCE CHARACTERISTICS OF EXPERIMENTAL TUNNEL DIODE DETECTORS

151 0 0.1-8.0 Ge I1 200 - 54 8.0 2 I20 - 23

152 0.07 6.0 Ge 120

(l.sV,) 6.0

Ge 950 10,Ooo - 85 0.25

loo0 - 76

0.1

150 0 9

Ge 12 480 - 60

-

- 57 -

~

1.o

1

0

0

-

44 0 70 GaAs

.o

149 0 50

114 0 0.01-8.0

144 0 2-18

- 55

- 44

8 2

16 2

Ge 4 - 46 0.04 >> 290 -2

-

~

0

-7

598

H. C. OKEAN

in the zero bias mode and bandpass bandwidths of about 20 % in the active bias mode.

TUNNEL DIODEAPPLICATIONS 19. MISCELLANEOUS SINUSOIDAL a. General Network Synthesis

The small-signal negative-resistance property of the tunnel diode has stimulated investigations' 2,1 54-1 5 9 on the use of tunnel diodes in general frequency-domain network synthesis. In particular, numerous treatments have been presented on the synthesis of k R, L, C networks in which tunnel diodes provide the - R elements. Each tunnel diode is usually represented in somewhat oversimplified fashion by its parallel - G , C junction immittance, although some treatments consider the series parasitics R , and L, as well. The network functions dealt with in these generalized synthesis procedures include, in addition to the previously discussed power amplification, voltage and current amplification, realization of nonminimum phase ladder networks, realization of high-selectivity low-loss filters, and the realization of multiport networks with specified impedance or admittance matrices which are not possible with purely passive RLC elements. The details of these various synthesis procedures are more relevant to abstract network theory than to the particular limitations imposed by the tunnel diode as a device, and are therefore beyond the scope of this chapter. However, several basic limitations on the physical realizability of general networks employing tunnel diodes are imposed by the tunnel diode device parameters. These usually relate to the complex natural frequencies p I = uI jm,, 1 = 1,2,. . . , exhibited by a general network N terminated in a tunnel diode, where p l has uI 2 0 corresponding to steady or growing oscillatory network responses of the form exp[(a, jo,)t].These limitations may be summarized as follows in terms of reciprocal network N .

+

+

(a) N is physically realizable provided

G/C <

min[l, D,J,

(151)

where min(X, Y ) = the smaller of X or Y, P = C;=Ipl, and D,, is the limit, as p becomes infinite, of the ratio of certain network determinants. (b) The regions in the complex frequency plane (p-plane) of possible

'56

15’

L. Weinberg, IRE Trans. Circuit Theory CT-8,66 (1961). H. J. Carlin and D. C. Youla, Proc. I R E 49, 877 (1961). V. W. Chang and 1. T. Frisch, Univ. of Calif. Elect. Res. Lab., Int. Tech. Memo TM-24, July 1963. B. K. Kinariwala, I R E Trans. Circuit Theory CT-8,389 (1961). B. A. Shenoi, Proc. Nat. Electron. ConJ 18, 114 (1962). D. L. Losee and S. K. Mittra, I E E E Trans. Circuit Theory CT-11, 357 (1964).

8.

TUNNEL DIODES

599

natural frequencies p I , and hence the quantity P , all decrease with increasing values of the normalized parasitics rs = R,G < 1 and 1, = LsGZ/C6 3. (c) Therefore, as rs and 1, increase, the realizability of a given network is possible only with a tunnel diode of decreasing frequency capability, that is, of increasing RC product. (d) To maintain the parallel - G, C idealization of the tunnel diode used in many of the general network synthesis procedures, it is desirable that parasitics R , and L, be restricted to satisfy 1, < r s , with a particularly useful relationship being I, x 0 3 , . Further treatment on the synthesis of general networks utilizing tunnel diodes may be found in the literature on network t h e ~ r y . ' ~ * ~ * , ' ~ ~ - ' ~ ~ b. Electromechanical Transducer

Experiments have shown160-'67that it is possible to modulate the energy band gap and hence the peak current of a tunnel diode by the application of compressive force perpendicular to the plane of the diode junction. The dependence of I , (and hence G,) on the magnitude of this force F has been found to be essentially linear in Ge and GaSb diodes, with sensitivities between 5 and 50 pA/g and maximum large-signal-to-noise dynamic range as high as 60 dB. The sign of d l , / d F may be positive, as for Ge diodes, or negative, as for GaSb diodes. The net result is a sensitive, linear electromechanical transducer. A suitable tunnel diode structure for transducer application utilizes a steel sphere to couple the applied force F uniformly to the diode junction area and uses epoxy to provide support to the junction and to further equalize the junction force distribution (Fig. 36). A transducer using such a diode to convert a mechanical input force perturbation AF to an electrical output may be implemented as (a) a static current modulator in which AF is converted to a peak current perturbation A l p through a diode biased at Vp, (b)a variablegain amplifier in which the gain presented to an rf carrier is modulated by AF by virtue of the resulting perturbation AGM, and (c) a variable-output rf oscillator having an output level modulated by AF through perturbation AGM. Any of these approaches results in an extremely sensitive electromechanical W. Rindner and A. Garfein, Solid-state Electron. 10, 1227 (1967). E. S. Rogers, J . Acoust. Soc. Amer. 34, 883 (1962). I b 2 T. R. Kiggins and A. G. Milnes, ISA Paper 43-3-63, 1963. 163 L. Esaki and Y. Miyahara, Solid-state Electron. 1, 13 (1960). 1 6 4 W. Bernard, W. Rindner, and H. Roth, J . Appl. Phys. 35, 1860 (1964). 165 S. L. Miller, M. 1. Nathan, and A. C. Smith, Phys. Rev. Lett. 4. 60 (1960). 16'

lh6

M. E. Sikorski, Dig. 1962 Int. Solid State Circuits Con/:, Philadelphia. Pennsylvania V, 14

16'

(1962). A. 1. Yerman, ASME Paper 63-WA-264, 1963.

600

H. C . OKEAN APPLIED FORCE

EPOXY

CERAMIC SPACER

TUNNEL DIODE SEMICONDUCTOR CHIP

BOTTOM DIODE CONTACT

-

FIG.36. Cross-sectional view of tunnel diode electromechanical transducer. (After Rindner and Garfein.’ 6 0 ) Scale 100: 1 ; mesa region not to scale.

transducer, with the single disadvantage that the temperature dependence of the p n junction, which can be as high as f5 p A r C , can introduce a significant additional noise component on the transducer output. However, this temperature dependence can be significantly reduced by compensatory doping of the semiconductor junction or thermistor compensation of the bias network. c. Use in Physical Research

The distinctive nature of the tunnel diode I-V characteristic, with its negative-resistance region and its strong dependence on various physical phenomena, makes the tunnel diode a useful tool for physical re1.22.168-173 1n particular, the following physical phenomena have N. Holonyak, I. A. Lesk, R. N. Hall, J. J. Tiemann, and H. Ehrenreich, Phys. Rev. Lett. 3, 167 (1959). R. N. Hall, Proc. I n t Con$ Semicond. Phys., Prague, 1960, p. 193. Czech. Acad. Sci., Prague and Academic Press, New York. 1961. 7 0 R. N. Hall, IRE Trans. Electron Devices ED-7, 1 (1960). A. G . Chynoweth, R. A. Logan, and P. A. WollT, Phys. Rec. Lett. 5, 548 (1960). 1 7 2 M. J. Nathan and S. L. Miller, Bull. Amer. Phys. Soc., Ser. I I 5, 265 (1960). 173 R. E. Blair and J. W. Easley, J. Appl. Phys. 31. 1772 (1960).

’”

8.

TUNNEL DIODES

601

been investigated with the aid of the tunnel diode: (a) The existence of electron-phonon (or electron-polaron, in type 111-V compounds) interaction in the tunnel diode semiconductor has been observed by noting, at liquid helium temperature, characteristic "kinks" in the forward voltage characteristic'68 [Vb > V,, Fig. 14(b)] or sharp spikes in a corresponding region of the d21,,/dVb2character is ti^.'^^.' 'O The voltages corresponding to these spikes are a measure of the energies of the various phonons in the semiconductor. (b) The effective mass of the charged carriers flowing through the diode junction has been determined from the value of the Bohr magneton, obtained via the de Haas-van Alphen effect by observing the frequency of current oscillations exhibited by the tunnel diode I- V characteristic in a strong magnetic field.' ' , ' 7 0 * 1 " (c) The tunneling probability has been determined by measuring the forward and backward components of diode current." (d) The width of the forbidden band gap has been measured' 1 1 6 5 , 1 7 1 at varying values of hydrostatic pressure on the diode junction. (e) The existence of deep traps in the forbidden band gap of the semiconductor has been verified and their energy levels located by noting the existence of subsidiary current maxima in the valley region of the currentvoltage characteristic,' 1 , 2 2 , 1 7 0 * 17 2 an approach known as "tunnel spectroscopy." I

i'

FIG.37. Basic tunnel diode switching circuit configuration.

602

H. C. OKEAN

VII. Tunnel Diode Applications in Pdse and Digital Circuits 20. GENERAL PROPERTIES

OF

TUNNEL DIODES IN DIGITAL CIRCUITS

a. Switching Properties of Tunnel Diodes

The tunnel diode, in addition to its wide application in sinusoidal circuits, is extremely useful as the active element in pulse and digital c i r c ~ i t s , ~ , ' l4~ " ~ due primarily to : (a) the extremely high-frequency, high-speed (subnanosecond) capability of the tunnel-diode junction, which is an order of magnitude faster than other existing switching devices ; (b) the existence of a highly nonlinear current-voltage characteristic, in which the junction voltage is a double-valued function of current over a considerable range of its positive region ( I , < I , < I , and V, > 0), thereby making binary (two-state) operation possible; and (c) the extremely low power levels requiring to switch between the two bias states. The above properties give rise to a large variety of large-signal, nonsinusoidal tunnel diode circuits generally classed as pulse, digital, or switching c i r c ~ i t s . ' ~ ~Th - ~ese ' ~include free-running and triggered waveform generator^,'^^-"^ binary logic circuits such as flip-flops and 96 sequenand memory tial circuits such as timing circuits and c i r ~ u i t s . ~ ~The ~ - ~circuit ' description and design procedure pertaining to the many variations of each of these circuit types are beyond the scope of this chapter. However, a general circuit description of some of the more common tunnel diode digital circuit functions will be presented following a description of the fundamental modes of tunnel diode switching operation and a presentation of the basic limitations on the corresponding switching parameters. I. Aleksander and R. W. Scarr, J. Brit. Inst. Radio Eng. 23, 177 (1962). J. C. Balder, Tvdschrift Ned. Rudiogenoot 26, 167 (1961). 1 7 6 W. F. Chow, IRE Trans. Electron. Computers EC-9,295 (1960). ' 7 7 R. S. Foote and W. V. Harrison, IRE Trans. Circuit Theory CT-8.468 (1961). 1 7 ' H. Fukui and T. Matsushima, J . Inst. Elec. Commun. Eng. (Japrrn)44,479 ( 1961). "9 A. Hemel, Proc. Nut. Electron. Con$ 17, 163 (1961). ''O G. B. Herzog, Onde Elect. 41, 370 (1961). M. H. Lewin, A. G. Samusenko, and A. W. Lo, Dig. 1960 fnr. Solid State Circuirs Con$, Philadelphia, Pennsylvania, p. 10 (1960). T. A. Rabson, Nucl. Instrum. Methods 12, 127 (1961). C. A. Renton and B. Rabinovici, Proc. IRE 50, 1648 (1962). M. Schuller and W. W. Gartner, Proc. IRE 49, 1268 (1961). J. J. Gibson, G. B. Herzog, H. S. Muller, and R. A. Powlus, Dig. 1962 inr. Solid State Circuits ConJ V, 54 (1962). E. Goto, K. Murata, K. Nakazawa, K. Nakagawa, T. Moto-oka, Y. Matsuoka, Y.Ishibashi, H. Ishida, T. Soma, and E. Wada, IRE Trans. Electron. Computers EC-9. 25 (1960). M. S. Axelrod, A. S. Farber, and D. E. Rosenheim, I B M J. Res. Develop. 6, 158 (1962). 74 75

8. TUNNEL

DIODES

603

h. Fundamental Modes ojswitching Operation

The fundamental modes of tunnel diode switching operation are defined in terms of the simple, basic switching circuit configuration of Fig. 37, in which it is assumed that a trigger pulse input available directly across the tunnel diode is capacitively coupled from a constant-current (high-impedance) source. In the most general case, the dc bias voltage is applied to the tunnel diode anode through resistor R , and inductor L,, whereas the tunnel diode cathode is connected to ground through resistor Rb'. The output of the switching circuit, containing the desired pulse waveform and/or digital information, is taken as the voltage across, or current flow through, load resistor R , across the tunnel diode. The switching modes to be considered are those exhibiting bistable, inverted bistable, monostable, and astable (relaxation oscillation) operation with respect to two operating points on the diode current-voltage characteristic, one in the "low-voltage region" ( V b < V,) and one in the "forwardvoltage region" (Vb > V,). The static load lines, dynamic load trajectories, and output waveforms corresponding to each of these modes of operation R. H. Bergman, I R E Trans. Electron. Computers EC-9, 430 (1960). W. N. Carr and A. G . Milnes, / R E Trcrns. Electron. Computers EC-11. 773 (1962). 1 9 0 P. Franzini, Rev. Sci. Instrum. 32, 1222 (1961). 19’ F. H. Mitchell. Jr.. Elect. Ind. 21. 105 (1962). 19’ Y. Komanaiya, Dig. IY63 I n t . Solid Sture Circuits Conf V1, 24 (1963). 193 J. F. Kruy, Dig. 1963 Int. Solid State Circuits Con/: VI. 28 ( I 963). 194 H. S. Miller and R. A. Powlus, R C A Reu. 23.497 (1962). 19' C. A. Renton and B. Rabinovici, I R E Trans. Electron. Computers EC-11. 213 (1962). 196 G . P. Sarrafian, IRE I n t . C o w . Rec. ( P i . 2) 9. 271 (1961). 197 B. E. Sear, IRE Trans. Circuit Theory 10. 48 (1963). 1 9 * J. Nagumo and M. Shimura, Proc. IRE 49, 1281 (1961). 199 E. Iwahashi, J. Inst. Elec. Commun. Engr. (Jupun)44,1199 (1961). R. A. Kaenel. Proc. IRE 49, 622 (1961). ' 0 1 L. U. Kibler, Proc. / R E 49. 1204 (1961). 'O' V. Uzunoglu, Proc. / R E 49. 1440 (I9611. ' 0 3 F. P. Heiman, Proc. / R E 49, 1215 (1961). '04 K. Hillman, G . T.& E . Res. Develop. J . 1. 87 (1961). '05 R. A. Kaenel, 1960 / R E Wescon. Con[>. Rec. ( P t . 3), 53 (1960). 'Oh B. Rabinovici, Proc. / R E 50,473 ( 1962). '07 P. Spiegel, / R E Int. Conr. Rec. (Pt. 2) 9, 164 (1961). ’08 G . J. Veth, Solid Stare Design 4, 30 ( 1963). ' O ' ) D. L. Berry and E. A. Fisch, Dig. 1961 /nr. Solid State Circuits Con/. IV. 112 (1961). 210 J. C. Miller, K. Li, and A. W. Low, Dig. Int. Solid Stare Circuits Con$, Philadelphia, Pennsyluania 111. 52 (1960). ’I1 J. Y. Payton, 1962 Wescon. Conrr. Rec. ( P t . 4), 2.1-1 (1962). ' 1 2 R. A. Kaenel, I R E Trans. Electron. Conipirters EC-10, 273 (1961). ' I 3 T. Kiyono, K. Ikeda, and H. Ichiki. / R E Trans. Electron. Computers EC-11, 791 (1962).

lS9

’I4

See P. S p i e g e ~ . ' ~ ~

604

H . C. OKEAN

are depicted in Fig. 38(a-d), respectively. A brief qualitative description of each of these modes is as follows. (a) In the bistable mode of operation (Lb,Rh‘ = 0), bias and load resistors Rb and R L and bias supply voltage E b b are chosen sufficiently large (R,, R L >> 1/GM; E b b >> V,) to yield an essentially constant-current bias supply, as exemplified by the near-constant-current static load line superimposed on the diode current-voltage characteristic [Fig. 38(a)]. Therefore, two stable static operating points exist, as defined by the intersections of the static load line with the positive-slope segments of the I-I/ characteristic at 1/b1, (1/bi < v,) and Vb2, (Vb2 > <),with 5 % E , b / R b . The negativeslope portion of the I-1/ characteristic (V, d 1/b d V,) is excluded as an available operating region, since the condition RbG, > 1 precludes the establishment of a stable operating point within it. Bistable switching occurs when a positive (negative) current pulse of amplitude I, > I, - I b l (I, > - I,) is applied to a tunnel diode initially biased at V b l , I b 1 ( & , I b 2 ) . The tunnel diode junction voltage, in response to + I, (IbZ - I,), is forced into the forward (low) instantaneous current voltage region, arriving and remaining at the second operating point v b z , 1 b 2 (Vb1, I b 1 ) upon removal of the trigger pulse. The dynamic currentvoltage trajectory and output waveform describing this switching process is shown in Fig. 38(a). The tunnel diode may be switched back to its initial operating point by application of a trigger pulse of opposite polarity. (b) The inverting bistable mode of operation (Lb = 0, R, = a)differs from the normal bistable mode by the inclusion of R,’ > 0 and the choice of E b b > V, and Rb > considerably lower than in the previous case, such that, for bistable operating points ( I b l , Vb1) and (IbZ, 1/b2), I b 2 2 I , is considerably less than I,,,, as shown by the load-line, I-1/ superimposition in Fig. 38(a).The switching process between the two operating points under positive and negative triggering, as defined by the trajectory in Fig. 38(a), is similar to that characterizing the normal bistable process. The output is taken across R;, resulting in the output waveform shown in Fig. 38(a). (c) Dynamic monostable switching ( R h ’ = 0, L b > 0) occurs when Rb > l/GM and Eh,, are chosen such that only one stable operating point, that is, only one intersection with the positive-slope I-V characteristic, is obtained, at or l/b2, I b 2 , as shown in Fig. 38(b). The monostable switching process occurs upon the application of a positive (negative) trigger pulse of amplitude I, > I, - I,, (I, > - I,) to a tunnel diode initially biased at I,, Vb, ,(I,,, &) as shown in the trajectory on Fig. 38(b). Junction voltage V, is initially forced into the forward (low) voltage region, arriving at the second operating point Vb2, I,, (Vb, ,I, I ) upon removal of the trigger, and simultaneously inducing an initial voltage IV,l = 1/b2 - Vb1 across L b . As

8.

605

TUNNEL DIODES

TIME-

(a)

TIME

--D

FIG.38. Trajectories and output waveforms of various modes of tunnel diode switching. (a) Bistable modes; bistable mode, V, is output for I,, = I , , , R,' = 0; inverting bistable mode, V( is output for I,, >> I,,, R , = cc~.(b) Monostable mode. (c) Astable mode.

IVJ decays toward its zero steady-state value, however, Vb and I , decrease through V,, I , (increase toward V,,, I & , at which point v b is forced into the low (forward) voltage region, inducing another voltage step across L b . As the latter decays toward zero, Vb and 1, increase (decrease) to the original

606

H. C. OKEAN

operating point Vb1, (VbZ, I,,), thereby completing the monostable cycle. The duration of the cycle is determined by the time constants associated with L b . The switching trajectories and output waveforms corresponding to stable bias point Vb,, and VbZ, I,, are presented in Fig. 38(b). (d) Astable oscillation (R,,' = 0, L b > 0) occurs when Rb > l/GM and Ebb are chosen so that no stable operating points exist on the positive-slope segments of the I-V characteristic but two unstable operating points exist in the negative-conductance region (V, < < V,) as shown in Fig. 38(c). However, as Ebb is turned on and V,, I b increase through (V,, I,), V, is forced I,. Then, the decay toward zero into the forward-voltage region at V,, I , of the voltage step (V, - V,) across Lb causes Vb, I, to decrease from V,, I , toward K , I , , a t which point Vb is forced into the low-voltage region at V,,I, I,. Finally, the decay of the second voltage step V, - V, across L b causes Vb, I b to increase from V,, I, through V,, I , , at which point the process repeats and a single cycle of oscillation is completed. The complete oscillation trajectory on the I-V characteristic and the corresponding output waveform are presented in Fig. 38(c).The period of oscillation varies essentially directly with &.

-

-

Two interesting additional variations on these modes of operation depart from the basic model of Fig. 37. The first utilizes a balanced pair of tunnel in a bistable switching circuit as shown in Fig. 39(a). The composite I-V characteristic and switching trajectory corresponding to this configuration is shown in Fig. 39(b), and the output waveform in Fig. 39(c). A variation of the astable relaxation oscillator utilizes a length of shortcircuited transmission line' 98 as shown in Fig. 40(a). Relaxation oscillation results from regenerative switching between states (Ib1, Vb1) and ( I b 2 , Vb2) brought about by propagation and rereflection of prior waveform components on the transmission-line length, as shown in the oscillation trajectory of Fig. 38(c), and the output waveform of Fig. 40(b). In this case, the period of oscillation is given by twice the line length-to-propagation velocity ratio. The switching parameters describing these processes include switching time, triggered or astable repetition period, switching current gain, and trigger power. The limitations imposed upon these parameters by the tunnel diode will be described in the following section. Fudamentaf Limits on Tunnel Diode Switching The basic limits on the basic tunnel diode switching parameters may be formulated in terms of the tunnel diode device properties by applying a piecewise linear transient analysis3 to the circuit configuration of Fig. 37. The details of the analysis tend to obscure the degree of dependence upon the tunnel diode parameters, and are therefore beyond the scope of this chapter. Therefore, only the pertinent results are presented as follows.

c.

8.

-E bb -V- o

607

TUNNEL DIODES

0

-vo-

"OoP-+

(C

1

FIG. 39. Balanced pair bistable tunnel diode switch. (a) Circuit schematic. (b) Switching trajectory; V, = E,, - Vbl = V,,, - Ebh.(c) Output waveform.

The switching time, that is, the time required to switch between the two bias states ( 1 b 1 , Vb1) and ( 1 b 2 , &,2) under constant-current triggering, is limited by the time required to charge terminal diode capacitance C, and is

608

H. C. OKEAN TRANSMISSION

Ebb

0

1 2

T

Z 2 T 5 T 2 2

-

1-

FIG.40. Tunnel diode relaxation oscillator utilizing short-circuited transmission-line section. (a) Circuit schematic; (b) output waveform.

expressible, with reference to Figs. 37 and 38, as

The general solution of Eq. (152), using a polynomial representation for I,,(Vb), is quite complicated and often can only be obtained numerically. However, an approximation which leads to the ultimate limitation imposed

8.

TUNNEL DIODES

609

by the diode parameters yields

under the assumptions: I , '2 I, over '2 1, over T2,1 ; R b , R,' >> and R , ; I,, + 1 1 1 '2 I , ; I,, + 112 '2 I,: Vb, % Vp; Vb2 % VF Vb > Vv at which I , = I,. Equation (153) shows that in order for a tunnel diode to have a potentially high switching speed capability, it must possess a high switching figure of merit lp/C, a high peak-to-valley ratio lp/lv, and a low case capacitance C , . Accordingly, a typical range of values of (qw)min valid for GaAs, Ge, and GaSb tunnel diodes, obtained from Table IV in the limit C, '2 0 and V, - Vp '2 2Vv, is given by Rb',

( 7&Jmin % 0.1-0.5

nsec.

( 154)

The difference in switching speed capability between diodes of the three semiconductor types is small because of the approximately linear relationship between Vv and Z,/C for various materials. A further twofold improvement in switching speed may be obtained by using a bistable balanced pair3 (Fig. 39). The triggered or astable repetition period TRcharacterizing the monostable or astable switching processes is the time required to complete a single switching cycle (Fig. 38), or TR= Tl,2 + Tz.l+ TZd+ TI,

+

TRx Tp,F

&,L

+ TF.v+ TL,,

in the monostable case;

in the astable case:

xi

( 155)

where T , jis the switching time from I b i , to I,,, xj(i# j = 1,2); Tp,F the switching time from I,, Vp to I,, V,: &.L the switching time from I,, Vv to I , , V,. TL,,the inductive rise time from I L ,VL to I,, V,; TF,v the inductive decay time from I,, V, to I,, V v : T'l,rthe inductive rise time from I,, VL to I , , , Vb1 or from I,,, V,, to I , , V,; and Tz,dthe inductive decay time from I b I , Vbz to I,, V, or from IF, VF to I,,, Vbz. The switching times T,,z, T 2 . , , Tp,F and &,L are obtainable from Eqs. (152) and (153), whereas the inductive rise and fall times TF,v, TL,,,T12,dr and T; are approximated from the piecewise-linear transient analysis ( R b ' = 0) as ,T

610

H. C. OKEAN

where L, = Lb

+ L, and

In the limit of satisfaction of the monostable and bistable biasing conditions, the dc load line is tangent to the current-voltage characteristic at V,, I,, SO that, for R, large,

+ KNM;

Rb

Ebb

VM

RFI

(liGM) + [(vF -

RLt ?Z(l/GM)

~/GM;

V~)/(lp -

+ (Vp/lp)

I,)]

(l/GM)[l

K ~ J ZM IM/GM, (l/GM)(l

+ kG),

(157)

+ (Vp/K)kil,

where k , = G,[(K - Vp)/(Ip- I,)] x 2.12 for quartic Gj(Vb), VF % 2Vv V,, lv/lp << 1. Therefore, substituting Eqs. (153), (156), and (157) in Eq. (155) in the limit of high-speed switching (Lb x 0),we obtain

where it has been assumed, in the logarithmic terms, that : V, x 6V, x 31/, M 4K,,. Hence, monostable triggering and astable relaxation oscillation can occur with repetition period TRof the order TRz 4(TsJrninx 0.4-2.0 nsec ,

(1 59)

and monostable and astable pulse durations Tp can be as short [Eqs. (156), (157)] as

(

Tp z (Tv,F)rnin x 0.45 l:;Iv;p) or T, x 0.03-0.1 5 nsec. Therefore, for short-duration, high-repetition-rate pulse generation, tunnel diodes with low L , and high lp/lvand Ip/C are desirable. In the limit of high speed switching, similar results are obtained with the transmission-line relaxation oscillator' 9 8 (Fig. 40). The maximum current gain experienced under tunnel diode' switching, given by

KI

z (1, - Iv)/l,,

(161)

also emphasizes the importance of utilizing diodes with high peak current and large peak-to-valley ratios. Clearly, the magnitude of K, is limited only

8.

611

TUNNEL DIODES

by the minimum separation of the bias points from I , or I , required to avoid astable operation, with values of K , sz 10 being perfectly reasonable. Finally, the amounts of peak pulse power required of the constant-current trigger to switch the tunnel diode from a low- to forward-voltage bias state and vice versa are given in terms of maximum switching current gain as

Therefore, switching powers of less than lOOpW are required for diodes of peak current as high as 10 mA, assuming K , z 10. For these values, typical z 20,30, and switching powers for each of three diode materials are : (Pt)2,1 60pW for GaSb, Ge, and GaAs diodes; (Pt)1,2 TZ 3.5,5, and 10 pW for GaSb, Ge, and GaAs diodes. These values of switching power are two to three orders of magnitude lower than those required to switch similar current levels in transistor digital circuits. The results of Eqs. (152H162) indicate that the switching-speed capability of tunnel diodes is essentially independent of the particular tunnel diode material. However, the required switching power is least for GaSb diodes and increases for Ge and GaAs diodes, as indicated by Eq. (162). On the other hand, GaAs diodes yield the largest output voltage swing, which is advantageous for high impedance loads. Therefore, the choice of diode material for switching application, usually confined to G e and GaAs, depends upon the particular circuit conditions. A general description of some of the more common digital circuit functions performed by tunnel diodes operated in the switching mode will be presented in the following section.

2 1. DIGITALCIRCUIT FUNCTIONS PERFORMED

BY

TUNNELDIODES

a. Logic Circuits

A logic gate is a digital circuit which provides a binary output (designated “0” or “1”) in response to a specified combination of n “0” or “1” binary inputs. The most common types of logic gates include the “AND” gate (‘‘1” output for n “ 1 ” inputs, “0” output otherwise), the “OR” gate ( 0 output for n “0” inputs, “1” output otherwise), the ‘ ‘ p out of n gate (“1” output, if at least p out of n inputs are “1,” “0” output otherwise), and the “majority” gate (“1” output for greater than n/2 inputs, “0” output otherwise). The tunnel diode bistable, inverting bistable, and monostable switching circuits may be used as “AND,” “OR,” or ‘ ‘ p out of n logic gates, whereas the bistable balanced pair circuit may be used as a “majority” gate. These

612

H. C . OKEAN

gates are all of the analog threshold type in which the currents f t j ( j = 1,2,. . . , n ) on n parallel inputs (Figs. 37, 39) are summed to form an overall trigger I , which activates the gate if it is of sufficient amplitude to exceed the built-in gate threshold AI. Thus, if “0” and “1” inputs are represented by currents of magnitude zero and I , respectively, the gate is triggered to provide a “1” output when the number m d n of “1” inputs is sufficient to satisfy I, = m l 2 AI, whereas, for m l < 111, the gate is quiescent and provides a “0” output. This differs from conventional diode threshold gates, which are triggered by the physical coincidence of a specified number of “1” inputs of varying amplitudes (above some minimum value) rather than by the magnitude of their sum. The general tunnel diode “AND,” “OR,” or ‘ ‘ p out of n” logic gate utilizes a bistable or monostable tunnel diode switch (Fig. 37) quiescently biased in the low-voltage region at (I,, , V b 1 ) . Then, for n parallel “0” or “1” current inputs of 0 or I respectively, the input-output characteristics of the various gates are : ml 2 ( I , -

Ihl)(l

m l < (I, -

Ibl)(l

+ 6) + 6)

for

“1” output,

for

“0” output,

(163)

where m = n for “AND” gate, m = 1 for “OR” gate, rn = p for “ p out of n” gate, and 6 << 1 is an overdrive factor that facilitates fast, precise triggering. The 0 and “I” outputs for each mode of tunnel diode switching employed in the gate are taken as currents through load resistance RL (or Rh‘ in the inverting bistable configuration) and are given by

for the direct bistable and monostable modes of operation, and

IL(“1”) = j h 2

%

I,,

jL(“0”) %

% i p

( 164b)

for the inverting bistable mode. The “majority” logic gate utilizes an input balanced pair of tunnel diodes, with n = 2m + 1 ( m = 1,2,. . .), as shown in Fig. 39(a). Here, the “0” and “1” inputs are characterized by negative and positive current pulses &I, respectively. The “0” and “1” output currents occur when the number of “1” inputs is less than and greater than m + 1, respectively, and are given by ZL(“1”) x 2Vp/RL,

IL(“0”) z -2Vp/RL.

(165)

The implementation of cascaded tunnel diode logic gates in logic systems requires adequate isolation between gate stages and a means of resetting each gate to its quiescent state for acceptance of new input information. The

8.

613

TUNNEL DIODES

former is usually provided by using conventional high-speed diodes of proper polarity in the interstage leads, whereas the latter is accomplished internally in monostable gates and by injection of external “clocking” signals in bistable gates. The use of tunnel diode analog threshold logic gates requires considerably tighter tolerances on input current magnitudes and on circuit component values than does that of conventional coincidence gates since the activation of the former requires a correct summation of m l = AI. However, this disadvantage is often more than offset by the high switching-speed capability and information-rate capacity of the tunnel diode gate. Finally, single-input bistable or monostable tunnel diode switches may be used to perform the logical functions relegated to conventional flip-flops with higher-speed capability and greater simplicity than the latter.

b. Waueform Generators The monostable and astable modes of tunnel diode switching operation [Figs. 37,38(b, c)] may be incorporated into various types of waveform generators much as is done with conventional flip-flops. In particular, the rectangular-wave output of a monostable or astable tunnel diode switch may be integrated or differentiated to yield a triggered or free-running ramp (sawtooth) waveform, or a bipolar impulse (sharp pulse) train, respectively. Alternatively, the inductive transition times may be adjusted to yield a direct output short-pulse waveform of high repetition rate, as indicated by Eqs. (15 8 H 160).As in other digital applications, tunnel diode waveform generators provide the advantages of potential high-speed operation and simplicity. c. Sequential Circuits

Monostable tunnel diode flip-flops [Figs. 37, 38(b)] may be used similarly to their conventional counterparts to evolve such sequential digital circuits3.203-208 as timing circuits, counters, frequency dividers, and shift registers. In particular, use of the monostable flip-flop in conjunction with a differentiator and an isolating diode yields a simple pulse-delay timing circuit as shown in Fig. 41(a), with the delay interval given by TF,”in Eq. (156). The same monostable flip-flop may be used as a staircase generator which can serve as a pulse counter or frequency divider, as shown in Fig. 41(b). d. Memory Circuits

The bistable tunnel diode flip-flop, by virtue of its high-speed, low-power switching capability, may be used as a binary memory element for application in a simple, compact, random-access memory array.3.209-2 The bistable tunnel diode switch constituting the basic memory cell is connected

’’

614

j h

It O

0

O

,

H. C. OKFAN

I-Jl

o}*

DIFFERENTIATED OUTPUT

T

0

0 1 -

*

I:

VO

DELAYED

[+

MONOSTABLE FLIP-FLOP

DlFFERE NTIATOR

ISOLATING DIODE

(a 1

1

ILU--L

0 T 2T

0 T 2 T nT

INPUT PULSE TRAIN

0 nT OUTPUT PULSE TRAIN

0 T 2T nT STAIRCASE WAVEFORM

nT

0

I+ pRF 0

=r

MONOSTABLE

.TD

FLIP-FLOP

v,

u n

-

--

,.

I L I

P,R ,F

=- n T

i

FIG.41. Sequential circuits utilizing tunnel diode flip-flops. (a) Pulse delay circuit; (b) pulse counter or frequency divider.

[Fig. 42(a)] to x and y control lines through large resistors R 1 and to a sensing winding through dc block C2 and sensing resistor R , . The M x N memory array using M N identical memory cells is presented in Fig. 42(b). The operation of this configuration as a destructive-readout, random-access memory may be summarized as follows, with reference to the bistable switching characteristics and waveforms of Fig. 38(a) : (a) Assume that each memory cell is characterized by a single bit of stored binary information in that it is biased in the “0” state (low-voltage operating point V,, ,Zb1)or in the “1” state (forward-voltage operating point Vb2, I,,), with Zbl = I,, = Zo. (b) To read out the bit of binary information stored in the rn x n

8.

TUNNEL DIODES

615

SENSING WINDING

y CONTROL LINES

FIG. 42. Destructive-readout tunnel diode memory array. (a) Individual memory cell ; (b) M x N array configuration.

memory cell in the array (in = 1 , 2 , . . . ,M ; n = 1,2,. . . , N ) , and to reset simultaneously the cell for the storage of a new bit of information, pulses applied to the mth x line and the nth y line are of sufficient magnitude to yield current pulses of magnitude 1,/2 at the x and y control inputs of the tunnel diodes in the mth row and the nth coiumn, respectively, of the array. The two coincident 1,/2 pulses on the x and y inputs to the m x n diode add to switch its operating point to zero bias ( V , = I , = 0), while simultaneously inducing a "readout" pulse on the sensing line proportional to V,, or V,,,

616

H. C. OKEAN

corresponding to its previous state “0” or “1,” respectively. The single 1,/2 pulses on the x or y inputs of the other m-row or n-column diodes switch their operating points from Vb] or Vb, at I , to Vil or V i 2 at 10/2, while simultaneously inducing relatively negligible pulses of amplitudes proportional to ( v b l - Vdl) or (Vb2 - T/d2) and below the readout threshold on the sensing line. (c) Upon removal of these “readout-and-reset’’ pulses, the m x n diode switches to the “0” state, while the other m-row and n-column diodes revert to their previous bias states. (d)To write in a new bit of information on the m x n memory cell, no additional inputs are required for the “0” state, whereas for the “1” state, positive pulses on the mth x and nth y lines, yielding 1,/2 current pulses at the corresponding diode control inputs, switch the m x n diode to the “1” state, but switch the other diodes to the VL1, V&, 1,/2 states. Upon removal of the “write” pulse, the latter revert to their original states, whereas the m x n diode remains in its new “1” state. Additional features may be incorporated into the tunnel diode memory array to provide it with a nondestructive-readout capability. In comparison with magnetic memory arrays, the tunnel diode array offers the advantages of extremely small size and high switching speed ( x 1-10 nsec/cycle), but requires dc standby power not necessary in magnetic memories. e. Miscellaneous

Other digital circuits utilizing tunnel diodes33212-214 include . analog-todigital converters, zero-crossing detectors, dc-to-ac power converters, and piecewise-linear function generators. In these applications as well as those discussed in the preceding sections, the tunnel diode offers the advantages of high-speed, low-power switching with simple, small-size circuitry. However, as with sinusoidal circuits, the stability problem is present, such that measures may have to be taken to suppress spurious oscillations, even under transient excursion through the tunnel diode negative-resistance region.

