Advances in Electronics and Electron Physics, Volume 35

ADVANCES IN ELECTRONICS AND ELECTRON PHYSICS VOLUME 35 CONTRIBUTORS TO THISVOLUME George Abraham Jean-Loup Delcroix R...

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ADVANCES IN ELECTRONICS AND ELECTRON PHYSICS VOLUME 35

CONTRIBUTORS TO THISVOLUME George Abraham Jean-Loup Delcroix Richard G . Fowler R. N. Jackson K. E. Johnson Armando Rocha Trindade

Advances in

Electronics and Electron Physics EDITEDBY L. MARTON Stnitlisoriiati Itwtitiitioil, Washitlgton. D.C. Assistarif Editor CLAIRE MARTON

EDITORIAL BOARD E. R . Piore T. E. Allibone M . Ponte H. B. G . Casimir A . Rose W. G . Dow L. P. Smith A . 0. C. Nier F. K . Willenbrock

VOLUME 35

1974

ACADEMIC PRESS

New York and London

A Subsidiary of Harcourt Brace Jovanovich, Publishers

COPYRIGHT 0 1974, BY ACADEMIC PRESS,INC. ALL RIGHTS RESERVED. NO PART O F THIS PUBLICATION MAY BE REPRODUCED OR TRANSMITTED IN ANY FORM OR BY ANY MEANS, ELECTRONIC OR MECHANICAL, INCLUDING PHOTOCOPY, RECORDING, OR ANY INFORMATION STORAGE AND RETRIEVAL SYSTEM, WITHOUT PERMISSION IN WRITING FROM THE PUBLISHER.

ACADEMIC PRESS, INC. 111 Fifth Avenue, New York, New

York 10003

United Kingdom Ediiion published by ACADEMIC PRESS, INC. (LONDON) LTD. 24/28 Oval Road, London NWI

LIBRARY OF

PRINTED

CONGRESS CATALOG CARD

NUMBER:49-7504

IN THE UNITED STATES OF AMERICA

CONTENTS CONTRIBUTORS TO VOLUME 35 . FOREWORD

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Vii

ix

Nonlinear Electron Acoustic Waves. Part I RICHARD G . FOWLER

I. 11. Ill. IV .

lntroduction . . . . . . . . . . Laboratory Experiments . . . . . Theories . . . . . . . . . . . Conclusion to Part I . . . . . . List of Symbols . . . . . . . . References . . . . . . . . . .

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. 1 . . 4 . 56 . . 83 . . 84

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85

Hollow Cathode Arcs JEAN-LOUP DELcnoix

I. I1. Ill . IV . V. VI . V11 . VIII .

AND

ARMANDO ROCHATRINDADE

lntroduction . . . . . . . . . . . . . . . . . Historical Review of HCA . . . . . . . . . . . . . Working Regimes of HCA . . . . . . . . . . . . . Operating Conditions for Low-Pressure HCA (N. LQ, and LI Regimes) Experimental Results for the Normal Regime . . . . . . . Theory of the HCA in the N Regime . . . . . . . . . . Applications of HCA . . . . . . . . . . . . . . Conclusion . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . .

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88 91 92 103 109 157 175 184 185

Gas Discharge Displays: A Critical Review R . N . JACKSON and K . E . JOHNSON

I. I 1. 111. IV . V.

Introduction . . The Characteristics dc Arrays . . . ac Arrays . . . Conclusion . . References . . .

. . . . . . . of dc Discharge Cells .

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191 195 204 235 . 264 266

Multistable Semiconductor Devices and Integrated Circuits GEORGE ABRAHAM

I . Introduction . . . . . . . . . . . . . . . . . . . 270 I1 . Generation of Multistable States . . . . . . . . . . . . . 272 V

vi

CONTENTS

111. Avalanche Device Physics . . 1V . Integrated Avalanche Devices . V . Multistable Circuits . . . .

. . . VI . Negative Resistance Interactions . VI1 . Multistable Dynamics . . . . VIII . Conclusion . . . . . . . References . . . . . . . . AUTHORINDEX

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SUBJECT INDEX .

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289 312 332 356 369 387 398 403 410

CONTRIBUTORS TO VOLUME 35 GEORGEABRAHAM.U.S. Naval Research Laboratory, Washington, D.C., and University of Maryland, College Park. Maryland JEAN-LOUP DELCROIX. Laboratoire de Physique des Plasmas, Universiti de Paris-Sud, Orsay, France

RICHARDG. FOWLER,Department of Physics, University of Oklahoma, Norman, Oklahoma Mullard Research Laboratories. Redhill. Surrey, England R. N . JACKSON,

K . E. JOHNSON,Mullard Research Laboratories, Redhill, Surrey, England ROCHA TRINDADE, lnstituto Superior TPcnico, Universidade de ARMANDO Lisboa, Portugal

vii

This Page Intentionally Left Blank

FOREWORD Our present volume consists again of four contributions on widely different subjects. The first, by R. G. Fowler, is an extensive treatment of nonlinear electron acoustic waves. In fact the subject turned out to be so extensive that its treatment will appear in two parts. The first part of the review is presented here, with the remainder to follow in the near future. It is an expansion of the views presented by Dr. Fowler in his earlier review published in our Volume 20 (1964). One of the important sources of ions are hollow cathodes. A significant feature of these devices is that they can be operated at high currents. J.-L. Delcroix and A . R. Trindade discuss the theoretical and experimental aspects of hollow cathode arcs, including their applications. Gas discharge, as applied to display devices, forms the subject of our third review. R. N . Jackson and K . E. Johnson point out that some such display devices (for instance, neon tubes) have been in existence a long time and are too well known to be discussed here. Their review concentrates on “matrix displays,” which have gained in importance since the need arose for large-scale displays.” The last review in this volume, by G. Abraham, deals with a potentially powerful component of computers-multistable semiconductor devices and integrated circuits. The author shows the different ways to generate multistable states and investigates the physics and technology of the resulting devices. Following our established custom, future reviews, with their authors, are listed below. “

The Effects of Radiation in MIS Structures Electrophotography Self-scanned Solid State Image Sensors Quantum Magneto-Optical Studies of Semiconductors The Photovoltaic Effect The Future Possibilities for Neural Control Technology of Electron-Bombardment Ion Thrusters Recent Advances in Hall Effect, Research and Application Semiconductor Microwave Power Devices The Gyrator ix

Karl Zaininger and R. J. Powell M. Scharfe and L. J. Fraser Paul K . Weimer Bruce D. McCombe and Robert J. Wagner Joseph J. Loferski Karl Frank and Frederick T. Hambrecht Harold R. Kaufman D. Midgley S . Teszner K . M. Adams, E. Deprettere and J. 0. Voorman

X

FOREWORD

Microwave Device Technology Assessment Whistlers and Echoes Experimental Studies of Acoustic Waves in Plasmas Multiphoton Ionization of Atoms Auger Electron Spectroscopy Nonlinear Electron Acoustic Waves, 11. Time Measurements on Radiation Detector Signals Interaction of Intense Photon Beams with Matter Research and Development in the Field of Walsh Functions and Sequency Theory Theoretical Studies of the Large-Scale Behavior of the Solar Wind The Excitation and Ionization of Ions by Electron Impact In-situ Electron Microscopy of Thin Films After Glow Phenomena in Rare Gas Plasmas between 0" and 300°K Physics and Technologies of Polycrystalline Si in Semiconductor Devices Advances in Molecular Beam Masers Electron Beam Microanalysis Charge Coupled Devices Development of Charge Control Concept Electron Polarization in Solids Charged Particles as a Tool for Surface Research Energy Beam Technology Energy Distribution of Electrons Emitted by a Thermionic Cathode Charge Coupled Image Sensors Interpretation of Electron Microscope Images of Defects of Crystals

Jeffrey Frey and Raymond Bowers Robert A. Helliwell J. L. Hirschfield J. Bakos N. C. Macdonald and P. W. Palm berg R. G. Fowler S. Cova M. J . Lubin H. F. Harmuth A. Barnes J. W. Hooper and R. K . Feeney A. Barna, P. B.Barna, J . Pocza, and I. Pozsgai J. F. Delpech I. Kobayashi D. C. Laine D. R. Beaman M. F. Tompsett J. te Winkel M. Campagna, D . T. Pierce, K. Sattler, and H. C. Siegmann J. Vennik E. D. Wolf W. Franzen and J. Porter C. H. Sequin M. J. Whelan

We would like to invite again suggestions for future reviews and suitable authors for them. L. MARTON CLAIRE MARTON

ADVANCES IN ELECTRONICS AND ELECTRON PHYSICS VOLUME 35


Nonlinear Electron Acoustic Waves, Part I RICHARD G . FOWLER Department of Physics, Uniiiersity of Oklahoma, Norman. Oklahoma

I. Introduction

....

I

11. Laboratory Exper A . Breakdown W

B. Secondary Breakdown Waves C. Electric Shock Tube Precursors ......................................................... D. Laser Precursors .................................................. E. Slow Proforce Waves ........................................................................ F. Tertiary Breakdown Waves III. Theories .. A. Early Approaches ... B. Fundamenta Equations in in One Dimension C. Solution of the Electron Equations for Proforce Waves IV. Conclusion to Part 1 List of Symbols .................................................................................... References

4 4 26 31 50 52 52 56 56 58 12 83 84 85

1. INTRODUCTION

In a world with large amounts of quickly disposable energy, a wealth of dynamical phenomena has come to light marked by a very high propagation speed, approaching that of electromagnetic waves. In most cases, the observation is based on a moving luminous domain in a gas, and the domain’s initial boundary is remarkably sharp, suggesting something of a discontinuity. Simultaneous observations of ionization have shown discontinuities to be present which are closely cosputial with those of the luminosity. In a previous article (I) it was hypothesized that these fast waves all involve organized electron motion, and hence all have electron acoustic speed as their reference speed in the Machian sense. In this article the entire subject will be elaborated, and new evidence for the validity of the fluid dynamical viewpoint of this phenomenon will be reviewed. It is probable that the first laboratory observation of visible effects from a wave of the electron acoustic family was by Hauksbee (2) in 1705. He combined the possession of a good vacuum pump and the requisite interest

2

RICHARD G . FOWLER

in electricity needed to bring the phenomenon to visibility. His earliest report to the Royal Society states that “mercury will appear as a shower of fire while descending from the top to the bottom of a long (partially evacuated) tube.” He termed the phenomenon the n?ercuriu/ phosp/iorus, stemming from a demonstration he had just made of the luminous oxidation of the element phosphorus at low pressure. More sophisticated inquiries were possible by 1835, the date which J. J. Thomson credits to Wheatstone as that of the discovery of the electrical breakdown wave. Wheatstone (3),who tried to investigate the propagation of conduction in the onset of Geissler discharges at a time when it was fashionable to wonder about the speed of telegraph signals in wires, truly observed only that the conduction set in through a 2 m long gas-filled tube faster than he could follow it with the rotating mirror he had just invented. In actual fact no phenomenon of this class was definitely detected until I891 when Thomson ( 4 ) himself reported resolution of a fast-moving luminous pulse generated in a long partially evacuated tube. By viewing images of tube segments 15 m apart as superimposed by a rotating mirror, he estimated a speed of about one half of the speed of light and determined that this luminous pulse moved from the anode to the cathode. Von Zahn ( 5 ) had previously asserted that there was no Doppler shift of the emitted radiation comparable with the limiting velocities expected by Wheatstone, indicating that there was either no phenomenon or no mass motion. It is well to emphasize at this point that although this absence of detectable motion in the heavy particles of the gas is assumed to exist in all the situations that will be discussed and is certainly a primary criterion for classification of these waves, it may never have been proved explicitly. Von Zahn was photographing end on what he describes as a Geissler discharge, and as such almost certainly saw light chiefly from the positive column of the steady discharge subsequent to the passage of the various breakdown waves. The breakdown waves themselves are low enough in intensity that one may now properly wonder whether they would have been accessible to nineteenth century spectroscopy at all, even had there been adequate time discrimination in the experiments. In the interval elapsing before the definitive 1930 research of Beams ( 6) , investigators seem to have had their attention diverted to the slower dynamical phenomena of the plasmacoustic class generally known as moving striations, although James (7), using a Kerr cell, reported failure to observe Thomson’s wave. Clearly this often cited negative result arose because again the wave is much too low in intensity to be visible under the severe light losses that handicapped early Kerr cells. Over the next fifteen years Snoddy and his co-workers (8) provided the first significant studies of the electrical breakdown waves or potential w m e s as they came to call them. Beams observed with a rotating mirror that a wave always left his un-

NONLINEAR ELECTRON ACOUSTIC

WAVES,

I

3

grounded electrode, regardless of polarity, and proceeded toward the grounded electrode, where it was succeeded by a much brighter wave (a return stroke) moving at higher speed in the reverse direction. In so doing he evidently became the first to observe a true breakdown wave, an ionizing wave proceeding into a neutral gas. It is almost certain from the observations reported that Thomson’s wave was a return stroke. i.e., an ionizing wave moving into a medium which has been seeded with electrons. usually by a previous wave. Beams observed speeds of 4 x 10’ nijsec with applied voltages of 30 kV in air at pressures of about 0.3 Torr. Although Beams began his research ( 9 ) in an effort to study lags in the order of appearance of spectral lines in spark discharges (a complex effect compounded of the finite radiation lifetimes of quantum states, the molecular transit times to the site of excitation of volatilized electrode materials, and finally of the transit time of the electron waves which initiate the discharges), he soon recognized (1936) that his research on the waves themselves would have an impact on the study o f man’s oldest electrical acquaintance, lightning, a field that was just beginning to have a well-grounded phenomenology. The 1916 techniques of Wilson (/O) provided information on the potentials, currents, and total charge transport of lightning strokes, and the Boys camera ( I 926) revealed the complicated structure of the stroke itself together with rough estimates of the propagation velocity. As first described by Schonland (I/), an initial faint wave called a leader was seen to propagate from the (usually) negative cloud base toward the ground, commonly in a series of 50 m advances at an average speed of greater than lo7 m/sec, interspersed with 50 psec pauses. When the observed potentials of lo8 V were scaled with the pressure, it was clearly probable that a root similarity existed between the phenomena being described. When research began in 1949 with electric shock tubes (12) and some of the other high current, low pressure discharges employed in plasma physics, it was quickly apparent that some form of preheating including preionization took place in (what seemed to be) every case in the expansion chamber of the apparatus well before the advance of the heavy particle shock waves and flows. The causative agent was first clearly identified as a wave by Josephson and Hales (13) who measured its velocity at around 5 x lo5 m/sec, others having tried to explain the effect as photopreionization by ultraviolet radiation. The phenomenon was dubbed a plasma precursor, although this led to a certain amount of confusion with a similar early ionization observed at about the same period in front of strong shock waves in an ordinary pressuredriven shock tube by Jahn ( 1 4 ) and later investigated by Weymann (/5) that proved to be caused by the free diffusion of electrons. Although this effect has had its place in clarifying our overall understanding of the electron waves, it is not sufficiently germane to receive detailed attention in this article.

4

RICHARD G. FOWLER

As phenomena accumulated, it became apparent that the unifying feature of this family of waves, intermediate in speed between electromagnetic waves, and acoustic waves, was the acoustic speed of the electron, (5kTe/3m)”’, and that a number of miscellaneous situations, some of them involving natural phenomena, were probable members of the family. Time lapse movies (16) of the sun have revealed waves of luminosity moving across the face of the sun at these high speeds in conjunction with violent activity. Radar reflection from the sun has shown outward moving waves at similar speeds (17). Satellites have detected shock waves in the interstellar media with speeds of 4 x 10’ m/sec (18). The transit time from the sun and steepness of onset of certain magnetic storms suggest that they involve waves of the same type. Following the 1962 Johnston Island “Starfish” test at high altitude, a worldwide ionspheric effect was observed which may have been simultaneous (19) or may have had a propagation velocity of 2.3 x lo6 m/sec (20). Recently precursors have been observed (21) at speeds of 0.3 to 3.0 x lo6 mjsec from around the explosion generated by focusing a pulsed laser. Since 1962, when Paxton and Fowler (22) first proposed that nonlinear fluid theory applied to the electron component of the gas should describe these waves theoretically, definite progress has been made both experimentally and theoretically toward that goal. 11. LABORATORY EXPERIMENTS

A . Breakdown Waves

Snoddy, Beams, and Dietrich (23) investigated breakdown waves chiefly through and in regard to their electrical properties. They applied the potential of a Marx circuit impulse generator to an electrode in one end of a 15 m long partially evacuated tube (Fig. 1 ) and observed potentials as they appeared along the tube with an oscillograph having about a 20 nsec risetime. Since I IOM

8 53M

.P

MIt

TO CHARGING SYSTEM Gu

io

OSCILLOGRAF&

II I E4

FIG.1. Diagram of Beams’ apparatus showing discharge tube and Marx circuit for supplying potential. From ( 8 ) with permission of Phys. Rev.

5

NONLINEAR ELECTRON ACOUSTIC WAVES. I

they used only a rotary oil pump to achieve vacuum, their gas purity is not free from challenge, but despite this the small difference observed between different gases (Fig. 2) suggests at once that ultrahigh purity would not have been of much import. They found that the principal factors governing the velocity of the wave were the applied potential, the gas pressure, and the radius of the tube in which the wave is confined. The velocity increased 40 c

V

w

: 35 I

-2

- -0--

ln

30

2

2

c

25

4

(1

d0

20

0:

a

LL

0

15

P

;10 P v)

0.2 0.4

0.6 0.8 1.0 1.2 PRESSURE (TORR)

1.4

1.6

1.8

FIG.2. Average speeds of antiforce wave propagation for dry air (-), C 0 2 ( . . . . .), and H, (- - - -), applied voltage 125 kV in 5 mrn tube. From (23) with permission of Phys. Reo.

linearly with applied potential (Fig. 3), and varied according to the similarity law product radius x pressure, increasing with this factor for low pressures. They observed that waves from a negative electrode were faster than those from a positive one and that, like the return stroke, a second wave that happened to move into an already ionized medium because it was launched too soon after the first wave passed traveled with extra speed. Examining the wave fronts with a rotating mirror, they found them quite straight.” They measured the input currents supporting the waves and found them to be large (Fig. 4 and Table I). Mitchell and Snoddy (24) subsequently added to this research as part of a general effort to tie the observations into the lightning problem, improving the data on variation of wave speed with gas pressure (Fig. 5), and offering a theory which will be discussed below. In what follows, the unambiguous terminology proforce ” and “ antiforce” will be used to describe the two polarities in which waves may be “

“

6

RICHARD G . FOWLER

TABLE I MAXIMUM CURRENT I N INITIAL WAVEFOR DIFFERENT TUBES Applied voltage

(kV)

Tube diameter (mm)

Maximum current

Pressure

(A)

(Torr)

18.0 5.0 5.0 1.7 18.0

230 171 143 91 226

0.60 0.45

+I32

+ 141 1180

+I32 -I32

Aim’

9.0 x 10-3 9.0 x lo-’ 7.5 x 1 0 - 2 4.0 x 10-1 9.0 x 10-3

0.08 0.45

0.45

generated. A proforce wave will be one in which the force on the electrons at the immediate front of the wave is in the direction of wave propagation; an antiforce wave is the contrary case. The modern phase of measurement dates from the work of Haberstich (25). To the general layout of a breakdown wave apparatus he added a 30.5 cm diam cylindrical ground shield around the breakdown tube. He experimented with replacing the spark-gap switch, used by Beams, with a vacuum switch but found it unsatisfactory and returned to the spark gap. His great advance was in the diagnostic equipment which he applied to the problem. He introduced photomultipliers to track the waves by their luminosities as well as 40

I

1

1

1

1

I

V W v) \

g 35-

-

0 2

-

0 30I-

a 0 a

n

-

0

a 25n

b.

0

-

20W

n cn

15

I

I

I

I

I

7

NONLINEAR ELECTRON ACOUSTIC WAVES, 1

0

-

110

I

I

I

I

I

I

I

voltage

FIG.5 . Spced pressure curves for proforce waves in air, in 14 cm tube. 6 25 kV, 55 kV, A 85 kV, U 115 kV. Froni (24) with permission of Phys. Rro.

8

RICHARD G . FOWLER

electrostatic probes rather similar to those used by Beams to detect them by their accompanying fields. In this fashion he was able to supply the basic evidence missing from the previous work, that the luminosity and charge configuration of the wave were cospatial within the risetime of his equipment which he estimated at better than 10 nsec. Haberstich worked with helium and argon and like Beams did not take any special precautions with gas purity. In his own words, Our unavoidable use of a mechanical pump is admittedly poor experimental practice for the study of electric discharges. But, because of the high speed of the potential waves, it appears reasonable to assume that the collisional phenomena associated with the propagation mechanism are little affected by the purity of the gas. Impurity effects may still be involved in radiative processes, such as photoionization in the gas or at the walls. Unfortunately the role played by these processes in the propagation of the wave is not well understood at present. Therefore, it is difficult to estimate the influence of photo-ionized impurities, for example, on the structure and velocity of the potential waves. In view of the excellent reproducibility of the speed and attenuation observed over a period of operation of our discharge tube of nearly two years, it appears that the results reported here have not been significantly affected by the low purity of the experiments.

His use of gases with well-known atomic constants, even it they were not absolutely pure, was an important advance if comparison with theory is to be made. As will be subsequently seen, the properties of the wave do depend on the ionization potential, ionization cross section, and elastic cross section of the gas, and so gas purity is ultimately desirable; but these are dominated by the mechanical properties of the free electrons to a point that the wave speeds are only moderately sensitive to gas composition. Having demonstrated that the luminosity and electron charge in the wave were cospatial, Haberstich selected the former for his velocity measurements because he noted that electrostatic probes interfered with the motion of proforce waves, especially at low pressures, to falsify the time interval measurements. He calibrated his probe by inserting a metal pipe inside his glass tube and moving it toward the probe under known potential. He arranged light pipes so that a single 1P21 photomultiplier could see four stations at once, and all the successive signals could be recorded in a single triggered sweep of a Tektronix 585 oscilloscope. His results are given in Figs. 6-9; they have been replotted as functions of position at constant pressure rather than vice versa as originally given. They bring out vividly for the first time exponential attenuation of the wave velocity with advance down the tube, a fact obscured in Beams’ apparatus by the lack of symmetry in the ground array and by the limited number of stations used. That the potential at the wave front attenuates was known to Snoddy et al., but again only two stations 8 m apart were employed. Haberstich followed

9

NONLINEAR ELECTRON ACOUSTIC WAVES, I

f

2.5

y to68 6 4

4.5

6.5

2

FIG.6. Wave velocity decrements. Haberstich data for proforce waves in helium. From Haberstich (25) with permission.

61 4 -

-

2 -

V

:10’ 8 r \

I

6 :

-6

4 2 :-

>-

g

-

--

106 8 6 4 -

4.1 TORR ‘I1

2 -

to1

I

I

-

REVISED II

I

FIG.7. Wave velocity decrements. Haberstich data for proforce waves in argon. From Haberstich (25) with permission.

10

RICHARD G . FOWLER

LOCATION ( M )

FIG.8. Wave velocity decrements. Haberstich data for antiforce waves in helium. Haberstich (25) with permission.

the attenuation of potential at the intervals of 0.5 m, obtaining the results in Figs. 10-13. When these are replotted from the viewpoint of subsequent theory one finds both that attenuation is exponential with either nearly the same or nearly one half the decrement found for the wave attenuation and that there is also an electrode drop in potential for the proforce wave which becomes especially pronounced at low pressures. The attenuations observed are substantial and show at once that the velocities computed by finite differences over such large station separations as 0.5 m require correction by use of the expression

dt

(1)

In the most severe case this amounts to a factor of 1.47. The curve for 11.O Torr in Fig. 7 has been replotted to allow for this factor. Having a measure of local velocities and local potentials, Haberstich plotted one against the other in a few cases and obtained what seemed superficially to be discordant behavior-linearity at some pressures and nonlinearity at others. Replotting all the data as in Fig. 14 indicates that proforce

11


I o6 8

6 4

t

5

10

2t

4

11.0 TORR

I o4 0

10

2LOCATION 0 3 ( M0I

4 0

50

FIG.9. Wave velocity decrements. Haberstich data for antiforce waves in argon. From Haberstich (25) with permission.

waves in both helium and argon (over the pressure and voltage range studied) together with antiforce waves in argon above 1 Torr when also below 10 kV follow the relation V K ( p 2 / p , while antiforce waves in helium (over the brief pressure range studied) together with antiforce waves in argon below 1 Torr follow the relation V CK (pp except when also below 10 kV. Haberstich also computed what he termed front thicknesses by multiplying the observed risetime of signals on the voltage probes, photomultipliers, and his microwave interferometer by the propagation velocity. A sample of these results is reported in Fig. I5 for proforce waves in argon. Essentially the same thicknesses were observed in helium. Using a microwave interferometer he detected substantial quantities of electrons behind the front, but the response time of the instrument was so slow that it is not possible to relate them i n any sure way to the front itself. A sample measurement was 10l6 electrons per cubic meter at 10 kV and 2.0 Torr He some 50 psec after wave passage. This slowness of microwave response has been a standing handicap in getting useful data about these waves. One of the striking qualitative observations made by Haberstich was that the luminous response of the photomultipliers was more rapid for waves in

'i 5

1.0

1

0

I

I .o

I

I

I

I

2 .o 3.0 LOCATION (MI

4.0

5.0

FIG.10. Wave potential decrements. Haberstich data for proforce waves in helium. Haberstich (25) with permission. 10

,

I

2 -

I.o

I

0.34

I

I

1.9

1

11.0 TORR

-

I

LOCATION ( M I

FIG.1 1 . Wave potential decrements. Haberstich data for proforce waves in argon. Haberstich (25) with permission. 12

FIG.12. Wave potential decrements. Haberstich data for antiforce waves in helium. Haberstich (25) with permission.

.

10

-3

5-

I

I

I

I

311.0 TORR

2

I 0

0

I

I

I

I .o

2.0

3.0

I

4.0

5.0

LOCATION ( M I

FIG.13. Wave potential decrements. Haberstich data for antiforce waves in argon. Haberstich (25) with permission. 13

2

I o6

8 6

+2/P OR + P FIG.14. Haberstich data plotted against an appropriate functional variable $ / p or qV (see text); n = 6,3, respectively. Various symbols distinguish different pressures and initial volt ages.

FIG.15. Apparent thickness d, of the potential rise for proforce wave in argon plotted in terms of the risetime T , at the potential probe,the velocity Vof the wave,and the pressure p of the gas. Waves generated by potentials of 15, 1 1, 7.5, and 5 kV and observed at I = 127 cm. From Haberstich (25) with permission.


15

argon than waves in helium. This he traced to the presence of A(I1) radiation at the outset of argon waves. The A( 11) radiations are generally much faster in radiation lifetime and thus appear and peak before the A(1) radiations become strong, in response to a pulsed excitation at the wave front. The He(I1) radiation was not observed because its excitation potential was too high for the waves generated, and so in helium only the slower He(1) radiations were seen. Haberstich in fact obtained rough time resolved spectra showing that A(I1) radiations are present at the very front and die out. The research of Haberstich was both satisfying and tantalizing. Haberstich himself, and Burgers (26), offered theories of the phenomenon based on the fluid dynamical approach of Paxton and Fowler. Shelton derived a solution of these equations (27) which predicted that the wave velocities should be mobility controlled and proportional to E/p. The existence of these new theories capable of being tested, their partial discord with the observations of Haberstich, and the general need for more extensive data on the breakdown wave phenomenon prompted the experiments described by Blais (28) and Blais and Fowler (29).Their wave apparatus included the following departures from the design used by Haberstich: (a) The breakdown tube was 7 m long and 51 mm diam. An adjustable spark gap was used to switch the potential as Beams had done. Tests proved that this simplified arrangement gave a more regular and reliable performance than a variety of more modern and sophisticated electronic equipment. The vacuum switches used by Haberstich had limited his voltages to 10 kV because of what he termed bouncing of the relay. Blais found that they broke down at high voltage owing to field emission before closure and that the entire wave propagation phenomenon could take place during the period of arcing and wild voltage oscillation that ensued prior to actual metal-to-metal contact. (b) A standard vacuum system with oil diffusion pump and liquid N, cold traps (to maintain the purity of spectroscopically pure commercial gases) was employed. (c) An improved version of Habersitch’s electrostatic ground was designed of twenty la in. diam aluminium pipes evenly arranged and rigidly mounted parallel to one another as generatrices of an open lattice cylinder 0.27 m i. d. This style of construction provided unlimited access ports to the wave tube. (d) Wave speeds were measured by compiling in a multichannel analyzer the time intervals for a large number of successive waves between given stations. With one photomultiplier at a reference station and a second at a downstream station, start and stop inputs were delivered to a time-to-pulseheight converter. The output pulse was then stored in the analyzer until a statistically significant number of events was obtained. The entire apparatus could be calibrated against measured delay lines to better than 2 nsec. The principal advantage of the method lay i n the time-to-pulse-height converter

16

RICHARD G . FOWLER

that has a higher time resolution, can deal with smaller time intervals, and can be calibrated more accurately than the time base of an oscilloscope. Lacking an analyzer, one might display the output of the converter on an oscilloscope and use the ability to calibrate its vertical amplifier with known voltages to achieve about the same accuracy. Care must be taken to be sure that the triggering waveforms remain constant in profile and amplitude, otherwise a falsification of the velocities can easily enter because the converter responds upon passing a given threshhold voltage of the trigger pulse. (e) The diagnostic methods they employed were chiefly optical, based on the observation by Haberstich that metallic probes, even external to the wave, could interfere with the wave propagation. From their optical observations they derived electron temperatures and electron densities in addition to wave speeds. Blais and Fowler noted for the first time that the attenuation of the wave velocity as measured by Haberstich was exponential; one purpose of their research was to investigate this matter in detail in order to determine whether the exponential behavior was exact or approximate. Because of the attenuation, as has already been mentioned, it is not possible to obtain true velocities from the finite ratios Az/At measured between stations. Rough plots of this finite ratio suggested, however, that dV/dz = -yV"

(2)

where 0.5 < n < 2.5. The cases of n = 1 and 2 could be treated by finite differences to yield linear plots of At vs. t for n = 1 and At vs. z for n = 2. After putting the two cases to as many tests as possible, they concluded that n = 1 (the exponential decay) was the more likely and probably was an exact result. It was found that y is strongly dependent on (po, the initial applied voltage, and on the pressure. The best fit was obtained by forming the quantity y ( p 0 2 i 3 , which then exhibits a linear change with pressure at low pressure and a saturation behavior above 5 Torr as shown in Fig. 16. The data of Haberstich can be placed on the same curve plot with an adjustment by a factor of 4for the relative tube sizes ( 2 in,/l in.). The general behavior suggests electron loss under diffusion as the controlling factor present in the constant y. The constancy with pressure at high pressures indicates that the column is selfconstricted in the radial direction as observed by Winn (see below), and as expected above an crp of about I0 for an electron-dominated column at high pressure (30). Since concern over the possible perturbation of the wave speed apparatus by any probes with which the local potentials might have been measured had led Blais and Fowler to avoid their use, they were compelled to adopt a different approach which is itself not without objection. The exponentially


9"

17

7l

5

TORR HE

FIG. 16. Decrement of wave velocity vs. gas pressure in helium 0 Antiforce, Proforce, a Haberstich proforce, A Haberstich antiforce. From Blais and Fowler (29) with permission of Phy.7. Fluids and Haberstich (25) with permission.

decreasing observed velocities at each point were extrapolated back, using the Ar,r plot of the data points, to the velocity that would have been observed at z = 0, i.e., in the vicinity of the electrode. This was then treated as the velocity

corresponding to a wave moving at the initial electrode potential as measured by a voltage divider connected to the electrode. The data they obtained for proforce waves are given in Fig. 17, plotted against cp/ap, the natural variable. The data for intermediate pressure seem to cluster around a linear dependence of Vupon cp/ap, but data for high pressures and low pressures are offset and at high pressures and weak fields the dependence seems to be going over into the cp2 dependence found in the Haberstich data. A t high pressures the shifted position of the data again indicates a column which is of smaller radius than the tube, 8 mm, in fact. At low pressures, the shift of the data to low velocities may be because of the ignored cathode fall in potential. The tacit assumption exists that there is no cathode drop in potential. Subsequent restudy of the Haberstich data has shown that this is a good approximation for antiforce waves and proforce waves at pressures above lmm, but not below.

18

RICHARD G . FOWLER

A

*

.

- 301 - 98 - 098 - 295 - 0.30 0 - 163

0

A A m

0 - HI45

e- 24 8 - 4 5 0 - 6 5

0

I

1

1

1

1

I

l

l

I

FIG. 17. Comparison with theory of observed initial velocities vs. applied potential for proforce waves in helium. Data symbols below H are from Haberstich, above are from Blais. From (29) with permission of Phy.~.Fluids and (25) with permission.

The data for antiforce waves are plotted in Fig. 18. As yet there is no theory with which to compare this data. It must be noted that these data do not show that c p / q is the simple controlling variable as clearly as do the proforce wave data. A striking prediction of the Shelton theory is that breakdown waves will not run into a neutral gas beIow a critical velocity of (2eqi/rn)'/'. In helium this is 2.99 x lo6 m/sec. The prediction was found to be borne out by experiment reasonably well in two different situations: (a) In the experiments from 1-3 Torr no starting discharges were observed below about 2.5 x lo6 m/sec, a fact that is in accord also with the observations of Haberstich. (b) In experiments where the velocity of the decelerating wave passed below 3 x lo6 at some point in the apparatus, no wave was detectable beyond this point. The waves at 30 Torr were an exception to this, showing starting and running values to below 8 x lo5 m/sec. The method used for determining electron temperatures and densities was an adaption of a spectroscopic method proposed by Sovie (31) and perfected


WAVES,

7t

19

I

5

A h

a d

.

..

16 L 7

@,

lo4

A

0

A

1

3

5

7

105

+

3

1

5

7

L . i

1

3

106

(V/rn/Torr)

FIG. 18. Antiforce wave velocities vs. applied potential in helium. I:', 2.95, A I .63, 0 0.98. From Blais (29) with permission of P/?)P.Y. Fhids.

30. .1,

9.8,

by Latimer. Mills, and Day (32) in a situation similar to this one, but quasistatic. It depends on taking the ratio of the intensities of two emission lines. When the excitation of gas atoms is due solely to random electron collisions, and multiple processes such as excitation transfer or excitation from the metastable states are negligible, the intensity ratio of two spectral lines, as measured by the signal S from a photomultiplier tube, is given by SjklSim = ( Q j r l l > I (

Qimzl>

(3)

or SjklSlm

== < . ~ k ( l ' ) L ' > . j h / < f i m ( ~ ~ ) Z 1 ) ~ l w i

(4)

where ojkand g l m ,respectively, are the values of the optical cross section of the two lines at maximum. The optical cross section Q.jk is defined as Q j k= Bj, Pi'. Bjk is the branching ratio for t h e j + k transition and Qj'is the apparent cross section for theJth level, i.e., the cross section of thejth level uncorrected for cascade from higher levels. The functions f ( v ) describe the shapes of the excitation functions with electron velocity, i.e.,

20

RICHARD G . FOWLER

The angle brackets mean that the cross section as a function of velocity has been multiplied by velocity and averaged over the plasma electron velocity distribution which is generally taken to be Maxwellian. Thus if the two cross sections are different functions of electron velocity then the ratio will be a variable function of electron temperature. The best pairs of helium lines to use are those which originate from the n'S and n3S levels, since the excitation cross sections of these lines have been shown by Miller (33) to be relatively free from pressure effects. These lines also have the advantage that the radiation from the electron beam cross section measurement experiments is unpolarized (34) and hence the available measured cross sections will be more accurate since no corrections for anisotropy of the emission of radiation are necessary. TABLE 11 MEASURED OPTICAL CROSS SECTIONS QIk FOR THE HELIUM SPECTRAL LINES

Optical cross section (10-l' m2) Line

(A,

Transition ~

5048 4713 4438 4141 4686

Electron energy (eV)

Jobe and St. John (35)

Present data

Branching ratio B,,

Lifetime (nsec)

0.59 0.62 0.47 I 0.477 -

89 62

~

2IP - 41s 2 3 -~ 43s 2lP - 5's 2 3 -~ 53s He+34

33.5 26.5 33.7 27.7 205

13.80 20.6 5.14 7.64 1.07

13.60 19.80 5.19 7.64 -

110

140 2.1

The cross section data (Table II) used are the recent data of Jobe and St. John (35)up to 400 eV. They were measured at pressures and currents low enough to ensure the absence of multiple effects. The data of Moussa (36) normalized to that of Jobe and St. John at 400 eV was used to achieve extrapolation to 1000 eV. A computer integration routine suggested by Elste (37) was applied 'to calculate the Maxwellian averages of the cross sections. When a Maxwellian velocity distribution of electrons is chosen ( Q j k u ) is given in terms of energy by u,,,.,

ju

( Q j Au ) = 3.583 x 107(l/kTe)3/2

"7

I

"

Qjk

(U)Ue-"lkTedU.

(7)

Here U is the energy in eV, kT, is the electron temperature in eV (i.e., 1 eV = 7737"K), Urninis the threshold for excitation and Urn,,is the maximum energy to which the integration was carried out, in this case generally IOkT,. These


21

averages for several lines and ratios for these line pair combinations are given in Table 111. When the 4686 A Hef line is visible, it can be used along with one of the atomic helium lines to check on the reliability of the plasma temperature measurements. If good agreement is obtained with that shown by pairs of atomic lines, one has a test of the validity of the Maxwellian distribution since the ionized helium line is excited by electrons in the tail of the distribution while the atomic helium lines are excited by the low energy electrons. In a time changing excitation, where changes take place more quickly than atomic systems can respond to them, the method must be modified. Thus, in practice the highest temperature in a breakdown wave is always observed at the leading edge of the wave even though the intensity of the optical signal there is zero. The fact that the quantum states providing the radiation have natural lifetimes and do not respond instantly to the excitation makes it very difficult to obtain early information about the structure of fast waves, a fact that is often overlooked in interpreting oscilloscope traces of luminous profiles. The slow linear rise usually present at the leading edge of a wave does not indicate a corresponding slow rise of the controlling variables in the wave, but rather the normal belated response of a linear system to a step function of excitation. In fact, until the atomic response is unfolded from the data, the observed profile is wholly deceptive and hidden wave structures may easily pass unnoticed. The differential equation governing the excitation process for the kth state is dNk/dt = - N J r I ( ~ ~ v ) n N (8) where Nk is concentration of excited states, T k their lifetime, and ( u ku> is the Maxwellian average given in Table 111. The electron concentration is n, and the neutral atomic concentration N . The photon flux at the photomultiplier is K(Nk/Tl),where K is an apparatus constant that varies with wavelength only as the cosine of the diffraction angle of the monochromator grating. The photomultiplier produces an output srgnal ski which is proportional to the input photon flux according to an efficiency factor hkj which is wavelength dependent. Substituting the observed photomultiplier signal skj for Nk in the differential equation yields

+

If the time history of a second line is observed as well, the ratio of these histories gives (on the right-hand side) the function tabulated by Latimer et. al. (32) and instantaneous temperatures can thus be determined

TABLE 111 MAXWELLIAN AVERAGES OF OPTICAL CROSS SECTIONS FOR HELIUM< Q l k v : A ~ CALCULATED D RATIOSAS OF ELECTRON TEMPERATURE"

5048

A

4113A ~

1.333 1.666 2.000 2.333 2.666 3.000 3.333 3.666 4.000 4.333 4.666 5.000 5.333 5.666 6.000 6.333 6.666

8.64E-5 8.83E-4 4.09E-3 1.24E-2 2.8 1 E-2 5.29E-2 8.76E-2 1.32E-1 1.86E-1 2.48E-1 3.16E-1 3.91E-1 4.70E-1 5.52E-1 6.37E-1 7.23E-1 8.10E-1

_

1.66E-4 1.62E-3 7.2953 2. I I E-2 4.63E-2 8.46E-2 1.36E-I I .99€-1 2.73E-1 3.55E-1 4.42E-1 5.33E-1 6.26E-1 7.19E-1 8.12E- I 9.03E-1 9.91E-I

4438 _

A

4121

A

4686 8,

5048 4713

7.93E-18 1.71E-I4 2.90E-I 2 1.15E-10 1.82E-9 1.58E-8 8.89E-8 3.68E-7 1.21E-6 3.30E-6 7.84E-6 1.66E-5 3.22E-5 5.77E-5 9.71 E-5 I S5E-4 2.36E-4

0.521 0.544 0.565 0.587 0.605 0.624 0.643 0.660 0.679 0.697 0.715 0.731 0.749 0.765 0.784 0.800 0.816

_

2.70E-5 2.85E-4 1.37E-3 4.16E-3 9.578-3 1X2E-2 3.05E-2 4.63E-2 6.55E-2 8.77E-2 1. I3E-I 1.40E-I 1.68E- I 1.98E-1 2.29E-1 2.61E-1 2.93E-1

4438 4121

A

FUNCTION

4121 4686

~~

4.59E-5 4.75E-4 2.22E-3 6.6OE-3 I .48E-2 2.75E-2 4.47E-2 6.63E-2 9.1 5E-2 1.2OE-1 I SOE-1 1.80E-1 2.15E-I 2.47E-1 2.80E-1 3.1 2E-l 3.44E-1

0.588 0.6 0.61 5 0.631 0.647 0.665 0.682 0.698 0.716 0.733 0.75 0.167 0.784 0.802 0.819 0.836 0.853

76000 36400 19100 I0960 6670 4280 2880 2070 1456

8.OOo 9.333 10.66 12.00 13.33 14.66 16.66 20.00 23.33 26.66 30.00 33.33 36.66 40.00 43.33 46.66 50.00 53.33 56.66 60.00 63.33

1.1 6E-0

1.49E-0 1.79E-0 2.06E-0 2.31E-0 2.52E-0 2.81E-0 3.19E-0 3.49E-0 3.73E-0 3.92E-0 4.07E-0 4.2OE-0 4.3 I E-0 4.41 E-0 4.48E-0 4.55E-0 4.61 E-0 4.66E-0 4.70E-0 4.73E-0

1.3lE-0 1.56E-0 I .76E-0 I .90E-0 2.01 E-0 2.08E-0 2.14E-0 2. I5E-0 2. I2E-0 2.06E-0 1.98E-0 I .90E-0 1.83E-0 I .75E-0 I .68E-0 1.62E-0 1 .SSE-O 1.50E-0 1.44E-0 1.39E-0 1.35E-0

4.21 E-l 5.43E-1 6.54E- I 7.55E-1 8.46E-1 9.26E- I I .03E-0 1. I7E-0 1.28E-0 1.37E-0 1.44E-0 1.49E-0 I .54E-@ 1.56E-0 1.61E-0 I .64E-0 1.66E-0 I .68E-0 I .70E-0 I .7l E-0 1.73E-0

4.57E-1 5.49E-1 6.19E-1 6.71E-1 7.08E-1 7.33E-1 7.55E-1 7.62E- I 7.48E- I 7.26E- I 6.99E-1 6.71E- 1 6.43E- 1 6. I6E- I 5.92E-1 5.68E-1 5.46E-I 5.26E-1 5.07E-1 4.89E- I 4.73E-1

9.04E-4 2.38E-3 4.96E-3 8.82E-3 1.40E-2 2.06E-2 3.28E-2 5.82E-2 8.83E-2 1.21E-1 1.55E-1 1.89E-I 2.23E-1 2.56E-1 2.87E-1 3.17E-1 3.46E-1 3.73E-1 3.98E-1 4.22E- I 4.44E-1

0.882 0.955 1.017 1.084 1.15 1.21 I 1.31 1 1.477 1.642 I .8l 1.971 2.135 2.30 2.46 2.61 8 2.77 2.935 3.07 3.22 3.36 3.505

0.921 0.989 1.057 1.13 1.195 I .26 1.366 I .54 1.71

1.885 2.056 2.226 2.394 2.56 2.72 2.884 3.042 3.2 3.35 3.5 3.65

506 230 I25 76.0 50.4 35.6 23.03 13.1 8.48 5.99 4.51 3.54 2.88 2.41 2.06 1.79 1.58 1.41 1.274 1.16 1.066

’ Multiply all averages by lo-” m3 sec-’.

h)

w

24

RICHARD G. FOWLER

Blais and Fowler applied this method to obtain time history temperature data for both proforce and antiforce waves, at 2.0 m and at 5.0 m flight distances (see Fig. 19). They used a Jarrell-Ash m monochromator. Mounted at the exit slit was a 7746 photomultiplier. The signal was sent to a Tektronix 519 oscilloscope, an instrument with a real time risetime of 0.28 nsec.

+

0

"

1

A

0

10

I

20

P 30

?

40

x 50

60

TIME (nsecl

FIG.19. Temperature profile for 3.0 Torr, 42 kV proforce and antiforce waves at 2.0 m 0 anti) and at 5.0 m (0 pro, anti). From (29) with permission of Phjs. Fhids.

(0 pro,

Although their data are for relativelyearly times ( 10 nsec) after the wave front arrival, it is not early enough to detect the temperatures believed by the theory to exist in the sheath layer and evidently applies to what Shelton called the quasineutral, or thermal region behind the front. As the data show and theory expects, the thermal region is relatively insensitive to the polarity of the wave. Examining the discrepancy between theory and experiment, however, suggests the desirability of repeating and improving the measurements; it also suggests that the thermal region, being one in which the electron gas is stationary, must be affected strongly by diffusion to the walls and by the presence of the conduction currents found in a real three-dimensional geometry, and that these must be ultimately added to the theoretical analysis. In Fig. 20, the data are present for the initial values of temperatureobserved at various stations for both proforce and antiforce waves. If the constants Kand h,, can be determined by absolute calibration against a standard lamp, then one can measure n, the concentration of electrons in the N

25

NONLINEAR ELECTRON ACOUSTIC WAVES, 1

W

W

a W

I

, 0

2

.~ ~

__-1

4 STATION LOCATION (rn)

6

1

.-

FIG. 20. Peak (earliest measurable) temperature observed for proforce and antiforce waves at various initial voltages and locations. From (29) with permission of Phys. Fluids.

wave, as a function of time by direct application of the differential equation. Referred to the photomultiplier signal from a standard lamp S,, through the same monochromator optics, with the lamp ribbon and experimental tube only partially filling the monochromator aperture,

where W is the width of the observation slot on the experimental tube, and R , is the tube center distance to the monochromator, s is the slit width of the monochromator, ,f is its focal length. N , is its grating line number, O1 is the angle of diffraction, A , is the standard lamp ribbon area, R , is its distance, S, is the lamp signal, and P, is its monochromatic photon radiance (photons/ unit wavelength/sec/cm2/sr). I n Fig. 21 are given some electron density measurements i n the thermal region of the wave at the two stations together with proforce wave theory calculations. Both the general trend and final values of 1 7 , are encouraging. It is evident, however, at the conclusion of this review of the existing experimental work, that much remains to be done on careful measurement of velocity and structure of the wave.

26

RICHARD G . FOWLER

2

I

I

I

I

1

I

,2.0

1

5.0

21

-

n I

I

I

1

I

I

B. Secondary Breakdown Waves In 1959, Westburg (39,proposing to study moving striations in glow discharges, found that he had developed an apparatus for the study of secondary breakdown waves-those in which an electron space charge moves in an already ionized gas, augmenting that ionization. In lightning discharges, and in the work of Beams. these waves were called return strokes. The glow discharge offers controllable degrees of preionization at almost exactly the right level to simulate conditions in a normal return stroke. Using a 40 mm diam Pyrex tube 1.5 m long and gas purity procedures of the highest quality (which he later found to be unnecessary-the results being insensitive to intentional impurities, even mercury), he began each run with an 0.05 pF (estimated) capacitor held by a power supply at 1-3 kV across a 100 kR resistance and the experimental tube in series. This produced a glow current that, depending on the gas and its pressure, could be 1-20 mA. The resistor (which was in the anode side of the circuit) was then shunted with a mercury

27


relay leaving a residual resistance of 100 R. The circuitry was coaxial, and the experimental tube was run inside a metal shield. Waves were then followed from cathode to anode and return, by means of five probes through the tube wall and a pair of movable photomultipliers. N o details are given on the risetime of the equipment. At some brief instant after the shorting of the 100 kR resistor, a glowing spot appeared on the cathode and the luminosity moved as a sharp-fronted wave toward the anode with an initial velocity in the 2 x lo5 m/sec range which slowed to about half of the initial value as the wave reached the anode, after which a wave with a less steep front returned to the cathode at about the same velocity as the first wave had initially. The former should be called a secondary proforce wave, the latter a secondary antiforce wave. The currents delivered by the cathode in support of the first wave were 1-10 A , and were a slight function of cathode material but a strong function of gas and gas pressure. Typical voltage distributions reported by the probe stations as a function of time are given in Fig. 22. In Fig. 23 the derivative of these

0 Cothode

0.50

1.00 M

I .46 Anode

Fici. 22. Westburg’s potential distribution plots for argon at 97 p and 1700 V during first 160 nsec of secondary wave propagation with A1 cathode in tube 146 cm long. Asterisks indicate zero time which is the instant the potential begins to change a t the first plasma probe. From (38) with permission of PItys. Rev.

28

RICHARD G . FOWLER 7.50

5.00 P9

-

n

X

0 0

0 z

2

-

\

X

I >

\

>

v

W

2.50

0 Co thode

0.50

M

1.00

0 I .46 Anode

FIG.23. Electrical field and reduced field (Ejp) distributions during the first 100 nsec of secondary wave propagation as derived from curves in Fig. 22. From (38)with permission of Phys. Rev.

gives some measure of the electric field as the wave progresses. They both show the progressive character of the phenomenon, but the spacing of probes is so great that the profile and magnitude of the electric field is largely a function of the French curve used to connect the points. In Fig. 24 the velocity data read from these figures is plotted against the reduced field. Westburg gave an analysis of the phenomenon as follows: There is a brief delay while the negative charge which has been applied to the cathode attracts ions and repels electrons. The high concentration of ions collecting on the cathode face breaks down an oxide layer to permit a large current to be released which augments the electron space charge in front of the cathode. A zone of very high field now forms between this cloud of negative charge and the plasma of the glow discharge containing very fast electrons, mainly at the front of the cloud. Owing to their high velocity and the low pressure these electrons only lose energy over distances of centimeters. The velocity of the wave will relate to the mobility of the electrons in this front. Losses of fast electrons to the walls must be compensated by acceleration of new electrons by the field in the front, but is probably never complete, and so the front decelerates.

29 I O ' ~I L

I

1

I

I

1

I

1

1

1

1

,

I

8 -

6 -

4 -

2 0 W

m

-I \

k

7

10

--

:8 -

-1 W

'

6 -

4 -

2 -

lo6

I'

IO*

I

2

4 P

I

6

I

o

8

n

1

1

lo5

2

(V/M/TORR)

FIG.24. Westburg's velocity data vs. reduced field. From (38) with permission of Phys. Reis.

Many important questions were left unanswered by this research. Could the waves equally well have been originated at the anode end by pulsing the anode? How did they vary with the degree of ionization of the glow discharge? Winn (39) undertook to obtain answers. He found the waves of both species could be made to originate at the anode end of the glow column by applying the voltage pulse to that electrode, although he found that a proforce wave could only be originated there if there was a neighboring temporary cathode available. He formed this by painting a silver coating on the wall around the anode.

30

RICHARD G. FOWLER

5x10~ W v) \

3 i-

u0

4x10’

3x10~

0

0

10

20

30

40

50

GLOW DISCHARGE CURRENT

60

70

80

(mA)

FIG.25. Secondary wave velocities in nitrogen as a function of shielding diameter and glow dischargecurrent __ f 2 4 kV, - - - -24 kV, pressure 0.5 Torr. After Winn (39) with permission of Phys. Rev.