VIII. Present and Future Role of Tunnel Diodes

22. CIRCUITCAPABILITIES OF TUNNEL DIODES COMPARED WITH OTHER DEVICES We may assess the present and future role of tunnel diodes in sinusoidal and digital circuit applications by comparing the state of the art in tunnel diode performance in these applications with that obtainable from other devices. The first useful basis for comparison in sinusoidal applications is that of the maximum realizable device-limited frequency of operation.

8.

TUNNEL DIODES

617

Accordingly, the maximum practical operating frequencies of tunnel diodes are compared with those of other solid-state devices for application in amplifiers (A), oscillators (O), mixers (M), and detectors (D), as summarized as follows: Tunnel diodes: (A, 0, M) 25 GHz; (D) 75 GHz. Transistors: (A, 0)8 GHz. Schottky barrier diodes: (M, D) 100 GHz. Varactors : (A) 35 GHz. Avalanche diodes : (A, 0, M) 100 GHz. Bulk LSA devices: (A, 0, M ) 100 GHz. Therefore, the frequency capability of tunnel diodes in sinusoidal circuit applications extends into the millimeter-wave region and compares favorably with other microwave solid-state devices. To evaluate the importance of the tunnel diode amplifier in the field of rf and microwave amplification, we compare its capability as a low-level, roomtemperature, low-noise broadband amplifier with those of its principal solidstate competitors, the transistor amplifier and the room-temperature

FIG.43. Noise performance capabilities of uncooled microwave low-noise receivers

618

H. C. OKEAN

parametric amplifier.” Accordingly, the demonstrated noise-figure capabilities of these amplifier typei-are presented as functions of frequency in Fig. 43, along with those of tunnel diode and conventional varistor (pointcontact and Schottky-barrier-diode) mixers. In addition, representative single-stage gain-bandwidth capabilities of the three amplifier types may be summarized as in Table XIX. TABLE XIX ~~

Amplifier Tunnel diode Parametric Transistor

Frequency (GHz) 0.25-20

0.5-35 0.3-6

~~

~

Power gain (dB) Half-power fractional bandwidth 8-20

0.05-0.5

8-20

0.014.20 0.14.7

4-10

Finally, typical large-signal capabilities of the tunnel-diode, parametric, and transistor amplifiers are characterized by output 1-dB gain-compression levels of - 20, - 10, and 0 dBm, respectively. The above results indicate that the noise performance of tunnel diode amplifiers is inferior to that of uncooled parametric amplifiers by about 2-3 dB over the entire rf-to-microwave range, is inferior to that of transistor amplifiers below about 2 GHz, and is roughly equivalent to that of a highquality varistor mixer. This, along with the superior power-handling capability of the other amplifiers, leads to the conclusion that the main area of usefulness of tunnel diode amplifiers is as low-level, moderately low-noise preamplifiers for microwave receivers in the 2-20-GHz range, in which simplicity and wide-bandwidth rf power gain are of prime importance. The role of the tunnel diode mixer in comparison with conventional varistor mixers may be evaluated with reference to Fig. 43 and to their relative output saturation levels (- 60 dBm and - 10 dBm for tunnel diode mixers in the small- and large-pump modes, and 0 to + 1OdBm for conventional mixers). The inescapable conclusion is that the tunnel diode mixer is only of use in applications where the extreme simplicity, small size, and low power drain of the self-oscillating, small-pump, simultaneous rf and if. amplification mode configuration is of importance. Passive tunnel diode detectors, (back diode detectors), on the other hand, compete extremely favorably with conventional point-contact and hot-carrier detectors, as seen in their relative tangential-sensitivity versus frequency characteristics as presented in Fig. 44, and in their relatively equal passive large-signal saturation capability, characterized by upper square-law power levels of -20 to 0 dBm. The actively biased tunnel diode detector provides a further 1&20 dB I5

W. G. Matthei, 1967 IEEE lnt. Conu. Rec. ( P t . 7) 15, 7 (1967).

8.

z

I

W

(3

2

I IIIIII

VIDEO BANDWIDTH = 2 MHz

z

619

TUNNEL DIODES

-40

\

\ \

- 30

FIG.44. Tangential sensitivity of microwave detectors.

advantage in tangential sensitivity by virtue of its built-in rf and video amplification, but has a relatively low upper square-law power limit ( = - 30 dBm), comparable to the saturation level of tunnel diode amplifiers, and a comparably reduced bandwidth capability. In general, the tunnel diode detector is presently superior to all other rf-to-video envelope detectors over the 0.1-50 GHz range. The role of the tunnel diode oscillator in the area of solid-state rf and microwave sinusoidal generators is limited by its relatively low CW output power capability, compared with other presently available solid-state sources such as transistor oscillators, with and without varactor multipliers,avalanche diode oscillators, and bulk-effect oscillators. This is seen in the power-output-frequency capabilities2 of representative solid-state oscillators presented in Fig. 45, in which it is shown that the tunnel diode oscillator output power at a given frequency is one to two orders of magnitude below that obtainable from the other oscillator types. However, an immediate advantage of the tunnel diode oscillator is its potential high conversion efficiency and low dc voltage requirement (25-50 % and 0.2-0.5 V) compared with values obtained for the other oscillator types G . W. Fitzimmons, Microwave J. 11,45 (1968).

620

w

H. C . OKEAN

100

w

10

w

.

0 > w

Q

y

a

I W

5

cn

Lz

0

.

100 mW

I-

3

a

k 3 0 Lz

w

I O ~ W -

2a 9

0

IrnW-

0.1 rnW

-

I

2

5

10

20

50

0

FREQUENCY, G H z FIG.45. CW output power characteristics of microwave solid-state oscillators.

(efficiency < 10% and V,, > 6 V). An additional possible advantage of the tunnel diode oscillator is its relatively high spectral purity (excess noise temperature ratio 2-4), compared with the values of 3-5, 10, 100, and 1000 characterizing transitor oscillator-multiplier chains, bulk LSA, bulk transittime, and avalanche oscillators, respectively. The above comparison suggests that the role of the tunnel diode oscillator will be limited to applications where dc power and voltage are at a premium and where an rf or microwave signal of high spectral purity rather than high power level is required. Possible applications along these lines include use as a local oscillator for microwave mixers and as a frequency-locking source for high-power, noisier solid-state oscillators.’ 35-138 Finally, tunnel diodes will play a large role in switching and digital circuit applications due to their high switching speed (one to two orders ofmagnitude better than other devices) and low power drain.3-’7”214 In summary, it has been shown that the major present and future circuit applications of tunnel diodes are in low-noise, broadband, low-level microwave amplifiers in the 2-25-GHz frequency range, in ultrasensitive rf and

8.

TUNNEL DIODES

621

microwave low-level detectors at frequencies as high as 75 GHz, and in subnanosecond digital and switching circuits.

23. ROLEOF INTEGRATED CIRCUITTECHNOLOGY IN POSSIBLE TUNNEL DIODEAPPLICATIONS The rapid expansion of the integrated circuit technology into the fields of rf and microwave sinusoidal circuitry and ultrahigh-speed digital circuit applications has significant implications with respect to the maximum performance capabilities of tunnel diodes in the various circuit applications described in the previous sections. The term “integrated circuit” as used here is defined as having the following properties :

(a) The integrated circuit is essentially planar, consisting of thin or thick film and discrete circuit elements deposited and/or mounted on one or both faces of a dielectric or semi-insulating semiconductor substrate, resulting in hybrid or monolithic circuits, respectively. (b) In the monolithic integrated circuit, the conductor pattern is deposited on a semi-insulating semiconductor substrate, with discrete components such as semiconductor devices, resistors, and capacitors formed by preferentially doping the substrate over selected localized areas. (c) In the hybrid integrated circuit, the conductor and resistor patterns are deposited on a dielectric substrate, with discrete components such as semiconductor devices, ferrites, and capacitors bonded to the conductor pattern. (d) The substrate is enclosed in a metallic housing of geometry compatible with the desired transmission-line medium. Potential improvements in the the performance capabilities oftunnel diodes in the various circuit applications described in the preceding sections are obtainable by utilizing integrated circuit realizations in conjunction with unencapsulated tunnel diodes [Fig. 13(a-e)]. These improvements arise from the substantial reduction in the tunnel diode parasitics, particularly L , and C , , obtainable in an unencapsulated configuration, and from the ability to reduce the effect of the remaining parasitics by introducing external thin-film microcircuitry (stabilizing and tuning networks, etc.) in extremely close electrical proximity to the tunnel diode j u n ~ t i o n . ~ ~An , ~additional ’ . ~ ~ source of performance improvement in the integrated circuit realizations is the elimination of all superfluous connectors, transmission-line lengths, impedance transformations, etc., associated with the external circuitry?8.2 ” An estimate of the degree of reduction of tunnel diode parasitics obtainable with a n unencapsulated diode in an integrated circuit realization, and of the resulting degree of improvement in performance parameters in the various

”’ J. D. Welch, I E E E Trans. Microwave Theory Tech. MTT-18, 1077 (1970).

622

H . C . OKEAN

circuit applications, may be summarized as follows (Table IV) : (a) Series inductance L, may be reduced to about 0.1 nH and parallel capacitance C, to virtually zero in an unencapsulated diode as compared with minimum values of about 0.2 nH and 0.2 pF, respectively, in an encapsulated diode. (b) The virtual elimination of C , implies a potential increase in the ultimate diode-limited bandwidth capability of a tunnel diode amplifier, mixer, and detector by a factor as large as two, although limitations imposed by external circuit elements usually reduce this degree of improvement. (c) The elimination of C , also implies a corresponding improvement in the ultimate switching-speed capability of tunnel diode digital circuits, and an increase in the tunability range of tunnel diode oscillators. (d) The halving of L, makes it possible to double the diode negativeconductance level Gwfor a given degree of stability margin, thereby doubling the potential large-signal-handling capability of tunnel diode amplifiers, mixers, and detectors and the potential power output of tunnel diode oscillators. (e) The reduction of L,, elimination of C,, and ability to realize microminiature external biasing, stabilizing, and tuning circuits arbitrarily close t o the tunnel diode junction make it practical for the first time to realize an N x N tunnel diode array (Fig. 28),'06 which would increase by N 2 the power output capability of a tunnel diode oscillator and the large-signalhandling capability of tunnel diode amplifiers, mixers, and detectors. An e ~ a m p l e7,38 ~ ~of. ~an integrated tunnel diode device including stabilizing, bias isolation, and tuning circuitry in conjunction with a beam-lead tunnel diode and suitable for incorporation in an N x N tunnel diode array is shown in Fig. 46. A family of tunnel diode amplifiers utilizing these devices has been successfully con~tructed,~' yielding the results previously described in Table IX.

24. CONCLUSIONS The tunnel diode is a degenerately doped p-n junction device which, by virtue of its nonlinear negative resistance and low parasitic properties, has wide potential application in high-frequency sinusoidal circuits such as amplifiers, oscillators, converters, and detectors, and in high-speed pulse and digital circuits. The performance limitations on each of these circuit applications derive from the fundamental device parameters of the tunnel diode, as obtained from a consideration of the quantum-mechanical tunneling through the p-n junction and of the perturbing effects of the device parasitics. In particular, it has been shown that these device properties are primarily functions of the semiconductor material used (GaSb, Ge, GaAs) and the

8.

623

TUNNEL DIODES

w 0.01 in.

D -I

~TUNING+STABlLIZING+T

I

I

I

I cN

I

I

I

I

I I

LN I

(b) FIG. 46. Integrated tunnel diode device. (a) Physical configuration. (bj Circuit schematic (after Okeanss); C , = dc block; coo = I/(L,C,j”* >> l/(L,Cb)”z.

junction size or junction impedance level, Representative performance limitations imposed by these device parameters result in tunnel diode amplifiers of 3-6 dB noise figure and oscillators of better than 1 mW power output at frequencies up to 20 GHz, detectors of tangential sensitivity better than - 50 dBm up to 75 GHz, and subnanosecond switching and digital circuits. These levels of performance, already competitive, under certain conditions, with those obtainable from other solid-state devices in similar circuit functions, can be further improved by utilizing integrated circuit technology in conjunction with unencapsulated tunnel diodes.

624

H. C. OKEAN

ACKNOWLEDGMENTS The author wishes to express his appreciation to Airborne Instruments Laboratory for providing the facilities and environment necessary for this effort. In addition, he gratefully acknowledges many helpful discussions with S. Okwit, P. P. Lombardo, E. W. Sard, and A. N. Leber relative to the preparation of this manuscript. Finally, the author wishes to thank Miss P. Zinn, Miss N. McKee, Mrs. L. Kerner, and Mrs. J. Larsen for typing the manuscript and the Illustrating Group in the Publications Department of Airborne Instruments Laboratory for preparing the illustrations.

CHAPTER 9

Silicon Carbide Junction Devices Robert B . Campbell Hung-Chi Chang

I . INTRODUCTION. . . . . . . . . . . . I1 . SILICONCARBIDE AS A SEMICONDUCTOR MATERIAL. 1 . Physical and Chemical Properties . . . . . 2. Methods of Preparation . . . . . . . . 3 . Semiconductor Properties . . . . . . . . 111. DEVICETECHNIQUES. . . . . . . . . . 4 . Introduction . . . . . . . . . . . 5 . Diffusion . . . . . . . . . . . . 6 . Mechanical Processiri,q . . . . . . . . 7 . Etching . . . . . . . . . . . . . 8 . Oxidation . . . . . . . . . . . . 9 . Alloying . . . . . . . . . . . . . 10. Packaging . . . . . . . . . . . . I 1 . Devices Fabricated . . . . . . . . . . IV . SILICONCARBIDE POWERDIODES . . . . . . 12. Fabrication Techniques . . . . . . . . 13. Characteristics of Sic' Rectifiers . . . . . . 14. Future Improvements . . . . . . . . . V . p-n JUNCTION DETECTORS . . . . . . . . 15. General Considerations . . . . . . . . 16. Nuclear Particle Detectors . . . . . . . 17. Ultraoiolet Detectors . . . . . . . . v1 . ACTIVEDEVICES . . . . . . . . . . . I8 . Tunnel Diode . . . . . . . . . . . 19 . Junction-Gate Unipolar Transistor . . . . . v11. IRRADIATION EFFECTS. . . . . . . . . . VIII . LUMINESCENT DIODES. . . . . . . . . . IX . SUMMARY. . . . . . . . . . . . . . . . . . . . . . . . . . X . ADDENDUM

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625 626 626 621 633 634 634 634 635 636 639 641

642 64? 642 642 645 650 651 651 654 658 660 660 663 671 677 682 682

I . Introduction Silicon carbide (hereafter SIC) is perhaps the oldest (historically) semiconductor . Although in the last fifty years considerable use has been made of its abrasive properties. only in the past fifteen years has its potentialities

626

ROBERT B. CAMPBELL AND HUNG-CHI CHANG

as a semiconductor been exploited. The last survey in this field, the proceedings of a conference devoted to Sic,’ was published in 1960. It is the purpose of this chapter to discuss advances in SIC device technology since that time and to give a brief review of the device properties of this interesting semiconductor. Since S i c device properties are so intimately connected with its material properties, crystal growth and fabrication techniques will also be discussed.

11. Silicon Carbide as a Semiconductor Material 1. PHYSICAL AND CHEMICAL PROPERTIES

Silicon carbide exists in the hexagonal (a) and cubic (B) phases, with the a phase occurring in a variety of polytypes.’ The various forms of SIC have the largest energy gaps found in common semiconductor materials, ranging from 2.39 eV (cubic)to 3.33 eV (2H).The bonding of Si and C atoms is basically covalent, with about 12 ”/, ionic bonding. The structures are temperatureTABLE I LATTICECONSTANTS AND ENERGY GAPOF COMMON SIC POLYTYPES’ Lattice parameters (A) Energy gap (0°K)

Structure a

2H 4H 6H 33R 15R 21R 8H cubic-3c

C

3.09 3.09 3.0817

5.048 10.05 15.1 183

3.079 3.079

31.78 52.88

4.359

(W 3.33 3.26 3.02 3.01 2.986 2.86 2.8C2.90 2.39

~~~

a

From Refs. 2a-21

“Silicon Carbide-A High Temperature Semiconductor” (Proc. Conf. Silicon Carbide, Boston, 1959). Pergamon Press, New York, 1960. A. R. Verma, “Crystal Growth and Dislocations.” Buttenvorths, London, 1953. 2aL.Patrick, D. R. Hamilton, and W. J. Choyke, Phys. Rev. 143, 526 (1966). 2bH. R. Philipp and E. A. Taft, in “Silicon Carbide-A High Temperature Semiconductor” (Proc. Conf. Silicon Carbide, Boston, 1959), p. 366. Pergamon Press, New York, 1960. 2cA. Taylor and R. M. Jones, in “Silicon Carbide-A High Temperature Semiconductor” (Proc. Conf. Silicon Carbide, Boston, 1959), p. 147. Pergamon Press, New York, 1960. 2dW.J. Choyke, D. R. Hamilton, and L. Patrick, Phys. Rev. 133, A1 163 (1964). “W. J. Choyke, D. R. Hamilton, and L. Patrick, Phys. Rev. 139, A1262 (1965). zrD.R. Hamilton, L. Patrick, and W. J. Choyke, Phys. Rev. 138, A1472 (1965).

9.

SILICON CARBIDE JUNCTION DEVICES

627

stable below 1800°C and thus form a family of semiconductors useful for high-temperature electronic devices. Table I shows the lattice parameters and energy gap (0°K) for the common polytypes. Silicon carbide is a brittle material, with a hardness of 9 on the Mohs scale, ranking just below diamond. When grown by a vapor-phase technique, the crystals are generally hexagonal platelets. The platelets vary in color from blue-black (heavy p-type doping) to water white (pure or compensated) to dark green (n-type doping). The &phase SIC crystal, generally prepared from a supersaturated melt or by an epitaxial growth technique, are normally cubes or parallelepipeds with a clear yellow color. Silicon carbide is inert to nearly all laboratory reagents, although it is reported to hydrolyze slowly in phosphoric acid at 215”C.3 The usual techniques for chemical etching employ molten salt or salt mixtures (NaOH, Na,O, borax) at temperatures above 600°C. Electrolytic etching, suitable only for p-type material, and etching with gaseous chlorine near 1000°C are also widely used. The physical hardness and chemical inertness impose great restraints on device fabrication techniques. Although SIC technology has progressed along the same lines as that of silicon, many techniques had to be developed which were peculiar to Sic and which inevitably made the fabrication more difficult.

2. METHODSOF PREPARATION a. Sublimation The sublimation method uses the techniques of vaporization near 2500°C of an S i c charge into a cooler cavity with subsequent c ~ n d e n s a t i o n . ~ ~ Initially, the charge formed its own cavity, but more uniform crystals are This grown when a thin graphite cylinder is used in the center ofthe thin cylinder also reduces the number of nucleations so that fewer but more perfect crystals are grown. The crystals are grown as thin hexagonal platelets, perpendicular to the growth cavity as shown in Fig. 1. Variations of this growth cavity, using thinner or thicker sections,* graphite cloth backing,’ and uniform or randomly spaced holes,’ have all been studied, but with

’

R. C. Ellis, in “Silicon Carbide-A High Temperature Semiconductor” (Proc. Conf. Silicon Carbide, Boston, 1959),p. 420. Pergamon Press, New York, 1960. J. A. Lely, Ber. Deur. Keram. Ges. 32,299 (1955). D.R. Hamilton, in “Silicon Carbide-A High Temperature Semiconductor” (Proc. Conf. Silicon Carbide, Boston, 1959), p. 43. Pergamon Press, New York, 1960. H. C. Changer a/., unpublished work, 1966. H. C. Chang and L. J. Kroko, AIEE Paper 57-1131, Chicago, 1957; H. C. Chang, Semiconductor Products and Solid State Technology, p. 29. January (1960). H. C. Chang er a / . ,unpublished work, 1964.

628

ROBERT B. CAMPBELL AND HUNG-CHI CHANG

FIG. 1. Silicon carbide growth in sublimation furnace. (After K r ~ k o . ~ )

9. SILICON CARBIDE JUNCTION DEVICES

629

FIG.2. Representative grown-junction silicon carbide crystals (scale in inches).

only slight improvement over the original design. The mechanism for this crystal growth technique has been studied by Chang’.’ and Kroko’ in the USA and Pichuhin et a1.” in the USSR. Both use thermodynamic arguments which assume the growing crystal dissipates the heat of condensation of the incoming silicon and carbon vapor species by radiation to the cooler ends of the cavity. Bulk thermal conduction is assumed to have little or no effect. Both also calculate a relatively small temperature difference between the cool ends and the growing crystal, on the order of 0.1-5°C. To prepare high-purity S i c crystals by this technique requires prolonged outgassing and gettering at elevated temperature. The major impurities to be removed are nitrogen (as n-type dopant), aluminum, and boron. The latter two, both p-type dopants, are generally present in the starting material. The crystals having the highest purity are n-type with a donor concentration of 10 5-10 6cm-3. These crystals have electron mobilities of 3W600cm2 v-1

sec-‘

11

Doped crystals, or crystals containing pn junctions, can be prepared by adding the proper dopants to the ambient during growth.6-8.’2 The highest lo

l2

L. J. Kroko, J . Electrochem. Soc. 113,801 (1966). 1. G. Pichugin, N. A. Smirnova, Yu. M. Tairov, and D. A. Yas’kov, “Influence of Several Factors on the Growth and Nucleation of SIC Crystals,” p. 309. Vysokotemperaturnye Neorganicheskiye Soyedineniya, Akad. Sci. Ukr. SSR, 1965 (In Russian). D. L. Barrett and R.B. Campbell, J. Appl. Phys. 38,53, 1967. C. Goldberg and J. W. Ostroski, in “Silicon Carbide-A High Temperature Semiconductor” (Proc. Conf. Silicon Carbide, Boston, 1959), p. 453. Pergamon Press, New York, 1960.

630

ROBERT B. CAMPBELL AND HUNG-CHI CHANG

rating power rectifiers are still produced by this technique. Figure 2 shows representative grown-junction crystals. The color difference is due to the difference in doping.

b. Epitaxial Techniques The isoepitaxial growth of S i c on S i c substrates has been accomplished using the thermal reduction of mixtures of the carbon and silicon tetrac h l o r i d e ~ . ' ~ .It' ~was found that either the a or phase could be deposited on hexagonal S i c substrates, depending on the substrate temperature. The structural perfection of the epitaxial layer is determined by the substrate temperature, the growth rate, the purity of the growth apparatus, and reactants and surface condition of the substrate. It was found that the hexagonal phase was grown at substrate brightness temperatures from 1725°C to 1775"C, while the cubic phase was grown from 1660°C to 1700°C. I n situ etching of the S i c substrate prior to growth was found to be most effective in promoting high-quality growth. Hydrogen was generally used as an etchant at 1600°C.l 5 Equal molar percentages of CC1, and SiCl, are used in the growth process, with concentrations between 0.060 and 0.075 % required for the preferred growth rates of 0.5-0.8 p min-'. Chemical etching and optical microscopy show that defects in the grown layer are generally associated with defects in the substrate. Figure 3 shows this effect. In the as-grown layer, a noted defect is correlated with the defects in the substrate after etching. Polycrystalline Sic has been grown6 on a Sic substrate using dimethyldichlorosilane [(CH3)2SiC12]at substrate temperatures between 1400 and 1450°C. The growth rates were on the order of 10 p min- '. These layers were tested as mechanical supports of thin crystals during the precise fabrication techniques needed, for example, for transistor studies. Ryan and co-workers at Air Force Cambridge Research Laboratory have investigated the growth of S i c onto carbon substratesI6 using the hydrogen reduction of methyltrichlorosilane (CH3SiC13)(called the vaporliquid-solid growth). At 1500"C, a-Sic whiskers on the order of 5 mm long by 1 mm diameter were grown. These whiskers were of the relatively rare 2H polytype. After further purification of the CH,SiCl, and careful cleaning of the substrate, no whiskers were grown. This would indicate that the growth was nucleated by impurities, and, in fact, by seeding the substrate with pure l4

l5 l6

V. Jennings, A. Sommer, and H. C. Chang, J. Electrochem. SOC.113,825 (1964). R. B. Campbell and T. L. Chu, J . Electrochem. SOC.113,825 (1966). T. L. Chu and R. B. Campbell, J. Electrochem. SOC.112,955 (1965). C. E. Ryan, I. Berman, R. C. Marshall, D. P. Considine, and J. J. Hawley, J. CrystulGrowfh 1, 255 (1967).

9.

SILICON CARBIDE JUNCTION DEVICES

631

FIG. 3. Defects in silicon carbide epitaxial layer propagated from substrate crystal. (After Campbell and Chu.14)

and doped silicon, tantalum-doped gold, rhenium, chromium disilicide, chromium, and iron, they were able to grow the whiskers. The authors suggest that the cr-Sic form is essentially a defect structure and growth at 1500°C may be caused by a slight deficiency of carbon in the lattice. The impurities then stabilize the tl phase. This model is strengthened by the experiment using chromium disilicide, where only P-SiC crystals were grown. In this case, the chromium disilicide would tend to increase carbon solubility and lead to a more stoichiometric condition, and therefore, p-Sic.

c. Traveling Solvent Silicon carbide crystals have been grown together, and p n junctions formed by passing a heat zone through two SIC crystals separated by a solvent

632

ROBERT B. CAMPBELL AND HUNG-CHI CHANG

metal.’ The temperature gradient across the thin solvent zone causes dissolution a t both solvent-solid interfaces. However, the equilibrium solubility of S i c in the solvent is greater a t the hotter interface, and a concentration gradient is established. The solute, then, will diffuse across the liquid zone and precipitate onto the cooler crystal. In this way, two S i c crystals of dissimilar conductivity type can be grown together. Silicon and platinum were originally used as solvents, but best results were obtained using chromium. However, since Cr does not wet chemically cleaned S i c uniformly, the Sic-Cr-Sic sandwiches were prepared by evaporating a thin film of Cr onto Sic surfaces which had been heat-treated in vucuo at 120(r13OO0C.At temperatures of 1750”C,growth rates of 0.75 mm hr - were obtained. Microscopic examination of crystals show small metallic inclusions, presumably Cr. Properties of rectifiers prepared by this technique will be discussed later.

’

d. Solution Growth In the solution-growth technique, a small amount of S i c is dissolved in molten Si (or in some cases Fe or Cr).’’-’’ As the melt is slowly cooled, the S i c becomes less soluble and S i c crystals nucleate and grow in the crucible on prepared graphite substrates. The grown crystals are normally of the /3 phase. Improvements” in the crucible geometry and cooling rates have led to cubic crystals up to 4 mm across and 0.1 mm thick. With the use of pure starting materials and extensive degassing, quite pure crystals can be grown, and electron mobilities approaching 1000cm2V - ’ sec-’ at room temperature have been measured with a donor concentration near l O I 7 ~ m - ~ . The crystals are generally twinned parallel to the (111) faces, and etching (NaNO, + 10% Na,02 at 500°C) shows few discernible dislocations. X-ray topographs confirmed that the crystals are free of dislocations. In later work, the chromium-siIicon<arbon alloy system was studied,22 with maximum growth being observed in the 3 5 4 0 atomic % chromium region. Again the crystals grown were thin p-SiC laths. In an effort to grow larger crystals, the p-Sic crystals were rotated in the melt. Although temperature conditions were not optimum, some coherent growth was obtained. Somewhat similar results were obtained by Ryan16 using a silicon melt. 10% silicon In addition to growing p-Sic crystals from silicon and iron

+

l9

2o

’’

L. B. Griffiths and A. I. Mlavsky, J . Electrochem. SOC.111, 805 (1964). F. A. Halden, in “Silicon Carbide-A High Temperature Semiconductor” (Proc. Conf. Silicon Carbide, Boston, 1959), p. 115. Pergamon Press. New York. 1960. R. C. Ellis, in “Silicon Carbide-A High Temperature Semiconductor” (Proc. Conf. Silicon Carbide, Boston, 1959), p. 124. Pergamon Press, New York, 1960. R. W. Bartlett and R. A. Muller, unpublished work, 1967. W. E. Nelson, F. A. Halden, and A. Rosengreen, J. Appl. Phys. 37. 33 (1966). W. J. Silva, A. Rosengreen, and L. E. Marsh, unpublished work, 1967.

9.

SILICON CARBIDE JUNCTION DEVICES

633

melt, Knippenbergz3was able to prepare small a-Sic crystals (together with 8-Sic) using boron carbide-silicon carbide melts.

3. SEMICONDUCTOR PROPERTIES In this chapter, we will be concerned mainly with the 6H polytype of a-Sic. Table I1 gives some electrical and transport properties for this polytype TABLE 11

ELECTRICAL A N D TRANSPORT PROPERTIES OF 6 H &SIC Temperature (“C) Band gap (eV) Effective mass mp/*r,

m“h? Mobility (cmZV-’sec- ‘ ) PP

Pe

600 2.68

L”

- 65

2.9 1

1.2 0.6 1-10 10-100

Lifetime sec) Diffusion length (b)

LP

25 2.89

0.5- I 1-5

10-30 50600 0.014 1

4&80 100-1000

0.54 1-10

1-10 2-50

at three temperatures. The transport properties are related to the donor or acceptor concentration in the given sample, and thus these values are given as ranges. In all cases, the second number given is for relatively pure samples (n, or np z i016cm-3). The relatively short diffusion lengths and lifetimes (as compared to silicon) pose one of the problems in designing S i c devices. Thus, for example, S i c transistor studies have concentrated on majority-carrier devices, since the junction structure in minority-carrier devices would require base widths on the order of 1-2p. The only dopants which have been extensively studied in S i c are nitrogen (n-type) and aluminum (p-type). Chang and his co-workers studied the diffusion of aluminum into in 1960, with further work reported by Grifin 1966. Slack2’ and Kroko28 studied fiths2’ in 1965 and Vodakov et W. F. Knippenberg, Phillips Res. Rep. 18, 161 1 (1963). H. C . Chang, L. F. Wallace, and C. Z. LeMay, in “Silicon Carbide-A High Temperature Semiconductor” (Proc. Conf. Silicon Carbide, Boston, 1959). p. 496. Pergamon Press, New York. 1960. ” L. B. Griffiths, J . Appl. Phys. 36. 571 (1965). 26 Yu. A . Vodakov, E. N. Mokhov. and M. B. Reifman, Fiz. Tverd. Tela8. 1298 (1966)[English Transl. : Sou. Phys.-Sotid State 8, 1040 (1966)l. 27 G. A. Slack, J . Chem. Plrys. 42, 805 ( 1965). L. J. Kroko and A. G . Milnes, Solid Stare Electron. 9, 1125 (1966).

23

’*

634

ROBERT B. CAMPBELL AND HUNG-CHI CHANG

the diffusion of nitrogen into p-type Sic. This will be discussed in a later part of this chapter. Although few quantitative data are available, boron (p-type),6,26beryllium (p-t~pe),’~ arsenic (n-type): and phosphorus (n-type)6 have also been used as dopants. Boron and beryllium were diffused into Sic, while arsenic and phosphorus were incorporated into epitaxially grown layers.

In. Device Techniques 4. INTRODUCTION

The specific device techniques used will vary from device to device, and it is the purpose of this section to discuss fabrication methods in a general manner. In later sections, when the individual devices are described, any special techniques required will be discussed. 5. DIFFUSION Chang and c o - w ~ r k e r s studied ~~*~~ the diffusion of aluminum into Sic from 1750 to 210O0C, using both closed-tube and open-tube flowing gas techniques. Since the S i c crystals will decompose at these temperatures, it was necessary to provide an equilibrium pressure of Si and C vapor species around the crystals during the diffusion process. Griffiths” in 1965 ~ 1966 reported further diffusion experiments. The and Vodakov et ~ 1 . ’ in activation energy for the diffusion of aluminum into S i c found in these three studies agreed within 5% (-4.8 eV). found an anisotropy in the diffusion parallel and perChang et pendicular to the c-axis in the S i c crystals. This difference was sufficiently great that it could not be attributed to the differences in surface concentrations on the two planes, and therefore was probably due to the diffusion mechanism. In unpublished work, Canepa3’ and Roberts3’ refined the aluminum diffusion process while studying the fabrication of SIC neutron detectors and Sic unipolar transistors. Using a combination of infinite-source and finite-source diffusion techniques, Canepa3 was able to prepare junctions having depletion widths up to 25 p. Roberts3’ studied the relationship between the background concentration in the n-type Sic crystal and the diffusant surface concentration. Using crystals with background donor E. Violin and G. F. Kholuyanov, Fiz. Tuerd. Tela 6, 1696 (1964) [English Transl. : Sou. Phys.Solid State 6, 1331 (1964)l. 30 H. C. Chang, L. F. Wallace, and C. Z. LeMay, unpublished work, 1960. 3 1 P. C. Canepa, Westinghouse Research Laboratories, private communication, 1963. J. S. Roberts, Westinghouse Research Laboratories, private communication, 1964.

29

’’

9.

SILICON CARBIDE JUNCTION DEVICES

635

concentrations between 5 x 1 0 " ~ m - and ~ 5 x 1017cm-3,he found the maximum surface concentration of the aluminum diffusant to be 2 x 10'' cm-3 with an Al-saturated furnace and 5 % H, in the argon carrier gas, and thus confirmed the earlier results of Chang et Chang et diffused boron into S i c and concluded that the surface concentration of boron was higher than that of aluminum under the same conditions. Using the same experimental techniques as with Al, VodakovZ6 found the activation energy for the diffusion of boron into S i c to be 5.6eV. first reported on the diffusion of nitrogen into Sic. No quantitative data are given, but he concludes that, above 1500"C, appreciable diffusion of nitrogen into S i c does occur. In this work, all the samples were able to obtain type conversion of were granular Sic. Chang et p-type S i c crystals using a nitrogen ambient below 2000°C. Slackz7studied the diffusion of nitrogen into Sic at high temperatures (up to 2450°C) and high pressures (35 atm of nitrogen). A diffusion depth of 84 ,u in 4 hr was obtained under these conditions. The diffusion depth was determined by a color change in the crystal. Kroko and Milnes" in 1966 carried out further studies of nitrogen diffusion at temperatures between 2000°C and 2600°C at 1 atm nitrogen pressure. They concluded from the slope of the diffusion curve that the diffusion of nitrogen into SIC at these temperatures proceeds by a different (undefined)mechanism than the diffusion of aluminum at lower temperatures. PROCESSING6*' 6. MECHANICAL

The mechanical shaping of a hard crystal such as Sic is generally accomplished by scribing and breaking, lapping and polishing, ultrasonic cutting, and air abrasive cutting. Boron carbide and/or diamond are used for these purposes, since they are the only materials sufficiently hard. Scribing the crystal with a diamond point and breaking it along the scribe line is still used to some extent. As will be discussed later, a number of field-effect transistors were fabricated on a single crystal, and these transistors were separated by scribing. Obviously, this is best carried out on a scribing machine. Boron carbide mesh is used for removal of surface material from the S i c crystal. Table 111 gives the amount of material removed as a function of mesh size. To obtain mechanically smooth, flat surfaces, diamond polishing follows the lapping. 33

P. Carroll, in "Silicon Carbide-A High Temperature Semiconductor" (Proc. Conf. Silicon Carbide, Boston, 1959), p. 341. Pergamon Press, New York, 1960.

636

ROBERT B. CAMPBELL AND HUNG-CHI CHANG TABLE I11 RATEOF REMOVAL OF SIC

WITH

BORONCARBIDE

Boron carbide mesh

Amount of crystal removed“ ( p min- ’)

600 800

1.5 0.7 0.05

1000

Crystal cross section, 0.8 cm’; holding assembly weight, 75 gm ; lapping machine speed, 6.75 rpm.

Ultrasonic cutting (again using boron carbide) is used to obtain uniformsized devices as well as to prepare specified sample shapes, e.g., bridge-cut for Hall measurements. The grit size in the slurry is important, since large grit will cut too rapidly and chip the crystal, whereas small grit cuts too slowly; 320 mesh is generally used. To remove areas of the bulk crystal (e.g., shorted regions), air abrasive cutting may be used. This technique, not unlike a dentist’s drill, rapidly removes the S i c by chipping and erosion. Again, a 320 grit size has been found most suitable.’ All of these mechanical shaping operations inevitably leave surface and bulk damage in the crystal. Some studies have indicated that the damage may propagate into the crystal by microcracks to a depth of tens of microns. For optimum device performance, this damage must be removed, e.g., by chemical etching.

7. ETCHING The etching of S i c using molten salts was described in detail by F a ~ s t ~ ~ in 1959. In his paper, Faust describes the side of the Sic crystal that etches in a rough, “wormy” pattern, using molten salt, as the carbon side, and the side where the etch is smooth as the silicon side. This was confirmed by B r a ~ in k ~1965, ~ using X-ray techniques. Gabor and J e n n i n g ~ investigated ~~ the etching of S i c in a 1 : 1 molten mixture of stirred NaF and Na,SO,. Gases used for stirring were Ar, O,, and N,. They found that oxygen stirring increased the etch rate by a factor of 2-3, indicating that the gas takes some part in the chemical reaction. In this work, they found that stirring the melt resulted in the formation of etch pits on both sides of the crystal. 34

35 36

J. W. Faust, in “Silicon Carbide-A High Temperature Semiconductor” (Proc. Conf. Silicon Carbide, Boston, 1959), p. 403. Pergamon Press, New York, 1960. K. Brack, J . Appl. Phys. 36, 3560 (1965). T. Gabor and V. J . Jennings, J . Ekcfrochem. Tech. 3, 31 (1965).

9.

SILICON CARBIDE JUNCTION DEVICES

637

Brander37studied the addition of potassium nitrate to potassium hydroxide and found that etching occurred at temperatures as low as 500°C. For device fabrication, the molten-salt etch has many disadvantages. First, it is a very rapid etch, removing as much as 1-2 p of material per second. Second, no suitable etch mask exists for the molten salt; therefore, only planar structures can be etched this way. Finally, it is selective, since, as mentioned above, the two sides of the S i c crystal etch in different patterns. A preferred technique is to use gaseous etching, e.g., chlorine at 95CL 1050°C (Thibault3*) or chlorine and oxygen (Smith39 and Chang et ~ ~ 1 . ~ ~ 1 . Apparatus which can be used for the etching is shown in Fig. 4. The silicon carbide crystal to be etched is placed on the quartz boat sample holder, which is fused to a hollow quartz rod containing the monitoring thermocouple. The roller track facilitates the loading and unloading of the crystals in nonoxidizing conditions.

Gas exhousi

FIG.

4. Apparatus for chlorine etching of silicon carbide.

Flowmeters are used for monitoring the flow of CI,, O,, and Ar, with a flow rate range up to 500 cc min-'. The cross-sectional area of the reaction tube is 6-7 cm2: therefore, the linear velocity can be varied from 0 to 1 cm sec- which is within the laminar flow condition. The following etching reaction occurs in the reaction tube :

',

Sic

+ 2C1,

SiCI,

+ C.

To remove the carbon from the surface, oxygen is added to the etching reaction to form CO and CO,. R. W. Brander and A. L. Boughey, Brir. J. Appl. Phys. 18.905 (1967). N . W. Thibault, Amer. Mineralogist 29, 249 (1944). 39 R. C. Smith, J. Electrochem. Soc. 110, 184C (1963). 40 H . C. Chang, N. P. Formigoni, and J . S. Roberts, unpublished work, 1966. 37

38

638

ROBERT B. CAMPBELL AND HUNG-CHI CHANG

01

1073

1273

1173 log T,

1373

OK

FIG. 5. Etch rate of silicon carbide crystals in 85 % chlorine-15 % oxygen, 74 cc min-'.

The etching rates obtainable with this method are shown in Fig. 5. This curve indicates that the etch rate can be varied two orders of magnitude over a 300°C temperature range. By varying the oxygen content from 15% by volume to 8 5 % by volume, the etching rate can be increased by a factor of two. In fact, it was not possible to determine a maximum etch rate (as a function of the Cl,, 0, mixture), as the etching rate increases monotonically with the 0, concentration. However, when the 0, concentration exceeds 50% by volume, large amounts of SiOz are formed, leading to rough, irregular etch surface. Similarly, the concentration of 0, cannot be drastically reduced, in that (1) the pure chlorine etch leaves a pseudolattice of carbon on the surface, and (2) the undercutting of any pattern becomes more pronounced with a high chlorine concentration. It has been found most feasible to control the etch rate by mixing varying amounts of argon with the etchants. The argon retards the etching rate without negative side effects. The optimum concentration was found to be 45 cc min- C1, , 120 cc min- Ar, and 10 cc min- 0,. This composition gives an etching rate of 0.25 +_ 0.02pmin-' at 900"C, and is sufficiently fast that excessive times are not required for the etching,

'

9.

639

SILICON CARBIDE JUNCTION DEVICES

These etching rates were determined on the carbon face of the crystal. The etching rate on the silicon face is several orders of magnitude less. Electrolytic etching of SIC is accomplished using a dilute solution of HF in water and methyl alcohol. Concentration of 49% HF in methyl alcohol from 1 :50 to 1 :500 have been used successfully. The etching is carried out at 30°C under reverse bias with nominal etching currents from 20 to 50mA. This etch is specific for p-type material and has been used to etch mesa structures on p-n junctions and to determine junction depth. Brander and Boughey3' found that smooth surfaces on p-type material could be obtained using 40 % HF in distilled water solutions. The distilled water contained 10% HCOOH. They were also able to attack to a slight degree n-type material by forward biasing the p-n junction and injecting the necessary holes by avalanche breakdown at the surface or by illuminating with ultraviolet light. Oxidation of the Sic crystal and subsequent removal of the oxide in HF can also be considered as an etching technique. This is discussed in the next section. 8. OXIDATION

Silicon dioxide can be grown on S i c with steam oxidation in a manner similar to that used for the growth of SiO, on silicon crystals. Oxidation takes place at 90G1200"C in a carrier gas such as argon or oxygen saturated with water vapor around 100°C.The oxide is found to grow at a significantly different rate on the carbon face of the S i c surface as compared to the growth rate on the silicon face, the growth rate being approximately 10 times faster on the carbon face. In addition, the growth rate of the oxide on the carbon face of the S i c surface is significantly slower than that on silicon crystals, but appears to obey the same square law found for the growth rate on silicon. The growth rate of SiO, on Sic given in Table IV is from Chang ef TABLE IV GROWTHOF SIO, ON CARBONFACEOF SIC AT 1173°C AND ETCHING HF SOLUTION AT 25°C RATEOF SIO, WITH BUFFERED

Run no.

2 4

5 6

Oxidation time Carrier gas (hr) flow (120cc/min) 11.25 15.0

Ar Ar

11.0 1.7

Ar

0 2

Thickness

(A) 17,000

20,900 17,050 5400

Etching rate of S i 0 2 in buffered HF (A jmin) 980 860 875 830

640

ROBERT B. CAMPBELL A N D HUNG-CHI CHANG

The oxidation of Sic follows the same parabolic law as the oxidation of Si, namely, log d

=

log K

+

log t ,

where d is thickness in angstroms, t is the time in hours, and K (a constant was found to be 3900 for Sic as compared to 6900 for Si. This was in A/hr 'Iz) determined at 1173°C. Brander37 used between 10' and lo4 ppm pure 0, in distilled H,O at 1200°C and found a slightly slower oxidation rate on the carbon side than found in Table IV. He also found, however, that the silicon side oxidized only slightly less rapidly than the carbon side. Silicon dioxide layers can also be produced on S i c by pyrolytic deposition or sputtering techniques. The SiO, layer may be utilized in several ways in the fabrication of Sic devices:

(1) as a mask for the chlorine etch in preferentially etching Sic to create various mask patterns ; (2) as a positive means of identifying the polarity of the SIC crystal surface, i.e., the C or Si face for processing : (3) for passivation of the junction region of the diode; (4)for contact confinement in the contact-alloying process to prevent excessive spreading or penetration ; and (5) as a means of delineating p-type regions from n-type regions on a crystal (see Fig. 6). This last ( 5 ) is an important and new contribution to Sic technology. It has been found that the oxide grows at different rates on p- and n-type

regions on a single crystal of Sic, leading to a different coloration of these

FIG. 6. Delineation of diffused junction in silicon carbide by oxidation.

9.

SILICON CARBIDE JUNCTION DEVICES

641

regions as a result of the interferences of thin films. That the difference in coloration is a result of at least a difference in the oxide thickness has been shown by long oxidation of a surface with both p and n regions and a delineation of these regions after the removal of the oxide. This difference in oxidation has also been used in the delineation of junctions after edge polishing a crystal to determine the junction depth after aluminum diffusion. It has been noted that the oxidation coloration is different on the edge of the crystal from that on the carbon face of the same crystal, indicating that the oxidation rate is anisotropic in crystallographic direction in addition to the anisotropy of the two faces. The delineation is clear and has been checked and found to be in agreement with the junction delineation observed on the electrolytic etch. It has also been noted that the time of oxidation required for edge delineation (- 1175°C) is considerably longer (minimum of 90 min for rather poor delineation) that that required for delineation on the carbon face (30 min gives a very clear delineation), indicating that the difference in oxidation rates on p type from n type is probably considerably greater in the C direction than perpendicular to the C direction.

9. ALLOY~NG Alloy contacts to the S i c crystal should be ohmic at all temperatures, and, in themselves, of high conductivity. The molten alloy must wet and react with the S i c and, on solidification. form a stable, void-free interface region. In addition, the alloy should melt below 2000"C, or gross decomposition of the S i c crystal will occur during the alloying cycle. The completed bond should nearly match the thermal expansion of Sic so that undue strain is not put on either the crystal or the contact during thermal cycling. A number of different materials have been studied for ohmic contacts to Sic. Hall4' fused tungsten to S i c at 1900°C to form ohmic contacts to p-type Sic. On larger-area contacts, there is some indication that the interface between the tungsten and the S i c contains voids.42 The wetting may be improved by depositing thin films of silicon on both the tungsten and S i c surfaces before alloying.43 Van Daal et ~ 2 1 . : ~ Greebe,45 and Canepa et ~ 2 1 reported that Au l-lOO/, Ta formed ohmic contacts to n-type Sic, while

+

*' 42

43 44

45 46

R. N . Hall,J. Appl. Phys. 29. 1914 (1958). R. B. Campbell, unpublished work, 1965. H. C. Chang and J. W. Ostroski. unpublished work, 1959. H. J. van Daal, C. A. A. J. Greebe, W. F. Knippenberg, and J. J. Vink, J . Appl. Phvs. Suppl. 32, 2225 (1961). C. A. A. J. Greebe. Phillips Rrs. Rep. Suppl. I (1963). P. C. Canepa, P. Malinaric, R. B. Campbell, and J. W. Ostroski, ZEEE Trans. Nucl. Sci. NS-11,262 (1964).

. ~ ~

642

ROBERT B. CAMPBELL AND HUNG-CHI CHANG

the same alloy with a small amount of A1 added formed ohmic contacts to p-type Sic. The alloying temperature was near 1225°C. Gold-tantalum alloys have been used as ohmic contacts to the source, gate, and drain regions of an Sic unipolar transistor by sputtering alternate layers of gold and tantalum through a mask.40 Chang and his c ~ - w o r k e r sused ~ ~ *an~ ~ alloy of platinum and tin doped with either 2% gallium or antimony (for p-type or n-type Sic) at alloying temperatures near 1800°C. These contacts, as well as the gold-based alloys , ~ and Canepa et are all amenable to by Van Daal et ~ l . Greebe,45 thermal compression bonding of lead wires. Titanium- and tantalum-base alloys have been used with less success.4' These alloys react rapidly with the Sic crystal near the fusion temperature and form deep, void-filled interfaces. Taylor used Si doped with As or P for contacts to n-type On very-high-resistivity n-type or p-type Sic ( p > lo3 ohm-cm), semiconductor-grade Si is reported to form ohmic and low-resistivity contacts49 where the gold-base alloys do not.

10. PACKAGING Various package designs have been used for Sic devices. The main considerations are thermal expansion matching of the components and the Sic device. In devices operating between - 65°C and 500"C, unless thermal expansion relief is built into the package, crystal fracture can result. In high-power rectifiers, heat extraction is a prime consideration. As will be discussed, Sic rectifiers have forward voltages several times those of silicon; therefore, appreciable heat must be extracted. For light- or particle-detecting diodes, quartz or film windows must be provided. The specific encapsulations will be discussed under the various devices. 1 1. DEVICES FABRICATED In the remaining sections of this chapter, the devices which have been studied, together with their pertinent properties, will be discussed. Unless specifically noted otherwise, the devices described were fabricated from either the 6H or 15R polytypes.

IV. Silicon Carbide Power Diodes 12. FABRICATION TECHNIQUES a. Alloy Junctions The physical and chemical requirements for fused alloy junctions in S i c are the same as for ohmic contacts, except that a few per cent of the proper 47

J. W. Ostroski, unpublished work, 1960.

9.

SILICON CARRlDE JUNCTION DEVICES

643

dopant is added to the alloy. During fusion, the dopant forms a p-n junction, generally quite abrupt. Chang et a1.24used platinum-base alloys doped with boron or aluminum for fusing to n-type material. Taylor48 prepared Sic rectifiers by alloying pure aluminum into n-type Sic at 1700°C. During the alloying, a film of aluminum carbide (Al,C,) was formed between the contact and the crystal. It was suggested that the rectifying junction was really a junction between AI,C, and Sic. In general, alloy junctions in Sic exhibit a low forward voltage but a correspondingly low reverse voltage. Perhaps due to the low reverse capability (on the order of tens of volts), little work has been done in this field since the last review.’ b. Grown Junctions

To prepare grown junctions, p-type and n-type impurities are serially introduced into the growth cavity of the sublimation furnace. In general, it has been found most satisfactory to introduce the p-type dopant (generally aluminum or boron) into the Sic charge and, after the aluminum or boron has been totally or partially depleted, introduce nitrogen gas. Thus, the grown crystals have a bulk p-type core with an n-type shell. The time and rate of introduction of the nitrogen into the growth cavity determine, to a great extent, the final electrical properties of the junction. That is, they control the width of the intrinsic region, degree of compensation in the junction, etc.6 Some interesting experiments have been performed where the dopants were changed as a function of time.7-’ In this case, the aluminum (as AI,C,) and nitrogen were alternately added to the growth cavity so that, as a function of time, the crystals grew as n type, then p type, then n type, etc. Figure 7 shows a crystal with layers defined by nitrogen doping. The banded structure of the different conductivity types are clearly evident. Experiments of this type could be a powerful tool in growth-rate ~tudies.’.~ The properties of these rectifiers will be discussed in more detail later. c. DifSused Junctions Diffused junctions in Sic have been used almost exclusively for smallsignal or active devices. Although some research directed toward the preparation of power rectifiers by diffusion has been carried out,8 the results have generally been negative. Diffused junctions have been used, however, T. C. Taylor, in “Silicon Carbide- -A High Temperature Semiconductor” (Proc. Conf. Silicon Carbide, Boston, 1959), p. 431. Pergamon Press, New York, 1960. 49 R. W. Ure, Westinghouse Research Laboratories, private communication, 1965. 50 R. B. Campbell and H. C. Chang, Solid State Electron. 10, 953 (1967). 5 ’ See, for example, luminescent diode papers in Mater. Res. Bull. 4 (1969).

48

644

ROBERT B. CAMPBELL AND HUNG-CHI CHANG

FIG. 7. Silicon carbide crystal grown in alternate ambients of argon and nitrogen. (After Kroko.*)

for unipolar transistor^,^^.^^ neutron detectors,46ultraviolet light detectors:' and luminescent diode^.^ The diffused junctions generally exhibit a wide depletion width. In aluminum-diffused junctions, the depletion width estimated from capacitance measurements varied from 3 to 50p, depending on the diffusion technique and para meters.'^^^ Aluminum-diffused junctions characteristically show quite stable reverse voltages (up to 400V PIV), but also high forward voltages (perhaps as high as 1OOV at 20mA).x*46In the one study of nitrogen-diffused junctions,6 lower forward voltages were obtained, but at the expense of the reverse capability. The electrical characteristics of boron-diffused junctions have been reported to have a greater temperature dependence than do aluminumdiffused junctions.30 d. Epitaxial Junctions

The epitaxial method of growth has been described in Section 2. The epitaxial layers can be doped either n type or p type during growth using

9.

SILICON CARBIDE JUNCTION DEVICES

645

nitrogen, arsine, or phosphine for n-type layers and diborane for p-type layers. Some preliminary Hall measurements showed that phosphorusdoped layers exhibited high mobilities." Rectifiers prepared from epitaxial junctions have generally exhibited low forward voltages (1.5-2.5V at 1.0-5.0A) with a reverse capability of 50 V (these measurements at 500°C). The reason for the somewhat low reverse capability of epitaxial junctions has never been satisfactorily explained. Epitaxial layers of high quality with no grown structural faults have been grown. Perhaps a more rigorous study of the junction structure and gradient would supply an answer. e. Processing for SpeciJic Structurt> Silicon carbide junctions have been processed into various structures, depending on their ultimate application. A mesa structure prepared by electrolytic etching of p-type material has been used for the S i c detectors. Since, as mentioned, the n-type material is not attacked, the etching action stops at the junction and a well-formed mesa can be delineated. Silicon carbide-junction rectifiers and diffused structures are more simply fabricated by removing the shorting edges (e.g., by ultrasonic cutting) and using an etch, either chemical, electrolytic, or gaseous, to remove damaged material. At this point, the blue microplasma breakdown in the junction can be used to find further damaged regions or imperfect structural areas. Ifthe junction is reverse-biased, bright blue spots appear at thedamaged area. These spots are small local regions of high reverse current and can generally be associated with structural imperfections. These areas can be mechanically removed and thus the reverse capability of the diode increased. The fabrication techniques used for the active devices are quite long and complicated and will be described in detail in that section.