6x1O7

1

O L

0

I

10

I

1

20

I

I

30

I

I

I

I

I

I

50 60 GLOW DISCHARGE CURRENT ( m A ) 40

I

1

70

I

80

FIG.26. Secondary wave velocities in nitrogen as a function of pressure and glow discharge current 24 kV, - - - -24 kV. After Winn (39) with permission of Phys. Rev. ~

+

31


Winn’s apparatus was a Pyrex tube 0.06 m diam and 1 m long. optionally surrounded by a 0.1 m diam copper shield. He found that the presence of the shield decreased the velocity of both species of wave, but not in exactly the same way (Fig. 25). Thus it must be concluded that in addition tothe strengthening of the electric field at the front which is introduced by the induced charge on the nearby shield, there is an adverse structural effect on the proforce waves. The effect of glow discharge current on the two species is shown in Fig. 26. If the electron density in the glow discharge is calculated, a curve like that in Fig. 27 can be obtained for the velocity as a function of degree of ionization. SPEED OF LIGHT POINTS FOR FALL-IN-POTENTIAL WAVES L I E IN THIS REGION V

k-“ +24 kV

1014

lod5

1Ol6

10”

lOl8

ELECTRON DENSITY AHEAD OF THE WAVE FRONT (M-’)

FIG.27. Secondary wave velocities as a function of electron density ahead of the wave front, 0, 0.5 Torr; 0 , m 0.25 Torr. After Winn (39) with permission of Phys. Rev.

C. Electric Shock Tube Precursors As the electric shock tube became an increasingly interesting research tool in plasma physics, the question of the discrepancy between Rankine-Hugoniot predictions and the excessive velocities observed (40) became a matter of increasing concern. Voorhies and Scott (41) called attention to the high intensity of the radiation which could be observed in advance of the plasmacoustic shock wave and its singular features. It showed small Doppler broadening and so was radiated by cold atoms. It would pass through a 0.4 W/m2 field seemingly without hindrance. It was not noticed in a sidearm off the main expansion chamber. Polarity reversal of the electric driver current had no effect. These motional results must be construed in the light of their apparatus’ minimum resolving time which was certainly very low, probably no better than 50 nsec.

32

RICHARD G . FOWLER

The research of Voorhies and Scott was done with a Josephson conical driver shock tube of 0.075 m diam, and shortly thereafter, Josephson and Hales conducted a detailed study of this device under higher resolution. They observed the precursor with both photostations and probe stations. The precursor was clearly distinguishable on the probes as a progressive wave of negative charge in both polarities of the driver current, with 24 kV on the capacitor, and showed up as a more slowly rising intensity of light on the photomultipliers. Sample figures from their work are shown in Fig. 28. A

C

FIG.28. Josephson and Hales’ observations of 24 kV precursor waves in deuterium. (A,B) probe, (C,D) phototube; (A,C) end electrode positive, (B,D) end negative. Numbers are distances from ring electrode in centimeters. From (13) with permission of Phys. Fluids.

They operated with the ring electrode of the shock tube grounded and observed that when the end electrode was positive the wave was of simpler structure and about tenfold higher velocity than when it was of negative polarity. The velocities they obtained were in the 106-107 mjsec range. Among other striking observations was the fact that the front of the plasmaacoustic shock wave, owing to the loss of negative charge into the precursor, bore a residual positive charge which accorded well with the energies available in the shock, Fig. 29, and that since the expansion tube in which the electrostatic probes were placed was made of copper rather than glass, it is apparent that the precursor can be propagated through a metal-walled tube. Finally, the parabolic shape of the probe potentials implies a slab of electrons passing the probe, and if one applies Poisson’s equation to the probe curves in Fig. 28, he can estimate the electron concentration behind the wave at 1.5 x 1013 mP3.Typical gas pressures ranged upward from 100 p.

33


1 1

to4

/

,

2

1

1

1

1

1

l

4 6 8 lo5 V =VELOCITY OF SHOCK FRONT ( M I S E C )

2

FIG.29. Potential jump across plasmacoustic shock vs. velocity. From Josephson and Hales (13) with permsision of Phys. Fluids.

McLean, Kolb, and Griem (42),recognizing that many of the peculiarities of the electromagnetic (T) shock tube derived from the precursor, examined the radiation with essentially the same results as Voorhies and Scott but worked with a 0.03 m diam quartz tube. Fowler and Hood (43), testing a new design of shock driver that was intended to eliminate the blast wave behavior of electric shock tubes having short drivers, discovered an intense wave precursor on their mirrorgrams of the shock tube flow. The wave had a speed in the lo6 m/sec range which seemed to increase linearly with capacitor potential, Fig. 30, and be unaffected by gas pressure at low pressure, decreasing as perhaps p-”’ above 0.5 Torr of H, . The wave did not seem to be affected by the electrical arrangements of surrounding conductors, or by a transverse magnetic field of 0.1 W/m2, and was of higher velocity in argon than i n hydrogen. When the recombination afterglow of a I A pulsed glow discharge was present in the region through which the wave was moving there seemed to be a suppression of the afterglow just in advance of the wave. They hypothesized that heat conduction from the

34

RICHARD G . FOWLER 6-

I

-

I

-

1

G 4W

I n \

I

g

-

I

I

-

i

0

-

0

2 -

0

0

-1 W

>

0

0

-

lo6

-

0

0

-

ff-

I

2

3

4

5

6

7

CAPACITOR POTENTIAL

8

9

10

II

(kV)

FIG.30. Wave velocity vs. capacitor potential. From Fowler and Hood ( 4 3 ) with perniission of Pliys. Rev.

plasma driver somehow supported the advance of this self-sustaining space charge wave. Pugh (44), using a simple single segment electric shock tube of 0.075 m diam, observed the precursor in hydrogen at essentially tlie same speeds as Josephson and Hales had found in deuterium, thus negating their explanation based on a beam of deuterium ions. He observed two additional effects that shed new light on the phenomenon. He observed that a Lucite endplate reflected the precursor wave with increased intensity that decreased somewhat when the plate was a metallic one, and that a round-ended rod inserted centrally into the expansion chamber from the downstream end developed a luminous sheath around itself of a thickness that increased linearly with distance along the rod. These effects resembled a reflected shock wave and a fully developed boundary layer, respectively. Pugh calculated the flow velocity from the wedge angle if the gas were hydrogen at room temperature as 7 x lo3 mjsec. This was very nearly the velocity of the plasma-acoustic wave, but that could not yet have reached the rod at this epoch. Unless one invokes some process like that seen by Schreffier and Christian (45),it seems more consistent with the rest of the picture to treat the flowing gas as composed of electrons. If then one introduces the electron mass in tlie boundary layer formula and a temperature of perhaps 3 x 104"K, the indicated fow velocity becomes 3 x lo6 m/sec, a result quite consistent with those of other observers for the precursor wave. Haberstich (46) began research on the precursor of the electromagnetic T shock tube and quickly decided it was a potential wave deriving from the high voltages present, so that he revised his apparatus and directed his attention to the research already reported above.


35

Gerardo, Hendricks, and Goldstein (47) observed the precursor in the course of microwave studies of an electric shock tube. They found that there was a background electron density in the first 130 p e c of 10l6 m-’. They believed that pliotopreionization accounted for the ionization observed. lsler and Kerr (48) embarked on a study of the electric shock tube as a spectral source in local thermodynamic equilibrium. They observed a luminosity front traveling faster than lo6 m/sec, but only when the ring electrode was positive. They observed also a second precursor that had an intensity maximum at about 1 p e c after discharge initiation and independent of polarity. They assigned the latter to scattered light and fluorescence, believing that it coincided temporally with a pinch in the driver gas. Lubin and Resler (49) injected shock waves from an electromagnetic T tube into a glass-lined wave guide and examined the behavior of microwaves entering at the other end of the wave guide and reflected from the advancing plasma. They found clear evidence for a wave precursor for which they measured speeds up to 6 x lo6 m/sec, as shown in Fig. 31. They used a transverse microwave cavity to acquire data on the electron concentration (Fig. 32) and the riselength to 900.; of final electron concentration in the front (Fig. 33). From their work they concluded that the precursor exhibits a wavelike structure with a definite electron density front; that the rise length of electron concentration as well as the average electron concentration behind the front are dependent on both the discharge field and ambient pressure; that the rise length and precursor velocity varied monotonically with the parameter E/p; that the precursor begins propagating down the tube prior to the main discharge, immediately (time resolution unspecified) upon application of the high voltage to the electrodes; and that currents of the order of one ampere were found to be distributed throughout the precursor electron density distribution. Much of the confusion involved in understanding the nature of precursor waves in the electrical shock tubes has been due to the difficulties in resolving possible photon and electron contributions. It was therefore a step forward when Russell (50), in spite of the negative results of Voorhies and Scott and McLean et at., found it possible to detect a clear-cut wave precursor in a 50 mm sidearm off from a 50 mni expansion chamber on a single segment collinear electric shock tube. I n a sidearm, arranged perpendicular to the main expansion tube, the luminous plasma in the shock tube can only be seen by double scattering, but a wave was still observed in this sidearm which propagated with the electron acoustical speeds predicted by theory. Mills, Naraghi, and Fowler (51) took up the research where Russell left off. During the course of their investigation, the apparatus, formed around a linear electric shock tube, evolved through several stages until the causes of the various precursor phenomena were finally established. In the

36

RICHARD G. FOWLER 10’

-u W

u)

- o6 \

I t

I

cu

0

-I W

>

t

I

los

I

I

I 1 1 1 1 1

Io6

I

I

I

I

I Ill1

10’

FIG.31. Precursor velocity dependence on E / p for (a) hydrogen and for (b) argon. Experimental data: 11 kV, 0 8 kV, A 6 kV, x Fowler and Hood. From Lubin and Resler (49) with permission of Phys. Fluids.

first stage, the multiple 3egment linear electric shock tube constructed by Hamberger and J o h n s r , ~(52) was used, as in Fig. 34. Failing to observe recognizable common phase points in the signals at two photomultiplier stations, Russell had introduced the sidearm expansion chamber, and in the process of reconstruction had simplified the driver to a single segment enclosed in a grounded metal box intended to reduce stray electrostatic fields which might generate breakdown waves. He observed a well-defined low intensity wave precursor in the sidearm, while the gross early luminosity in the main tube remained largely unchanged. He was able to measure the speed

10’’ 8 :

I

r21:-:

I

I

6-

-

I

-

I

--

200 M TORR

4 -

-

n

-Ia C

100 M TORR

10’6

8 6

-

42 -

I 0‘’

1

I

I

I

I

IIV

Flu. 32. Average electron density determination of (a) hydrogen and (b) argon by nanosecond pulse technique and transverse cavity technique. 0.: j Microwave pulse technique; 0.. microwave cavity technique. From Lubin and Resler ( 4 9 ) with permission of Phys. Fluids.

I

I

Fit,. 33. Experiinental E?iperimenlal precursor precursor front front thickness thickness dependence dependence on on E/p Eip for for hydrogen hydrogen and and Fici. argon. 0 I 1I kV, kV, 0 C 88 kV, kV. .',.66 kV. kV. From From Lubin I.ubin and and Resler Kesler (49) (4Y)with with permission pernlission of ofPhys. Phys. for argon. Flit ds. N i li id$.