13. CHARACTERISTICS OF S i c RECTIFIERS a. Current-Voltage Characteristics Figures 8 and 9 show the I-V properties of a S i c rectifier prepared by the grown-junction method, operating at 1 A and 500"C.52The forward voltages ofthese devices, even at 500°C are always larger than 1 V (half-wave average). Thus far, rectifiers operating up to 10 A have been and specially processed, low-current devices have exhibited reverse capability of 600 V PIV.'3 The reverse characteristics of S i c rectifiers generally show a "soft" breakover, rather than the avalanche breakdown sometimes noted in silicon. This is generally attributed to the carrier generation mechanism at

'' H.C . Chang ef al., unpublished work. 1964. 53

H . S. Berrnan, Westinghouse Astronuclear Laboratory, unpublished work, 1968.

646

ROBERT B. CAMPBELL AND HUNG-CHI CHANG

7

1000

Q

x

t

C

Y

" 7

u) W

W

E! m W

e

>

O

W

0 I

-

L

0

I

I

I

40

80

I

I

I

I

i

120

160

200

240

280

Peak reverse voltage,

V

FIG. 8. Reverse characteristics of a silicon carbide grown-junction rectifier.

the junction and to local areas breaking down at different voltages, so that the total effect is one of gradually increasing reverse current. Figures 10 and 11 show the I-Vcharacteristics of a larger-current S i c device.54 Rectifying junctions have been prepared using the traveling solvent technique with chromium.",55 Although the reverse breakdown occurs at a low voltage (6-15V PIV), Griffiths" and Griffiths and Mlavsky" were able to interpret the junction capacitance at zero bias and the forward, dark I-V characteristics in terms of the diffusion of the major dopants across the junction resulting in compensation.

b. Encapsulations The basic requirements of the encapsulation are to provide protection of the rectifier package components from the operating environment. The s4 55

H. C. Chang and J. Ostroski, unpublished work, 1966. L. B. Griffiths, J . Appl. Phys. 36,571 (1965).

9.

SILICON CARBIDE JUNCTION DEVICES

647

FIG. 9. Forward characteristics of the silicon carbide grown-junction rectifier of Fig. 8

main concern is the tungsten which is generally used as a base plate to the S i c crystal, which must be protected from oxidation. Aiso, since the rectifier is to be used from -65°C to 5OO0C, the encapsulation must provide for the differing thermal expansions of the rectifier components. The realization of these requirements is a study in compromises. One package which has been successful is shown in Fig. 12.' In this package, the base is nickel and the header is a composite assembly consisting of a 96% alumina tube gold-brazed to a weld flange of nickel. The upper part of the header has a nickel cap gold-brazed to the alumina, with a nickel collar joined to the cap using 950°C (18Ni-82Au) solder; joined to this collar by 780°C (BT) solder is the silver pinchoff tube. Another type of package has been designed that is essentially a zero In this package, copper and tungsten inserts are used inside expansion a ceramic-nickel package. The lengths of the copper and tungsten are adjusted so that their expansion nearly matches that of the nickekeramic capsule. A nickel flange acts as a spring member to take up any small deviations.

648

ROBERT B. CAMPBELL AND HUNG-CHI CHANG 300

> a; 200 m

c

0

s W

p1 1 0 W

100

a

0

Half-wave average forward current, A

FIG. 10. Characteristics of a silicon carbide grown-junction rectifier of larger current than that of Figs. 8 and 9. Unit L-70, 500°C; IR (rnA): (010.5, ( 0 )1.0, ( A ) 2.0. (0) 3.0, ( W 5.0.( 0 )10.0.

0 H o l f - w a v e average forward voltage, V

FIG. 11. Forward characteristics of the silicon carbide grown-junction rectifier of Fig. 10. Unit L-70; (0) 300"C,(0) 500°C.

9.

SILICON CARBIDE JUNCTION DEVICES

649

FIG. 12. Silicon carbide rectifier housing.

As with all power-handling devices, it is important to transfer efficiently the internally generated heat to the external ambiant. In the case of silicon carbide power rectifiers, the problem of transporting heat from the devices is particularly difficult because the thermal conductivity of suitable metals is greatly reduced at the high operating temperature. With the device case at 500"C, internal temperatures are significantly higher when large forward currents are conducted. There are relatively few materials with appropriate chemical and physical properties which are usable as components in the device assembly at these temperatures. Many appealing metals(Pt, Rh, etc.) are far too costly, and most otherwise acceptable materials have thermal conductivities which are relatively low at room temperature and which decrease rapidly as temperature rises. The thermal impedance, defined as the ratio of the case-to-junction temperature difference to the total power input, has been determined for the package shown in Fig. 12. The junction temperature was measured by the forward drop method. A curve of the thermal impedance versus case temperature is shown in Fig. 13.

650

ROBERT B. CAMPBELL AND HUNG-CHI CHANG Case temperature,

O C

15-

P "

aJ C U 0

g l0E -

n

n

E

400

500

Case temperature,

600

700 800

"K

FIG.13. Thermal impedance of silicon carbide rectifier.

Thermal impedances from 3 to 8°C W - ' have been measured on S i c devices of the type shown. A computed thermal impedance value, obtained by considering the thermal conductivity of the various components in the encapsulation, was in good agreement with the experimental value, being about 34°C W-'.' c. Life Testing

Although very limited life-test data have been obtained for the 10-A devices, a few devices have been operated at several amperes for up to 200 hr at 500°C in air with no change in electrical characteristics. One-ampere devices using approximately the same capsule design have been successfully life-tested for 1000 h at 500°C. 14. FUTURE IMPROVEMENTS

At the present time, S i c rectifiers have been fabricated with a forward current capability of 10 A (half-wave average). It would appear that greatly increased current capability is limited only by the need for (1) large, perfect junction crystals, and (2) an efficient encapsulation. The latter is needed to

9.

651

SILICON CARBIDE JUNCTION DEVICES

extract the heat generated in the junction, which in a 50-A unit may be as high as 300 W. This would require quite efficient heat-sinking. Higher peak reverse voltages should be obtainable when an ideal p-i-n structure can be fabricated. Chang et al. have shown that with such a structure a 600V PIV can be obtained with a relatively narrow intrinsic-layer width ( 2-3 pm), which would also permit a low forward voltage.6

-

V. p-n Junction Detectors 15. GENERAL CONSIDERATIONS

The operation of a p-n junction nuclear-particle or photon detector depends on the collection of electron-hole pairs produced by the ionizing particle or photon as it passes through the detector. The electron-hole pairs are separated in the junction region, collected, and give rise to a charge or voltage pulse. a. Charged-Particle Detector

The ionizing particle passing through the detector loses a small amount of energy for each electron-hole pair produced (for SIC, about 10 eV/pair). lO-’sec) before These pairs have a relatively short lifetime (for Sic, they recombine. Thus, any pairs created outside the junction region may well recombine before they are collected, since they must diffuse to the junction region (a relatively slow process) before they are accelerated by the p-n junction electric field and collected. These conditions on pair creation and collection place certain restrictions on the junction design of the detecting device. First, the surface layer (lowfield region) through which the particle must pass should be narrow so that the particle loses no appreciable energy. Second, the depletion region where there are the same number of electrons in the conduction b a n i a n d holes in the valence band (intrinsic material) should be nearly as thick as the range of the ionizing particle in the material, thus effectively stopping the particle in the high-field region. The width of the depletion region can be controlled by the technique used to prepare the junction (e.g., diffusion parameters), or by the application of a reverse voltage on the junction. When an external voltage is applied across the depletion region, the electron and hole distributions, which are determined by the electric field and the electron and hole diffusion coefficients, change. The net result is that the depletion region widens and the electric field at the junction increases. For a given particle detector, these two factors result in a lower detector capacitance, and if the widened depletion region

-

652

ROBERT B. CAMPBELL AND HUNG-CHI CHANG

more nearly matched the range of the ionizing particle, increased counting and collection efficiency. b. Ultraviolet Detectors

Silicon photovoltaic diodes have been developed for the detection of infrared and visible radiation. These diodes exhibit a sharp drop in response as the wavelength of the incident light approaches the ultraviolet region, with most detectors showing negligible response below 3000A. This decreasing response is due to the increase in the absorption coefficient with decreasing wavelength. A large absorption coefficient indicates that nearly all the light will be absorbed at the surface of the device and electron-hole pairs generated may be at a great distance from the pn junction. Thus, surface effects, such as carrier recombination, will decrease the response of the detector. Silicon carbide, with a band gap near 3.0 eV, has an absorption coefficient several orders of magnitude less than that of Si at 4000 A, and therefore surface effects would not be so important. Detectors have been prepared from S i c and these devices were found to have spectral responses which peaked in the ultraviolet region and which could be shifted by varying the junction depth. A simple theoretical model was originally d e r i ~ e d ~which ~ ~ ~quanti" tatively explained the dependence of the peak wavelength on the junction depth and the depletion width of the diode. Considered in this model were the wavelengths and temperature dependences of the absorption coefficient in Sic below the band edge. An approximation was made that at the peak response wavelength the total number of electron-hole pairs generated in the depletion layer is a maximum for a given intensity of transmitted radiation at the surface. Figure 14 shows the variation of peak-response wavelength calculated from this model. The curves are shown for values of the effective depletion width w from 1 to lop. (The experimental data will be discussed later.) This simple model proved to be adequate for photovoltaic diodes fabricated from materials having very short carrier diffusion lengths and lifetimes and under the conditions that the junction depth is greater and the depletion layer not much greater than the carrier diffusion length. The variation of the peak-response wavelength with temperature was not adequately explained with this model, which took into account only the temperature variation of the absorption coefficient, i.e., the experimental value of the rate of increase of the peak wavelength was 2-3 times that calculated. A more rigorous calculation was later carried out which included such sb

H. C. Chang and R. B. Campbell, unpublished work, 1965.

9.

653

SILICON CARBIDE JUNCTION DEVICES

T

- 0

2800

3000

3200

I

1

I

3400

3600

3800

P e a k wavelength,

I 4000

I 4200

A

FIG. 14. Peak spectral response of silicon carbide junction diode as a function of junction depth. (After Campbell and Chang.50).

parameters as carrier lifetime, carrier mobility, surface recombination velocity, and their temperature dependen~e.~’*~* This treatment considered the junction to be close to a p-i-n structure. Greebe4’ has treated a symmetrical p i - n structure by assuming that the generation of carriers was uniform throughout the system and that the thicknesses of the p-type and n-type layers approached infinity. Chang and Campbell5’ and Campbell 57 58

H. C. Chang, Westinghouse Research Laboratories, private communication. 1967. R. B. Campbell and H. C. Chang, Paper Y.1, Int. Electron Deuices Meeting, Washington, October 2967 (to be published).

654

ROBERT B. CAMPBELL AND HUNG-CHI CHANG

and Changs8, assumed a more realistic, asymmetrical junction, and the calculated peak-response wavelength and its temperature dependence agreed quite well with the experimental data.

16. NUCLEAR PARTICLE DETECTORS Silicon carbide structures have been prepared that are capable of detecting a-particles up to 700°C and, with the addition of a conversion layer, thermal neutrons have been counted.46 For these detectors, n-type S i c crystals grown by the sublimation techn i q ~ eand ~ ? doped ~ with nitrogen to a level of about 10l6cm-3 were used. To prepare the detector structure, aluminum was diffused into these n-type crystals, producing a p-type layer with the diffusion parameters set to produce a graded-junction structure. After the edges of the diffused crystal were removed, an electrolytic etching procedure was used to produce a mesa structure. The electrically poorer of the two p n junctions was removed by lapping. The remaining p-n junction was then processed until the p-type layer was about 6 8 p thick. At this point, a noble-metal-alloy top contact and a tungsten base tab were soldered to the crystal and chemical etching was used to reduce the junction depth to the desired value. Precautions were taken so that the surface leakage current was minimized, although it has been reported that such leakage current has no deleterious effect on the counting characteristics of the diode.59 Figure 15 shows the room-temperature a-particle spectra of one of these detectors at a series of reverse voltages. As can be seen, the collection efficiency of this diode, which is measured by the distance along the abscissa, appears to saturate at the higher voltages, thus indicating nearly 100% collection efficiency. Figure 16 shows the a-particle spectra of another diode as a function of reverse voltage and temperature. The collection efficiency does not change greatly between 25 and 400°C. A correlation of the electrical and physical parameters of the diode with their counting behavior indicated that crystals of high resistivity and purity are needed. This criterion is understandable, in that low-resistivity crystals usually contain many impurities which act as trapping or recombination centers, effectively reducing the diffusion length (lifetime)of the electron-hole pairs. This would lead to a counter with a low charge-collection efficiency. The junction profile and the junction depletion width were determined from capacitance-voltage curves. When these data were compared to the counting characteristics, it was noted that the junction should neither be abrupt nor highly graded. The inverse of the capacitance per unit area is a measure of the depletion width and was near 102cm2pF-' for the better 59

W. Hansen and E. S. Goulding, NSS Rep. No. 32, 1962 (Proc. Con5 Semiconductor Nuclear Particle Detectors, Asheville, North Carolina, September 1960).

9.

SILICON CARBIDE JUNCTION DEVICES

655

+ f D

.-

I

Pulse height (relative units)

FIG. 15. a-Particle counting characteristics of silicon carbide junction diode at 30°C and noted reverse voltages. (After Canepa er ~ 1 . ~ ~ )

diodes. This was interpreted as follows : For a very narrow depletion width, say 1 p or less, an insufficient electron-hole pair production density in this region results in a diode of poor collection efficiency. For a very wide depletion width, the pair production in this region may well be reduced by recombination before the pairs are swept out. The reverse characteristics of the diode were important, in that the effective collection efficiency is related to the externally applied voltage. Diodes exhibiting excessive reverse leakage inherently generate electrical noise at low reverse voltages. Thus, in diodes which have this characteristic, any counting properties may very well be obscured in the noise level. The junction structure was further investigated by using the scanning electron microscope. Figure 17 shows a micrograph of one of these diodes obtained in this way. In the photograph, the secondary and photovoltage scans are superimposed. The rather fine line going around the edge of the diode is the position of the pn junction. The small black spots on top of the surface are etch pits which penetrate deep into the p region, occasionally

656

ROBERT B. CAMPBELL AND HUNG-CHI CHANG

o v

20

v

40 V

80

v

FIG.16. Alpha-particle spectra of silicon carbide junction diode as a function of temperature at several reverse voltages. (After Canepa et

going into the junction structure. This diode had relatively poor counting efficiency. As can be seen, the diffusion front in the Sic crystal is quite planar; however, the etch pits on the diode surface cause variations in the junction depth. If the density of these etch pits is high, several very definite effects on detector properties occur, i.e., decreased spectral resolution, increased junction leakage, etc. The ability of these diodes to count neutrons was also studied. This was done by using a converting film of 235Uover the detector and subjecting it to a thermal neutron flux obtained through the use of a Van de Graaff generator. The fission products of 235Uirradiated with thermal neutrons are not unique but have a distribution with two peaks occurring in the fissionproduct mass-distribution curve. The total energy liberated is 157 MeV, with peaks at 66 and 91 MeV. Figure 18 shows a comparison of the a-particle

9.

SILICON CARBIDE JUNCTION DEVICES

657

FIG. 17. Photovoltage scan of silicon carbide junction diode. (After Canepa ef a/.46)

and fission-product spectra for an SIC diode. The fission-product spectrum is very close to that predicted from the a-particle response, taking into account the different distributions in the incident energy. (As may be seen from this figure, the abscissa and ordinate are of different scale.) The SIC diode, which had a peaked a-spectrum, also shows a peak fission-product spectrum; in fact, the fission spectrum of the diode resolves the double peaks. Superposition of the background spectrum for both diodes shows that the low-amplitude monotonic portion of the spectrum is actually due to fission products rather than noise. Ferber and Hamilton6' have studied the use of these detectors in a reactor for flux mapping. They concluded that the S i c detectors could be used over a dynamic flux range of at least lo4, with the limits determined by diode size and neutron conversion layer thickness (in this case, a 235Ufoil). Radiation-damage studies on these detectors will be described later. 6o

R. R. Ferber and G. N. Hamilton. Westinghouse Research Laboratories, private communication, 1965.

658

ROBERT B. CAMPBELL AND HUNG-CHI CHANG

a-Particle energy, MeV 0

t

0.5

I .o

1.5

I

I

I

Fission-products spectrum

a-Particle spectrum expanded 10x along

background noise Fission spectrum background noise 5.0

0

10.0

15.0

Fission energy, MeV

FIG. 18. Comparison of a-particle and fission-fragment counting of silicon carbide junction diode. (After Canepa er

17. ULTRAVIOLET DETECTORS

The crystal used to prepare the ultraviolet detectors were grown by the sublimation The resistivity and Hall constant of the crystals were measured as a function of temperature using the van der Pauw technique.61 Representative electrical properties of crystals used in this study are given in Table V. TABLE V REPRESENTATIVE ELECTRICAL PROPERTIES OF U-TYPESIC CRYSTALS

61

Measurement temp. (“K)

Resistivity (ohm-cm)

300

0.10

800

0.43

Hall mobility Carrierconcentration (cm’ V - ’ sec-’) ( x lo” 360 55

L. J. van der Pauw, Phillips Res. Rep. 13, 1 (1958).

1.8 2.7

9.

659

SILICON CARBIDE JUNCTION DEVICES

0 I6

0 14

0 12

-300 K; A, =3600

a

0 IC

> m 0 0

r, ooe 0 > c

.c 0

a 0 OE

00 4

0 02

A,

,800"K,

=

3900 8

C 3700

3000

2600 Wavelength,

2300

2100

1900

1

FIG. 19. Spectral response of silicon carbide junction diode. (After Campbell and Chang5')

The junctions were prepared by diffusing aluminum into n-type SIC crystalsz4 at about 1950°C. The diode structure was formed by lapping and etching with the final junction depth being determined by electrolytic etching or oxide delineation. Figure 19 shows the spectral response of one of these detectors at 30°C and 500°C. Due to band-gap considerations, there is only a slight response at wavelengths greater than 4000A. The photovoltage decreases and the photocurrent increases with increasing temperature. As mentioned before, the peak-response wavelength moves to longer wavelengths with increasing temperature. The experimental points in Fig. 14 show the peak wavelength exhibited by a number of detectors at room temperature as a function of the measured

660

ROBERT B. CAMPBELL AND HUNG-CHI CHANG

depth. The majority of the diodes are included within these two curves of w = 1 p and w = lop. The junction depth was measured by electrolytic delineation and may be in error by 2 4 p. The overall trend is obvious: as the junction depth increases, the peak wavelength increases, i.e., occurs at longer wavelengths. The agreement with the model described is fairly good. Similar results are reported on Si solar cells by Rappaport and Wysocki.62

VI. Active Devices It is technically difficult to fabricate a bipolar transistor from low-mobility and short-lifetime semiconductors, such as silicon carbide. The tunnel diode has the simplest active device structure, and high-purity materials are not required for the fabrication of this device. However, such a twoterminal active device has limited applications. Thus, the construction of a-Sic unipolar transistors appears to be the first choice. In fact, the first silicon carbide active device made in 1960 was a junction-gate type of unipolar t r a n ~ i s t o r . ~ ’ .The ~ ~ metal-insulator-semiconductor type of S i c transistor should also be feasible. The operation of such a device depends on the interface properties of the S i c surface and a suitable high-temperature insulator, which are not well understood. An operable S i c MIS transistor has not been reported. In this part, the Sic-tunnel-diode and junction-gate unipolar field-effect transistor will be described. 18. TUNNEL DIODE The tunnel diode can be made by forming a heavily doped, alloyed junction in either n- or p-type degenerate Sic crystal, using a very fast alloying cycle similar in principle to that originally used to produce Ge tunnel diodes. Degenerate n-type Sic can be grown readily with heavy nitrogen doping. The p-type degeneracy in Sic cannot be established until ~ , is the uncompensated acceptor level approaches 1020-1021~ m - which comparatively difficult to achieve by the alloying technique. The first investigation of Sic tunnel diodes was reported by Chang ef in 1960, along with the unipolar transistor. The tunneling alloyed junctions were formed in heavily doped n-type S i c crystals with various alloys of Al, B, and Si at temperatures up to 2300°C. During this investigation, only the negative-resistance phenomenon was observed.

’’ P. Rappaport and J. J. Wysocki, “Photoelectronic Materials and Devices.” Van Nostrand, 63

Princeton, New Jersey, 1965. H. C. Chang and L. F. Wallace, Missiles und Spuce, p. 30 (June 1961).

9.

SILICON CARBIDE JUNCTION DEVICES

66 1

An operable Sic tunnel diode was reported by R ~ t z "in~1964. The junction was formed by alloying Si in a Ni-containing atmosphere to very heavily Al-doped a-Sic crystals (4.5-9 x 10,' uncompensated acceptors ~ m - ~ The ) . highest peak-to-valley current ratio achieved was only 1.37 at room temperature, but negative resistance was observed at temperatures as high as 500°C. The peak voltage is unusually high, approximately 0.9V at 24°C. The Sic crystals in various thicknesses from 10 to 40 mils were cleaved into sections having areas of approximately 3000 mil2. These were fused to tungsten tabs at a temperature of approximately 1900°C after a method first described by Hall4' This formed the ohmic contact to the p-type Sic. Small fragments of Si were then alloyed to the exposed (0001) face of the S i c chip. The alloying was carried out in a tungsten strip heater furnace, and a forming gas atmosphere (10 H,, 90% N,) was generally used. The heating cycle lasted 10-15 sec and the units were quenched to room temperature. The maximum temperature reached was in the range of 200G 2200°C. The Si dot was etched off either in CP, or in a mixture of H F and HNO,. A pressure contact was then made to the area that had been wetted by the Si. To facilitate good contact, aluminum was sometimes alloyed to the Si dot at 600°C after the tunnel diode had been formed. Experiments have been performed to establish that the active donor dopant was N, from the forming gas and that the tunneling effect was not due to a junction formed in the Si itself or was affected by the tungsten-Sic contact. Figure 20 shows the I-I/ characteristics for a diode taken at different ambient temperatures. The characteristics at liquid helium temperature ( - 269"C), which are not shown in the figure, almost coincide with those shown for liquid nitrogen temperature ( - 196°C). For this unit, the roomtemperature peak-to-valley ratio is 1 : 1. The series resistance is not accurately known, but a measurement of the slope of the I-V curve at a negative current of 100 mA, where it is not yet linear, gives a value of 3.3 ohm, which represents an upper limit. The peak current densities of diodes showing a negative resistance at room temperature varied from 10 to 150Acm-2. The capacitance per unit area at 1.1 V forward bias was measured to be 2pFcm-' for a particular diode which had a peak current density of 120 A ern-,. An unusual characteristic of some of these diodes, one not normally observed in tunnel diodes made from other semiconductors, is the appearance at liquid H, temperature of another negative resistance of the voltagecontrolled variety. An example is presented in Fig. 21, which shows characteristics taken on a curve tracer. In addition to the tunnel diode charac-

<:

R. F. Rutz, IBM J . Res. Develop. 8, 539 (1964).

662

ROBERT B . CAMPBELL AND HUNG-CHI CHANG 55 50 45 40 35 30

25 4

20

2

15

l3

10

E

?

5

0 -5 -10

-15

- 20

- 25 -I

L 1-02

-400°C - 200°C - -196°C and 24°C I

1

I

I

02

04

06

08

I

10

I

I

I

12

14

16

I

18 2 0

Voltage, V

FIG. 20. The I-V characteristics of a silicon carbide tunnel diode from - 196°C to 400°C. (After R ~ t z . 6 ~ )

teristics in the forward direction, there are two negative resistances at low currents, approximately symmetrical with respect to the origin, for both forward and negative voltage biases. These are extremely temperaturedependent and do not repeat themselves from trace to trace. The self-heating removes the low-current negative resistance for the fully swept-out traces, which include the tunnel diode characteristic. A possible explanation is a thermal breakdown in an extremely thin layer of less heavily doped n-type material in the Sic, which at low temperatures has a high resistivity. This layer might be produced in the highly nonequilibrium alloying process.

9.

SILICON CARBIDE JUNCTION DEVICES

663

FIG. 21. The I-Vcharacteristics of a Sic tunnel diode at 4°K. (After R ~ t z . ~ ~ )

One of the devices having a tunnel diode negative-resistance region at 500°C was incorporated in a simple self-exciting oscillator circuit. It was operated at 330 Hz at 500°C in an air ambient for 20 min, delivering 20 pW into a 10-ohm load.

19. JUNCTION-GATE UNIPOLAR TRANSISTOR a. Design

The present SIC technology has not reached such an advanced state that an accurate and quantitative design of the junction-gate type of S i c unipolar transistor can be made. The basic theory of the device, developed by S h ~ c k l e yand ~ ~Dacey and Ross,66can provide sufficient information on 65

66

W. Shockley, Proc. IRE 40, 1374 (1952). G. C. Dacey and I. M . Ross, Proc. IRE 41, 970 (1953).

664

ROBERT B. CAMPBELL AND HUNG-CHI CHANG

the required device dimensions and characteristics. This information can be used as a guide for controlling the processing parameters. The device structural parameters to be determined are the channel thickness, lengths, and width, which depend on material parameters and the desired operating voltages, currents, and frequencies. The design is limited by the values of certain parameters that we can achieve. For instance, the tolerance of the gate contact area dictates the channel length to be no less than 50 p. The highest-purity a-Sic crystals presently available are n type and have donor concentrations greater than 10l6cmP3 and electron mobilities less than 40cmZV - ' sec-' at 500°C. Based on these limiting parameters, the design data can be theoretically calculated. Those data are listed in Table VI that clearly indicate the need for precise dimensional control in making the transistor. TABLE VI DESIGNDATAFOR SIC UNIPOLAR TRANSISTOR Donor concentration of the channel material, N o Electron mobility of the channel material at 500°C. p Channel or gate length, L Channel or gate width, Z Channel thickness, 2a Pinchoff voltage, Wo Maximum drain current, l o Maximum power density, P,, Maximum device power, P Cutoff frequency, fmaX

<40cm2 v-' sec-' 25Op

2 mm 3P

20 v 5 mA 100Wcm-2 100 mW 5 MHz

b. Early Work and Results The feasibility of such a Sic high-temperature active device was deThe key success was the development monstrated in 1960 by Chang et u1.30*63 of the aluminum diffusion and electrolytic etching processes, as described by Chang et al.24The fabrication sequence of this device is shown in Fig. 22. High-purity n-type a-Sic platelets having a room-temperature resistivity between 10 and 100 ohm-cm were processed to about two mils thickness and scribed into small sizes between 0.005 and 0.02cm2. A diffusion run 16 hr long produced junction depths approximately 20pm deep in the crystal. The electrolytic etching process was used to remove two specific adjacent areas of the p-type diffused skin for source and drain contacts. The distance between the two open n-type areas is the channel length,

9.

665

SILICON CARBIDE JUNCTION DEVICES

n-Type parent crystal

I

I

n

t

A l diffusion

I Fuse contacts

2 mils

I L p - T y p e silicon

1 FIG. 22. Fabrication sequence for a double-gate, diffused-junction unipolar transistor. (After Chang and Wallace.63)

which was between three and four mils. Contacts were applied to the source, drain, and gate by alloying extremely small chips of silicon to the areas where low-resistance contacts are desired. The process cannot provide accurate control of the device dimensions, especially the channel thickness. Only a few devices prepared showed pinchoff effect. The dc drain characteristics at room temperature of a good unit are shown in Fig. 23. These curves were taken with a 1 kohm load resistance, which is small in comparison to the channel resistance. Drain characteristics of the same unit with zero gate voltage are shown in Fig. 24 as a function of temperature. The load resistance for these measurements was matched with the channel resistance, resulting in a change of curve shapes. It is apparent from these curves that characteristics of the transistor are strongly temperature-dependent from room temperature to 500°C. The static transconductance of this unit changes from 190 pmho at 26°C to 13 pmho at 500°C for a 2-V bias.

666

ROBERT B. CAMPBELL A N D HUNG-CHI CHANG 0.9

0.8

0.7

0.6

Q

0.5

E D CI

0.4

0.3

0.2

0.I

0

0

5

10

15

20

25

30

35

FIG. 23. Drain characteristics of S i c transistor at 30°C. R , = 2100 ohms; values of on each curve in volts. (After Chang and Wallace.63)

V, given

AC power gain as a function of temperature was measured at 60Hz under optimum operating conditions at each temperature. The power gain was as high as 380 at 26"C, and at 500°C a power gain of 7 was still observed. c. Photolithographic Planar Techniques

The techniques used in establishing the feasibility of the device as described above cannot provide sufficient accuracy and reproducibility for controlling the device structure. Further progress in Sic diffusion, oxidation, and gaseous etching techniques led to the recent development of a precision fabrication process based on the modern photolithographic mask approach employed for silicon planar devices and integrated circ~its.~'Because of its technological importance, this process will be described in some detail.

9.

667

SILICON CARBIDE JUNCTION DEVICES

06

0.5

04

a 0.3 n U

0.2

0.1

0 1

FIG. 24. Drain characteristics of S i c unipolar transistor with V, = 0 as a function of temperature. (A) 2 6 T ), .( 350°C; (0) 500°C. (After Chang and Wallace.63)

(i) Self-masked d i g i s i o n process. Aluminum diffusion in Sic requires temperatures from 1800°C to 2100°C. At these temperatures, SiO, can no longer be used as a diffusion mask. Various refractory materials have been investigated, but only S i c itself has proved effective and practical to date. On the other hand, SiO, is very effective as a mask for chlorine etching at 1000°C. By using the photoresist technique, a precision configuration of openings can be etched into the SiO, mask and, in turn, a corresponding configuration of Sic mask can be formed on Sic by the chlorine etching. The principle of the self-masked diffusion technique is illustrated in Fig. 25. The essential fabrication procedures are listed as follows : (1) First, aluminum diffusion is used to form a p-type skin into an n-type platelet, which was lapped to a prescribed thickness. (2) Material is removed by precision lapping from the carbon-face side of the platelet until the n-type layer reaches a prescribed thickness. (The diffused junction on the silicon-face side constitutes the lower gate.) (3) Silicon dioxide is grown over the entire carbon-face surface of the platelet by the steam oxidation technique. (4) Photoresist etching of the oxide layer is used to expose areas of n-type surface for chlorine etching [Fig. 25(a)].

668

ROBERT B. CAMPBELL AND HUNG-CHI CHANG S 1 0 2 Mask

Carbon f a c e

n-type SIC

I

D i f f u s e d p - t y p e SIC

Source

I

f

Gate

Drain

Gote

Source

I I

'1

Gate

1

Gote

(d) FIG.

25. Self-masked diffusion technique (see text for description)

(5) Chlorine etching of the Sic through the openings of the SiO, mask is used and oxide, in a buffered H F solution [Fig. 25(b)j, is removed. (6) A second aluminum diffusion [Fig. 25(c)] is accomplished. (7) The S i c self-mask is removed to obtain a planar structure [Fig. 25(d)]. (8) Evaporated Au-Ta contacts are applied to source, gate, and drain regions using the photoresist A1 rejection mask technique. This self-masked diffusion process is the key technology which contributes to the success of achieving precise control of the device structure. The epitaxial process has not been developed either to replace diffusion or to use the self-masked technique. The major problem is that epitaxial S i c of device quality could apparently be grown only on the silicon face of the S i c crystal, while most of the fabrication procedures, such as oxidation and

9. SILICON

Mask No. 11014

CARBIDE JUNCTION DEVICES

669

Micrometer scale

FIG. 26. Photoresist masks to fabricate Sic field-effect transistor.

chlorine etching, require processing of the carbon face, as discussed in Sections 7 and 8.

670

ROBERT B. CAMPBELL AND HUNG-CHI CHANG

(ii) Device fabrication. The detailed fabrication procedures are highly sophisticated and involve four or five photoresist masking operations, three chlorine etchings, three oxidations, and a minimum of two aluminum diffusions. Figure 26 shows a set of photoresist masks used in the fabrication of the planar device. Mask 110/1 provides an etch pattern in the oxide for chlorine etching of the isolation grooves. Mask llOj2 provides an etch pattern in the oxide for the gate region. During chlorine etching of the gate, the isolation grooves are etched even deeper. Mask 110/3 provides an etch pattern in the oxide for electrical contacting to the Sic. The aluminum rejection mask is also etched along the same areas. Mask 110/4 is used in conjunction with 110/3 to expose the alignment pattern around the device. If this is not done, there is danger of shorting the lower gate to the source. Mask llO/5 is designed to allow a metal etching procedure for making contacts as an alternate to the aluminum rejection mask technique. The smallest division of the scale of the masks in Fig. 26 is 0.01 mm (or lop). In designing the masks, the behavior of the chlorine etching through the SiOz opening into a-Sic must be taken into consideration. First, the side etch effect on the (1000) surface of a-Sic (i.e., undercutting of the oxide mask during chlorine etching) is negligibly small. The top area of the etched Si c region is therefore not much greater than the oxide opening area. Second, the width of the etched trough decreases uniformly as the etching proceeds in depth, forming a flat-bottomed wedge. In fact, the etching practically stops at a specific depth when the width of the etched trough decreases to zero. It has been determined that the sides of the wedge maintain a constant angle of about 55" from the top surface of etched Sic, or the reduction of the etched trough width per unit etching depth is equal to 2 cot 55". The width at the bottom of the etched trough controls the gate area of the transistor and dictates a limiting size of the metallic contact area. The mask must therefore provide a gate length at the contact surface of a reasonable value (e.g., 60 p ) for the expected ranges of etching and diffusion depths, and to allow a reasonable tolerance in alignment of the masks. A finished S i c unipolar transistor (without lead wires) is shown in Fig. 27. (iii) Deuice evaluation. Completed field-effect transistor structures fabricated using the techniques described were evaluated on a transistor curve tracer. In order to obtain the electrical charactristics of these devices as a function of temperature, the transistor was heated gradually from room temperature up to 520°C and then cooled to room temperature again. As the temperature of the unit was increasing and decreasing, several pictures of the family of the field-effect transistor drain characteristics and of the selected diode characteristics were obtained from the curve tracer. The electrical measurements were taken with probes connecting the contacts.

9.

SILICON CARBIDE JUNCTION DEVICES

671

FIG. 27. Completed Sic unipolar transistor

All measurements were made with a continuous flow of argon over the units. Figure 28 shows the family of characteristics of one of the field-effect transistors as a function of temperature. The maximum transconductance of the device, approximately 90 pmho mA- decreases as a function of the gate voltage. The saturation drain resistance measures approximately 150 ohms. The characteristic with V, = 0 does not show saturation because the drain voltage is still smaller than the pinchoff voltage. The most evident consequence of the temperature increase is the decrease in drain current, while the transconductance does not decrease very much.

',

VII. Irradiation Effects The principle mode of radiation damage in semiconductors is a displacement of atoms from their proper positions into the interstices of the crystal lattice. These vacancy-interstitial pairs act as recombination and trapping centers and tend to decrease the lifetime and mobility of the carriers and the conductivity of the material. The number of vacancy-interstitial pairs is a function of the number of incident damaging particles. Since the damage sites remove charge carriers from the material, the damage effect can be measured as a carrier removal rate, i.e., the number of carriers removed per unit flux of radiation. The carrier removal rate for silicon carbide is not precisely known, but some information has been obtained which indicates that it is slightly better than silicon. In addition, it should be possible to operate Sic devices

672

ROBERT B. CAMPBELL AND HUNG-CHI CHANG

FIG.28. Family of drain characteristics of S i c field-effect transistor at the following temperatures and gate voltages (5 V/div horizontal, 0.5 mA/div vertical): (a) 25°C. 1.35-0.9 V/step; (b) llO'C, 1.24.8 V/step; (c) 290"C, 1 4 . 7 V/step; (d) 400"C, 0.95-0.7 V/step; (e) 500"C, 1.24.8 V/step; (f) 200°C, 1.4-1.0 V/step; (g) 25"C, 1.4-1.2 V/step.

at a temperature high enough to allow appreciable annealing of the damage as it occurs. Radiation-damage experiments have been conducted on Sic for fast neutrons and high-energy electrons and protons. The samples have consisted of homogeneous bulk crystals with various impurity concentrations and p-n junction diodes. Nagels and Denayer6' have studied the conductivity and Hall coefficient following reactor irradiation of p and n-type hexagonal Sic single crystals.

'' P. Nagels and M. Denayer, Center for Nuclear Studies, Mol, Belgium, private communication, 1954.

9.

SILICON CARBIDE JUNCTION DEVICES

673

The crystals were supplied by Philips Research Laboratory and were Al~ . types of and N-doped, respectively, at levels exceeding 10'' ~ m - Both samples became highly resistive n-type after irradiation to 2 x 1O"nvt. The removal rate was about one carrier/cm3 for each fast neutron/cm2. In initially p-type material, the predominant defect found was a donor state with an ionization energy of about 0.20 eV. In initially n-type material, the electron traps were located 0.13 eV below the conduction band. They also studied the effect of annealing on these defects, measuring conductivity at room temperature between 1 hr annealing pulses over the temperature range 8&950"C. In the initially p-type samples, a small reverse recovery first occurs in the range 8&150"C, which is attributed to the release of holes by an unidentified set of hole-trapping centers. Over the range 40&800"C, about 1 % of the total conductivity decrease is recovered. Complete recovery occurs somewhere in the range 95&16OO0C, since these samples fully recovered their initial conductivity when heated to 1600°C for 2min to replace the alloyed contacts. In the initially n-type samples, two recovery stages were seen: between 80°C and 200"C, about 1% of the damage recovered, and about 12% of the original conductivity reappeared between 400 and 800°C. The Hall mobility of a p-type crystal decreased steadily from a preirradiation value of 30cm2 V-' sec-' to 4.5 cm2 V - ' sec-' after 5 x 10" nvt,. In an n-type crystal, the initial Hall mobility of 134cm2V-' sec-' increased steadily to a final value of 14cm2V-' sec-' at 1.8 x 1017nvt,. Auckerman et irradiated bulk n-type Sic and SIC junctions with fast neutrons and y rays. The current-voltage characteristics of the diodes were studied before, during, and after irradiation. Up to 10l6nvt,, no permanent charges were noted. It was also found that, if a reverse voltage were applied during the irradiation, the reverse current would slowly decrease with time. This "field effect" is postulated to be due to free electrons and holes which are trapped by defects generated in the barrier region by radiation. Canepa et a1?6 irradiated S i c neutron detectors up to 1014 protons/cm2 (roughly equivalent to 10l6nvt). At this dosage, some permanent degradation of the properties resulted. They also found that, although some repair of damage took place as low as 200"C, appreciable repair of damage did not occur until 800"C, at which temperature about 70% of the collection efficiency of the device was recovered. They concluded that the S i c detectors were perhaps 100 times as radiation resistant as silicon detectors when annealing effects are considered. 68

L. W. Auckerman, H. C. Gorton, R. K. Willardson, and V. E. Bryson, in "Silicon CarbideA High Temperature Semiconductor" (Proc. Conf. Silicon Carbide, Boston, 1959), p. 388. Pergamon Press, New York, 1960.

614

ROBERT B. CAMPBELL AND HUNG-CHI CHANG

In later work, Chang and Davis69 studied the carrier removal rate and mobility change in bulk S i c and the current-voltage characteristics and variation of the junction capacitance of diodes with reactor neutron ( E > 0.1 MeV) radiation. The carrier removal rate was in the expected range of 1-10 carriers removed per neutron. Table VII shows the data on bulk Sic. Little change was noted up to 1.6 x 10l6nvt, with nearly complete degradation after 10’’ nvt. An annealing experiment was performed with one of the neutron irradiated crystals, D39-2. The crystal was placed in the Hall apparatus at 500°C and measurements were made at intervals up to a total elapsed time of 610 min. The crystal was then removed to a furnace at 1000°C for 5 min TABLE VII FAST-NEUTRON DAMAGE DATA’

Sample

Carrier concentration Carrier mobility ( ~ m - ~ ) (cm’ V - ’ sec - I )

Initial data

c347 D23 D23-1 D39-2 D42-B D48- 1

7.03 x l o t 8 2.70 x 10” Not available 2.00 x 1017 1.32 x 1015 4.66 x l o t 6

After first irradiation 1.6 x 10LSnvt ( > 10 keV)

c347 D23 D23-1 D39-2 D42-B D48-1

7.05 2.09 6.64 1.87 1.17 4.30

c347 D23 D23-1 D39-2 D42-B D48-1 (2347 D23

6.72 x loL8 4.40 x 10’5 5.30 x 1014 9.9 x loi6 Not measurable Broken 6.20 x l o L 8 2.03 x 10”

D23-1 D39-2 D42-B

Not measurable

Condition

After second irradiation 1.71 x 1016nvt (> 10 keV)

After third irradiation

9.90 x 1016nvt (> 10 keV)

x loL8 x 1015 x 1014 101~ x x

10’’ 10I6

’Irradiation and measurements made at 25°C. 69

H. C. Chang and J. R. Davis, unpublished work, 1965.

47.5 14.5 Not available 365.0 74.5 208.0 45.3 14.5 53.3 367.0 62.2 179.0 44.6 4.6 72.8 198.0 -

36.9 6.2 (changed to P-tYPe) -

9.

675

SILICON CARBIDE JUNCTION DEVICES

TABLE Vlll DAMAGE-ANNEALING BEHAVIOR~~SAM D39-2 PLE

Treatment

Resistivity (ohm-cm)

Before irradiation After 10’’ nvt (fast)

0.39 > 100

Carrier concentration Mobility (cm--’) (cmZv-’ sec-’)

3.12 x 1017 Not measurable

49.2

Total anneal timeb (min)

60 Not measurable 33.60 90 3.23 120 3.16 150 3.14 180 210 3.12 250 3.08 430 3.10 3.09 610 0.942 5 (additional)’ 300 (additional)’ 0.947

Not measurable Not measurable 5.80 x 1OI6 5.83 x 10l6 5.90 x 1OI6 5.95 x 1OI6 5.95 x 1016 5.95 x 10l6 1.56 x 1017 1.57 x 1017

34.2 33.9 33.4 34.1 34.1 34.2 42.5 42.5

All measurements made at 500°C. Anneal temperature, 500°C. ‘Anneal temperature, 1000°C.

and remeasured at 500°C. An additional 300 min at 1000°C produced no further effect. The results are listed in Table VIII. Although the results of this experiment are of limited value, since only one crystal was annealed, it is clear that considerable annealing occurs at 500°C and therefore the life of any Sic device in a neutron flux will be appreciably increased. The junction capacitance (per unit area) as a function of applied reverse voltage and total irradiating flux was studied for S i c diodes. In all cases, the capacitance decreased and the slope of the capacitance-voltage curve decreased as the neutron dosage increased. This change in slope was due to a widening of the depletion layer in the pi-n junction structure. After several irradiations, the diodes behaved essentially as parallel-plate condensers, with no change in capacitance with voltage. Figure 29 shows this effect for one of the diodes. The effect of neutron irradiation on the I-V properties of the diodes confirmed Auckerman’s data. With increasing dosage, the forward current (at a given forward voltage) and the reverse current (at a given reverse voltage) both decrease. After 9.90 x 10”nvt, all the diodes showed essentially

676

ROBERT B. CAMPBELL AND HUNG-CHI CHANG

I00

N

E

E

IL-

a

0) u

C 0

.+ _ V

0“

10

C 0 ._ +

V

3 7

1

10 Applied reverse voltage,

I00

V

FIG. 29. Junction capacitance of diode D as a function of applied reverse voltage. Area, 3.27mm’; temperature, 25°C; (0) initially, (V)after 1.6 x lOI5 nvt, (0) after 1.71 x l o L6nvt, after 9.9 x nvt.

a)

resistive characteristics. Figure 30 shows this effect on the same diode as Fig. 29. No damage-annealing studies were made on the diode structures. This also included a study of 1-MeV electron damage on bulk Sic. The data are given in Table IX. The damage rates are approximately one order of magnitude smaller than for the similar neutron fluxes. This 10: 1 correspondence is consistent with the damage behavior measured for other s e m i c o n d u ~ t o r s . ~ ~ Schott” has studied the effect of irradiation on Sic diodes in a half-wave bridge circuit at 250°C. Fast neutrons with energy greater than 0.1 MeV were used. The maximum dose on one diode was 1.12 x 10l6 nvt. Several diodes failed at 2.5 x 1015nvt, but this was probably due to device or ’O

L. W. Aukerman, AIEE Summer Meeting, Denver, 1962 L. E. Schott, unpublished work, 1967.

9.

SILICON CARBIDE JUNCTION DEVICES

I

677

I I

+ 100

FIG. 30. Effect of neutron irradiation on the I-V characteristics ofa S i c diode. Temperature, nvt, ( 3 ) after 9.90 x 10l6 nvt. 25°C; (0) initial data, (1) after 1.6 x 10’’ nvt, (2) after 1.71 x

circuit failure, perhaps unconnected with the radiation. In a second experiment, diodes were irradiated to 1.03 x 10'' nvt before appreciable changes in forward and reverse characteristics were noted. The bridge circuit was still operable near 2 x 10l6nvt, although by this time appreciable degradation had occurred. Experiments of this type are important, since they may give some idea of the simultaneous radiation damage-annealing effect in Sic at elevated temperatures. Although more definitive work needs to be done on irradiation effects in Sic, it is clear that S i c crystals and devices are more radiation-resistant than silicon. One obvious experiment needed is to irradiate the samples at 40MOo"C to determine if simultaneous radiation with annealing will further enhance the radiation resistance of Sic.

VIII. Luminescent Diodes The light observed at the junction region of a forward-biased diode is called low-field electroluminescence or more simply, injection luminescence. This luminescence is due to the injection of minority carriers at the junction

678

ROBERT B. CAMPBELL AND HUNG-CHI CHANG

TABLE IX ONE-MEV-ELECTRON DAMAGE DATA" Carrier concentration Condition Initial data

Sample

Carrier mobility ( ~ r n - ~ ) (cm2 V-' sec-')

lok6

c22 D39-1 D40- 1 1E163

2.42 1.70 1.62 2.96

After first irradiation 1.4 x 10l6 (1 MeV)

c22 D38-1 D40- 1 1E163

2.37 x 1.52 x 1.55 x 2.96 x

1OI6

After second irradiation 1.03 x 1017 (1 MeV)

c22 D39- 1 D40- 1 1E163

2.08 1.20 1.09 2.93

10l6 10l6

After third irradiation 9.73 x 10'8 (1 MeV)

c22 D39-1 D40- 1 1E163

1.62 x lox6 1.09 x 1015 Contacts failed 2.89 x 1Ol8

x

x 10l6 x 10i7 x loL8

x x

loE6 10'' 10"

x 10" x 10"

108.0 280.0 368.0 73.8

107.0 296.0 363.0 72.8 124.0 258.0 292.0 72.4 109 292 -

69.6

Irradiation and measurements made at 25°C

and their subsequent recombination at recombination centers in the band gap. The color, i.e., the wavelength, of the luminescence is dependent on the position of the recombination centers in the band gap, and in no case can this wavelength be shorter (have energy greater) than the bandgap. Violin and K h o l u y a n o ~ have ~ ~shown ~ ~ ~ that the color of the emitter radiation is a function of both the dopants used to form the p-n junction and the polytype of the starting crystal. For example, n-type 4H crystals diffused with boron luminesce in the green, while n-type 6H crystals diffused with boron luminesce in the yellow. Beryllium doping generally yields a yellow-to-red luminescence. In later work, Violin and c o - ~ o r k e r scontinued ~~ their study of the electroluminescent spectra of boron- and beryllium-doped Sic. The borondiffused junctions showed peaked electroluminescent spectra at 2.05 eV.

'' E. E. Violin and G . F. Kholuyanov, Fiz. Tverd. Tela 6,593 (1964)[Eng/ish Trans/.:Sou. Phys.So/id State 6, 465 (1964)l.

'' E. E. Violin and G. F. Kholuyanov, Fiz. Tuerd. Tela 6, 1696 (1964)l [English Transl.: Sot!. 74

Phys.-Solid State 6, 1331 (196411. E. E. Violin, A. A. Kal'nin, V. V. Pasynkov, Yu. M. Tairov, and D. A. Yas'kov; Mater. Res. Bull. 4, S-231 (1969).

9.

I

0

679

SILICON CARBIDE JUNCTION DEVICES

1.2

I .4

I 1.6

1

I

I

1.8

2.0

2.2

E, eV FIG. 31. The typical EL spectrum of alloyed p-n junction in Be-doped p-Sic crystals at 293°K. (After Violin et

The luminescence occurs mainly in the space-charge region, with the radiative recombination mechanism being one in which boron-nitrogen pairs take part. Both n-type and p-type Be-doped Sic were fabricated, and alloy junctions prepared in the p-type (Be-doped) SIC gave an electroluminescent spectrum with a maximum at 1.85 eV as shown in Fig. 31. Since this spectrum is quite similar to the photoluminescence spectrum of p-type material, they assume that the recombination occurs in the p-type region of the p-n junction. Blank,75Potter,76and their co-workers studied the diffusion of aluminum and aluminum plus boron into Ni-doped (n-type) S i c crystals. They suggest that the boron diffusion leads to the most efficient luminescence at room temperature. Quite high diffusion temperatures were used (215&2250"C) and these diffused junctions were linear-graded with a high specific capacitance of 2 x lo3 p F mm-2 at zero bias. This would indicate a space-chargeregion width of about 0.04 p. The brightness increase with current of the luminescent diodes was superlinear to linear at low current densities but became sublinear at higher currents. The brightness increased up to 200°C. The luminescent diodes were prepared by diffusion of boron or boron plus aluminum into large SIC crystals which were subsequently lapped, 75

J. M. Blank, Muter. Res. BdI. 4, S-179 (1969).

'' R. M. Potter, Mater. Res. Bull. 4, S-223 (1969).

680

ROBERT B. CAMPBELL AND HUNG-CHI CHANG

sawed, and broken into 1-mm2dies. A Au-2 % Ta alloy was used for contacts to the n-type material, while a coating of aluminum powder in silicon resinate (liquid) was used for the p-type diffused surface. The devices were mounted in TO-46 headers so that the emitted radiation came out of the n-type side. At a current density of 50 mA mm-* and a forward voltage of 3 4 V, the devices had a brightness of 5Of-L with a spectral peak at 5900A. The devices have an internal quantum efficiency of 2 x 10-4-10-3. Brander77 and Todkill and Brander7' prepared junctions by either solution epitaxy or vapor-phase epitaxy. The solution-grown junctions were prepared by growing consecutive layers of boron- and nitrogen-doped S i c on a p-type S i c crystal. These were called type 1 and type 2 junctions, respectively, and showed quite different characteristics. The type 2 junction %) at 150"C, whereas the type 1 was most efficient (approximately junction efficiency decreased steadily from room temperature. This temperature dependence is shown in Fig. 32. The type 1 junction (solution epitaxy) showed a linear increase in brightness with junction current, while the light output of the type 2 junction was proportional to the square root of the junction current (see Potter76). The difference in the characteristics of the two types of junction was accounted for by the presence of a trapping center in the type 2 (vaporphase-epitaxy) junction. From the temperature variation of the rise time of the light output pulse at constant current, this trapping center was shown to have an activation energy of 0.2eV. It should be noted that the type 2 junctions were totally epitaxial, that is, the emitting junction was formed between two deposited layers, while the junction in the type 1 devices was formed between the substrate and the deposited layer. Brander77 has fabricated numeric displays from Sic luminescent diodes. The device was fabricated using a thermally grown SiO mask and by etching the regions between the numerics using a chlorine-oxygen etch. Brander has found that these devices have remained quite stable for long periods of time. Diodes have been tested for over 15,000 hr at temperatures of 3WOO"C and current densities of 5CL200 mA mm-' with no degradation of light output. Mlavsky and G r i f f i t h ~suggest ~~ that the overall light output of the S i c luminescent diode can be improved by incorporating certain transition metals, such as titanium, zirconium, or manganese, in the crystal. These impurities introduce energy levels in the band gap which can be electrically pumped and affect the efficiency of the recombination process. These R. W. Brander, Muter. Res. Bull. 4, S-187 (1969). A. Todkill and R. W. Brander, Muter. Rer. Bull. 4, S-293 (1969). 79 A. I. Mlavsky and L. B. Griffiths, unpublished work, 1965.

l7

78

9.

3

681

SILICON CARBIDE JUNCTION DEVICES

t

Vapor-phase epitaxy

..

c

w

.-

C

3

eL

2

c ._ n L

0 v)

C W c

r

Solution growth

" 1 m

I

01 0

1

I

I

I00

200

300

r

T, " C

FIG. 32. Temperature variation of the light output from a solution-grown (type 1) and a vapor-phase-epitaxy (type 2) lamp. (After Todkill and Brander.")

impurities are not dopants in the usual sense. The p-n junctions are formed by a solution-growth method using the usual p-type and n-type dopants. The devices exhibit a luminescent spectrum in the range of 4500-6000~, with the peak occurring at 510G52OoA. The best S i c luminescent diodes prepared still have lower efficiencies than competing devices. For instance, GaP diodes are now fabricated which have a nominal efficiency of 3%, with the best devices being near 6 7 % . The reason for the relatively low efficiency of the Sic devices has not been determined. Certainly, much of the recombination radiation never leaves the crystal, but, due to the high index of refraction of Sic, is absorbed by internal reflection. If the edge of a diode is polished and a forward bias applied, the emitted light is seen to come from a very narrow region (certainly less than 10 p wide). This light is of high intensity since less is lost by internal reflection ; such thin, high-intensity sources may be useful for film marking or similar applications. Perhaps the most important property of these S i t diodes is their luminescence in various colors. Devices emitting light from blue to red can be fabricated, and these may find their best application in multicolored displays and simulators.

682

ROBERT B. CAMPBELL AND HUNG-CHI CHANG

IX. Summary In this chapter, we have shown that S i c devices have distinct properties which lead to specific applications: they are operable up to 5OO0C, they have enhanced radiation resistance, and certain particular characteristics (e.g., band gap) lead to specific device applications. Applications in these areas will determine the final utilization of Sic devices. The future development of Sic devices probably depends more on engineering perseverence than on semiconductor physics breakthrough. Nearly all fabrication techniques possible with silicon can nowin theory-be performed on Sic. The sophisticated active devices and integrated circuits now being prepared from silicon will be prepared from S i c when suitable crystals are available and the fabrication techniques are refined.

X. Addendum Since the major part of this chapter was prepared, the International Conference on Silicon Carbide-1968, was held and the proceedings published as a special issue (Volume 4) of the Materials Research Bulletin (Pergamon Press, 1969). Although most of the 34 papers presented were concerned with growth mechanisms, physical and optical properties, and band-structure studies, seven papers dealt with device properties. Silicon carbide injection luminescent devices were discussed by Blank,75 and Todkill and Brander.78 These Brander,77 Potter,76 Violin et devices were prepared both by diffusion and solution epitaxy. Although most of the devices discussed exhibited a yellow color, other colors were obtained by using various dopants in the several p ~ l y t y p e s . ~ Several ~,~' devices of this type are now on the market. The results have been summarized in Part VIII of this present review. Brander and Todkil180 discussed the fabrication of a Sic cold cathode electron emitter. Emission currents of up to 50pA were obtained and the current could be modulated in excess of 1 MHz. The emission current decreased with temperature, falling perhaps 1-2 orders of magnitude between 100°C and 500°C. Devices have been life-tested up to 15,000 hr with no deterioration. Campbell and Berman" reviewed the electrical properties of various S i c devices. Most of the work discussed has been referenced in this present review.

*'

R. W. Brander and A. Todkill, Muter. Res. Bull. 4, S-303 (1969). R. B. Campbell and H. S. Berman, Muter. Res. Bull. 4. S-211 (1969).

9.

SILICON CARBIDE JUNCTION DEVICES

683

ACKNOWLEDGMENTS The authors would like to acknowledge the support of the Westinghouse Electric Corporation and research agencies of the Air Force, Army. Navy, Atomic Energy Commission. and National Aeronauticsand Space Administration for support of much of their work reported in this paper. We also wish to thank them for their permission to use unpublished data. We would particularly like to acknowledge D. L. Barrett, L. J . Kroko, and J. W. Ostroski for their work on crystal growth and power rectifiers, N . P. Formigoni and J . S. Roberts on the junction-gate unipolar transistor, and R. V. Babcock and J. R. Davis on the radiation studies.

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Rectifiers

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C H A P T E R 10

- xPx

High-Temperature Power Rectifiers of GaAs R.E . Enstrom H . Kressel L . Krassner 1. INTRODUCTION . . . . . . . . . . . . . . 11. HIGH-TEMPERATURE RECTIFIER DESIGN CONSIDERATIONS . .

I . Maximum Junction Temperature . . . 2. Breakdown Voltage . . . . . . . 3 . Peak Current Capacity . . . . . . 4. Specific Rectijier Design. . . . . . 111. p-n JUNCTION FORMATION . . . . . . 5 . Rect$er Structure . . . . . . . 6 . Growth of Epitaxial Layers . . . . . 7 . Evaluation of Epitaxial Layers . . . . IV. DEVICE FABRICATION. . . . . . . 8. Contact Metallization . . . . . . 9. Etching . . . . . . . . . . 10. Junction Surface Projection and Passivation 11. Rectifier Mounting and Packaging . . . V. RECTIFIER TESTRESULTS . . . . . .

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687 688 688 690 696 698 699 699 I01 707 7 11 7 12 713

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I. Introduction High-temperature rectifiers are highly desirable in a number of specialized systems. An important application is in supersonic aircraft, where, by using rectifiers capable of operation at 3Oo0C,substantial savings result in cooling capacity and hence aircraft weight. Another potential application is in nuclear reactor power generation. The range of applications will undoubtedly depend on the cost of these devices compared to the alternative of providing extensive cooling of Si rectifiers. As the III-V compound technology is further developed, the use of high-temperature rectifiers may become economically attractive in increasingly broader areas. The maximum operating temperature of semiconductor devices increases with the band-gap energy. However, numerous design and technological factors enter into the choice of the semiconductor. The materials that have been seriously considered for high-temperature rectifiers are Sic, Gap, Al,Ga,-,As, GaAs, and GaAs,-,P,. Of these, the latter materials are 687

688

R. E. ENSTROM, H. KRESSEL, AND L. KRASSNER

technologically the most developed at this time for this application ; rectifiers have been fabricated capable of operation (at 300°C ambient temperature) at a current of 50A with reverse breakdown voltages in excess of 150 V. Another material of practical interest is Al,Ga, -,As, in which highvoltage diodes have been reported.' This chapter describes the design considerations of high-temperature GaAs, -,P, rectifiers, the materials preparation techniques that have yielded large-area junctions relatively free of imperfections affecting electrical behavior, and, finally, the detailed fabrication processes. The design and packaging considerations are quite general in their application to other materials. The detailed epitaxial fabrication technology is more specific in its application to GaAs or GaAs, -xPxdevices.

11. High-Temperature Rectifier Design Considerations

The junction parameters of interest in high-temperature power rectifier design are listed in Table I. Besides the maximum operation temperature, the main concerns are the attainable breakdown voltage for a given rectifier area, and the electrical and thermal resistance of the device. The rectifier performance will be determined by a careful choice of the various parameters for particular applications. In this part, we consider the parameters that enter into rectifier design and, for illustration, discuss a rectifier designed for 50-A operation at an ambient of 300°C with a minimum breakdown voltage of 150 V. 1. MAXIMUM JUNCTION TEMPERATURE

The maximum operating junction temperature in any semiconductor can be estimated from the properties of Ge junctions at 100"C.2Since Ge diodes are still useful at that temperature, one estimates the temperature at which the intrinsic-carrier concentration in any other semiconductor reaches the same value as in Ge, 7 x l O I 4 ~ m - For ~ . Si, this value is reached a t 250°C and for GaAs at 400°C. Maximum temperatures for other semiconductors are shown in Table 11. A more practical temperature limitation is imposed by the ability to form a good quality ohmic contact with a high melting point. Thus, it is questionable whether the full temperature potential of materials like a-Sic will be utilized.

' Zh. I. Alferov, V. M.

Andreev, V. I. Korolkov. D. N. Tretyakov. V. M. Tuchkevich. Fiz. Tekh. Poluprou. 1, 1579 (1967) [English Tmnsl.: Sou. Phys-Semicond. 1, 1313 (1968)l. D. A. Jenny and J. Wysocki, J . Appl. Phys. 30, 1692 (1959).

10.

HIGH-TEMPERATURE POWER RECTIFIERS OF

GaAs, -xPx

689

TABLE I RECTIFIEK

DESIGN FACTORS

Parameter

Factors ~~

Peak forward current

Area Thermal dissipation

Maximum junction temperature

Band-gap energy Ohmic contacts Surface properties

Rated breakdown voltage

Impurity level Junction gradient Band-gap energy Imperfections Surface properties

Power dissipation

Band-gap energy Lifetime (possibility of conductivity modulation) Ohmic contacts Thermal conductivity Package Reverse current at rated reverse voltage

TABLE I1

ELECTRICAL CHARACTERISTICS OF SELECTED SEMICONDUCTORS

Semiconductor

E , at 300°K (eV)

Approx. max. device temp. (theoretical) ("C)

Electron mobility at 300°K (cm2v-' sec-')

Hole mobility at 300°K (em2V-’ sec-')

100 250 400 450 500 650 800 800 1200

3900 1500 6000 5000 4800

1900 500 300 300 200 200 100

Typical Thermal 300°K conminorityductivity carrier (lattice lifetime component) (sec) (Wac-' cm-') ~

0.67 1.1

1.42 1.55 1.65 1.95 2.26 2.2 3.1

500

350 2000 600

10-5 10-5

10-6-10-9

lo-s-lo-' lo-"lo-q 10-8-10-9 10-8-10-'

0.64 1.45 0.44 0.40 0.20 0.10 1.10

690

R . E. ENSTROM. H. KRESSEL. AND L . KRASSNER

t FIG.1. Theoretical and experimental values of breakdown voltage of abrupt and near-abrupt zinc-diffused GaAs diodes as a function of the carrier concentration of the more lightly doped base region. (@) Experimental. (After Weinstein and MIavsky.'*) I-) Theory. (After Sze and Gibbons.2b)(- - -) Experimental. (After Kressel et a!.")

2 . BREAKDOWN VOLTAGE The diode breakdown voltage first will be considered in ideal, defect-free junctions. In practice, the technological limit is set by the presence of small junction imperfections which directly or indirectly are responsible for regions of enhanced electric field in the space-charge region. As a result, local multiplication or tunneling occurs which gives rise to premature breakdown at so-called "microplasma" sites. a. Ideal Junctions

The breakdown voltage is a function of the impurity concentration and distribution, the band-gap energy, and junction temperature. The basic parameter is the impact ionization coefficient a, which is the reciprocal of the distance required for an electron to acquire the necessary energy for impact ionization. For a uniform electric field E in region W,the criterion for infinite multiplication is a(E)W = 1. The value of a as a function of electric field has been experimentally determined in G ~ A s , ~ GaAs, - ' ~ - xPx16and From 2aM.Weinstein and A. I. Mlavsky, Appl. Phys. Lett. 2. 97 (1963). 2bS.M. Sze and G. Gibbons, Appl. Phys. Lett. 8, 1 I 1 (1966). "H. Kressel, A. Blicher, and L. H. Gibbons, Jr., Proc. IRE 50,2493 (1962). R. A. Logan, A. G. Chynoweth, and B. G. Cohen, Phys. Reo. 128, 2518 (1962) H. Kressel and G. Kupsky, Znt. J. Electron. 20, 535 (1966). R . A. Logan and S. M. Sze, Proc. I n t . Conf Phys. Semicond., 1966. Kyoro, J . Phys. Sac. Jap. Suppl. 21,434 (1966).

10.

HIGH-TEMPERATURE POWER RECTIFIERS OF

GaAsl - x P x

691

Impurity gradient

FIG. 2. Theoretical and experimental values of breakdown voltage of graded GaAs diodes Experimental. (After Kressel and Blicher.') (-) as a function of impurity gradient. (0) Theoretical. (After Sze and Gihhomzh)

these values, it is possible to predict the theoretical breakdown voltage ofideal junctions. A plot of these values for GaAs, as computed by Sze and Gibbons,2b is shown in Fig. 1 for abrupt p+-n junctions as a function of the electron concentration in the n side of the junction. Figure 2 is a similar plot for graded junctions. A simple expression relates the breakdown voltage to the carrier concentration n and the band-gap energy E, in abrupt junctionslb: VB = 60(E$l.l)3i2(10’6/n)314 V.

(1)

Similarly, for graded junctions,Lb V,

=

60(E$1.1)6’5(3ax 1020)-2'3 v,

(2)

where a is the impurity gradient. The above values of V, assume that the spread of the space-charge region with increasing reverse bias is not limited by "punchthrough" to a highly doped substrate as is sometimes the case with p+-n-n+ diodes. It is of interest to estimate the minimum n-region width W, required to sustain a desired 5"Fora recent review, see W. Munch, Phys. Status Solidi 36,9 (1969). R. Williams, J . Appl. Phys. 39, 57 (1968). ' R. A. Logan and H. G. White, 3. Appl. Phys. 36, 3945 (1965). H . Kressel and A. Blicher, J . A p p l . Phvs. 34, 2495 (1963).

692

R. E. ENSTROM, H. KRESSEL, AND L. KRASSNER

50

c

Breakdown voltage VB (V)

FIG. 3. Minimum theoretical width of the n layer in an abrupt p+-n-n' function of reverse-bias breakdown voltage.

GaAs diode as a

breakdown voltage in such a structure. The simplest assumption consists in considering the electric field to be uniform in the n region with breakdown occurring when a critical field value Em is reached such that ct(E,,,)W, = 1. Then the maximum breakdown voltage for a given W, value is

V, = E,W,.

(3)

The dependence of VB on the width of the n region is shown in Fig. 3 for abrupt p+-n-n+ GaAs diodes a t 25"C, as calculated from the ionizationrate data of Kressel and K ~ p s k y . ~ The breakdown voltage is also a function of temperature, which can be approximately described by the empirical expression'

Here, V,, is the breakdown voltage at the reference temperature To, and is a constant which depends on the carrier concentration or impurity gradient, and on the semiconductor. This constant has been experimentally K. G. McKay, Phys. Reo. 94, 877 (1954).

10.

HIGH-TEMPERATURE POWER RECTIFIERS OF

I

I

I

Temperature coefficient

GaAs, -xP,

693

I

I

(xl0-j

OC-'

)

FIG. 4. Reverse-bias breakdown voltage as a function of the temperature coefficient 8. -) silicon graded junctions. (After Kressel and Blither.*)

(A) Manganese-diffused junctions ; (0) zinc-diffused junctions; (-

determined for GaAs junctions' and is shown in Fig. 4 as a function of the breakdown voltage. Note that p approaches zero for heavily doped junctions, and can become negative. This is because the electrical breakdown results primarily from tunneling in very narrow junctions. As the temperature is decreased, the band-gap energy increases, thus decreasing the tunneling probability and increasing the voltage required to achieve a given current density. Tunneling in reverse-biased GaAs junctions has been investigated by Williams." In wide junctions, however, charge multiplication by impact ionization is the dominant mechanism. With increasing temperature, u(E) decreases' because of reduced interaction between hot carriers and optical phonons, hence the breakdown voltage for a given electric field value also increases. The condition fi = 0 occurs for the junction width where both avalanche multiplication and tunneling occur simultaneously in proportions such that the temperature dependence of the two processes balance one another. In the dopant region of interest for rectifiers, /3 = 1.6 x " C - '. Here, avalanche multiplication is clearly dominant. Thus, for an increase of 300°C in junction temperature, for example, the breakdown voltage is increased by about 50%. I'

R . Williams, R C A Reu. 27, 336 (1966). Y. Chang and S. M . Sze, J. Appl. Phys. 40, 5392 (1969).

694

R . E. ENSTROM, H. KRESSEL, A N D L. KRASSNER

6. Technological Limitations to Diode Breakdown Voltage Premature breakdown is due to avalanche multiplication and/or tunneling in regions of the junction where the electric field is above average. Thus, local currents, called “microplasmas,” are formed. Microplasma formation and its correlation with various junction imperfections has been studied most extensively for Si, but the effect is quite general in all semiconductors. The subject has been reviewed by Kressel.l2 Nonuniform p-n junction breakdown is typically detectable by one or more of the following symptoms : (1) Slope discontinuities in the I-V characteristics in the breakdown region. (2) “Soft” reverse-bias I-V characteristics of the form I cc V”, where n is a constant greater than one (values between three and six are typical). These characteristics are not to be confused with those of junctions that break down as a result of an appreciable current component resulting from internal field emission. This effect, however, is typical only for diodes fabricated on heavily doped substrates. (3) Light emission in discrete spots. (4) Large-amplitude fluctuations of the current in the breakdown region. These fluctuations are particularly pronounced as the junction temperature is reduced. The absence of the above symptoms is not proof that uniform breakdown is observed. In certain diodes, for example, the emission of light may not be observed because of reabsorption. Furthermore, not all microplasmas emit light. It is also possible that a smooth I-V curve is observed because the current is carried by a single, large microplasma; a slope discontinuity may therefore not be readily observed a t a convenient current level. A further possibility in diodes fabricated from low-resistivity substrates is that the slope discontinuities may be difficult to detect because of the relatively low series resistance of the microplasmas. The observation of sharp I-V characteristics on an oscilloscope may thus be incorrectly interpreted as representative of bulk breakdown. A number of additional and more refined measurements may, however, be made to determine whether this is in fact the case and, if microplasmas are present, what the bulk breakdown voltage is. It has been shown by S h ~ c k l e y that ’ ~ the degree of junction “patchiness” may be determined from a plot of the current multiplication factor (as

l3

H. Kressel, R C A Rev. 28, 175 (1967). W. Shockley, Sofid-State Electron. 2, 35 (1961).

10.

HIGH-TEMPERATURE POWER RECTIFIERS OF

GaAs, -xPx

695

determined from a photocurrent multiplication measurement) as a function of the junction voltage: l/M = n(vB - V)/V,, (5) where M is the current multiplication factor, V the junction voltage, VB the bulk breakdown voltage, and n a constant. This expression will hold if the multiplication is uniform over the illuminated region. Deviation will occur if this is not the case, and from these deviations one may estimate the ratio of the microplasma area to the total illuminated area. The value of V, may also be calculated from these data by extrapolation. Haitz ef ~ 1 . ’ ~ have investigated the variation of the multiplication coefficient within a given junction by scanning with a small light spot and have shown that Eq. ( 5 )holds for values of M up to about 100 in small regions where uniform multiplication may be assumed to take place. A crude but frequently convenient check on the degree of junction uniformity requires only the use of an oscilloscope. If a junction contains microplasmas that severely reduce the breakdown voltage, then, when the junction is illuminated, the photocurrent variation as a function of voltage will be as shown in Fig. 5(a). Very little photocurrent multiplication will be observed before the I-V curve is dominated by the dark current carried by the microplasmas. If, on the other hand, the junction is reasonably uniform, then appreciable multiplication will be observed, as shown in Fig. 5(b). This simple test is based, of course, on the assumption that the total microplasma area is small compared to the total junction area. In Si, microplasma sites have been shown to result from certain imperfections. Of these, the most bothersome are precipitates,” junction “spikes” which locally enhance the local field, and nonuniform distribution of dopants. Isolated dislocations that are not decorated with impurities generally do not cause microplasmas. However, clusters of dislocations in the substrate prior to diffusion may cause enhanced diffusion along the dislocation cores, with the result that spikes are formed in the junction front.I6 Furthermore, dislocation clusters will frequently be sites for sizable precipitates. Specific flaws in GaAs and GaAs, -*PXjunctions will be discussed in Section 7b. Despite all the possible sources of difficulty in fabricating good-quality GaAs junctions, the theoretical and experimentally observed breakdown voltage values are on the average in good agreement for sufficiently small cm diameter). This is illustrated in Figs. I and 2, which diodes (2-5 x show experimental values superimposed on the theoretically predicted values. l5 l6

R. H. Haitz, A. Goetzberger, R. M. Scarlett, and W. Shockley, J . Appl. Phyr. 34,1581 (1963). A. Goetzberger and W. Shockley, 1.Appl. Pkys. 31, 1821 (1960). S. Prussin, “Metallurgical Society Conferences,” Vol. 15 (Properties of Elemental and Compound Semiconductors), p. 132. Wiley (Interscience), New York, 1961.

6%

R. E. ENSTROM, H. KRESSEL, A N D L. KRASSNER

FIG.5. (a) Oscilloscope trace of silicon junction containing a microplasma that breaks down at 70V (in the dark and under illumination). Note the very small degree of photocurrent multiplication. (b) Oscilloscope trace of more uniform silicon device fabricated on the same substrate as the diode shown in (a). Note the change in the voltage scale and the shape of the photocurrent versus voltage curve.

3. PEAKCURRENT CAPACITY For a given junction area, the maximum peak current I,- which a diode can safely carry is determined by its temperature rise. Power is dissipated because of the following factors: (1) Builtin junction potential; (2) semiconductor series resistance; (3) resistance at the metal contact-semiconductor interface; (4)significant saturation current during the reverse-bias part of the cycle. (1) The first contribution to the power dissipated is proportional to FI,-, where y is the junction potential given by =

(kT/q)ln(np/ni2).

(6)