38

1IICHAKD C . FOWLER

t

.. 70 ern MOLYBDENUM E L E C T R O D ES ~.

~~~~

CONSTANT FLOW G A S INLET

% 0-20KV de

-

FIG. 34. Multisegmented electric shock tube. From (52) with permission of J . Qirant. Spertrosc. Radiat. Transfer.

of advance of the former at 3 x lo6 m/sec and that of the latter at 3 x lo8 mjsec, confirming the general opinion that the bulk of the early luminosity and ionization associated with the normal configuration of the electric shock tube can arise from energy transferred at light speed away from the driver plasma, yet isolating a wave phenomenon of the type reported by many observers, under circumstances where radiant energy support was clearly lacking. That there was also a wave precursor in the main expansion tube, which could not be perceived because of scattered light, was quickly shown by introducing a second sidearm downstream from the first and determining the time delay between the waves seen in the two sidearms. I t corresponded exactly to flights from a common point. Moreover, using a photostation near the head of a sidearm as a reference point, Liou (53)now found it possible to follow (with some difficulty) the precursor along the main expansion tube even in the presence of the scattered light, which proved to have little or no effect upon the wave. At this point in the research, replacement of the 99.95 % helium employed by Russell with 99.9995% helium resulted in such a great reduction in the scattered luminosity that the wave could be clearly followed even in the main expansion chamber, suggesting impurity as one more of the many causes of


39

discrepancy between various observers. In fact it was observed that the intensity and structure of the wave precursor were so sensitive to impurities that, for reliable results, it was necessary to flush out the apparatus after each discharge to remove the gaseous contaminants formed by wall disintegration in the preceding discharge. It is perhaps noteworthy that Hales and Josephson who first saw the precursor so clearly, had used a flowing deuterium system of gas filling. Russell had looked for any influence of electrical geometry on the wave precursor by introducing various configurations of shields around the sidearm and connecting them in various ways to the active elements of the driver, and had found no effect. Mills, Naraghi, and Fowler carried this idea further, showing that a metal section could be used in place of the Pyrex pipe with the wave reappearing at the far end after a delay corresponding exactly to the transit time through the tunnel. It was also possible to place a metal screen across the throat of the metal tube, with only a modest reduction in the intensity of the reappearing wave, and again, apparent normal transmission. It began to seem that the wave was independent of all support from the electrical circuits. Finally compelled to undertake a complete rebuilding of the apparatus in which the modifications i n Fig. 35 were made, however, Mills et a/. found that the wave was no longer observed at all. It then became clear that the wave is a breakdown wave, although not an electrostatic breakdown wave driven by the potential applied to the capacitor as is commonly the case with breakdown waves. It occurs when maximum rate of rise of current sets in in the driver, which then generates very large potentials across small inductances in the circuit of the driver discharge. Anything other than SHIELDING CHAMBER

/ ALUMINA TUBE

IGNITRON SWITCH

b-H

CAPACITOR

Fiti. 3 5 . Precursor-free electric shock tube arrangement. From (51) wilh permission of

P/I.I.S. Fluids.

40

RICHARD G . FOWLER

the most careful grounding and symmetrizing of return circuits can result in induced voltages of lo4 to lo5 V for about Q cycle of the discharge between some point in the driver and infinity, when currents change at 101’-10’2 A/sec across inductances of 10-7-10-8 H ; during this interval a breakdown wave can move as much as 3 m. Not only self-inductance in the ground circuit but also mutual inductance to it must be avoided. When mutual inductance is involved, the driving voltage can be larger than the capacitor voltage. Whereas Russell had taken adequate precautions against a breakdown wave of electrostatic origin (i.e., proportional to the instantaneous voltage on the capacitor) and against self-inductance, he had not considered the possibility of mutually induced potentials. One striking observation is that if a sufficiently long run is provided the precursor, it comes to a sudden halt as the current in the driver nears a maximum.

SHIELDING HIGH POTENTIAL DRIVING ELECTROD:

CAGE

2,in. I D EXPANSION CHAMBER

IGNITRON SWITCH

1 -

FIG.36. Precursor-producing electric shock tube arrangement. From (51) with permission of Phys. Fluids.

Russell’s actual arrangement is shown in Fig. 36. The inductance labeled L is formed by the very short heavy connection from electrode No. 2 to the capacitor (including any interior wiring of the capacitor). The inductance L , was a heavy strap 8 in. long and 3 in. wide running from the capacitor to the shield can. The mutual inductance between circuit A and circuit B developed the potential difference between the shield can and electrode No. 2 that initiated the precursor. No one can determine from published work alone, without examination of the actual apparatus structures used, whether the necessary emf’s in the ground circuit were present in any given experiment. It seems evident, however, that Hales and Josephson had them, that Fowler and Hood most certainly did, and since it is probably never possible to be free from such a


41

wave in the Kolb T-configuration, it seems reasonable to look for a similar cause in the experiments of Lubin and Resler. It is probable also that the apparatus of Hamberger and Johnson was free from this effect, since they in fact (and Russell, subsequently, in that same apparatus) looked for it and apparently could not find it although one cannot be certain for they did not look at sidearm flow. Finally, the observations reported by Isler and Kerr of a precursor wave under only one discharge polarity may well have been a result of shifting a small amount of inductance to or from the ground circuit while achieving the polarity reversal. It is worthy of remark that the observation of a precursor by Hood and Fowler, but none by Hamberger and Johnson, although superficially in the same style of apparatus (a multisegment electric shock tube) is reasonable because Hamberger and Johnson, in the hope of increasing the efficiency of the shock tube for higher power operation, carefully tailored the return circuit of each segment into a parallel-plate, double-coaxial structure which minimized ground circuit inductances. Mills et al. found, however, that although the connection to an electrical emf is necessary for the existence of this precursor, it is not sufficient to account for all of its peculiarities. They proved that the precursor derives the bulk of its vitality from the adjacent driver plasma by secondary processes and it is this which gives it its intense luminosity, insensitivity to intromittent electrodes, insensitivity to electrostatic grounds, etc. They then designed an apparatus which would produce the precursor intentionally. They used a linear constant bore shock tube with a 2 in. expansion chamber of Pyrex pipe. The driver chamber was made from a special high purity alumina tube. The electrodes were either of platinum or molybdenum with indistinguishable results. They used fast rise photomultipliers (low sensitivity with 1 nsec risetime, high sensitivity with 2.5 nsec) and observed the luminosity associated with the precursor to obtain velocities, temperatures, and electron densities. Each photomultiplier was tested against the inverse square law to set linearity limits on usable signal size. Photomultiplier signals were fed through terminated 50 R cables to an oscilloscope of risetime commensurate with the photomultiplier used. Wave-speed studies of the precursor were made of both proforce and antiforce waves utilizing the same techniques. By applying Lenz' law to the circuit of Fig. 35, it can be seen that if the floating electrode of the driver section is pulsed positively, then the induced emf is such that electrode No. 2. becomes positive with respect to ground, thus generating antiforce waves. When electrode No.1 is pulsed negatively, proforce waves are propagated. The driving voltage on the electrode was measured in relation to the capacitor voltage and found to be 0.80 of the latter. Wave speeds were obtained by measuring the time of flight of the wave for viewing slots 0. I m apart along the discharge tube. The widths and effective

42

RICHARD G. FOWLER

heights of the slots were adjusted to insure signals of near constant amplitude for accurate velocity measurements. The wave-speed data were plotted as a function of distance and the results for waves of both polarities appear in Figs. 37 and 38. The attenuation that is a well-known characteristic of breakdown waves (23,25) is clearly visible. Blais and Fowler had found the attenuation to be generally exponential with a decrement that was both pressure a n d voltage dependent. Mills

0 85 0 77

I

I O ~ L A - L - - .

I L - L _ . POSITION ( m )

FIG.37. Velocity vs. position curve, proforce waves. Numbers on each curve are 17 kV, 0.2 T o r r ; 1 3 16 kV, 0.2 T o r r ; 0 14 kV, 0.2 Torr; attenuation i n n i - ' . 0 I 7 kV, 0.65 Torr; 16 kV, 0.65 Torr; A 16 kV, 1.25 Torr. After Mills, Naraghi a n d Fowler (51) with permission of Phjs. FINids.

et at. found that precursor breakdown is under a n entirely new regime, with the attenuation not only as much as 30 times greater but increasing slightly with applied voltage rather than decreasing as i n the electrostatic apparatus. The increase was not marked over the small range of variation studied and might have been either linear with voltage or merely constant at 0.95 m-' within the experimental error. N o clear distinction was found between proand antiforce precursors in this respect.

43


,"

08

10

I2

14

I6

18

20

22

POSITION ( m )

FIG.38. Velocity vs. position curve, antiforce waves A 17 kV, 0.2 Torr; n 16 kV, 0.2 Torr; V 14 kV, 0.2 Torr; 0 17 kV, 0.65 Torr; 17 kV, 1.2 Torr; A 14 kV, 0.65 Torr. Numbers on each curve are attenuation in m - ' . From Mills er a / . ( 5 l ) with permission o f P h ~ s Flitiris. .

When the technique of Blais and Fowler was used, and thevelocity data were extrapolated back to the electrode, it was found that they then fell somewhere near where corresponding data taken in the electrostatic breakdown apparatus would have fallen. However, their trend more nearly indicated that the velocity has a q 2 p - " 2 dependence than the 'pp-' dependence found in the breakdown wave apparatus and expected by theory. In Fig. 39 they are plotted against this new parameter. Figure 40 shows the measured peak electron temperature in a proforce wave as a function of wave advance. Figure 41 shows the measured electron temperature through the wave. The temperatures were obtained by using the line ratios at the points on the optical profiles corresponding to 10 nsec intervals after the onset of luminosity. Figure 42 shows the measured peak electron temperature of an antiforce wave as a function of gas pressure at a fixed position along the sidearm. When a single spectral line was used and the system calibrated absolutely against a standard lamp, the electron densities in Fig. 43 were obtained.

44

RICHARD G . FOWLER

I

105

5

3

lo3

C2

7

lo4

6‘”(orb units)

FIG.39. Extrapolated initial velocity vs. q*p-’’’, From (51) with permission of Phys. Fluids.

They are quite similar to those reported by Blais and Fowler for breakdown waves. Although the precursor cannot exist without a driving voltage, it is apparent that given that voltage there is another and more important mechanism aiding. Mills et al. had satisfied themselves that this could not be radiation from the driver. Fowler and Hood, believing that there was no field at all present, had postulated that the very hot electron gas existing in the shock tube driver after the initiation of the discharge might provide an energy

0

0

t“ 4

12

14

16

18

20

DISTANCE (rnl

Fro. 40. Peak electron temperatures in an advancing proforce wave at 17 kV and 1.2 Torr. After Mills, Naraghi, and Fowler (51) with permission of Phys. F1uid.r.

45


oLLLu_i 1

0

40

80

I20

-

1

I60

200

TIME (nsecl

FIG.41. Temperature profile in time of a 17 k V proforce wave at 1.5 m from the electrode, 1.2 Torr. After Mills, Naraghi, and Fowler (51) with permission of Phjss. F/uids.

source for precursive effects. Energy could then be transported to the wave front via electron-electron collisions. To test this mechanism, which seemed to be the only remaining one for energy transport to the wave, several experiments were conducted. The first was to examine the breakdown wave which could be produced by the apparatus without plasma contact. A brass plate was pressed tightly into the ring electrode of the driver. Once in place, the driver was completely closed while the discharge circuitry _

_

~

w [

L

-

3

50U

w

Q

0

? I L

+

0

0 50

I 00

I50

PRESSURE (Torr)

FIG.42. Peak temperatures vs. gas pressure for an antiforce wave at 17 kV, 1.5 m from the electrode. After Mills, Naraghi, and Fowler ( 5 / ) with permission of Phj7s. Fluids.

46

RICHARD G. FOWLER

I

I

I

I

I

I

I

I

I

1

I

I

I

I

1

1

TIME (nSECI

FIG.43. Electron density vs. time for a proforce wave. After Mills, Naraghi, and Fowler (51) with permission of Phys. Fluids.

of the shock tube was not affected. In this way none of the hot driver gas could escape into the expansion chamber, but a breakdown wave precursor might still be launched and propagated. All measurements were made in the sidearm. The plugged driver resulted in a decrease in the velocity and a marked decrease in the intensity of the wave, but the wave still existed. N o further tests were made to see if the attenuation and E / p dependences returned to normal. Instead the hypothesis that there might be another major energy transfer mechanism operating in the precursor prompted the initiation of investigations with magnetic fields. It is well known that a transverse magnetic field has the effect of reducing the flow of heat in a plasma, to a first approximation, by a factor (1 + m t e c r 2 ) - * ,where w,, is the electron cyclotron

N O N L I N E A R E L E C T R O N ACOUSTIC' WAVLS, I

47

frequency and T is the electron collision time. To the extent that the precursor relies on transport processes, the establishment of a transverse magnetic field along the shock tube should increase the heat insulation properties of the gas and thus impede the propagation of the precursor. I n the experiments discussed below, both ;I transverse and axial magnetic field were utilized. The latter was invariably found to have no first order effect upon the Now. Magnetic fields of up to 0.27 W/mZ were employed. Figure 44 shows the temperature profile observed for the wave at a point downstream from a transverse magnetic field. The temperature was measured as a function of the axial distance behind the onset of the wave. The reduction in the temperature of the supporting column is striking. -

7--0 ~

. "

1

o l ' L ' . 0

0.2

04 06 DISTANCE (rn)

08

10

FIG.44. Electron temperature along the wave profile at a point downstream from a transverse magnetic field : B 0 G, .B = 800 G B = 1400 G , I ,B =~ 2400 G. After Mills. Naraghi, and Fowler ( 5 1 ) with perinissioii of' Phj..~.Nuids.

Accompanying the reduction in downstream wave temperature is a reduction i n wave velocity. The velocity was measured over a 0.27 m span at a distance of 0.16 m from the magnetic field. Using the Ramsauer value of 5 of 0.95 x sec for 10 eV electrons, the theoretical curve in Fig. 4.5 was plotted. These results certainly indicate an energy transport process, but

48

RICHARD G . FOWLER I .8 x

lo-'

I

I

I

I

I

1

I .6

c

1.4

\

u

W

v)

1.2

-I> I .o

0.8

0.6 0

1

I

1

I

I

I

2

3

4

5

0'

I

6I

(w'/ M 4 )

FIG.45. Wave velocity after passage through a transverse magnetic field. After Mills, Naraghi, and Fowler (51) with permission of Phys. Fluids.

0

I

2

3

4

5

6

7

8x162

B2h2/m4)

FIG.46. Wave velocity during transit of a transverse magnetic field. After Mills, Naraghi, and Fowler (51) with permission of Phys. Fluids.


49

whether it is conventional heat transport as envisioned by Hood and Fowler or some sort of Thomson effect has not been established. Although the wave speed downstream is slowed by a magnetic field, the wave speed in the field may have been enhanced (Fig. 46). This result is not unreasonable because the field can produce a rise in the local electron pressure, both via T, and n,. Using the two probes opposite each other and passing through the walls of the confining tube, Mills et al. determined the emf set up by the electron flow in the magnetic field. The region of electron motion in the ionizing wave was found to be about 0.154.3 m long and of fairly constant speed. The electron speed calculated from this experiment was found to be less than the value found by previous methods, indicating that it is smaller than the velocity of advance of the luminous wave front, as it should be. By introducing an electric field probe into the flow, Mills et al. were able to determine the critical value of the B-field at which the electric force on the electrons becomes equal to the magnetic force to be about 0.16 W/m2, with u = 8 x 10' m/sec, giving an EZ in the wave front of 1.28 x lo5 V/m. Using an antenna probe calibrated at 1.5 M H , they searched for rf fields around the apparatus. At a point 0.3 m down the sidearm, signals for E, and EB were detected as having approximately one fourth the magnitude of the signals for EZ. The approach of the electric field E , was sensed some 100 nsec before the arrival of the luminosity of the front, and Er underwent a sharp lowering of rate of increase at the onset of luminosity. The frequency spectrum of Ez contained at least three components: the base frequency of the capacitor discharge 3 x 10' H, a second frequency of 2.5 x 10" H, and a third of 2.5 x lo7 H. Applying the probe calibration they estimated the amplitudes of these fields as 8 x lo4 V/m, lo3 Vim and 10' V/m. The probe was probably insensitive above lo8 H. In an earlier version of this apparatus, Latimer et a/. reported finding two 6 x IO5"K peak excursions of temperatures at 30 and 55 cm from the driver electrode which may have indicated standing waves of 5 x lo8 H, whose amplitude would then have been 2 x lo4 Vjm. These peaks were found to build up late in the history of the flow (10 psec) and no peaks were found further down the tube than 30 crn nor were they observed subsequently in the Mills et a/. apparatus. A search for microwaves in the latter apparatus was made without success. Mills et a/. therefore concluded that the delivery of energy to the precursor primarily related to the base (quasi-dc) frequency of the capacitor discharge. The work reported by Latimer et a/. is of additional interest because it bears on conditions in the photopreionized gas in the main expansion chamber, which is seen to range in temperature from a minimum of 20 eV to a maximum of 70 eV as shown in Fig. 47.

50

RICHARD G . FOWLER

90

I

I

I

I

I

1

I

I

I

80

-> 70 u

W

5

60

l-

a

50

4

40

z

0 [L

I0 W

30 20 10

0 DISTANCE FROM DRIVER (M)

Fro. 47. Measurements using three ratios, of the electron temperature in the precursor as a function of distance from the driver at a time 10 psec after the driver is triggered. The driver voltage was I2 k V and the helium pressure was 0.65 Torr. After L a t h e r , Mills, and Day ( 3 2 ) with permission of J. Qunnr. Spec/rosc.Rarlint. Tramfir.

D. Laser Precursors At the outset of the research of Mills, Naraghi, and Fowler it was believed that a component of the electric shock tube precursor would be found, caused purely by energy transfer processes from the extremely hot driver plasma, sans electric field support. This proved to be an illusory belief. There remained the untested possibility that the driver plasma was not hot enough, and that something in the thermonuclear range would still display an energy transfer supported precursor. Koopman (21) has now demonstrated that an electron precursor does accompany the generation of a focused laser plasma. He observed a spherical electron flow at distances up to 0.3 m from a carbon target on which a 6 J , 30 nsec laser pulse at 6943 A was focused by a 0.1 m lens. He observed the plasma with Langmuir probes and X-band microwave interferometry. The probes indicated the near instantaneous arrival of a small negative charge excess, followed by a fairly thin strong double layer, first negative then positive, followed by a relatively long zone


WAVES,

51

I

of negative charge excess, and finally positively charged plasma-acoustic flow of the laser plasma itself. The microwave probes indicated that the electron concentration itself increased abruptly near time zero and inverse square law tests proved this to be ultraviolet photopreionization. The concentration then underwent a sudden step-up as the double layer passed, followed by a plateau during the passing of the long zone of negative charge, and an enormous increase when the plasma-acoustic wave arrived. These results are summarized in Figs. 48 and 49. Observations at larger distances resulted only 0.50

I

1

I

I

1

I

I

TIME ( p S E C )

FIG.48. Position vs. time graph of features observed on probe and microwave diagnostic devices. 0 Front, x plateau, 0 laser plasma. From Koopnian (21) with permission of Phys. Fluids.

in a dispersion of the features above. In Fig. 50 the effect of gas pressure was investigated, and the results fitted to a theory that the momentum loss rate of the electrons is dominated by ionization. This yields the correct density dependence of P ' ' ~ for the empirical constant CI describing an exponential growth of the velocity of the wave front. Koopman concluded that he indeed had an electron ionization wave for the propagation of which no high voltage or electric current is required. He felt it could be described as a self-consistent balance of electron diffusion and space charge coupled to collisional ionization processes. This raises once again the question of whether the ordinary shock tube diffusion precursor observed by Weyrnann and analyzed by Pipkin (54) is capable of becoming a shock-fronted electron ionization wave at extreme energies.

52

RICHARD G . FOWLER

"""'"

+ 60

- 3

?

5

LD

-0 2

+ 40

u

c

I

+20:

0

O

-> A

?z F

0

n

- 20 LASER PLASMA I

0

I

I

I

2

3

I

4

1

5

I

6

- 40 7

- 6_ 0 _

TIME ( p S E C )

FIG.49. Electron density n, (A), plasma potential V , ( O ) ,and floating potential Vf (0) as functions of time at a location 14.9 cm from the plasma origin, as measured by a cylindrical Langmuir probe. After Koopman (21) with permission of Phys. Fluids. 2.5

2.0

-

1.5 u 1

w

cn

r-

E

1.0

a 0.5 0

0

I 2

3

4

5

6 7 8 9 1011 1 2 1 3 1 4 (MTORR)"~

FIG.50. Plot of velocity proportionality constant A vs. square root of gas pressure, using data on average velocity of ionizing fronts obtained from microwave apparatus. After Koopman (21) with permission of Phys. Fluids.


53

E. Slow Proforce Waves Although the broad assumption is made that primary breakdown waves are always fast waves and secondary waves are even faster, some evidence has always existed dating even from Mitchell and Snoddy (1947) that supposedly primary waves could travel at speeds below the ionization minimum (2eq1,/m)”~. Scott (55) has investigated this matter and found that inherent in it lies the possibility of further understanding of the entire phenomenon. Antiforce waves, he finds, are unique in structure for all pressures, gases, and voltages and exist without any apparent lower bound of velocity at ( 2 e q 1 J m ) ~ / ~ . Proforce waves, on the other hand, are found to exist in two styles, not one, as supposed. One style shows velocities below the ionization velocity minimum and has a slowly rising intensity at its front. The other does not exist below the velocity minimum and shows a discontinuity in structure at its front. Since, as Shelton showed, the velocity minimum arises from the shock conditions at the breakdown front, it is apparent that the slow proforce wave need not meet this shock condition and that the theory must be reexamined in search of other initial conditions. F. Tertiary Breakdowti Waves

Barach and Sivinski (56), working with a collinear electric shock tube with the rear driver electrode grounded and spaced a few centimeters from the ring electrode, introduced a second grounded electrode downstream in the expansion chamber at a distance of 14 to 30 cm. They worked in argon and observed the existence of a primary breakdown wave with speeds greater than lo6 m/sec moving away from the ring electrode, which was followed (probably after an unobserved secondary return wave) by a slow-moving wave having a large current (Fig. 51) at its front. They called the latter a precursor arc and observed that it was present only in the proforce mode (i.e., when the ring electrode was negative). They found that it produced substantial preheating of the expansion chamber gas so that the speed of the plasma-acoustic shock wave was strikingly enhanced. Figure 52 gives this increase as a function of initial pressure; Fig. 53 gives it as a function of capacitor voltage. The passage of the waves was detected on Langmuir double probes flush with the wall in small side tube recesses and with a photomultiplier. Barach and Sivinski determined that the velocity of the front fitted well with the equation V = E/pne or, in other words, was primarily governed by electron drift. This is illustrated by Fig. 54 where they plotted V VS. conductivity ( I / p ) at constant E. The electron concentration 11, they found to be nearly constant at 1.75 x l O I 9 m-j. It seems certain that we have here the first clear-cut information on tertiary breakdown waves.

FIG.51. Precursor current vs. capacitor voltage. Initial pressure 0.55 Torr, 0 magnetic probe, 0 single probe. After Barach and Sivinski ( 5 6 ) with permission of P ~ J ' sFluids. . I

0.018

50

0.016 0.014

0

40

0.012

W

P

ln

W

a.

m

' zi 0.010

-

30

P

;0.000

52

I

V

a

a

z

v)

20

0.006

0.004 10

0.002 I

I

0 0

500

1000 BANK VOLTAGE

I

1500 (V)

0 2000

FIG.52. Shock wave speed vs. capacitor voltage for an initial gas pressure of 0.55 Torr,

0 with arc, 0 without arc. After Barach and Sivinski (56)with permission of PIiys. Fluids 54

I

0 014

-

0 012

-

0002

-

I

I

I

50

I

I

-

40

- 10 1

I

I

I

I

FIG.53. Shock velocity vs. initial pressure. Capacitor voltage 1000 V, 0 with arc, 0 without arc. After Barach and Sivinski (56) with permission of Phys. Fluids.

VELOCITY

(M/SEC)

FIG.54. Electron front velocity vs. gas conductivity for constant voltage gradient 0 0.345 V/m. After Barach and Sivinski (56) with permission of

0 0.12 Vim, A 0.16 Vim, Phys. Fluids.

55

56

RICHARD G . FOWLER

111. THEORIES A . Early Approaches The breakdown of gases between closely spaced plane parallel electrodes led in 1889 (57) to Paschen’s law that for a given gas and electrode material, the breakdown potential is a simple concave-upwards function of pd. Thereafter it is a strong function of the nature of the gas and a weaker function of the electrode material. Townsend (58) undertook to explain this by the concept of an electron avalanche in which electrons with energies acquired in random flights in the electric field produced ionization ( a processes). He envisioned a single electron as the initiator of each avalanche and the avalanche as connecting the electrodes in establishing conduction. Since a single avalanche might initiate a discharge but could not sustain one because the electrons in it, however multiplied, would eventually all be swept to the anode, he supplemented the a process with an in-gas process in which the positive ions produced by the electrons replaced the initial electron by their collisions with the neutral gas (p processes). Subsequently this process was shown to be quite improbable and Townsend advanced an electrode process in which the positive ions or excited atoms released new electrons from the cathode (y processes). With the discovery of the photoelectric effect, the promptness of the y processes could be better understood, and new life was given to the p processes, although they remained less probable sources of electrons than they processes, Much investigation of the Townsend hypothesis has been made. Paschen curves taken under these conditions can certainly be explained by these processes, of which the first and third are preponderant with closely spaced electrodes (59). The beauty of the concept of the Townsend avalanche dominated efforts to explain spark discharges in all their configurations for a half century. The overly brief transit and current growth times observed by Rogowski (60) were explained with superficial adequacy by von Hippel and Franck (61). The existence of long sparks with both pro- and antiforce directions of advance was regarded by Loeb and Meek (62) as rationalizable by a concatenation of Townsend avalanches aided by photoelectric fi processes. Even Mitchell and Snoddy, at the culmination of the research begun by Beams on low pressure breakdown in tubes, invoked the avalanche as a fundamental building unit in the wave advance although it led to a velocity dependence on field strength of El’’ which was not the dependence found by them or by any observer since. As time passed it became evident that although the Townsend avalanche


57

theory does indeed describe the growth of one single electron's ionization swarm until the Debye length in the swarm becomes less than the dimensions of the swarm, thereafter a general fluid response of the system must be considered. Raether's cloud chamber studies of the avalanche revealed this dramatically (63). He found departures from avalanche behavior at electron densities of I O l 5 m-3 with electron temperatures of -1O'"K and swarm dimensions of 1 mm. Penning (64) made the strong case that space charge and multiple processes must be considered before a solution of the long spark problem could be expected. Paxton and Fowler (22) advanced the hypothesis that when the ionization has transcended the swarm theory limits, the electron gas can be described by fluid dynamical equations. They assumed that the leading edge of the ionization wave was amenable to treatment as a shock front. In their view, the principal drive force for the wave came from the electron pressure generated by the high temperatures of the electrons in the electric field. Thus no great distinction was to be expected between proforce and antiforce waves. They called attention to the importance of the zero current condition at the leading edge of primary waves, but neglected to include ionization energy losses in their equations (which will subsequently be seen to make their results apply to secondary or tertiary waves rather than primary waves). Their model was that of an infinite plane wave, while the experimental situation is always strongly three-dimensional, and they had very scanty data with which to make comparison ; nonetheless, the results were encouraging. The chief advantage of the photoionization-avalanche (streamer) theory had been its ability to permit the existence of antiforce as well as proforce waves. The fluid theory could also do this. The chief disadvantage of the streamer theory was that it used a spherically symmetrical energy transfer mechanism to transport ionization forward to new sites while the streamer is in fact strongly filamentary and grows always at its end, in a direction roughly parallel to the cylindrical sides of the filament. The fluid theory expects growth at this tip because the electric field will be strongest there. It is probable that the budding" of branches onto a spark streamer is caused by and therefore is a measure of the frequency and importance of photoionizing processes as in lightning, or in the Lichtenberg branching studied by Nasser and Loeb (6.5). Burgers (26) attacked the problem of the structure of a one-dimensional electron wave by formulating the collision operators which Paxton and Fowler had left undefined and attempting an overall solution of the equations by integrating them through the wave from -co to +a.He found that the velocity of the wave must be of the order of electron sound speed (kT,/rn)1'2, but his attempts to relate the velocity to the impressed electric field did not

-

"

58

KICHARD G. FOWLER

agree with the experimental results of Haberstich. He found V K E"'. The difficulty may have lain in the form he chose for the electron ionization coefficient, postulated as

dnldt = aiNn(v - V ) . He chose this form because it made the integration simple, but there is no reason to expect that ionization will cease when the electrons are at rest in the frame of the heavy particles, i.e., when u = V. Thermal ionization may continue for some time afterward if T, is large. The formulation of the zeroorder approximation should have been

Lubin (66) approached the problem of the electric shock tube precursor on the assumption that it was electromagnetically coupled to a transmission line formed by the plasma-filled tube and moved at the group velocity for that line. The idea was an appealing one, since experimenters on all types of these electron waves have expressed the feeling that there is a resemblance between the wave's behavior and that of a transmission line. The analysis provided by Lubin begs the question on two essential points, however. ( 1 ) He chose an ad hoc equation for electron production which has no theoretical basis and was justified only in that it produced velocity dependence agreement with the observations

and ( 2 ) he selected the velocity of his unloaded line as that value which gave scale agreement with the observations despite the fact that the magnetic coupling is less than that of the electric coupling. The agreement can thus only be regarded as contrived. B. Rinu'anienial Equatioris it1 One Diiiietuion The fundamental equations are those of a three-component fluid (I). It is in this respect that the formulation differs from the problem so commonly treated in plasma physics, the fully ionized two-component case. Only small differences exist between the individual equations in the two cases, but they are crucial. The principal one is that the charged particles interact with each other only by way of the electric field, but both species interact with the

59


preponderating neutral gas viscously. The interaction of the positive ions with the neutral molecules is so great that it has been found necessary to separate the equations of momentum and energy for heavy particles. In one dimension, the system of equations descriptive of the above model is

etrE -

1

W)V = eN, VE

+ A,

(i 1 -it7iu2

-

(: 1

Ai -niv2

.

(21)

In the above equations, the ion iind atom velocities and temperatures are set equal because of the strong collisional interaction between the two species. The symbols t 7 , z i , p and MIdenote electron density, velocity, pressure and internal energy, respectively; capital letters denote corresponding quantities for heavy particles, with a subscript i if special reference to ions is needed. E is the electric field (applied field plus space charge field) and q is the heat conduction vector. The ionization frequency is denoted by /I while A, denotes an elastic transfer operator for the indicated quantity and A i is a similar inelastic transfer operator. These will receive detailed discussion later.

60

RICHARD G . FOWLER

That the basic equations already imply Kirchhoff’s fundamental statement about the electric current can be shown as follows. Subtracting Eq. (15) from (16) and multiplying by the electron charge, one has

(ajar) [e(N, - n)] + (a/dz) [e(Ni V - nu)] = 0.

(22)

Employing Poisson’s equation, this becomes

(a/&)

+

[EO(dE/dt) e(Ni V - nu)] = 0,

(23)

or E,

(aE/at)+ e ( N , V - nu)

=

i, ( t ) .

This is Kirchhoff’s law and says that in one dimension the total current, convection plus displacement, is independent of position. The application of this result will vary from one set of conditions to another, but in the important case of a wave moving into a neutral gas, one can generally evaluate io( f ) as zero on the argument that N and n are zero ahead of the wave, while E must be constant somewhere sufficiently in advance of the wave. This result is known as the zero current condition. Its corollary is that if one places himself in the wave frame of a steady profile wave, he observes that N i V = nu.

(25)

By summing the system of individual species equations, the ordinary global equations of fluid dynamics can be obtained (68). It was first noted by Paxton and Fowler (22) that these equations lead to the description of an electron fluid wave if and only if one is meticulously careful not to ignore the small difference between ion mass and neutral mass. Adding Eqs. (16) and (17), one obtains a second theorem

mi+N)+ -(Ni a + N ) V = 0, at aZ

(26)

which can be fittingly termed, in nuclear jargon, the continuity of baryons. In the hypothetical steady profile rest frame, one can integrate across the wave to obtain (Ni

+ N)V = N o Vo ,

(27)

where N = N o , N i = 0, and V = V, in the neutral gas ahead of the wave, Vo being the frame velocity. One can express this result in the words “ baryon flux is conserved in a steady profile wave.”

61

NONIJNEAR ELECTRON ACOUSTIC WAVES, I

1. The Collision Operators and the Electron Equations

Before one can proceed to investigate the detailed structure of electronacoustic waves it is necessary to ascertain as Burgers did the forms of the collision operators. The elastic collision operators are well known. The momentum operator for m e M is

Ae(mu) = K , n ~ ( t 7 V).

(28)

In a n approximation which has a maximum inaccuracy of about 40//,, the coefficient K , takes the form (with Maxwell-Boltzmann statistics)

where n is the experimentally determined total elastic collision cross section for momentum transfer. The elastic energy operator, also for m < A4 is

Ae (+mu2)= (2m/M) nK, [$kT,

+ (m/2)(c

-

V j 2 ]-tK,mn(z’- V )V . (30)

At high temperatures in helium ( >5 x 1 0 ° K ) . K , is temperature independent and K , i p = 2.41 x lO’/sec-Torr. The essential feature of this operator is that, n o matter what the value of n , the well-known factor 2 m / M is present in two of the three terms. Consequently they may be neglected when V. The average K , is one of a generally useful family of averages over distribution functions which occur in these problems. In the serious studies of swarms made in 1930-1950 it was frequently noted that the distribution function could be non-Maxwellian. A complete theory of such distributions was devised by the efforts of many workers [Morse et a(. (68), Smit (69), Druyvestyn (70)l. The non-Maxwellian character usually took the form of a n enhancement or depletion of the number of fast electrons relative to the mean velocity and therefore would have more effect on the ionization rates than on mechanical constants such as K , . Accordingly, as a first approximation it is still useful to have Maxwell-Boltzmann averages for this and similar quantities. These were given in a previous article in this series but have been revised for the new data of Golden and Bandel ( 7 / ) and recomputed on the assumption that all cross sections decrease reciprocally with velocity (Born approximation) at large velocities. The new results are given in tables in the next section of this article It is difficult to impossible to approach the inelastic collision operators from first principles because the more interesting ones involve three-body collisions. Shelton has shown how the vector terms which are involved can be rl#

62

RICHARD G . FOWLER

identified by requiring that the basic equations be invariant under a Galilean transformation. Then the essential new terms are

Ai (mu) = pnin V

(31)

and

Ai(fmu2) = +pmnV2 - pnecp,, where we must add the term -jnecpi ad hoc, to recognize a portion of the inelastic energy loss which eludes the transformation test because it is a scalar. Physically speaking, the inelastic terms state that the nascent electrons bring to the electron system only the momentum and energy they possessed when they were attached to the heavy particle system. The transformation technique presents additional terms of the form K ( P- V ) in the momentum operator and K(n - V ) V in the energy operator which can be recognized as the exchange to be expected even if the collision were elastic and which can be regarded as included already in the elastic coefficient K , by choosing the total cross section for the cross section 0 . There is likewise a term K ( v - V)' presented in the energy operator that must be of the same character as the similar term occurring in A e ( ~ m t l z )and hence must bear a factor of order 2m/M making it negligible. Including these terms, the steady profile equations for the electron component of the fluid can now be written

dni)/dz= /In,

(33)

+ nkTJ = -enE - K,mn(o - V ) , ( 34) (d/dz)[rnn(u2 - V2)u+ nc(SkT, + 2e(pi)+ q] = -2envE - 2K,mn(u - V ) V . b

(d/dz)[mn(u- V ) v

(35) In reaching this result, the new inelastic terms have been transferred into the divergence term by using the first equation to eliminate p.

2 . Collision Probabilify Averages The averaged collision probability (P:.") (see Tables IV and V) is defined as

and is expressed in collisions per meter per torr. The abscissas are given in square root of electron volts, with one electron volt being equal to 7737°K.


63

If one wishes t o use these averages to compute the collision rate per unit volume of B quantity A which is a power function of such as 11,

then

Averages suitable for calculation of the transport coefficients have also been computed. They (see Tables VI-IX) are defined as

((k,"") ~ J p , o ' 1

Pn

df

=

(39)

For (P,"') and (P,'"). which are rarely needed, the values in Volume 20 of Adiwnces in Electronics arid Electron Plijisics may be consulted. Averages for cesium and methane are also given there. 3. ltiitiul Conditions .for Steady Profile Wares

The only complete solutions of the equations which have been obtained so far have been developed on the assumption that a wave frame exists and that viewed from this frame the dependent variables change with position only. Then in one dimension the global differential equations can be integrated (67) to yield t1P = N i v, (40) (Ni t ~ n / tt' (

mnr(

t j 2

+ N ) V = No vo,

(41)

- V ) + M N , Vo ( V - V,) + N o k(T - 7'0) - V2)

+ MN,

+ nkT, + ( ~ , 1 2 ) ( E , -~ E 2 ) = 0 V , ( V 2 - V o z )+ 5 N , Vo k(T - To) + 5kT, + (2eyi)nr+q + iy = 0.

(42) (43)

Equations (42) and (43) have been simplified by the use of Eqs. (40) and (41). We can use these equations to determine the leading edge condition on the wave. The arrival of the wave is signifed by the existence of electrons with some velocity r1 and some temperature ( T e ) l while , El = E, since there can be no surface charge singularity on the interface; V , = V0 since there is n o time to accelerate the ions across the interface: and (Ti), = To. Moreover i and q must be zero at the front. Hence, n,[z1,(v, ),'b

and

+ k(Te),/n7]= 0,

(44)

+

(45)

n1z1,[z112- Vo2i- (5k(Te),,h7i) ( 2 e y i / m ) ] = 0.

TABLE IV

T"

Argon

co

Helium

Hydrogen

Mercury

Neon

Nitrogen

Oxygen

Thallium

Xenon

7.7 x lo3 1.3 x lo4 1.7 2.2 3.1 4. I 4.8 5.8 7.0 9.5 1.2 x 10'

0.226 0.113 0.0817 0.0604 0.0417 0.0327 0.0298 0.0276 0.0271 0.0286 0.0308 0.0358 0.0382 0.0462 0.0532 0.0616 0.0753

0.0195 0.0193 0.0215 0.0239 0.0267 0.0281 0.0288 0.029 0.0295 0.0306 0.0317 0.0346 0.03585 0.0413 0.0463 0.053 0.0643

0.0634 0.0663 0.0697 0.074 0.0825 0.0922 0.0998 0.1093 0.121 0.143 0.1605 0.190 0.2045 0.248 0.286 0.331 0.407

0.02485 0.0245 0.0258 0.0280 0.0327 0.0378

0.0290 0.01255 0.01 11 0.01163 0.01 39 0.01605 0.0172 0.0183 0.0193 0.02035 0.0207 0.0218 0.02205 0.0241 0.0264 0.0300 0.0360

0.190 0.158 0.1445 0.133 0.119 0.1 125 0.109 0.1045 0.1027 0.101 0.1005 0.1052 0.106 0.1176 0.129 0.1495 0.1735

0.2555 0.247 0.2635 0.282 0.301 0.3085 0.3125 0.312 0.315 0.3265 0.336 0.37 0.3835 0.445 0.504 0.578 0.705

0.0598 0.0544 0.0515 0.04825 0.0438

0.0505 0.0390 0.0345 0.0320 0.0309 0.03145 0.0325 0.0334 0.0349 0.0375 0.0395 0.0437 0.0454 0.0528 0.0595 0.0682 0.0830

0.0652 0.0336 0.0241 0.0180 0.01377 0.0217 0.0218 0.01335 0.01476 0.01795 0.0213 0.0269 0.0300 0.0389 0.0460 0.0543 0.0670

1.6 1.9 2.8 3.8 5.0 7.7

0.0415

0.0457 0.05099 0.0600 0.0670 0.0793 0.0852 0.1035 0.120 0.1 395 0.171

Multiply tabular values by 10' to obtain collisions per meter at 1 Torr.

0.0405

0.0393 0.0376 0.0369 0.0367 0.0368 0.0392 0.04025 0.0456 0.051 0.05825 0.0708

9

3 G 73

TABLE IX

< 1IP:

T"

Argon

co

Helium

7.7 x lo3 1.3 x lo4 1.7 2.2 3.1 4.1 4.8 5.8 7.0 9.5 1.2 x lo5 I .6 1.9 2.8 3.8 5.0 7.7

0.373 0.198 0.1415 0.1403 0.0840 0.0746 0.0745 0.0763 0.081 6 0.0940 0.105 0.1245 0.133 0.1615 0.186 0.220 0.258

0.0525 0.06375 0.0737 0.145 0.08675 0.0880 0.0887 0.0889 0.09075 0.0961 0.1015 0.1137 0.1195 0.1405 0.1595 0.184 0.22

0.194 0.208 0.223 0.242 0.278 0.319 0.348 0.384 0.426 0.503 0.565 0.669 0.716 0.872 1.004 1.16 1.40

Hydrogen 0.0716 0.0755 0.0837 0.1915 0.1 I45 0.134 0.147 0.162 0.1795 0.211 0.2335 0.278 0.2985 0.365 0.423 0.731 0.588

5'>

Mercury 0.0265 0.0265 0.0324 0.0395 0.0493 0.0557 0.0586 0.0605 0.0622 0.0634 0.0642 0.0683 0.06975 0.0796 0.0893 0.1027 0.1115

Neon 0.503 0.418 0.385 0.359 0.328 0.31 1 0.306 0.298 0.2965 0.301 0.306 0.33 0.339 0.386 0.4325 0.740 0.592

Nitrogen

Oxygen

Thallium

Xenon

0.692 0.781 0.860 1.58 0.945 0.94 0.95 0.947 0.964 1.02 1.08 1.22 1.284 1.525 1.74 2.01 2.30

0.1 70 0.1525 0. I43 0.1985 0.1187 0.1 117 0.109 0.1067 0.107 0.1 103 0.1 142 0.1255 0.131 0. I54 0.175 0.2025 0.242

0.133 0.0968 0.0900 0.1555 0.0929 0.0985 0.104 0.1073 0.1 123 0.1213 0.1285 0.1443 0.1515 0.1 80 0.205 0.354 0.284

0.121 0.0574 0.0428 0.0359 0.0340 0.0370 0.0403 0.04525 0.0522 0.06675 0.0798 0.1007 0.1115 0.141 0.165 0.195 0.231

z 0 z

c

3> 7J

m el 7J 0

8e vl

=!

0

5 5

M

H

Multiply tabular values by lo2 to obtain collisions per meter at 1 Torr.

QI

W

70

RICHARD G. FOWLER

This condition can be satisfied in three ways. The first is n, = 0 with u, and ( T J , undetermined. The second is u1 = 0, T, = 0 with n , undetermined. The third case is n , # 0. It results in true shock solutions, although the shock is recognizable only in the electron gas. Solving for v l and (Te)lgives

5V0 [9Vo2+ 16(2ecpi/m)]”2

u,=-+

8

8

(46)

Since ( T J , > 0 and since the zero-current condition requires Vo and u to be of the same sign, V, < u1 5 0 . It then follows that dE/dx must be negative at the front, so E always increases as one passes from the undisturbed region in front of the wave toward - 03. Thus there is always a negative charge at the front, regardless of the polarity of the potential driving the wave. The actual lower limit on til is, however, considerably higher than V , . As Vo goes to infinity, 2ecpi/m becomes negligible and u, approaches a limit of V0/4,the usual strong shock result. Thus in general,

Vo/45 01

0. (48) It is perhaps easier to understand this condition when written in absolute values (49) 0 < IU, I < I v0/41. From the upper limit, v1 5 0, one concludes by substitution in Eq. (46) that + m v O 2>ecp, (50) and that there is a lower limit on wave speed for the shock fronted wave. The wave must also be bounded on its backside with certain conditions. Since there can be no current in this one-dimensional case, while there is a conducting plasma present, the electric field must approach zero. Nor can there be any relative motion of the charges, so u must approach V . The wave thus replaces a neutral gas with a partially ionized quiescent plasma and is basically analogous to the N wave in shock theory except that the discontinuity on the leading edge where the flow abuts on neutral gas is a strong discontinuity, while that on the backside may be and usually is a weak discontinuity. 4. The Heavy Particle Equations, a Priori Approximations

The basic approximation under which a solution of the problem is possible was actually first suggested by Thomson and Thomson (72). It is that the heavy particles are mechanically undisturbed by the wave passage. One can


71

verify this assumption empirically before using it to solve structural problems, and afterwards can check the fact that a given solution continues to fulfill the assumption. We write the heavy particle equations for a steady profile wave as follows

( d / d z ) [ M N V 2 + Mi N i V 2

dN V / d z = pn,

(51)

dN V / ~=Z -/It?,

(52)

+ (Ni + N)kT]

+ K,inrz(v - V ) - PmnV,

(53)

(didz)[MNV3 MiN, V 3 + 5(Ni + N ) V k T ] = 2eNi V E + 2VK,mn(v - V ) - flmriV2.

(54)

= eN,E

+

By carrying out the indicated differentiation of these equations and eliminating dT/dz, one can obtain, by use of baryon conservation

[ M N o Vo

- ntNi V - 3 M N o Vo ( k T i M V ' ) l ( d V , ' d ~ ) = eNi E

+ K , m n ( ~- V ) .

(55)

Now on the left side, n7Ni is certainly less than M N , and k T / M V 2 is much less than unity, so only M N o Vo remains. Of the two terms on the right-hand side of the equation the first is the electric force and the second is the viscous damping, which must always be the smaller of the two, so we retain only the first, convert the equation to an inequality, and set E = -dcp/Jz. Integrating through the wave

AViV I (cci/MVo')Acp.

(56)

Empirically, at 40 kV the wave velocity is 2 x 10" cmjsec and so A V / V I a i , ai being the fractional ionization. In practice cci < as measured with microwaves by Haberstich and optically by Mills. Thus A V / V - l o - * and the change in velocity of the heavy particles seems superficially to be so small as to be completely negligible. Shelton (73) has examined the consequences of a rigid application of the assumption that any changes in velocity of the heavy particlescan be neglected. He found that the structure of the wave cannot be consistently developed under this assumption. The relative velocity of the electrons and heavy particles cannot be brought to zero behind the wave and dE/dz therefore remains nonzero so that E becomes singular eventually, a result which is physically unacceptable. Further examination of the basic equations shows that constant V is not really a good approximation for universal application. The forces acting on one fluid are essentially the same as those acting on the other, so that the total changes of momentum and energy of the two fluids are similar in magnitude. Thus even though the velocity change of the heavy particles is small,

72

RICHARD G. FOWLER

the vastly greater density of the heavy particle fluid gives it comparable changes in total fluid quantities. This does not mean, however, that the nearly constant value of V is a useless fact. If one returns to the electron fluid equations, he notes that nowhere in them is the velocity V multiplied by the heavy particle density so that it may be treated as constant there. This decouples the equations and makes a solution possible. C . Solution of the Electron Equations f o r Proforce Wazies

Since Vis only slightly varying with respect to u, Shelton and Fowler used this quantity to form dimensionless variables in which to express the electron equations. Let these variables be $

v = (2etpi/e, Eo2)n, ’I = EIEo

0 = kTJm V 2 ,

= u/V,

< = (eE,/mV)z

9

and let a set of dimensionless parameters also be introduced, p

= (mV/eE,)P,

CL

= 2eqi/inVZ,

and

K = (mV/eE,)K.

(57)

The electron equations (including Poisson’s equation) then become

(4&)(v$) (d/ds)[v$($- 1)

+Vo]

(58)

= pv9 = -Vq

(d/dq relations and the results differ only slightly. as can be seen in Figs. 58 and 59 in which they have been compared for four initial fields. Attention i s called to the extremely long tail on the 0, v curves found in the quasineutral region (Figs. 60-63). It is evident that under most experimental situations this i s all that the time resolution available permits one to observe. Referring to Fig. 16 in the section on experiment, the theoretical curves given by models I, 11, and Ill have been plotted against the data of Blais and Haberstich. The actual placement of the theoretical curves with respect to the data involves many complicated unsolved questions of factors of order unity that must be considered in a true calculation from first principles. These relate to the electrostatic geometry of the apparatus plus wave which fully described a t any instant i s that of a charged partially conducting rod with a cloud of charge of arbitrary shape at the end inserted into a glass sleeve and surrounded by a larger conducting cylinder. Some discussion of this will be given in Section 1V. The relation between the central field and potential at the

80

RICHARD G . FOWLER

c FIG.58. Sheath profiles for

4 and 17 vs. (, 4, = 0.01.

end of a fully conducting plane-ended rod is E = 0.502 $/a, but the geometrical constant is increased by the presence of a glass tube. If the conductor is a poor one with a somewhat extended volume of charge at its tip, the constant is also increased. There is added uncertainty as to a possible factor that comparison of the one-dimensional fluid theory to three-dimensional experiments may introduce. Therefore, in plotting the theoretical curve, these geometrical factors have been arbitrarily set at unity. The agreement then shown between

10

08

06

04

02

'0

01

02

03

04

05

06

07

08

E

FIG.59. Sheath profiles for (CI and 71 vs. 6,4%= 0.238.

09

07

06

05

04 0. I

03

02

01

'0

02

04

06

08

I0

12

14

16

I

18

E

FIG.60. Sheath profiles for electron temperature 0 and concentration v as function of position 5, Initial velocity I,!J, = 0.01. (Multiply ordinate scale by 80 to obtain v.)

20

I

\

\

\

04L2-L2 '0

01

02

03

04

05

0'6

0;

08

09

0

E

FIG.61. Sheath profiles for electron temperature 0 and concentration v as function or position 5. Initial velocity 4, = 0.238.

82

RICHARD G . FOWLER

.20

9

10

0 lo-'

Io3

lo'

I00

lo4

E

FIG.62. Quasi-neutral (thermal) region profiles for 8 with

'

4, = 0.01 and 0.238.

'I

0'

,

I

1

U

L

1

1

-

1

_

l

i

L

E

Fic. 63. Quasi-neutral (thermal) region profiles for v with

I/,= 0.01 and 0.238.

83


theory and experiment seems adequate in the present state of both theory and experiment. Scale factors for the conversion of 0, v, and ( to physical variables T,, n, and 2 are given in Fig. 64 for theory 111. '

0

I

6

3

7

5 7 1

-~~ ~~~~

3 5 7

I

ABSCISSAS

3 AS

5 7 1

3

5 7 1

3

5 7 1

LABELLED

FIG.64. Scale factors for conversion of 6, v, and 6 to T, ,n,and z for the third (elliptical relation) theory.

IV. CONCLUSION TO PARTI It seems apparent that a theoretical resolution of the various aspects of the breakdown wave is now at hand. Following the direction of the Shelton solution for the shock-fronted proforce wave in one dimension, solutions for the other waves now seem possible within the overall requirement that they exhibit only small differences in dependence of velocity on reduced field. Moreover, Turcotte and Ong (77) have indicated solutions for the cylindrically restricted thermal region, and Albright and Tidman (78) have discussed the time dependent case, if it should prove to be needed to understand any of these waves. It is now of importance to ascertain to what extent these theories describe various natural phenomena such as lightning and to perform improved experiments on all these waves both in nature and in the laboratory. It is proposed to deal with these questions as far as possible in a continuation of this article at a subsequent date.

84

RICHARD G . FOWLER

LISTOF Tube radius Dimensionless ionization constant Ion fraction Ionization frequency Wave velocity decrement Speed of Light Electron charge Electric intensity mks permittivity Dimensionless electric field Dimensionless electron temperature Total electric current density, conduction plus convection plus displacement Dimensionless electron flux Boltzmann’s constant, also angular wave number Momentum constant (proportional to elastic collision frequency) Dimensionless collision frequency Electron mass Neutral particle mass Ionic mass Dimensionless ionization rate Electron concentration, also an arbitrary integer Neutral concentration Initial neutral concentration lon concentration

SYMBOLS

Dimensionless electron concentration Dimensionless position variable Electron pressure, also ambient gas density in Torr Heavy particle pressure Collision probability Electric resistivity Heat conduction vector Cross section, with appropriate subscripts Time Heavy particle temperature Electron temperature Electron collision interval Radiation lifetime of state k Electron velocity either in a general frame or special (as specified) fluid frame of reference Heavy particle velocity either in a general frame or special (as specified) fluid frame of reference Initial heavy particle velocity Electron internal energy Coordinate along flow direction Dimensionless electron velocity Electric potential Ionization potential Capacitor potential Cyclotron frequency

REFERENCES 1. R. G. Fowler, Aduan. Electron. Elecfron Phys. 20, 1 (1964). 2. F. Hauksbee, Phil. Trans. Roy. SOC. London 24, 2129 (1705) 3. C. Wheatstone, Phil. Trans. Roy. SOC.London, 124, 583, (1834). 4 . J. J . Thomson, Proc. Roy. SOC. London 49, 84 (1891). 5. W. von Zahn, Wied. Ann. 8, 675, ( I 879). 6. J. W. Beams, Phys. Rev. 36,997 (1930). 7. J. James, Ann. Phys. Phys. Chem. 15,954 (1904). 8. L. B. Snoddy, J. W. Beams, and J. R. Dietrich, Phys. Rev. 50,469,1094 (1936); 51, lo08 (1937). 9. J. W. Beams, Phys. Rev. 28,475 (1926).

NONLINEAR ELECTRON ACOLISTIC WAVES, I

85

10. C . T. R. Wilson, Pruc. Roy. Soc., Ser. A 92, 555 (1916). 11. B. F. J. Schonland, fror. Roy. Soc., Ser. A 164, 132 (1938). I Z . R. G . Fowler, Electrically Energized Shock Tubes. Oklahoma University Research Institute, Norman, Oklahoma, 1963. 13. V. Josephson and R. H. Hales, Space Tech. Lab. Rep. STL/TR-60-0000-19313; Phys. Fluids 4, 373 (1961). 14. R . G. Jahn and F. A. Grosse, f h . w . Fluids 2,469 f 1959). 15. H . D. Weymann, Phys. Fluids 3 , 545 (1960). 16. G . E. Moreton, Sky Telescope p. 145 (March, 1961). 17. J. P. Wild, J . fhys. Soc. Jap. 17, Suppl. A-I 1, 249 (1962). 18. L. H. Burlaga and N. F. Ness, Solar Phys. 9, 467 (1969). 19. J. Roquet, R. Schlich, and E. Selzer, J . Ceophys. Res. 68, 373 I ( 1 963). 20. R. G. Fowler, J . Ceophys. Res. (submitted for publication). 21. D. Koopman, Phys. Fluids 15, 56 (1972). 22. G . W. Paxton and R. G . Fowler, fhys. Rec. 128, 993 (1962). 23. L. B. Snoddy, J. W. Beams, and J. R. Dietrich, Phys. Rec. 52, 739 (1937). 24. F. H . Mitchell and L. B. Snoddy, Phys. Re!).72, 1202 (,I 947). 25. A. Haberstich, Ph.D. dissertation, University of Maryland, College Park, Maryland, 1964. 26. J. M. Burgers, see Appendix to Haberstich dissertation (25). 27. G . A. Shelton, Ph.D. dissertation, University of Oklahoma, Norman, Oklahoma, 1967; G. A. Shelton and R. G . Fowler, f h y s . Fluids 11, 740 (1968). 28. R. N. Blais, Ph.D. dissertation, University o f Oklahoma, Norman, Oklahoma, 1971. 29. R. N. Blais and R. G . Fowler, fhys. Fluids, in press. 30. R. G . Fowler, Proc. f h y s . Soc., London 68, 130 (1955). 31. R. J. Sovie, Phjss. Flitids 7,613 (1964). 32. I . D. Latimer, J. I . Mills, and R. A . Day, J . Quant. Spectrusc. Radiat. Transfhr 10, 629 ( I 970). 33. F. L. Miller, Ph.D. dissertation, University of Oklahoma, Norman, Oklahoma, 1964. 34. B. L. Moiseivitsch and S. L. Smith, Rru. Mod. f h y s . 40, 1 (1968). 35. J. D. Jobe and R. M. St. John, Phys. R ~ L 164, . . 117 (1967). 36. H. R. Moustafa Moussa, F. J. DeHeer, and J. Schlutter, fhysica (Ufrecht)40, 517 (,I 969). 37. G . Elste, J . Qimnt. Spectrusc. Radiat. Tramfer 3, 209 ( I 963). 38. R. G . Westburg, Phys. Rev. 114, 1 (1959). 39. W . P. Winn, J . Appl. Phys. 38, 783 (1967). 40. W. R. Atkinson, Ph.D. dissertation, University of Oklahoma, Norman, Oklahoma, 1953. 41. H. G . Voorhies and F. R. Scott, Phys. Flitids 2, 576 (1959). 42. E. A. Maclean, A. C. Kolb, and H. R. Griem, Phys. Fluids 4, 1055 (1961). 43. R. G. Fowler and J. D. Hood, Pltys. Rec. 128, 991 (1962). 44. E. R. Pugh, Ph.D. dissertation, Cornell University, Ithaca, New York, 1962. 45. R. S. Schreffler and R. H. Christian, J. Appl. fhys. 25, 324 (1954). 46. A. Haberstich, Bull. Atner. fhys. Soc. 9, 585 (1963). 47. J. B. Gerardo, C. D. Hendricks, and L. Goldstein, Phj)s. Fluids 6, 1222 (1963). 48. R. C. Isler and D. E. Kerr, Phys. Fluids 8, I176 (1965). 49. M . J . tubin and E. J. Resler, fhys. Fluids 10, 1 (1967). 50. G . R. Russell, fhys. Fluids 12, 1216 (1969).

86

RICHARD G . FOWLER

51. J. I. Mills, M. Naraghi, and R. G. Fowler, Phys. Fhids (in press). 52. S. M . Hamberger and A. W. Johnson, J . Quani. Specfrosc. Radiui. Transfer 5, 683 (1965). 53. P. Liou, Master’s thesis, University of Oklahoma, Norman, Oklahoma, 1971. 54. A. C. Pipkin, fhys. Fluids 4, 1298 (1961). 55. R. P. Scott, personal communication. 56. J. P. Barach and J. A. Sivinski, f h y s . Nuids 7, 1075 (1964); 8, 2158 (1965). 57. F. Paschen, Wied. Ann. 37, 69 (1889). 58. J. S. Townsend, f h i f . Mug. 6, 389, 598 (1903). 59. L. B. Loeb, “Electrical Coronas.” Univ. of Califorina Press, Berkeley 1965. 60. W. Rogowski, Arch. Elektroiech. (Berlin) 16, 496 (1926). 61. A. von Hippel and J. Frank, Z. f h y s . 57, 696 (1929). 62. L. B. Loeb and J. M. Meek, “The Mechanics of the Electric Spark.” Stanford Univ. Press, Stanford, California, 1941. 63. H. Raether, Z. Phys. 107, 91 (1937); 110, 61 I (1938); 112, 464 (1939). 64. F. M. Penning, “Electric Discharges in Gases.” Macrnillan, New York, 1957. 65. E. Nasser and L. B. Loeb, J. Appl. Phys. 34, 3340 (1963). 66. M. J. Lubin, Phqx Nitids 10, 1794 (1967). 67. H . Abraham and J. LeMoine, Ann. C‘hitn. f h y s . 20, 264 (1900). 68. P. M. Morse, N. P. Allis, and E. S. Lamar, f l i p . Rer. 48, 412 (1935). 69. J . A. Smit, fhysico (Utuechi) 3, 143 (1936). 70. M. J . Druyvestyn, fhysicu (Utrechf) 10, 69 (1930). 71. D. E. Golden and H . Bandel, fhys. Rec. A 138, 14 (1965); 149,58 (1966); 151,48 (1966); D. E. Golden and J . A. Salerno, ibid. 146, 40 (1966); f h y s . R w . Left. 14, 1010 (1965); 17, 847 (1966); A . Salop and G. Nakano, fhys. Rw. A 2, 127 (1970). 72. J. J . Thoinson and G. P. Thomson, “Conduction of Electricity and Theory of Gases.” Cambridge Univ. Press, London and New York, 1933. 73. G. A. Shelton and R.G . Fowler, Phys. Fluids, (in press). 74. N. E. Kochin (1926). See L. D. Landau and E. M . Lifshitz, ”Fluid Mechanics,” p. 360. Addison-Wesley, Reading, Massachusetts 1959. 75. P. T. Smith, Phys. RPU.36, 1293 (1930). 76. A. V . Phelps, J. R. Pack, and R. S. Frost, fhys. Rev. 117, 470 (1960). 77. D. L. Turcotte and R. S. B. Ong, J . flusnzu fhys. 2, 145 (1968). 78. N. W. Albright and D. A . Tidman, Phys. F h d s 15, 86 (1972).

Hollow Cathode Arcs JEAN-LOU P DELCROIX Laborntoire rle Physique des Plasmas, Universitk de Paris-Surl, Orsay, France AND

A R M A N D 0 ROCHA TRINDADE Instiluto Superior Tkcnico, Uniuersidade de Lisbon, Portugal

88 91 92 93 A. Normal Regime (N Regime) B. Low Gas-Flow Regime (LQ Regime)................................................... 97 98 C. Low-Current Regime (LI Regime) . 99 D. High-Pressure Regime (HP Regime) E. Concluding Remarks on HCA Operation .... 102 103 IV. Operating Conditions for Low-Pressure HCA (N, LQ, and LI Regimes) ... . . . . . 103 A. Experimental Requirements ................ 5. Working Parameters for the Low-Pressure Regimes .... ... ..... ....... ........... i06 V. Experimental Results for the Normal Regime ..... .. ..... ... . . ... .. ............... ..... i09 A. Current-Voltage Characteristics ........ ...................................... 109

I. Introduction

11. Historical Re view of HCA 111. Working Regimes of HCA .....................................................................

5. The External Plasma ......__._._.... C . Oscillations and Noise in HCA ........... D. The Cathode Region ................ VI. Theory of the HCA in the N Regime A. General Comments ........................................................................ 157 B. The Nature of the "Active Zone" C. Balance of the Current in the Cathode Region .................................... 166 ... .... .. .. _ _ ... . 170 D. The Ionization Term in the IPC E. Prospects of Improving the The0 F. Conclusion .................................................................................... 175 .........._...... VII. Applications of HCA . A. Multichannel HCA .. ................... 175 B. HC Ion Laser C. Ion Sources for Electric Propulsion Systems ........................... .._........ 180 D. HC MPD Thrusters ........................................................................ 182 ................. E. ac Operation of HCA F. Other Applications of . .... ......... .... ............ .. ., ......, ., ............ ..... 184 .... .. .. VIII. Conclusion ... References .., ., .., ....., ...., ......, .. . .. . .. .. . ..., ....... .. ,, ........, ........, ,....., ....... .. I85 ...........................

.

87

88

JEAN-LOUP DELCROIX A N D ARMAND0 ROCHA TRINDADE

1. INTRODUCTION Hollow cathodes have been used for some years in different discharge devices, working under varying conditions in widely extended ranges. All of these devices have one common feature: the cathode presents a hollow cavity, enclosed or at least partially bound by walls made of conducting, refractory materials kept at the cathode potential. The geometry of such cathodes is such that their open side faces the anode side of the discharge, so that the plasma existing at the interelectrode space can penetrate the hollow cathode, thus assuring a strong interaction between the plasma and the cathode internal surface (Fig. 1). CATHODE

ANODE

I PLASMA POSlflVE SHEATH

CATHODE WALL

FIG. I . Plasma penetration inside the channel of a cylindrical hollow cathode.

In general terms, this interaction affects an extensive area of the cathode wall; a positive space-charge sheath builds up, so that the incoming ions are strongly accelerated before neutralization upon the wall. If the current is large enough (arc regime) the resulting high wall temperature enhances the thermionic emission; on the other hand the emitted electrons inside the hollow cavity, accelerated by the sheath voltage, have a high probability of making several inelastic collisions with the neutral particles before reaching the interelectrode space.

HOLLOW CATHODE ARCS

89

Considering, for instance, a longitudinal discharge between opposing electrodes, the hollow cathode cavity can present plane-parallel, cylindrical, or spherical geometry (Fig. 2 ) . For a transverse discharge, the electrode

A-

- PLANE

A

PARALLEL

w

8,- CYLINDRICAL SINGLE CHANNEL

$

1

3

8,- CYLINDRICAL MULTICHANNEL

&-

B3- CYLINDRICAL "MACARONI PACKET"

f i T @ ._.-

C

- SPHERICAL

CAVITY

FIG.2. Hollow cathode geometry (longitudinal discharge).

arrangements can, in principle, take one of the basic forms shown in Fig. 3 (orthogonal or coaxial electrodes). The performances of this type of discharge are generally better than those where the cathode presents a plain surface to the anode side; for the same gas pressure, discharge voltage, and general geometric parameters, the resulting discharge current in generally higher for hollow cathode discharges than for conventionally shaped ones. This was probably the point that aroused interest about those discharges in early investigations; later, several other advantages were acknowledged when more detailed research was accomplished on the subject. Hollow cathode glow discharges (low current I 6 I A , high cathode voltage drop V, > 100 V, thermal effects relatively small) were first discovered and their remarkable performances recognized as early as 1923 [Guntherschultze (I)]; but more than 30 years elapsed ( 1958) [Luce (Z)] before the same kind of interest arose about hollow cathode arcs (high current I 2 5 A, low voltage drop V , < 50 V, cathode temperature T 2 2000°C).

90

JEAN-LOUP DELCROIX AND ARMAND0 ROCHA TRINDADE

t+

A,- P L A N E PARALLEL ANODE; CYLINDRICAL CATHODE

?-

--

.- - - - . - - - - - - *

-

A,- P L A N E PARALLEL CATHODE; R I N G - S H A P E D ANODE

B2- COAXIAL GEOMETRY, E X T E R N A L CATHODE

6,- COAXIAL GEOMETRY. I N T E R N A L SLOTTED CATHODE

FIG.3. Hollow cathode geometry (transverse discharge).

It can be said that HC glows and HC arcs have been, up to now, two independent fields of research; at least, it is difficult to find significant contributions from the studies of one type of discharge to the other. This is most certainly due to the specialization in the experimental setup required for one or the other type of discharges: power supplies, cooling facilities, electrode erosion problems, specific diagnostic methods to be used, etc., depend strongly on the type of discharge in which one is interested. On the other hand, the emission, excitation, ionization, and transport mechanisms of particles, present at the onset and in the steady-state regime of both types of discharge, are again specifically different, and call for different theoretical and experimental methods of approach. These are sound reasons for the tendency of the various research laboratories to specialize either in hollow cathode glow discharges or in hollow

91

HOLLOW CATHODE ARCS

cathode arcs, seldom in both of them. The same reason applies to the present review; it will be concerned only with HC arcs, which we have been studying extensively since 1964 (2-10). A point on nomenclature should now be raised, considering the number of papers in the scientific literature dealing with either hollow cathode glow or arc discharges. Usually in the literature, the term “hollow cathode effect” concerns a glow discharge, while following Lidsky er a/. ( / I ) ’‘ , hollow cathode discharge” is supposed to mean a high-current device. Still, some authors do not take these views; so, the title and even the abstract are sometimes not sufficient for a reader to decide whether a given paper on hollow cathodes concerns a glow or an arc discharge. For the sake of clarity we propose the designation of hollow cathode arc (HCA) to distinguish such a discharge from a hollow cathode glow (HCG). 11. HISTORICAL REVIEW OF HCA

The first results on HCA discharges were reported by Luce in 1958 (2). The experimental device was constituted of a rather large (1-2 cm i.d.), thick-walled tungsten tube as a cathode, with a gas flowing through into the evacuated interelectrode space. It was found that the discharge began in the interior of the cathode tube, several diameters from the open end, and extended to the anode. The same basic arrangement was used in arc discharges studied at the Oak Ridge National Laboratory and the Research Laboratory of Electronics of the Massachusetts Institute of Technology. The research groups concerned published jointly the results of their pioneer work on HCA discharges [Lidsky er al. ( I / ) ]such as various electrode configurations, cathode materials and injected gases, range of the parameters for proper operation. They measured the external plasma density and temperature and studied the current and energy balances at the electrodes. The combination of tantalum cathode-argon gas was found to be the most satisfactory one for good efficiency and proper operation of the discharge. Important features of the discharge have been pointed out: ( 1 ) the discharge creates a very pure external plasma (low contamination by the cathode material), dense (n, 10’3-10’4 ~ m - and ~ ) highly ionized (up to 95%); (2) the cathode presents a reasonably long lifetime, despite high current densities and high cathode wall temperature (higher than 2500°K). Those characteristics were interesting enough to encourage further research on the subject. Reasonably enough, the next few years saw a steady amount of experimental work being performed to improve the knowledge of HCA discharges, mainly concerning the influence of the various parameters (geometry, external pressure, gas flow rate, axial magnetic field strength, electrode temperature, etc.) on the performance of the discharge as an efficient

-

92

JEAN-LOUP DELCROIX A N D ARMAND0 ROCHA TRINDADB

source of dense, highly ionized plasma [see for example, 6, 12-15)]. An important part of this research work dealt with the study of the noise and oscillations of the discharge (16-19) since it was interesting to evaluate the possibilities of using an HCA as a source of quiet plasma for experimental work on wave propagation. The next step of the research o n HCA consisted mainly of a theoretical effort to understand thoroughly the internal mechanisms of these discharges, namely to account for the high current density that can be drawn out of a hollow cathode without serious damage. In spite of the amount of work already produced [see, for example, (15, 20-23)] by a theoretical approach, this problem is still an open one, especially for very high current densities; nevertheless it can be stated that we have now a fair knowledge of the physical processes involved inside the cathode channel and a reasonable understanding of the reasons for the high efficiency of this type of discharge. The research on HCA has now been stimulated by a number of interesting applications; the possibility of delivering high currents with little damage makes these cathodes very useful devices for ion lasers (24-27); ion thrusters (28, 29); flowing afterglows for chemical applications (9); welding; MHD generators and motors (30); and quiescent plasma machines (18, 31). The many applications already in existence should keep interest high in the next few years. 111. WORKINGREGIMES OF HCA

Considering a cylindrical hollow cathode, with the exit hole facing a plane anode (by far, the most extensively used geometry), several arc regimes can occur, depending on the range of the discharge parameters (pressure vessel y,; gas-flow rate Q ; discharge current I ) . A qualitative classification of operating arc regimes is shown in Table I. where the magnitudes of the determining parameters are indicated. TABLE I WORKING REGIMES OF HCA

Name

Code

Normal regime

N

Low gas-flow regime

LQ

Low-current regime

L1

High-pressure regime HP

Pe

Q

I

Low ( i O . 1 Torr) Not too low Not too low cm3 STP) (>10 A) Low (10 A) Low ( 0.1i Torr) Indifferent Very low ( < l o A) Moderate, high Indifferent Indifferent (> 1 Torr)

HOLLOW CATHODE ARCS

93

A . Normal Regime ( N Regime) Earlier research reports pointed out that the “proper” regime of operation of HCA was obtained when a gas was injected through the cathode channel into the discharge vessel, kept at low pressure ( ~ 0 . 1Torr). This mode of operation is easily recognized by an extensive hot zone set at some distance from the tip of the cathode (up to a length of several diameters); this diffuse hot zone is clearly different from the extremely hot, localized cathode spot of the classical (plain cathode) arc discharges (Plate I). Further research on the nature of this active zone required the knowledge of the longitudinal profile of the cathode wall temperature. For a very thin cathode wall (e.g., 0.2 mm), optical pyrometry of the outer cathode surface can give the temperature of the inner emitting surface to a very good approximation. Figure 4 presents a typical profile, showing a maximum at some distance 1 of the cathode (measured from the tip). The temperature range is high enough to provide high thermionic emission from an important area of the cathode wall; however, calculations show that electron multiplication by ionization must take place to account for the measured discharge currents. From the very beginning of the research on HCA it was noticed that the location of the maximum wall temperature moved farther from the open tip of the cathode when the gas-flow rate was reduced; increasing the cathode inside diameter for a given flow rate yields the same result (Fig. 5). It is felt therefore, that the neutral gas pressure inside the cathode channel probably would be the determining parameter for the location of the maximum wall temperature. The pressure varies along the cathode channel due to the gas flowing through; and the maximum temperature would occur at a distance where this pressure reaches an optimum value depending on the exact experimental conditions. Estimates of this optimum pressure (at the hottest zone level) are of the order of a few Torr (fl, 3 1 , 3 2 ) . The reasons for the above requirements for the N regime become more obvious when the origin of the extensive hot zone at the cathode wall is considered. It is clear that a plasma must exist inside the channel, and that a strong ion bombardment is necessary to account for the wall heating. Those ions are mostly created inside the cathode channel (if they were created by ionization in the interelectrode space, the discharge would be affected by lowering substantially the vessel pressure, which is not observed), by inelastic collisions of wall-emitted electrons upon the neutral particles. Thus the pressure requirement inside the channel is due simply to the fact that the mean free path of the fast electrons for inelastic collisions must be short enough for significant ionization to take place inside the hollow cathode. “

”

94


Plate I. The same cathode situation photographed with different exposures to show the brightness profile of the cathode cylinder (Q: 0.8 atm cm3 sec-', I 20 A, R = 1.9 mm, B = 100 G ) . L , - 7.5 cm, film: llford HP4, I ) - l/SOO. A 1 / 2 2 , green filter; B / / 3 . 5 , green filter; C f / 2 2 ; D f / 3 . 5 . ~

95

HOLLOW CATHODE ARCS

1

CATHODE

7

6

5

4

ANODE --

3

2

1

0

FIG.4. Typical longitudinal profile of wall temperature in the N regime.

In a fully established N regime the plasma inside the channel transfers a positive potential from the anode to the vicinity of the cathode wall; this creates a space-charge sheath that accelerates the walls-emitted electrons and enhances the ionization inside the hollow cathode. It is found that for the same current the overall cathode drop (and the discharge voltage as well) increases strongly as the hottest zone is made to move deeper inside the cathode tube by varying the flow rate (Fig. 6). This increment attains several volts per centimeter, depending on the cathode inside diameter. An overall cathode drop up to about 50 V, can be measured for deep plasma penetration (several centimeters); since the cathode drop equals the maximum sheath voltage, at the tip of the cathode, several ionizations can be produced by every emitted electron. The N regime is very steady and the current density through the channel cross section can be rather high (typically lo2 A cm-2) without significant damage to the cathode wall, since its temperature is everywhere well below the melting point of the metal (T,,,,,, = 3270°K for Ta; 3653°K for W cathodes).

96


4 (mm)

50

40

30

20

10

0

0

1

2

3

Q

4

(at rn c m . 3sec

I)

FIG.5. Abcissa I of the cathode where the maximum wall temperature occurs for various channel radii R, as a function of the argon gas-flow rate, Q (atm ~ m sec-’) - ~(e = 0,2 mm; I : 15 A ; B = 400 G ) . From Delcroix ef al. (6, p. 414).

;;I

100

Vd ( V I

I.....

.............

- ------

I ........... --

N regime

_.i.

LQ regime

40

2o

t

01

10.’

I

I

10.‘

I

I

1 P (atm cm3 s e i ’ ~10

FIG. 6. Discharge voltagc as a function of the gas-flow rate showing the transition between the normal regime (right hand branch) and the low flow rate regime (left-hand side) ( I = 15 A ; R = 1.8 nim; L = 2 1 . 5 cni; p r = 2 x Torr; 8 = 4 0 0 G). From Minoo (31, p. 96).

97

HOLLOW CATHODE ARCS

The portion of plasma inside the cathode channel is called (32) the "internal positive column" (IPC), due to the plasma potential polarity respective to the cathode. It is however, rather different from the usual positive columns of glow or arc discharge because in the present case the wall acts as an emitting electrode, and moreover, is at a constant potential, thus producing an ion sheath with a voltage drop increasing toward the tip of the cathode.

B. Low Gas-Flow Regime ( L Q Regime) Let us consider the following experiment: while working with an HCA in the N regime, the gas-flow rate is made to decrease step by step keeping the vessel pressure and the discharge current constant. As stated before, the hottest zone of the cathode wall will recede from the extremity and the curves T(x) become progressively flatter; the discharge voltage will be increasing steadily (Fig. 6 ) . If the gas-flow rate is made to decrease past a certain value we enter a new regime: a sudden disturbance of the wall temperature takes place over the whole length of the cathode and evolves during some ten seconds. After that time, a new temperature distribution can be observed, where T(x)is decreasing monotonically from the tip of the cathode to the holder (Fig. 7). The new discharge voltage is lower than the extrapolation of the V ( Q )curve for the N regime would indicate (Fig. 6 ) .

1500

1000 I

4

x(cm)

I

I

I

T

3

2

1

0

FIG.7. Transition from the normal regime to the low gas-flow regime, decreasing progressively the gas injection through the cathode channel ( I = 15 A ; R = 0.18 cm; B = 400 G ; p E = l o - * Torr). From Delcroix er oi. (5, p. 267).

98


If the gas-flow is further reduced, down to complete cutoff, the discharge voltage and the T ( x ) curve remain unchanged. This low gas-flow operation ( L Q regime) is characterized by the monotonic variation of the temperature with distance along the cathode wall, showing that the plasma does not penetrate significantly inside the cathode channel. This is mainly due to the fact that the gas flow is too low to impose an important pressure gradient along the channel; the pressure is then substantially the same as in the vessel. Under these conditions, the mean free path for the ionization of the neutral gas by the thermionic electrons is too long for significant ionization to take place inside the channel.? This regime is not very interesting for it requires a higher voltage than the normal one. The hottest part of the cathode is less extensive, and so less efficient, as a thermionic source than in the N regime, with the same maximum cathode temperature; furthermore, since the ionization rate inside the channel is very low, the thermionic emission must be completed by ionization in the external plasma to provide for the required discharge current. The LQ regime was first reported in 1968 ( 5 ) ; later articles (21, 26, 31,32) provided additional information on the subject. The transition from this mode of operation to the “ high-pressure regime” (Section IV) has been analyzed by Minoo (31) who studied the external plasma, the magnetic confinement effect when the vessel pressure is increased from to 10 Torr and measured the longitudinal electric field under those conditions (Fig. 8). \

C. Low-Current Regime (LI Regime)

This other low-pressure regime of an HCA will be analyzed very briefly, as it is an undesirable one. It occurs when an attempt is made to ignite the N regime of an HCA with a current that is too low. The easiest way to achieve ignition is to set the correct pressure requirements (Section 111, A) and create afterward an abnormal glow discharge between the electrodes (Section IV). When the cathode begins to get rather hot, an increasing current causes an arc to ignite; the current is at first provided by the ionization in the external plasma and the thermionic emission from a cathode hot spot. If the discharge current (determined by the external circuit) is high enough, this hot spot mode evolves quickly into an N regime with a diffuse cathode active zone; the externally created ions enter the cathode channel, impinge upon the wall, and heat a large area of it up to thermionic temperatures, and a plasma is created inside the hollow cathode.

-

t Taking for instance, p e = lo-’ Torr, estimated gas temperature To 2500’K and for typical electrons having 20 eV kinetic energy, the mean free path for ionization is 50 cm; even taking into account their elastic collisions upon the neutrals (mfp 15 cm), those electrons will leave the channel without producing ionization. N

N

99

HOLLOW CATHODE ARCS E/p ( V/cm Tori

10’

CONFINED. HIGHLV IONIZED PLASMA

i

,

CONFINED. “INTERMEDIATE” PLASMA

NONCONFIHEO ~

PLASMA

10

1

10’ 10.~

10.l

lo-’

1

10 P (Torr)

FIG.8. Experimental values of € / p in the external plasma column as a function of the vessel pressurep. From Minoo (31, p. 29). ( I = 15 A; R = 0.18 cm; Q = 0; B = 400 G). * For the definition of “intermediate” plasma see Delcroix (33, p. 92).

However, if the ion current is too low, it is unable to heat the cathode wall enough to create an internal positive column. The hot spot remains at the periphery of the cathode end, moving around it, or it may run erratically along the cathode outer surface, causing strong fluctuations of the discharge voltage. In either case, vaporization and damage to the cathode is expected. This unsteady mode of operation is called the low current (LI) regime (21) and must be avoided during ignition, when it is most likely to occur. Reduction of the discharge current when an N regime is in operation does not usually produce a typical hot spot LI regime. The discharge voltage increases progressively up to the point when it cannot be provided by the power supply; then, the discharge is simply cut off.

D . Higli-Pressure Regime ( H P Regime) If the vessel pressure in an HCA working in the normal regime is made to increase past some lo-’ Torr, the cathode wall temperature maximum is observed to approach the electrode tip. For an external pressure of the order of 1 Torr, a monotonic axial variation of the wall temperature is observed (Fig. 9). Reducing or cutting of the gas injection through the channel does not affect the regime significantly, provided that the vessel pressure is not allowed to change. This cathode mode of operation in the moderate pressure range (up to some 10 Torr) is similar to the LQ regime, in the sense that a plasma is not formed inside the cathode channel in either case. An arc-type cathode spot