Here, n and p are majority-carrier densities on the two sides of the junction and ni is the intrinsic-carrier concentration. Typically, F 0.7Eg.A semiconductor with E, as low as possible commensurate with the temperature of operation should be used to minimize K. (2) In p+-n--n+ structures, only the n- region contributes significantly to the series resistance. In semiconductors with high minority-carrier lifetime, such as Si, conductivity modulation of the n- region in forward bias greatly reduces its resistance. This is generally not the case for 111-V compounds, where the minority-carrier lifetime is so low (Table 11) that the diffusion length is only 1-7 pm. Also, the mobility for a given carrier density is important because the resistance of the n- layer is inversely proportional to it.

-

10.

HIGH-TEMPERATURE POWER RECTIFIERS OF

GaAs, -,P,

697

In the GaAs, -,P, system, the electron mobility is constant up to a 25 %P concentration." Thus, this alloy system has the advantage that a 1.65 eV band-gap energy may be obtained (which allows a temperature limit of 500°C) without a penalty in series resistance. (3) The resistance of the contact-semiconductor interface is a technological problem which differs in difficulty in various semiconductors, but increases with increasing band-gap energy. (4) The power dissipated during the part of the cycle when the diode is reverse biased is proporational to V l , , where V, is the peak reverse voltage and I , is the saturation current, To determine its relative importance, we now consider the junction saturation current and its dependence on temperature. In semiconductors where the minority-carrier lifetime is low, the dominant contribution to the saturation current is from surface leakage and generationrecombination in the space-charge region, at least at moderate temperatures, as will be illustrated below. An order-of-magnitude estimate of the ratio of this current density JGRto that due to diffusion JD is given for p + - n junctions by JGRlJD Z p W (V)/2niL,.

(7)

Here, p is the acceptor concentration in the p side of the junction, W ( V ) the width of the space-charge region, ni the intrinsic-carrier concentration, and L, is the minority-carrier diffusion length. Assuming values of W ( V )= cm, L, = 3 x cm, p = lOI8 ~ m - and ~ , ni = l O I 3 cmP3(the value for GaAs at 300"C), we find that J,,JJ,

z 1.7

x 105.

(8)

Using the above material variables (with T = sec appropriate to lightly doped material), it is found that JGR is significant at 300°C: 3GR 5 q n i ~ ( ~ ) / 2 1.6 t x 10-19 x 10-3 x 101312 x 10-8

(9) At room temperature, on the other hand, JGRis only lo-' Acm-2, since ni N 9 x lo6 cm-3, for a constant T. Figure 6 shows the reverse-bias current dependence on voltage and temperature from 25 to 400°C for a GaAs rectifier having an area of 4.7 x 10- cmz and demonstrates that the theoretical estimates are reasonable. At I/ = -20 V, W ( V )N 4 x cm, the leakage current is calculated to be 9 x 10-4A at 300°C. The observed value is 5 x A. At room temperature, however, the t0-7-A current is much higher than the predicted A, probably because surface currents dominate. These value of about =

". I. J.

8x

Acm-2.

Tietjen and L. R. Weisberg, Appl. Phys. Lett. 7, 261 (1965).

698

R . E. ENSTROM, H. KRESSEL, AND L. KRASSNER

Reverse leakage current ( A )

FIG.6. Reverse-bias current as a function of reverse-bias voltage and temperature

currents may increase only slowly with increasing temperature, in contrast to the space-charge-region generated current. For a GaAs,~s,Po~l,diode, the saturation current is evidently reduced because of the higher band-gap energy. With ni = 3 x 10" cm-3 at 300"C, z = lo-* sec, W = cm, and the current becomes JGR= 0.027 A cm-'. A. As is the Thus, for a rectifier having an area of0.16 cm2,J , R = 4.3 x case with GaAs described above, later results will show that the observed value of the saturation current is of this order of magnitude.

For given operating conditions, the junction temperature rise is determined by the thermal resistance of the device. This resistance depends on the thermal conductivity of the semiconductor, the package design, and the metallic contact properties. Table I1 shows that the thermal conductivity of the GaAs,_.P, compounds decreases with increasing P content. This is fortunately not significant in epitaxial structures because the thin, active GaAs, -xPx junction region is grown on thick, high-conductivity GaAs substrates. 4. SPECIFIC RECTIFIER DESIGN

We now consider in detail the specifications for a rectifier designed for 50-A peak-current operation at an ambient temperature of 300°C. The minimum required breakdown voltage is 150 V. The alloy composition GaAs,,,,P,, is a good compromise among the various design factors discussed earlier. From Eq. (11 we estimate that, for a p+-n--n+ diode, a breakdown voltage value of 150 V requires n < 6 x l o z 5~ m - ~ The . minimum thickness of the n-region is about 5 pm. In order to provide a margin of safety and to take into consideration

,

10.. HIGH-TEMPERATURE

POWER RECTIFIERS OF

GaAs, -xPx

699

the fact that the n- region may not be uniformly doped because of outdiffusion of dopants from the substrate during epitaxial growth, n values of about 1 x 1015cm-3 and thicknesses of 15-3Op should be used. It is obviously desirable to minimize the rectifier area since the probability of encountering defect breakdown sites increases with the area. However, the thermal and electrical resistances dictate a minimum size. As a compromise, a practical rectifier dimension is a circular area 0.175 in. in diameter (0.16 cm'). Thus, the peak current density (at 50 A) is 320 A cm-2. The thermal resistance of the diode, computed for a pellet 0.4 mm thick mounted upon a 46 % Ni-54 Fe alloy insert 0.4 mm thick and a copper stud 5 mm thick, is about 1°C W-'. We now turn to the thermal dissipation of the device and consider two alternative structures: (a) p+-n--n+ and (b) p+-p--n--n+. The second structure was found to yield higher voltage diodes than the first, as will be discussed in Part 111 and is therefore of practical interest. cm-3 and pf = 1OI8 ~ m - r/;~ = , 0.97 V (a) p + - n - - n + . With n = at 300°C. With a resistivity of 0.6 ohm-cm and a thickness of 15 x lop4 cm, ohm. The computed power the resistance of the n - region is about 6 x dissipation is therefore, at 50 A peak current, PdissN ~ I f 2 + R l f v )= 16 W. (10) The reverse-bias contribution for a saturation current of a few milli100 V is under 1 W. Hence, with a thermal resistance of amperes and 1°C W - ' , the junction temperature is about 317°C. This represents a lower limit to the estimated power dissipation.

-

(b) p+-p--n--n+. The reduction in the acceptor concentration in the junction vicinity reduces the builtin potential, but adds to the diode series , 0.65 V at 300°C. The thickness resistance. With p - = 2 x 10" ~ m - ~ = of the p - layer for the highest breakdown voltage was found to be about 25 x cm. This layer contributes about 1.5 x ohm to the diode ohm. The power dissiseries resistance, which is now a total of 2 x pation of this structure is equal to about 21 W, which is higher than that of the p+-n--n+ diode, but the disadvantage is in practice compensated by the higher breakdown-voltage values obtainable with this device. 111. (I-n Junction Formation

5. RECTIFIER STRUCTURE Generally, p+-n--n+ or p+-p--n--n+ structures have been used. In the case of GaAs,-,P, rectifiers, several additional layers are present to grade the composition between the GaAs substrate and the epitaxial

700

R. E. ENSTROM, H. KRESSEL. AND L. KRASSNER P+ GaAs,- px Graded t o GaAs

P- GaAs,-x PI

ir

n- G U A ~ , -Px ~

n + Epitoxial

n+ Epitaxial GaAs graded 10 GaAs,-x Px

n+ Substrate (a)

n+ Epitaxial

1

GUAS

nt GaAs Substrate

FIG.7. Schematic representation of vapor-grown layer strucures used for the fabrication of (a) GaAs and (b) GaAs, -xPx rectifiers.

GaAs, -xPx layers not present in GaAs rectifiers." The whole structure can be grown sequentially in the growth tube when the (ASH,, PH,) method is used," as discussed in the following section. The discussion that follows is with reference to Fig. 7.18 The epitaxial n+ region is not essential ; however, 175-mil-diameter diodes prepared with this layer present have higher reverse breakdown voltages than those in which the n+ layer is absent. For the GaAs,-,P, alloy structure, the n+ layer serves as a compositional grading region to reduce strain caused by latticeparameter differences. The n- layer has an electron density of 5 x lOl4 to 1 x 10' cm- for both GaAs and GaAs, -xPxalloys, and is about 25-5Op thick. In the best rectifier, the n- layer is 50 p thick, and provides a breakdown voltage of 450V for a 50mil mesa diameter. The p - layer is incorporated into both GaAs and GaAs, -,PX rectifiers i junction and thus primarily to reduce the Zn concentration at the p reduce the possibility of precipitate formation. In addition, some degree of junction grading is introduced. The carrier level in the p - layer of the best rectifier is about 2 x lOI5 holes/cm3 and the thickness is 25 p . The p -

'

R. E. Enstrom and J. R. Appert, in "Gallium Arsenide" (Proc. 2nd Int. Symp., Dallas, Texas, 1968), p. 213. Inst. Phys. and Phys. SOC.,London, 1969. l 9 J. J. Tietjen and J. A. Amick, J . Electrochem. Soc. 113, 724 (1966).

la

10.

HIGH-TEMPERATURE POWER RECTIFIERS OF

GaAs, -,P,

701

layer increases the yield of high-breakdown 30-mil and 175-mil diameter diodes. The p + layer serves as a low-resistance contact, but the Zn-doping level must not be excessive because the surface is then rough due to groovelike surface imperfections lying parallel to the (1 10) direction on the (100) substrate. A Zn concentration of 7 x 1O1’crnP3 results in mirror-smooth surface. The p + layer is also about 25 p thick and, for GaAs,-,P, alloys, is graded to GaAs at the surface to allow contacts developed for GaAs to be used.18

6. GROWTHOF EPITAXIAL LAYERS The main problems have been in attaining the necessary purity in GaAs and GaAs, -,P, alloys for the preparation of the n- layer, and in attaining a high voltage breakdown over a large area. The n- layers can be prepared by numerous methods. Foremost of these are the (AsC1, , PCl,) and the (ASH,, PH,) methods of vapor growth in open-tube flow systems. Both of these systems are capable of producing GaAs in the required < 1 x lo” cm-, level. In addition, the (ASH,, PH,) method has produced GaAs,-,P, alloys in this electron carrier concentration range. The p-n junctions can be prepared by (1) diffusion, (2) vapor-phase growth, and (3) liquid-phase epitaxy. To date, liquid-phase epitaxy has been used principally to grow p-n junctions in GaAs and Al,Ga, -,As on highly doped n and p layers for injection lasers.20-2l a Successful preparation of high-voltage rectifiers has been achieved to date with several combinations of nP-layer growth method and p-n junction formation. While 200-V, 1G20-mil diameter GaAs diodes have been prepared with n- layers prepared from AsCl, and diffused p-n junctions, the most successful technique to date has been the (ASH,, PH,) method combined with vapor-phase growth of the p-n junction. With this technique, breakdown voltages up to 450 V in 50-mil diameter and 250 V in 175-mil diameter diodes have been achieved in a GaAso.,,Po, alloy. These characteristics represent the highest breakdown voltages yet reported for GaAs and GaAs - ,P, alloys. In subsequent sections, several methods of preparing the high-purity n- layer are described and compared. The details of the substrate preparation are important since proper preparation can lead to material with lower imperfection densities. Finally, in this section we describe the principal methods of fabricating p n junctions. Other methods of limited application, such as ion iqplantation, have not been included. 21

H. Nelson, RCA Rev. 24, 603 (1963). H. Rupprecht, in “Gallium Arsenide” (Proc. Intern. Symposium. Reading, 1966). p. 241. inst. Phys. and Phys. SOC., London, 1967. Nelson and H. Kressel, Appl. Phys. Lett. 15. 7 (1969).

’IaH.

702

R. E. ENSTROM, H . KRESSEL, AND L. KRASSNER

a. Growth Methods

Undoped GaAs and GaAs, - xPxalloys have been prepared by closed-tube and open-tube methods. The closed-tube method refers to the encapsulation of the reactants into a tube, usually quartz, prior to reaction. Open-tube methods, on the other hand, have a flow of carrier gas and reactant species continuously into the growth tube and the exhaust products out of the tube. Closed-tube transport is a simple technique for producing GaAs, - xPxalloys but is inflexible. Once the growth has started, it is almost impossible to alter the doping or chemical composition. In addition, since the GaAs and GaP must be prepared beforehand, the purity is usually not as good as could be achieved in a one-step process. Therefore, most attention has focused on the open-tube methods for the growth of materials suitable for fabrication into rectifiers. Several open-tube methods can produce high-purity GaAs and GaAs, -xPx and also allow changes in both the composition and doping during growth. Most of these methods involve growth from the vapor. However, liquidphase epitaxy has been shown to be capable of producing high-purity GaAs.22,23Other liquid-phase growth methods for GaAs, -xPx24 and have been described, but the purity is not as high as that demonstrated in GaAs. Gallium arsenide has been vapor grown using water vapor,27HCl,2s-30 HI,31 and GaC1332transport. This latter technique yielded the first highvoltage, high-frequency GaAs varactor diodes,33 and, with the former?7 > 200 V reverse-bias breakdown voltages have been measured for 10-mil diameter Schottky-barrier diodes. However, the purest C. S. Kang and P. E. Greene, Appl. Phys. Lett. 11, 171 (1967). A. R. Goodwin, J . Gordon, and C. D. Dobson, Brit. J . Appl. Phys. ( J . Phys. D.) Ser. 2 1, 115 ( 1968). 24 G. A. Wolff, H. E. LaBelle, Jr., and B. N. Das, Trans. Met. Soc. A I M E 242,436 (1968). 2 5 T. S. Plaskett, S. E. Blum, and L. M. Foster, J . Eleftrochem. SOC. 114, 1303 (1967). 26 D. G. Thomas and R. T. Lynch, J. Phys. Chem. Solids 28,433 (1967). 2 7 K. L. Lawley, J. Elecrrochem. SOC. 113, 240 (1966). 2 8 D. Effer, J . Electrochem. Soc. 112, 1020 (1965). 2 9 D. P. Holmes and P. L. Baynton, in “Gallium Arsenide” (Proc. Int. Symp., Reading, 1966), p. 236, Inst. Phys. and Phys. SOC.,London, 1967. 30 J . A. Amick, R C A Reu. 24.555 (1963). 3 1 H. R. Leondardt. J . Electrochem. Soc. 112,237 (1965). 32 N. Goldsmith and W. Oshinsky, R C A Rev. 24, 546 (1963). 3 3 H. Kressel and N. Goldsmith, R C A Rev. 24, 182 (1963). 34 D. E. Bolger. J. Franks, J. Gordon, and J. Whitaker, in “Gallium Arsenide” (Proc. Int. Symp., Reading, 1966), p. 16. Inst. Phys. and Phys. SOC.,London, 1967. 34aG. E. Stillman, C. M. Wolfe, and J. 0. Dimmock, Solid Srate Commun. 7 , 921 (1969). 22

23

10.

HIGH-TEMPERATURE POWER RECTIFIERS OF

GaAs, -xPx

703

GaAs, -xPx alloys,IM. ,35 and have been prepared with the (AsCl,, PCI,) and (ASH,, PH,) methods of vapor-phase growth and therefore these methods have been used principally for the growth of rectifier materials. The (AsCI, , PCl,) method was developed before the (ASH,, PH,) method and has produced some of the purest GaAs to date. But the latter technique is more flexible for multilayer growth and excels in the production of GaAs, -xPxalloys. The deposition of high-purity, vapor-grown GaAs on a GaAs substrate using AsCI, has been described in detail.28*34,3840This method uses AsCl, purified by d i ~ t i l l a t i o nor~ a~ gradient freeze technique,2899.9999 %pure Ga, and Pd-diffused, high-purity H, or Ar4I as the carrier gas. The AsCI, is used both to transport the Ga to the substrate and to serve as the source of As to form the epitaxial GaAs layer, which grows at about 3 p min-’. Some disadvantages associated with the use of the AsCI, method are partly circumvented with the use of gaseous ASH,, and PH,. The foremost of these is that the partial pressures of the volatile species HCl, P, and As are more difficult to control since the halide is used both as a transport agent for the Ga and a source of the As and P. In addition, because AsCI, and PCl, are liquids, their vapor pressures are exponential functions of temperature and it is therefore difficult to maintain the constant partial pressures needed to prepare homogeneous alloys. In contrast, the partial pressures of the HCl, PH,, and ASH, are not strong functions of the temperature, and can be controlled independently with precision gas flowmeters. This latter feature is important since the net carrier concentration and mobility in the vapor-grown layer are influenced by the Ga :As ratio in the gaseous ambient.40.41aThe apparatus for the (ASH,, PH,) method of vapor g r o ~ t h ’ is~ shown , ~ ~ in Fig. 8 and has been used to prepare high-voltage, large-area rectifiers described in the following sections. Gaseous ASH,, PH, , 99.9999 % Ga, HCl, and Pd-diffused H, serve as the starting materials. The HCl reacts with the G a at one end of the quartz reaction tube and the highW. F. Finch and E. W. Mehal, J . Elrcrrochem. Soc. 111, 814 (1964). W. G. Oldham, J . A p p l . Phys. 36,2887 (1965). ” G. S. Kamath and D. Bowman, J . Electrochem. Sac. 114, 192 (1967). ” J. R. Knight, D. Effer, and P. R. Evans, Solid-State Electron. 8, 178 (1965). 39 J. Whitaker and D. E. Bolger. Solid State Commirn. 4, 181 (1966). 40 D. W. Shaw, R. W. Conrad, E. W. Mehal, and 0. W. Wilson in “Gallium Arsenide” (Proc. lnt. Symp., Reading, 1966), p. 10. Inst. Phys. and Phys. Soc., London, 1967. 4 1 R. C. Taylor, J . Electrochem. Soc. 114,410 (1967). 41aB.E. Berson, R. E. Enstrom, and J. F. Reynolds, RCA Rev., 31, 20 (1970). 4 2 R. A. Ruehrwein, “Use of Hydrogen Halide and Hydrogen in Separate Streams as Carrier Gases in Vapor Deposition of Ill-V Compounds,” US. Patent No. 3,218,205, November 1965. 35 36

704

R. E. ENSTROM, H. KRESSEL, AND L. KRASSNER

-

HZ Se+H,

Mixing Chamber

GO

HC1+Hz

Gallium zone

775°C

I

Continues t o exhaust and stopcock

I

I Reaction

I Deposition

I zone I85O"C

I

I

zone 750OC

FIG.8. Schematic representation of vapor-deposition apparatus.

purity H, carries the GaCl formed from this reaction to the deposition zone containing the GaAs substrate at the other end. Arsenic and phosphorus vapors formed from the pyrolyses of ASH, and PH, react with GaCl in layer on the the deposition zone to form a homoepitaxial GaAs or GaAs, -xPx GaAs substrate. The growth rate of the epitaxial layers is about p min-'. Sequential epitaxial layers doped n and p type with uniform, gradual, or rapid changes in composition in the growing layer can be made without removing the sample from the apparatus. Therefore, the high purity and crystal perfection is not reduced by a separate junction-forming operation as in diffusion.43The net carrier level achieved by Tietjen and Amicklg was -5-8 x I O l 5 electrons/cm3. Enstrom et a1.18,44*44a reduced it to 1 x 1014 electrons/cm3. High purity was obtained by use of a leak-free apparatus and high-purity ASH,, PH,, and HCl. The purity of the HCl is especially important but is troublesome because it is highly corrosive. Higher-purity HCl perhaps could be prepared by reacting high-purity AsCl, with H, in s i t ~ . ~ O

-

b. Growth Procedures ( i ) Substrate. Since the reverse breakdown voltage in a rectifier is inversely related to the imperfection density, it is important to have nearly 43

J. J. Tietjen, G. Kupsky, and H. Gossenberger, Solid-State Electron. 9, 1049 (1966).

44

R.E. Enstrom and C. 6. Peterson, Trans. Met. SOC. A I M E 239, 413 (1967).

44aJ. J. Tietjen, R. E. Enstrom, and D. Richman, R C A Rev. 31. 635 (1970).

10.

HIGH-TEMPERATURE POWER RECTIFIERS OF

GaAs, -xPx

705

defect-free vapor-grown layers. Many of these defects originate in the substrate and can be reduced by using the proper substrate orientation, minimizing surface damage, and having a very clean surface on which to grow. Some of the more important details to achieve low-imperfection-density layers are outlined here. and on (111) Power rectifiers have been vapor grown on both (100)18*4s oriented substrate^.^^ It is thought that a misorientation of 2-3% off the exact (100) plane promotes a smoother surface.46 While Se-, Si-, and Tedoped n + substrates have been used, some difficulties at the n--n+ interface have been observed with each dopant. With S e - d ~ p e dand ~ ~ Te-doped4’ substrates, diffusion of donors from the substrate into the epitaxial layer during vapor growth to a distance of more than l o p has been observed when the AsCl, method has been used,40although this has not been observed for n layers on Te-doped substrates prepared by the ASH, or the watervapor transport te~hnique.’~ This type of autodoping has not been observed in Si-doped substrate^,^^,^^ but a potentially more detrimental highresistance layer can occur at the n--n+ interface.48Such a layer will increase the rectifier series resistance. Mechanical polishing” and chemi-mechanical polishing with a 5 % sodium hypochlorite solution reduced 20/1,34*46,49or with 0.05 Br, in methan01,~’ have been used. Mirror-smooth surfaces and epitaxial layers on (loo)-, (1lo)-, and (1 11)-oriented substrates have been reported with the latter. Just prior to vapor growth, the wafers are usually chemically polished’ 8,19+34 with 3 4 parts H , S 0 4 , 1 part H,O, and 1 part H,02 to clean up the surface and remove any residual work damage. The damaged layer can be anywhere from 5 p deep after sawing and mechanical polishing operations, to more than 2011 deep for tweezers1 and initial grinding damage.” Thus, the chemical polishing step should remove from 20p19 to 60 p.I8 The latter value was found to give rectifier surfaces more free of defects (growth pits) than the former. EDTA at pH 748 and KCN28.53 45

4b

47

48 4y 50 51

52

53

W. P. Bickley and J. P. McCarthy, “Gallium Arsenide” (Proc. Int. Symp., Reading, 1966). p. 241. Inst. Phys. and Phys. SOC..London, 1967. D. V. Eddolls, J. R. Knight, and B. L. H. Wilson, in “Gallium Arsenide” (Proc. Int. Symp., Reading, 1966), p. 3. Inst. Phys. and Phvs. SOC.,London, 1967. 1. B. Bott, D. Colliver, C. Hilsurn, and J. R. Morgan, in “Gallium Arsenide” (Proc. Inter. Symp., Reading, 1966), p. 172. Inst. Phys. and Phys. SOC., London, 1967. C. M. Wolfe, A. G. Foyt, and W. T. Lindley, Electrochem Techno/.6, 208 (1968). A. Reisman and R. Rohr. J . Elecrrrdiem Soc. 111, 1425 11964). M. V. Sullivan and G. A. Kolb, J . E/ec,rrrx.hem.SOC.110, 585 (1963). E. S. Meieran, Trans. M e t . Soc. A I M E 242, 413 (1968). C. E. Jones and A. R. Hilton, J . Electrochem. Soc. 112.908 (1965). A. G . Foyt and C. M. Wolfe, ‘Gallium Arsenide” (Proc. Int. Symp., Reading, 1966), p. 181. Inst. Phys. and Phys. SOC.,London, 1967.

706

R . E. ENSTROM, H. KRESSEL, AND L. KRASSNER

rinses have been used after the chemical polishing step to complex any heavy-metal ions, such as Cu, on the substrate surface. To prevent drying stains, which can lead to defects during the deposition, the final rinse can be made with isopropyl alcohol54 and blown dry with nitrogen. Storage of organic solvents in polyethylene containers leads to particularly bad stains. Further etching of the substrates in situ by raising the substrate temperature to 900°C in conjunction with 2” off (lOQ-oriented substrates has led to epitaxial layers substantially free of defects46produced by the AsCl, method. Heating of the growth tube and Ga in H, to drive off any oxides prior to growth has been useful in reducing the growth-pit density on the major grown s u r f a ~ e . ’ ~ * ~ ~ The substrates may be placed either parallel or perpendicular to the gas flow in the growth tube. It has been found with the substrates parallel to the flow that a face-down orientation leads to a 50% lower defect density in the vapor-grown layer compared to upward-facing substrates made simultaneously.l 8 The former result in higher-voltage rectifiers. A substrate temperature in the range 725750°C has been used for both the AsCl, and ASH, systems. In this range, the deposition rate is kinetically limited, i.e., surface-reaction-controlled.56Higher and lower temperatures can lead to lower-purity layers.” (ii) Doping. Doping is used to make low-resistance contact layers, n+ or p + , and to fabricate p-n junctions. The various doped layers in the rectifier structure can be prepared by a separate diffusion step or by doping the various layers n or p type during vapor-growth of the entire rectifier structure. Doping during vapor-growth minimizes contamination, allows control over the depth of the p-n junction, and is relatively convenient to do. Diffusion is useful for complex planar devices, but the diode properties are greatly affected by the substrate and can be quite erratic. Diffused p+-type layers have been made by solid-to-solid diffusion from a Zn-doped SiO, layer,” and by vapor-to-solid diffusion from a Zn-containing alloy,58 a ZnAs, compound,59 a Mg compound,60 and elemental Cd.45 Zinc-doped SiO, gives abrupt junctions with little sideway diffusion, which C. E. E. Stewart, Solid-State Electron. 10, 1199 (1967). J. J. Tietjen, M. S. Abrahams, A. B. Dreeben, and H. F. Gossenberger,in “Gaftium Arsenide” (Proc. 2nd Int. Symp., Dallas, Texas, 1968), p. 55. Inst Phys. and Phys. SOC.,London, 1969. 5 6 D. W. Shaw, J. Electrochem. SOC. 115, 405 (1968). 5 7 G. R. Antell, Brit. J . Appl. Phys. ( J . Phys. D.) Ser 2, 1, 113 (1968). 5 8 H. C. Casey, Jr., and M. B. Panish, Trans. Met. Soc. AIME 242,406 (1968). 5 9 F. V. Williams, “Gallium Arsenide” (Proc. Int. Symp., Reading, 1966),p. 27. Inst. Phys. and Phys. SOC.,London, 1967. 6o M. Belasco, Base Diffusion for a Gallium Arsenide Transistor, U.S. Patent No. 3,357, 872, October 1967.

55

10.

HIGH-TEMPERATURE POWER RECTIFIERS OF

GaAs, -xPx

707

is particularly useful in the fabrication of planar devices. For n + layers, S, Se, Sn, and Te can be used.6 Doping of the epitaxial layer during vapor-growth has been done with both the AsCl, and ASH, methods. For this purpose, the dopant is preferably introduced separately, and not by simply adding it to the Ga melt.j4 The compounds H2S, S2C12,62 and H4Se18 have been used to prepare n-layers doped in the range 2 x 1015 to 2 x loL8electrons/cm3. Heated elemental Cd62 and Zn1s319340 as well as diethyl zinc6, have produced layers doped in to 4 x 1019 holes/cm3. The Cd doping has not been as the range 2 x useful as Zn doping for high-voltage rectifiers because soft I-I/ curves were obtained.'8 With the use of elemental Cd, only a little residual doping remains in the deposition tube from one run to the next so that successive p- and n-type vapor growths can be accomplished.62 Zinc-doping results in a residual doping level in the growth tube (H,Se does not) which necessitates cleaning the tube before another p-n junction device can be prepared. However, this can be easily done with the apparatus assembled by reversing the growth and removing the previous deposits with HCl gas.18 It is by this technique that successive high-voltage rectifiers with breakdown voltages as high as 475 V in 50-mil diameter diodes have been prepared. A p+-i-n rectifier with an i region a few micrometers wide has been made by diffusing Cd at 1000°C into n-type boat-grown GaAs to prepare 10-20-mil and 60-mil-diameter diodes with breakdown voltages of 190 and 150 V, re~pectively.~~ The latter diodes conducted 1.1 A at a temperature of 200°C for 3000 hr. However, the results are not reproducible, due to variations in diffusion characteristics of the bulk n-type crystals even though they exhibited similar electrical properties. More reproducible diodes have been prepared as n+-n--p+ structures by (1) the diffusion of Zn into a vapor-grown layer, n < 2 x 10" ~ m - on ~ an , n + substrate, and (2) by the vapor-growth of an n- layer, n 1 x 1015cm-,, onto a p + substrate.45 Both of these methods have given 200 V, 10-20-mil-diameter diodes, but 60-mil-diameter diodes have a low breakdown voltage due to microplasmas in the p n junction. Method 2 looks most promising, however, since it is not as sensitive to dislocation content as is a diffused layer, and, furthermore, more planar junctions are obtained.45

'

-

7. EVALUATION OF EPITAXIAL LAYERS a. Electrical Hall-effect measurements are a useful means of evaluating the net carrier density, conductivity type, and mobility. Furthermore, the degree of comR. G. Frieser, J . Electrochem. Soc. 112, 697 (1965). E. W. Mehal, R. W. Haisty, and D. W. Shaw, Trans. Met. Soc. A I M E 236,263 (1966). 6 3 R. W. Conrad and R. W. Haisty, J . Electrochem. Soc. 113, 199 (1966).

" 62

708

R. E. ENSTROM. H. KRESSEL, AND L. KRASSNER

pensation can be calculated from Hall These measurements are also useful to determine the effect of process variables on purity since the mobility, particularly at 77"K, is a sensitive function of the material purity. The layer of interest can be removed from the high-conductivity substrate or it can be prepared on a semi-insulating substrate and measured in situ. The layer can be contacted as in a conventional bridge-type Hall measurement or in a six-hole matrix rectangular sample prepared by sandblasting,l 9 or to the edge of a random, singly contacted sample.64The measurements appear to give similar results. The magnitude of the carrier concentration and mobility are a function of the state of the art; the latter has increased continuously during the past several years. Currently, for GaAs, values up to 8600cm2 V-' sec-' at 300°K and 200,000 cm2 V-' sec-' at 77°K have been obSerVed,34,34%65 and values up to 340,000 cm2 V-' sec- i at the mobility maximum are possible with the AsC1, method.34aWith the ASH, method, values up to 8700 cm2 V-' sec-' at 300°K and 108,000 cm2 V-' sec-' at 77°K have been o b ~ e r v e d . l * .For ~~~ GaAs, * ~ ~-xPx ~ alloys, the mobility is nearly constant up to x = 0.3 for materials prepared by the (ASH,, PH,) method,"*'9 in contrast to earlier work66-6s using f 2 transport. The point-contact reverse-bias breakdown-voltage measurement is a convenient method of quickly evaluating the carrier concentration in the n- layer of an n+-n--p+ or similar structure. Hall measurements cannot be made since the n- layer is usually too thin to permit lapping off the n+ and p + layers. Prior to point-contact measurements, the sample is angle-lapped at 3 4 , stained with sodium hypochlorite, and cleaned with concentrated HC1. From the point-contact breakdown voltage of an n layer, its electron density can be estimated from curves for abrupt p-n-junction diodes (see Fig. 1) over a range of voltage 6 to 200V, corresponding to 5 x 1017 to 1 x loi5cm-,, respectively. Measurements of capacitance as a function of reverse voltage are useful to determine the exact carrier concentration profile through the n- layer and to determine the type of junction impurity d i ~ t r i b u t i o n . ~ ~ b. Imperfections

Imperfections can cause microplasmas in the rectifier junction that lead to low reverse-bias-breakdown devices. It is important therefore to identify L. J. van der Pauw, Philips Res. Rep. 13, 1 (1958). M. Maruyama, S . Kikuchi, and F. Hasegawa, Preparation and properties ofepitaxial gallium arsenide (Abstract No. 62), J . Electrochem. Soc. 115, 66C (1968); also M. Maruyama, S. Kikuchi, and 0. Mizuno, J . Electrochem. SOC.116,413 (1969). 66 F. A. Pizzarello, J . Electrochem. Soc. 109, 226 (1962). S. Ku, J . Electrochem. SOC. 110,991 (1963). 6 8 M. Rubenstein, J . Electrochem. Soc. 112, 426 (1965). 69 J. Hilibrand and R. D. Gold, RCA Reo. 21, 245 (1960). 64

65

''

10. HIGH-TEMPERATURE

POWER RECTIFIERS OF

GaAs, -xPx

709

and then to eliminate or minimize by altering the rectifier processing those imperfections that degrade the device characteristics. This is particularly necessary for high-power rectifiers, since imperfections are usually randomly distributed and the number therefore increases with the pn-junction area. Imperfections that have been observed in GaAs and GaAs, -,PXinclude: dislocation^,^^ decorated d i s l o ~ a t i o n s , ~stacking ~ * ~ ~ faults,73 t ~ i n s , ~ ~ , ~ ~ growth facets,76 growth and impurity dopant clustering,” precipitate^.'^.^ These imperfections can be seen with optical microscopy, transmission electron microscopy, scanning electron microscopy, and x-ray topography on the as-grown or on the polished surface. Optical microscopy is useful in relating premature breakdown to defects on the as-grown surface such as hillocks and growth pits.“ Transmission electron m i c r o s ~ o p y and ~ ~ ~x-ray ~ ~ ”topographyg2are useful for looking into the bulk of the material for defects, and scanning electron microscopy is a valuable method of looking at microplasmas in the p n Dislocations are usually grown into the bulk substrate material and can propagate into the epitaxial layer during vapor-growth. But the number of dislocations in the vapor-grown layer can be lower than in the substrate.” In addition, dislocations can be introduced into vapor-grown layers to accommodate changes in composition and doping type which cause lattice mi~rnatch.~’ Formation of the p n junction by diffusion can also nucleate many d i s l o c a t i ~ n swhile , ~ ~ ~decoration ~~ of others can occur during growth of heavily doped n+- and p+-type layers. In particular, Ga,Te380a and Ga,Se,’l precipitates may form in Te- and Se-doped materials. M. S. Abrahams and L. Ekstrom, “Properties of Elemental and Compound Semiconductors,” p. 225. Wiley (Interscience), New York, 1959. 7 1 M. S. Abrahams and C. J. Buiocchi, J . Appl. Phys. 37, 1973 (1966). 7 2 J. F. Black and E. D. Jungbluth, J . Electrochem. SOC. 114, 188 (1967). 7 3 M. S. Abrahams and C. J. Buiocchi, J . Phys. Chem. Solids 28, 927 (1967). 74 H. Holloway and L. C. Bobb, J . A p p l . Phys. 38, 2893 (1967). 7 5 B. D. Joyce and J. B. Mullin, in “Gallium Arsenide” (Proc. lnt. Symp., Reading, 1966). p. 23. Inst. Phys. and Phys. SOC.,London, 1967. 7 6 B. D. Joyce and J. B. Mullin, Solid Stare Commun. 5, 727 (1967). 77 T. S. Plaskett and A. H. Parsons, J . Electrochem. Soc. 112, 954 (1965). G . R. Cronin, G . B. Larrabee, and J. F. Osborne, J . Electrochem. SOC.113, 292 (1966). 79 P. Wang, F. Pink, and J. Sciola, J . Electrochem. SOC. 114,879 (1967). M. S. Abrahams, C. J. Buiocchi and J. J. Tietjen, J . Appl. Phys. 38, 760 (1967). ‘OaH. Kressel, F. Z. Hawrylo, M. S. Abrahams, and C. J. Buiocchi, J . Appf. Phys. 39, 5139 (1968). J. F. Black and E. D. Jungbluth, J . Electrochem. Soc. 114, 181 (1967). E. D. Jungbluth, J . Electrochem. Soc. 112,580 (1965). 8 3 I. G. Davies, K. A. Hughes, D. V. Sulway, and P. R. Thornton, Solid State Electron. 9, 275 70

f1966). 84

85

J. W. Gaylord, J. Ekctrochem. SOC. 113, 753 (1966). N. F. B. Neve, K. A. Hughes, and P. R. Thornton, J . Appl. Phys. 37, 1704(1966).

710

R . E. ENSTROM, H. KRESSEL, A N D L. KRASSNER

It has been reported that rectifiers prepared by diffusing a p + region in a vapor-grown n- on n+-layer structure showed a microplasma density that was about the same as the dislocation density. The correlation was further strengthened by the observation of dislocation etch pits on diodes exhibiting microplasma behavior and the absence of pits in microplasma-free diodes which had been subsequently etched.45 By contrast, in vapor-grown rectifiers,” dislocations are not the primary cause of microplasmas, since no deleterious effect of the substrate dislocation density on breakdown was found up to densities of 10’ cm-’. In fact, highdislocation-density substrates give diodes of higher reverse breakdown TABLE 111

EFFECT OF SUBSTRATE AND VAFQR GROWTH PROCEDURE ON REVERSE-BIAS BREAKDOWN VOLTAGE OF 175-MIL-DIAMETERGAS DIODE V, (at 0.01 mA)/Vs (at 1 mA) W/V)

n- -layer point-contact breakdown voltage (V)

Substrate with about lo5 dislocations/cmz with vaporgrown n+-n--p--p+ structure

601250 601250 551225 Short/l5

15&180

191

Substrate with about lo3 dislocations/cm2 with vaporgrown n+-n--p--p+ structure

25/45 651160 25/50

130

190

Substrate with about lo5 dislocations/cm2 with vaporgrown n--p--p+ structure

Run

Variable

188

5/60 5/35

I8&2OO

voltage than do low-dislocation substrates, as shown in Table 111. Dislocations are believed to provide sites for precipitation of metallic and other impurities in the vicinity of the p-n junction and are therefore only indirectly responsible for microplasmas.86 Thus, a one-to-one correlation between microplasma sites and dislocations need not exist. Scanning-electronmicroscope studies seem to confirm this view since dislocations can exist in diodes without contributing to the leakage c ~ r r e n t . ~ ’ W . Shockley and A. Goetzberger, “Metallurgy of Semiconductor Materials,” p. 121. Wiiey (Interscience), New York, 1962. N. F. B. Neve and P. R. Thornton, Solid-State Electron. 9, 900 (1966).

10.

HIGH-TEMPERATURE POWER RECTIFIERS OF

GaAs, -xP,

711

Hillocks are a major defect in undoped layers, particularly those grown in the AsCI, system. They can arise either from twins caused by c ~ n t a m i n a t i o n ~ ~ or from Ga droplet^.'^ The latter can result from not saturating the Ga source to form a continuous GaAs film or from a GaAs substrate containing Ga inclusions. The deterimental effect of hillocks has been demonstrated in 135-270-mil Si diodes. Diodes with breakdown voltages below 150 V generally had hillocks on the surface, whereas diodes with reverse breakdown voltages above 150 V had no hillocks on the surface. Etching of the substrate prior to growth decreased the defect density significantly, presumably by reducing surface contamination.88 In vapor-grown rectifiers, it appears that microplasmas are related to growth pits seen on the p + surface after growth. The growth pits were associated with microplasmas in the finished diodes by scanning electron microscopy of reverse-biased junctions with breakdowns ranging from 60 to 250 V and by detection of infrared radiation emitted by the microplasma with an infrared image converter and with infrared-sensitive film. Low reverse breakdown voltages were correlated with the presence of pits on the surface. Therefore, to attain higher breakdown voltages, the layered structures had to be made more pit-free and the diodes were fabricated from the pit-free area on the wafer. Reduced growth-pit and microplasma densities resulted from longer substrate polishing time, baking out the system prior to growth, growing on high-dislocation-content substrates, facing the substrate down during growth, growing a p'- layer above the n- layer, and growing sufficiently thick n- and p - layers in the rectifier structure.18

IV. Device Fabrication The following is a brief outline of the rectifier fabrication process for vaporgrown n+-n--p--p+ structures. A more detailed discussion of the individual steps follows the outline. The process sequence is as follows : (a) The wafers are cleaned, and the contact metallization evaporated and sintered on both sides. (b) A film of SiO,, which protects the metallization during the subsequent processing is deposited over the metal on both sides of the wafer. The layer structure of the wafer at this stage is outlined in Fig. 9. (c) The wafer is wax-mounted and areas are selected from which rectifier pellets are cut out by ultrasonic abrasive machining on a Cavitron. (d) After pellets are removed from the wax, they are individually etched and the reverse characteristic read on a transistor curve tracer. Etching and

'*

G. L. Schnable, A. J. Serta, and L. F. Wallace, I E E E Trans. Electron Devices ED-13, 896 (1966).

712

R. E. ENSTROM, H. KRESSEL, AND L . KRASSNER

FIG.9. Schematic representation of rectifier pellet with evaporated-metal contacts and protective film of S O , .

testing continue until no further improvement in the reverse characteristic is obtained. (e) The rectifier pellet is prepared for mounting by depositing a protective SiOz layer over the freshly etched surface and etching the SiO, layer off the metal contacts. Wax masking is used to ensure removal of the SiO, only from the contacts. (f) The rectifier is assembled in the sandwich structure of Fig. 10. The junction electrical characteristics are examined, and, after a final cleanup etching, the rectifier package is sealed. The final assembly is shown in Fig. 11. The details of the various steps will be discussed in the following