100


is still not observed; this is, obviously, a distinct advantage of HC over the plain, conventional cathode for low and moderate pressures. Unfortunately, if the vessel pressure in this arc discharge is made to increase further, past some tens of Torr up to atmospheric pressure and beyond, the cathode no longer behaves like a hollow cathode should, that is, with an extensive hot zone and low metal evaporation. As the pressure increases, the hot zone is observed to contract and finally it becomes a localized hot spot at the tip of the cathode; very high spot temperatures cause fierce local vaporization, quick cathode damage and metal contamination of the external plasma. The hollow cathode now behaves like a plain refractory cathode in the hot spot mode. For applications imposing high vessel pressures with strong discharge currents (for instance, MHD devices and chemical reactors) it would be most interesting to achieve typical hollow cathode behavior as in the normal, low pressure regime. Study of the energy balance at the cathode has shown that it is not possible to achieve the heating of an extensive area of the cathode wall by the discharge itself (34). The simplest solution found was an auxiliary heating of the cathode wall by an external circuit. Curves showing the cathode behavior when imposing an external current along the wall are presented in Fig. 10 (8).

x(crn)

7

6

5

4

3

2

1

0

FIG.9. Transition from the normal regime to the high-pressure regime by increasing the vessel pressure. ( I = 20 A ; R = 0.145 cm; Q = 6 x lo-* atm cm3 sec-'; B = 0). From Trindade (21, p. 16).

101

HOLLOW CATHODE ARCS

-5 I

a

Q-

-- L A+

c -

X

i

{-

2400

I

I

FIG.10. High pressure behavior of the HCA: wall temperature profile. (a) Without auxiliary heating (Ih= O), (b) with auxiliary heating in absence of the discharge ( I = 0); (c) working as a “cathotron.” I-Cuthode channel (tantalum wall); 2, tantalum disk; 3, tantalum outer cylinder; 4, insulator; 5, cathode holder. From Delcroix er crl. (34, p. 19).

102


The main conclusion of these experiments is that, when the cathode wall temperature reaches the thermionic range over a significant area, the hot spot disappears and a steady discharge is obtained, without significant damage to the cathode. Delcroix, Minoo, and Popovici (34) found the performances of this device to be better when a strong gas flow is injected through the cathode channel. They named the arrangement “ cathotron” (35), since it is (under a conceptual point of view) something like the association of a plasmatron with a hollow cathode. E. Concluding Reniarks on HCA Operation 1, Low-Pressure Discharges ( p E< 0.1 Torr)

a. N regime. Characteristic features of the N regime are extended cathode hot zone and internal positive column. This is the most interesting regime of low-pressure HCA operation, for it provides high arc currents with the lowest discharge voltages. As a drawback, a gas injection must be running through the cathode, imposing a continuous pumping of the discharge vessel. The best way to obtain this regime is to increase the discharge current sufficiently, starting from an abnormal glow discharge. The convenient ignition current density is about 1 A/mm2 through the tube cross section; once the N regime is fully established the current can be reduced about threefold without cutoff. b. LQ regime (including Q = 0). Characteristic features of the LQ regime are extended hot zone, cathode temperature decreasing monotonically from the tip to the cathode holder, and absence of an internal column. This regime requires a higher voltage than the N regime for the same discharge current. Since gas injection is unnecessary, it can operate in a sealed vessel; however, some difficulties must be expected for ignition in those conditions, since the easiest way to establish the LQ regime is through the normal one by reducing gradually the gas flow rate (which is not possible in a sealed vessel). c. LZ regime. Characteristic features of the L1 regime are unsteady operation, hot spot mode, and low cathode lifetime. A suitable choice of the supply voltage and the charge resistor is necessary to avoid this regime during ignition. It is possible that a steady operation with low current density, without cathode spot, could be obtained by providing an external heating of the cathode wall. There are no published data concerning this experiment to insure that a proper operation can be obtained. 2. Moderate and High-Pressure Discliarges a. Moderate range (pE 5 10 Torr). Characteristic features of the moderate range are extended hot zone, cathode temperature decreasing monotonically

HOLLOW CATHODE ARCS

103

from the tip, and absence of an internal column. The absence of a hot spot insures fair cathode lifetime. This regime is easier to establish departing from a N regime by increasing the pressure vessel. A gas injection is not necessary afterward. b. High-pressure range (pE > 10 Torr). A characteristic feature of the high-pressure range is the hot spot mode unless cathode auxiliary heating is provided (cathotron). The best operation is obtained with high gas flow through the cathode. Lack of further published data, either experimental or theoretical on the HP regime, causes the remainder of this work to concentrate in the lowpressure operation of HCA.

IV. OPERATING CONDITIONS FOR LOW-PRESSURE HCA ( N , LQ, A N D LI REGIMES) A . Experimental Requirements

a. Cathode assembly. For a cylindrical geometry, hollow cathodes are usually made of a thin-walled tube of a refractory metal (Ta, W, Mo, the first being the most extensively used), either isolated or as a bundle assembly of tubes (multichannel cathodes, Section VlI, A). The thick-walled or drilled rod variety is not very interesting, for it increases the heat conduction to the cathode holder and consequently lowers the wall temperature. To make the substitution of cathode tubes easier they are not usually welded to the cathode holder; a vacuum-tight and good heat-conducting contact between cathode and holder is obtained by compressing an intermediate washer or ring of soft metal (indium, gold, lead). To prevent the vaporization of this material, the holder is usually water cooled. On the other hand, it is interesting to maintain a high cathode wall temperature at the active (emitting) region, and a radiation shield is quite useful. It may take the form of one or several refractory metal tubes simply put around the cathode, without any type of clamping device (Fig. 11). A ceramic arc stop (alumina or zirconia) is useful to prevent the initial arc (during ignition) from starting at the wrong place, and eventually damaging the cathode holder. 6 . Anode. Anodes are usually cooled, to take away the high power dissipation that occurs there [more than 50 of total input power ( 6 ) ] .They may be shaped as a large ring (sometimes larger than the cathode diameter) or as end-anodes, either plain disks or hollow cylinders. The latter are found to lower the anode drop when they work at high temperatures, and simultaneously reduce plasma oscillations and noise (36). Gas injection through the anode was reported to have a similar effect (37,18); it may also be useful to reduce pressure gradients that could exist along the column.

104


CATHODE CHANNEL

I \

t

RADIATION SHIELDS

ARC STOP

FIG. 11. Typical cathode assembly with two radiation shields.

c. Discharge vessel. Vessel dimensions and geometry are determined by the purpose of the discharge; the length of the column does not affect strongly the discharge voltage since the external plasma is almost field-free (12), although a long column may make arc ignition more dificult. For such a long column, an auxiliary anode is sometimes used to make ignition easier. Slender columns such as those used in lasers are, of course, different since the axial electric field is much higher and the discharge voltage increases accordingly (38). The use of baffles inside the vessel may strongly modify the column behavior, introducing local gradients of pressure. This is a common arrangement used in some plasma experiments to separate the source region (cathode region) from a high-vacuum region where the external plasma is allowed to diffuse (18). Differential pumping is used in those cases. Protection of the vessel walls against excessive heating may be obtained by appropriate cooling facilities or, most efficiently by an axial field, confining the plasma in the central part of the vessel. It is also found that the axial magnetic field makes arc ignition easier in the N regime, for it collimates the externally created ions into the hollow cathode. However, a magnetic field is strictly not necessary for HCA operation, even if it generally lowers the discharge voltage for a given current (see Section V, A , 1). d. Vacuum system. As a steady gas injection is usually present, high pumping speed is necessary to maintain the vessel volume at a low pressure. Torr), it is normally necessary Even at moderately low pressures ( p E to provide a high-speed secondary pump (Rootes or diffusion type) of some lo2 1 sec-' pumping speed, backed by a suitable rotary pump. e. Electrical circuit. Two straightforward circuits are presented in Fig. 12 for ignition and operation of a HCA. Ignition is obtained through the abnormal glow regime.

-

105

HOLLOW CATHODE ARCS CATHODE

ANODE

sw2

IHdX= SOA V,

5

1.2 K V

IHix: SOA

FIG.12. Typical circuit arrangements for arc ignition (through abnormal glow discharge) and for steady-state operation. (a) Parallel circuit: ( I ) close Swl, Sw2 is kept open; (2) after cathode heating, close Sw2; (3) after arc starts, open Swl. Swl must take full abnormal glow current; Sw2 must take full arc current. (b) Series circuit: ( I ) close S w l ; Sw2 is kept open; (2) after cathode heating, close Sw2. Swl and Sw2 must take full arc current.

I06


3. Working Parameters for the Low-Pressure Regimes

To compare thoroughly the results obtained by various authors, it would be necessary to know the exact conditions of the experimental setup, i.e., working gas; interelectrodes conditions (column length L, pressure pE and pressure gradients, arc confinement situation and vessel geometry, heat exchanges); anode conditions (geometry, material, heat transfer conditions); cathode conditions (cathode material and geometry, heat transfer conditions, gas-flow rate Q); discharge current I and voltage V ; magnitude and geometry of the external magnetic field B. Unfortunately a great number of articles in the literature lack complete information about many of the above parameters, making the actual comparison of results difficult. Nevertheless, most of the authors working on HCA deal with the same general type of discharge described as follows: longitudinal discharge (opposing electrodes); cylindrical geometry, (one hollow cylindrical cathode channel, along the discharge axis); gas-fed cathode, usually made of tantalum, with a flow of a rare gas, usually argon; strong longitudinal magnetic field ( B > 100 G) or no magnetic field applied; external pressure (at the interelectrode space) lower than 0.1 Torr. For this type of discharge the principal independent parameters to be considered are the channel radius R , the gas flow rate Q, and the discharge current I ; while the T(x) curve of the cathode temperature and the discharge voltage Vare the most readily available dependent variables. The cathode and anode drops (V, and VA),the longitudinal electric fields inside and outside the cathode channel ( X , and X,) and the external plasma parameters (n,, n, ,n o , T, , T i , To) involve more elaborate measurements. The principal independent variables R , Q , I , can be varied a priori within very wide limits: R = 0.05 cm to several centimeters; I = 1 A to several 10' A up to several 10' atm-cm3 sec-'. (permanent regime); Q = 0 through However, if an N regime is sought, with rather high efficiency and a fair cathode lifetime, those parameters are not completely unrelated. This point is emphasized in Fig. 13, where we have represented the working conditions of some reported experiments as the loci of composite coordinates Q/Sand I/S ( S being the area of the cathode channel cross section ). The parameter I / S (current density through the cathode cross section) is related to the cathode temperature; Q/Sis the characteristic parameter of the pressure drop inside the channel, having an obvious effect on the phenomena occurring in this region. The choice of the points represented was rather arbitrary and their number limited for the sake of clarity. As a matter of fact, large portions of the diagram ( Q / S ,I / S ) have been extensively studied, mostly in the N regime with Kr and Ne ( 4 3 , argon, but also with other gases [H,(13), N2(43), D2(44, He (53)], and in the LQ regime (31).

107

HOLLOW CATHODE ARCS 102

r

!

i*

INCREASING GAS COOLING EFFECT 0

I I

L I REGIME (UNSTABLE)

I I I *

I

0

I I

N REGIME

I I

0

I)

10.’

10

’

I

10 2

DECREASING CATHODE LIFETIME

I

1

10

10

’

I / S (A/cm2)

FIG. 13. Working conditions in some reported experiments on low-pressure HCA: Delcroix et a / . (6); Lidsky et N / . (I/); Ahsmann and Van Benthein (12); Kretschnier et cil. (17); Brunet (39); Gritzniacher e / d . (40); Chung (41); Lorente-Arcas (42); Gerry (50).

The experiments show that there are two fairly well-defined forbidden zones for the operation of HCA in the N regime, corresponding to the lower values of the parameters Q / S and t / S . Q / S being too small, the discharge works in the LQ regime (see Section 111, B) and the cathode wall temperature presents a monotonically decreasing longitudinal profile. If the current density is too small, either the discharge is unstable upon ignition, working in a hot spot mode (LI regime), or when evolving from a normal regime by decreasing the discharge current the arc suddenly cuts off. The N regime corresponds to higher values of both parameters; however, one should notice that too big ;1 current density at the cathode channel will impair the cathode lifetime by excessive wall temperature. 500 A/cm2 seems to be a good compromise between a high thermionic current and a fair lifetime. The high gas-flow, low-pressure upper part of the diagram has not yet received much attention, for there seems to be no point in increasing the gas

108


consumption while maintaining low vessel pressure by intense pumping. However, some modifications may occur in the discharge behavior in this range, due to important changes in the gas-flow regime, as follows: (i) Flow velocity approaching the speed of sound. Let us take for instance a channel cross section of area S , a local gas pressure equal to 1 Torr (order of magnitude of the pressure at the abscissa where the wall temperature is maximum), and a gas temperature supposed to be at thermal equilibrium with the cathode wall (say, T = 2500°K). The veIocity of sound at this abscissa is then for argon us = 9 x lo4 cm-sec-', while the local gas velocity is numerically given by usas(cm-sec-')

=7 x

103

Q (STP cm3-sec-') S(cm)2

So, a gas flow such that Q / S N 13 cm-sec-' is an upper limit for the flow to remain subsonic at the active zone level (Mach number M < 1). This limit is represented in Fig. 13. (ii) Possibility of a turbulent flow. The limit for a turbulent regime to occur is given numerically for Ar at 1 Torr, 2500"K, by the inequality

N R = 0.59

Q (STP cm3-sec-l) R (cm)

> 1000

This condition is never attained at the active zone level. (iii) Extreme cooling of the cathode wall. This point, which has not been thoroughly studied, concerns the cooling effect of a high gas-flow rate on the cathode wall. Qualitatively it is expected that in these conditions, no extensive portion of the cathode wall can attain thermionic temperatures; then, only by evolving to a hot spot mode can the current requirements be met, and the normal regime probably disappears. The relatively small latitude allowed for variation of the parameters Q and Z for the normal regime (when a cathode of a given diameter is chosen), is one of the drawbacks of the system. If, for instance, a 100 A maximum current must be drawn from an HCA and a high cathode lifetime is desired, choice must be made of a cathode having at least 0.8 cm i.d., imposing a minimum consumption of argon of about 1 atm-cm3-sec-', and a minimum steady-state discharge current of around 20 A (roughly 60 A ignition current). The need for a wider current range and a n economic consumption of gas in every circumstance has been at the origin of multichannel hollow cathodes (7) (see Section VII, A). One could also investigate the effect of an auxiliary heating of the cathode to extend, toward low flow rate values, the domain of existence of the N regime; there are no publications on this subject at the present time.

HOLLOW CATHODE ARCS

v.

109

EXPERIMENTAL RESULTSFOR THE NORMALREGIME A . Current- Voltage Cliaracteristics

1. Comporzents of the Discharge Voltngi>

For a given experimental setup of a n HCA, the V ( I )characteristics depend mainly on the gas-flow rate Q, on the presence and magnitude of the external magnetic field B, and on the vessel pressure p k . Because the total discharge voltage is the sum of three terms (overall cathode drop V c , voltage drop at the external column VE, and anode drop V,), we must evaluate the relative weight of those terms and their dependence on the parameters, in order to understand the behavior of the hollow cathode itself. Considering first the influence of 5 and Q, let us analyze a low pressure discharge where the vessel pressure is kept constant (irrespective of the gasflow rate) at a typical value of Torr. The relative importance of Vc against V , depends both on the depth of penetration of the plasma inside the cathode channel and on the length of the interelectrode space L. Assuming that the length of the internal positive column is I, X , the average field strength in the IPC, and that Y o is the residual value of the cathode voltage drop at the limit of the IPC (x = I ) , one can write (Fig. 14)

FIG.14. Schematic diagram of the potential distribution at the axis of an HCA (N regime).

110


Typical values are (6) V , = 12 V ,

,'A

= 0.1

V/cm,t

X I = 8 V/cm, VA = 20 V/cm.

Due to its much higher electric field strength, an IPC some centimeters long clearly dominates the external column influence on the discharge voltage, even in a rather long discharge. For the latter to be dominating, the IPC must really be very short (very high flow rates). As a general rule, for low gas-flow rates the effect of the external column may be neglected; for high gas-flow rates, the IPC is too short, and a long external column may influence strongly the discharge voltage. The V(1)characteristics of HCA in the N regime are typically arc-type; in the range of the lower currents, the voltage is a decreasing function of the current. The V ( I )characteristic goes through a somewhat flat minimum and then acquires a positive slope for the remaining, high-current range. The exact shape of the curves and the current values for the minimum voltage depend strongly on the discharge parameters (p,, R, Q, B), and on the anode geometry and temperature (6, 36, 466). 2. Magnetic Field Effect

To extract coherent information from published experimental data concerning many different discharges, it is necessary to select arbitrarily three kinds of magnetic field effects on HCA. a. Conjinement of the external plasma. This effect starts at relatively low values of B (10-100 G). It changes a diffusion-type external plasma into a well-defined cylindrical column; but the radius of this column is still larger than the cathode channel radius, due to collisional effects. The net result is a substantial reduction of the charged particle loss due to recombination upon the vessel walls. Consequently, a lower electric field X , is expected in these conditions. b. Constriction of the external column. A further increase of B will reduce the radius of the plasma column down to the cathode dimension. For this effect to be apparent, higher values of the magnetic field are necessary. c. Effects on tlie internal column. The net result of the B action is difficult to predict, but the following considerations can be made; (i) the conditions

t Does not apply to wall-confined, small diameter columns.

HOLLOW CATHODE ARCS

111

for plasma confinement vary along the channel, as the pressure gradient makes the collision frequency dependent on the distance along the channel; (ii) the effect of the magnetic field on the sheath near the cathode wall should be taken into account; (iii) the radial diffusion of charged particles is affected by the magnetic field strength; (iv) the magnetic field effect on the IPC is emphasized for low gas-flow rates (longer IPC). Figure 15A presents the V(Z)characteristics for a long discharge (14) with a high gas-flow rate (very short IPC). Thus, the magnetic field acts mostly on the external column; the rather high values of the magnetic field strength insure that column confinement is well achieved. The V ( I ) characteristics are seen to displace upward as B increases. We consider this effect to be mainly due to the constriction of the external column. The field X , in this column varies as l / o R 2( I , total discharge current; R , column radius; o, external plasma conductivity). The conductivity is not affected by variations of electron density and the B effect on T, is not expected to be important (46b); then X, should vary as 1/R2. In the present case the phenomenon is emphasized by a very long column (3 m), but it is still a rather small effect, since the observed 20 V increase in the discharge voltage represents only a 0.07 V/cm increase in the axial electric field. It must be noted that in this case the current for minimum voltage is lower than 100 A, and is not represented in these characteristics. Figure 15B represents the V(2)characteristics for the same discharge, now for a very low flow rate (long IPC). First of all we notice a global increase in the discharge voltage (as compared with the former, high flow rate conditions), due to the voltage drop in the IPC. In this case, too, the V(Z)characteristics are generally displaced upward for increasing B ; however, the curves have changed their shape and the magnetic field effect is in this region strongly dependent on the discharge current. This may be considered as a consequence of the phemonena occurring in the IPC; however, their intrinsic complexity does not allow for a convincing explanation of this effect. Finally, Fig. 16 shows, forlow values of B, the transition between the diffusion-type external plasma and a well-confined plasma column. It occurs at B 50 G for this experiment; when transition takes place, the Ar plasma changes color from pale pink [(Ar I) dominant], to bright blue (Ar 11) as the column takes shape. In general, when the plasma becomes confined the discharge voltage will decrease; in some cases, a change in the anode drop may reverse this phenomenon. The onset of magnetic confinement can be observed by imposing an alternating current on the magnetic coils and recording simultaneously the variation of the discharge voltage and current (for a given external circuit

-

v (V) 100 1510 G 90 1330 C 80

940 G

70

570 G 360 G

60

o = ~ .a tcm cm'sec'

50

0

0

100

200

300

I(A)

V(V) 150

140

1510 G

130

1330 G

120

940 G 360 G

110

100

0 '0

I

I

100

200

, * 300

1(A)

FIG. 15. V ( I )characteristics as a function of the magnetic field strength for two gas-flow rates ( R = 20 mm, L = 300 cm). From Can0 er a[. (14).

HOLLOW CATHODE ARCS

a0

-

60

-

20

-

20

-

0

/

B=o

B=50G B=1OOC B=4OOC B = 200 G

20

0

113

40

60

[(A)

FIG.16. Effect of the magnetic field in the range where confinement occurs, for deep plasma penetration inside the cathode channel. ( Q = 0.2 atm cni3 sec-’, R = 1.45 mm, L = 21.5 an). From Delcroix ef 01. (6, p. 405).

and fixed supply voltage). The result of one of these experiments is presented in Fig. 17. It shows that minimum voltage and maximum current occur when the magnetic induction reaches a certain critical value B,. For a given maximum current and fixed gas-flow rate, B, was found to vary inversely

125 G 0

25 A

13 6 A

( 5 r n sec/dlvision)

FIG.17. Alternating magnetic field effect on the V U ) characteristics. Urnax = 25 A, R = 1.05 mm, Q = 0.14 atni cm3 sec-’,f- 50 Hz). From Delcroix et nl. ( 6 , p. 415).

114


with the cathode channel radius; its order of magnitude corresponds to Larmor radii of a few millimeters, for electrons of 2-5 eV (3).

3. Efect of the Vessel Pressure (pE < 0.1 Torr) For large diameter vessels and magnetically confined plasmas, the V ( I ) discharge characteristics are not affected significantly by changes in the vessel pressure provided it is kept below a few tenths of Torr ( N regime). The reason for this is that the neutral gas density is not higher than a few times 10'' cm-3 in these conditions? and so the external plasma behaves like a highly ionized one. Its parameters are then determined by the Coulomb collisions, and the electric field is almost independent of the gas pressure. The situation is slightly different if no external magnetic field is present. The plasma fills the vessel volume, and the electron density at the axis may drop to 10'1-10'2 cm-3 (46), depending on the discharge current and vessel diameter. The external plasma is then an " intermediate " one (33, p. 92), and the electron temperature now depends on the neutral density. Increasing the gas pressure in the interelectrode space enhances the radial diffusion and consequently the recombination upon the vessel surface increases; a higher electric field should result. The impact of this effect on the total discharge voltage depends on the interelectrode length and on the overall cathode fall; it may be totally negligible for short arcs. 4. EfSect of the Gas-Flow Rate and of the Cathode Diameter

Increasing the gas flow rate in the N regime while the gas pressure is kept constant generally causes the discharge voltage to decrease for a given current (Fig. 18). The same effect is observed for decreasing cathode diameters (6, p. 417). The very important dependence of the discharge voltage on the gas-flow rate and on the cathode diameter, must be ascribed to the varying length of plasma penetrating inside the cathode channel [which is very sensitive to those two parameters (see Fig. 5 ) ] . Obviously, the external plasma and the anode fall cannot play an important role in the matter. Further confirmation lies in the saturation of this effect for higher gas-flow rates (Fig. 19). When the active zone is located at the tip of the cathode, the overall cathode fall is minimum for that cathode and a further increase in the flow rate yields no change in the discharge voltage.

t The temperature of the gas in the vessel is something between 300 K (wall temperature) and 2500°K (cathode temperature). The corresponding densities for pt = 0. I Torr are 3 x 1015 and 4 x ~ m - ~ .

115

HOLLOW CATHODE ARCS 180

-

'*,

v (V)

140 160

J

'2,

'< z ,.

\I

+?--x-*-a+

100 80 -

~-

120

60

-

20 -

40

0

1

1

I

L

I

1

I

1

I

1

I

1

FIG.18. Influence of the gas flow rate Q on the V ( I ) characteristics. ( R 7 mm, B = 8 7 5 0 G , L = lOOcm,deuteriuni).* 5.0ati1lCm3seC-', ( . ' 4.0atnicm3sec-', 0 3 . 0 a t m 1.5 atm cni3 s e c - ' . From Gibbons and Mackin (44, 2.5 atm cm3 sec-I, cm3 sec-', p. 1775).

r

70

lo

-

0

t

0

0.5

I

I

I

1

1.5

2

a (otm

cm'sec')

FIG.19. Influence of the gas-flow rate Q and thc cathode radius R on the discharge voltage ( I - 15 A, E = 400 G ) . From Minoo (31, p. 79).

I16


In the lower limit of gas-flow rates, the N regime changes into the LQ mode, without an external positive column (maximum wall temperature at the tip of the cathode). It presents a higher voltage than the N regime for the same current. B. The External Plasma

1 . Releoant Parameters From the point of view of the external plasma, a hollow cathode can be considered to behave simply as a high-density plasma source; the outside positive potential is only needed for an electron current to be drawn. The mechanism of plasma production is irrelevant for the time being; it may be reasonable to postulate that no ion current is supplied by the external plasma tothecathode region once the N regime is properlyworking (see SectionV, C). Thus the first logical parameter to consider is the magnitude of the electron current drawn from the cathode itself, which roughly equals the total discharge current. The second relevant parameter is the gas pressure in the cessel, supposed to be low in the N regime (pE < 0.1 Torr); its exact value is determined both by the total flow rate injected into the vessel and the pumping capacity of the vacuum system. The mean free path for collisions between neutral particles is, for this pressure range, greater than 1 cm and possibly as large as several meters. In these conditions strong pressure gradients are not expected inside the vessel, unless deliberately introduced by baffles and differential pumping. The plasma density at the discharge axis and its radial gradient depend strongly on the confining situation; an axial rnagnetic$eld is either present, producing a confined plasma column, or is not (diffusion-type plasma). In a less pronounced way, the density at the axis depends on the anode geometry jointly with the arc length (a short arc with a ring-shaped anode, or a distant end-anode, are two extreme situations). As the external plasma column in an HCA is not fundamentally different from plasmas created by other devices (47), we shall limit ourselves to brief comments on the reported data.

2. Electron Densify The electron density for HCA in the N regime is found to vary between 10" and 10" cm-3 for nonconfined plasmas at moderate discharge currents ( I < 100 A); for confined columns, n, reaches from 10" up to some ~ m - ~ .

Table I1 shows a summary of the results obtained by various authors. The

TABLE I1 SUMMARY OF

Ref.

Authors

(12) Ahsmann et al. (51) Aldridge and Keen (13) Boulassier et a / . (14) Can0 et a/. (52) Flannery et ai. (50) Gerry et a/. (44) Gibbons (40) Gritzmacher et al. (15) Hudis et a/. (17) Kretschmer et al. (53) Leonard (53) Leonard (11) Lidsky er al. (54) McCormick (16) Morse (55) Noon e f al. (56) Roberts and Benett (46) Van der Sijde (57) Silk a

PE (Torr)” 10- 4-1 0 - 2

-

10-4

* 10- 4-2.10-

1

10-3 2 x 10-4 10-5**

I(A)

T, (eV)

TI (eV)

Diagnostic method

7-8

25

1000-2350

1013

5.5

30-50

700-2800 360-1510

1-6 X lo‘.’ 1.2 x 10-14

2.5-7 1-5.5

-

Microwaves; probe Microwaves; emission; probe

> 1013

2-15 L 8 50

0.2

15-20

Double probe; emission Thomson scattering Emission ; microwaves

3-5 3.8

0.40.8

250 5

IN0 150

150

-10-3 ,10-3***

-

n, (cm-j)

-

5 x 10-4

several 10-3 1-2 x 10-3

EXTERNAL PLASMA

-

20

10-3-10-4

B(G)

THE

60-80

4 x 10-5 3.15 x 10-4

1.2 x 10-4 10-3-10-4

MEASUREDDATAON

530 25M50 7000

14x 1-2 x

1013

1014

I -2 10’2 1013

-1 1-2 x 1013

** deuterium; *** h e l i h .

4

0.2-2 0.3-0.6

Spectroscopy; double probe

Plasma scanner Spectroscopy; probes Microwaves; emission; probe Spectroscopy Spectroscopy Probe Probe Probe Probe Retarding potential Spectroscopy; microwaves Spectroscopy

118


electron density increases with the discharge current. (It would be proportional to it (16), if the drift velocity were independent of the current.) Likewise, increasing the magnetic field causes the plasma density to increase at the axis; however, a saturation effect is observed for higher values of B. Figure 20 presents typical results of Van der Sijde (46a), obtained by

0 E N D ANODE 2 0 A 0 E N D ANODE GOA

*

lo'L

10"'

'

210

do

6tO

8;:"

,*:lo

RING ANODE 2 5 A RING ANODE 1 5 6

1 2 : J O ; T ( . - ; )

FIG.20. Electron density vs. magnetic field strength, for different values of the discharge current and anode geometries. ( R = 1.25 mm, p s = 1.25 Torr, vessel diameter 30 cm). From Van der Sidje (460, p. 1533).

phase-shift measurements with a 70 GHz interferometer. Two anode geometries have been studied: plain end-anode, and ring-shaped anode. In this figure the effect of confinement by the magnetic field is observed to set in at about 100 G, where the plasma density grows steeply by two orders of magnitude; the saturation effect begins around 400 G . The effect of the discharge current is also apparent in this figure. The radial profile of the electron density is represented in Fig. 21, by the same author (46b);the constricting effect of the magnetic field is very important at the onset of confinement, becoming less so as B increases. The efolding radius for the electron density is in this case around 18 m m for the higher magnetic fields. The effect of the vessel pressure on the plasma density (and on the plasma temperature as well) may be observed in Fig. 22 [from Hamawi and Lidsky (@)I. It concerns a magnetically confined, differentially pumped HCA in argon; 11, and T, were determined at various radial distances r from the axis by probe measurements, for vessel pressures varying from 2 x to 7x Torr. As the pressure increases the electron temperature is observed

119

HOLLOW CATHODE ARCS

"0

5

10

15

20

30

25 r(rnrn)

FIG.21. Radial profile of the electron density for different values of the axial magnetic Torr). From Van der Sijde (466, field (plain-end anode) ( I = 60 A, pE -:= 1.25 Y p. 1512).

to reduce; this may partly account for the corresponding increase in plasma density on the basis that radial diffusion in a highly ionized plasma is an increasing function of the electron temperature. This point of view is supported by the higher density gradients observed on the constant-p curves, on the left-side of the diagram. External ionization (enhanced at higher vessel pressures) may contribute also to increase the electron density. The factors that caused T, to be a decreasing function of the vessel pressure are dealt with in the next section.

3. Particle Temperatures The external plasma of HCA in the N regime at low vessel pressures displays electron temperatures commonly ranging from 1 to 10 eV, while the ion and neutral temperatures are somewhat lower, typically some tenths of electron volts for Tit and T o .Figures 22-25 and Table I I present some typical results concerning these three temperatures and their dependence on the experimental parameters: discharge current, magnetic lield strength, and vessel pressure.

t In the very high current (150 A), high magnetic field (4 kG) HCA reported by Kretschmer et a / . [17], TI was found to reach 10 eV; even if strong instabilities were present, causing abnormal ion heating, this value seems much too high.

120


i pE= 7 0 ~ 1 0torr -~

f

I

I

" 0

2

4

6

8

(0

'.

(8V)

FIG.22. Dependence of n, and T. on vessel pressure; results from probe measurements at fixed radial distances r from the column axis (magnetically confined HCA in argon). From Hamawi and Lidsky (48, p. 134).

The effect of the discharge current upon T, , T i , and To is represented in Fig. 23. T, is observed to present a small increase for growing currents, while Ti and To are obviously most influenced by this parameter, presenting in this current range a steady increase without any tendency to saturate. Figure 24 shows the effect of the magnetic field strength. Comparison with Fig. 20 (17, vs. B in the same conditions) shows that the region between 100 and 400 G corresponds to a sharp increase of the electron density; in this range, T, decreases by about 30%, while Ti a n d To both increase at a much larger rate. In the higher magnetic field range, To stabilizes, Ti and T, increase with about the same slope. Figure 25 concerns the effect of the vessel pressure pE upon the ion temperature at constant discharge current and for two values of the magnetic field strength. It shows that the pressure does not affect Tisignificantly in the range considered.

121

HOLLOW CATHODE ARCS T

( OK:

50x10’

LO x 10’

30x10’

*’ *‘ 20x10’

10 x103

0

0

L

1

I

1

I

20

LO

60

80

100

I (A)

FIG.23. Effect of the discharge current o n T,, T i , T o . ( B = 900 G , pa = 1.6 x Torr, ring-shaped anode). From Van der Sijde (46c, p. 718).

Returning now to Fig. 22 we see that, at constant I and B, the electron temperature at a given distance from the discharge axis, decreases when the vessel pressure is increased; it must be kept in mind that the plasma density varies in the opposite sense. The above experimental results are not easy to account for in a quantitative way, as all the measured quantities are interdependent; however, some additional considerations may clarify this problem. Following Hudis et af. (IS)the three temperatures T, , T i , T o , are related through the energy balance equation for the ions. Postulating that the ion temperature is the result of their heating by the Coulomb collisions with the electrons (considering the external plasma to be a highly ionized one), and the cooling effect due to kinetic energy transfer during charge-exchange collisions with neutral particles, one can write, in steady state:t IIi(d/dt)(Ei)

=

R,i - Rio 1 0 ,

t The validity of this equilibrium is insured by the long lifetime of the ions in the column, as they are repelled at the anode by the space charge and pushed away from the cathode by the gas flow.

122


44 -

LO

-

32

-

24 -

16 -

8-

170

500

1000

1500 B(G)

FIG.24. Effect of the magnetic field on T,, Ti, To. ( I = 75 A, pr: = I .25 x ring-shaped anode). From Van der Sijde (460, pp. 1533, 1534).

Torr,

where Eiis the average energy of the ion population, and R e i t Ri,are the energy exchange term for electron-ion and ion-atom collisions. It is, or course, surmised that other independent heating processes for the ions are not present (like ion cyclotron resonance, for instance). In those conditions T, > Ti > T o . This problem cannot be solved in a self-consistent way without determining the electron and neutral particle temperatures. With an almost field-free external plasma, the electron temperature is mostly determined by processes in the internal positive column ; there the electrons emitted by the cathode wall are accelerated by the cathode sheath potential (in a long IPC it can reach 40-50 V). Their energy decays afterward

G

123

HOLLOW CATHODE ARCS

1 0.71 A

(ev)

0.8

-

=2'akG

0 6

k

4

'

1

2

:

0.4 0.3

-

o0.10

.

3

5

7

z

9

11

13

15

P, (los4 Torr)

FIG.25. Effect of the vessel pressure on the ion temperature, for two values o f the magnetic field ( I = 40 A, differential pumping, hollow anode). From Hudis et al. (U, p. 3298).

through successive elastic and inelastic collision with the neutrals inside the cathode channel. At the beginning of the interelectrode space, the electrons present a thermal energy between 2 and 10 eV; possibly, a population of fast electrons up to 50 eV is still present. This high-energy tail will wear off along the plasma column, due to inelastic collisions with the neutrals and Coulomb collisions. The latter achieve the Maxwellianization of the distribution function with high efficiency, for the corresponding mean free path is typically 1 cm, smaller than the plasma dimension. In those conditions, it is expected that the value of T , in the external plasma does not differ strongly from its value in the cathode region, even if somewhat lower; its exact value depends on the losses by collisions and on the lifetime of the electrons in the column before collection at the anode, or surface recombination on the vessel walls. As to the neutral particle temperature its radial profile is determined by a radial heat conduction equation, taking into account the boundary condition To = Twa,,for r = R,,,,,, , and the heat-transfer processes in the central region of the discharge, mainly, charge-exchange collisions with ions in the column,

124


longitudinal heat conduction along the discharge axis, and gas heating inside the cathode channel. Gas-injection conditions into the vessel and neutral gas pressure are obviously relevant parameters for the radial profile of T o . Commonly accepted values of To include (a) ambient temperature, as it would be imposed by the vessel walls (15) (300”-400”K), which seems too low a value for the central region of the discharge; (b) around 2500”K, as it would result from thermal equilibrium with the cathode wall-which is reasonable for cathode-fed HCA of short length, at low vessel pressure (32); and (c) up to the order of 1 eV (46b) if strong heating from ion collisions is expected. If, on the other hand, T, and To are considered to be known through measurements, the ion energy balance equation may be used to do a n independent check of Ti. Referring now to the ion energy balance equation, the terms corresponding to the electron-ion and ion-neutral energy transfer, respectively, may be written as (49, 58) qc2qi2 n, ni me In A ( 1 - Ti/Tc) R CI. = ‘ 271 cO2(2nm, K TJ“’ mi Rio N (8/n)’i2n, no ci0[(KTo+ KT,)/mi]”2(kT, - kTo), where oio is the charge-transfer collision cross section between ions and neutral atoms. For steady-state

where T, is a reference temperature for comparison of the Coulomb cross section with the nearly hard-sphere cross section for the neutral-ion collision; T, is given by

or, in more practical form

lo4

T, (”K) = 6.6 x

where A is the atomic mass of the gas (40 for argon). On the basis of the preceding discussion, let us consider To and Te to be determined independently so that their ratio ( a = To/Te< I ) is a “known” quantity; we calculate Ti= x T, from the equation 1-x

(s- a)(..

+

which we solved numerically (Fig. 26).

2

125

HOLLOW CATHODE ARCS

'

P=Ti'Tp

:To / T , = 0.5

0 '

I

I

I

0

5

10

15

FIG.26. Diagram for the theoretical prediction of the ion temperature and the ionization degree are known.

I

)

20

c ,when T,,T o ,

Considering In A to have only a small dependence on n, and T,, we take In A = 10 (59) and, for the argon gas c,"= 7 x lo-'' cm2 for Ti < 10 eV (60); then T, N 104"K, of the same order of magnitude as the electron temperature in HCA, even if somewhat lower ( T , -2-5 eV). Then, the interpretation of the curves of Fig. 26 is straightforward. When the plasma in the external column is highly ionized (low vessel pressure, magnetically confined column), the situation fits the left-hand regions of the plot where T , approaches T, (.Y -+ I ) , becoming significantly higher than To (x > a); in the opposite situation (higher vessel pressure, nonconfined arc) Ti To (x a), being much smaller than T,. Finally, let us remark that the ion temperature is extremely sensitive to small variations of the vessel pressure, in the highly ionized region of the diagram [small values of (n,/n,) (T,/Tc)2],while for lower ionization degrees it must be almost independent of the vessel pressure. These conclusions are consistent with the experimental data presented in Figs. 22-25; however, a poor accuracy is expected if T , were evaluated from

- -

126


the balance equation.7 I t should further be noticed that the neutral gas temperature is the most difficult to evaluate experimentally and is subject to large uncertainty (46b);obviously thevalues we have been considering concern the gas temperature in the plasma region, as it would be measured spectroscopically. To conclude this section, we must remark that several authors (f2,14, 46, 61) have studied the influence of the gas-flow rate on the external plasma parameters. Unfortunately, as far as we could ascertain from the reported data, those experiments were made without the precaution of keeping the vessel pressure constant while the gas injection was varied; thus, it is difficult to ascribe the reported effects to the gas-flow rate variation, or to the joint effect of changing the vessel pressure.

C. Oscillations and Noise in HCA 1. General Coninients

Let us now review the reported data on the noise and oscillations in an HCA. Generally speaking, the external plasma may display different kinds of spontaneous density fluctuations such as plasma rotation, possibly with deformation of the cylindrical shape of the column, coherent oscillations, possibly nonsinusoidal (discrete spectrum), incoherent oscillations in some frequency bands (continuous spectra due to random fluctuation of phase and amplitude, causing uncertainty in frequency definition), wide spectrum, random oscillations (white noise). The study of these different kinds of oscillations has been the subject of many reports in the literature, dealing mostly with the description and identification of the nature of the observed fluctuations and trying to find their origin. If one succeeds by proper means to damp nearly all kinds of oscillations, then a quiescent plasma can be obtained with an HCA. The experiments are generally conducted by picking up the fluctuations of density with adequately biased Langmuirprobes. Direct frequency measurements are possible for quasimonochromatic oscillations, or with a wave analyzer for coherent oscillations, but only if the background noise is not too high; otherwise, autocorrelation of the measured signal yields the corresponding power spectrum through Fourier transform. Central frequency and linewidth measurements are then straightforward. Proper identification of

t Such a n attempt is reported by Hudis ei ol. (15). with qualitative agreement between experimental and calculated values of T , . I t should however, be noticed that the authors considered To == 400 K , which seems too low a value in the plasma region. The balance equation presented here is believed to be niore accurate for computing T , .

HOLLOW CATHODE ARCS

127

modes requires the use of adequately placed probes along the plasma; cross correlation techniques provide detection of phase shifts between different points. This way, the propagation path, the direction of propagation, and the azimuthal mode number of a given wave can be inferred. Rotation velocity of a fluid of ions can be measured spectroscopically as the corresponding lines will be Doppler-shifted with respect to reference emission; deflection of a movable device and streak photography can also be useful to measure rotational velocity (5f). 2. Arc Rotation Although arcs are known to display rotating instability, generally associated with hot spot motion, HCA plasmas have been reported to rotate, even if a localized hot spot is absent. The aximuthal macroscopic motion of the charged particles may deform the cylindrical shape of the column, so that a “Jlutelike” rotating vane may develop as in the experiment described by Morse (16). In this experiment, probe measurements in the region outside the central core of a magnetically confined HCA showed rotation for B > 350 G; at the same time, the plasma grew eccentric in relation to the axis, as shown in Fig. 27 A. The angular velocity was found to be an increasing function of the magnetic field strength, corresponding to about 2 kHz. The author suggests this motion to be due to an E x B drift which is compatible with an outward directed radial electric field; evidence of this is presented in Fig. 27B, showing an inversion of E, outside the plasma core, as compared to the inward E, before the instability appeared. Previous theory by the same author predicted that, for the calculation of the rotation period

T,

= 2nBz/E,

one should take E, = 0.9 E,, where E, is a “corrected” field given by:

where Eo is the measured (outward) radial field; r o the e-folding distance for the unperturbed density gradient; W T is the product of the cyclotron frequency with the collision time of the relevant charged particle upon the neutrals. In Fig. 27C the calculated period is seen to agree fairly well to the measured one. It is interesting to note that in this experiment the plasma did not rotate in the central core of the column, while a somewhat similar instability reported by Hudis ei al. (62) behaves differently. Again a rotating azimuthal rn = 1

128

JEAN-LOUP DELCROIX AND ARMAND0 ROCHA TRlNDADE

“1

1000

CALCULATED

I

MEASURED

t

012

300

1

400

500

600

700

-

B(G)

FIG.27. Plasma rotation in two experiments. From Morse (16, pp. 51 8,519) ( I = 10.5 A, Torr, R = 1/16 in., L = 13 in). A. Lines of constant density ( m = I ) ; B. space potential before and during unstable regime (f= 2 kHz); C . measured and calculated rotation period. From Hudis et. a1(62, p. 199 63). D, E. Sense of rotation and corresponding space potential (f=8.4 kHz, in = 1); F. Sense of rotation for a smaller magnetic field ( m = 2, f= 2 X 25.4 kHz).

p ~ 6= X

HOLLOW CATHODE ARCS

I29

instability (f=8.4 kHz) is observed but in the opposite direction, only compatible with a Hall drift if E, is pointing inward (space potential increasing with radius). As a matter of fact, this situation occurs in this case (63, with the further detail that inversion of the field in the plasma core causes it to rotate in a reverse sense with respect to the periphery. Figure 27 D,E provides data for comparison of both experiments. Furthermore Hudis et al. (62) report that an m = 2 azimuthal rotation ofthe core of the column occurs a t f = 2 x 25.4 kHz for a threefold reduction of the magnetic field strength without apparent rotation of the plasma periphery (Fig. 27 F). The sense of rotation would again be compatible with E, pointing inward. However, as stated in another report on the same experiment (64) the authors believe the instability to be caused by a drift wave due to a radial density gradient; Hall rotation would be, with this point of view, a superimposed effect, increasing the measured frequency (see Section V, C, 3). Quite the opposite point of view is taken by Aldridge et al. (51). Theory by these authors shows how a Hall-induced rotation can create growing instability, with a frequency and a growth rate closely related to the rotational E x B velocity. This angular velocity is given by [see also Boeschoten and Demeter (61)] wR =

- V,/r

I

+ (I/%’) + ( VE/rw,)’

where Y E is the azimuthal drift (Hall) velocity due to the radial electric field, and a is the product w ,T ,(gyromagnetic frequency and collision time pertaining to ions). This expression is only accurate for w , < 0,.Using a plasma slab model ( B = B Z ,density gradient parallel to OX, drift along OY), with the assumptions that k, = 0, kZ = 0 (no “radial” or “axial” propagation), a I , k, = 177/r0 of the order of the inverse scale length for gradient of the unperturbed density, a, given by a = l / t i o (dn’ijax) one obtains an instability of complex frequency w with

< 0 ; this requires w,/a < 0 or, which presents a positive growth rate if Im (0) which is the same, EJa > 0 (density and space potential increasing in opposite radial senses). Experiments with a HCA yielded satisfactory agreement between theoretical predictions and measured data, as it is seen in Fig. 28.

130


12

-

-

0 -

4 -

-

0 .

f(kHz)' 25

PREDIC?ED VALUES

20

-

15

-

10

11

EXPERIMENTAL VALUES

-

5' 0

I

0.5

I

1.0

I

1.5

1

2.0

I

2.5

I

3.0 B ( k G )

(b)

FIG.28. Comparison between theory and experiment for an azimuthal instability induced by a radial electric field [I=25 A; Q ==2.5 atm cm3 sec-' (cathode) and 0.3 atm cm3 sec-' (anode)]. W , T ~G 1 in the cathode region, W ' T ~> 1 in the drift tube. (a) Rotational velocity at various radii vs. magnetic field strength, -__ theoretical predictions, . . . . measured data. (b) Frequency of the m = 1 instability vs. magnetic field strength. From Aldridge and Keen (51, pp. 10, 14).

Another experiment with a much denser plasma (2 x loL4cmP3) higher current ( I = 150 A) and magnetic field strength up to 5 kG, is reported by Krestschmer et al. (17). Plasma rotation is observed at a frequency of 137 kHz at 3.3 kG. However, the authors do not identify this rotation with the presence

HOLLOW CATHODE ARCS

131

or an E, x B drift, for the hollow anode they use is supposed to prevent important radial electric fields from building up in the plasma column. Instead they show, by means of the single-particle fluid theory, that the ion diamagnetic drift frequency wd corresponds to one-half the ion cyclotron frequency in the conditions when a maximum radial gradient of density is compatible with magnetic confinement. The value of this gradient (for w = coi/2) is given by (KTln

17

+ ycp) = $nrwi2.

This mechanism is only possible if the ion Larmor diameter is compatible with the arc radius (limited by the electrode dimensions); these conditions occur for this plasma. The most abundant species in this discharge is the ion A r f + ; the corresponding value of wi/2 matches the rotational velocity measured by the Doppler shift technique. Plasma rotation in the absence of an external magnetic field can also occur in HCA outside the N regime of operation; in the high-pressure regime, when pE > 10 Torr, an anode spot is observed to form. If a hollow anode is used, this spot rotates about the anode tip and the plasma column turns accordingly around the column axis (36); this is a known type of instability which is not characteristic of HCA (65, 66), and is more apparent at high current. The low-current regime, when a hot spot appears on the cathode tip, provides another example of rotational motion due to spot movement (21). 3 . Ion Acoustic Waces ldentification of ion acoustic waves is thoroughly convincing in the experiment reported by Gunshor et al. ( 4 5 ) . Probe measurements and cross correlation techniques have shown the following propagation characteristics of the oscillations in He, Ne, Ar, and Kr: (i) Frequencies (in the range of 2-12 kHz, depending on the gas) are inversely proportional to the arc length (Fig. 29A). Detection of no phase shift between probes at constant azimuth and radius, spaced along the arc, confirm the character of axially standing waves. (ii) Cross correlograms of signals from two orthogonally spaced radial probes at fixed abscissa display a rr/2 phase shift, thus showing an 111 = 1 azimuthal propagation, in the sense of the electron diamagnetic drift (axial B, inward it-gradient). The authors consider this to be a propagation at an angle to the axial field, possibly influenced by the plasma rotation. As the radial electric field is directed inward in this experiment, rotation occurs in the direction of the electron diamagnetic drift; allowance for ion diamagnetic " slip " must be considered.

132


A

f (kHr)

14

-

12

-

10

-

oo”o N e

8 -

0 246 I

20

-

10

-

I

I

1

I

I

c

I

5 -

Kr 2 -

1

I

I

I

I

1

1

D

FIG.29. Identification of an ion acoustic wave in an HCA: wave frequency vs. the reciprocal arc length and the atomic mass (I=20-30 A , R = 1/16 in., Q 0.11 atm cm3 sec- I , p e Torr). From Gunshor et a / . (45, p. 1764).

-

133

HOLLOW CATHODE ARCS

(iii) The oscillation frequency is found to be a decreasing function of the ion atomic mass M ; logarithmic plot offvs. M shows good agreement with a theoretical straight line with slope - 1/2 (Fig. 29B). (iv) Finally, the frequency is found to be almost insensitive to variations of the discharge current. As this is roughly proportional to the plasma density, a drift wave (density dependent) must be excluded. Experimental data quite agree with theory. The frequency for an ion acoustic wave propagation in these conditions is given by w = k , oD

+ (1 + kk,’, ,(ykTe/mi)”2 y kTe/miwi)

2 112’

where T, is the electron temperature, y the ratio of specific heats, wi the ion cyclotron frequency, k , , = n/L, k, = rn/ro, where m is the mode number (azimuthal) and L , y o , the characteristic arc length and radius. So, the rotational velocity is the net result of a Hall rotation in the E x B sense, deducting the ion diamagnetic velocity (which is in the opposite sense because E is inward). With the proper values (measured) of B and ro (where the density gradient is maximum), and with an accommodating factor 1/2 for the measured radial electric field, kLt>Dis found to be about 1.5 kHz, in good agreement with the ordinate at the origin on Fig. 29A. The ion acoustic waves appear at relatively low vessel pressures. If pE is increased, the line profile is observed to broaden and a drift wave appears instead (45, 55). 1lD

4. D r f t Waves

In the experiment reported by Chung et al. (64) already mentioned, identification of an unstable drift wave follows from the evidence: (i) The wave is localized near the region of maximum density gradient ( y o = 2.2 cm) and the fluctuations decrease exponentially toward the axis ( r = 0). Figure 30A shows the mean square potential fluctuation vs. the radial coordinate. The result of a cross correlogram at constant abscissa shows an m = 1 azimuthal mode to occur, in the direction of the electron diamagnetic drift. (ii) The measured frequency falls within the range predicted by theory. Neglecting axial propagation in an inhomogeneouscollisionless plasma with an axial magnetic field B,, the frequency of oscillation of the drift wave (w 4 mi) rotating in the sense of the electron diamagnetic drift is given by w = u d with

134


(arb. units)

1

0

0 (

I

I

1

I

1

2

3

4

5

p h - ' Torr) E

b)

FIG.30. Identification of a drift wave ( m = 1) in an HCA ( B = 2 kG, T, = 3 eV; (l/n)(an/ar)= 0,5 cm-I). (a) Mean square value of space potential fluctuation and azimuthal wave number m, for different radial distances. (b) Measured wave frequency and electron temperature vs. vessel pressure p E. From Chung and Rose (64, p. 248).

The fact that this wave is superposed on a Hall drift with the same direction (E, inward) causes the measured frequency to be somewhat larger than the calculated wd = 5.5 kHz (for Bo = 2 kG, T, = 3 eV, k1-' = 2.2 cm, (l/n) (an/&) = 0.5 cm-'). The effective measured frequency of 8.4 kHz shows quite an acceptable agreement betweeen theory and experiment. (iii) As the plasma column is more constricted when B, is increased, the quantity [ ( k , dn/ar)/nB,] is expected to be almost independent of the magnetic field; wave frequency measurements at different values of B without

135

HOLLOW CATHODE ARCS

significant differences, support this point of view. However, one would expect the measured frequency to be affected by different values of Hall drift unless EJB, is (again) almost constant with B, . (iv) Dependence of the drift wave frequency on T, as predicted by the equation above was checked by independent measurements of o and T, while the vessel pressure was made to change. Figure 30B shows again satisfactory agreement as to this point.

5 . Coexistence of Ion Acoustic and Drft Waves Several authors (17,45, 55) have observed ion acoustic and drift waves in HCA either coexisting or changing into the other, by suitable (sometimes slight) variations of the experimental conditions. In an article by Noon et al. (55) a detailed study of conditions of existence was reported. The fundamental parameters were found to be the vessel pressure and the magnetic field, their effects being strongly related. Figure 31 illustrates this point. As can be seen, for a fixed magnetic field of 1 150 G, ion acoustic waves exist at the lower vessel pressures. Their amplitude drops Torr, while the drift wave amplitude is at first quickly in the range 1-2 x an increasing function of pressure, decreasing again beyond about 6 x Torr. At constant vessel pressure ( Torr) ion acoustic waves appear for B > 250 G reaching maximum amplitude for B 500 G. At the higher (6 x Torr) vessel pressure, drift waves are dominating, their amplitude increasing with the magnetic field strength. These results were theoretically predictable. Increasing B causes the plasma diamagnetism to be reinforced, as well as reducing the ion Larmor radius. Both effects are known to enhance conditions for instability of dissipative drift waves [see Kadomtsev (67),p. 991. On the other hand, both waves can be unstable at the lower values of gas pressure and magnetic field: the ion acoustic wave is damped for increasing pEand B (both parameters leading to higher plasma densities).

-

6. Other Types of Coherent Oscillations

Besides the oscillations reported in the previous sections, some other results are worth mentioning. Kretschmer et al. ( 1 7 ) (see Section V, C, I ) describe a hollow cathode, hollow anode arc at high magnetic field (4 kG) and discharge current ( I50 A). The high ion temperature measured in those conditions is related to the presence of important instabilities, namely an azimuthal m = 2 mode, corresponding to a traveling wave along the magnetic field. The wave propagates in the direction of the electron diamagnetic drift, with a wide spectrum and

I36


1

/

S

3

FIG.31. Simultaneous excitation of drift (D)and ion acousitc ( A ) waves in a HCA; amplitude (arbitrary units) vs. B and p e . From Noon el a / . (55, pp. 10, 14).

broad band of frequencies centered at 45 kHz; it is independent of the magnetic field strength. This is identified asadeceleratedAlfvPn wave(67,p. 84). This oscillation occurs with cathode gas feed. With anode gas feed only, a coherent oscillation, nonsinusoidal (eight largeamplitude harmonics) isobserved a t f = 14 kHz. It is an azimuthal m = I mode propagating in the same direction as the former wave, but its frequency is proportional to the magnetic field strength. It is identified as the driftresistiue wave compatible with finite plasma conductivity (67, p. 84). Again with gas feed through the anode a radiallypropagatingrn = Omode, axial standing wave is observed. It is the slow AlfvPn waue excited by the

HOLLOW CATHODE ARCS

137

B, x Vn radial diamagnetic drift ( B , is induced by the intense longitudinal current). With combined anode-cathode gas feed the coherent oscillations disappear, except in the range = I kG, where a m = I ion cyc/otron wave is observed. In a report by Chung ( 4 )axial , propagation of a n , f = 75 kHz wave (almost exactly the ion cyclotron frequency for the value of B used) was observed. This oscillation was nonsinusoidal, with a large amplitude of harmonics and was more intense in the central core of the plasma column. However, a small addition of gas feed through the anode reduced considerably the amplitude of the harmonics. For a magnetic field in the cathode region beyond a critical value (keeping constant B in the column), the oscillation disappeared. For values of B in the cathode region, far beyond this critical value, fluctuations were observed near the plasma edge. Both oscillations are identified as electrostatic rriodes propagating axially. The higher frequency wave ((0 wi) was found to have a phase velocity close to that of the ion acoustic wave. In a n HCA experiment reported by Minoo ( 3 0 , without magnetic field, coherent oscillations in the range 2-4 kHz were observed when a hollow anode heated by the discharge current was used. The oscillation frequency is a linear function of the discharge current and (approximately) of the vessel pressure, up to about 4 x lo-* Torr (where the oscillation disappears). The frequency varies inversely with the anode channel diameter which suggests that this electrode plays a n important part in the instability. Although it is not directly related to this section, where only self-excited oscillations were described up to now. we shall mention that several authors have studied wave propagation in HCA excited by external means. Ceglio ef al. (68) accomplished wave generation by means of a coil wound around the plasma column. using frequencies in the rf range t o perturb locally the applied steady-state B field. Waves were observed in the range near and above the ion cyclotron frequency; normally two superposed waves, a n ion acoustic and a fast wave were observed, propagating along the discharge axis and with n o phase structure in the transverse direction. N o cyclotron resonance effects were noticed. in spite of the product w i t i 2 5 being rather too large to d a m p the effects of resonance. I t is worthwhile mentioning the important work of Keen and Aldridge ( / 9 . 5 / . 69-72) in the field of nonlinear wave mixing in a n HCA. By means of a n externally applied electromagnetic wave. o r using a feedback technique with a suitably amplified part of a self-excited wave, reinserted in the plasma with an adequate phase shift, these authors were able t o enhance o r subdue plasma oscillations in the column and to determine experimentally the dispersion curve for drift waves in an HCA plasma. To excite density oscillations

-

I38


in the plasma, either magnetic field coils at different azimuthal positions or symmetrical plates around the periphery of the column, were used. When oscillations with suitable phase shifts are imposed at those points, different m modes can be excited easily. 7. Incoherent Noise Let us now examine the wide-spectrum noise in HCA. In an exhaustive study of oscillations in an HCA column, Noon et al. (55) present the result of a measurement performed in the situation when the coherent oscillations are unimportant (intermediate magnetic field strength, B = 770 G). The signal is picked up by a floating probe; its frequency spectrum is shown in Fig. 32A, for two values of the cathode gas-flow rate. Ascan be seen, the noise amplitude for this value of the magnetic field depends strongly on the vessel pressure, which in this experiment is determined by Q : a 20 dB decrease of the noise amplitude is observed whenp, ( Q )increases from to 7 x 10-4Torr. The amplitude of this turbulent noise spectrum shows a n f - ’ dependence for the most part of the frequency range. The dependence of the noise amplitude on the magnetic field strength is not explicitly described in this report; it is only mentioned that the incoherent noise level increases about 30%, in the conditions where the coherent oscillations are suppressed. This is done by a reinforcement of the magnetic field strength in the cathode region only. The same effect of the vessel pressure on the noise amplitude is described by Minoo (.?I), in an HCA without confining magnetic field. In the pressure range where coherent oscillations are absent, the white noise level is a decreasing function of the vessel pressure (Fig. 32B). 8. Noise and Radial Diflusion

Studies on instabilities in a magnetically confined plasma column are closely related to the problem of determining the radial diffusion regime. A collisional (“ normal ”) diffusion yields a transverse diffusion coefficient proportional to B - * ; with the onset of turbulence, radial losses increase and D, becomes proportional to 1/B (“enhanced” or Bohm diffusion) (72a). For a fully ionized plasma of different ionic and electronic temperatures, the radial ion flux Tr may be written (52), for the normal diffusion regime

ev .

a

r r =-el - [n,(T, - Ti)] new,’ ar

(Spitzer)

or

eve,

rr= - new,’ -(? ar [ n e ( T e- Ti)]- 12 n

’-“I ar

(Kauffman),

HOLLOW CATHODE ARCS

I39

NOISE R M S AMPL. (dB)

+ 20

i: 0.15

FIG.32. Epiect of the vessel prcssure o n the white noise amplitude. (a) White noise spectrum ( I - 20 A, B 770 G , R - I .58 nini). From Noon er rrl. (55, p. 481). (b) Relative amplitude of incobcrent plasma fluc[lS?tions ( B 0 , I IS A, R = 1.3 mm, L - IS cni). From Minoo (31, p. 45). ~

~

~

where ( J I ~is the electron cyclotron frequency. These expressions differ by a corrective term, the second one being in principle more accurate. The c~rihar~cetl iori ra(lialLflirx is given by

where the numerical factor

ct

is taken as 1/16 in the theory by Bohm (72m),

I40

JEAN-LOUP DELCROIX A N D A R M A N D 0 ROCHA TRINDADE

while Yoshikawa et af. (73) considers it as a function of the relative mean square density fluctuation, S CI =

$ITS

with

S

=

( ( n - no)2)/no2,

no denoting the unperturbed (quiescent) plasma density. The latter author establishes a criterion for the existence of one of the two possible regimes of diffusion. If one assumes that the mean square relative deviation of the density fluctuation, S, is independent of the magnetic field (which is not often the case, as we have seen in the preceding section), one compares it with the nondimensional quantity a, defined as the ratio of the collision and gyromagnetic frequencies a = v/w,

and one gets the desired criterion S % a -+ Bohm diffusion, S @ a -+ normal (collisional diffusion).

The validity of the above equations for an HCA depends on the degree of ionization, because they neglect the ion-neutral collisions. In a highly ionized plasma the equations apply and the diffusion is ambipolar. Otherwise, a radial electric field may exist or not, depending on exact experimental conditions (52). Several experiments report an inward-directed radial field or some volts per centimeter, although its exact value is not very accurately known, due t o the perturbing effect of the magnetic field (52, 55, 62). Indirect measurements of the radial diffusion rate are complicated by lack of accurate knowledge of other losses of charged particles (axial drift, volume recombination, charge-exchange collisions); on the other hand, the direct measurements are complicated since they tend t o introduce perturbations in the diffusion regime. However, some results are worth mentioning. Flannery ef a/. (52) use a diffusion wave technique to study the secondary plasma around the central core of the plasma column. The waves are excited by means of an alternating current superimposed on the discharge current (74). Measurements of the spatial distribution of the phase and amplitude of the radial traveling (diffusion) wave yielded data for comparison with the theoretical predictions of the various diffusion regimes. The collisional theory (Spitzer) seems the one t o best fit the experiment, when the plasma is quiescent (R = 0.318 cm; I = 5 A ; p E = Torr; B = 530 G ; L N 30 cm). In those conditions, the difference between the theoretical and (indirectly) measured diffusion coefficient is only 20% (D,= 2.8 lo3cm2 sec-' for the latter). When the magnetic field strength was different from this optimum value so that the plasma was no longer quiescent, measurements yielded a smaller phase shift of the radial wave, showing a higher diffusion velocity, consistent with a transition to an enhanced (Bohm-type) diffusion regime.

141

HOLLOW CATHODE ARCS

Hudis and Lidsky (75) used a one-sided, rotating probe t o evaluate the radial ion velocity in an HCA column (5 = 1.1-1.8 kG) ni(r = 3.5 cm) = 5 x 10" ~ m - T, ~ = ; 1-2 eV). The probe was positioned eccentrically ( r = 3.5cm), orthogonal to the column axis, so that its active side faced alternatingly upstream and downstream relative t o the radial ion current. From the difference AZsi between the extreme values of the ion saturation current, the electron temperature, and the plasma density, an appropriate relation yields the ion radial velocity ui A],' (L'(Ul/Uo)' - e-(Ux/Uo)2) u0 = ( 2 k T , / t ~ ~ ) ' ' ~ .

Using this technique, the radial diffusion rate is observed t o decrease strongly when the magnetic field strength is higher than a critical value ( B = 1.54 kG) (Fig. 33), showing a definite change in the diffusion regime. Simultaneous

3.9

-

3.3

-

2.7

-

2.1

-

1.5

-

0.9

-

-5

- L

- 3

FIG.33. Radial velocity and plasma density in the secondary region ( r = 3.5 cm) of an HCA column, as a function of the magnetic field strength. Radial velocity, 0 plasma velocity. From Hudis and Lidsky (75,p. 146).

measurements of the density fluctuations have shown, by spectral analysis, that the higher diffusion rate region was associated with the presence of a coherent, f = 12 kHz instability, strongly damped past that critical value of the magnetic field strength. For the quiescent situation, the calculation of the diffusion coefficient agrees with the predictions of the collisional theory. A similar conclusion is drawn by Noon et al. ( 5 3 , ascribing the situation of enhanced diffusion to coherent fluctuations of the plasma density, rather than t o wide-spectrum turbulence. In their HCA experiment (R = 3.85 mm; I = 2 0 A; p E= Torr; B=200-2000 G), they found that the local

142


variation of the magnetic field strength at the cathode region determined the amplitude of an observed coherent oscillation identified as an ion acoustic wave. Variations in that amplitude were concomitant with substantial changes in the density radial profile, without significant differences of the incoherent noise level. Calculating the transverse coefficient D, from the knowledge of the e-folding distance, q, of the density profile, supports the viewthat enhanced diffusion is present. Since this coefficient is proportional to y 2 (SS), a q dependence on B - ' / 2 as they observed, means that D , is inversely proportional t o the magnetic field as in Bohm diffusion. Moreover, the magnitude of the calculated coefficient is considerably higher than collisional diffusion predicts, again suggesting an enhanced diffusion. Can0 and Mattioli (76),working with an arc of higher density and higher neutral pressure (I = 250 A ; Q = 8.5 atm cm3 sec- I ) and without the presence of instabilities, calculate the diffusion coefficient in the two hypotheses of normal and enhanced diffusion and find them to be, for their experimental conditions, of the same order of magnitude. They raise an interesting point: since in some conditions the plasma density can increase almost linearly with the magnetic field strength, the normal diffusion coefficient, proportional t o n/B2, can present a n overall dependence as B - ' , yielding the misleading conclusion that an enhanced diffusion might be present. Working with lower gas-flow rates ( Q < 1.4 atm-cm3-sec-'), these authors found that the density fluctuations increase substantially and that in those conditions Bohm diffusion might be present, under Yoshikawa's criterion (S/a %- I ) . Direct measurement of the radial current can be made by means of a suitably biased auxiliary annular electrode placed around the plasma column. Extrapolation of data obtained with variable bias, in the very low bias range, can yield information on the diffusion regime. Yoshikawa and Rose ( 7 3 ) report such an experiment; the ratio I/Vfor the auxiliary ring electrode should be proportional to either n / B or n 2 / B 2 , according to the regime of radial diffusion. The authors find that classical diffusion is present in the lower range of magnetic field strength. and approaches the theoretical predictions of Bohm diffusion when the magnetic field is increased. This is in accordance with the already mentioned criterion t o distinguish between Bohm-type and normal diffusion (S/a % I =+. large magnetic fields correspond t o enhanced diffusion). Figure 34A illustrates the results of this experiment. A similar experiment was performed by Chung and Huang (77) using a ring collector composed of four identical parallel thin rings, the two inner ones being biased with respect to each other, and the outer ones floating so that the diffusion regime is not disturbed. Figure 34B shows the collected current; a transition is observed to occur at a magnetic field of about 1.2 kG. I n the same figure the relative rms density fluctuation is plotted as measured by probes at I .25 cm distance from the column axis. Clearly, the transition in the

143

HOLLOW CATHODE ARCS

o

-

I, (mA)

- n*

18

“0

10

0.2

0.1

TRANSITION

0

I

700

1200

1700

-

2200

B(G)

(b) FIG.34 Direct measurement of radial diffusion. (a) Voltage-current ratio for a ring collector; solid curves represent theoretical predictions. (Q= 1 atm cm3 sec- I, p c several 10 Torr, L 12 crn, I = 20-50 A S I , = 30mA). From Yoshikawa and Rose (73, p. 338). (b) Collected radial current and relative rms density fluctuation (Q= 1 atm cm3 sec-‘, p F - 2 i. Torr, L = 2 m, I = 20-40 A). From Chung and Huang (77, p. 35). ~

144


diffusion regime is related to the onset of an instability, in this case identified as an m = 1 ion cyclotron instability (f= 70 kHz). 9. The Quiescent Plasma Machine

Let us recall briefly some useful information about suppressing or subduing oscillations in an HCA, as it was presented in the preceding sections: ion acoustic waves, which may originate in the cathode region (55), are damped by a suitable increase of the magnetic field strength of the neutral gas pressure at the cathode region; drift waves can be suppressed by lowering the magnetic field strength or the vessel pressure at the column region(see Fig. 31); cyclotron waves do not exist at too low or too high magnetic fields ( 1 7 ) ; combined anode-cathode feed of the discharge tends to damp or even suppress some instabilities (17, 41). All these points are relevant to understanding the remarkable performance of the device designed by Woo et al. (18, 78) for the production of a quiescent plasma (Fig. 35). The machine is composed of a cathode region ( I ) and a drift REGION

REGION

- D R I F T TUBE R

E

t

l

O

N

d

CATHODEp FEED

ANODE

FEE0

FIG.35. Diagram of the HCA quiescent plasma machine. From Woo ef a / .(78, p. 13 I ) ,

tube region (3) separated by a short baffle region (2). The relevant parameter for the design is the product w i * t i(ion cyclotron frequency times collision time), which is made much higher than unity in the drift tube by means of an energetic pumping; in those conditions, the plasma tends to run quiescently. In the cathode region, when the gas flow imposes a moderate pressure, O ~ @ T ~1 is the normal situation. However, changing the local value of the magnetic field can suppress most of the instabilities. The transition between

HOLLOW CATHODE ARCS

145

the two zones is assured by an intermediate step in a region where mi T~ z 1 ; in this baffle region a universal instability can, in principle, exist (79),for long axial wavelengths. Thus, a short length of this region is unsuitable for this type of oscillation and we can expect the plasma to be quiescent in the drift tube. In such a device, relative density fluctuations as low as lo-’ were observed experimentally in the drift tube. Construction details can be found in Woo et a/. (78); a similar device is described by Aldridge and Keen (51).

D. The Cathode Region 1. Cathode Wall Temperature

The cathode wall presents a maximum temperature at some distance (measured from the tip), in the N regime. This distance is strongly dependent on the gas-ffow rate and on the cathode internal diameter (see Fig. 5); in a less pronounced way, it depends also on the discharge current. As t o the dependence on other experimental parameters: 1 is found to be independent of the vessel pressure p E provided it i s lower than about 0.1 Torr; a slight decrease i n the distance occurs in the case of a magnetically confined discharge, as compared to the case B = 0 (31, p. 74). This effect is only detected when I is long enough. Referring to Fig. 7 (Section 111, B). it will be noticed that the T(x) curves become flatter when 1 is made to increase at constant discharge current by gas-flow rate reduction; simultaneously. the absolute value of T,,, decreases slightly. This effect is qualitatively explained by the effect of a more extended ion bombardment of the cathode wall, compatible with a longer internal positive column. The higher sheath potential and corresponding enhanced ionization rate in the IPC balances the lower thermionic emission associated with the T,,, reduction. As to the influence ofthe discharge current upon the T(x) curves, lappears as a slowly decreasing function of I , while T,,, is observed t o be rather sensitive to increasing the discharge current density across the channel section, as is seen in Fig. 36 [(from Minoo (31)].In this figure T,,,ispresented as a function of 1 for various values of Q and various discharge current (longitudinal) densities (corresponding to constant I across cathode channels of different diameters). The cathode wall temperature is an important parameter for HCA in the N regime: its influence on the discharge voltage is very marked, as it can be seen in Fig. 37 (7). In the conditions of these experiments, the cathode wall temperature was varied as an independent parameter. by altering the heat balance at the cathode without changing the other experimental independent

146


Tmox

“C 1 240c

230(

220

210

FIG.36. Effect of the gas-flow rate and of the longitudinal current density (1,’s)on the cathode wall maximum temperature ( I = 1 5 A, B = 0,R = 1.8 to 3.3 mm). From Minoo (31, p. 81).

variables (vessel pressure, gas-flow rate, discharge current). This was done by means of tantalum tubular shields placed around the cathode to prevent cooling by radiation. The increase of cathode wall temperature produces enhanced thermionic emission, making operation at a lower voltage possible, as the figure shows.

2. Power Dissipation in the Cathode Region The total power dissipation in an HCA can be written as

w,=VZ=(W,+ w,+We),+(Wr+ WJ,+ w,,, where the capital subscripts refer to the discharge regions (cathode, external plasma, anode), and W,, W , , and We are, respectively, the radiation, the

147

HOLLOW CATHODE ARCS

60

V(V)

40

A

20

n

0

I

I

I

10

20

30

I

I(A)

40

FIG.37. Current-voltage characteristics, showing the effect of reducing the radiative loss (pyronietric measurement of temperature at the cathode orifice shows 10% increase for the shielded cathode). From Delcroix e/ trl. (7, p. 1560).

thermal conduction, and the electron emission dissipative losses. The latter concerns exclusively the cathode region. As the anode is. in most cases, a water-cooled one and is not emissive, the corresponding power loss is mostly caused by thermal conduction toward its holder. It was found by calorimetric measurements (6) that the power dissipation at the anode by this process represented about 607: of the total input power,? this value being almost independent of the gas-flow rate and of the discharge current (Fig. 38). I n the same figure is presented the result o f a similar calorimetric measurement for the cathode. Again its value ( 5':(; W , )is found to be independent of Q and I, keeping, of course, the same cathode geometry (thin-walled, unshielded cathode, R = 1.45 nim for this experiment). As t o the other terms of the above equation, it is easy to evaluate the cathode radiation loss

-

f Conditions for this experiment were: 1 20-50 A; B 400 G ; plain anode. A similar measurement i n an HCA with very different parameters (1- 150 A; B - 1.5 kG; hollow anode) yielded W,, 70%W, (17). 1

-

~

148

* 0.6

-

0.4

-


o

* O

Y

,t 0

0 0

. * 0

*

* *

*-*

WCA ’W!

0

* 0

0.2

I=20A

30A LOA 50A

-

FIG.38. Fractional power transferred at the cathode and anode regions, toward the electrode holders (thermal conduction), as a function of the gas-flow rate ( I = 20-50 A, B = 400 G , R =: 1.45 mni, e = 0.3 mni; plane end anode). From Delcroix et nl. (6, p.407).

where (Iext is the cathode external diameter, ~7the Stefan-Boltzmann constant and E ( T )the metal emissivity. This calculation, based on the experimental T ( x )curves, yielded a power dissipation by radiation of around 15-20 W , , which is a slowly decreasing function of the gas-flow rate. This result is quite understandable, as the cathode becomes more extensively hot as the gas-flow rate is made to decrease. As to the calhode wall cooling by electron emission a nai’ve approach would lead one to ascribe this effect to the thermionic current only; indeed, those electrons produced by wall emission require an energy ecp to be freed from the cathode material. However, it should be noted that every electric charge going through the cathode region causes a cooling effect on the cathode wall, the electrons produced by ionization in the channel being balanced by an equal number of ions which require the energy ecp to recombine upon the wall. Thus we,= Icp, cp being the work function of the cathode metal (4.35 V for tantalum); this amounts to about 10 ”/, W , ,

149

HOLLOW CATHODE ARCS

-

The remaining part of the dissipated power ( 10% W,) concerns the external plasma region, and is the most difficult to obtain by direct measurement. There, radiation occurs in the visible and ultraviolet range due to neutral deexcitation, radiative recombination, and e-i and e-o Bremsstrahlung radiation; calculations are, therefore, too complicated to be reliable. On the other hand, heat conduction toward the entire vessel surface is difficult to measure accurately enough, and we must not forget that neutral gas at a temperature higher than ambient is pumped away, without an obvious method of measuring the corresponding heat loss.

3. Cathode Voltage Drop V,; Minimuni Cathode Fall Vo It is possible to evaluate the overall cathode voltage drop Vc, either by subtracting from the discharge voltage the more readily measurable values of the anode fall ( VA) and of the external plasma voltage drop ( VE); or by the heat balance of the cathode region. The anode fall and the external plasma voltage drop are measured readily enough by Langmuir probe techniques; V, can also be accurately measured by changing the interelectrode distance, which provides a direct measurement of the axial electric field. The power balance at the anode WA = ( VA cp)I yields an independent measure of VA. The vicinity of the cathode region is not healthy to Langmuir probes, due to its high temperature; however, the heat dissipation at the cathode region is accurately known (see the preceding section) and yields the overall cathode drop v, = WJI.

+

Both techniques (difference and heat balance) yield comparable results (6, 21, 31, 32); the overall cathode voltage drop is observed to vary between 12 and 50 V, depending on the gas-flow rate; the higher values correspond to a deeper penetration of plasma inside the cathode channel (higher values of the distance I). It is reasonable to ascribe the increase of Vc to an axialvoltage drop in the internal positive column, corresponding to a longer IPC. Due to the geometry of the cylindrical hollow cathode, the equipotential surfaces must have the approximate shape shown in Fig. 39. Along the axis the electric field is purely longitudinal; in the vicinity of the cathode wall the field is radial and its value increases as /approaches zero (tip of the cathode). The effective length of the IPC is, of course, not accurately known; however, it must be related to the value of I at the maximum wall temperature (see Section VI), and we may take / as a reference length of the IPC. Thus, postulating an axial electric field of average magnitude X I along the IPC. and a "residual" voltage drop Vo in the extreme limit of the IPC ( x I), one can write vc = v o X , l

-

+

150

JEAN-LOUP DELCROIX A N D ARMAND0 ROCHA TRINDADE CATHODE

V.

I

4

I

X.1,

+i

vo/

t

X'L,

vc :vo

I ' \ ~~

~~

~

~

~~~~

1, = O (c1

FIG.39. Model for the equipotential surfaces inside the cathode channel, as a function of the flow rate Q. (a) Low Q, (b) moderate Q,(c) high Q.

with 1 '

and

L, being the total cathode length.

151

HOLLOW CATHODE ARCS

V , can be measured when 1 4 0 (high gas-flow rate); in these conditions V, z V , (see Fig. 39c) and one obtains V , = 10-12 V. This is called “minimum cathode fall” and its value is similar to the cathode fall of a classical cathode arc discharge, using the same combination of tantalum metal and argon gas. This value is confirmed by the following experiment. Let us vary the gas-flow rate Q so that different values of I are observed, while recording the total discharge voltage. If the vessel pressure and the discharge current are meanwhile kept constant, it is expected that the changes of the discharge voltage are not due to the external plasma or the anode region, but only to the cathode region. A plot of V ( / )yields the rate of increase of the cathode voltage drop as the IPC becomes longer. The result of such an experiment is presented in Fig. 40. From this plot it would be rather crude to infer that the IPC presents a uniform axial electric field along its length; it is more exact to consider the slope of V / l as the average value of the electric field X , along the IPC. Table I11 presents the values of X , for constant discharge current ( I = 15 A ) and various cathode channel radii. All values are fairly high (several volts per centimeter), decreasing with increasing diameter, as would be expected from a crude comparison with an ordinary positive column.

!.

(cm)

6

4

2

-

60

-

20

0

FIG.40. Discharge voltage vs. coordinate of the maximum wall temperature, obtained by varying the gas-flow rate at constant vessel pressure and discharge current, V / / - 8 V cm-’ ( R 1.45 mm, I - 20 A, B = 0). From Trindade ( 2 1 , p. 23). -

152

JEAN-LOUP DELCROlX A N D A R M A N D 0 ROCHA TRINDADE

TABLE 111 AVERAGE AXIAL ELECTRIC FIELDI N THE IPC“

R(mm) X,(V/cm)

1.05 10

1.3 8

1.45 7.8

1.8 4.3

2.3 3.7

2.8 3.3

a Measured by the growth-rate of the discharge voltage with the IPC length, for I = 15 A. From Minoo (31, p. 100)

The presence of a longer IPC is associated with an increase of the (radial) sheath potential near the tip of the cathode, where it is maximum (see Fig. 39); as a conclusion, we may state that the hollow geometry, allowing for a plasma column to form inside the cathode channel, provides a high sheath potential which is responsible for the large ionization activity of the wall-emitted electrons. Based on these results, we shall use for a simplified description of the potential along the axis of the IPC the expression

4. Pressure Drop Along the Cathode Channel The local values of the pressure along the cathode channel are important quantities to evaluate, since the direct ionization rate is a linear function of the neutral gas density. The latter is dependent on the gas temperature (another quantity to evaluate) and, through its relation with the gas pressure, on the gas-flow rate and vessel pressure. Direct measurement of the pressure along the cathode channel is not easy to perform, due to the high cathode temperatures; so, either this quantity is calculated for the gas-flow situation of the experiment or an “overall cathode pressure drop is directly measured, between an upstream cold region (where a pressure gauge can be inserted), and the discharge vessel. The calculation of the neutral gas density along the terminal length of the cathode channel (including the IPC) was done by Trindade (21) with the following assumptions: the reference pressure is taken at the exit hole, (x = 0) and p ( x = 0)= p E (vessel pressure); the neutral gas is everywhere in thermal equilibrium with the cathode wall (this is approximately true in most cases unless the gas-flow rate is too high);? the gas-flow regime inside the cylindrical tube of radius R is laminar (cf. Section IV, B) and is intermediate between a viscous and a molecular flow. ”

t Numerically, the length Llhthat the gas has to travel in contact with the wall to reach the local value of the wall temperature within 10% maximum error is given (for argon gas) (22). by Llh(cm)= Q(atm-~rn~-sec-~)/3

153

HOLLOW CATHODE ARCS

Under these assumptions one obtains the relation between the pressure at the points A and B (corresponding t o distances . y A , xBfrom the end) in a tube of average temperature T ,

R4 ( \ ? A ~- , O B ~ ) / ( X A- X,)

+ 2BR3

- P B ) / ( ~A XB) -

(/-’A

CQ =0

with

B

= 6.3kTm/a

and

C = 16qp0 Tn,lnTo,

where 0 is the elastic cross section between atoms; q is the dynamic viscosity of the gas; p o , To are the standard pressure and temperature; and Q is the STP gas-flow rate. Considering the theoretical dependencies of o and q on the temperature (84) one obtains, putting x B = o and p R = pE

where a(Tn,)and b(Tm)are the functions presented in Fig. 41A for argon gas. When the vessel pressure is low enough so that PE

G ( b / R )kTm

3

the equation above reduces t o

+

p(x)=(kT,b/R) {[a(xQ/R’)

- I}.

In Fig. 41 B we present the curves relating the neutral gas (argon) density n, = p / k T , to the flow parameters for three different values of the average temperature T,. Obviously, these curves apply only t o the regions where the cathode wall temperature is fairly constant; specifically, t o the hot zone of the cathode (say, T 2 0.7 T,,,), excluding the vicinity of the cathode support. Direct measurement of the overall pressure drop in the cathode channel has been performed by some authors, with interesting results. Minoo (80, 81) measured the pressure inside a large diameter cathode support at the entrance of the cathode channel (10 cm long, 2.6 mm i.d.), with the results shown in Fig. 42A. The vessel pressure was lower than lo-’ Torr and was thus negligible as compared with the measured values (of the order of tens of Torr). Measurements by Lorente-Arcas ( 4 2 )and Brunet (39) in similar conditions yielded comparable results, and are shown on the same figure (it must be noticed that the cathode dimensions are not the same and so, quantitative comparisons are not directly possible). In Fig. 428 the ordinate concerns the absolute pressure p I at one point inside the cathode channel; however, Lorente-Arcas (42) considers the pressure drop between this point and the region upstreams t o be negligible and, as the vessel pressure is also comparatively small, p , z Ap. As t o Fig. 42C, the right-hand side of the curves should

154

JEAN-LOUP DELCROIX A N D ARMANDO ROCHA TRINDADE

0.6

0.4

0.2

0

I

0

-

1000

1

100

I

80

2000

3000

LO00

I

I

L

60

40

20

T,PK)

-

0

(b)

FIG.41. Data for calculation of the neutral gas density (argon) inside the cathode channel. (a) Functions a ( T , ) ,b(T,); (b) no R vs. x Q / R 2 for different values of the average temperature T,,,. From Trindade (21, pp. 44,45).

be disregarded for the purpose of this comparison, since the vessel pressure in this regime becomes high enough to affect significantly the pressure in the cathode channel. In the discussion of these results, it should be kept in mind that the cathode wall temperature along the channel is dependent on the current density across the cathode section (see Fig. 36); and one can show that a thermal equilibrium is established between the flowing gas and the surrounding wall (unless flow rates that are too high are used (21)).Therefore, considering that

I55

HOLLOW CATHODE ARCS

A D (Torr)

t

50 25

0

p

=

1

2

3

crn3sei')

~p (Torr)

100

0.1 27 a t m c m 3 s e i '

a:i

23

75

(bl

50

25

*

I

I

I

0

10

20

30

j(Amm

3

0.0.6

0 0.01

I

1

0.1

1

lo

p (Torr)

-2

)

p, (Torr)

12

0

E

FIG.42. Pressure measurements upstream the cathode channel. (a) Overall cathode pressuredrop(R = 1 . 8 m m , B = O , p , - IO-'Torr)(BO, p.21).(b)Overallcathode pressure drop vs. current density ([is)(42, p. 183). (c) Upstream pressure p , vs. vessel pressure p , (39, P 22).

I56


for a constant mass flow through the channel the pressure drop for a given length is approximately proportional to T I , it is expected that the pressure gradient downstream is much higher when the arc is operating (T,,, 2500°K) than in the situation I = 0 ( T 300°K). In general terms, the pressure drop along the cathode channel must be an increasing function of the current density across the cathode section. However, while this temperature effect explains fairly well the difference between the curves for f = 0 and for f = 10 A, for instance (Fig. 42A), it fails to account for the separation between curves for 10, 20, 30, and 40 A (in the same figure), as the variation in cathode temperatures is a small effect for low and moderate currents. This causes a discrepancy to exist between measured and calculated values of the overall pressure drop, which are consistently lower. The following explanations for this " overpressure effect " are proposed. (i) Lorente-Arcas (42) and Minoo (81) consider the electron pressure at the active zone of the cathode channel to be responsible for an important increase of the total pressure at this level; this would cause a higher pressure to be measured upstream, where the gas is not ionized. Minoo (81)calculates the electron density which it is necessary to postulate in order to make the agreement, between experimental measurements and theoretical predictions, of the pressure drop along the channel; the resulting value of the plasma density, in excess of lo'* cm-3 seems a bit too high$ but cannot beexcluded. (ii) An additional effect can be ascribed, possibly, to neutral gas pumping due t o the charged particle drift, which may occur in the vicinity of the cathode and inside it. This effect is unfortunately rather tricky to analyze ( 8 3 , and the gross result is known t o depend on the precise experimental conditions, for it can operate in either sense (pumping into o r from the cathode channel). (iii) It is possible that, with very high flow rates, a sonic throat may occur at the channel exit (39);this would cause, again, an upstream overpressure not accountable by a straightforward Poiseuille-law calculation. However, this effect should not occur in most experiments, as there is no point in increasing the gas-flow rate more than is strictly necessary for N regime operation. (iv) Finally, we remark that all three experiments were made with rather high flow rates, which caused the IPC length to be very small (a few millimeters) and the T ( x )curves in those conditions to decrease steeply for x > 1. It is possible that in these conditions thermal equilibrium with the wall will not be reached; this is known to influence the radial velocity profile of

-

N

t This applies, for argon gas, to the range 1500 < T < 3000'K; for lower temperatures, the dependence is a slower function of T ( 2 1 ) . 2 The only measurement of the electron density inside the cathode channel, thoroughly reported, was done by laser interferometry along the channel ( 6 ) .It yielded 17. < 5 Y I O l 4 Another (briefly) reported result, without mention of the measuring method and no further confirmation, reached as high as 10Ih (82).

HOLLOW CATHODE ARCS

157

the gas stream, and the pressure drop calculations must be made carefully to account for this complicating factor. It would be very interesting to know if an “overpressure effect is noticed for lower values of the gas-flow rate. ”

vr. THEORY OF THE HCA I N THE N REGIME A . General Comments A complete, self-consistent theory for the HCA in the N regime should be able to explain qualitatively the various phenomena occurring in these discharges and, more specifically, should permit calculations of the discharge parameters when the values of the independent variables (materials, geometry, vessel pressure, gas-flow rate, discharge current or voltage, and external magnetic field) are specified. The most directly available experimental, dependent quantities are the discharge voltage (if the current is imposed, or conversely), the cathode voltage drop, and (most important in these discharges) the T ( x ) wall temperature distribution. It is possible to obtain full knowledge of the external plasma through appropriate diagnostic techniques; as to the plasma in the IPC, those techniques must be more elaborate and, so far, the reported data are extremely scarce. We think that an effort should be made on this subject, as any direct measurement pertaining to the plasma in the IPC could be very valuable indeed in assessing the peculiar mechanisms of the HCA. The difficulties of a self-consistent theory are mostly due to the longitudinal dependence of the parameters pertaining to the cathode channel. The ionization rate in the IPC depends on the local values of the neutral gas density, on the density of the primary (wall-emitted) electrons, and of their energy (sheath potential.) All those quantities may vary strongly over a length of a few centimeters. The density gradients and the separation of the charged particles determine the shape of the electric field inside the IPC and the ion current distribution upon the metal wall. Finally, the heat balance on the cathode surface, depending on the above quantities, should yield the T(x) curve, if enough accuracy was possible in the previous calculations. At the present time, to build such a theory would probably be too ambitious an aim, as the T ( x )function is the solution of a heat-transfer differential equation of the second order in T. To write and solve this equation, one would need a perfect quantitative knowledge of all the processes of heat gain and loss on the cathode wall, even if only a modest degree of accuracy was sought. Since it is easy to measure, it seems more reasonable to consider the temperature distribution T ( x )as a given datum and try to deduce all other unknown quantities on the basis of a specified theoretical model.

158


B. TJie Nature of the Actiae Zone” “

The most characteristic feature of the N regime is the longitudinal T ( x ) profile of the cathode wall temperature, which presents a maximum at some distance x = 1. This distance is a decreasing function of the gas-flow rate and (in a less pronounced way) of the absolute value of the cathode maximum temperature. This hottest region of the cathode has often been called the actioe zorie as it is associated with the highest current density of thermionic origin ; however, there is not full agreement on its nature, as viewed by the various authors. It is tempting to compare this active zone to the localized hot spot of a plain, conventional cathode. Its spatial extension in an HCA. and the absence of a definite boundary, could be explained in terms of a hypothetical azimuthal motion of a localized spot on the metal surface, with a slight fluctuation of the distance. However, there is no experimental evidence to support this hypothesis, up to this time. Before presenting our views on this subject we shall review three different points of view reported in the literature, ascribing some particular properties to the active zone. (i) The active zone occurs at a distance where a definite condition is satisfied by the neutral gas pressure. This point was first raised by Lidsky er al. (If), pointing out that “the arc runs from the cathode interior. deep enough that p o x d = I cm Torr” ( p o is the local value of the gas pressure and d the channel diameter). Delcroix et al. ( 4 ) working with a larger range of experimental conditions, have established a general rule for the location of the active zone: at this level (x = I) the gas pressure, as calculated by gas-flow conditions, is approximately constant ( p l z = 2 Torr). Further work by one of his co-workers (31)detected a small increase of the product p 1 x R with the gas-flow rate QCO. I < p , R < 0.8 Torr-cm in the range lo-’ < Q < 2atmcm3 sec- ‘), irrespective ofthechannel radius. It must be pointed out that this result refers to a constant discharge current ( I = 15 A) with no magnetic field applied. Even if these rules are only empirical and approximate, they are rather useful to predict the IPC length (at low and moderate currents) for given flow rates and channel radii ; they account also for the IPC length-reduction effect when separating the gas flow into several channels (see Section VII, A). (ii) Another point of view by Minoo (22) suggests that the active zone is established at a level of the channel where the neutral gas density is the most suitable for the production of metastable atoms. The following assumptions have been made to reach this conclusion: the fast electrons (emitted by the cathode wall) possess an energy of 12 eV, for the Ar-Ta combination; the

I59

HOLLOW CATHODE ARCS

balance of production and destruction of metastable atoms in a unit length of cathode channel is written as 0 = dn,/dt

=P

+

D, 1

where P is the metastable production term (by electron collisions upon neutral atoms) and D,the destruction terms, by radial diffusion and subsequent annihilation upon the cathode wall; ionization by electron impact ; two- or three-body deexcitation upon unexcited atoms; inelastic collisions between metastable atoms. Comparing only the two terms concerning the metastable production and destruction, both by electron impact (cross sections respectively CJ* and a‘) the author writes that ”0

o* > I?, oi

as the whole production mechanism must outweight one of the destruction processes. This yields for 12 eV electrons and, according to that author?, nm/nO< 8.3 x as a maximum value of the “degree of excitation of metastables in the IPC. On the other hand, as all the appropriate cross sections are fairly well known for argon, the author solves numerically the metastable balance equation and, for given values of the neutral gas density, obtains the corresponding metastable density 11,. From this point of view, the maximum metastable density was found to correspond to a neutral density of 2 x 10l6 ~ m - which ~ , is (roughly) the estimated density at the active zone level. Commenting on these results, we think this method of approach is slightly oversimplified, as it amounts to calculating a balance equation over a volume where homogeneous conditiotis preiwil (without a n axial diffusion term); this condition does not apply to the hollow cathode in the N regime, as a density gradient is present along the channel. Also, we must keep in mind that the sheath voltage may vary significantly even within a length of 1 cm; this opens the possibility of a very different balance of the metastable atoms when the emitted electrons possess kinetic energies higher than 12 eV. However, the proposed model is not so crude as might be inferred from the preceding remarks: it should apply to short internal columns (up to several millimeters long) where the sheath voltage does not reach much higher than 12 V at any point. The fact that in those conditions the profile of the wall temperature falls steeply for x > / insures that the electron emission is limited t o the distances x < I ; furthermore, the electrons which fail to perform inelastic collisions within this distance are effectively lost as far as ”

t We think that a more accurate value for 0*(12 eV) in argon is cr* (85), instead of 8.5 x as was used in those calculations.

=

3

i,

cm2

160


metastable production is concerned. So, the basic assumptions of this model are satisfied in this case. On the contrary, the conclusions now discussed do not apply at all for long IPC; as the emitted electrons can now acquire an energy of a few tens of electron volts, they can perform several successive inelastic collisions of different kinds, before complete thermalization. It should further be noted that, in the range of 20 eV energy, the cross sections for metastable production and ionization by electron impact are of the same order of magnitude (85), and the limit for the “degree of excitation of metastables” in the IPC can be considerably higher than the value stated before. (iii) According to Lorente-Arcas (20),the active zone has a quite different character. It is a limited region, centered at the region of the maximum wall temperature where all the emitted electrons are coming from. The plasma density in this region is determined by the balance between the ionization of the neutral gas and the volume recombination between electrons and ions. The ionization process goes through previous creation of metastables (twostep ionization) ; the only ionizing particles are those thermalized electrons of the plasma (Maxwellian distribution function) which possess an energy higher than eVim( V i m= Vi - V , = 4.2 V for argon). The upstream limit of the active zone is a sheath determined by ambipolar diffusion and volume recombination of the charged particles. The downstream limit is not explicitly given. Since we do not agree with some of the postulates of this theory we shall comment (briefly) on the most controversial points. First of all, we question the generality of the proposed theory. Stating that “the electron emission occurs in the active zone is accurate enough in the situations where a high gas flow is present, for the hot zone is then limited to the vicinity of the cathode tip. This is true in the case studied experimentally by Lorente-Arcas (20), where 1 = 3 mm (I is the distance where the wall temperature is maximum). On the contrary, for low gas-flow rates, I can attain several centimeters and the limits of the so-called “ active zone ” need precise definition. This is not a minor point; we know that long IPC are associated with larger cathode falls. The presence of an axial electric field in the IPC and a radial field in the vicinity of the wall, have not been taken into account in the theory discussed here. The hypothesis of a Maxwellian distribution for the electrons in the active zone is a dangerous oversimplification. Again, this is a very important point; in a Maxwellian distribution with T, of the order of a very few electron volts, only the high-energy tail is able to produce ionization; then, to satisfy the requirements of the discharge current, a very high electron density must be postulated which in turn causes a very high recombination rate. This may account for the very high values of n, (of the order of 10l6cm-3) calculated in that paper. ”

161

HOLLOW CATHODE ARCS

Assuming that the electron distribution function is not Maxwellian, having instead an extended high-energy tail due t o electrons injected through the sheath, the balance between creation and destruction of charged particles is satisfied with much lower plasma densities. In that case, even the hypothesisof volume recombination must be reexamined and usually surface recombination upon the wall will be the dominating annihilation process. We think that the two objections above are serious enough t o question the validity of the conclusions of Lorente-Arcas (20). (iv) As t o our own views on the nature of the active zone, we d o not consider it as a limited region with discontinuous properties; the existence of a maximum in the wall temperature profile is only the result of a heat-transfer process which is essentially continuous along the cathode wall. With this point of view, the hollow geometry and the fact that the cathode wall is made of conducting, emissive material, favor the deformation of the equipotential surfaces so that they penetrate inside the channel. This is simultaneously the cause and effect of the existence of a plasma inside the hollow cavity. The plasma heats the metal wall up t o thermionic temperatures; becoming emissive, the cathode surface is the source of the primary electrons. Those which are produced by the inner surface ionize the streaming gas if the pressure conditions in the channel are adequate. The resulting secondary electrons, guided by the reflecting sheath potential, reach the discharge vessel, while the ions are absorbed by that sheath and impinge upon the cathode wall, delivering their kinetic and potential energy. All those phenomena influence the cathode wall temperature, as they contribute to the wall heating or cooling. An independent cooling process is imposed by the heat sink at the cathode support. Considering an elementary slice of the cathode wall cylinder at a distance x (length d x , wall thickness e I ] , where the radial loss balances the heat input upon the wall. Let us examine now the principal radial heating and cooling processes of the cathode wall, i.e., heating processes: ion, metastable and photon bombardment, Joule effect, gas-metal conduction; and cooling processes: thermal radiation, electron emission, metal evaporation, metal-gas conduction. The corresponding quantities are given by the following expressions : a. i o n bombardment.

where,ji,(x) is the radial ion current density upon the metal wall; V is the local value of the sheath potential; Vi is the ionization potential of the gas,

HOLLOW CATHODE ARCS

163

and cp is the work function of the cathode material. This expression assumes that all ions impinging upon the wall recombine with an electron from the metal, yielding a neutral atom with negligible energy?. T o calculate this term it is necessary to make a hypothesis about the sheath voltage distribution (see Section V, D, 3) and t o calculate the radial ion current density (Section VI, C ) . h. Metastable bombardment. If the working gas possesses metastable levels (as in the case of argon 4s3Py.,, V , = 11.55; 11.72 eV), their contribution to the wall heating may be important. Due to the long lifetime of these particles, they may reach the cathode wall in the course of their thermal motion and suffer deexcitation, releasing their potential energy. The corresponding energy flux upon the metal wall is given by G,,(X) = 17, ( X . 4 ~ , , , c I eV”,/4

in the hypothesis of a Maxwellian metastable distribution function (average velocity F,,,); 17, (x,].) is the metastable density near the wall, within one mean free path distance A ; q, is the electronic charge. c. Photon bonibardment. This term is not easy to calculate, as we are dealing with a complicated system consisting of a plasma not in thermodynamic equilibrium ( T , # Ti ,To) surrounded by a metal wall. The plasma radiation, due to radiative deexcitation, recombination, and bremsstrahlung due to electron-ion and electron-neutral interactions, may contribute to wall heating, enhance the electron production by photoemission, or be reflected back to the plasma. Only the electron-ion bremsstrahlung power density is easy t o evaluate; for a plasma (n,,Te)not absorbing this radiation, the power density on the surrounding cylindrical wall (radius R ) is given by Gb(x)= 7.6 x

17,’

Te‘’2R[W/cm’; ( ~ m - ~ )(eV)’”; *; cm].

d. Joule heating. The Joule power produced per unit area of the cathode wall is given by

p being the metal resistivity ( p = IW4 R cm for Ta at 2500°K) and e the wall thickness; ji,is the radial ion current density collected by the cathode wall andj,, is the electron current density emitted by the cathode surface.

t Ecker (66) who has analyzed thoroughly the cnergy balance on the cathode of arc discharges, suggests that this term should be divided into two separate effects, concerning the energy transfer of kinetic and potential energy, with different acconimodation coefficients.

I64


e. Thermal conduction from the hoi gas in the IPC to the wall. Considering the cathode channel from the support to the tip, there is an initial length t o consider, full of neutral gas; and the remaining length where a plasma exists. The latter is the only region where the gas can be at a higher temperature than the wall, due t o the collisions of its atoms with faster particles (mostly electrons, either primary or secondary). Let us assume that the gas attains thermal equilibrium with the cathode wall before reaching the IPC; it is then overheated in the IPC by various collisional mechanisms. The power delivered t o the gas through these processes is an upper limit t o the gas-metal conduction heat transfer. f. Thermal radiation of the cafhode wall. The power radiated per unit area of the outer cathode surface is given by

D, ( T )= &(T)(rT4, and E ( T )the where D is the Stefan constant [o= 5.67 x lo-' W,Jcm' emissivity of the cathode metal: for tantalum, this is approximately a linear function of the temperature between 300 and 3000°K.

+

E(T)= &(TO) a ( T - To),

(OK)-' with To = 300"K, &(TO) = 0.05, and CI = 1.05 x g . Thermionic emission. Consideration of the Richardson-Dushmann equation for electron emission, yields, for the power loss per unit area of the emissive surface (inner and outer wall surfaces)? D t h ( T )=2 A (PT' C b o i T

for tantalum, A = 55 A (cm"K)-', b, h. Metal evaporation.

= 4.86 x

D,, ( T ) = Q, C T -

J2

lo4 ( O K ) , and cp = 4.12 V

e - DJT,

where Q,is the sublimation heat; C and D are constants depending on the gm/cm' cathode metal (for tantalum, Q, = 4.17 x lo3 J gm'; C = 8.1 x D = 9.2 x 10-4(0K) sec-'("K)"'; i . Metal-to-gas heat conduction. This effect occurs in the cathode channel in the zone preceding the IPC. It is obviously dependent on the gas-flow rate; when this is not too high, thermal equilibrium is achieved within a short length and the power transferred t o the gas flow (mass flow rate: qm)is given by AW=q,C,,(T-T,)

t We suppose that thermal emission is not field enhanced. Other emission mechanisms were neglected, which may be reasonable for low and moderate discharge currents.

165

HOLLOW CATHODE ARCS

-

where C , is the specific heat of the gas and T , the temperature of the gas entering the channel ( T , 300°K if no preheating is used). For argon gas at 2500°K C , = 0.52 J/gm"K and the average power flux from the length of the wall preceding the IPC is

Dm-g,( T )= A WI2xR(L,

-

I)

L, being the cathode length. For a given experimental situation the cathode wall temperature is known at each distance x ; so. the radial dissipation terms are therefore easy t o calculate, as they are known functions of T . As to the radial heat input upon the wall, the corresponding terms depend on quantities not directly available through experiment, which must be calculated on the basis of some theoretical model. For instance, the ion bombardment term, which is probably the most important contribution to G , ( x ) , depends on the local values of the sheath potential and on the ionization rate inside the IPC, both depending on the theoretical model used for their computation. Thus, rather than using the heat balance equation as a way to obtain the curve T ( x ) ,it is more sensible t o use this equation to verify the compatibility of a theoretical model with the experimental evidence. From this point of view. any theory of the HCA in the N regime may be checked in two independent ways: the discharge current requirements must be met, so that the various mechanisms of charged-particle production, acceleration and annihilation, justify the magnitude of the discharge current; the power balance equation for the cathode wall must be verified, so that the calculated radial heat input term (resulting from the choice of a given model), exceeds the radial heat dissipation (as calculated from the experimental T(x) curve), in the region where d2T/dx2 < 0. This method was used (21) to verify the validity of the model for the HCA that we have been presenting throughout the present section. By calculating the ionization rate along the IPC, (using a method described in detail in Sections VI C, D), we were able to evaluate the various terms of the heat balance equation. for a given experimental situation. These calculations concerned an HCA discharge with the following parameters: argon gas; vessel pressurep, = 5 x l o w 3Torr; Q = 6 x atm cm3 sec-'; cylindrical tabular, tantalum cathode: R = 0.145 cm: c = 0.2 mm; L, = 8 cm; I = 20 A ; B = 0; V = 77.5 V ; Vc = 45 V , I = 4.5 cm; A', = 8 V/cm. We obtained the following results ( 2 / ) :(i) The most important radial dissipation term concerns the black-body emission of the cathode wall ; the electron emission cooling was about seven times lower at T = T,,,(x = !),

166

JEAN-LOUP DELCROIX A N D ARMANDO ROCHA TRINDADE

and the remaining mechanisms were negligible for those conditions. (ii) The most important radial heat flux to the cathode wall was due to the ion bombardment; among the remaining terms calculated, only the one due to metastable bombardment was significant (even so, about 15 times lower than the former). (iii) The calculated discharge current presented a defect of about 30% in relation to the experimental value: (iv) The maximum heat gain to the wall was about 50 % lower than the maximum radial heat dissipation at x = I, while it should be higher. Both defects are compatible with an underestimation of the radial ion current t o the cathode wall; and a possible underestimation of the photon bombardment term, as the resonant photons were neglected. However, these difficulties raise more questions about the quantitative exactitude of the calculations than the validity of the proposed model, which we shall discuss in the next sections.

C . Balance of the Current in the Cathode Region Let us consider a length dx of the IPC, located at abscissa x (see Fig. 44). The conservation of charged particles in the volume Sdx ( S being the IPC cross section) yields the following equations, for the ion and electron current densities : Zon current (Fig. 4 4 a ) :

Sdji, + j i , dS‘ = 4i (9- 9 ) S d ~ , whereji,(x) is the net radial ion current density leaving the IPC across the cylindrical boundary (area d S ’ ) ;ji,(x) is the longitudinal ion current density across the transverse section S (the positive direction of the axial ion flow is indicated on the figure);Y(x) and B(x) are the ionization and recombination rates (number of pairs of electron-ions created and annihilated at abscissa x, in the volume of the IPC, per unit time and volume). Taking S = nR12, dS‘ = 2nR’ dx one obtains ( d j i ~ / d x+ ) (2/R’)jir= 4i (9- 9) Electron current (Fig. 44b) : Considering the corresponding quantities for the electron current density, with the positive directions of the radial and axial electron flows, taken as indicated in Fig. 44b [j,,(x) = q e y e r ( x )jeL ; = 4,yrL; ye, is the net electron flow entering the IPC across the cylindrical boundary], one obtains:

(djeJdx)

+ (2/R’)jer= 4e (4- 9).

Accepting now the simplified model for the potential in the IPC, as outlined in Section V, D, 3, we postulate that: (i) The electric field is purely axial over

167

HOLLOW CATHODE ARCS

*

I

+ x+dx

I 1--

Y

1 0

(b)

FIG.44. Conservation of charged particles in the 1PC. (a) Ion flux y , ( j , = y , q , ) ; (b) electron flux yc ( j , = 9. ye).

the greater part of the channel cross section ( r < R ‘ ) ,with the exception of a thin sheath in the vicinity of the cathode wall ( R > r > R’)where the field is purely radial. ( i i ) The axial field will be taken a s constant along the IPC ( I > x > 0) and its value equals the average axial field determined experimentally as in Section V. D, 3. I n these conditions, the sheath potential is a linear function of the abscissa, and is maximum at x = 0 (channel exit hole); (iii) The ions of the IPC which attain the sheath boundary ( r = R’)in consequence of their thermal motion, are accelerated by the local sheath voltage and finally recombine upon the cathode wall; ( i v ) The electrons emitted by the wall (by thermionic emission, photoemission and secondary emissionl.) are accelerated by the radial field and enter the 1PC volume, where their kinetic energy is partly lost through successive inelastic and elastic collisions. These electrons cannot again cross the sheath boundary in the opposite sense, as they are repelled by the sheath potential; ( v ) As to the actual direction of the longitudinal ion flow, it is necessary to evaluate in the first place the Also by field eniission or T-F emission, if the local current density is high enough

(j c r

> lo5 A/cniZ)(66); unless very high currents are drawn from the cathode, as in the case

of the pulsed regime. this condition is not likely to occur, due to the absence of in the N regime.

it

hot spot

I68


relative importance of the gas streaming effect and the electric mobility processes, under the specific experimental conditions. The longitudinal ion velocity is the sum of the electric drift and of the macroscopic velocity imposed independently by the gas flow toward the channel exit hole. The average gas-flow velocity is given by uo = ( Q / S ) ( n ~ / n o )

where no is the (distance-dependent) neutral gas density and nL the Loschmidt number (nL = 2.687 x l O I 9 ~ m - ~ The ) . resulting axial ion current density is given by . i i L = Ei q i (pi X , - i d == ~ i q i ( n L / ~ o ) [ p i o - (Q/S)l, Ei being the radially averaged value of the ion density at a given abscissa and p i 0 the reduced ionic mobility;jiL, referred to the OX axis, can be positive or

negative. Analysis of the magnitude of the parameters under actual experimental conditions shows that jiL may reverse its direction when Q varies within the range where the N regime occurs. Calculations of the values of Peril(argon gas) for whichjiL= 0, with the aid of data from Table I11 [ W , ( R ) ]and from TABLE I V GAS-FLOWRATE CORRESPOND~NG 1PC LENGTHS"

CRITICAL VALUES OF THE

R (cm)

Qcri,(atmcm3 sec-')

0.105 0.13 0.145 0.18 0.23 0.28

0. I98 0.240 0.291 0.248 0.348 0.459

AND

lcrit(cm) 1.1

I .48 1.8 3.36 4.94 4.6

Fig. 5 [ / ( Q ,R)],show that in long TPC, the ions flow against the neutral gas stream, penetrating deeper inside the channel; while for higher values of Q (shorter columns), the ions follow the direction of the neutral gas flow. Table 1V shows the result of these calculations (pie = 1.6 cm2 V-' sec-' at STP).?

t pio(T)= plo(To)x (To/T)"2;in the present case we took T - 2500 K , so p l o= 0.57 cm2 V - l sec-l.

HOLLOW CATHODE ARCS

169

Introducing the expression for the radial ion current density, in agreement with the previous hypothesis (radial motion as a consequence of the ion thermal agitation), and assuming that the ions have a Maxwellian velocity distribution. with average value Fi j i ,= ni ( R ’ )qiEi/4,

where ni ( R ’ ) is the ion density in the IPC near the sheath boundary ( r = R’). I n the case of the lPC, the ionization is produced by the primary electrons emitted by the wall; it can also be shown that ionization occurs mainly in a peripheral region of the IPC (annular ionization). Both facts (ionization created by “external” agents and within a short distance from the wall) contribute to flatten the radial profile of the electron density(21). It is then a reasonable approximation to neglect the t i i dependence on the radial coordinate in the TPC (x < R’). In those conditions n i ( R ’ ) N iii and one obtains the following relation betweenjiLa n d j i , :

Introduction of this relation in the ion current equation yields tC+iL/dJ

+ An0

jiL

=41(

4 - A?,

where the quantity A (independent of the distance if one takes the ion temperature as constant along the IPC) is given by

Two different situations arise, depending on the magnitude ofthe gas-flow rate: ( I ) Q > QCri,( A < 0 ) . In this case the ion current flows from the channel toward the vessel; this current is produced by internal ionization and the externally produced ions d o not contribute at all-they are kept from reaching the channel by the gas flow. The radial current is also provided by the internal ionization but the maximum ion bombardment upon the wall occurs nearer and nearer to the exit hole ( x --* 0) as the flow increases. (2) Q < Qcri,( A > 0). In these conditions the ion current flows into the channel, against the gas flow; the externally produced ions may contribute to the ion current inside the cathode channel. This case has been studied by Trindade (21), performing a numerical integration of the differential equation of the axial ion current. Formal integration of this equation yields

170


wherejiL(0)is the ion current entering into the cathode through the section x = 0 (external ion current). This equation was solved with the following simplifications (21): the ion velocity was taken as determined by mobility alone [we considered the case of a long IPC ( Q 6 Qcri,)];the ion current ,jiL(0)coming from the external plasma was neglected as compared with the one generated in the IPC (this is justified when the cathode is working at high temperature and the vessel pressure is low); the volume recombination was neglected, as compared with the radial ion loss (surface recombination).? In these conditions ( A > 0)

For this current t o be an increasing function of the abscissa in the range

(0, I) it is sufficient that the ionization rate 4 ( x ) is itself an increasing function of x in this length range. This is likely to occur in the N regime, where the electron emission increases in the range I > x > 0; as t o the pressure gradient

along the channel, the mfp. for ionization has a tendency to decrease for increasing distance. So, the fact that the axial ion current (and consequently, the radial component as well) increases with the distance between 0 and I, complies with the requirements of the heat balance equation for the cathode wall (see the preceding section), ensuring that a strong ion bombardment exists in the same region where the radial heat dissipation is the highest (x I ) . Further we notice that, when the internal ionization term is not high enough to overcome the externally produced ion current (which may happen due to the existence of pressure conditions adverse to internal ionization in the LQ or HP regimes; or due to insufficient cathode heating in the LI regime), we obtain

-

showing that the T ( x )curve must be decreasing from the cathode tip toward the holder, which agrees with the experimental evidence. We next study the method for calculating the ionization term inside the IPC. D. The Ionization Term in the IPC

The calculation of the inelastic collisions in the IPC and the corresponding charged-particle yield, is complicated by the dependency of the intervening parameters on the axial distance: the current density of the primary electrons depends on the local wall temperature; their energy when entering the IPC is a function of the local value of the positive sheath voltage; the

-

f Recombination is negligible in respect to radial diffusion loss when (33, p.156) n. G 1020/rroh2a. Taking the recombination coefficient c( lo-” cm3 sec-’ (86); tio 1OI6 cm-3, and A of the order of magnitude of the cathode radius R 1 mm, one obtains G lo’* which certainly applies in the IPC. N

N

HOLLOW CATHODE ARCS

171

densityof the neutral particles varies along the column as a result of the gas flow. An approach to this problem has been made by Trindade (21), using a simplified description where the IPC is decomposed in homogeneous slices of finite length Ax along the longitudinal axis. Thus, the neutral gas density, as calculated from gas-flow conditions, the electron emission current density (assumed purely thermionic) corresponding to the local values of the wall temperature, the sheath potential, calculated at each point from the overall cathode drop and the hypothesis of a uniform axial field, were taken as constant quantities within each slice, in a stepwise description. Their value in a slice is then the local average of the highest and lowest values calculated therein (see Fig. 45). The criterion for the definition of the appropriate length Ax was based on the following assumptions: the primary (wall-emitted) electrons acquire, from crossing the cathode sheath, quantized amounts of kinetic energy (in accordance with the stepwise description of the sheath potential profile); this energy depends directly on the abscissa of the emission point; a simplified three-level model for the rare gas atom reduces the number of different kinds of heavy particles to ground-state and metastable neutral atoms, and ground-state singly charged ions. In these conditions. a primary electron can only lose energy by inelastic collisions by amounts equal to: e V i ; e V , ; e( Vi - V , ) (where V i and V , are the first ionization and the metastable excitation potentials, the third quantity being the energy required to ionize a metastable atom): We took, for the argon gas ( Vi = 15.7 V; V , = 11.6 V), e( Vi - V,) h~ 4 e V as one writ of energy loss by inelastic collision, corresponding to ionizing a metastable atom. Thus, direct ionization (from ground state) amounts to 4 units of energy loss, and 3 units correspond to metastable excitation. Depending on the energy of the primary electron (after crossing the sheath), one or several successive inelastic collisions of the preceding kind can be performed until this electron reaches thermalization. The probability for a collision of a given type to occur is proportional to the product of the corresponding cross section and the local density of the target particle (no or 4,). The energy loss by elastic collision of the primary electrons upon the heavy particles was considered negligible ; however, those collisions were taken into account when calculating the axial drift along the IPC. On the basis of the preceding assumptions, an adequate length x of the slices composing the IPC is given by the condition:

X , A x = I unit of energy loss

( X , is the axial gradient of the sheath potential). In these conditions, the electrons emitted at adjoining slices differ by 4 eV in initial energy; those of

172

JEAN-LOUP DELCROIX AND ARMAND0 ROCHA TRINDADE I I

Q Q

-

I I I I I I

ANODE

I I

I

e

1 UNIT

ENERGY LOSS

- 2.4 -

* x

e

12

- 0 0

“0 (arb. units)

I

4

X

e

FIG.45. Stepwise approximation of the cathode sheath potential ( V ) and the neutral gas density ( n o ) for the computation of the ionization yield in the IPC.

higher energy can perform one more inelastic collision than their neighbors which is the reason they should be regarded as separate populations. Now, a balance equation must be written for each slice, and for each discrete energy level of the electrons in that slice; the rates of production, annihilation and transit of heavy particles and electrons of definite energy are the raw material for these calculations. This rather tedious computation was performed for a given experimental situation (21) (argon gas; R = 1.45 mm; Q = 0.06 atm cm3 sec-’; I = 20 A ; B = 0). The principal quantitative results are shown in Fig. 46.