section^.'^ 8. CONTACT METALLIZATION Special metallization for high-temperature rectifiers is required to fulfill severe operating requirements. Low-resistance contact to GaAs and GaAsl -,Px is the prime requirement, but, in addition, the contact must be compatible with soldering operations to mount the semiconductor pellet and must not form a liquid phase at temperatures below about 350°C. The last requirement allows for reasonable temperature rise when high current is carried in a 300°C ambient. A system of evaporated metal contacts was evolved which meets these requirements. The combination of metals employed is illustrated in Fig. 9. Each of the layers serves a particular function in the contacting and mounting system. The 15,OOO-ii silver layer is vacuum-sintered immediately after evaporation. It serves as the ohmic contact to the highly doped p + and n+ surfaces. Because the contacted surfaces are degenerately doped, the complication of adding dopant materials to the silver is avoided. 89

R. E. Enstrom and L. A. Krassner, unpublished work, 1968.

10.

HIGH-TEMPERATURE POWER RECTIFIERS OF

1-

I

I

GaAs, -xPx

713

Flexible copper leod

I

Copper stud Gold- germanium solder preforms

gold-nickel plated

FIG.10. Schematic representation of rectifier assembly.

A 1000-A layer of chromium between the silver and the 5000-Agold layer serves as a barrier to gold diffusion through the silver. Initial failures associated with the connection of the lead to the p + side of the rectifier were found to be caused by penetration of the gold-based solder through the silver, and formation of Au-GaAs alloy spikes through the p layer into the n region (see Section 11). The outer layer of gold enhances the wetting of the germanium-gold eutectic solder used to mount the semiconductor pellet in the package. 9. ETCHING The maximum possible breakdown voltage that can be realized from a grown p-n junction depends upon the quality and characteristics of the material, but the junction surface must be capable of sustaining the maximum reverse bias. The improvements in material purity and perfection achieved required matching improvements of etching techniques. A number of etch compositions were evaluated and compared. It was concluded that both the etch used and the rinsing and drying procedures are important. Eliminating water as completely as possible from the process produced the greatest improvement in reverse characteristic and surface stability. Drying with methanol rinses, instead of heat, improved surface stability significantly. The most outstanding success was achieved with bromine diluted in methanol. This etch is the only one employed that excluded water completely from the etching process, and this exclusion is probably its greatest virtue.

714

R. E. ENSTROM, H . KRESSEL, AND L. KRASSNER

n

il?

Copper

Rectifier cose Alumino body

L

n

I

t -Copper

connector

Gold- germanium preform

/ solder

yy: Gold-germanium solder preform

czzII--

Mounting insert (molybdenum or # 4 6 alloy1 Gold- germanium

1 -

Steel

FIG. 1 1 . Schematic representation of rectifier contacting, mounting, and packaging materials.

A summary of the various etch compositions and rinsing procedures is given in Table IV. The first three etches were found superior to the others, and an improved rinsing procedure led to the definite preference for the Br,:CH,OH system. It is possible that aqua regia or hydrogen peroxidesulfuric acid etches could be equally effective if nonaqueous rinsing were possible. The Br, :CH,OH etch, however, is the only composition used with complete success on GaAs, -xPxalloys. These materials, as noted earlier, have the best reverse breakdown characteristics, but degrade rapidly to 20 V or less after aqueous etching. The Br, :CH,OH etching and methanol rinsing result in a stable reverse breakdown of 450V even without a protective coating.

10. JUNCTION SURFACE PROTECTION AND PASSIVATION

P-N junctions operated at high temperatures generally require surface protection to prevent their degradation from surface contamination.

TABLE IV

COMPARISON OF ETCHING AND RINSING PROCEDURES 4

0

Rinse results Etch composition 1 % Br, in CH,OH, 5540°C

Aqua regia (3HCl 25°C

5H,SO, 25°C

+ IHNO,),

+ lHzOz + 1H,O

Typical etch time

Etch rate (pmin-I)

Water rinsed

Methanol rinsed

8.5

Good breakdown results, but some instability of breakdown is generally found with aqueous rinsing

Best etch and rinse combination to obtain stable high-breakdown voltage; stable junctions on Ga(As, P) alloys ;makes for very smooth, shiny surfaces

2-3 min

5

Makes fairly good surfaces with good breakdown; with water rinsing, this etch is not better than peroxide sulfuric acid etch

Next in quality to brominemethanol; good stability with GaAs, but Ga(As, P ) junctions degrade over short time

10 min

3

Very slow etch, used as polishing etch to prepare surfaces for growth; intermittently good low-leakage junctions

Good results obtained with this etch, but leakage and stability were poorer than with other systems

2 min

22H2O2 + lHF, 25°C

30-90 sec

High leakage, unstable Not used breakdowns ; not compatible with SiO, for protecting contacts

lHCl + 1H,O, 25°C

1-2 min

Some success with this etch, but inferior to etch above

1 min

Used as cleanup etch on mounted pellets; metal could not withstand other etches; when used with methanol rinse, the cleanup is reasonably successful, but inferior to Br, :CH,OH

lNH,OH 25°C

+ 5H20,

+ 1H2O2+ 5H,O,

Not used

i

cd

716

R. E. ENSTROM, H. KRESSEL, A N D L. KRASSNER

Deposited silicon dioxide and phosphosilicate films and hot-pressed glassing have been used as protective and passivating layers. In particular, phosphosilicate films deposited at a low temperature have been used on both GaAs and GaAs, -xPxjunctions. Best results have been obtained with a deposited film of phosphosilicate approximately 6300 A thick. Junctions in GaAs, -xPx have been particularly unstable, degrading rapidly on standing even at room temperature. When the bromine-methanol etch was combined with deposition of phosphosilicate, stability was achieved for breakdown voltages as high as 415 V. 11. RECTIFIER MOUNTING AND

PACKAGING

Mounting and packaging of the finished rectifier pellet serves three purposes : (a) Convenient, sturdy electrical connections are provided to the semiconductor pellet ; (b) an effective thermal conduction path is established for cooling the device ; and (c) physical protection from the atmosphere and exposure to gross contamination is assured. To function effectively, the packaging process must not degrade the electrical characteristics of the semiconductor in any way, and the materials used should not limit the operating temperature or environment of the semiconductor. For large-area, high-current semiconductor devices, the preferred method for mounting and lead attachment is broad-area soldering. This technique provides the necessary high electrical and thermal conduction, and distributes current and heat flow uniformly in the semiconductor. Many solder materials have low melting temperatures, and cannot be used in a device operating in a 300°C ambient. Braze materials are available with higher liquidus temperatures, and the problem is to select a joining material that liquefies in the range between 350°C and the upper limit set by the possible formation of liquid phases between the GaAs, evaporated contacts, and braze material. A practical upper limit for brazing is about 600°C. Gold-germanium eutectic solder (12 wt. % Ge) and gold-indium braze (25 wt. % In) have been used for joining operations. The gold-germanium solder melts at 356“C, and the gold-indium at about 460°C. Preform disks two mils thick of the gold-germanium can be prepared from rolled sheets, but the gold-indium is brittle and can only be used in powder form. The wetting and flow of the gold-germanium were far superior to the gold-indium, which “balled,” when used to braze GaAs pellets to molybdenum slabs. The gold-germanium flows best when the surfaces with which it is in contact are precoated with plated or evaporated gold. In this way, no chemical flux, which might leave contaminating residues or be difficult to clean, is required. The mounting of the rectifier pellet involves rapid heating and cooling between 25°C and 360”C, and this operation will subject it to cycling between

10.

HIGH-TEMPERATURE POWER RECTIFIERS OF

GaAs, -xP,

717

300°C and 20°C. The differences in thermal expansion between the various materials of construction generate stresses in the structure that must be regulated to prevent fracture failures. The most sensitive part of the structure is the semiconductor pellet itself, and any cracking of the pellet generally results in catastrophic electrical failure. The mechanical properties of gallium arsenide are such that compressive stresses are less likely to cause failure than tensile stresses. Therefore, it is preferable to subject the pellet to moderate compressive stresses rather than to risk tensile stress at all. The high thermal conductivity of copper is very desirable to remove the heat generated in the pellet, but the large expansion mismatch between copper and gallium arsenide can cause fracture of the pellet, Thus, a stress-relief insert between the copper stud and gallium arsenide pellet is employed. Stress-relief inserts of iridium, molybdenum, tantalum, and #46 alloy89a (46% Ni-54X Fe) have been considered. The pertinent properties of these materials, and of copper and gallium arsenide, are tabulated in Table V. TABLE V PROPERTIES OF RECTIFIER AND PACKAGE MATERIALS

Material

Coefficient of thermal expansion (x

Coppergo Molybdenum9' Iridiumgz Tantalum" #46 Alloy93 Gallium arsen~de'~.''

~o-~oc-')

Thermal Conductivity ( c a ~see-' cm-'PC)

I66 39 68 65 71

65

0.94 0.35 0.355 0.130 0.05 0.10

As shown in Table V, only #46 alloy produces the desired compressive stress. All the other insert materials would produce tensile stresses below the soldering temperature, except for the copper stud itself, which would exert excessive compression. The low thermal conductivity of # 46 alloy requires that the insert be thin. But because #46 alIoy has a large EI product (Young's modulus x moment of inertia), which provides rigidity, even a 89"Manufacturedby the Wilbur B Driver Co.. Newark, N.J. Inst. Metal. Bull. (1965). 9 1 Fansteel Metallurgical Corp., North Chicago, Illinois (1960). 92 R. W. Powell et al., Platinum Metals Rev. 6 , 138 (1962). y 3 Data from Wilbur B. Driver. Newark. N. J. 94 Pierron et al., Actu Crystall. 21, 290 (1966). 9 5 P. D. Maycock, Solid State Electron. 10, 161 (1967). yo

718

R. E. ENSTROM, H. KRESSEL, A N D L. KRASSNER

10-mil-thick shim prevents transmission of the stresses from the copper stud to the gallium arsenide pellet. Referring to Fig. 10, the sequence of assembly is as follows: (a) The stud is prepared by soldering to it a gold-plated #46 alloy insert with a Au-Ge preform. (b) The top connector assembly is prefabricated by soldering the #46 alloy shim and copper lead to the copper shoe. (c) The rectifier pellet is placed on the stud assembly and the top connector portion is placed on the pellet. (d) The assembly is soldered in an induction-heating apparatus. The entire assembly is held in place with a carbon jig. Two problems occurred in the attachment of the top lead. The first was eliminated when a flexible copper ribbon connector was substituted for the rigid lead to reduce mechanical damage. The second problem was the frequent occurrence of short circuits during the mounting process resulting from the breakthrough of the gold past the Ag-Ni-Au layers of contact metallization and the subsequent penetration through the p + layer into the n layer via a shallow growth pit. A good barrier to gold diffusion was achieved by substituting chromium for the nickel layer, and this greatly reduced mounting failures. The final step in the packaging process is to seal the rectifier case. Referring to Fig. 11, the process is a standard sealing operation in which the Kovar ring attached t o the alumina insulator body is welded to the steel weld ring on the stud by a combination of heat and pressure. At the same time, the flexible copper connector is crimped inside the copper tube on the other side of the alumina, completing the electrical connection to the p + side of the rectifier. A hole is later drilled in the flattened tubulation for easy connector attachment. V. Rectifier Test Results

The electrical resistance of the highest-voltage units is about 0.02 ohm at room temperature (0.16 cm2). This equals the calculated resistance value for structure (Section 4). At 25"C, the measured forward voltthe p+-p--n--n' age drop a t 50 A is 2.6 V. The measured difference in the forward voltage beV"C-', hence the forward voltage is tween 25°C and 300°C is 2.2 x about 2 V at 300°C. The power dissipation at 50 A peak current is therefore about 25 W, which compares to the calculated value of 21 W. With a thermal resistance of 1°C W-', the temperature rise of the junction above ambient is 25°C. A at 50 V reverse bias, close The 300°C saturation current is 2 x

10.

HIGH-TEMPERATURE POWER RECTIFIERS OF

GaAs, -xP,

719

to the predicted value of 4.3 x 1 0 - 3 A for the generation-recombination sec. current assuming z = Three completed rectifiers were stored at 300°C for 100hr without any degradation in their characteristics. These units also withstood a temperature cycling test consisting of 10 cycles between 25°C and 300°C. Furthermore, the mechanical structure was sturdy enough to pass rigid mechanical tests consisting of a total of 48 min of vibration testing. One of these tests, of 4-min duration, required vibration at 20 g acceleration through the frequency range from 100 to 2000Hz back to 100Hz. The above results concerning the rectifier properties are evidently incomplete from the applications point of view because long-term reliability at the rated conditions remains to be determined on sufficiently large numbers of samples for meaningful conclusions to be drawn. It is clear, however, that the electrical and mechanical requirements of a 3WC, 50-A rectifier have for the first time been met with GaAs0,85P0,15 prepared by vapor-growth.

ACKNOWLEDGMENTS The authors are grateful to L. Weisberg for many valuable technical discussions and to A. Mayer for making available some unpublished information concerning rectifier fabrication. This work was supported in part by the Air Force Aero Propulsion Laboratory, Air Force Systems Command, Wright-Patterson Air Force Base, Ohio, under Air Force Contract AF33(615)-5352.

This Page Intentionally Left Blank

Author Index Numbers in parentheses are footnote numbers and are inserted to enable the reader to locate those cross references where the author's name does not appear at the point of reference in the text. Baynton, P. L., 702 A Beddows, M. P., 516 Abraham, M. S., 706,709 Belasco, M., 706 Adler, A.. 552 Bergman, R. H.. 602( 188). 603. 620(188) Aleksander, 1.. 602, 620( 174) Berman, H . S., 645.647, 682 Alferov, Zh. I., 688 Berman. 1.. 630. 632( 16) Amick, J. A,, 700, 702, 704, 705(19), 707( 19). Bernard, W., 599 708( 19) Berry, D. L., 602(209), 613(209), 620(209) Anderson, R. L., 501. 502(28). 506(28), Berson, B. E., 703, 708(41a) 5 lO(28) Bertram, W. J., Jr., 501, 503(26), 505(26), Anderson, W. W., 558, 559(111). 562(1ll). 509(26), 544(26), 621(26), 622(26) 570( 1 1 1). 571( 1 11) Bickley, W. P., 705, 706(45). 707(45), Andreev. V. M., 688 710(45) Antell, G. R., 706 Black, J. F., 709 Appert, J R., 700, 701(18), 702(18), 703(18), Blair, R. E., 600 704(18), 705(18), 706(18), 707(18). 707( 18), Blank, J. M., 679, 682 709(18), 710(18), 711(18) Blicher, A.. 690, 691, 693 Armstrong, L. D., 500, 501(25) Blurn, S. E., 702 Aron, R., 530, 531(57), 544(57), 549(57). Bobb, L. C., 709, 71 l(74) 550(57), 589(57) Bode, H. W., 531 Auckerman, L. W., 673,676 Bode, J. D., 451 Axelrod, M. S., 602, 620( 187) Bohm, D., 494 Bolger, D. E., 702, 703. 705(34), 707(34), 708(34) Baird, J . R., 537, 538(71), 542(71) Bonch-Bruevich, V. L., 476, 479(19). 490(19), Balder, J. C., 602, 620(175) 491( 19) Bandler, J. W., 539, 542(77), 543(77). 544, Bonin, E. L., 537, 538(71), 542(71) 551(85), 560(85) Bott, I. B., 705 Baraff, G. A., 379 Boughey, A. L., 637, 639. 640(37) Barber, M. R., 501, 503(26), 505(26). 509(26), Bowers, H. C., 385 544(26), 574, 575(147), 580(147). 583( 147). Bowman, D., 703 584( 147), 621(26), 622(26) Bowman, L. S., 432,449.458 Barnes, W. C., 531, 533(61) Boyer, R. H., 516 Barrett, D. L., 629 Brack, K., 636 Bartelink, D. J., 381, 421, 427(30), 428(30), Brandli, A., 531, 532(60) 448(30), 459(30), 468 Brander, R. W., 637, 639, 640, 680, 681, Bartlett, R. W., 632 682 Batdorf, R. L., 379,403,421(24). 444,446(41), Breitzer, D. I., 574, 575(143). 580(143). 451(10) 583(143), 584(143)

721

722

AUTHOR INDEX

Bncker, C. H., 448,459(47) Brody, T. P., 516 Bryson, V. E., 673 Buiocchi, C. J., 709 Bums, C. A., 432, 449, 458, 501, 503, 505(32,33,34), 509(32,33,34), 544,551(89), 560(88), 562, 573(1IS), 584, 596(149) Butler, J. H., 503, 504(41), 509(41), 510(41)

C

Campbell, R. B., 629, 630, 631, 641, 642(46), 644(46, 50), 652(50), 653, 654, 655(46), 656(46), 657(46), 658(46), 659, 673(46), 682 Canepa, P. C., 634,641,642,644(46), 654(46), 655,656,657,658,673 Card, W. H., 475, 476(4), 477(4), 481(4), 482(4), 491(4), 501(4), 515(4) Carlin, H. J., 598, 599(155) Carr, W. N., 602(189), 620(189) Carroll, P., 635 Carslaw, H. S., 435(34), 436 Casey, H. C., Jr., 706 Cawsey, D., 562, 573(130) Chan, Y. T., 550,599(98) Chance, D. A., 503, 504(41), 509(41), 510(41) Chang, H. C., 627, 629, 630, 633, 634, 635, 636(8), 637,639,641, 642,643, 644(6,8,24, 30, 40, 50), 645, 646,647(8), 650(8), 651, 652(50), 653,658(6), 659,660,664,665,666, 667,674,676(69) Chang, K. K. N., 449, 458(55), 459(55), 501, 574, 575(141), 580(141), 583(141), 584, 596( 153) Chang, V. W., 598, 599(156) Chang, Y., 693 Chase, P. E., 584, 596(153) Chodorow, M., 467 Chow, W. F., 475, 476(3), 477(3), 481(3), 482(3),491(3), 501(3), 510(3), 512(3),515(3), 537(3),538(3),539(3), 542(3), 544(3),552(3), 562(3), 569(3), 574(3), 584(3), 602, 606(3), 609(3), 613(3), 616(3), 620(3, 176) Choyke, W. J., 626 Christensen, H., 451 Chu, T. L., 630, 631 Chynoweth, A. G., 377, 379,380, 384(6), 488, 489(22), 491(22), 495(22), 501(22), 510(22), 512(22), 513,600,601(22, 171), 690

Cicolella, D. F., 445 Clorfeine, A. S., 466,470 Coerver, L. E., 562, 573( 123) Cohen, B. G., 372,448(2), 460(2), 690 Collinet, J. C., 568, 620(135) Colliver, D., 705 Conrad, R. W., 703,704,705(40), 707 Considine, D. P., 630, 632(16) Coupland, M. J., 503, 504(36) Cox, D. C., 533, 534(67), 544(67), 551(67), 560(67) Cronin, G. R., 709 Crowell, C. R., 379 Cuccia, C. L., 568, 620( 136) Cuttriss, D. B., 451

D Dacey, G. C., 663 Das, B. N., 702 Davies, I. G., 709 Davis, J. R., 674, 676(69) Davis, R. E., 503, 504(39), 505(39), 509(39), 510(39) De Andrade, C. A,, 488, 489(23) Decker, A. J., 475, 476( 13), 477(13), 480(13), 482( 13), 486( 13), 491(13), 506(13) De Loach, B. C., Jr., 372, 444, 447, 448(2,42), 458(42),460, 461(42),466, 541, 552. 565 Denayer, M., 672 Dickens, L. E., 475, 476(2), 477(2), 481(2), 482(2), 483, 491(2), 501(2), 515(2), 516(2), 527(2), 543, 544(2), 556, 574, 575(145), 580(145), 583(145), 584(145) Dimmock, J. O., 702, 708(34) Dobson, C. D., 702 Dreeben, A. B., 706, 709(55) Dunn, C., 501, 503(26), 505(26), 509(26), 544(26), 621(26), 622(26)

E Easley, J. W., 600 Eddolls, D. V., 705, 706(46) Effer, D., 702, 703, 705(28) Egawa, Hideharu, 385

723

AUTHOR INDEX

Ehrenreich, H., 600, 601(168) Ekstrom, L., 709 Ellis, R. C., 627, 632 Engelbrecht, R. S., 552 Enstrom, R. E., 700, 701(18), 702(18), 703, 704, 705(18), 706(18), 707(18), 708(18,41a. Ma), 709(18), 710(18), 711(18), 712 Esaki, L., 475, 476(1), 477(1), 481(1), 482(1), 488, 489(21), 491(1, 21), 495(21), 501(1), 515(1), 599 Evans, P.R., 703 Evans, W. J., 421, 429, 448, 458(27), 459, 461(50), 470

F Farber, A. S., 602, 620(187) Faust, J. W., 636 Feldman, W. L., 488, 489(22), 491(22), 495(22), 501(22), 510(22), 512(22), 513(22), 600(22), 601(22) Ferber, R. R., 657 Ferendici, A., 516 Finch, W. F., 703 Fisch, E. A., 602(209), 613(209),620(209) Fisher, S. T., 404,405 Fistul, V. I., 475, 476(11), 477(11), 481(11), 482(11), 491(11), 493(11), 501(11), 503(11), 504(11), 506(11), 512(11), 515(11), 527(11), 537(11), 539111). 542(11), 544(11), 558(1l), 562(1 I), 57ql I), 600( 11). 601(11) Fitzimmons, G. W., 619 Foote, R. S., 602, 620(177) Formigoni, N. P., 637, 639(40), 642(40), 644(40), 666(40) Fortgang, M. M., 562, 567(128), 573(128) Foster, L. M., 702 Fox, G. E., 537, 542(70) Foyt, A. G., 705 Franks, J., 702, 703(34), 705(34), 707(34), 708(34) Franz, W., 475,476(6), 477(6), 481(6). 482(6), 491(6), 493(6), 501(6), 515(6) Franzini, F. H., 602(190), 620(190) Frederick, W. L., 562, 567(125), 573( 125) Freiser, R. G., 707 Frisch, I. T., 531, 598, 599(156) Fukui, H., 539, 542(75), 568, 570(138), 573(138), 602, 620( 138, 178)

Funada, H., 475,476(9),477(9), 479(9), 481(9), 482(9), 490(9), 491(9),493(9), 501(9), 515(9) Fype, T. A., 537, 542(68)

G

Gabor, T., 636 Gabriel, W. F., 584, 588(152), 593( 596(152) Gallagher, R. D., 544, 551(82),560(82) Gambling, W. A,, 574, 575(146), 580( 583(146), 584(146) Garfein, A., 599, 600 Gartner, W. W., 602.620(184) Gaylord, J. W., 709 Getsinger, W. J., 507, 534(43), 550 Gibbons, G., 379. 384(7), 436, 438. 439, 440, 441, 442, 444, 445, 448, 456(48), 503, 504(39), 505(39), 509(39), 510(39),690 Gibbons, L. H., Jr., 690, 691 Giblin, R. A,, 538, 542(73) Gibson, J. J., 602, 606(185),620(185) Gilden, M., 399, 445(23) Ginzton, E. L., 539 Giorgis, J., 501 Glasford, G. M., 475, 476(4), 477(4), 481(4), 482(4), 491(4), 501, 502(28), 506(28), 510(28), 515(4) Gneiting, C. R., 574, 575(145), 580(145), 583(145), 584( 145) Goetzberger, A., 695, 710 Gold, R. D., 708 Goldberg, C., 629 Goldsmith, N., 702 Goodwin, A. R., 702 Gordon, J., 702, 703(34). 705(34), 707(34). 708(34) Gorton, H. C., 673 Gossenberger, H., 704, 706, 709(55) Goto, E., 602,620(186) Gottlieb, E., 501 Goulding, E. S., 654 Greebe, C. A. A. J., 641,642,653 Greene, P. E., 702 Griffiths, L. B., 632,633,646,680 Guillemin, E. A., 531 Gummel, H. K., 393, 421, 422, 423, 424, 432(28), 451 Gunn, J. B.. 385

724

AUTHOR INDEX

H Haddad, G . I., 421, 458(27) Haisty, R. W., 707 Haitz, R. H., 695 Halden, F. A., 632 Hall, R. N., 503, 504(35), 600, 601(168. 169, 170), 641, 661 Hamasaki, J., 533, 534(66), 544(66), 551(66), 554, 560(66) Hamilton, D. R., 626. 627, 654(5), 658(5) Hamilton, G. N., 657 Hansen, W ., 654 Harbourt, C. O., 475, 476(4), 477(4), 481(4), 482(4), 491(4), 501(4), 515(4) Harrison, S. W., 552 Harrison, W. V., 602, 620(177) Hasegawa, F., 708 Hauer, W. B., 542 Haus, H. A,, 552 Havens, R. C., 544, 551(88), 560(88) Hawley, J. J., 630, 632(16) Hawrylo, F. Z., 709 Hefni, I., 531, 533(61) Heilmeier, G. H., 574, 575(141), 580(141), 583( 141), 584(141) Heiman, F. P., 602(203), 613(203), 620(203) Hein, V. L., 436 Hemel, A., 602, 620(179) Henoch, B. T., 531, 533(63), 534(63), 544(63), 551(63), 560(63) Herzog, G. B., 602, 606( 189, 620(180. 185) Hilibrand, J., 708 Hill, P. C. J., 547 Hillman, K., 602(204), 613(204), 620(204) Hilsden, F., 584, 596(150) Hilsum, C., 503, 504(36), 705 Hilton, A. R., 705 Hinden, H. J., 562, 567(128), 573(128) Hines, M. E., 399,445, 531, 532(62), 533(62), 544(62), 558, 559( 11I), 562(11 l), 570( 11l ) , 571(111) Hoefflinger, B., 385,459,461(64) Hoffins, C. C., 562, 567(124), 573(124) Holloway, H., 709, 711(74) Holmes, D. P., 702 Holonyak, N., 501, 600, 601(168) Hornbostel, D. H., 562, 567(127), 573(127) Hornung, H., 503, 504(42), 509, 510(42) Hughes, K. A,, 709

I Ichiki, H., 602(213), 613(213), 620(213) Iglesias, D. E., 448, 456, 459,461(50) Ikeda. K., 602(213), 616(213), 620(213) Ikola, R. J., 466,467(71), 470(71) Im, S. S., 503, 504(41), 509, 510(41) Irvin, J. C., 451 Ishibashi, Y ., 602, 620( 186) Ishida, H., 602, 620(186) Ishii, T. K., 562, 567(124), 570, 573(124) Iwahashi, E., 602( 199), 620(199)

J Jaeger, J. C.. 435(34), 436 Jennings, V. J., 630,636 Jenny, D. A,, 688 Johnston, R. L., 372,421,427, 428,444,445, 447. 448, 454(53), 455, 458(42), 459. 460, 46 l(42) Jones, C. E., 705 Jones, R. M., 626 Josenhans, J. G.. 445,448,452,453,454,455, 456(48).459, 567. 568(134) Joyce, B. D., 709, 711(75) Jungbluth, E. D., 709

K Kaenel, R. A., 602(200, 205, 212), 613(205), 616(212), 620(200,205,212) Kal’nin, A. A., 678, 679(74), 682(74) Kamath, G. S., 703 Kaminsky, G., 403,421(24), 444,446(41) Kane, E.O., 475,476(8),477(8),479(8), 481(8), 482(8), 490(8), 491(8), 493(8), 494, 496(8), 497, 501(8), 515(8) Kang, C. S., 702 Keldysh, L. V., 475, 476(7), 477(7), 481(7), 482(7), 491(7), 493(7), 494, 496(7), 501(7), 515(7) Kennedy, D. P., 435, 514 Kholuyanov, G. F., 634, 678 Kibler, L. U., 602(201), 620(201) Kiggins, T. R., 599

125

AUTHOR INDEX

kkuchi, S., 708 Kim, C. S., 531, 532(60), 539, 542(76), 574, 575(144), 580(144), 582(144), 583(144), 584 (144)

Kimura, H., 562, 569(120), 573(120) Kinariwala, B. K., 598, 599(157) King, B. G., 517, 518(53), 538 Kiyono, T., 602(213), 616(213), 620(213) Kleimack. J. J., 379, 451 Knight. J. R., 703, 705. 706(46) Knippenberg, W. F., 623,641,642 (44) KO, W. H., 516 Kolb, G. A,, 705 Kolk, P., 544, 547(83), SSl(83). 560(83). 562(83) Komanaiya, Y ., 602( 192), 620(192) Korolkov, V. I., 688 Kovel, S. R., 448 Krasilov, A. V., 454 Krassner, L. A,, 712 Kressel, H., 690, 691, 692, 693, 694, 701. 702, 709 Krieger, J. B., 475, 476(10), 477(10). 481(10), 482(10), 491(10), 493(10), 494, 501(10), 515( 10) Kroko, L. J., 627,628,629,633,635.643(7,9), 644 Kruy, J . F., 602(193), 620(193) Ku, S., 708 Kuh, E. S., 550, 599(98) Kupsky, G., 690,692,704 Kurzrok, R. M., 544, 551(91), 560(91) Kvaerna. Y., 531, 533(63), 534(63), 544(63), 551(63)

L La Belle, H. E., Jr., 702 Larrabee, G. B., 709 Lawley, K. L., 702, 705(27) Lebenbaum, M. T., 552 Leber, A., 554, 555(106), 556, 557, 558(106), 622( 106) Lee, C. A,, 379, 403, 421, 444. 446. 451(10) Lee, C . W., 539, 542(76), 556 Lely, J . A., 627 Le May, C. Z., 633, 634, 635(30), 642(24, 30). 643(24), 644(24, 30), 659(24), 660(30). 664 (24,30)

Leondardt, H. R., 702 Lepoff, J. H., 544, 551(87), 560(87) Lepselter, M. P., 451 Lesk, I. A., 501,600, 601(168) Levy, R., 550, 589(100) Lewin, M. H., 602, 620(181) Li, K., 602(210), 613(210), 620(210) Lim, J . T., 550, 551(103) Lindley, W. T., 705 Lo, A. W., 602, 620(181) Loar, H. H., 451 Logan, R. A., 379, 451(10), 488, 489(22), 491(22), 495(22), 501(22), 510(22), 512(22), 513(22), 600, 601(22, 171), 690 Losee, D. L., 598, 599(159) Low, A. W., 602(210), 613(210), 620(210) Lowry, H. R., 501 Lueck, A,, 503, 504(40), 508(40) Lynch, R. T., 702 M McCarthy, 705, 706(45), 707(45), 710(45) MacDonald, R.W., 451 McKay, K. G., 692 Macpherson, A. C., 547 Malinaric, P., 641, 642(46), 644(46), 654(46), 655(46), 656(46), 657(46). 658(46). 673(46) Mallick, S. B., 574, 575(146), 580(146), 583 (146), 584(146) Mano, K., 562, S69( 120). 573(120) Marinaccio, L., 437, 438, 449. 45353). 456, 459 Marmiani, A., 503, 504(40), 508(40) Marsh, L. E., 632 Marshall. R. C., 630. 632(16) Martinelli, G., 530 Maruyama, M., 708 Matsuoka, Y ., 602, 620(186) Matsushima, T., 602, 620( 178) Matthei, W. G., 618 Maycock, P. D. Mehal, E. W., 703, 704(40), 705(40). 707 Meieran, E. S., 705 Meyer, C. S., 517 Miles, T. P., 533, 534(67), 544(67), 551(67), 560(67) Miller, B. A., 533, 534(67), 544(67), 551(67), 560(67) Miller, H. S., 602( 194), 620( 194)

726

AUTHOR INDEX

Miller, J. C., 602(210), 613(210), 620(210) Miller, S. L., 599, 600, 601(165, 172) Milnes, A. G., 599, 602(189), 603, 620(189), 633,635 Misawa, T., 378, 385, 390, 392, 393(17), 398(17), 404, 405, 406(26), 408, 409(26), 410, 429(26), 433, 436, 437, 438, 439, 440, 441, 445(39), 446, 448, 449, 452, 453, 454, 455(39, 52, 53), 456, 457, 459, 460(52), 461, 464,465,466 Mishizawa, J., 458 Mitchell, F. H., Jr., 602(191), 62q190) Mittra, S. K., 598, 599(159) Miyahara, Y ., 599 Mizuno, O., 708 Mlavsky, A. I., 632, 646, 680, 690 Mokhov, E. N., 633,634(26), 635(26) Moll, J. L., 432,434(32), 475,476( 15),477(1 3 , 480(15), 482(15), 486(15), 506(15) Moody, N. F., 558 Moreno, T., 460 Morgan, J. R., 705 Moto-oka, T., 602,620(186) Mouw, R. B., 584, 588(151), 593(151), 596 (151)

Neve, N. F. B., 709, 710 Nielsen, R. J., 451

0 Okabe, T., 458 Okean, H. C., 503, 504(37, 38), 505(37, 38), 509(37, 38), 510(37, 38), 519, 527(55), 530(55), 531(55), 532(55), 533(55), 534(55), 539(55), 542(55), 543(55), 544(38, 55), 549 (5% 550(55), 551(55), 554, 555(38, 106), 556,557,558(106), 560(38,55,106), 569(38), 589(55), 621(37,38), 622(37,38, 106), 623 Oldham, W. G., 703 Ondria, J. G., 568, 620(135) Osborne, J. F., 709 Oshinsky, W., 702 Ostraski, J. W., 629, 641, 642, 644(46), 646, 654(46), 655(46), 656(46), 657(46), 658(46), 673(46) Oxley, T. H., 584, 596(150)

P

Muller, H. S., 602,606(185), 620(185) Muller, R. A,, 632 Mullin, J. B., 709, 711(75) Mumford, W. W., 552 Murata, K., 602, 620(186)

N Nagels, P., 672 Nagumo, J., 602(198), 606(198), 610(198), 620( 198) Nakagawa, K., 602,620(186) Nakazawa, K., 602,620(186) Nanavati, R. P., 475, 476(4, 17), 477(4, 17), 480(17), 481(4), 482(4, 17), 486(17), 488, 489(23), 491(4), 501(4), 502(28), 506(28), 510(28), 515(4) Napoli, L. S., 466,467(71), 470(71) Narud, J. A., 517, 537, 542(68) Nathan, M. I., 599,600, 601(165, 172) Neilsen, E. G., 544, 551(92), 552(92), 560(92) Nelson, H., 701 Nelson, W. E., 632

Panish, M. B., 706 Parsons, A. H., 709 Pasynkov, V. V., 678,679(74), 682(74) Patrick, L.,626 Patterson, J. D., 550 Payton, J. Y., 602(21I), 613(211), 620(211) Pedinoff, M. E., 544,551(92), 560(92) Persky, G., 38 1 Persson, D. R., 562, 568(122), 573(122) Peterson, C. C., 704 Philipp, H. R., 626 Pichugin, I. G., 629 Pink, F., 709 Pizxarello, F. A,, 708 Plaskett, T. S., 702, 709 Potter, R. M., 679, 680, 682 Powell, R. W., 717 Powlus, R. A., 602, 603, 606(185), 620(185, 194) Prager, H. J., 449, 458, 459, 574, 575(141), 580(141), 583(141), 584(141) Presser, A., 562, 573(121) Prussin, S., 695 Pucel, R.A., 574,575(142), 580(142), 583(142), 584( 142)

AUTHOR INDEX

R Rabinovici. B., 602.61 3(206),62q 183, 195.206) Rabson, T. A,, 602, 620(182) Rappaport, P., 660 Read, W. T., Jr., 372, 374(1), 376, 378, 381. 399, 41 1.442 Redheffer, R. M., 391 Reifman, M. B., 633, 634(26), 635(26) Reindel, J., 574, 580(148), 584(148) Reisman, A,, 705 Renton, C. A., 602, 620(183, 195) Reynolds, J. F., 703,708(41a) Richman, D., 704, 708(44a) Rindner, W., 599,600 Roberts, J. S., 634, 637, 639(40), 642(40), 644(40), 666(40) Rogers, E. S., 599 Rohr, R., 705 Rosengreen, A,, 632 Rosenheim, D. E., 602,620(187) Rosenzweig, W., 451 Ross, I. M., 663 Roswell, A. E., 562, 573(121) Roth, H., 599 Rubenstein, M., 708 Ruehrwein, R. A., 703 Rulison, R. L., 448,456(48) Rupprecht, H., 701 Rutz, R. F., 661,662,663 Ryan, C. E., 630, 632

S Samusenka, A. G., 602,620(181) Sard, E. W., 544, 551(86), 560(86) Sarrafian, G. P., 602(196), 620(196) Savarin, A., 568, 620(136) Scanlan, J. O., 475, 476(12), 477(12), 478(12), 480(12), 481(12), 482(12), 483(12), 491(12), 494, 496, 497, 499(12), 501(12), 506(12), 515(12), 516(12), 517(12), 523(12), 530(12). 531(12), 533(12), 543(12), 544, 547(12), 549(12), 550, 551(94, 103), 552(12), 554(12), 560(94), 562(12), 564(12), 567, 570(12), 571(12), 572(12), 573(12), 574(12), 580(12), 581(12), 582(12), 583(12), 584(12), 598(12), 599(12)

727

Scarlett, R. M., 695 Scarr, R. W., 602,620(174) Scharfetter, D. L., 393, 421, 422, 423, 424, 427(30), 428(30), 429, 432(28), 448(30), 459(30), 466,468,469,470 Scherer, E. F., 568,620(137) Schnable, G. L., 710 Schott, L. E., 676 Schultz, W., 503, 504(40), 508(40) Schumacher, F. M., 584, 588(151), 593(151), 596( 151) Sciola, J., 709 Scott, A.C., 558, 562,570(112, 131), 571(112, 131). 572(131), 5731131) Sear, B. E., 602(197), 620(197) Seidel, T. E., 377 Serophirn, G. R. S., 562, 565(115). 573(115) Serta, A. J., 71 I Sharpe, G. E., 517, 518(53), 538 Shaw, D. W., 703, 704(40), 705(40), 706, 707 Shaw, R . C., 562 Shelton, W. L., 562, 567(125), 573(125) Shenoi, B. A., 598, 599(158) Shepherd, F. D., Jr., 475, 476(5), 477(5), 481(5), 482(5), 491(5), 501(5), 515(5), 525, 527(5) Sherwell, R. J., 503, 504(36) Shimura, M., 602(198), 606(198), 610(198), 620( 198) Shockley, W., 374, 377,381,387,475,476(14). 477( 14), 480( 14), 482( 14), 486( 14). 506(14). 663,694,695, 710 Shuller, M., 602, 620(184) Shvarts, N. Z., 475,476(11), 477(11), 481(11), 482(11), 491(11), 493(11), 501(1l), 503(11), 506(11), 512(11), 515(11), 527(11), 537(11), 539(11), 542(11), 544(11), 558(11), 562(11), 574(11), 600(11), 601(11) Sie, J. J., 544, 551(90), 560(90) Sikorski, M. E., 599 Skalski, C. A., 558 Slack, G . A., 633 Slepian, P., 550, 589(99) Smilen, L. I., 531, 532(59), 543(59), 544(59), 549(59), 550(59), 589(59) Smirnova, N. A,, 629 Smith, A. C., 599, 601(165) Smith, K. D., 451 Smith, P. H., 519 Smith, R. C., 637 Snapp, C. A., 459, 461(64)

728

AUTHOR INDEX

Sokolnikoff, I. S., 391 Soma, T., 602, 620(186) Sommer, A., 630 Sommers, H. S., Jr., 501 Spenke, E., 475, 476(16), 477(16), 480(16), 482( 16), 486( 16) Spiegel, P., 602(207), 613(207), 620(207) Sproull, R. L., 476,478(18), 491(18) Stark, L. A., 459,461(64) Steinhoff, R., 544, 551(84), 557(84), 558(84), 560(84) Stephenson, I. M., 562, 5 6 3115), 573(115) Sterzer, F., 516,544,551(84), 557(84), 558(84), 560(84), 562, 569, 573(116, 119) Stewart, C. E. E., 706 Stillman, G. E., 702, 708(34a) Sullivan, M. V., 705 Sulway, D. V., 709 Susskind, C., 467 Swan, C. B., 437,438,448,459 Sze, S. M., 379,384(7), 387,442,444,445,451, 476, 479(20), 490(20), 491(20), 494(20), 495(20), 496(20), 690, 691, 693

T Taft, E. A., 626 Tager, 454 Tairov, Yu, M., 629, 678, 679(74), 682(74) Takeuti, Y ., 475,476(9), 477(9), 479(9), 481(9), 482(9), 490(9), 491(9), 493(9), 501(9), 515(9) Tarnay, K., 567 Taylor, A., 626 Taylor, R. C., 703 Taylor, R. J., 508, 584(44), 596(44) Taylor, T. C., 642(48), 643 Tarnay, K., 516 Theuerer, H. C., 451 Thibault, N. W., 637 Thomas, D. E., 539, 542(74) Thomas, D. G., 702 Thompson, G., 562, 567(126), 570(126), 573 (126) Thornton, P. R., 709,710 Tiemann, J. J., 600,601(168) Tietjen, J. J., 697, 700, 702(19), 703(19), 704, 705(19), 706, 707(19), 708(17, 19, 44a), 709 Todd, C. D., 537,539(69), 542(69) Todkill, A., 680, 681, 682

Tolopko, L. N., 560 Torrey, H. C., 514,575(46), 576(46) Trambatulo, R., 544, 551(89), 560(89), 562, 573( 118) Tretyakov, D. N., 688 Tuchkevick, V. M., 688

U Udelson, B. J., 421,425, 426, 427 Ure, R. W., 642(49) Uzunoglu. V., 602(202), 620(202) V Val'd-Perlov, V. M., 454 van Daal, H. J., 641,642 van der Pauw, L. J., 658,708 Vema, A. R., 626 Veth, G. J., 602(208), 613(208), 620(208) Vickers, V., 475,476(5), 481(5), 482(5), 491(5), 501(5), 515(5), 525(5), 527(5) Vink, J. J., 641, 642(44) Violin, E., 634,678,679, 682 Vodakov, Yu.A., 633,634,635

W Wacker, A. G., 558 Wada, E., 602, 620(186) Wallace, L. F., 633, 634, 635(30), 642(24, 30), 643(24), 644(24, 301, 659(24), 660, 66424, 30,63), 665, 666,667,711 Wang, P., 709 Ward, A. L., 421,425,426,427 Weinberg, L., 550, 589(99), 598, 599(154) Weinstein, M., 690 Weisberg, L. R., 697, 708(17) Weisbrod, S., 449,458(55), 459(55) Weischedel, R. C., 501 Welch, J. D., 621 Westgate, C. R., 508, 584(44), 596(44) Whitaker, J., 702, 703, 705(34), 707(34), 708(34) White, H. G., 690(7) Whitmer, C. A., 514, 575(46), 576(46) Wiegmann, W., 379, 403, 421(24), 444,446 (41), 451(10)

729

AUTHOR INDEX

XYZ Wilfinger, R. J., 537, 542(72) Willardson, R. K., 673 Williams, F. V., 706, 709(59) Williams, R., 690(6), 693 Wilson, B. L. H., 705, 706(46) Wilson, 0. W., 703, 704(40). 705(40). 707(40) Wolfe, C . M., 702, 705, 708(34a) Wolff, G . A., 702 Wolff, P. A., 600, 601(171) Wright, M. L.. 562. 567(129), 573(129) Wysocki, J. J., 660, 688

Yajirna, T., 488,489(21). 491(21), 49321) Yang, A. C.. 475. 476(5), 481(5), 482(5). 491(5). 501(5), 5135). 525(5.7) Yas’kov, D. A., 629, 678, 679(74), 682(74) Yerman, A . I., 599 Youla, D. C., 531, 532(59). 543(59), 544(59), 549(59), 550(59), 589(59), 598, 599( 155) Young, D. T., 562, 573(117) Zolotar, B. A , , 537, 542(72) Zook, D., 503, S04(42), 509, 510(42)

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Subject Index

A

Abrupt junction, 394397, see also Diode, abrupt junction breakdown voltage, 690 GaAs diode, 690 Q, 396-398 small-signal admittance, 394396 Absorption edge, 309-312 shift due to strain, 304 Accumulation layer, LSA oscillator, 18-20 Admittance parameters GaAs FET, 184198 MOS-FET amplifier, 233-245 p v - n diode, 397, 398 Read diode, 403 Scharfetter-Gummel diode, 423 IAIGa V\s-GaAs heterojunctions. 347 band profiles, 363 recombination-emission spectra, 347 Amplifiers, bulk negative resistance, 2 4 3 2 Anisotype heterojunction, 323, 327, 337, 341, 342,359 interface photocarrier properties, 342 Avalanche breakdown, 375 condition, 384 Avalanche multiplication, 372-382, 390-393, 693

B Band bending, 101,207,213-215 Band edge, discontinuities, 3 10, 347 measurement, 325 Band-edge tailing, 487489, seealso Degeneratively doped semiconductor, p n junction Band profile, idealized, 300, 309-3 I3

Band profile, interface, 309-326 capacitance, 319-326 inclusion of surface states, 31 3-3 19 neglect of surface states, 313-319 Band structure bulk negative resistance, 4, 5 degeneratively doped pn junction, 483-485 degeneratively doped semiconductor, 475480 discontinuities (heterojunction), 307-3 13, 325, 347 transferred electron effects. 4-6 Barrier capacitance, 93,96103, 146, 164169 Barrier height determination capacitance measurements, 93.99 photoelectric response, 93, 95, 146 Barrier height variation, 84-88 electric field, 8488,95-99 temperature, 92, 93 Bethe diode model, 360, see afso Diode theory BNR, see Bulk negative resistance BNR device fabrication contacts, 61-67 examples, 67-72 material growth. 55-60 Breakdown abrupt junction. 690-692 GaAs, 690-692 avalanche multiplication, 372-376. 693 GaAs junction, 690-696 graded junction. 691 impact ionization coefficients Ga(AsP), 690,693 p n junction I- Y characteristics, 383-390 negative resistance, 375, 376 temperature dependence, 692,693 Built-in voltage measurement in GaAs, I63 Schottky barriers, 163-166

731

732

SUBJECT INDEX

Bulk negative resistance, 3ff McCumber-Chynoweth model, 8 , 9 mean-length model, 6 8 Bulk negative resistance devices, see also Negative resistance, BNR device fabrication amplifiers, 24-32 impedance, 2 6 3 0 noise figure, 24 design considerations, 43-54 device performance, 67-72 fabrication technology, 55-72 operation, 1 4 4 3 Burgers vector, 302 C

Capacitance heterojunctions, 3 17-326 importance of surface states, 3 19-326 junction, frequency dependence, 324 Schottky barrier, see Barrier capacitance semiconductor surface, 214 B C junction, 675, 676 tunnel diode, see Tunnel diode Capacitance-voltage ( C - V ) dependence heterojunctions, 31 7-326 high frequency, 214 importance of surface states, 319-326 impurity profile, Read diode, 444,447 measurement, 224-226 MOS structures, 214219 Carrier bunching, 374, 39 I , 392 Carrier concentration, temperature dependence BNR devices, 43 Carrier density, doped semiconductor, 48 1 Carrier mobility, 44, 689 temperature dependence, BNR devices, 44 Carrier velocity, see Charge carrier velocity, Electron velocity CdO-Si heterojunction photoresponse, 335 wideband detector, 365 CdS domain formation, 4 piezoelectric amplification, 4 CdTe, bulk negative resistance, 4 Charge-carrier velocity, 5, see also Drift velocity Charge traps, 300,305,344, see also Trapping centers

Classical transport model, negative resistance devices, 13 Contact potential, 3 1&3 12, 337 Contact resistance measurement, 178-1 83 transfer length, 179 Contacts BNR devices alloy, 62 high-low heterojunction, 62-64 metallic layer depositions, 6 4 6 7 sintered, 62 GaAs transistor, 288, 289, see also GaAs transistor metal-semiconductor, see also Metal-semiconductor contacts, Ohmic contacts, voltage-current characteristics, 75ff Continuity equation, IMPATT diode, 381 Crystal lattice discontinuities, 299-307 misfit, 300, 301,357 strain, 304,305, 357 Cu,S-CdS heterojunctions, photoresponse, 336 Current multiplication, 384, see also Avalanche multiplication Current saturation, see also Saturation current mechanisms, 234 diffusion-limited operation, 234 space-charge-limited operation, 234 velocity-limited operation, 234 Current transfer length, see Transfer length Current, tunneling, 48-90, see also Tunneling Current-voltage characteristics forward characteristic, 89-94 GaAs FET, 150, 171 source, 150 metal-semiconductor contacts, 758 p-n junction breakdown, 383-390 p-v-n structure, 387-389 reverse characteristics, 9 4 9 9 Si abrupt junction, 386, 387 Sic junction, 677 tunnel diode, 498-50 I , 504, 5 13, 5 15, 5 I6 SIC, 662 stability criteria, 528-53 I

D Dangling bonds, 30&302,304 heterojunctions, 301-307

SUBJECT INDEX

Debye length, 25 intrinsic, 209 Degeneratively doped p n junction, see ulso Tunnel diode, terminal properties band-edge tailing, 487489 current components, 485,486 current-voltage characteristics, 490, 491, 498 energy-band structure, 483485 minority-carrier current, 486 tailing states, 479,487 tunneling current, 48&490 transmission probability, 487, 489, 495498 tunneling probability, 487, 489, 495498 Degeneratively doped semiconductor, 475483 band-edge tailing, 487,489 density of states function, 478,479 energy-band structure, 475480 requirements on doping levels, 480483 tailing states, 479, 487 Density of states function, 478481 heavily doped semiconductor, 479 Density ofstatesmeasurement, GaAs Schottky barrier data, 120, 121 Depletion approximation, 210 Depletion layer width FET, 169, 170 MOS capacitor, 212 Schottky barrier, 103 Depletion region, MOS capacitor. 20621 7 Destructive phenomena, BNR devices current filament formation, 50-54 metal migration, 50-52 Device design considerations, BNR, 43-55 degradation, 50-54 heat dissipation. 47-50 planar or coplanar design, 49 materials parameters, 4 3 4 7 Device operating temperatures, maximum theoretical GaAs, 689 Ga(AsP, 689 Gap. 689 Ge, 689 Si, 689 SIC, 689 Device performance, BNR, 67-72

733

Dielectric relaxation negative, 16 relaxation time, 296 Diffusion coefficient, electron, 12 Diffusion component, heterojunctions, 331, 333 Diffusion length. minority carrier, 276 Diffusion theory, Schottky barrier, 83-89, 131 Diffusion voltage, 310, 31 I, 318, 337 temperature dependence, 325 Diode, see also IMPATT diode, Schottky barrier, Abrupt junction abrupt junction admittance, 394398,453 breakdown voltage, 446 differential negative resistance, 388-390 efficiency, 448 fabrication, 448451 fieldament distribution, 385-387 high frequency performance, 448 I- V characteristics, 386 performance vs. Read diode, 445 p-v-n. power output and efficiency. 455457 Q , 397,398 Ge diode efficiency, 429 large-signal analysis, 424427 linear-graded junction diode, 448-449 p-i-n structure, 404,405,449 high frequency performance, 449 small signal admittance, 404.405 p-v-n structure, 385-388,421,452 admittance, 397, 398 differential negative resistance, 388-390 fabrication, 449451 field, current distribution, 387-388 power output and efficiency, 455457 Q. 397 Q , 395-398 Scharfetter-Gummel diode, 42 1-424 large-signal analysis, 42 1 4 2 3 small-signal admittance, 421 Si n + - p p + , 424 Diode theory, 82.93.94. 360 Discontinuities band edge, 310, 325, 347 band structure,. 307, 308 crystal lattice, 299-307 electron affinity, 31 I

734

SUBJECT INDEX

Dislocations, strain-induced, heterojunctions, 301-307, 357, 358 Doping concentration, semiconductor films from differential capacitance, 162, 166-169 discrepancies, I 6 6 169 from Hall data, 162, 166-169 related to Fermi level, 209 Doping fluctuations, LSA oscillator, 18-22 Doping-length product bulk GaAs devices, 24 Gunn devices, 32, 29 Domain formation high-field, 4 raised cosine, 37 triangular, 37 Doping-to-frequency ratio, LSA oscillator, 18-20 Drain conductance, 236,237 saturation, 238,241 current, MOS-FET, 236 C- V characteristics, 237-240 I- V characteristics, 238, 239 GaAs FET, 149 MOS-FET, 232 Drift velocity, 6 1 2 , 14 field-dependent Ge, 378 Si, 378 LSA mode, 15 measurement, 10-13 space charge accumulation problem, 10, 11

saturation, 374 scattering limited, 374, 375

E Early effect, 239 Efficiency Gunn oscillators, 39 LSA oscillators, I 6 2 3 doping fluctuations, effect, 20-22 Ehrenberg’s approximation, 316 Einstein relation, 276, 381 Electron affinity, 31k312, 337 discontinuity, 3 1 1 Electron velocity, 5-12, see also Chargecarrier velocity

Energy-band structure, see Band structure Energy-momentum relationship, determination, Schottky barrier, 121-127 Epitaxial fi,!m evaluation, electrical evaluation, lW163,707, 708 differential capacitance, 16Q163, 708 Hall effect, 160-162, 707 reverse bias breakdown, 708 Equal areas rule, Gunn devices, 34-38 Esaki diodes, see Tunnel diodes Excess current, see Excess tunneling current Excess temperature, Schottky barrier, 103 Excess tunneling current. 488.489. 491 Excess voltage, domain. Gunn devices. 35-38

F Fermi function, 478,481 Fermi level, at surface of GaAs, 165 FET, see Field-effect transistor Field-effect experiments, 204 Field-effect transistor circuit model, 184 comparison with bipolar transistors, 154 cutoff frequency, 185, 186 deviations from ideal behavior, 151 drain characteristics experimental, 196- 198 theoretical. 149-151 fabrication, 175-178 GaAs, 147ff, see ulso GaAs FET heterojunction, 367 high-field considerations, 190, 19I material requirements, 155 maximum available gain, I86 maximum frequency of oscillation, 187-189 maximum stable gain, I86 methods of realizing in GaAs, 152-154 noise figure, 195 pinchoff voltage, 149, 151 resistance, measurements, 172-174, 195 saturation, 151 Schottky-barrier gate, 153, 183 Sic, 671,672 source-drain resistance, in saturation, 1 9 6 199 stability factor, 186 transconductance, 15 1 transit time, 190

735

SUBJECT INDEX

Field-effect transistor (conrinued) unilateral gain, 186 y-parameters, I93 Field emission regime forward characteristics, 123 large applied biases, I I0 reverse characteristics, 127 Schottky barrier tunneling, 107- I32 small applied biases, I14 Forbidden energy gap, 309-312 G GaAs band structure, 4, 5 bulk negative resistance, 4 domain formation, 4 intrinsic carrier concentration, 274 LSA oscillator, 20-23 negative-resistanceamptifier, 24 physical properties, 274 piezoelectricamplification,4 preparation, see also GaAs epitaxial film bulk growth techniques, 55 liquid epitaxy, 59-61, 155, I56 organometallic synthesis, 59 vapor-phase epitaxy, 5 6 5 8 , 155- 160 Schottky barriers, 89-100, 113, 119-145 transistors, see GaAs transistors GaAs epitaxial film deposition, 155. see also GaAs FET deposition technique, 159 high-purity films,155-157 substrate preparation, 159 vapor phase versus liquid phase, !56 vapor-phase reactor, design, 157, 158 vapor-phase transport, chemistry, I57 GaAs epitaxia1 film evaluation, 160, see also GaAs FET cryslal properties, x-ray topography, 160 doping concentration, 160-163, 166-169 epitaxial defects, source, 160 epitaxial film characterization, techniques, 160 Hall samples, I6 1, 162 mobility, 162 Schottky-barrierdiodes, 161, 168 GaAs FET, l47ff characteristics, 148-1 52 drain characteristics, 149-1 52 high-frequencyconsiderations, 152

GaAs FET (continued) comparison with bipolar transistor, J 54, 155

device fabrication, 175-183 electrical behavior, I8>199 evaluation, 163-175 built-in voltage, 163-166 surface states, 1 6 3 1 68 fabrication, 175-183, 292 contact resistance measurement, 178-1 83 ohmic contacts, 177 Schottky-barrier gate, 183 source-drain contact, 177, 178 gradual-channel solution, 149 insulated gate, 154 material, 155, see also GaAs epitaxial film film deposition techniques, 155- 160 liquid phase epitaxy, 155, I56 substrate preparation, 159 vapor epitaxy, 155- I59 film evaluation, 160-163 crystal properties, 160 electrical evaluation, 160- I62 film pinchoff voltage, I55 film properties and FET characteristics, 172-175 film thickness, I55 trapping center limitation, I55 performance, 152, 153 admittance parameters, 184-198 circuit model, 183, 184 feedback capacitance, 184 field-dependent mobility, 190, 191 high-field considerations, 190- I92 high-frequency behavior, I 8 6 198 cutoff frequency, I 8 6 189 maximum available gain, 186 noise figure, 194 source-drain characteristic, 195-198 unilateral gain, 186, 194 pinchoff biases, I49 pinchoff voltage, 15 I saturation, I5 I Schottky barrier gate 153, 154 GaAs transistors, 273ff, see afso Transistors, GaAs advantages, 273 base diffusion techniques, 282-286 copper contamination, 285 copper segregation at junction, 285

736

SUBJECT INDEX

GaAs transistors (continued) base diffusion techniques (continued) magnesium diffusion, 282 oxygen contamination, 283, 284 silicon contamination, 282 zinc diffusion, 283 zinc-doped silica film, 283 base transport factor, 276 contacts, 288, 289 distribution of diffusants, 279 effect of traps, 290-292 electrical characteristics, 29C292 emitter-to-collector channel, 291 frequency, 290 gain, 290 emitter diffusion techniques, 28&288 silcon, 286 sulfur, 288 tin, 287 emitter efficiency, 276 field-effect transistor, 292 gain-bandwidth product, 274 impurity diffusants, 280 maximum oxcillating frequency, 274 n - p n versus pn-p structures, 275 surface films phosphate glass, 281 silica, 28 I, 282 surface-masking film, 281 GaAs-(Ga1n)As heterojunction, 308,359,361 forward characteristics, 353, 361 ideality factor, 361 photoconductive response, 327-329 photoresponse, 336, 366 GaA-Ge heterojunction, photoresponse. 335 GaAs-Ga(AsP) heterojunction, 342, 366 forward characteristics, 353 photoresponse, 335, 336,338,366 quantum efficiency, 335 Ga(AsP), 687ff, see also High temperature Ga(AsP) power rectifiers GaAs-Sb heterojunction, photoresponse, 335 Gap, Schottky barriers, 89,90,94 GaSb(Ga1n)Sb heterojunction, 306 Gain-bandwidth product MOS FET amplifier, 244 transistor, 274 Ge-GaAs heterojunction, 302-305, 308 Ge-Si heterojunction, 302-305 fast switching, 367 photoresponse, 305

Generation-recombination rates, IMPATT diode, 381,389 localized levels, 381 Germanium negative resistance, 4 physical properties, 274 Gradual channel solution, FET, 149 Gunn diode, see also Gunn oscillator doping-length product, 32 equivalent circuit, 38 frequency-length product, 32 logic funcfions, 4 W 2 wide-band amplifiers, 38 G u m oscillator, 3 2 4 3 doping-length product, 32-34, 39 efficiency, 39 equal areas rule, 24-38 performance, 70

H Heavily doped semiconductor, 475, see also Degeneratively doped semiconductors Heteroepitaxy, 297-299 crystallographic variables, 297 dislocation grids, 304, 305, 357 interface states in, 297 metallurgical variables, 297 misfit dislocations, 301-303, 357 thermal mismatch, 307 Heterojunction(s), 293ff, see also specific materials anisotype, 323, 327, 337, 341, 342, 359 avalanche breakdown, 356 band structure discontinuities, 307-31 3 capacitance, 313-325 crystal lattice discontinuities, 299 dislocations, 302-306 lattice parameters, 300 mismatch, 300-307 dangling bonds, 301-307 definition, 294 fabrication, 297-299, 356359 evaporation, 298 heteroepitaxy, 297 interface alloying, 298 liquid-phase epitaxy, 298 solution growth, 298

SUBJMST INDEX

Heterojunctions (continued) fabrication (conrinued) vapor-phase epitaxy, 298 fast switching. 367 field-effect transistor, 367 ideality factor, 360, 361 injection, 356356,363,364 interband tunneling, 308, 348, 349 interface reflection coefficients, 308 intraband tunneling, 308, 349-353 isotype, 312, 314,326,337-341, 359 rectification, majority carrier, 367 laser action, 356,363-365 noise, 356 principles and applications, 295 radiative recombination, 355 recombination-mission spectra, 347 reverse bias, 353, 354 spacecharge-limited triode, 367 strain sensing, 356 thermally assisted funneling, 359 transistor action, 360-363 transistorlike devices, 367 transport phenomena, 345-356,359, 360 interface transport mechanisms, 347 tunneling emission, 348 tunneling-recombination model, 348, 349 window effect, 295,304, 327, 342, 365 Heterojunction photodetectors, 296, 367, see also Photoelectronic phenomena. specific materials carrier generation rate, 333 collection region width, 33 conversion, 333 doping conditions, efficient conversion. 333 optical transistor, 366 quantum defficiency, 336338 wide band, 365 Heterojunction window effect, 295.365 High-field-domain devices, 3243, see also Gunn oscillator logic functions, 4 W 2 pulse regenerator, 40 voltage tuneable oscillator, 40 High-temperature Ga(AsP) power rectifiers. 687ff breakdown voltage, 69CL696 abrupt junctions, 6 9 M 9 6 avalanche multiplication, 693 graded junctions, 691 impact ionization, 69&693

737

High temperature Ga(AsP) power rectifiers (continued) breakdown voltage (conrinued) junction “patching,” 694 microplasmas, 694-696 nonuniform junction, 694 photocurrent multiplication, 694 punchthrough, 691 temperature dependence, 692, 693 tunneling, 694 device fabrication, 71 1-7 I8 contact metallization, 712, 713 etching, 713-715 mounting and packaging, 71671 8 surface protection and passivation, 7 1 4 716 wafer treatment, 711,712 maximum junction temperatures, 688,689 GaAs, 688,689 Ga(AsP), 689 Gap, 689 Ge, 688,689 Si, 688, 689 Sic, 689 p - n junction formation epitaxial layer, 707-71 1 electrical properties. 707. 708 imperfection characterization, 708-71 I epitaxial layer growth, 701-707 doping, 706, 707 high-purity GdAs. 703 liquid-phase growth. 702 substrate treatment, 704-706, 7 10 vapor-phase growth, 701-704 peak current capacity, 69-98 performance characteristics, 7 18. 71 9 forward voltage, 7 I8 power dissipation, 71 8 saturation current, 718 temperature cycling, 7 I9 rectifier design considerations, 688-699 area voltage, 698 breakdown voltage, 698 p+-p--n--n+ structure, 699, 700 p + - n - - n + structure, 699, 700 peak current, 698 thermal dissipation, 699 thermal resistance. 699 High-temperature S i c rectifiers, 645-651 Homogeneity, material, LSA oscillator, 18-21

738

SUBJECT INDEX

I Ideality factor, 360, 361 Impact avalanche transit-time diode, see IMPATT diodes Impact ionization coefficient, see also Ionization rate Ga(AsP), 690 I M PATT diodes, 37 1ff, see also Read diode abrupt junction, 385 avalanche multiplication, 375, 384, 3% 393 avalanche region, 399405 narrow, 399-404 wide, 404,405 carrier drift velocity, 377 carrier space charge, 384-390 current-voltage characteristics, 383-390 definition, 372 design considerations, 430441 current distribution, 438-441 temperature distribution, 4 3 8 4 1 material parameters, 432434 dielectric constant affecting impedance, 433

direct versus indirect gap, affecting tunneling, 434 ionization rate, 432 field derivative, 432,433 noise characteristics, 434 scattering-limited charge-carrier velocity affecting frequency, 433 thermal conductivity, 434 scaling factor, 429,430 structure parameters, 4 3 M 3 2 tunneling current constraint, 430 width avalanche region, 43 1,432 space-charge region, 430 thermal considerations, 434,441 annular geometry, 437439 diamond heat sink, 437 junction temperature, 435,436 thermal resistance, 434441 thermal runaway, 434 drift region, 399 electrical characteristics, 382429 electron temperature. 377 energy transfer mechanism, 377-380 equivalent circuit, 406, 407

IMPATT diodes (coniinued) fabrication, 43245 1 impurity profile. 4 4 2 4 9 Read diode, 442-445 general discussion, 372 large-signal analysis, 4 11429. 464466 mathematical formulation, 377-382, 462466

model, 406 negative resistance in junction breakdown, 372-376

normalization of units, 382 observed electrical characteristics, 451466 oscillator characteristics, 454461 efficiency, frequency dependence, 458, 459

output and efficiency Ge abrupt diode, 456 p-v-n diode, 455457 Read diode, 454-455 Si abrupt diode, 455457 p-v-n diode, 385 Q , 408410 Read diode, 375,376 saturation drift velocity, 374 scattering-limited velocity, 375-377 Si avalanche region, 407 admittance, 408 breakdown voltage, 407 Q. 40841 I small-signal analysis, 39341 I, 463 small-signal admittance, 407409 space charge layer, pn junction, 382, 383 transit time effect, 374 TRAPATT mode, 46M71,see also TRAPATT mode Impurity bands, 476 Impurity concentration, see Doping InAs, Schottky barrier, 127 InP, bulk negative resistance, 4 Insulated gate FET, 154 Interface dipole layer, 339 Interface electric field, 96-99,3 1 I , 317 Interface layer, Schottky barrier, 88,89 Interface states, 204, 294, 297, 299, 300, 305, 306,309, 312, 326,337, 341, 348

current transport phenomena, 348-353 delocalized, 321, 326 effect on junction capacitance, 319-326

SUBJECT INDEX

Interface states (continued) heterojunction band profile, 3 I I , 3 I2 photoresponse, 338-341 Inversion layer, MOS structure, 208-2 15,234 Ionization rate, 378-380 electric field derivative, 432434 GaAs. 433 Gap, 433 Ge, 433 Si, 433 field dependence, Read diode, 414,415 GaAs, 378 Ge, 378 Si, 378 temperature dependence, 379 unequal, electron and hole, 421 lsotype heterojunction, 312, 314, 326, 337341,359 interface states, 338-341 rectification, majority carrier, 367 J

Junction, degeneratively doped, see Degeneratively doped junction

K Keidysh effect, 345, 346 KMER photolithography, 222

L Laser action heterostructures, 363-365 room temperature, 365 Lattice parameters heterojunction materials, 299-306 of wurtzite, sphalerite, and diamond types, 300,301 Lattice strain, 304, see also Heterojunctions Leakage current, Schottky barrier space charge generation-recombination, 98 surface recombination, 98 Limited space-charge accumulation, see LSA Logic functions, high-field-domain devices, 4042 LSA mode versus Gunn mode, 19,22, 23 LSA oscillators, 14-24 accumulation layer, 19

739

LSA oscillators (continued) efficiency, 1 6 2 3 material homogeneity requirements, 18, 19 performance, 67-71 Luminescent diodes, Sic, 677482

M McCumbe-Chynoweth model, bulk-negative resistance, 8. 9 Material preparation, BNR devices, 55-61 liquid-phase epitaxy, 59-61 organometallic synthesis technique, 59 vapor-phase epitaxy, 5tL-58 Maxwellian distribution. hot electrons, 9. 10 Mean length model, bulk-negative resistance, 6 9 Memory device, MOS-FET, 260-269 Metal-oxide semiconductor, see MOS Metal-oxide semiconductor field-effect transistor, see MOS-FET Metal-semiconductor contacts, 75ff device applications, 76 Schottky barriers, 77ff Metal-semiconductor device applications avalanche diode, 76 cold cathodes, 76 hot electron ballistic range determination, 76 hot electron mobility measurement, 76 microwave mixer and varactor, 76 photodetector, 76 semiconductor band structure studies, 76 surge protection, 76 switching, 76 transistors, 76 Microplasmas, 694-696 imperfections, 695, 708 Mobility, see Carrier mobility MOS capacitor, 206ff, see also MOS-FET devices accumulation, 206 C-t measurements, 232 C- V characterizations, 217-23 1 depletion region, 20621 2 fabrication considerations, 22C232 MOS-FET circuits. 26S269 bilateral switching, 263 capacitive storage, 26&262 complementary circuits, 264 inverter, 264266

740

SUBJECT INDEX

MOS-FET circuits (continued) complementary circuits (continued) memory array, 267-269 dynamic shift register, 262 p-channel, 260-264 voltage-controlled resistor, 26&262 MOS-FET devices, see also MOS transistors, MOS capacitors channel-length modulation, 241 contrasted with FET devices, 233, 234 drain current, 236 enhancement mode, 220,221 fabrication considerations, 249-260 MOS capacitor, 22C229 chemical cleaning, 226228 gate oxidation, 227 metallization, 227, 228 TBS sequence, 228-231 observed characteristics, 255-260 pentode region, 237 quasi-Fermi levet, 234 small-signal amplifier, 241-245 admittance parameters, 243-245 amplification factor, 243 equivalent circuit, 245 gain-bandwidth product, 244 intrinsic cutoff frequency, 244 switching characteristics, 245-249 transconductance, 237-241 triode region, 237 two-dimensional versus one-dimensional analysis for MOS capacitor, 234 MOS transistors, 203ff, see also GaAs-FET, MOS-FET devices depletion mode, 233 device structure, 232-234 device theory, 234245 enhancement mode, 233 general considerations, 203-205 ion migration, 21 8 MOS capacitors, 206, 232 C-Vcharacteristics, 217-231 theory. 206-21 7 N Negative resistance, 3ff, see also Bulk negative resistance basic requirements, 7-9 differential, DC, 388-390

Negative resistance (continued) dynamic, in junction breakdown, 372-376 Negative-resistance amplifiers, 2 4 3 2 doping-length product, 42 frequency-length product, 42 impedance, 26-30 noise figure, 24 thermal noise, 31 Negative-resistance oscillator. LSA versus G u m mode, 19, 22 Noise figure, bulk negative resistance amplifier, 24 Nonparabolic energy-momentum relationship, Schottky barriercharacteristics, I 2 1-1 32 0 Occupation probability, hot electron, 6 Ohmic contacts, see also specific materials contact resistance, 131 measurement, 178-1 83 FET sourcedrain, 177 alloy systems, 177, 178 contact areas, preparation, 177 contact resistance, measurement, 178183 metal, choice of, I77 substrate temperature, importance, 178 tunneling calculations, 130 Optical phonon scattering, 377-379 Optoelectronic devices, 295, 365, 366

P PbS-PbSe heterojunction, 304 Photodetector, See also Heterojunction photodetectors heterojunction, 365-367 Sic, 652,658-660 Photoelectronic phenomena, 326-341, 365, see also Heterojunction photodetectors anisotype heterojunction, 327 carrier generation rate, 333 conversion, 333 depletion effects, 331-333 diffusion effects, 331-333 doping conditions, efficient conversion, 333 heterojunctions, 326345 frontal illumination, 327-338

741

SUBJECT INDEX

Photoelectronic phenomena (continued) isotype heterojunction, 326 pi-n heterojunctions, 334 photoconductivity, 327 photocurrent, 328 photovoltage, 328 secondary, 341 sign reversal, 338-341 surface barrier photocells, 335 Piezoelectric amplification, 4 Pinchoff bias, 149 FET, 149 Pinchoff voltage, 233, 234 GaAs, FET, 151 Planar diffusion technology, 204 Poisson’s equation, 24, 209 IMPATT diode theory, 381 Read diode theory, 413 Polaron effect, GaAs Schottky barriers, 118, 130 Power generation, 70, 374 current-field relationships, 373 negative resistance diode, 373

Reade diode (continued) fabrication considerations, 442445 double diffusion technique, 444 impurity profile, 444-448 ionization rate, field dependence, 414 large-signal analysis 41 1-42 I, 464466 microplasma effects, 444 operating frequency, 445 oscillator output and efficiency, 45-53 oscillator power limitation, 417 output power, 419 parasitic resistance, 419 performance, versus abrupt junction diode, 445 phase relation degradation, 420 saturation current, 420 small-signal admittance, 403, 417419 structure, 401404 Rectification, majority carrier transport, 367 Richardson constant, 83,92,93,99 Ridley-Watkins-Hilsum effect, 4 6 , see also Transferred electron effect S

Q Q,395-398 definition, 395 Quantum-mechanical tunneling, 49 1-498 via deep impurity states, 495 degenerate p n junction, 487489,495498 direct, 496-498 energy-momentum conservation, 49-98 indirect, 496, 498, see also Tunneling, phonon assisted potential barrier, 493,494 wave-particle duality, 49 1 4 9 3 WKB approximation, 494497,498

R Read diode, 375,376, see also IMPATT diode avalanche region, 413 4 16 , 4 4 2 4 impurity content, 443, 444 peak field, 414 average diode voltage, 419,420 breakdown field, 442-445 complex current transfer factor, 400 efficiency, 420 equivalent circuit, 400-402 drift region, 400

Saturation carrier drift velocity, 374, 375 Saturation current, 134139, see also Current saturation ungated FET, 169-172 Scattering hot electrons, 9 intervalley, 23 in-valley, 13 optical phonon, 377-379 Scattering-limited velocity, 375377,433 Schottky-barrier diodes epitaxial film evaluation, 161, 168 FET gate, 153,183 Schottky-barrier fabrication, 78-82 guard ring, 80,81,95 interface layer problem, 78, 79 surface leakage, 8 I , 95 Schottky barrier-gate FET, 153, I54 Schottky barriers, transport properties anisotype heterojunction, 359 barrier height deduction, 84-86 built-in voltage, 164-166 diffusion theory, 83-89 diode theory, 82 forward characteristics, 89-94 heavily doped material, 103-145

742

SUBJECT INDEX

Schottky barriers, transport properties

Sic (continued) luminescent diodes, 677-682 miscellaneous devices, 660-67 1 interface layer, 89 p-ri junction devices, 651460 isotype heterojunction, 359 leakage current, 98 physical and chemical properties, 626, 627 lightly doped material, 82-102 power diodes, 642-651 minority carrier injection ratio, 87 alloy junctions, 642, 643 oscillatory diode, 451 characteristics, 645-65 I reverse characteristics, 94-99 diffused junctions, 643, 644 thermionic emission, 82-89 epitaxial junctions, 644,645 trapping effects, 100-103 grown junctions, 643 Schottkyjunction model, 313, 317, 318, 341 preparation techniques, 627-633 Sic, 625-683 epitaxial techniques, 630. 631 asolution growth, 632 band gap, 633 sublimation, 627-630 carrier diffusion length, 633 traveling solvent method, 631, 632 carrier effective mass, 633 Si-GaP heterojunction, 349, 350 carrier mobility, 633 I- V characteristics, 349, 350 minority carrier lifetime, 633 Silicon device fabrication techniques, 634642 physical properties, 274 contacts, 641, 642 Schottky-barrier diode, 114, 115 diffusion, 634,635 Sn0,-Si heterojunction, 335 etching, 636639 Source electrode mechanical processing, 635,636 FET, 148 oxidation, 639-641 MOS-FET, 232 electrical properties, 633, 634 Space charge irradiation effects, 661478 ionic, 2 I8 annealing, 674 at substrate, 168, 169 junction devices, 625ff Space-charge barrier, nonuniform, 99-103 luminescent diodes, 677-682 Space-charge growth fabrication, 679-682 from negative dielectric relaxation, 1621 spectra, 678-682 negative resistance amplifier, 24-26 miscellaneous devices, 660-67 1 Space-charge layer field-effect transistor, 671,672 carrier, 384-390 junction-gate unipolar transistor, 663p-n junction, 382,383 67 1 Space-charge neutrality, 312 tunnel diode, 660-67 I Space-charge wave p n junction detectors, 651460 amplitude, 29, 30 charged particle detector, 65 1 avalanching plasma, 390-393 nuclear particle detector, 654-658 phase velocity, 25 ultraviolet radiation detector, 652454. Substrate-film depletion layer in GaAs, 168658460 112 radiation resistance, 673-677 Surface depletion layer, 167 Surface inversion, threshold voltage, 214 junction capacitance, 675, 676 rectifier characteristics Surface research, importance to MOS devices, encapsulation requiremen<s. 64-50 205 I- V data, 64-648 Surface states thermal impedance, 650 effective charge, 212 lattice constant and energy gap of polytypes, GaAs FET, 164-167 628 MOS transistors, 204209 (continued)

SUBJECT INDEX

Surface states (continued) MOS transistors (conrinued) fast. 218, 219 slow, 218, 219

T TBS (temperature-bias-stress) sequence, 228- A .

L11

Temperature, electron, 6 1 0 . 377 Thermal conductivity, BNR devices, 4547 Thermal energy transfer, hot electrons, 6, 7 Thermal runaway, BNR devices, 45 Thermionic emission, 82-89 Thermionic field emission regime, I3 1- 145 forward characteristics, 133-138 importance of statistics, 145 reverse characteristics, 139- I45 saturation current, 134139 Threshold field, Gunn devices, 34-39 Transfer diffusion, 12 Transfer length, contact resistance measurement, 179- 1 8 1 Transferred-electron effect, 4 8 Transistors, GaAs, see also GaAs transistor bipolar, 277-282 alloyed emitter, 277 double diffused. 280 postalloyed diffused, 280 Transit time domain, Gunn oscillator, 32 effect avalanche region, 376 carriet bunching, 374 IMPATT diodes, 374 TRAPATT mode, 46-71 avalanche shock front, 469 carrier profile, 470 definition, 466 field profile, 468, 470 Trapping centers, 344 GaAs in FET, 154, 155 GaAs transistor, 29&292 Schottky barriers, 100-103 Tunnel diode, 473E equivalent circuit dependence on diode parameters, 525-527 experimental characterization, 536543 conclusion, 542,543 general approach, 53G536 mounting configurations, 534-536

743

Tunnel diode (conlinued) experimental characterization (conrinurd) low-frequency measurements, 537-539 I-Y characteristics, 536, 537 junction capacitance, 538-542 junction conductance, 536, 537,539-542 series resistance, 536, 537, 539-543 shot noise, 538 I0 fabrication., 501-5..doping agents, 502, 503 planar process, 505, 508 pulse-bond process, 505, 508 formation of junction, 501-505 ball-alloy process, 504, 505, 508 geometries. 507-5 10 encapsulated, 507. 508 unencapsulated. 508. 5 10 materials parameters, 501 -503 overall configuration, 505-507 parasitics, 505, 506 series resistance, 507 frequency limit, 5 I5 I- V characteristics, 498-501, 504 stability criteria, 528-531 limitations on operation, 5 10-5 I5 burnout limit, 514,515 frequency, 5 15 maximum power, 5 14.5 15 radiation, 512, 513 temperature, 510-512 maximum power, 514, 515 mounting configurations, 534536 noise bandwidth, 517 noise current, 5 17 peak-to-valley ratio, 524, 526, 527 physics of operation, 475-501 present and future role capabilities compared with those of other devices, 6 12-623 amplifier, 617,618 detector, 618, 619 mixer, 61 7.61 8 oscillator, 619, 620 in switching, 620 integrated circuit technology, 6214 2 3 examples, 56 I , 622, 623 performance improvement, 621,622 reduction of parasitics, 621, 622 pulse and digital circuit applications, 602616

744

SUBJECT INDEX

Tunnel diode (continued) pulse and digital circuit applications (continued) logic circuits, 61 1-616 analog threshold logic gate, 61 1 4 1 3 AND,ORgates, 611,612 cascaded logic gates, 612,613 majority logic gates, 61 1, 612 memory circuits, 613416 sequential circuits, 613, 614 switching, 60241 t astable oscillation, 605,606 balanced pair bistable switch, 606,607 bistable mode, 604, 605 current gain, 610,611 dynamic load trajectories, 603-607 inverting bistable mode, 604, 605 limitations, 606,607 modes of operation, 603-607 monostable switching, 604606 power drain, 61 1, 620 relaxation oscillator, 606, 608 speed, 607610,620 waveform generators, 605-61 3 Si, I-V characteristics, 513, see olso Tunnel diode, terminal properties Sic, 6 6 M 6 3 sinusodial circuit applications amplifiers, 543-560 AM-PM conversion, 555 bandwidth, 547-551,558-561,618 degree of broadbanding, 548-551 distributed traveling wave, 557-559 gain compression, 554, 555 gain expansion, 554,555 insertion phase, 545, 547 insertion power gain, 545, 547-550 integrated circuit realization, 555, 557, 561,621,623 interated traveling wave, 557-559 intermodulation levels, 555 large-signal handling, 553-558, 560, 561,618 multistage, 557-559,561 negative-resistance amplifier, 5 6 5 5 1 noise performance, 552, 553, 558, 560, 561,617,618 output saturation level, 554-558, 560, 561,618

Tunnel diode (continued) sinusoidal circuit applications (continued) amplifiers (continued) passivation outside stability bandwidth 55 1

performance characteristics, 560, 561, 617, 618 push-pull amplifier, 556 reflection amplification, 543-549 series-parallel aray, 556, 557, 622 single-stage configurations, 553-557, 560, 561 transmission amplifier, 544553, 561 converters, 573-584 circuit configuration, 556579 frequency conversion mechanism, 573576 gain-bandwidth capability, 580, 581, 585 junction conductance, 575 linear, 514-579 mixer operation, modes, 583-585,618 noise performance, 581-583, 585,617 performance characteristics, 584, 585 self-oscillating versus externally pumped, 574577,585.617.618 stability conditions, 580 three-frequency circuit models, 5 7 6 579 detectors, 584-598 bandwidth, 589-593, 596598 circuit model, 586588 comparison of modes of operation, 596, 597, 618,619 dynamic range, 595-597,618,619 figure of merit, 594 input-output characteristics, 586593 mechanisms, 584,586 modes of operation, 589-593,59&598 noise performance, 593-597 performance characteristics, 596598 short-circuit current sensitivity, 588592, 595, 597 square-law operation, 588-596 tangentialsensitivity, 593-597,618,619 video resistance, 588-592 miscellaneous applications. 598-60 1 electromechanical transducers, 599, 600 network synthesis, 598, 599

745

SUBJECT INDEX

Tunnel diode (conrinued) sinusoidal circuit applications (con/inued) miscellaneous applications (continued) studies of material properties, 600.601 oscillators, 560-573 above-cutoff oscillations, 570 dc t o rf conversion efficiency, 564566, 574,619,620

electronic tuning, 562, 566, 567. 573, 5 74

frequency, 560, 562, 573,574,617.620 amplitude stability and, 567-569, 573

frequency tunability, 566,567,573,574 general configuration, 560. 562. 563 multiple and distributed configurations 5 70-574

noise characteristics, 568, 569, 620 output power, 562-566, 573, 574. 620 performance characteristics. 573. 574 phase locking. 568. 573, 620 stabilization, 560. 569, 570 small-signal equivalent circuit, 506, see also Tunnel diode, terminal properties stabilization, 533, 534 stabilizing networks, 533. 534, 544. 545,

Tunnel diode (continued) terminal properties (continued) shot-noise constant. 521-523, 525. 527. 552

small-signal equivalent circuit. 505-507. 5 17-522. 525-528

small-signal impedance. 5 18 small-signal terminal immittance, 5 18.521 Smith chart loci. 5 19, 520 terminal noise current. 520-523. 525. 527 terminal quantities. numerical values. 527, 528

terminal stability, 528 534 fundamental criteria. 528-53 I specific stability criteria, 531 -533, 569, 570

stabilization, 533. 534 triple-tuned negative-resistance mode, 519. 522

Tunneling. 344. 476, 4 8 6 4 9 0 current. degrading negative resistance. 430 via deep impurity states. 495

direct, 496, 498 excess current. 488. 489. 491 tield emission regime nonparabolic energy-momentum rela550. 551. 560. 570.622.623 tionship. I 2 I - I32 switching figure of merit, 524, 526, 527 parabolic energy momentum relationterminal properties, 5 13-534 ship, 107-121 emittance, stability criteria, 530 Fowler-Nordheim. 342 equivalent excess noise temperature ratio, interaction-induced, 488 520, 527, 552, 567 deep impurity levels. 488 incremental junction resistance, 501,507, interband, 308. 348. 349. 359 5 16, 5 17, 525, 521 intraband, 308, 349-353. 359 I-Ycharacteristics, 498-501, 515-51 7 multistep. 348, 349. 359 polynomial respresentation, 5 16, 5 17 phonon-assisted (indirect). 496,498, 5 I 2 transcendental approximations, 5 15, quantum-mechanical. 491 -498. see also 516 Quantum-mechanical tunneling junction capacitance. 506. 507. 525. 527 Schottky barrier, 103-132 junction frequency. 507. 518. 525, 527 thermally assisted. 359 large-signal equivalent circuit. 523. 524, thermionic field emission regime, 132- 145 564-566 tunneling emission. 348 minimum noise bias. 521. 522, 527 tunneling recombination model, 348, 349 parallel capacitance. 506. 525. 527 W K B approximation. 351 parallel resistance. 519. 526. 527 parallel-tuned model, 519, 522 Tunneling probability. 487,489,494,495-498 resistive cutoff frequency. 518, 526. 527 degenerate p-n junction. 487, 489.495-498 series inductance. 506. 525. 527 W K B approximation, 105-1 10 series resistance, 507, 525, 527 Two-valley effect. see Transferred-electron series self-resonance. 519, 525, 527 effect Two-temperature distribution, 10 series-tuned operation, 520, 522

SUBJECT INDEX

V Vacuum energy level, 3 10 Voltage-controlledresistance, MOS-FET, 260-262

W

Window effect, 309, 327, see also Heterojunction window effect WKB approximation, 105-110, 351, 494, see olso Quantum mechanical tunneling Work function, 310, 31 1, 338

Y

y-parameters, see Admittance parameters Z Zerbst plot, 231 ZnO-Cu,O heterojunction. injection luminescence, 361 ZnS-Cu,S heterojunction, injection luminescence, 367 ZnSe-ZnTe heterojunction. injection luminescence, 367 ZnSe, bulk negative resistance, 4

Willardson Semiconductors & Semimetals V7b (v. 7B)

SEMICONDUCTORS & SEMIMETALS

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SEMICONDUCTORS & SEMIMETALS

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SEMICONDUCTORS & SEMIMETALS V38, Volume 38 (Semiconductors and Semimetals)

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Semiconductors and Semimetals Volume 72 Silicon Epitaxy (Semiconductors and Semimetals)

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Semiconductors and Semimetals Volume 72 Silicon Epitaxy (Semiconductors and Semimetals)

Semiconductors and Semimetals, Vol. 12: Infrared Detectors II (v. 12)

Semiconductors and Semimetals, Volume 67: Ultrafast Physical Processes in Semiconductors (Semiconductors and Semimetals)

Semiconductors and Semimetals Infrared Detectors

Semiconductors and Semimetals. Volume 25: Diluted Magnetic Semiconductors (Semiconductors and Semimetals)

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Germanium Silicon: Physics & Materials (Semiconductors and Semimetals, Volume 56)

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The Spectroscopy of Semiconductors: Volume 36 (Semiconductors and Semimetals)

Germanium Silicon: Physics & Materials (Semiconductors and Semimetals, Volume 56)

Semiconductors and Semimetals, Volume 51A Identification of Defects in Semiconductors

Hydrogen in Semiconductors II, Volume 61 (Semiconductors and Semimetals)

Semiconductors and Semimetals, Volume 71: Recent Trends in Thermoelectric Materials Research: Part Three (Semiconductors and Semimetals)

Semiconductors and Semimetals, Volume 26 III-V Compound Semiconductors Semiconductor Properties of Superionic Materials

SEMICONDUCTORS & SEMIMETALS V30, Very high speed integrated circuits: heterostructure

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Nanostructured Systems, Volume 35 (Semiconductors and Semimetals)

Semiconductors and Semimetals, Volume 14 Cadmium Telluride

Willardson Semiconductors & Semimetals V7b (v. 7B)

SEMICONDUCTORS & SEMIMETALS

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SEMICONDUCTORS & SEMIMETALS

SEMICONDUCTORS & SEMIMETALS

Semiconductors and Semimetals v. 4

SEMICONDUCTORS & SEMIMETALS V38, Volume 38 (Semiconductors and Semimetals)

Semiconductors and Semimetals: Transport Phenomena v. 10

Infrared Detectors (Semiconductors and Semimetals: v. 5)

Semiconductors and Semimetals Volume 72 Silicon Epitaxy (Semiconductors and Semimetals)

Semiconductors and Semimetals: v. 1: Physics of III-V compounds

Semiconductors and Semimetals Volume 72 Silicon Epitaxy (Semiconductors and Semimetals)

Semiconductors and Semimetals, Vol. 12: Infrared Detectors II (v. 12)

Semiconductors and Semimetals, Volume 67: Ultrafast Physical Processes in Semiconductors (Semiconductors and Semimetals)

Semiconductors and Semimetals Infrared Detectors

Semiconductors and Semimetals. Volume 25: Diluted Magnetic Semiconductors (Semiconductors and Semimetals)

Semiconductors and Semimetals, Volume 67: Ultrafast Physical Processes in Semiconductors (Semiconductors and Semimetals)

Germanium Silicon: Physics & Materials (Semiconductors and Semimetals, Volume 56)

Semiconductors and semimetals: Indentification of defects in semiconductors

The Spectroscopy of Semiconductors: Volume 36 (Semiconductors and Semimetals)

Germanium Silicon: Physics & Materials (Semiconductors and Semimetals, Volume 56)

Semiconductors and Semimetals, Volume 51A Identification of Defects in Semiconductors

Hydrogen in Semiconductors II, Volume 61 (Semiconductors and Semimetals)

Semiconductors and Semimetals, Volume 71: Recent Trends in Thermoelectric Materials Research: Part Three (Semiconductors and Semimetals)

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SEMICONDUCTORS & SEMIMETALS V30, Very high speed integrated circuits: heterostructure

Semiconductors and Semimetals, Volume 59 Nonlinear Optics in Semiconductors II

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