173

HOLLOW CATHODE ARCS

1-

0.1

-

( 0 )

x(crn) 7

6

5

*(c)l

xkm) 8

L

3

2

1

0

I

I

,

7

6

5

.14

n,(d

3

2

1

0

3

FIG.46. Theoretical results for a HCA in the N regime ( R = 1.45 mm, Q = 0.06 atm cm3 sec-', I = 20 A, B = 0). (a) Cathode wall temperature (measured), thermionic current density; (b) radial ion current density, electron production by ionization in the IPC; (c) unexcited and metastable atoms deosity. From Trindade (21, pp. 106-1 14).

174


The following conclusions have been obtained : The internal ionization efficiency (secondary electron yield for one primary electron) calculated by this method, was of the order of 50%. This rather modest value is due to the fact that the higher values of the ionization cross sections occur for the electrons emitted at the lower values of the abscissa, where the neutral gas density is lower. Metastable atoms are of extreme importance in the ionization process, chiefly at the higher abscissas (x /) where the sheath potential is too low for one-step ionization to occur. However, the calculated value of the metastable density in the IPC (of the order of magnitude of n, loi4~ m - is~probably ) too high. As a matter of fact the only metastable destruction mechanisms considered by Trindade (21) were the volume ionization and the surface deexcitation upon the metal wall ; the possibility of their deexcitation by collision upon slow electrons, unexcited, or other metastable atoms, would yield a lower metastable density. Nevertheless, it is possible that the metastable density is high enough in a HCA to make it an interesting source of that kind of particles. This point has been raised by Delcroix, who suggested the use of HCA in chemical reactors (87). Experiments are being done to assess the metastable density in HCA by optical absorption: preliminary results (9) have shown that the metastable yields can be some two orders of magnitude larger in HCA than in the best glow discharge. As we have pointed out (Section VI, B), only qualitative agreement between theoretical and measured discharge current was obtained, indicating the necessity for improving the HCA theory.

-

-

E . Prospects of Improving the Theoretical Approach As compared to the method of calculation of the internal ionization outlined in the previous section, Allis (88) proposes a finer approach, to obtain simultaneously the electron distribution function in the IPC. It is based on his “gain-function” method, which takes into account the influence of both elastic and inelastic electron collisions upon neutral particles (89). The gain function is defined as the flux (in velocity space) of the electrons crossing the surface of a sphere of given radius w (electron velocity). Changes of this velocity can occur through: elastic collisions upon neutral particles (or Coulomb collisions, depending on the ionization degree); acceleration by an electric field ; inelastic collisions upon heavy particles. The balance of charged particles in velocity space appears as a differential equation of the gain function the steady-state solution yields, through appropriate relations, the electron distribution function.

HOLLOW CATHODE ARCS

175

The adaptation of this method to the IPC requires that the energy of the primary electrons is a continuous (linear?) function of the abscissa. The resulting analytical complexity (it must be kept in mind that the appropriate cross sections must be introduced to integrate the balance equation in velocity space) probably requires extensive computation ; the first preliminary results of these calculations are still unpublished (90). F . Coriclrrsioii Obviously, the theory of the HCA is not a closed subject. Even if we may consider that, in the moderate current range, qualitative agreement was found between theory and experiment, several points need closer scrutiny, i.e., the possibility of photoemission of primary electrons; the possibility of field emission, at least in the higher current range and in the pulsed regime; the possibility of secondary emission by ion bombardment, mostly when doublecharged ions are present (higher current range); the exact shape of the positive sheath inside the cathode must be assessed (this is closely related t o the problem of determining experimentally the exact depth of the plasma penetration in the IPC). The metastable production by the HCA is a n important matter as to its possibilities of application, and needs further research. A better experimental knowledge of the plasma inside the IPC (density, temperature, electron distribution function) is badly needed to guide and support the theoretical research on the internal mechanisms of the HCA.

VII. APPLICATIONS

OF

HCA

A . Multichannel HCA

As we pointed out in Section IV, B, single channel hollow cathodes are not suitable for working with an extended current range. To support the highest current, a larger diameter channel must be used to guarantee a reasonable lifetime; this causes difficulties during ignition and may impair the lowcurrent performances. Moreover, a strong gas flow is necessary to insure the N regime in a large diameter cathode; this may be undesirable from the point of view of the pumping capacity of the vacuum system. As to the problem of the discharge efficiency, the IPC should not be too long, as this is associated with a high cathode voltage drop, which increases the discharge voltage. A problem arises, therefore, when a high discharge current (imposing a large diameter cathode) and a low gas consumption are simultaneously required. Multichannel cathodes were conceived and developed for these purposes by Delcroix ef al. (6, 7, 91). The idea was to divide the gas flow among

176

JEAN-LOUP DELCROlX AND ARMAND0 ROCHA TRINDADE

parallel, cylindrical channels which compose the cathode device. Such a structure can be made in several ways; we describe here the most interesting one, a multitube assembly named by its authors the “ macaroni packet.” Figure 2(B3) (Section 1) shows this device, made by introducing a great number of slender tubes inside a large diameter cylinder. No special clamping is necessary to hold the tubes, if the packet is reasonably tight, because the metal evaporation occurring during arc ignition is enough to weld the structure firmly together. The outer cylinder is fixed to the holder as with a single channel cathode. In these conditions, the gas flows inside the internal tubes as well as in the spaces left among them. Comparison of the gas-flow conditions between a single channel and a multichannel cathode with equal area of the hollow cross section shows that the latter presents a steeper gradient of the neutral gas pressure for the same total gas-flow rate. So, considering the empirical rule stating that the active zone in the cathode channel occurs for a fixed value of the neutral gas pressure (Section ID, A), it becomes possible to assess the IPC length in a multichannel cathode. The relation between this value (1” )for a cathode having n elementary equal channels, and the IPC length I, for the equivalent (same hollow cross section) single channel cathode, is given approximately by (7, p. 1557)

I2!=

4

[

l/n

+ (I0.9/Jn(A0/d,) 1 + 10.9(A()/dI)

I,

where A, is the mean free path of the neutral atoms at average temperature and pressure in the channel, and dl is the internal diameter of the single channel cathode. Table V shows the result of the calculations for argon gas at 2500”K, TABLE V

I P c LENGTHREDUCTION EFFECTOF MULTICHANNEL CATHODES

9

I,

= 11/36

I,

= 11/14

1,

= 1,/1.8

1 Torr for a different number of channels, and two diameters of the equivalent single channel cathode. Knowing that the discharge voltage is strongly dependent on the IPC length (due to the high values of the axial electric field inside the cathode channel), multichannel cathodes are expected to need lower discharge

HOLLOW CATHODE ARCS

177

voltages (for given values of the current and the gas-flow rate) than single channel cathodes. However, for this effect to occur in agreement with the theoretical predictions it is necessary to postulate that the gas flow is parted equally among the n elementary channels; this is not always the case, as we shall see now. It has been stated in Section 111, C that hollow cathodes do not ignite when the discharge current density is lower than a certain threshold value; in the case of multichannel cathodes of large diameter this phenomenon is particularly obvious. In a low-current operation only a few channels are ignited, their number increasing as the discharge current is augmented ; only at high enough current does the whole cathode section participate in the discharge. This can be considered as an autoniatic adaptation of the cathode cross section to the variable current requirements. Thus, a cathode can be designed to support very high discharge currents (large overall diameter cross section) while insuring a good low-current performance by using very slender elementary channels, of which only few are ignited. It is obvious that the gas flow does not divide evenly among all elementary channels when the cathode cross section is only partly lit; this is due to the unequal gas temperatures inside the active channels and the remaining ones. Analysis of this effect (7) shows that the gas flows preferentially through the inactive channels; the IPC length reducing factor given before ( A = /J/,) is now affected by a corrective term: /in//,

+(I -4(~7~np*],

= A[@

where CL is the fraction of the cathode cross section corresponding to the active channels and T' and T" are the gas temperatures inside the lit channels and the inactive ones (T'> T"),respectively. As the factor between brackets is bigger than unity, the IPC length reducing effect in the case of partly lit cathodes is seriously impaired. Figure 47 shows the comparison between multichannel and single channel cathodes, from the point of view of the IPC length and the discharge voltage, the latter for steady-state and pulsed operation. The advantages of these cathodes, namely their higher efficiency and wider current range, make them very useful for operation under stringent conditions. I n the next sections we present some selected applications of HCA reported in the literature.

B. HC Ion Luser Large laser continuous radiation power in the ziisible region (up to 100 W) witha fair efficiency( z IOP3)canbe obtained with argon ionlasers; moreover, the fact that their light is in the blue-green region of the spectrum, corresponding to the highest sensitivity of the receivers, makes them very interesting

I78


60

60

x(rnrn)

I

0

0

20

60

I

10 (C)

20

-

\

$>6.?/------

-

I

1

I

0

20

40

60

I

I(A)

80

I

2o

I(kA)

FIG.47. Performances of multichannel HCA (dimensions on drawing). (a) IPC lengthreducing effect; (b) V-I characteristics in steady state; (c) V-I characteristics in pulsed regime. From Delcroix ef al. (7, pp. 1559, 1560).

devices for a great number of applications. On the other hand, it seems that the most promising way to increase the output power and efficiencyof the Ar' laser is to use large diameter discharge tubes and very high discharge currents (92). The high power Art laser presents two serious technological difficulties : the huge power dissipation at the column, and the capacity for the cathode to deliver the required current without serious damage to itself, and for the

HOLLOW CATHODE ARCS

179

necessary purity of the rest of the laser. We shall examine briefly the electrode problems of the Ar’ laser and discuss the use of hollow cathodes as a possible solution. The first attempts to use an HCA as the excited medium in cw ion laser operation, have been reported to meet no success (93, 94). In these experiments the arc ran between tantalum hollow electrodes and a gas flow was injected through the cathode into the interelectrode space. The reasons for this device’s failure to show laser action were concerned more with the external column conditions (which were not adequate) than with the cathode itself; the plasma was magnetically confined inside a discharge tube of excessive diameter. This was shown later by Huchital and Rigden (24, 95) who first obtained laser action with an HCA external column as the active medium. ln order to obtain the necessary current density, they used, either small diameter discharge tubes (a few millimeters i.d.) o r another type of wall confinement, consisting of several radiation-cooled disks placed along the discharge axis, with a small central aperture to limit the radial diffusion of the plasma. In these devices, the hollow cathodes appear as a possible alternative against the thermionic cathodes. Other authors followed this trend, using HC more because of its ruggedness and current delivering capacity, than for a definite idea about their possible influence on the excitation mechanisms of the ion laser (25, 27, 96, 97). Nevertheless, there is at least one point of difference between hollow cathodes and conventional ones, which may affect the excitation mechanisms in the laser column. The distribution function of the electrons leaving the cathode region is obviously not the same in the two cases because of the different shape and magnitude of the cathode sheath, and the occurrence of internal ionization in the hollow cathode (97). I n order to analyze this problem, Jennings et d . (26) made a careful comparison of the performances of these two types of cathodes, using the same geometry for the active length of the laser (external column), with the following results: the total output (radiation) power was the same for the two systems for given values of the discharge current and of the vessel pressure (an optimized value of the axial magnetic field was imposed for each case); the same applies for the threshold currents needed, at different pressures, to start the laser action; finally, the total input power (including the heating power for the “ h o t ” cathode) was found to agree within 2 for the two systems operating in similar conditions. The authors concluded that, for the moderate pressure range necessary for ion laser operation, any differences in the composition of the electron current just outside the cathode region, for the two cathode systems, were destroyed by collision interaction within a very short length. This makes the HC and the thermionic hot cathode fairly equivalent as far as laser performance goes; however, a few remarks are felt to be necessary about this conclusion.

180


As a matter of fact, no mention is made in this reference t o the opfinzizcifion of the HCA for one o f t w o possible aims, either to obtain the maximum output power for a given geometry, or t o secure the maximum efficiency in the light generation process. Compared with the thermionic hot cathode, the hollow cathode has one more degree of freedom when a given current is required : the gas-flow rate through the cathode channel, which has a strong effect on the cathode sheath potential. Obviously, for this optimization research t o be meaningful it is necessary that the cathode gas-flow rate could be varied without influencing the vessel pressure. Another word o f caution about the comparison between hollow cathodes and conventional ones for laser devices: even if their performances are found to be nearly equal for the moderate current range, it is obvious that in the high-power ion laser, the HC is the more adequate, for its current-delivering capacity is much higher than the known systems of thermionic hot cathodes (98); and the conventional cathode working in the hot spot arc mode is not suitable for laser operation. C. Ion Sources for Electric Propitlsion Systenis Among the various systems useful for orbital maneuvering of spacecraft, electric thrusters based on ion acceleration have been most extensively studied. In those devices, the highly ionized plasma from which the ions are extracted may be created by different methods; one of them incorporates a cathode producing a copious supply of electrons, with energy adequate for ionization of the neutral propellant atoms (electron bombardment ion engines) (28, 29, 99-105). For the production of the electron current, different cathode materials and geometries have been tested; froni the point of view of cathode durability and current-delivering capacity, hollow cathodes were found to be the most adequate (29, 100). As to the global efficiency of the thruster, it is not clear whether hollow cathodes are the best cathodes for this purpose (104) as it is generally assumed. We first describe a hollow cathode geometry which has been extensively used in ion thrusters, formerly developed by Rawlin and Pawlick (102). A hollow tantalum tube is supplied with a gaseous mercury feed from a suitable vaporizer; a pierced disk of thoriated tungsten ( - I mm thick) is welded to the cathode tip to restrict the gaseous flow (orifice diameter: 0.1 t o 1 mm). The cathode wall is electrically heated by a wire wound around i t , and embedded in an alumina coating. The hollow cavity may be coated with low workfunction materials; or an insert of tantalum foil coated with the same materials may be placed inside the tantalum tube. The pressure inside the cathode channel is determined by the mercury feed, and is much higher (several Torr up to several tens of Torr) than the pressure in the discharge vessel (below Torr).

181

HOLLOW CATHODE ARCS

Experimental results showed that this discharge worked in two different cathode modes: “plume” mode, with a bright discharge between cathode and anode, corresponding t o low vapor feed rates through the cathode, low discharge currents (some 100 mA), and a voltage of about 15 V (100, 101); and a “spot” mode where only the cathode orifice is specially bright, corresponding t o currents of a few amperes and lower discharge voltages (10 V). It is remarked by Csiky (101) that self-heating of the cathode is possible even at moderate currents, due to the ion bombardment of the cathode wall. We identify the “ s p o t ” mode described above with the N regime of a gasfed HCA which we have discussed in the present review. In fact, the presence of a small diameter orifice at the end of the cathode causes most of the pressure drop in the cathode channel to occur at about this level; the active zone sets in at the very end of the channel and the TPC is virtually absent in this regime. However, due t o the small thickness of the aperturing disk, some plasma penetration may occur into the cathode channel due t o incoming ions and ionization by the electrons emitted at the orifice level. The fact that a minimum current density is found t o be needed for the spot” mode t o set in is in accordance with our results for the LI -,N regime transition; the threshold current corresponds t o the minimum ion bombardment required for self-heating of the emitting region. An additional point in favor of this assimilation is given by the results of a very interesting experiment described by Fearn et a/. (103):introducinga probe inside the cathode channel, the authors were able t o measure the plasma density at a point -2 mm upstream from the cathode orifice. This density was found t o be lower there than at the interelectrode space and, moreover, density was a decreasing function of the mercury vapor feed rate. Viewed under the light of the known characteristics of the N regime, these results are easy to understand; the probe was probably placed at a transition region, upstream in respect t o the active zone, where the plasma density is much lower. The increase of the gas flow, “pushing” the plasma farther downstream causes the density measured at a fixed point t o be a decreasing function of the gas-flow rate. Pawlik et al. (28) studied more thoroughly this “orifice” cathode, analyzing the output and input heat flux on the cathode wall, and comparing the theoretical predictions with experimental temperature measurements on the various regions of the cathode. Their conclusions agree with our expectations for the HCA N regime, as the electron emission from the metal was ascribed entirely to the orifice region, while the power input by ion bombardment was found t o occur either at the cathode inner surface o r at the orifice but no? at the cathode face (the end disk)-thus excluding the contribution of an externally created ion current. A most interesting point made by Pawlik et a/. (28) concerns the comparison, for the same “ orifice ” cathode, between their performances with and “

182


without external wall heating. It was concluded that: running the cathode at a higher temperature while in the self-heating regime (by reducing the cathode heat losses by radiation or thermal conduction) decreased the power extracted from the plasma to heat the cathode wall, and increased thedischarge efficiency; the external heating of the cathode consumed more power than self-heating by the discharge current; finally, it was found that coating the cavity with low workfunction material causes the cathode temperature to lower (for the same discharge current) and the discharge voltage is smaller in these conditions. However, running the discharge for several hours (even at moderate currents) causes depletion of the coating material inside the cathode. Then, the discharge efficiency is found to decrease accordingly, after some 50 hr of operation. In conclusion we suggest that using multichannel hollow cathodes, either “orifice” or tubular shaped, might contribute to increase the efficiency of these thrusters. Other hollow cathode configurations which are not of the axial HCA type we are most interested in have been used in ion sources for propulsion puposes; only brief descriptions will be given of these devices. Zeyfang (106) describes two different hollow cathode ion sources, working in the high-current glow regime. The first has an axial geometry (the anode opposing a hollow cylinder as a cathode); the external column is wallconstricted (bore diameter I .5 t o 6 mm). The gas is fed through the anode and the ions are extracted from the back of the cathode channel. The second type of ion source mentioned in the same article has a transverse geometry, in the form of two ring-shaped electrodes: the annular anode faces two concentric rings constituting a circular slotted cathode. Thus the discharge is also circular in shape, running from the anode (in which vicinity the gas is injected), into the slot between the two ring cathodes; the ions are extracted past the latter region. Another transverse geometry is described by Ibadov (107),concerning an ion source with coaxial electrodes. The anode is a rod placed at the axis of a cylindrical hollow cathode which also serves as a discharge chamber; the ions are extracted from an opening in the cathode wall. In the interelectrode space the pressure is uniform (no gas flows between the electrodes): the cathode is heated only by the ion bombardment, up to a temperature of the order of 2500°K. This discharge may even be made to run on the vapors of the cathode material.

-

D. HC MPD

Thrusters

Magnetoplasmadynamic (MPD) arc thrusters have been proposed for spacecraft missions ranging from auxiliary propulsion systems (satellite station keeping, altitude control) t o the high-power, primary propulsion

HOLLOW CATHODE ARCS

183

system for deep-space exploration (30, 108). Usually the device consists of an annular anode and a cathode centered at the anode axis; a magnetic field diverging in the downstream direction provides the MPD acceleration for the charged particles. The article by Fradkin et a/. (f08)concerns a high-power (25 kW) thruster working with Li vapor fuel; comparison is made between its performances when using a conventional arc (plain cathode) and a HCA. The latter was found to be superior in many respects, i.e.. higher thermal efficiency (ratio of the total power in the plasma beam to the total input power); smaller current and voltage fluctuations; the hollow cathode was not damaged by operation in the “high voltage mode” (occurring when the vapor feed was smaller than a given threshold value), nor when extinguishing and restarting the arc at the pressure and flow rate running conditions. In both situations, the conventional cathode suffered serious damage; the hollow cathode (and the remaining parts of the system) were not damaged while running without the magnetic field. We further remark that the high voltage mode” occurring at low vapor feed rates may possibly be identified with the LQ regime we have studied for noble-gas HCA (even if in our conditions the current range was much lower, which may weaken the validity of the comparison). Burkhart (30) reports using an Xe-fed HCA in a low power (up to 1 kW) MPD thruster. The most interesting point in his experiment is the downstream position of the cathode, at the exhaust side of the thruster. The author finds that this arrangement improves the system efficiency in the whole range of specific impulses (Z5p < 2000 sec), as compared with the more usual position of the electrodes (anode downstream). He further remarks that the best performances occur at zero cathode flow, all the gas injection being made at anode level. This is quite understandable, as the cathode flow would be running opposite to the exhaust direction. “

E. ac Operatioti of HCA Two interesting applications were reported in this domain of HCA operation : electrodes for low pressure discharge lamps and high-power rectifiers. An electrode design for a gas discharge lamp as described by Bouwknegt and van der Kooi ( f 0 9 ) ,consists of a hollow cylinder with one closed end. The inside surface is of the nickel matrix type, where an emitting material is embedded. The two identical electrodes whose open ends face each other. are positioned at opposite sides of the discharge tube; the gas filling is 3 Torr Ar plus saturated Hg vapor (standard filling for fluorescent lamps). Measurements of the temperature distribution along each electrode show that the discharge penetrates a little distance into the electrodes. This mode of

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operation is not exactly comparable to the dc regimes in HCA operation; if any, it shows some similarities with the H P (moderate pressure) regime. When a rectifying effect is sought in the ac operation of a n HCA, we must take a n approach just opposite to the one in the preceding reference (symmetrical electrodes). Now the electrode design must emphasize the difference between cathode and anode, so that the current passes preferentially in one direction. Articles by Koltypin et a l . ( / / U - / 1 2 ) describe such a device. A cylindrical box-shaped metal chamber serves as the hollow cathode, enclosing a flat circular anode ; a n axially symmetrical, nonuniform magnetic field is created by a solenoid placed under the base of the chamber. Using this geometry with a chamber pressure p E 10-’-10-2Torr, a n arc ignites between the electrodes when the anode potential is several hundred volts positive with respect t o the cathode; when the polarity is reversed, the arc does not start up to voltages of several kilovolts between the electrodes. This performance is due to the proper choice of the interelectrode distance and the chamber pressure. When the “hollow cathode effect” is not present (during the cycle when the box is positive with respect to the disk) the ignition voltage is very high and no current flows; when the situation is reversed, the ignition voltage drops strongly and glow-to-arc transition occurs. The shape of the magnetic field helps to enhance this asymmetrical behavior. This device was found to be suitable for high-power rectification (discharge currents up to 100 kA).

-

F . Other Applications of H C A

We will only mention several other reported applications for HCA: plasma jets and torches (113). high current thyratrons 1/14}, thermionic converters (115, 1/61, electron sources ( / / 7 ) , metastable sources (9, l o ) , plasma accelerators (118). We finally report their use in plasma machines for research work, which we have mentioned before (18, 37, 78).

VIII. CONCLUSION We have studied hollow cathodes in the arc regime operation (HCA), where their advantages with regard to ruggedness, construction simplicity, and current-delivering capacity are the most interesting. A gas feed through the cathode channel allows a plasma to exist inside the hollow cavity; diffuse, extensive heating of the cathode wall by this plasma, causes a high electron emission yield, without damage t o the cathode itself, o r to the purity of the external plasma. As the cathode sheath voltage can be varied by adjusting the gas-flow rate, optimal conditions can be obtained for efficient ionization of the streaming gas; on the other hand, as no contribution of the external plasma is required for proper cathode operation, a n HCA can work in near vacuum conditions. So, the ionization degree of the external plasma is mostly limited by the pumping capacity o f the vacuum system.

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One of the most interesting features of HCA is the possibility of working in a very extended current range; when using multichannel hollow cathodes, the hollow cross section adapts automatically to the current requirements. However, the high-current performances of HC. either single o r multichannel, have not received much attention up t o now and extensive lifetime tests have not been performed. Another point deserving further research is the pulsed, high-current operation of these cathodes, which has scarcely been studied (6, 119). This regime presents many complicating phenomena (generation of shock waves, high field emission processes, thermal fluctuations) which are interesting to examine, and the experimental setup is quite easy to assemble due t o the low (average) power requirement. Finally, we must state that the theory of HCA operation still needs improving; a most decisive contribution would be given by better experimental knowledge of the internal plasma column parameters.

ACKNOWLEDGMENT The authors wish to thank Professor W. P. Allis, of the Massachusetts Institute of Technology and Dr. H. Minoo of the Laboratoire de Physique des Plasmas, Universite de Paris Sud for many discussions and helpful comments and Mr. F. Ronieiras of the lnstituto Superior Tecnico, University of Lisbon for his help in the bibliographic research work. The authors are also indebted to the Editors of the following publications: Applied Physics Letters, Coniptes Rendiis de I’Academic rles Sciences (Paris), Journal of Applied Physics, Journal of Quaiifum Spectroscopj, and Radiatiae Tramfer, Phjwks of Fluids. Pla.rma Physics, Proceedings of the 1st Interna~ioiialConference on Holloiv Cathode Discharges and Their Application.s, Quarterlv Progrrw Report (Research Laboratory of Electronics, Massachussets Institute of Technology), rapport.^ dii Cbmmissariar d I‘Energic. Atomiqiie (France), Rapportx Interno.\ c/u Laboratoiri. de PIiy.sicliie des Plasmas (Orsay), Revue Roumaine cle Plij~sique,Reoiew of Scientific In.w/tments,who graciously granted permission for us to use material previously published in these sources.

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K . W. Liewer, Experiments using a 25-kW hollow cathode lithium vapor MPD arcjet. AIAA J . 8(5), 886 (1969). 109. A. Bouwknegt, and A. G. van der Kooi, An electrode design for low pressure gas discharge lamps. Proc. Int. Conf: Gas Dbcharges, Ist, 1971 p. 217 (1971). 110. A. E. Koltypin, A. I . Nastyakha, and P. A. Smirnov, A valve effect in the low pressure arc discharge in the system of electrodes with a hollow cold cathode. Proc. Z.C.P.Z.G., 9th, I969 p.164 (1969). 111. A. E. Koltypin, A. I. Nastyakha, and P. A. Smirnov, Rectification in a low-pressure arc with a hollow cold cathode. Sou. Phys. Tech. Phys. 15(10), 1703 (1971). 112. A. E. Koltypin, A. I. Nastyakha, and P. A. Smirnov, Arc dynamics in a high current hollow cathode rectifier. Sou. Phys.-Tech. P h y ~ 15(10), . 1710 (1971). 113. A. S . An'shakov, V. V. Koslov, and M. I. Sazonov, Study of the free plasma jet. Proc. Z.C.P.I.G., Yth, 1969 p. 247 (1969). 114. B. 0. Baker, and J. Gowar, Hot hollow cathode phenomena. Pvor. Znt. ConJ Hollow Cathode Discharges Appl., Is?, 1971 p. 48 (1971). 115. E. G. Busygin, V. G. Grigor'yants, and 1. P. Yavor, Hollow cathode thermionic converter operating with a low-voltage cesium arc. Sou. Phys.-Tech. Phys. 2(1 l), 1593 (1970). 116. H. L. Witting, Hollow cathode discharge with thermionic cathodes. J . Appl. Phys. 42(13), 5478 (1971). 117. A. S. Roberts, J. L. Cox, and W. H. Bennett, Electron beams from a Duoplasmatron using a hollow cathode arc as an electron source. J . Appl. Phys. 37(8), 3231 (1966). 118. H. C. Cole, and A. J. Travis, The hollow cathode as a means of triggering and sustaining a plasma accelerator. Proc. Int. ConJ Hollow Cathode Discharges Appl., Is!, 1971 p. 46 (1971). 119. W. S . Bickel, Acoustical plasma wave in a hollow cathode discharge. J . Appl. Phs. 37(11), 4300 (1966).

* General references, not dealing specifically with HCA.

Gas Discharge Displays : A Critical Review R. N. JACKSON

ANt)

K. E. JOHNSON

Mullurd Reseurch Laboratories Redhill, Surrey, England I. Introduction

............................

............................................

191

11. The Characteristics of dc Discharge ....................... A. Static Voltage-Current Characteristic of a Gas-Filled D'

B. Dynamic Electrical Characteristics .......................... C. Light Output from Glow Discharge Cells ......... D. Sputtering of the Cathode .............................. ............................ dc Arrays ........................... A. Introduction ............................. 8. Basic Structures ....................... C. Sputtering and Leakage Resistance D. Priming ................................... E. Switching Conside F. ........................................... ............. F. Some Some Practical Practical dc dc Displays Di G . Color ................ H. Conclusions on dc IV. ac Arrays ................... . . .. . . . . . . .. . A. Introduction ................................................. B. Operation of the ac Panel ........... C . Characteristics of ac Cells D. Development of Present ac Panels .................................. E. Crossbar Address Methods F. Electron Beam and Optical Address Methods .............. ............. G. “Gray-Scale” Operation of ac Panels ..................... H. Other Features .............................................. V. Conclusion references

203

220

257 263

I. INTRODUCTION Gas discharge lamps were first used i n displays as modulable light sources in early mechanical television systems. Neon lamps have done duty as simple " on-off" indicators for nearly as long and counters and numerical indicators have been used in instrument displays for nearly 20 years. It is all the more remarkable. therefore, that the present time sees the gas discharge display not at the end of its development but rather at the beginning of a 191

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new and interesting phase. Gas discharges are entering new applications, offering special advantages to display designers and challenging the more highly developed rival cathode ray tube in the field of high resolution display. In this paper we attempt a review of the current state of the art in this interesting field. Such a review must, since the field is very wide, be somewhat selective in nature. We have chosen to concentrate on the newest forms of gas discharge display represented by the so-called “ matrix displays”: arrays of large numbers of cells forming a flat, planar, and relatively large-area display. These displays are not only newer but also pose special problems which are currently receiving much attention in research and development laboratories. Since two distinct forms of such display have arisen, with ac and dc drive circuits, respectively, we devote two complete sections of the paper to these topics. However it is appropriate to review briefly the smaller and more traditional forms of display in the numeric display field. There have recently been a number of changes both in the form of these displays and the technology used for making them. The mainstay of the numerical display field has been the formed character numerical indicator tube (NIT). These devices consist of (typically) ten cathode electrodes, each formed into the shape of a numeral, 0 to 9. The electrodes are stacked one behind another on insulating rods so that they are electrically isolated and are surrounded by a mesh which provides a common anode. The assembly is sealed into a glass envelope containing inert gas at a low pressure. Application of a dc voltage of the order of 170 V between the anode and any one cathode results in a negative glow discharge invested on the cathode in question, so that an illuminated numeral is formed. There is now a very wide range of such devices available from many suppliers with numerals ranging from less than in. high to about 2 in. high for various applications. The display suffers from the disadvantages that the numerals are not all in the same plane and viewing angle can be somewhat restricted. The contrast is also marred by the slightly blurred outline of the glow. Recent developments of this principle have been the planar array and the multidigit array. Planar numerical displays make use of the technique known as “barmatrix” operation to form the numerals. The cathodes of the array (usually seven in number) are all held in one plane and arranged as shown in Fig. 1. By addressing various cathodes simultaneously, numerals can be formed as shown. These tubes are proving extremely popular both because of the planar nature of the display and because the drive circuits required are cheap. In a typical arrangement a number of tubes forming an in-line multinumeral array are addressed sequentially by applying a positive potential to the anode of each tube in turn. The rate of switching is fast enough to ensure that an apparently static display is seen. As the potential is applied

+

GAS DISCHARGE DISPLAYS

193

to each anode, negative potentials are applied to the required cathodes to form the number. The corresponding bars of each tube may be interconnected and a single integrated circuit decoder-driver converts the input (usually binary) information to the required seven-bar form and switches the appropriate lines. Using individual tubes for an array of say 10 to 16 numerals calls for a substantial number of connections to be made and causes digit spacing to be relatively wide because of the envelope sizes. To overcome this, manufacturers have introduced multiple digit tubes containing up to 16 numerals in one envelope with all connections made internally. The first of these was a multiple formed cathode tube ( I ) . This tube contains 14 digit positions within a glass tube about 180 mm long and 28 min in diameter. The connections to the array are brought out at each end of the tube. Formed character cathodes are

FIG.1. Seven-segment bar matrix numbers.

used with a separate anode for each stack on the rear side. The arrangement provides a convenient display package with some restrictions of viewing angle. More recently bar-matrix multiple tubes have been introduced to the market (2, 2a). These devices, which are available in up to 16 digit in-line form, come closer to the display “panel” format. A flat glass back plate and a flat glass front window are separated by a spacer. Within this panel envelope up to 16 sets of bar matrix cathode segments are held, together with the necessary intercathode connections. A separate anode for each digit position is also provided. In some versions the bar matrix format includes two extra central vertical bars in addition to the seven-bar basic set. This allows a central numeral 1 and some other characters to be formed. A further development of significance in the numeral indicator field is the application of thick film technology to display fabrication (3). In a typical thick-film bar-matrix multiple-digit tube, a flat glass substrate is used to support printed conducting patterns which form both the electrodes and their connections. The conductors are arranged in a number of layers, insulated from one another by thin interleaving glass layers except at points where through connections are required. The uppermost layer is similarly covered by insulating glaze except at the electrode positions. The electrodes are left exposed and covered with a metal layer to reduce effects of sputtering.

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R. N. JACKSON A N D K. E. JOHNSON

A glass front plate and pump stem are sealed to the substrate to complete

the panel. The thick-film technique enables thin, flat, and rugged multiple digit arrays to be made, including small digit size types suitable for calculating machines. For example, the display described in reference (3) has 0.3 in. high characters and a 16 digit array is reported to have a brightness of 100 fL for a 5 mA mean current from a 175 V supply. With the introduction of this type of display, gas discharge devices continue to hold their own against other displays such as light-emitting diodes and liquid crystals for applications requiring up to 20 numerals.

.. ............... .. .... .. .... . .. ..... ......... .. .. ... .. .. .... ... ...... ...... ...... . . . .... . .... .... ... ....... . . .. . .. ... .. . .. . .. ... .... ... . . . . .. ... .. ... ... .. ... ... ... . ... ... . ... . .. . ... ... .... ... .... ... .... ....... .. ..... .. ...... .. .... ... . ... .... ... .... .. .. .. ... .... .. . .. . ... .......... ..... ... . ...... .... ........... .... ........ .... .......... ......... .... .... ..... .... .... . ... . . . . . . . .. .................... . . . . . . . ..... ... ...... ..... .......... . ... .. .. ........ . .. . .... ... ... . .. ... ........... . ..... ... . ... ... . . . . . . . . . . . . . . . . . ...... FIG. 2. Dot-matrix characters. (Courtesy of Institution of Electronic and Radio Engineers).

In addition to numerical displays, there is now a demand for those in which both alphabetic characters and symbols are also available. While a limited number of these can be provided by adding additional preformed or bar cathodes, there is clearly a limit to what can be done with such techniques. The alternative is to use the dot-matrix technique. Figure 2 illustrates the dot-matrix method. Each display character is formed by exciting the relevant cell of (for example) a 35-element array of discharges, arranged in a matrix seven cells high by five cells wide. Some of the characters that can be formed are illustrated. A 35 element array can provide all numerals, upper case letters, and some symbols. More sophisticated symbols and lower case letters can be formed from larger dot arrays. With the introduction of the dot-matrix technique a wide spectrum of display applications has been opened up. A single character device can be made having only 35 elements. Multiple chrvracter registers can be formed by extending the array to, for example, 7 x 100 elements. Message displays can be envisaged having thousands of dot elements, while for graphical data and television tens or hundreds of thousands are necessary.


195

A study of matrix displays is given in Sections 111 and I V of this paper. To assist the understanding of these sections, however, we present first, in Section 11, a brief resume of the fundamental physical characteristics of gas discharges between metal electrodes, with particular reference to those which are important to matrix display techniques. The special characteristics of capacatively coupled cells, in which the discharge takes place between electrodes covered with insulating material, are diacussed i n Section IV.

11. THECHARACTERISTICS o i - dc DISCHARGE CELLS A . Static Voltage-Current Characteristic of'a Gas-Filled Diode

Consider a simple structure composed of two plane-parallel metal plates contained in a glass envelope filled with gas at a pressure below I atm. A steady voltage, say, a few tens of volts applied across the electrodes causes a very small current (typically less than lo-") A) to flow. This is initiated by the few ions and electrons which are always present in such a gas through the action of normal ambient radiation, e.g., cosmic rays. As the interelectrode voltage is increased slowly, the observed effect is that the current also increases slowly at first, but then much faster until a point is reached at which the voltage no longer controls the current. When this condition occurs the current increases rapidly and can build up to a high level which may damage the diode unless a suitable current-limiting impedance is connected in series w i t h the diode and the voltage source. A characteristic curve of voltage against current which illustrates this behavior is shown in Fig. 3. The values shown do not represent any particular diode but could be typical of a neon-filled device. Three areas. or states. are marked on the characteristic. Each of the5e state5 will now be discussed in more detail. 1. The

"

Of' Stare

The "off" state includes t w o maiiL regions. the first from zero current to the point A, and the second from A to B in which the current may increase by approximately two orders. The latter is called the Townsend region. In the first region the current is limited by the supply of available ions and electrons. This IS dependent on incident radiation (either photons or other particles) and on the rate at which ions and electrons recombine before reaching the electrodes. Since increasing voltage accelerates the ions and electrons, more will reach the electrodes in a given period. causing an increased flow of

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R . N. JACKSON AND K. E. JOHNSON

current. If the rate of generation of free ions and electrons is increased, e.g., by stepping up the incident radiation or injecting electrons from another source such as an auxiliary discharge, the whole characteristic can be moved in the direction of higher current, having the effect of reducing the height and width of plateau in the Townsend region. This is commonly called “priming.” In the Townsend region A B the rapid current increase is due to two factors: ion multiplication and secondary electron emission from the cathode. Both Trans it i on state

c

I I I I

I I I I I

t

1\___1 0 2 E f f e c t of prlmlng current

FIG. 3 . Static voltage-current characteristic of a gas-filled diode.

factors can be the result of several different effects, e.g. ion multiplication can occur when free electrons reach a sufficient energy owing to the accelerating field ionizing a gas molecule, the ejected electron in its t u r n acquiring sufficient energy to repeat the process before recombination or collection by the anode. In this way an avalanche can build up. Ionization by ion-atom collision does not take place until the velocity of the ions is of the same order as that of the electrons, and since the energy required is several orders higher than for electrons, the ions themselves do not contribute significantly to further ionization. However, some of them, in striking the cathode, will eject additional electrons which in t u r n will contribute to the ionization process. In varying degrees, photons and metastables also cause secondary emission of electrons from the cathode.


197

2. The Transition State As soon as the number of electrons generated in the process described above becomes greater than the number leaving the cathode, the current increases almost independently of the interelectrode voltage, and ignition is said to occur. In general the high mobility electrons tend to leave a space charge of the slower moving ions near the cathode. This space charge can be thought of as a virtual anode since most of the interelectrode voltage occurs between the space charge and the cathode and there is only a low field between the space charge and anode. As the current increases, the space charge moves toward the cathode. This movement increases the local field around the cathode, yielding more efficient ionization and causing the current to increase still further, while the interelectrode voltage actually decreases. Thus the negative resistance part of the characteristic BC is produced. The maximum voltage Vi at point B, which must be exceeded for space charge effects to begin to control the discharge current, is known as the ignition voltage.

3 . The ‘‘ On” State The transition state continues until a value ofcurrent densityat thecathode, which produces the most efficient ionization of gas molecules, is achieved. For subsequent increases in current, the density remains constant but the glow expands to cover more of the available cathode area. The interelectrode voltage is now typically almost constant with varying current, rising perhaps 10 to 20 V over two or three orders of magnitude of current increase. However. as soon as the discharge covers the whole of the cathode, the ionization efficiency begins to drop and the voltage rises more rapidly with current. The nearly flat portion of the characteristic is known as the “normal glow” region; when the voltage begins to rise, the discharge is said to be in the “abnormal glow” region. We will call the voltage in both these regions the maintaining voltage V,,, of the discharge. It is normal practice to limit the current in the “on” state by a series resistance. The discharge can be extinguished by either increasing the value of this series resistance or by reducing the voltage applied across resistance and cell, the latter being the more common method. Thus, assuming a fixed resistance, as the applied voltage is reduced the voltage between anode and cathode decreases by a few volts until it reaches a minimum value (point C). Further reduction of applied voltage causes the operating point to move into the unstable region BC. In this region there is a minimum current, called the holding current, below which the discharge cannot be maintained. For a given series resistance, the holding current defines a particular applied voltage, called the extinction voltage, V,.

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R. N . JACKSON A N D K. E. JOHNSON

4. Factors Affecting Ignition and Maintaining Potentials Both ignition and maintaining potentials depend on the ionization of the gas and the secondary effects at the cathode. A mixture of neon with l.O?/,argon has the highest ionization efficiency of any of the commonly used gas fillings, and with suitable cathodes therefore gives the lowest attainable ignition and maintaining voltages. An important reason for this is the interaction which occurs between metastable neon atoms (Le., atoms which are in a quasistable excited state having a lifetime of typically several milliseconds) and argon atoms. In pure neon two metastables can give one ion, thus: 2Ne* = Nef k e -

+ Ne,

but since it requires the direct impact of two metastables the process contributes little to the ionization. When argon is added, the neon metastables can ionize the argon atoms according to the equation Ne*

+A=

A+

+ e- + Ne.

Since the energy of the metastable (16.6 ev) only slightly exceeds that required to ionize the argon atom (15.6 eV), the reaction has a high probability, about 3 x lo3 times the probability of ionization in pure neon by metastable collisions. As a result, the ionization efficiency is increased compared with pure neon. This is known as the Penning effect and gas mixtures i n which the effect occurs are called Penning mixtures. It has been found by experiment that ignition voltage Vi depends on the product of pressure p and electrode separation d, a fact usually known as Paschen’s law after its discoverer. Curves of Vi against p d commonly show a minimum value of Vi for a particular value, or range of values, of pd. This reflects the drop in ionization efficiency, and therefore increase in V i , at very low or very high pressures. For example, with iron electrodes, neon shows a minimum ignition voltage of about 250 V at about 3 Torr-cm; for neon plus 0.1 argon the corresponding values are about 200 V and 30 Torr-cm. Lower values can be obtained with other cathode materials, e.g., molybdenum. B. Dynamic Electrical Characteristics 1. Switching froni ‘‘ Of’

to ‘‘ On” States

If the voltage across the cell is suddenly increased from below V, to above

V i ,a discharge does not immediately occur. The time lag depends on two factors: (1) the availability of free ions and electrons to initiate breakdown; and (2) the time taken, once breakdown has begun, for the current multiplication processes to build up. The first of these factors, the time which

199


passes in waiting for an initiating particle or particles, is usually called the statistical lag since it is essentially a random quantity. The second is known as the formative time. The statistical lag can have a very wide range of values. In the absence of light, which can provide photoelectrons, breakdown depends on a suitably energetic cosmic ray which may take minutes to arrive. However, priming agents in the form of radioactive material or a nearby auxiliary discharge can reduce the lag to the order of milliseconds or less. The effects of a neighboring discharge are particularly important in displays composed of an array

t\

l50l

0

Necln-clrqln m i x t u r e

25

50

I 75

100

Ignition delciy (Dsec)

FIG.4. Applied voltage versus ignition delay.

of closely packed but not completely isolated cells. In such a case the lag can be reduced to the order of microseconds; furthermore, ignition voltages are reduced. The reduction in Vi can become almost large enough to remove the transition state from the V-l characteristic and allow Vi to approach V,. The formative time is usually short in comparison with statistical lag, being typically of the order of ten microseconds, but it depends on the actual voltage applied to the diode. This relationship is illustrated in Fig. 4 for a neon-argon filled diode with an auxiliary discharge to overcome statistical lag. In this case the switching pulse would have to be at least 5 psec in duration to be effective, even for very large overvoltages, i.e., voltages in excess of the dc ignition voltage. 2. ‘‘ On” to ‘’ Off”Transitions A discharge will switch “off” if the applied voltage falls below the extinction potential V,. However, the current will not fall to the level dictated by the characteristic in the Townsend region immediately and may take several

R. N. JACKSON AND K. E. JOHNSON

200

milliseconds to decay to this value. If the voltage is increased above V, too soon then the discharge may switch “ o n ” again due to the priming of the remaining ionization products. A typical example of this behavior is shown in Fig. 5, again for a neon-argon gas mixture. Address pulses 100 psec long with a variable repetition period T were applied to the diode in series with a 68 kQ load resistor. A fixed bias level between pulses, V,, of 100 V was used, ie., V, was about 20 V below V , . For a particular value of T the pulse amplitude

100 0

1

2

3

I n t e r v a l b e t w e e n pulses, T (msec)

FIG.5. Minimum reignition voltage versus address interval.

was reduced until the discharge extinguished, when the applied voltage was noted. This represented the minimum level at which reignition occurred for that repetition period. It can be seen from the graph of the minimum reignition voltage versus the address interval that a sufficient number of ions remain for a period of up to 2 msec or so to prime the succeeding discharge. Thereafter the discharge reignites only with much higher voltages and eventually, unless other priming agents are available, will fire erratically. The period which must elapse before the interelectrode voltage can be switched above V, during an “ o n ” to “off” transition is often called the recovery time. Recovery times are a function of the gas used, its pressure, and the residual field between the electrodes. The residual field in turn depends on the interelectrode spacing and voltage. Other factors are the initial discharge current and the composition of the cathode surface. A review of


201

recovery time measurements by various workers who investigated the effects of these factors has been given by Weston ( 4 ) . In general recovery times increase with increasing discharge current but decrease with increasing residual field. However, a minimum time is reached when the ‘* sweeping-out effect of the field on the ions and electrons is counterbalanced bytheionization due to the field. Further increase of field results in a rapid increase of the recovery time, tending to infinity as the voltage across the electrodes approaches the maintaining potential. An interesting empirical law which enables recovery times in different gases to be compared was discussed by Acton and Swift (5). They established that the fraction t,p/d was approximately constant for various gases, where p is the pressure, d is the interelectrode distance, and t , is the recovery time. t, was defined as the time period after extinction for the reignition voltage to have risen to half way between the maintaining and ignition voltages, with the interelectrode voltage during deionization held constant at half the maintaining potential. For neon they found a value of 30 msec-Torr/cm, but for a mixture of neon and 0.5% argon the constant was much greater, having a value of 120 msec-Torr/cm. However, the addition of 4 % hydrogen to this mixture, keeping the proportion of argon constant at 0.5%, gave a value of only 3.0 msec-Torr/cm. The ability to procure different recovery times by adjusting the gas mixture can be important for display panels. For cyclically addressed panels it can be convenient to make the recovery time as long as possible, thereby preventing flicker due to unreliable ignition (see Section 111, D), while for dc storage panels short recovery times are needed to allow fast update rates. ”

C. Light Outpur from Glow Discharge Cells When glow discharge devices are examined it is apparent that light is emitted from a region near the cathode but separated from it by a small distance. These regions are usually known as the negative glow and the cathode dark space, respectively. If the cathode and anode are sufficiently far apart and depending upon the pressure, a second light-emitting region may be observed between the negative glow and the anode but separated from each by two dark regions. Passing from the negative glow toward the anode, these regions are called the Faraday dark space, the positive column, and the anode dark space. Occasionally a glow may also be observed around the anode itself. If the interelectrode distance is made progressively smaller, the positive column reduces in length but there is virtually no change in either the negative glow or the cathode dark space. Movement of the anode into the Faraday dark space results in the disappearance of the positive column. The

202


geometry and gas pressure of most display panels is such that the negative glow represents the only glowing region. In this situation virtually all the potential drop occurs across the cathode dark space. This cathode fall voltage, as it is called, is then almost exactly equal to the maintaining voltage Within the relatively low field of the negative glow region, free electrons have insufficient energy to ionize many gas atoms but the large numbers of electrons passing through the region excite a correspondingly large number of atoms to energy levels above their ground states. These higher energy states typically have lifetimes of only about lo-' sec and in the transitions back to the ground state, either directly or through intermediate levels,

Wavelength ( n m )

FIG.6. Eye-corrected spectral distribution.

photons are emitted at various wavelengths. The effect of these photons on the eye depends on their distribution within the sensitive range which extends from about 400 to 700 nm, peaking at about 555 nni under normal levels of illumination. A typical spectrum for a neon-argon-mercury mixture with correction for the sensitivity of the average viewer is shown in Fig. 6. For some types of discharge a single neon line at 585 nni can contribute more than 30% of the total light affecting the eye. The efficiency of light production in the negative glow of a neon-argon dischargeis typicallyoftheorderofO.1-0.2Im/W, and for neon this figure may be a factor of three higher. These values compare favorably with red solid-state light emitters but are two orders lower than the highest practically achievable values obtained with cathodoluminescent or ultraviolet stimulated phosphors. For a display, the subjective brightness, or in physical terms the luniinance (defined as the intensity per unit area), is more important than the intensity. Unfortunately it is not a quantity which can be measured as reliably as the intensity, since different workers may assume different areas over which the measurement is made. For example, depending on the aperture of the equipment used, luminance values may be measured by integrating over many


203

simultaneously addressed cells, or only over the area of one cell, or perhaps over only part of one cell. The first method would be suitable where individual cells are not resolvable by the average eye under the viewing conditions adopted. For present-day gas discharge matrix displays used in desk-top instruments under normal room lighting, individual cells can be resolved ; the second method, integrating the light over the area of one cell, is therefore preferable. Measured in this way, dc-driven cells containing neon can easily achieve luminance values of several thousand candelas per square meter; these cells are visible in bright sunshine. In dynamically driven displays where the duty factor may be as low as 0.5”,, brightness suitable for viewing in normal room lighting can still be achieved.

D . Sputtering of the Cathode In a gas discharge the cathode is subjected to bombardment by gas ions which may have sufficient energy to dislodge atoms from the cathode surface. Many of these atoms will be deflected by collisions with gas atoms. However, some will take a random path directed away from the cathode region and be deposited on other surfaces within the device. This process is known as sputtering. As might be expected from the above description of the effect, the sputtering rate depends on the type of gas and the cathode material, the gas pressure and the current flowing in the discharge. The most important of these factors appears to be pressure; it has been found empirically that the sputtering rate varies inversely as the nth power of the pressure, where n is usually greater than 2 and, according to Acton and Swift (6),may be as high as 5. The effect of current is almost as important; in practice the rate varies directly with the square or cube of the current. In general the heavy gases, e.g., krypton, cause a greater rate of sputtering than the light gases such as helium. The amount of sputtering from a metal cathode for a given type of ion and energy seems to depend on the position of the metal in the periodic table. For example, i n ascending order of atomic number, titanium sputters less than iron, which sputters less than copper. As a rule, sputtering increases with atomic number in any one period of the table. Control of sputtering is very important to the device designer. In the initial processing of a device, sputtering can be beneficial in allowing really clean, and therefore stable, cathode surfaces to be formed. This thorough cleaning of the cathode, together with the fact that the sputtered layer often acts as a good “getter” of impurity atoms within the gas, results in steady electrical characteristics and improved life of the device. However, continued sputtering after this initial stage is a nuisance, especially in matrix displays

204


where the deposition of sputtered material over the window can cause significant reduction of the light output. The geometry of the device can be arranged to reduce this, a good example being the design of the recessed cathode matrix (see Section 111, C ) . Two other important effects of continuous sputtering are the production of electrical leakage paths between conductors; and gas “cleanup,” i.e., trapping of inert gas by sputtered deposits, with consequent loss of gas pressure. Each of these effects can shorten the life of the device by changing its electrical characteristics in an adverse way. For example, if the resistance between cathodes of neighboring cells decreases, “cross-firing’’ can eventually occur; that is, an unwanted glow can occur in the neighbor when the required cell is addressed. Lowered pressure due to gas cleanup gives a higher rate of sputtering, and a runaway situation can be produced in which the ignition and maintaining voltages rapidly move out of the specified ranges unless the gas is replenished. Where possible, this effect is avoided in practical devices by designing thedevice to have a sufficient volume so that pressure changes during the required lifetime are small. Preferential cleanup of argon from a neon-argon Penning mixture is a particular problem due to the small argon percentages normally used. Sputtering can be considerably reduced by adding mercury to the gas mixture. The reasons for this are not clear, but the usual theory that is suggested involves a dynamic equilibrium between mercury vapor in the gas space and mercury atoms condensed on the cathode surface. When an ion ejects an atom from this surface, a mercury atom condenses from the vapor to take its place, thus maintaining a constant surface state although material is continually moving. 111. dc ARRAYS A . Introduction

In displays based on dot-matrix arrays of gas discharge diode cells, as opposed to the formed character and seven bar-types discussed in Section I, a number of new problems arise. These all stem from the fact that there are a large number of individual light-producing elements in close proximity one with another and having an unusually small size. Elements typically are of the order of 1 mm (0.04 in.) or less in diameter with a similar spacing between them. The anode-to-cathode spacings involved are similarly close and with Penning mixtures, breakdown voltages of a few hundred volts are obtained at pressures of 100-200 Torr (see Section 11, A , 4). In this section we discuss these arrays with particular reference to dc operation. So far as possible, reference is made to published information.


205

However, although there are known to have been a fairly large number of researchers engaged in the early history of dc panels, the authors have found relatively few papers in the standard literature relating to that work. The bulk of the available papers are of recent origin and come from only two or three sources. Thus we draw much on our own experience in this area. B. Basic Structures

Consider a simple display designed as a replacement for a formed character indicator. As previously mentianed an array of 35 cells in seven rows of five cells will suffice. One way to achieve such a display is to adopt a similar Glass

\

Plate cathode

Cavity

/

Corinectilq lead

FIG.7. Plate-cathode structure. From Hall (7).

principle to that of the formed character tube and employ a single anode electrode with 35 separate cathode electrodes, each of which has an external connection. An early attempt to make such a tube has been described by Hall (7). Molybdenum pins were sealed into a hard glass foot so that the heads of the pins formed the cathodes on which the glow was invested. The anode was a transparent tin oxide layer deposited on a glass viewing window which formed part of the envelope. While this tube had satisfactory characteristics, its construction was expensive and problems of interconnection were encountered. An alternative construction has been described by Weston and Hall (8) and is currently used in a manufactured tube ( 9 ) . In this construction a “plate” cathode structure is used with the leads brought out at the sides (Fig. 7). The 35 cathode plates, together with their lead-out connections, are formed simultaneously by photoetching a sheet of suitable glass-sealing metal. The resultant “lead franie” is sealed i n a glass molding so that the wires are isolated from the gas, but each cathode plate is at the bottom of a small gas-filled cavity as shown. I n this case an etched frame anode is dlso employed and the tube is completed with a flat glass viewing window; the

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R. N. JACKSON A N D K . E. JOHNSON

three components being sealed together with enamel (Fig. 8). Commercial versions of the tube incorporate two additional cells so that a decimal point can be shown either to the left or right of the numeral. With the diniensions used in this tube, where the cathode plates are at 1.5 mm (0.06 in.) center-to-center spacings, the lead-out diniensions and disposition are such that connection can be made to printed circuit boards by standard soldering techniques and arrays of characters can be built up by mounting the tubes on suitably wired interconnection boards. It is clear,

View I ng w I ndow

c o v i t ies

FIG.8. Assembly of 35-dot matrix indicator tube. From Hall (7).

however, that this technique is limited to displays which show only a small amount of information having a relatively coarse structure. For this reason most workers have turned to the X- Y address or “crossbar” construction for larger arrays. Figure 9 shows a typical form of crossbar tube. The electrodes are two sets of parallel strips which are mounted orthogonally. One set constitutes all the anode electrodes and the other, all the cathodes. When a positive voltage is applied to an anode strip and a negative voltage to a cathode strip, a discharge takes place at the intersection of the two. I n this way a total of n x rn cells may be addressed by means of only rn + n external connections. An aperture plate or mosaic structure between the electrodes has been used since the earliest experiments (10-11~).In the case of ac panels reviewed below it has subsequently been found possible to remove much of this structure. However, in dc arrays it has been retained, even though it complicates the construction. Reasons for this retention are cross-firing and sputtering. Figure 10 shows a section of a hypothetical unstructured panel having

FIG.9. Typical crossbar array construction.

A

B

C

V+

V-

FIG.10. Spurious discharges i n a n unstructured crossbar panel.

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R. N . JACKSON AND K. E. JOHNSON

cathodes ABC and anodes DEF. Ignoring the status of the unselected electrodes, assume that a positive potential is applied to E and a negative to B with the intention of establishing a discharge at the intersection BJE.In the absence of a structure, discharges may occur in principle from any point of electrode B to any point on electrode E. Spurious discharges are indicated, for example, from the cathode at B/F and B/D to the anode at B/E and from the cathode Window

\

sputter

t rav Cathode strlp

FIG.11. Isometric view of molded crossbar panel with ridges. From Hall et 01. (,12).

at B/E to the anode at A/E and CJE (dashed line). Others may take place such as from B/F to C/E or A/E (dotted lines). While it is generally true that the field will be strongest at the wanted intersection and hence a preference for breakdown at that position exists, in practice the points between which discharge occurs will depend upon a number of other factors such as the local surface properties of the cathode strip and the local degree of ionization of the gas. Since the surface properties will not be completely uniform even when the tube is new, and since both these and the ionization will vary with time, cross-firing can occur. The presence of the cellular structure serves to isolate the individual cells of the matrix and prevent this.


209

The anode-cathode spacing in some panel arrays is so small that positive column and anode glows are suppressed. Light output is obtained only from the cathode glow. Weston (personal communication) has pointed out that, provided a cathode glow alone is involved, spurious discharges from the wanted cathode (B/E) to other points on the same anode are relatively unimportant since the light output still comes from the wanted position. This implies that a complete honeycomb structure may not be required so long as parallel ridges isolating the anodes are included. So far as the authors are aware no experiments with ridge-only dc panels have been reported, but a panel described by Hall et al. (12) makes partial use of this feature of negative glow discharges.? An isometric view of this panel is shown in Fig. 1 1 . The panel consists of two molded glass components: a base containing the cathode strips and cell structure-similar to that described for the single character tube-and a viewing window to which the anodes are attached. Each row of cells with its respective anode strip is isolated by molded glass ridges which also serve to support the window plate. Smaller ridges are formed between cathodes. The gap along the rows allows free passage of ionizing particles to assist priming (see Section 111, D). The ridges between the cathodes are included to minimize effects of sputtering. C . Sputtering and Leakage Resistance Sputtering in dc panels poses formidable problems and was a major factor limiting the life of early displays. In addition to the problems noted in Section 11, such as gas cleanup, there is a strong possibility in matrix displays that material sputtered from the cathodes will be deposited in such a manner as to impair the cell characteristics. Hall et al. found that the recessed cathode arrangement (Fig. 7) limits some of these effects by trapping the sputtered material in the cavity so that window blackening and anode-cathode shorts, for example, are reduced. However, in structures such as in Fig. 1 I , the additional possibility of a leakage path from cathode to cathode arises. Unless this is kept to a low value, cell switching may become difficult as the sputter film builds up with life. Figure 12 represents adjacent cells in a matrix which share a common anode crossbar but have separate cathodes. Suppose cell I is on and cell 2 is off and it is desired to reverse this condition. As shown in Section I 1 there is a finite time before discharge current builds up when a potential is applied. There is also a finite time after potential is removed before deionization occurs. At the moment S, is opened and S2 closed therefore, current can flow through

t The panel described by Harman (22) also makes partial use of ridges (see Section 111, E, 2).

210

K. N . JACKSON A N D K. E. JOHNSON

cell 1 via the leakage resistor R,. With cell 2 off, the potential at K , becomes V2 = V,.R,/(RL + R,) which reduces the applied voltage V,,, by V , . With the values shown a leakage resistance of 1 M a reduces the applied voltage by 9 V which may be sufficient to prevent cell 2 from striking. Provided cell 1 extinguishes, V , returns to zero and cell 2 is permitted to strike. However if the current through R , + R, exceeds the holding current of cell I , the unwanted cell may remain lit.

Anode crossbar

V h t + 200v

R, = R 2 = l O O k

v, =1oov

FIG.12. Switching circuit including cathode-to-cathode leakage resistance.

This effect of leakage can be offset by increasing the supply voltage such that the ignition potential of cell 2 is always exceeded. Then as cell 2 takes current this assists extinction of cell 1 . However the penalty is that the switching voltages are increased and semiconductor switches become more costly. The condition illustrated in Fig. 12 presents an extremely simplified view of one particular instance of the leakage effect that affects switching performance in a number of ways. In reality, there are also other reactive effects that have been ignored in this discussion. As stated in Section 11, sputtering can be inhibited by the introduction of mercury to the gas mixture. On the other hand, sputtering is a useful method of cleaning the electrode surfaces and stabilizing the tube characteristics. A procedure described by Hall et al. (12) is to clean the cathodes by screening” under high peak pulse current conditions. During this process the effects of sputtered material escaping the molded cavities are reduced by “

G A S DISCHARGE DISPLAYS

21 1

the contouring which presents the maximum path length between cathodes. After screening, mercury vapor is introduced to inhibit further sputtering with life. Little has been published about the procedures adopted in other types of panel construction but it is known that mercury vapor is widely used as a sputter inhibiter. Similarly burn-in ’* procedures for cleaning electrodes are common. Walters (13) also mentions the use of nickel cathodes as contributing to improved life characteristics in a tube with a thick film electrode construction. However, no figures are given which would permit this to be compared with tubes of conventional construction. “

D. Pritiiitzg Another feature which must be carefully considered in the basic panel design is priming. As explained above the degree of priming influences both the time taken for a cell to strike when the switching voltage is applied, and the value of this voltage. These in turn have an important influence on the size and cost of the display. I n order to reduce statistical delay time, some panels incorporate a small quantity of radioactive gas such as tritium in the gas mixture. Using this method Walters (13) quotes address pulse lengths of 500 psec down to I00 psec (with 6.5 ?< overvoltage) as necessary for the “worst case” condition where an isolated cell must be struck with no adjacent cells in the “ o n ” state. For slowly updated panels this may be satisfactory but for continuously refreshed displays (see below) the delay must be much shorter. Two alternative methods of reducing delay time and providing a stable display are known. The first is to provide cells in the array which are permanently on and to arrange for these to supply the necessary initial ionization by diffusion of the charged particles. The second is to readdress the cells suficiently frequently that there is remanent ionization from one address to the next. This is known as self-priming.” The latter method has the difficulty that it does not become effective until the cell (or a near cell) has struck at least once-i.e., there is a “cold start” problem. Some fixed priming may therefore also be needed. A convenient method of providing priming is to arrange for rows or columns of “ o n ” cells at the edges of the panel. The value of this method is critically dependent on the size of the panel and the type of internal structure employed. Jackson and Johnson (14) have evaluated this for structures such as in Fig. 1 1 in which the open channels along the anode rows ensure very high coupling between immediately adjacent cells. As an addressed cell becomes further away from an “ o n ” cell, the priming effect is reduced. “

R. N. JACKSON AND K . E. JOHNSON

212

; i 9oot , , , l , l , l , , 5.0, .4-

20

10

9g

t

30

Cathode position

Prime

FIG.13. Ignition voltage Johnson (14).

8s a

40

ii’

I ’I‘ ir in

8

function of distance from prime cells. From Jackson and

Figure 13 shows the ignition voltage as a function of cell position for a row of 50 cells with one priming cell at each end of the row. The relative values with a 50 Hz pulsed address and end primes, compared with the values for the same pulse condition and adjacent priming are shown. This method is clearly limited to relatively small arrays although it has been successfully used in conjunction with self-priming for a 56 character display having rows 90 cells in length. A more effective method of ensuring a high level of priming has been described by Holz (15). A separate (unseen) priming cell is provided for every cell in the array. Figure 14 shows the arrangement. A common cathode electrode separates two back-to-back cells that have independent anode electrodes and are filled with a Penning gas mixture. A hole “ a few thousandths of an inch” in diameter allows metastable atoms from the gas of the rear priming cell to diffuse into the display cell and create ionization of the Penning additive in that cell. The size of the hole is such that positive column discharges cannot be set up and the two cells behave as essentially separate discharges.

Ceramic sheets rontoinmg 25 psec for a conventional single layer panel with 40% overvoltage. However Hall ef a/. (12) claim a delay of 10-15 psec for a single layer panel in which both end priming and self-priming are used. Persanal communication with the authors established that this corresponds to a 20 % overvoltage.

E. Swifching Considerations In the course of work on dc arrays some general conditions of switching have been noted and some particular methods have become established. These will now be described. I . The Basic Switch-Clamping

If a potential is applied across a pair of crossbars such as B and E in the array of Fig. 10 it might at first appear that cell B/E will be unambiguously selected and no other cell can strike. Even with internal cell structure this is not so unless some precautions are taken. In practice there will be switches attached to all other electrodes. These will not be ideal and the unselected

214

R. N. JACKSON AND K. E. JOHNSON V j : HT+

Cathode cr ossbar

crossbar

FIG.16. Typical switching circuit for a dc panel.

or " floating " electrodes could therefore be at ground or supply potential causing unwanted cells to ignite. Cross-firing due to this cause is avoided if the unselected rows andcolumns are clamped to suitable potentials via relatively low impedances. [See also Sobel (16) for an analysis of clamped and unclamped crossbar selection systems.] Thus a typical switching circuit is as in Fig. 16. In the on state both transistors are driven into saturation and the full ht supply voltage is applied to the cell. The diodes are biased off and resistors R , and R , form the transistor collector loads. In the off state the transistors are substantially nonconducting and the cell electrodes are connected to the intermediate potentials V 2 and V , . The diodes conduct to limit the maximum potentials which can appear across the transistor switches. Figures 17a and b show simple voltage-time diagrams indicating the

I

V.

Time

(a 1

-

-

IIfr>c

(b)

FIG. 17. Voltage versus time diagrams showing (a) anode and cathode potentials, and (b) potential across the cell.


21 5

potentials to which the switches are connected and the potentials appearing across the cells with this arrangement. The spread in ignition potential which occurs between various cells in the array is also shown. The potential across the “off” cells, or the bias V , (= V , - V,) is important. If Vb is below the extinction voltage, V , , of the cells then there will only be light output during the actual address period. In order to maintain the display each point must be continuously readdressed (or cycled) at a rate fast enough to avoid flicker. On the other hand, if Vb is between the extinction and ignition voltages then a cell, once having been ignited, will remain glowing after the address period and until it is extinguished by switching the electrodes to a third potential below V , . There are thus two distinct modes of operation in dc discharge displays: cyclic and storage,” the latter being so termed because the data written into the display are stored there as a light pattern by virtue of the maintaining bias. “

”

“

2 . Cyclic Mode of Operation As pointed out by van Houten et al. (17) in this mode of address coincident pulses are applied to the anode and cathode crossbars such that either (a) one cell at a time is addressed-so-called “dot-sequential’’ operation, or (b) a number of cells on either the same row or the same column are simultaneously addressed (“ row-sequential or “ column-sequential ” operation). The control of current through the discharge is effected by external current limiting resistors of which there need be only one resistor for each column or one for each row electrode. These resistors are time shared between all cells on the electrode to which they are connected. The limiting factors associated with this form of address for dc panels are due to the duty factor. For the same brightness, the lower the duty factor the higher the peak current required. Van Houten (17) estimates that for negative glow cells which have an efficiency of 0.2 Im/W a maximum duty factor of 1 :250 can be allowed if acceptable brightness is to be combined with good life characteristics. This effectively rules out dot-sequential operation. The conditions for row-sequential operation have been described by Jackson and Johnson (14). Each row is addressed in turn and during the row address period the appropriate columns are simultaneously addressed. The following conditions apply (Fig. 18) : ”

-

-

(a) The sum of the row and column pulse voltages together with the bias voltage must exceed the maximum ignition potential of any cell in the array: vb

f

VR

+ vc >

vimax,

216


(b) The row pulses (plus bias) alone must not be able to ignite any cell in the array, i.e., must be lower than the minimum striking voltages: Vb

+ VR < Vj

min.

(c) The sum of the column pulse voltage and bias voltage must be less than the minimum extinction voltage of any cell: Vb+

VC
ve max .

For both conditions

ve max < v b < iJ‘

min


218

An important conclusion is Vi min - Ve max > (Vi max - Vi min)

+ (Ve max - Ve min)

i.e., the sum of the spreads in ignition potential and extinction potential must be less than the “gap” between the minimum ignition potential and maximum extinction potential. From the above it follows that for dc storage panels the design criteria are that there should be the smallest possible spread in individual values of both Vi and Ve so that small switching pulses are ensured. In this case, however, the difference Vi - Ve should be relatively large to allow a high switching margin. Thus such panels will have a gas mixture that gives rise to relatively high values of Vi and will require a higher supply rail than cyclic panels, although the switching pulse amplitudes required may well be lower than in the cyclic case. For example, Walters (13) quotes values of V , in the region of 370 V with 60 V pulses for a storage panel whereas Hall et al. (12) give values Vi 220 V with 80 to 100 V pulses for a cyclic panel. A detailed account of criteria for storage and nonstorage arrays has also been given by Smith et al. (18). In practice it has been found difficult to achieve the necessary margin of operation for true (single cell) random write, random erase operation. However van Houten (17) points out that conditions are eased if the address is limited to random writing of the information with simultaneous whole panel erasure or, alternatively, if the whole panel or a portion of the panel is switched on and unwanted cells are selectively erased. In the latter case not only can the gap be reduced but firing cells simultaneously improves the ignition delays by adjacent cell priming. Disadvantages are the introduction of an unwanted “flash” of light during the address and some loss of selective editing. In general, dc storage by the above methods has the important advantage of continuous working at a low average current rather than intermittent working at high peak currents. Very high brightnesses may be achieved without the use of excessive currents and therefore with reduced sputtering and improved life. An alternative to the internal resistor storage method which merits some attention has recently been described by Holz (19).

-

N

4. Pulsed Storage Mode

Holz points out the fabrication problems associated with forming the resistors and reports that with high resistor values and low currents, relaxation oscillations can occur because gas discharges have negative resistance characteristics at low current. His solution is to apply pulses “ significantly greater

219


than the cell firing voltage and of low total duty cycle” in place of the normal dc bias-i.e., a continuous series of short unidirectional pulses. Effective current limitation is obtained without the use of series resistors. Holz attributes this to a combination of factors such as limitations of carrier mobility, current build-up time, and low duty factor. This method depends critically on the history of the cells-particularly the residual ionization. Only if the ionization is sufficiently high at the start of the short “sustainer” pulse will a cell turn on. Below a certain critical W r i t 1ng

1.5 psec sustaining pulses

,

pulse

300

-> -

Anode

P 0 50psec-I

Time ( p s e c )

FIG.20. Basic anode and cathode waveforms for a pulsed storage panel.

level of ionization (sufficient to allow a space charge to form) the cell remains (or turns) off. The state of ionization is governed by the gas mixture and the sustainer waveform such that a cell that has previously been ignited will continue to reignite with each sustainer pulse. However, the amplitude and duration of the sustainer pulses are not sufficient to ignite cells which have not previously been on and are therefore unprimed. Figure 20 shows the anode and cathode sustainer pulse waveforms. Typical values are I .S psec pulse duration and 50psec pulse repetition interval. Also shown in this figure is the method of securing initial switch-on of wanted cells by adding “writing” pulses to the waveform between sustainer pulses. These pulses are referred to as “current limited.” For writing pulses external resistors could be used for current limitation, although this is not stated. Erasure may be effected by selective reduction of the sustainer pulse amplitude. A feature of Holz’ article (19) is the published V-1 characteristic for

220


the gas discharge cells used. Figure 21, based on data from this reference, indicates a remarkably high internal impedance. A similar high slope characteristic has been given by Josephs (f0,p. 1389). Application of 500 V was shown to give a current of only 350 pA with no series impedance. Josephs attributes this characteristic to Findeisen (20) who gives no further data but comments only that the normal constant voltage characteristic is altered by using “ proper cell geometry, gas pressure etc.” Factors which could be relevant are the use of fine wire cathodes and low pressures. However, both of these lead to increased sputtering and shortened lifetimes.

0

0

1

C e l l current ( m A )

FIG.21. Typical characteristic of a pulsed storage cell. Based on data from Holz (19).

It should be emphasized that the cell operating conditions in the pulsed storage mode are different from those encountered in the normal dc storage mode. In a recent letter, published late in the preparation of this review, Lustig ( f 9 a )also reports work on the pulsed storage mode and comments on the stability and operating margins involved. In terms of light output this method is a “ halfway house between cyclic and resistor storage operation. Data storage is provided but a fixed duty factor of about 1/33 is employed. Holz reports 100 f L brightness with an average power of 3 mW per cell.” ”

F. Some Practical dc Displays

Based on the principles outlined above, a number of complete display systems have been developed in various laboratories, some of which have reached production. These will now be reviewed briefly.


22 1

1. Scanned Data Displays Displays based on the molded glass technology described by Weston and Hall (8) were mentioned above. The single character tubes now in production are operated basically in the cyclic mode. Figure 22 illustrates one circuit configuration for a simple numeric display. Pulses are applied to the anode of each tube in turn, the relevant cathode dots being simultaneously addressed. The input data in binary form is held in the register and decoded to decimal

register gating circuit

Input

FIG. 22. Dynamic drive for matrix indicator tube readout. Courtesy Society for Information Display.

by conventional TTL circuits and the correct cathode selection pattern is derived via the pattern decoder which typically consists of a network of 45 diodes. The logic and pattern decoder in this case is shared between all the tubes, the cathodes of which are interconnected The displays give characters I cm (l3/32 in.) high. A brightness of 350 fL (1 200 cd/m2)at 1 : 10 duty factor (10 character display) is specified for a mean current per dot of 100 "A. Alternatively with parallel address 800 fL may be obtained. Experimental larger arrays have been demonstrated using crossbar panels based on the molded construction of Fig. 11. A system for 56 alphanumeric characters (four lines of 14 characters) is described by Hall, Johnson, and Sharpless (12). The panel has approximately 3000 cells at a pitch of 1.5 mm

222


(0.06 in.) and is filled with a neon-argon gas mixture. A block diagram of the address system for this panel is shown in Fig. 23. The system is row sequential with parallel address of the column electrodes during the row address period and is typical of the general method employed for cyclic crossbar displays designed for alphanumeric data display. In order to hold the information during the row period, a row store that has a capacity equal to the number of actively used columns in the display is required. This is updated at the beginning of each new row with appropriate

4 x 14 Character display

A 14 Character row store

Data inputs

memory

memory

FIG.23. The 56-character alphanumeric display system. From Hall er

trl.

(12).

information from the read only memory (ROM) or character generator. This results in some “dead” loading time during which the display is blanked. Any cyclic system either must be continuously refreshed from the data source (as in television) or must have a local “buffer” memory capable of storing the information for the whole panel. In data display systems the latter course is usually adopted to allow for differences in timing between the data system and the display and to conserve storage at the data source and bandwidth in the access link. In Fig. 23 the input data takes the form of six-bit binary words such as are available from standard digital hardware. Each word describes one displayed character-a choice of 64 numeric, alphabetic, or other symbols being available. This information is stored in six recirculating MOS shift registers. Other systems employ, for example, random access

223


memory elements (RAMS).The stored information is passed to the row store via the ROM which converts from the six-bit to the 35-dot form. A feature of this particular design is the use of the so-called “submatrix” drive system to reduce circuit complexity (see also Section IV, E, 2). An array of 28 rows is addressed from a four-way line decoder and a seven-way row decoder via 28 gates. In the circuit due to Sharpless, the drive transistors themselves are used to perform the gating function. The method allows considerable saving compared with, for example, shift register scanning. Submatrix scanning has also been described by other workers such as Hoffman (21) who reports a different approach to the address problem in which pulse transformers are used to provide the high-voltage switching pulses for a storage array. The 56-character display gives a bright flicker-free presentation, and the possible extension of this principle to an 825-character display has been studied by the authors. Problems which arise are the fabrication technique and the electrical characteristics. As stated by van Houten eta). (17) molded glass panels could be extended to achieve up to 512 characters but are probably limited to panels up to about 6 in. square. However an alternative fabrication method due to de Boer in which aperture plates are formed from perforated aluminum plates, anodized to make them insulators, is capable of extension to larger panel sizes. Another method described by Moore (110) is to use etched Fotoform aperture plates. The electrical considerations are critically related to the refresh rate, delay time, and duty factor. As the amount of data to be displayed rises, the duty factor worsens and the panel refresh rate must be slower so that the address time is substantially larger than the delay time. To illustrate this, Table I compares conditions for the 56-character system from Hall et 01. (12) and a simulated 825-character system described by Jackson and Johnson (14). TABLE 1 COMPARISON OF LARGE AND SMALL CYCLIC DISPLAYS -~

Number of characters Number of active rows Number of active columns Row address time Row store load and delay time Effective duty factor Peak cell current Mean cell current Luminance Refresh rate

56 28 70 70 psec 24 psec 1.40 2.0 mA 50pA 100 f L 500 H z

N

--

5

825 175 I65 1 I4 psec

19 psec 1 :210

5 mA 24 pA 27 f L 50 Hz

224


It can be seen that by lowering the refresh rate a factor of 10 times for the 825-character panel, comparable circuit timings are obtained. However the achievement of suitably short delay times at the 50 Hz refresh rate requires heavy priming. In the larger display, the peak current is greater by a factor of 2.5 but the display brightness is more than three times lower. This reduction is due mainly to the very much (five times) lower duty factor, but is aggravated by an apparent reduction in light efficiency at high peak currents (14). Since it is undesirable either to increase the peak current further or to reduce the brightness, considerable increase in light efficiency is required if the cyclic technique is to be extended to beyond about 1000 characters. A possible means of achieving this is described in Section 111, G. 2. Glow Trmsfer Display The need for large numbers of switching elements in conventional crossbar displays has given rise to an important variation in the case of dc cyclic gas discharge panels. This is the SELF-SCAN? display first described by Harman (22, 23). This display incorporates both glow transfer and heavy priming similar to that described in Section 111, D. Figure 24 shows an “exploded view” of the display structure from the paper by Holz (15). There are two complete crossbar arrays having common cathode electrodes. The rear (lower) array constitutes the glow transfer part of the panel. Vertical cathode electrodes are opposed to horizontal anode electrodes that are set in grooves in the rear plate. All these anode electrodes are connected via current-limiting resistors to a common supply line of about 250 V. The cathode electrodes are interconnected such that, for example, every third cathode is taken to a common line, i.e., columns 1, 4, 7, 10, etc., are connected together as are 2, 5, 8, I I , etc., and 3, 6,9, 12, etc. In operation, a complete column of discharges is initiated by applying a large negative pulse to the reset cathode at the left-hand side of the display. This column of discharges is then scanned from left to right by pulsing each set of cathodes in sequence using (for example) a three-phase pulse switching system, the glow transferring one electrode for each time interval. Because of the interconnection system only four drive switches are required for the column electrodes. At the front side of the panel there is an insulation sheet in which are found display cavities, a further set of anodes, and a glass front plate. The cathodes have small holes drilled in them corresponding to each cavity so that where a rear column of glows is initiated, priming takes place through

t SELF-SCAN is a registered trade name of Burroughs Corporation, Plainfield, New Jersey.


225

FIG.24. Exploded view of a SELF-SCAN” gas discharge panel.

these holes to the front cells as described above. As the rear glow is transferred along the panel, the requisite front anodes are energized according to the data to be displayed and glow discharges form i n the front cavities. The panel is filled with a Penning gas mixture which is predominantly neon with a small percentage of xenon and mercury at a pressure between 100 and 250 Torr (24). Correct choice of priming characteristics is essential both to the selfscanning and display functions of the panel. On the rear side the anodes are permanently held at 250 V and the cathodes alone are switched between + 100 V (off) and zero (on). The priming must

226


be such that discharge takes place preferentially to an adjacent (next in line) column of cells and not to an unwanted column of cells which is at the same potential and only a few (e.g., three) cells distant. When scan has started, the heavy priming from column to column along the grooves in the rear plate is used to ensure that this condition is met. Depending on the size of the array, however, more than three switching pulses may be needed. For example, in a large high-resolution display the physical distances between elements may be smaller and the time interval between readdress pulses shorter. Increasing the number of phases increases the distance between wanted and unwanted cells at the same potential and increases the readdress period allowing more time for deionization. At the end of a scanning cycle or when the display is first switched on, it is essential to re-establish theglow at the correct point. A separate reset electrode gives an unambiguous location once per cycle. A keep alive anode and cathode pin are also incorporated as a permanent priming source adjacent to the reset cathode. On the front side of the panel a similar critical dependence on priming is found. Unaddressed front anodes are held at 100 V so that the bias voltage between off anodes and cathodes is virtually zero. When (150 V) anode pulses are applied there will be cells on wanted (primed) columns and cells on unwanted (unprimed) columns which have the same applied potentials. Thus, again, the preferential breakdown must be ensured by means of the priming. In effect the minimum striking potential of an unwanted cell must be greater than the maximum striking potential of a primed cell. Holz (15) shows how this can be achieved. Figure 25 shows a block diagram of a typical data display designed around a self-scanning system. It will be seen that this is similar to the non-selfscanning system of Fig. 23. The major difference is, of course, the substitution of the N-phase column scanning system for the (anode) row scanner with a consequent saving in drive transistors. Both systems require recirculating buffer memories and ROMs and both employ the same basic technique of parallel address of all points on an addressed row (or column) which calls for an additional column (or row) store. The self-scanning technique has the highest component cost advantage for rectangular displays in which the dimensions of one side greatly exceed thoseof the other: for example, a single register of 16 alphanumeric characters using the 7 x 5 dot format. A self-scanning array of 7 x 96 dots will be arranged to scan the horizontal, long, direction so that only four column drive transistors are needed rather than the 80 needed for a non-self-scanning display. If a non-self-scanning array of the same dimensions were column scanned in the same way as for the self-scanning panel, the performance of the two would be very similar. However, since the same number of cathode drivers


227

FIG.25. SELF-SCAN'J,display system.

is required whatever the direction of scan, in an externally scanned panel it is more reasonable to scan the short vertical dimension. This increases the duty factor by more than ten times thus giving a greatly increased brightness and/or a lower peak operating current in the cells, with consequent improvement in life. As the display becomes more nearly square, the cost advantage of selfscanning panels and the brightness advantage on non-self-scanning panels decrease. However even for square panels, when the duty factors are equal, the self-scanning principle retains a clear advantage in quantity of drive transistors. The crucial issue is thus whether the complex panel with fewer drivers can be made more cheaply and reliably than the simpler panel with a larger semiconductor count. SELF-SCAN" panels are commercially available in a variety of sizes from 16 digits in line to large systems for eight rows of 32 digits, and even larger panels have been announced. Resolutions of 0.03 and 0.04 in. (0.75 and I mm) center-to-center dot spacing are available and a brightness of 50 fL (170 cd/m2) is claimed for a 256-digit panel. There is no doubt that these panels constitute an important contribution to the data display field.

3. Storage Displays While the cyclic method of address has achieved a fair measure of success and has resulted in commercially available displays, dc storage panels have proved much more difficult and have not yet left the research laboratories.

228

R. N . JACKSON AND K. E. JOHNSON

The majority of experiments have concerned panels with internal resistors and the method of fabricating them. a. Internal Resistor Panels. Typically [see Smith et al. (IS)], panels of this type are designed to have a relatively high ignition voltage ( - 300 V), a low extinction voltage ( - 150 V), and are run from a bias between these two (200 V). Assuming the maintaining voltage of the cells is close to their extinction voltage, the voltage across the resistor will be about 50 V and a mean current of 25 pA will be obtained with a resistor of 2 MR. In the operating condition, the power dissipated by the resistor will be only 1.25 mW. In order to ignite the cells, however, the applied voltage must be raised above Vi so that for the duration of the address pulse the peak current can be much increased; in the above instance to as much as 75 /.LA corresponding to a peak power of over 10 mW. The resistor must, of course, be able to withstand this pulse condition. It must also be fabricated in such a way that it is closely associated with the relevant cell (e.g., between one electrode and its appropriate crossbar) without limiting the cell density in the panel. It should have a reasonably close value tolerance, since variations in load resistor value decrease the operating margins and cause variations in light output. A number of different fabrication techniques have been tried. In the earliest form of resistor storage tube, individual connections were brought out from each cell of the array and connected via discrete resistors to bus bars. This clearly does not lead to a cheap convenient solution. De Boer (25) has described a technique in which the anode electrodes of the panel are wires which are coated with a thin resistive layer. This layer must have a high resistivity ( lo6 Q-cm). Conducting glass such as phosphorus vanadate has been tried using a dip coating method (17). A major problem with this method is obtaining a sufficiently uniform coating. A n alternative use of glazes has been described by van Houten et al. (17). The resistive glaze is extruded into holes in a plate of Fotoceram. The cathodes of the display cells are then formed by electroplating over the top of these resistor columns. This is necessary to avoid sputtering of the resistive layer from ion bombardment. Hoffman (2f) describes a panel in which cathode resistors are formed as follows. First, conductive strips are laid down on a glass sheet. On top of these strips resistive patches (material not specified) are laid down in positions corresponding to the cells. These are then covered with a metallic layer which forms the cathode surface. The resultant plate is used as the rear of a panel “sandwich” similar to that shown in Fig. 9. Indications are that the above specialized methods of fabrication have run into severe problems of uniformity and tolerances. The method recently described by Walters (1.3) uses a standard technique of growing popularity

229


for circuit construction, uiz. thick-film printing. The basic form of Walters' panel is similar to that shown in Fig. 9. The anode plate is transparent glass with thick-film conductors. The aperture plate is formed by etching a photosensitive glass. The cathode plate (Fig. 26) is similar to the anode plate but L-shaped resistors are incorporated, one for each cell. One end of each resistor is connected to a cathode crossbar conductor that is offset from the cell cavities. At the other end a nickel cathode plate is deposited. A covering glaze is deposited over the whole plate except for the cathode areas that are exposed. Crossbar electrodes Glass

Cathode plate

Thick film resistor

FIG.26. Section of storage panel showing Walters' method of forming resistors.

Clearly one limitation of this type of approach is the resolution that can be achieved when the resistors occupy the area between cells. At high cell densities the problem is particularly acute since, for the same brightness, smaller closer cells require a lower current per cell and hence a higher resistor value than do larger more widely spaced cells. Walters quotes results for arrays of 16 x 16 cells at a density of 64 cells/cm2, corresponding to a cell pitch of 1.25 mm (0.05 in.). He states that manufacturing techniques have been extended to give 256 cells/cm2-twice the linear resolution. Resistor spreads within +_ 25':;) after lo00 hours of life are claimed for the low density panels. Voltage spreads in the panel are also a problem and results published so far indicate that random writing or random erasing may be achieved but not both with the same maintaining voltage. A brightness of over I100 f L (4000 cd/m2) is claimed at 20 /iA mean current and a panel suitable for 40 characters is being developed.

230


Another method of forming resistors using thin film techniques has been used by Smith (personal communication, to be published). As with the thick film method, the resistors are formed in the land between crossbars. In this case, however, anode resistors are used. Each resistor is a very fine spiral track of evaporated nichrome. The outer end is connected to the crossbar and the inner terminates at an anode pad. A thin silicon monoxide layer isolates the resistors from the gas except at the anode. The discharge is viewed through the resistors which are deposited on the front window with light passing both through and between the spirals. A proposal to use “film resistors” for current limiting was also made by Moore ( I l a ) in 1963 but no details were given and we do not know whether samples were made. Smith has made arrays of 7 x 35 cells to display six alphanumeric characters with a brightness of over 800 fL (3000 cd/m2).The cell pitch used was 1 mm (0.04 in.). Problems with respect to cell density and voltage spreads have been encountered that are similar to those described above. b. Pulsed Storage Panel. Holz (19) shows a photograph of a 5625-element (probably 75 x 75) panel display operating on the pulsed storage technique described above. The construction is conventional in that an aperture plate is used to form the cell cavities with wire anodes and cathodes. The cell density is 526 cells/in2. corresponding to a pitch of 1.5 mm or 0.06 in. As mentioned in Section E4 a brightness of 100 fL (340 cd/m2) has been achieved for an average power of 3 mW per cell. c. Summary. In principle, storage arrays offer the possibility of really large panels having high brightness with low operating currents. However, it can be seen that for arrays using internal resistors, the fabrication problem is severe and it has yet to be proved whether really large storage displayssay 250,000 to lo6 elements at a spacing of 0.5 mm (0.02 in.) can be achieved by this method. Further problems are that random writing and erasing, which are important for graphical displays, have not so far been achieved because of voltage spread problems. The pulsed dc storage method may prove to be a viable alternative. However, this type of display is not so attractive as the resistor type since it does not fully overcome the duty factor problem and so does not achieve the high brightnesses obtainable with resistor type panels.

4. Halftone Displays The achievement of dc gas discharge displays having variable brightness poses special problems. Voltage control of the gas discharge is not possible. The alternatives are current control by means of variable load impedance, or time control, that is, varying the duty cycle of individual displayed elements. The combination of a display operating in the storage mode with variable

23 I

GAS OlSCHARGE DISPLAYS

brightness by means of variable load impedances implies an almost impossible set of criteria. As with fixed resistor storage operation, a separate (variable) impedance for every cell of the panel would be needed. Since electrical control of the current level would be needed, this variable impedance would need to be, for example, a high voltage transistor with each impedance set to the correct level and held there. In effect an analog store having a capacity equal to the total number of cells in the panel would be required. With the alternative pulsed storage method of Holz some variation of brightness should be possible by variation of the drive pulse width and/or frequency. However it seems open to some doubt whether the margin of storage operation allows much latitude for brightness variation. I n the cyclic mode the prospects are more promising. The use of rowsequential address coupled with an analog row store and driver in place of the binary store used for the data displays described above can be envisaged. Current controlling drivers would then be shared between all cells on a given column. Alternatively the time variation method is relatively easy to execute and provides a reliable method of adjusting cell brightness. Time modulation systems operate at constant current and are relatively unaffected by cell characteristics unless very short on times (very low brightnesses) are required -for instance, times close to the ignition delay time of the cells. Until recently only one example of a true halftone display using dc gas discharges was known. This is the work on television displays reported by de Boer (26) using a drive system in which cell brightness is controlled by pulse width modulation. More attention is now being paid to halftone displays and in particular work on self-scanning television displays has recent 1y been announced (27-28). De Boer displayed a 40-line television picture on a 40 x 100-cell dc panel. This was subsequently extended to a 100-line picture as described by van Houten et al. (17). The signal source was a standard European 625-line 50 field per second television video signal. The necessary compression of the information was secured by applying three successive lines of video information to a single row of cells on the panel and by ignoring the interlace” in the television signal so that each field was treated as a 3124 line sequential signal. Thus (see Fig. 27), the rows were driven from a 100 counter which was clocked from line synchronizing pulses via a scale of three divider. The resulting row pulses were therefore each 192 psec long (3 x 64 psec). The line synchronizing pulses also synchronized a 100 counter which was used to provide 100 samples of the video signal during the line period. The signal was fed to 100 pulse width modulators, each of which consisted of a gate, a memory capacitor, and a Schmitt trigger circuit. The counter outputs operated the gates and the capacitors were charged to the appropriate video signal level. The pulse length of the Schmitt triggers was determined by the “

232

R. N . JACKSON A N D K. E. JOHNSON

amount of charge on their respective capacitors. Thus the cell on time varied according to the video level. Van Houten et a/. (17) reported that a brightness modulation of 1 O : l and a mean surface brightness of 25 fL (40 fL at peak video level) was achieved for a peak operating current per cell of 3 mA. A more complex circuit would probably be required for a full specification television display. In this case the need to switch from row to row of the panel in step with the television line scanning (rather than one in three) would lead to the need for two sets of gates and storage capacitors. One of these would be updated with video information while the other was connected to the panel.

------

I

I

I I

I I I

Line d r i v e r s

I I I

I

1 1 Reset

Reset

Display panel

I

I

I I

.--------

I

,

Line sync-pulse Frame sync pulse Video.

1

I

100 c o u n t e r

c

FIG.27. 100 x 100 element television display system. From Van Houten et ul. (17).

At a late stage in the writing of this review, two papers were presented as “late-news’’ items at the 1972 IEEE Conference on Displays. Both refer to the use of SELF-SCAN”’ panels for television picture reproduction. Chodil et al. (27) report a display of dimensions 6.3 in. high by 2.4 in. wide having 212 rows and 80 columns. This was used to display part of a standard television picture and a brightness of 8 f L at 40: 1 contrast ratio was demonstrated. Chen and Fukui (27a) report a similar display (222 rows, 77 columns) in which a highlight brightness of 22 fL and eight gray levels have been realized. Another brief reference relates to work of a similar kind in Japan (28). Both Chodil et al. (27) and Chen and Fukui (27u) have used the panels such that the vertical scanning is provided by the glow transfer method and both have also employed current modulation rather than time modulation to control the brightness.


233

It is interesting that in addition to the scanning feature. current modulation techniques (as opposed to time modulation) may be easier to achieve with SELF-SCAN" panels than with other types due to the heavy priming from rear cells of the panel to front cells. One difficulty with current modulation systems is that for very low brightness (low current) the discharge may be unstable due to relaxation oscillations. According to Holz the adjacent cell priming method eliminates this since the negative resistance portion of the voltage-current characteristic is greatly reduced. C. Color

The need to produce alternatives to the red-orange glow of the normal predominantly neon-filled cells was recognized in the early days of glow discharge matrix displays and experimental panels capable of displaying blue, orange, and white were reported by Markus (11) in 1965. However no details of the technique used are given i n this article. A neon-argon Penning mixture produces output at a number of wavelengths (Fig. 6). One simple method of producing alternative colors which might therefore be considered is optical filtering. Stredde (29) states (for the ac panel) that this method will not give adequate brightness. This was confirmed by an experiment performed by Wilson in the authors' laboratory. Using a neon-argon-mercury tube in conjunction with green filters he found that the visible light output was reduced to only 6a4 of the unfiltered value. This implies a luminous efficiency of the order of 0.01 Im/W leading to display brightness of the order of 10 fL. The use of gas mixtures other than these with a high percentage of neon to give direct emission of alternative colors is also not satisfactory since again the luminous efficiencies achieved are too low. The remaining alternative is the indirect method in which photosensitive phosphors are stimulated by ultra violet emission from a suitable gas mixture. Forman ( 2 4 ) has reported work on panels in which between 5 and 15 7; of xenon is added to the neon gas. This gives strong emission in the region of 129 and 147 nm with reduced direct visible radiation. Green light output has been obtained by the use of zinc orthosilicate (manganese doped) in conjunction with such a mixture. A problem with this direct method is linding a suitable phosphor which needs a fast rise time, a relatively long persistence, and a high efficiency. These are not readily available. Forrnan used a medium persistence phosphor, as a compromise, having a decay time i n the region of 10 msec and a higher efficiency than alternative fast rise phosphors with short persistence. The result quoted for a 16-digit self-scanning display in which the on time was

234


of the order of 150 psec and refresh rate 60 Hz is a brightness of only 9 fL. Figures for the appropriate cell dissipation are not given. A second problem encountered is where to locate the phosphor. The cathode is not suitable because the phosphor becomes damaged by sputtering. According to Forman the deposition of the phosphor on the front window has the disadvantage that much ultraviolet ra iation is absorbed before reaching the layer. The solution he uses is to coa the cavity walls. This tends to give a display in which, for normal viewing angles, an orange neon glow is surrounded by a green (or other colored) ring. Frosting the front window glass is necessary to overcome this. Good life is reported for phosphors in this position; less than 10% variation in output over 5000 hr. Van Houten (17) has also described a technique in which ultraviolet radiation is combined with use of phosphors. In this case, however, use has been made of a positive column discharge to give improved luminous efficiency. An experimental two-layer panel has been used. Rear cells provide auxiliary glows which are selected by addressing crossbar electrodes. The positive column discharges are then formed in the front side cavities, which have a high ratio of length to diameter, by energizing the main anodes. As in the previously described panel, the phosphor materials are coated onto the walls of the front (positive column) apertures. The gas for this panel is a mercury-argon mixture and a luminous efficiencyof 1 Im/W has been recorded. It seems likely that the resolution capabilities of panels with phosphor coated cell walls will be lower than for direct emission types although Forman states that panels with dot spacings 0.04 in. (1 mm) and 0.03 in. (0.75 mm) have been built with cavity diameters as small as 0.024 and 0.02 in. Brightness of these panels was only 5 fL, however.

4“

H . Conclusions on dc Arrays Dc panel arrays working in the continuously addressed or “cyclic” mode are proved for data displays of up to a few hundred alphanumeric characters and may be extended up to 1000 character arrays in the near future. A useful feature of these arrays is their ability to incorporate the scanning function in the display tube. Beyond this size the cyclic addressed types depend upon the discovery of a way to improve luminous efficiency. This is also true for television applications where low duty factors are inevitable. Halftone reproduction has been demonstrated but provision of colors other than red is also a problem. The use of ultraviolet excited phosphors may be viable for this and a method- using positive column discharges with a phosphor holds some hope for increased efficiency. For large data displays using dc gas discharges, storage in the panel is a necessity. It is theoretically possible using a method in which a resistive ele-


235

ment is associated with each cell of the array. This promises high brightness and low average current with potentially long life. The problems of fabricating such panels and obtaining satisfactory electrical tolerances have been studied by a number of workers over more than ten years. It remains to be shown whether they can be overcome. An alternative pulsed storage method may be possible which has a number of features in common with ac arrays.

IV. ac ARRAYS A . Introduction

The ac, or plasma panel, was proposed by Bitzer, Slottow, and Wilson in 1964 at the University of Illinois. As described in 1966 by Bitzer and Slottow (30), it was constructed from a sandwich of three glass plates each typically 0.15 mm thick (see Fig. 28) The central plate contained a regular array of I

Transparent

con r i l l c t o r

Transparent condurtor

FIG.28. Cross section of an early ac panel.

holes each with a diameter of 0.375 mm and at 0.635 mm centers. On each of the outer plates was deposited a set of parallel transparent conductors with a pitch equal to the spacing of the holes in the central plate. The glass plates were assembled with the sets of conductors on the outside of the sandwich and arranged to be orthogonal to one another and to be registered with the lines of holes in the central plate. Thus a matrix of cells was formed, similar to earlier dc panel designs but with the electrodes on the outside of the glass walls. The next stage involved sealing the plates around their edges, evacuating the internal spaces, and filling with a suitable mixture of pure gases to a defined pressure. By this arrangement the inventors of the plasma panel hoped to overcome one of the most serious disadvantages of earlier panels, namely that of sputtering of the electrodes under ion bombardment from the discharge, since each electrode was now protected from the discharge by a layer of glass. However, the immediate implication was that steady discharges could not be maintained

236

R. N . JACKSON A N D K . E. JOHNSON

in any cell. When a discharge is initiated in an ac cell the charged particles that are produced rapidly flow to the end walls of the cell. Since these walls are insulating, the charge builds up and a voltage which opposes the initiating voltage quickly develops. The field within the cell falls, the avalanche processes necessary to sustain the discharge are reduced, and eventually it is quenched. Toovercome the effects of this buildupof wall charge i t is necessary to reverse the voltage across the cell at regular intervals-hence the term ac panel. An additional advantage of this type of cell construction as compared with dc panels is that no current-limiting resistors are needed. The discharge current depends on the capacitive reactance in series with each cell, which in turn is a function of the frequency of the activating signal, the geometry of the cell, and the dielectric constant of the glass between the gas and conductors. These reactances also serve to isolate each cell electrically from its neighbors in the matrix.

B. Operation of the ac Panel The effects of the wall charge enable an array of ac cells to be operated in a memory mode analogous to that of a dc panel whose cells each have an associated resistance. An alternating voltage, called the sustainer, is applied across each set of electrodes in parallel. This voltage has an amplitude which

-100

Time usec

Discharge

current Light o u tp u t

FIG.29. Voltage, current, and light waveforms for a plasma cell.

237


is insufficient to initiate a discharge in any cell, but which, if such a discharge has occurred, will continue to maintain it. This is possible because the wall charge causes a voltage that adds to the sustainer during each halfcycle. The firing voltage of the cell Vf (defined in Section IV, C, 2) can be exceeded in each half-cycle so that a discharge occurs and the wall voltage reverses. This is illustrated in Fig. 29 in which the sustainer V, is shown as a sine-wave voltage and the voltage across the cell V, is compared with V, and with the wall voltage V , . Voltage and time scales are typical of modern panels. The current or light pulses which occur are also shown; the amplitude and width of these pulses vary considerably with the gas filling and its pressure. Column conductor

Iw ( t ) D I 5charge b

1

Row conductor

\

current

Glass

FIG. 30. Simple equivalent circuit of a plasma cell.

The relationship between V,, V,, and V , can be established with the help of the simple equivalent circuit of Fig. 30 (3f).In this circuit C , represents the capacitance due to each of the glass layers and C, represents the capacitance of the cell with no discharge. The effect of the wall charge is included by means of the ideal current generator I,(?). The voltage V,' across the cell capacitance C, must be the sum of that part of the applied voltage V , which appears across the cell and the wall voltage V,' due to I,. Thus V,' = [C,/(C,

+ 2Cc)]V , + V,'.

To avoid the inconvenient fraction Co/(Co+ 2CJ it is useful to define two terms V , and V , such that and Then

238


and all voltages are now directly measurable on the electrodes of the cell. Similarly the firing voltage of the cell Vf' is related to an external voltage Vf by We shall henceforth refer only to the external voltages V,, Vw, and Vf . In modern panels Co >> C, so the internal and external voltages do not differ greatly. In the simplest situation the current generator , Z behaves as an ideal voltage switch such that when V, is less than Vf no current flows, but when V, exceeds Vf charge flows to neutralize the electric field in the cell and V, becomes zero. This case is shown in Fig. 31 in which the wall voltage has been

vc = vs+ v, FIG.31. Wall voltage diagram for ideal cell in which complete wall charging occurs.

drawn superimposed on the sustainer, but inverted so that the cell voltage is given by the difference between the two waveforms. This convention is retained in the following text. At the instant when the wall charge reverses, the wall voltage is equal to the applied voltage and the walls are fully charged. For a11 values of V, between Vf and Vf , the cell will refire on each half-cycle. It can therefore be said to have a bistable range equal to 4Vf . In practice, of course, the wall charge takes a finite time to reverse and the vertical changes of V , shown in Figs. 29 and 31 are an approximation to the real situation. In general the cell walls are not fully charged during each half-cycle as in the simple model and the bistable range is therefore less than + V f . A measure of the extent of wall charging in a typical case is given by the difference between Vr and the minimum sustainer amplitude to maintain a steady series of discharges, which we will call V, , This is analogous to the extinction voltage of a dc discharge. In discussing the memory properties of ac panels some writers have found it convenient to use a figure of merit, M , defined as the actual bistable range divided by the theoretical maximum range; or in mathematical terms

+

= (Vf

- VJ4Vf

*

239


C . Characteristics of ac Cells 1. General Properties It was established early in investigation of ac cells that the extent of the wall charging, as measured by the bistable range, was related to the intensity and duration of the discharge (32). An illustration of this relationship can be seen by comparing the experimental results shown in Figs. 32 and 33.

(A)

0% N,

((

1

0 . 4 4 % N,

(€1

(F) 4 . 3 % N,

1.45"Io N1

T i m e scale 0 , 5 p s e c / d i v

FIG.32. Oscillograms of sustaining voltage and light pulse for increasing proportions of nitrogen in a neon-nitrogen mixture. From Willson (33). 3

2

0

7

180-

240~ 2000

0

1

?

3

4

C "lo

,

F

7

,

,

8

9

N

FIG.33. Influence of nitrogen content on bistable voltage range for a neon-nitrogen mixture. From Bitzer and Slottow (34).

240


Figure 32 shows that as the nitrogen content of a neon-nitrogen mixture is increased, the light output duration decreases from nearly 1 psec to only about one-tenth of this, but its peak value increases (33). In Fig. 33, the corresponding change in Vf - Ye is shown (34);as the proportion of nitrogen increases, this voltage difference also increases (note that it is nearly zero with pure neon). The results of these and other experiments can be summarized in the general rule that the wall charging is greatest when the discharge is short ( N 100 nsec) and of high intensity. Veron and Wang (35)have recently explained theoretically the temporal behavior of the wall charging and discharge current in neon-nitrogen mixtures. 50nsec I-+

Y

Sustolner

Light pulses

FIG. 34. Light from 12 cells in early plasma panel showing negligible jitter. From Bitzer and Slottow (34).

The bistable range is not only dependent on gas composition but also on the sustainer waveshape, and in particular on the slope of this signal when the cell fires. For example, Titchmarsh (36) has reported measurements on experimental cells which show that V, - V, rapidly decreases when the slope of the sustainer is less than 400 V/psec. However with a rectangular sustainer waveform in which the risetime of the signal is faster than the formative time of the discharge, firing occurs when the cell voltage is at a constant value. It has been found that in this case both the firing voltage and the bistable range show little variation over a wide range of frequency and pulse width [see, for example, Nakayama and Andoh (37)J. A remarkable property of plasma cells that was noted in early experiments was the regularity of the light pulses emitted by a sustained cell. An example of this feature is shown in Fig. 34 (34) in which the light pulses from 12 cells are repeatedly superimposed with no apparent “jitter,” or delay in ignition. This indicates a high degree of self-priming when an initial discharge has occurred. In other words, ionizing particles formed during one discharge help to initiate the following discharge. Bitzer and Slottow considered these particles to be metastable atoms which diffuse relatively slowly to the walls of the cell where they can then cause the emission of electrons. As the frequency of the sustainer is reduced, the time between discharges increases until, when it is comparable with the metastable lifetimes, the discharges


241

become irregular. This lower frequency limit is typically about 10 kHz. The upper frequency limit of operation is dependent not only on the halfperiod of the sustainer being sufficiently long to allow for the formative time of the discharge, but also on sufficient buildup of wall charge during the discharge period and some cancellation of charge by remaining ions and electrons when the cell voltage reverses. Gas filling and cell geometry have a considerable influence on this upper limit, but in practice operation above about 1 MHz is not possible. A serious problem with early ac panels as already described for dc panels was the dilficulty of switching cells to the on state when they had previously been off for a long period. It was found that this statistical lag, due to a lack of particles within the cell which could initiate a discharge, could be overcome for a chosen cell by maintaining neighboring cells in the on state. Since the spacer plate probably prevented any gas flow between cells, this effect was attributed to photoelectrons emitted when light from the neighboring cells struck the walls of the addressed cell. A similar effect was obtained by shining ultraviolet light on the panel. An alternative method, used by Nakayama and Andoh (37), was to incorporate radioactive material in the cell. Tritium gas was used and a concentration of about 1 pCi/cm3 was said to give an effect approximately equivalent to ultraviolet light. Another suggested possibility was to fire all cells in the panel at intervals just less than the diffusion time of metastable atoms to the walls, so that some initiating particles were always present. However, this method has the disadvantage of reducing display contrast. For modern panels the first method is often used and a border of cells is maintained around the panel (see Section IV. D, 2). Under these conditions cells can be switched with a single pulse only a few microseconds long.

2. Switching Cliaracteristics

To change the state of an ac cell it is necessary to alter its wall voltage from. e.g., zero for an off cell to a finite equilibrium value Vw, in an on cell. This is usually accomplished by nieans of one or more voltage pulses applied to the cell electrodes, though switching by light or electron beams is also possible (see Section IV, F). In general a voltage V, applied across the cell in conjunction with any wall voltage V w already present will, if a discharge occurs, lead to a change of wall voltage which can be denoted by A V w . These voltages can be measured (31) and a characteristic curve of AVw against the cell voltage V , ( = V, + V w )can be plotted. Such a characteristic, or voltage transfer function according lo Johnson et al. (31) is shown i n Fig. 35. The shape of this function depends on cell geometry and gas filling as well as the sustainer waveshape.

242


FIG. 35. Change of wall voltage AV, versus cell voltage V,. Based on data from Johnson ef al. (31).

For a cell in equilibrium in the on state the change in wall voltage AVwe at each discharge is equal to 2Vw, (see, e.g., Fig. 29). Thus to change state the wall voltage must change by half the equilibrium wall voltage change, or +AVwe. This situation is depicted in Fig. 36 for a cell being turned on by two address pulses V, and Vyon its electrodes in addition to the instantaneous value of the sustainer V , . (In the erase mode V, is replaced by Vwe.) It can also be seen that the “half-pulse” condition V, + V , or V, V y should cause no change in wall voltage. The sustainer, the wall voltage, and pulse voltages in a typical case are shown in Fig. 37. The reasons for the choice

+

FIG.36. Transfer characteristic showing conditions for state changes.


243

FIG.37. Square-wave sustainer and address pulses for state changes (wall voltage shown as dashed line).

of a stepped square-wave sustainer are discussed in Section IV, E. Slottow and Petty (38) discuss a second type of transfer function, valid for equilibrium conditions, that can be obtained from the first by making use of the relationships and

If Vwc is plotted against V , an equilibrium characteristic curve results (Fig. 38). The dashed central portion indicates an unstable region discussed in the following paragraph. They define the firing voltage Vf and extinction voltage V , to be the limiting values of V, determined by the vertical tangents to the Vwc versus V , characteristic. The stability of ac discharges when the wall charge is disturbed by external

FIG.38. Curve of wall voltage versus sustainer for equilibrium conditions. Based on data from Slottow and Petty (38).


244

voltage pulses or other means has also been investigated theoretically by Slottow and Petty. They found that the condition under which any disturbances of equilibrium will be damped out in succeeding cycles is given by the expression

I [d(AV,.,)/dV,]- 1 I 5 1. Then equilibrium is determined by the boundary conditions O I y 1 2 ,

where y = d(hV,)/dV,, the slope of the first voltage transfer characteristic. The tangents of slope 2 to the curve of AV, against V , are shown in Fig. 35. An area of unstable operation can be seen where y > 2. This corresponds with the negative slope portion of the Vwe versus V, characteristic in Fig. 38. An example of this instability is shown in Fig. 39 where y is assumed to have vt

-V

f

FIG.39. Change of state for y

=

3.

a constant value of 3. When the wall voltage is disturbed, e.g., by a pulse of light, the cell rapidly switches off. A stable case is shown in Fig. 40 where,

FIG.40. Approach to equilibrium for y = 1.5.

although a similar disturbance is assumed, the cell reverts to its equilibrium on state in one or two sustainer cycles; a constant y of 1.5 is assumed in this case. It is interesting to note from Fig. 38 that there is a small range of values of P,' just less than Vf for which two stable on states can occur. This is because the upper limit of the bistable range, which is defined as Vr , is slightly greater than the actual ignition voltage denoted by Vi in Fig. 38. The existence of two

245


stable states has been confirmed by Petty and Slottow (39) who observed two light output waveforms as shown in Fig. 41 for the same sustainer. The asymmetry of the light waveform in the dim state is said to be due to a lack of ions and electrons within the cell at the time of the positive-going edge of the sustainer. Thus, although Vi is exceeded and breakdown could occur, the buildup of a discharge during the subsequent half-period is slow. Before a complete discharge can occur, the sustainer reverses. There is an initial

L i g h t o u t p u t o f bright s t a t e

L i g h t o u t p u t of dim state

I

Sustaining signal

FIG.41. Sustaining signal and light outputs from two stable states. From Petty and Slottow (39).

increase in current due to ions and electrons remaining in the cell volume and then a succession of weakening avalanches which produce light of decreasing intensity and restore the wall charge to its original level at the beginning of the cycle.

D . Development of Present ac Panels

I . Construction Techniques The original ac panel design developed at the University of Illinois posed some problems for the construction of large area, high resolution displays. For example, to obtain low cell operating voltages and high discharge currents, the capacitive impedance in series with each cell should be small. Thus the glass walls should be thin, but large area glass sheets with a thickness of 0.15 mm, as originally used, would be very difficult to handle. Nolan (40)

246


overcame this problem in the DIGIVUET panel by depositing electrodes on relatively thick glass plates (about 6 mm) and subsequently covering the electrodes with a glass dielectric film having a thickness of about 0.025 mm. A second problem is the central glass plate of the early panels. This must also be thin and have accurately made holes. Furthermore these holes must register with the intersections of the electrodes. Since the cells formed by the holes are effectively isolated it is also difficult to evacuate the panel and to fill it with gas. In addition, the spacer prevents the flow of gas or charged particles during operation of the panel. While this is an advantage in assisting the prevention of " cross firing," some open structure between cells is desirable to aid priming of cells which have remained unaddressed for long periods. Nolan found that ac panels could be successfully constructed and operated without the central plate by a suitable choice of dimensions and gas pressure. A cross section of this construction is shown in Fig. 42. A few

" tr

ode5

FIG. 42. DIGIVUED panel construction. Courtesy of Institute of Electrical and Electronics Engineers.

glass spacers, whose number was determined by the panel area, were needed to maintain the critical spacing of the two plates bearing the electrodes. In this way panels with an active area of approximately 10 x 10 cm and a cell spacing of about 0.76 mm (33.3 lines/in.) were produced. Hoehn and Martel (41) have compared " open-cell " geometries like Nolan's with the original " isolated-cell " structure. Figure 43 shows the results of their calculations of electrostatic charge distribution along the surface of the dielectric normal to the electrodes. It is clear that as resolution is increased, so the likelihood of cross coupling between cells becomes high for the open-cell case unless the gap between the plates is correspondingly reduced and the gas pressure is increased. In work to improve on Nolan's design, Hoehn and Martel examined the light intensity profile across a discharge for various electrode widths at a resolution of 60 lines/in. Their

t Registered trademark of Owens-Illinois, Toledo, Ohio 43651


L

247

0-1 geometry

F ro-,?, I

Electrode edge, 0-1 (open cells)

A f .-

VI

W c

Electrode edge, U1 (isolated cells)

V W

P c

0

I

Distance from center of cell ___)

FIG.43. Electrostatic charge distribution. From Hoehn and Martel (41)

measurements led to a choice of 0.075 mm as the optimum width for this pitch of 0.42 mm. The light profile for this case is shown in Fig. 44 for three electrodes; the electrodes intercept approximately 25-30% of the light at the center of each of the three light spots. Welber and Tynan (42) have shown how electrode geometry can be modified to reduce the masking of light by the front electrode strips. By employing a torus-over-disk arrangement (see Fig. 45) they have increased spot luminance by a factor of up to three times compared with stripline geometry, without degrading the electrical characteristics of the cells. Materials and fabrication techniques for the electrodes and dielectric layers must be carefully chosen for a successful panel design. To achieve a resolution of 60 lines/in., Hoehn and Martel made their electrodes by photoetching a gold film which was previously evaporated onto the substrate glass.

Distance

FIG.44. Light intensity profile for 0.075 mm electrode width at 24 linesicni (60 lines/ in.). From Hoehn and Martel (41).

248


Gold was used to give high conductivity (less than 100 R total resistance per line), compatibility with the glass layers and high temperature processing cycles, and ease of connection to the ends of the lines. A lead glass (43) dielectric layer about 25 p thick (44) was then deposited on top of the conductors. Using these techniques, panels with 512 x 512 elements in an area of approximately 22 x 22 cm have been made. The gas filling was a Penning mixture of neon and argon (44).

4 N

Rear electrode

F r o n t el ect rode

FIG.45. Torus-over-disk electrode geometry.

Recently a new type of construction has been disclosed by Mayer and Bonin (45). Rectangular cross section glass tubes are stacked side by side between two glass plates. The tubes are sealed at one end and open to a gas reservoir at the other. Electrodes are deposited on the inner surfaces of the two outer glass plates. The quoted dimensions of the tubes are 0.75 by 0.3 mm with walls 75 p thick. Panels capable of displaying over 1000 characters have been produced. Two separate groups of workers have reported at a late stage in the preparation of this paper that plasma panels with a resolution of 83 lines/inch (a pitch o f 0.3 mm) are feasible. Ernsthausen et al. ( 4 5 ~ have ) constructed several panels with 1024 x 1024 lines at this resolution using an open chamber construction. Modeki and Nakayama (456) have described a new method in which grooves were etched in a glass plate at 0.3 mm intervals; these grooves were then filled with gold conductive paste, and the plate was covered with a thin dielectric layer.

249


2. Electrical and Light Output Characteristics For a 128 x 128-element array the static voltage characteristics measured by varying the amplitude of the 30 kHz square-wave sustainer, were reported (41) to be in the ranges 159-165 V for V , and 131-1 39 V for V , . Thus random addressing of elements could in principle be achieved since the “gap” of 20 V separating the ranges was larger than the sum of the spreads in V, and V , , namely 14 V. However, the important characteristics for drive purposes are those measured under dynamic conditions. These were given for an array of only 20 x 20 elements and the pulse lengths and priming conditions were not quoted, so the results give only a limited indication of large panel behavior. The range of half-select pulse amplitudes for writing without “cross talk” is shown in Fig. 46 between the curves labeled “max write” and ‘‘min write”; the range for unambiguous erasing is similarly shown, both ranges depending on sustainer amplitude. The area labeled window” defines the operating “

40

1

I

1

I

range for the sample of cells. For a sustainer of 150 V typical half-select pulses of about 65 V are required for both writing and erasing. On the question of the need for priming, Johnson and Schmersal(46) have found that, for reliable writing, it is necessary to maintain a border of on cells around the edges of the panel. They assumed that light from these border cells produced photoelectrons from the dielectric layers of the panel and these primed the addressed cells. For maximum beneficial effect, the border cells were driven from a separate sustainer whose phasing was adjusted so that the discharges in the border cells were synchronized with the writing pulses.

250


The mean luminance of a display element is typically about 170 cd/m2 (50 fL) under normal operation with a contrast ratio between on and off cells (presumably under dark ambient conditions) of better than 25:l (41). Differences in luminance between on cells typically do not exceed 15% of that of the brightest cells. The power dissipation in these panels has not been given but it can be estimated from characteristics of peak current and period of discharge given by Johnson and Schmersal (46) (Fig. 47). For a sustainer of 150 V the peak cell current is about 50 pA and the width of the current pulse measured at the 50% amplitude points is about 100 nsec. The power dissipated during the current pulse is therefore of the order of 7.5 mW for 100 nsec. The duty ratio, assuming a sustainer frequency of 30 kHz, is about 0.6 % (two 100 nsec current pulses every 33 psec), so the mean power for one element is about 45 pW. If all elements were on together, the total power dissipation would be about 12 w. Slottow (44) has commented on the life expectancy of these panels. Two kinds of change in the electrical characteristics have been noted under operating conditions. There was a steady long-term drift in average firing voltage and extinction voltage but also a short-term differential change between cells depending on the data displayed. These differential changes have been minimized by a suitable choice of glass dielectric layer over the conductors. One panel was said to have been tested for over 5000 hours with negligible changes in its electrical characteristics. 3. Other Measurements Investigations of different dielectric layers have been reported by Nakayama and Osawa (47).Their aim was the achievement of lower operating voltages than those of Hoehn and Martel by the deposition of cesium on the dielectric, thus increasing its emission of secondary electrons. They used a lead glass dielectric covered with a film of alumina or silica. Gaseous cesium was introduced to the panel from one corner and allowed to diffuse throughout the gas space, depositing on the walls as it did so. The greatest reduction of firing voltage, from 160 to 80 V, occurred with a 3 pm thick layer of alumina, and consistent voltages were measured along a panel diagonal of about 120 mm. The memory margin appeared to be unaffected; typical values of about 0.36 were quoted. No comments were made about the effect of cesium on panel life, however. Some interesting observations on cross coupling between cells have been published by Umeda and Hirose (48). They have shown that for electrodes at intervals of 0.6 mm, an on cell can affect the firing and extinction voltages of cells up to 8 or 9 cells away (Fig. 48). The enhanced priming effect


0 0

25 1

130 140 150 160 170 Sustainer voltage

FIG.47. Peak current and discharge period versus sustainer voltage. Based on data from Johnson and Schmersal (46).

1601

1

IlO!

'_2_ _ - _ _0_ _ -----p 7 -

m

y

-

-

ADistance ; : 5 ; on cell

k l b

from the

FIG.48. Dependence of firing voltage and minimum sustaining voltage on distance from on cell. Applied voltage to the on cell - - - 120 V, --- 140 V, -I50 V. From Urneda and Hirose (48).


252

when the current through the on cell is increased (by raising the applied voltage) can be clearly seen, but the effect falls off rapidly with distance. For a randomly addressed panel this amount of cross coupling would significantly affect operating margins since the bistable range of a group of on cells with a sustainer of, say, 140 V would only be about 18 V compared with about 39 V for an isolated on cell. However, these authors were investigating a selfscanning system in which a line of cells could be used to behave like a shift register. The characteristics may therefore not be typical of other ac panels.

E. Crossbar Address Methods 1. Sine- Wave Methods

An early method of addressing ac panels is shown in Fig. 49. In principle, Panel

FIG.49. Early sine-wave drive system. Data from

comp generator ? \

a single sine-wave sustainer source supplied the whole panel and address pulses were fed to selected rows and columns by switching networks controlled by the input data source. In the unaddressed or “ read mode only sustainer signals were supplied to the panel. To “write” a particular cell the first operation was to interrupt the sustainer when its instantaneous value was zero. For a short period of 3 0 4 0 psec (33) no cells received a sustainer signal. Instead, a slowly rising voltage was applied to the selected row and column electrodes, as shown in Fig. 50. Next the sustainer was reapplied to all cells. The firing voltage of a selected cell was exceeded because of the additional voltage pulse it had received and a discharge occurred. The applied pulse was now steadily removed but the cell remained on because the wall voltage followed the applied voltage. ”


253

The reverse procedure was used to switch a cell off. First, a slowly rising bias voltage was applied to the selected row and column. The wall voltage followed the applied voltage (see Fig. 51) and after several cycles the sustainer was removed at a time when the cell voltage was close to zero. The row and

FIG.50. Slow write method.

column voltages were then removed over a period of two or three more sustainer cycles ; following this period the sustainer was reapplied. Since the wall voltage of the cell was zero, it did not refire. Willson (33) stated that at least two sustainer periods had to be allowed for writing or erasing a cell by this method so that correct "tracking" of the pulse voltages occurred. Furthermore if the sustainer was removed for too long, some unaddressed on cells did not refire. Oberg and Sauter (49) proposed a sine-wave method by which it was possible to address required cells without disturbing unselected cells. According to this method, one set of electrodes received a sustainer having relative phase of + 90" or - 30°, while the orthogonal set received a signal with phase equal to - 90" or + 30". Any electrode could also be switched to zero voltage. To write a cell, the selected pair of electrodes received phases 90" and - 90°, respectively. The peak voltage appearing across the cell was then was twice the amplitude of either applied signal, e.g., 2Vs(,,,, where Vs(max) the amplitude of one signal and lay between V, and Vf. The cell therefore switched on. To erase a cell each selected electrode was switched to zero volts. A cell was normally sustained by the signals with phase + 30" and - 30", which gave a peak cell voltage of Vs(max). For all other combin-

+

FIG.51. Slow erase method.

ations of signals the peak cell voltage was also VF(max). Thus those cells in the same row or column as the addressed cell, and which would normally have received half-select signals, were not disturbed by the addressing signals.

254


A disadvantage of Oberg and Sauter's scheme, which was pointed out by Owaki et al. (50), is that small phase angle variations between the signals could cause large amplitude changes across a cell, which might be enough to disturb its state. They described a method to overcome this problem in which a small amount of third harmonic signal was added to the fundamental. By choosing the amplitude of third harmonic to be about 0.4 of that of the fundamental, half-selected cells still remained undisturbed. 2. Square- Wave Methods The sine-wave drive methods which were used with early ac panels have been superseded by square-wave driving for later panels. Square-wave voltages have several advantages in this application. The firing and extinction characteristics vary much less with frequency (37) and the timing of address pulses is less critical. The design of sustainer generators is eased since with square waves the circuit has switched to a steady low impedance state before becoming heavily loaded by many cells firing at once. Power dissipation is therefore reduced and the wave shape is more readily maintained. Simple square-wave drive voltages are shown in Fig. 52. Typical address

I

-" '0

FIG.52. Simple square-wave drive.

X~ Y

pulse widths are of the order of a few microseconds and pulses have a fairly wide tolerance in their position relative to the sustainer switching times. However, a disadvantage of the method is the requirement for unequal write and erase pulse amplitudes; this increases the circuit complexity. An improved method which overcomes this disadvantage is shown in Fig. 53. The individual row and column waveforms are as easily generated as in the first method, but the simple expedient of introducing a phase shift between them generates the stepped square sustainer waveform which enables the erase pulses to be smaller. An additional advantage is that the address pulses can be of equal height. They can therefore be generated by the same circuits, the timing of the pulses relative to the sustainer and the pulse widths determining the

255


mode of address. The erase pulse may be of shorter duration than the write pulse for the largest operating margins. The tolerances on address pulse amplitude can be greater if the pulses occur with the phase shown in Fig. 54. However this method has the disadvantage that higher voltage switching transistors are needed. Square-wave ac drive systems have been described by Trogdon (511, Er a se

FIG.53. Stepped square-wave drive. x-Y

0

0

10

20

30

Time (used

40

Johnson and Schmersal(46), and Dick (52).To avoid the expense of individual drive transistors for each row and column of the panel they have used submatrix multiplexing principles similar to those described above for dc panels (Section 111, F, I). Trogdon’s submatrix used pulse transformers, but in the other work a diode-resistor submatrix was used. Each intersection of the submatrix was formed by a logical “ A N D ” circuit consisting of two diodes and a resistor. To select one of 512 electrodes, a submatrix of 16 x 32 of these AND circuits was required, the appropriate circuit being addressed simultaneously by one of 16 and one of 32 active drivers. A system for a 512 x 512-element panel therefore needed a total of only 96 drivers in addition to the row and column selection diode matrices.

FIG.54. System for increased address pulse tolerances.

’’

A square-wave drive system employing the principles of address signal cancellation for half-selected cells which were described in the previous section has been developed by Criscimagna (53). The waveforms for this system are shown in Figs. 55 and 56. When switching on a cell, the halfselect pulses added to the selected lines were subtracted from the remaining unselected lines. The effect of this action was to completely cancel these pulses

Write

I

I +V 0

I

Selected line

I

I +V 0

FIG.55. Criscimagna's drive method,write mode. From Criscimagna (53).

I I

+: -V

+: -V +V 0 -V

Selected cell

4

Half - selected cells

I

I Unselected cells

Erase

tv

0

wI m

Selected line

I

I

'K 7

Unselected lines

'1: &

nSelected line ~~

I

tv 0 -

V

I

1

Unselected line:

I

':,** S e l e c t e d cell

-V

I

' -V

~

"i** -V

~ Half selected cells~

I Unselected cells

I

FIG.56. Criscimagna's drive method, erase mode. From Criscimagna (53).

~

,

GAS DlSCHARGE DISPLAYS

257

at the half-selected cells but also to disturb the sustainer to all unselected cells. However, since this disturbance occurred after the main transition at which an on cell fired, and since it was not large enough to cause a second discharge, the cell was not affected. The waveforms in Fig. 55 also show a second modification introduced by Crisciinagna during the write mode in which the sustain period was doubled for one cycle and the write pulses were delayed relative to the leading edge of the square wave. This was claimed to minimize cell interactions by allowing the discharge in on cells to occur well before that in the cell which was being switched on. In the erase mode (Fig. 56) reapplication of sustain pulses was delayed after erasing a cell to allow the discharge activity to subside. This reduced the chance of the erased cell refiring, but too long a delay increased the risk that on cells would not refire, so a compromise had to be found. As in the writing mode, the disturbance to the sustainer produced by the added half-pulse did not affect unselected cells since its polarity was the same as the last sustain pulse. With this method, Criscimagna was able to obtain a bistable range virtually equal to the theoretical maximum for the 128 x 128-cell panel which he used.

F. Electron Beam and Optical Address Methods In addition to the crossbar address methods for plasma panels so far described, some workers have investigated other methods of addressing a panel. For example, Gregory et al. (54) have described an electron beam addressed panel. The principle of this method is shown in Fig. 57. Instead Spacer p l a t e ’

/

Sustoiner generator

Aluminizing ever r e a r s u r f a c e except for c e l l s

Plates

FIG.57. Principle of electron beam addressed panel.

of crossed grids the panel has continuous electrodes, one being transparent for viewing and the other, which faces the electron gun, being an aluminum layer with apertures over each cell. Electrons accelerated from the gun accumulate on the glass within the apertures and establish a field across the cells. Any initially off cell can be turned on if the field established by electron buildup is large enough. In their experiment Gregory et al. used a

258

R. N. JACKSON A N D K . E. JOHNSON

panel 2.5 cm square with 1600 cells filled with neon and nitrogen (5 %) to a pressure of 150 Torr. The electron gun was operated at a final anode voltage of 6.5 kV and a cathode current of 3 pA. Reproducible addressing was demonstrated and a maximum writing rate of 2.5 cm/msec was obtained, i.e., one complete row or column of cells could be written in I msec. A bistable range of 325-375 V was measured; this was large enough to prevent spurious writing of cells by noise pulses on the sustainer. While this is an interesting approach, it would not appear to offer really significant advantages compared with presently available storage cathode ray tubes. Of greater importance is the ability to write into, or erase, individual cells of a panel using a light beam. This was first suggested in Bitzer and Slottow's original paper (30) as a variation of the method of priming a panel by flooding it with ultraviolet light. In principle, the applied voltage is raised above the firing voltage so that theoretically all cells could switch on. Those that are required to do so are then illuminated, which results in the production of photoelectrons from the glass walls of the selected cells only. The photoelectrons initiate discharges in these cells and the applied voltage can subsequently be returned to the normal sustainer level. There is an obvious practical problem with this method since discharges in cells which are required to be off are readily initiated by any stray light or particles. Arora ef al. (55) proposed an alternative, and more reliable, method for sine-wave drive. This method has been investigated in detail by Weber (56), who described it for a rectangular sustainer. The timing of pulses and the related wall voltage changes are shown in Figs. 58 and 59 for the erase and write modes, respectively. To erase a cell, the sustainer is interrupted and light is flashed onto the cell. The photoelectrons which are generated are drawn to the end walls by the electric field and there they neutralize the wall charge so that the wall voltage falls towards zero. The sustainer is reapplied and in the next half-cycle or so the cell settles to its equilibrium off state. The procedure is similar for writing except that a bias voltage is applied across the cell during the light flash. In this case the photoelectrons charge, rather than discharge, the cell walls so that when the sustainer is reapplied the cell rapidly reaches its equilibrium on state. Weber reported that a plasma cell in the on state may have of the order of lo7 electrons on its walls. Since the quantum efficiency of the glass he about 10'' photons used for ultraviolet light at 253.7 pm is about 6 x may be needed to change the state of a cell. This represents a rather large amount of light and in these experiments a xenon flash tube was used which gave an energy of I .6 J in a pulse of half-width equal to 3 psec. Weber discussed two methods of reducing the light needed. In the first, a bias voltage is placed across the cell during erasing to give amplification of the initial photocurrent by electron avalanching. Theoretically, amplification by one or two orders

259


of magnitude should be possible. The second method involves flashing the light during a discharge, with the result that less wall charge is transferred across the cell than in the normal case. For certain gas mixtures, notably neon plus 1 nitrogen, this method is more sensitive for erasing cells than avalanche amplification, but it is not so well understood.

Fic. 58. Optical switching on to off. light; --wall voltage, without light; - sustainvoltage. Froni Weber (56).

--- Wall voltage, with

vw ",

FIG. 59. Optical switching off to on. voltage, with light; wall voltage, without light; - sustain voltage. Froni Weber (56).

--- Wall

%-D--%

--

- - -J

-

\-

_-

"W

-

"' I R , ( which has the same resistance for

0

I

-El e = TAN-' R~ -e EZ

-9 t3

FIG. 2. Voltage-controlled negative resistance and series load where I RLl >:

1 RN1 .

279

MULTISTAULE SEMICONDUCTOR DEVICES V

0

1

FIG.3. Voltage-controlled negative resistance as seen across series load where 1 RLI > IRNI.

steady and alternating currents over the frequency range being considered. Let us consider the idealized voltage-controlled or S-type negative resistance characteristic Oabc shown in Fig. 2. This characteristic is to be displayed by a voltage E in series with a load resistance R L . When the sweep has attained a voltage E , , a straight line is drawn from point E, making an angle whose tangent is R as shown in Fig. 2 . The intersection of this resistance with the curve Oabc shown at point a” determines the current that flows in the negative resistance device and the corresponding voltage across it. The point d” obtained by projecting from a and E , gives one point on the desired composite characteristic of the nonlinear device and its series load. Repetition of this projection process for additional assumecl voltages E, and E , , etc., makes it possible to determine the composite characteristic Odef. For the load value RL of this example the negative resistance region de of the composite characteristic is unconditionally bistable or multivalued in both current and voltage. In Fig. 3 is shown the case of an S-type negative resistance device characteristic Oabc in series with a negative resistance load in which only the positive linear portion R, of the load intersects the device under consideration where I RLpl > 1 R, 1 . The composite characteristic of the device and its nonlinear load, Odef. is determined in a manner similar to that of Fig. 2.

280

GEORGE ABRAHAM

Figure 4 represents an S-type negative resistance with an S-type negative resistance load. In this case the range of the load negative resistance does not result in more than one interaction with the device operating point. Interactions of device and device negative resistances will be considered in Section VI. Figure 5 represents the dual case of Fig. 2 for the current-controlled negative resistance whose I RLI < I R , I with the device and load resistances connected in parallel. V

0

I

RLP

_----FIG. 4. Voltage-controlled negative resistance and series voltage-controlled negative resistance load, where I RLpI > 1 RN1.

In Fig. 6 is shown an example of an N-type negative resistance which allows graphical representation over an extended region on the oscilloscope. In this case the load resistance R L is that of the sweeper and the nonlinear device characteristic Oabc when projected becomes the composite characteristic Odef. The device and its linear load RL are connected in parallel and the method of graphical representation is as follows. Assume a current Z, flowing through the device. A straight line is drawn from point Z3 making an angle whose cotangent is equal to A, as shown in Fig. 6 . The intersection of this line with the nonlinear device characteristic gives the voltage that is across the nonlinear element and the current through it. The projection of I , and point

I" b

\

C

I

FIG. 5. Current-controlled negative resistance as seen across parallel load where IRLI iIfGI.

I

0 -1

FIG.6. Current-controlled negative resistance and parallel load where I RLI < 1 RN1 .

GEORGE ABRAHAM

282

V

0

-I

Current-controllednegative resistance and and parallel current-controlled current-controllednegative FIG. 7. Current-controlled resistance resistance load where 1I RLp R,, 1 < 1I RN RN1.I .

a determines point d on the composite device characteristic. Repetition of this process for additional values of assumed currents I and I , facilitates the determination of the composite device characteristic Odef. Analogous to the case shown in Fig. 4 for the S-type negative resistance with noninteracting negative resistance load, Fig. 7 provides a graphical representation of an N type negative resistance and its negative resistance load when the load l&pl

rE/(N,M

- 1).

But since YE = K T / q I E ,

R > K T / q I E ( H F M - I),

(3.20)

or

qRIE(HFM - l ) / K T > 1.

(3.21)

Once avalanche multiplication has increased so that breakdown occurs (aFM 2 I ) , any additional increase in I, reduces r E and less voltage is needed

to satisfy Eq. (3.21). Punchthrough is defined as the reverse bias on the collector at which the base width W is reduced to zero. At this voltage the space charge region extends throughout the base to the emitter junction. Avalanche breakdown in a transistor is dependent on the high resistivity side of the collector junction. Normally, this is the base region. When the penetration of the depletion layer into the base reaches emitter junction before avalanche breakdown occurs, the device is limited by punchthrough voltage. Under this condition an electric field exists in the region between collector and emitter, providing a conductive path to the collector for the injected minority carriers. At punchthrough, the emitter loses control and its floating potential VEBO increases following the collector voltage until the emitter itself breaks down. In terms of the breakdown voltages (VB)EBO and ( Va)cso of the emitter and the collector to base respectively, the punchthrough voltage V,, is given by VPT = V(B)CBO

- ( VB)EBO

(3.22)

where the punchthrough voltage is dependent on the impurity profiles of the transistor base region. The punchtrough voltage may be increased by increasing the base width and/or decreasing the base resistivity. In order for a device to be useful in the avalanche range, the punchthrough

30 I

MULTISTABLE SEMICONDUCTOR DEVICES

voltage must be designed to be greater than that for avalanche breakdown of the collector junction. Hence, substitution of V,, > ( VB)cBo in Eq. (3.22) gives ( V,JEBO> 0. Accordingly, emitter breakdown will be realizable when avalanche occurs before punchthrough. This was the case for all discrete and integrated devices used in this investigation. The avalanche transistor will be utilized to demonstrate basic multistate principles in subsequent sections. Though the power dissipation of an avalanche transistor is higher that than of a comparable pnpn device, which we shall consider next, this is often offset by the higher speed capabilities of the former (44, 4 5 ) . The ideal switch should exhibit zero impedance in an o n ” state and infinite impedance in an “off” state. Transition between these states should occur instantaneously. Though ideal devices do not as yet exist, some actual devices approach characteristics of an ideal device better than others. For example, narrow base transistors have higher switching speeds than comparable four-layer devices. However, the latter provide a much better approximation to the voltage-current characteristics of an ideal switch and can also be designed to withstand higher voltages and currents. As the voltage between collector and base of a transistor approaches the breakdown voltage of the junction, the multiplication factor goes to infinity according to basic avalanche theory. Several mechanisms have been suggested that prevent M from realizing high values particularly at high current densities (46). These include surface breakdown which may become a problem in large-area devices, decrease in M due to scattering, reduction of M due to decreased field in the depletion region as the space charge builds up with carrier multiplication. It is, therefore, apparent that multiplication is not a voltage related function only. The dependence of A4 on current as well as voltage will be considered in further detail in the following subsection. ‘I

C . Breakdown in pnpn Deuices

In essence, the pnpn structure is a conjugate device involving the tandem interconnection of a pnp and an npn transistor as shown in Fig. 23. The device has two transistor-type emitters and a common collector. At a low terminal voltage, the emitters are biased slightly above cutoff and the current that flows through the device is essentially the leakage current of the collector or center junction. In this range the alphas are generally less than 0.1. As the applied voltage is increased, the small signal alphas increase until their sum reaches unity either with or without avalanche multiplication at the center junction. Breakdown occurs when, under this condition, internal positive feedback occurs as the device enters its active or negative resistance region. In the active region the terminal resistance of the device drops abruptly to the value of the series ohmic resistance of the structure. The negative resistance

302

GEORGE ABRAHAM

JI

J2 J3

Ih

FIG.23. pnpn Representation by tandem interconnection of pnp and npn transistors.

region provides a transition from one of high positive resistance to one of low positive resistance providing the necessary prerequisite for a solid-state switching. It is our purpose next to develop and analyze the voltage-current characteristic of the pnpn device in terms of the current amplification coefficients of a two-transistor model both without and with avalanche multiplication and in the negative resistance mode. Three terminal asymmetrical pnpn structures with unequal alphas have been fabricated (47) in which the bias of the center junction is kept below that required for avalanche breakdown. Operation of the device depends upon strong fields to assist carrier transport through the device thereby enhancing alpha and producing switching without dependence on avalanche breakdown.


303

In addition, Fulop (48) has shown by measurement that switching from a high impedance t o a low impedance state is controlled by the following condition : when the output admittance to a pnpn device becomes infinite, the sum of the small signal low-frequency alphas of the two transistors comprising it must be approximately unity. At this condition it has been shown (49) that an infinitesimal increase in voltage, gate current, or temperature will cause the onset of switching. At low voltages a pnpn structure may be represented by two transistors, namely, a p p and an npn with common middle regions as shown in Fig. 23. In this two-transistor mode, let uN be designated the forward-current gain of the npn transistor, and, similarly, u p that of the pnp transistor. In the case of diode operation of the device, the gate current is zero. In the model suggested by Ebers and Moll (50) the emitter and collector of each transistor are assumed to be junction diodes located sufficiently close t o each other so that they interact. The current at each junction will depend not only on the voltage at that junction but also on the voltage at the other junction. For each transistor of the pnpri device the equations are of the form:

where Ai

= [exp(qVi/KT) -

I E =.f,(AE

>

&)

1,

>

2,)

I]; i

=.f22(.2,

=

E, C .

Expressing the transistor equations as a linear combination of A's, IE= I E E 4 - I E C Ac 1, = fc,

AE

+

ICC

&.

(3.23) (3.24)

If Ac is eliminated in Eq. (3.23) using Eq. (3.24) and ,IE is eliminated in Eq. (3.24) using Eq. (3.23), the following additional forms may be obtained: IE =

-URIC

1, =

- CIF I E

f

IcoAE

(3.25)

1,

(3.26)

Ic = - CIF IE + I,, .

(3.27)

- I,.,

where

and

For reverse collector bias, ,Ic

=

- 1 and

304

GEORGE ABRAHAM

When the collector current is in the opposite direction, the sign of I,, will be changed and =

FIE + I,, .

(3.28)

In general, 1, = aFZ, - I,,

ac .

(3.29)

Let us now apply this to the two transistor models of the pnpn device shown in Fig. 23b. For thepnp and npn transistors, respectively, Eqs. (3.28) and (3.29) become (3.30) (3.31) where A,, = ,IcN = & , as the two transistors have a common collector region when interconnected to represent a pnpn device. The subscripts N and P represent the npn and pnp transistors, respectively. Equation (3.30) is the collector current of the pnp transistor, and as can be seen from Fig. 23b, is also the base current of the npn transistor. Similarly, the base current of the pnp is the same as the collector of the npn transistor. Accordingly, utilizing Eqs. (3.30) and (3.31) (3.32) (3.33) From Eqs. (3.32) and (3.33) we obtain aFNIEN

+ 1co&

= ZEp(1 - ~ F P )

(3.34)

where I,, = ICON= I c o p . If there is no base current or lateral current in the base ZEN

= Z E p = 1, = 1.

(3.35)

Hence, (3.36) When the collector junction is reverse biased and (3.37)

305


Rewriting Eq. (3.36) and using the abbreviated notation and Ac = A,

tlFN= c t N , aFp= C,L

(3.38)

I=C(~I+apl-lcoA,,

where Ac, ct,, u p , and I,, are functions of center junction voltage V , , and ctN and ctp are also functions of current I . First let us consider GI, and a, which are dependent on emitter and collector efficiencies and transport factor, and neglect the effects of avalanche multiplication which will be considered subsequently. Taking the total derivative of Eq. (3.38) with respect to I , one obtains

a/al {[&N(IlV2)II + b F U , V2VI - [Ico(V,)AC( - V2)Il = 1

(3.39)

which on carrying out the indicated differentiations becomes " a , aa,av dctNdV2 ar + I -av, ar + a 4-I -ar + -av, d l + & p ;Ircoav an,av A ---I

aaN I-

av,ai

SV,~I

=

1.

(3.40)

co

Solving for d V,/dI, the follohing equation is obtained: d VZ 81

_.-

a&N - ITda,

[l - I z

a&, - SI,, I+IAc av, av, av, a&,

[

I "I

- CIN - u p

(3.41)

- Ico-

a v2

which is a general form of dV/dl for the center junction. 1. Reverse Bias Case

Now let us consider the case when the center junction is reverse biased. In this event Ac = - 1. Hence

- carcopv2pC = a c 0 / av,

and - Ico(8&/4 V 2 ) = 0.

Accordingly, at reverse, bias Eq. (3.41) becomes

_d/

a&, arc, I-+I-+-av, dV, av, act,

(3.42)

306

GEORGE ABRAHAM

This becomes for

c!

independent of center junction voltage

+

+

I - I(a/aI)(@, up> - (aN ap>

ar

(3.43)

arco/a v 2

Near the switching point, as shown by Gibbons (54, aV2/dI = 0. Applying this to Eq. (3.43), the following may readily be obtained: (a/ar)(c!N

+ @ P I = [ I - (@N + a P ) l / l .

(3.44)

Letting c! = aN - u p

arjr = -2aa/(2c! - I).

(3.45)

This can be integrated with the substitution U = (2a - I ) from which In I = -In U + C

(3.46)

or

I-(2a-

(3.47)

I)-l

This gives the current-dependence on a at or near the breakover point.

2. Conducting State In the on or conducting state, on the other hand, let us consider Eq. (3.40).

In this case V , is negative and exp(y V 2 / K T )9 1. Hence

The term

av, ar av,

an, Ico = Ic04 exp - yv2 av2 - -KT

KT

a1

Hence in the on state aV,/I of Eq. (3.41) becomes dc!p

-- -

ar

ai

KT

al,, (3.49)

307


When uN = a p = CI

(3.50) 1-

i V2

In addition. when the differential resistance ?V/?I of Eq. (3.50) is zero, the following condition is satisfied :

(3.51) As the term on the left of this equation can be neglected

or I

- I/a

In I = In lju

on state

(3.52)

(7IjI & i x / x and

111 the

+ constant

near the holding point.

a p 2 1 and the p n p 1 device is in the conducting When, however, aN istate, the current that flows through the device is essentially limited by the external impedances and Eq. (3.23) doec not apply. When the foregoing inequality is satisfied the collector junction becomes forward biased in order that its current does not exceed the device current. I . The device is now in its on or low impedance state and the forward-biased center junction J 2 has changed role from that of a collector of minority carriers to that of an emitter of minority carriers into the respective base regions. This transition is effected as long as the sum of the alphas exceed unity and is not necessarily dependent on avalanche multiplication.

D. Total Dericc Resistance 111 general, the total device resistance can be obtained by piecewise linear addition of the incremental resistances of the junctions. When one or more of the junctions is in a high impedance state, the bulk resistances become negligible. The total device resistance rT then becomes

(3.53)

In order to express each of these terms as a function of the appropriate A’s for a given junction, we had by definition that

Ai

= exp(qVi/KT) -

1

308

GEORGE ABRAHAM

which becomes on solving for V i Vi = (KT/q)ln(A,

+ I).

(3.54)

The incremental resistance of the junction is obtained by taking the partial derivative of Eq. (3.54) with respect to total current through the device.

av,= -~ KT I an, r. = (3.55) ’ aI q (Ai + From Eqs. (3.53) and (3.55), the total incremental resistance of the pnpn device becomes

1)ar

When the center junction is reverse biased with the outer junctions forward biased, Eq. (3.56) becomes

I

rT = -

dI,

I] ,

(3.57)

where I , , and 13, are the saturation currents of the outer junctions. In view of Eq. (3.42) and on explicit substitution of the A’s, Eq. (3.57) becomes

For I > I,,, I , , and a independent of voltage, Eq. (3.58) becomes

2KT r,=-+91

KT 1 - I ( d / d l ) ( ~+, u p ) - (uN 4 a L l a v2

+ up)

(3.59)

With a = aN = ap and in order for the incremental device resistance to be negative, the following condition must be satisfied :

(3.60) The first term is negligible in the negative resistance region, hence

dI/I > - 2 d a / ( 2 ~- 1)

(3.61)

which on integration becomes In I > In (2a - I )

+ constant.

(3.62) Hence, in the negative resistance region of the device characteristic Z(2a - 1)-1.

309


E. Avalanche Multiplication Let us consider the additional effect of avalanche multiplication on the device characteristic. Previously, we considered only the current gain, a, which included the emitter and collector efficiencies and transport factor. With the added effect of avalanche multiplication in the collector junction of a pnpn device, let M , and M , be the voltage-dependent multiplication factors for electrons and holes, respectively. In this case Eq. (3.38) becomes

I = MN(v2)@-N(I, v,)

+ MP( v 2 ) a p ( I >v2)+ Ice(

v2)&(

v2).

Following differentiation and rearrangement as before, we obtain

(3.63) which for 1, = - 1 at negative biases reduces to the form given by Gibbons (51), and to that of Maclntosh (52)if, in addition, the dependence of alphas and Ic0 on center junction voltage is neglected. Equation (3.63) is the general form of dV,/c31 in terms of the alphas and multiplication factors of the pnpn device and in the event of avalanche breakdown should be used instead of Eq. (3.41) and as a basis for the equations derived from it. At reverse bias of the center junction (3.63) then becomes

At the breakover point dV,/aZ = 0 and the numerator of Eq. (3.64) can be set equal to zero as the denominator is now positive. Hence (3.65) This equation may be rewritten in terms of the dc and small signal alphas by returning to Eq. (3.24). At reverse bias of the center junction, Eq. (3.24) becomes

I = a,z+

a p l

+ I,,

(3.66)

310 For the

GEORGE ABRAHAM i i p

transistor portion of the piipi device. this becomes

where I , is the collector current, I , the emitter current, and ICONthe saturation current of iipri transistor. Noting that x N = , f l ( l E ]and ICON#J2(lE) the derivative of Eq. (3.45) with respect to emitter current becomes

(3.70) where uNoand u p , are the small signal ac alphas and and u p are the dc alphas. By substitution of Eqs. (3.69) and (3.70) into Eq. (3.65), the following expression for dynamic zero impedance of the center junction is obtained.

+ M N u N o = 1.

Mpxp,

(3.71)

Switching actually occurs at an increased current level where the sum of resistances of the center junction, the outer junctions, and bulk resistances of the pnpn device are zero. This requires that the ac impedance of the center junction be slightly negative i n order to offset the total positive dynamic impedances of the device. F. Radius af ' Citroati4re of Deuice Cliaracteristic

As switching is dependent upon the curvature of the voltage-current characteristic, let us consider the rate of change of the unit tangent vector T, as it moves along the I,, = f ( ~ curve. ) As the length of is constant, its direction will change from point to point along the nonlinear I,, curve. The curvature in this case is given by

K where cp

= dV,/rfl

and ds

= dcp/ds

(3.72)

+ d 1 2 ) 1 / 2Hence .

= (dVZ2

(3.73) where the plus sign indicates positive curvature (increase in d q / d ~and ) the negative sign represents negative curvature (decrease in dq/ds).


31 I

The radius of curvature R at a point P ( I c o , V ) is R = - I= - =U‘S K ckp

[I

+ (r/V2/dZ)2]3’2

+

- d2VjdI’

’

(3.74)

where R has the same sign as K . Accordingly, as shown in Fig. 24 the lower curved regions of a pnpn voltage-current characteristic near the origin and holding point have positive values of d2V/d12 whereas this second derivative becomes negative near the

FIG.24. Effect of curvature on suitching of pnpn device

switching point. For devices where these regions of curvature are high, the switching and holding points are close to the points at which dV2/r/I = 0. From Eq. (3.74), it is evident that when this equality is satisfied, the radius of curvature becomes infinite. Jn the case of a reverse-biased center junction with ct dependent on current but independent of junction voltage, we had that dV2 --

dI

-

“(J/m% + U P ) ( M N + %4l* a1,,/n v, -

(3.43)

312

GEORGE ABRAHAM

Neglecting terms involving a2Zc,/d V2 and (dZ/dZ2)(a, + u p ) one may obtain by substitution of Eq. (3.43) into Eq. (3.74) that the radius of curvature is approximately

From Eq. (3.75), it can beseen that at lowcurrentswhere(a, + a,)approaches zero, the radius of curvature approaches unity. The radius of curvature goes to zero when a, + ap = 1, and becomes a negative quantity when aN a p > 1.

+

IV. INTEGRATED AVALANCHE DEVICES

In many types of integrated circuits physical and electrical isolation are essential to minimize perturbation between independent devices and circuits on a common substrate. Only a few elementary circuit functions permit common connection to identical elements. In the majority of cases, it has been necessary to provide isolation of individual device structures. In nonintegrated and multichip integrated circuits this is achieved externally by physical separation and interconnection. Isolation in monolithic integrated circuits has been attained by a variety of methods including subdivision into groups of islands, use of reverse-biased p-n junctions to provide isolation at low frequencies, dielectric isolation, introduction of intrinsic isolation layers through epitaxial deposition, lateral isolation by diffusion, mesa etching in various forms, and by numerous other schemes. We shall now investigate the problems of interaction between multiple threshold devices in a monolithic array on a common substrate. When the array is connected to provide a composite negative resistance characteristic, the need for designed isolation will be determined by the nature and degree of interaction between devices. What is desired is a single chip integrated circuit in which the individual elements act as if they were phsycially and electrically isolated. The fact that silicon has a resistivity in the range from 1 to 100 0-cm precludes the possibility of ideal isolation. Both p-n junction and dielectric isolation provide parasitic capacitances which are detrimental to high-frequency response and may provide undesirable feedback loops. The former is also highly radiation sensitive. Before investigating the more complex problem of interaction among integrated active devices, let us first consider the circuit of Fig. 25. The externally connected discrete devices are represented in the diagram, namely, a sym-


313

FIG.25. Transistor and diode in parallel.

metrical transistor paralleled by a diode across the collector-base junction, where the diode current-voltage relationship is of the form 13

= 13,[expk V 3 I W - 1 I*

For the symmetrical transistor q 2= a Z 1and Ilo= Z20 and the transistor parameters are given by the following notation (53):I , , = saturation current of the emitter junction at zero collector voltage; I,, = saturation current of the collector junction at zero emitter current; ct12 = reverse alpha, namely, the transistor current gain with the emitter acting as a collector and the collector serving as an emitter; L Y = ~ ~forward alpha, or the transistor current gain with the collector and emitter serving in their normal roles. The two connected devices and their equivalent circuit are shown in Fig. 25. With S open, the Kirchhoff current equations become

314

GEORGE ABRAHAM

Letting AN = [exp(qVN/KT)- I ] and since a l l = a 3 3= I , Eqs. (4.1)-(4.3) may be rewritten I , = I I I A I - a12 1 2 2 A 2 ) (4.4)

+ a22122&

= -~2,4lAl

I2

(4.5) (4.6)

13=0+I33A3,

With parallelconnection of the transistor and diode ( S closed), these equations become, letting f4 = I, + I3

I1 I4 =

(4.7)

= flIA1 - % 2 I 2 2 ~ 2 ,

-

aZlfllA1

+ ( I 2 2 f 133)A2.

(4.8)

Since ZNF = I N N A N , these equations may be written as

I1 1,

= I I F - @I2

f

= -Cf21IIF

(4.9)

9

14F

(4.10)

*

In this case 14,

= 12F

+

f3F

= I 4 4 2 2 = (f22 f 133)AZ.

(4.1 1)

The later equations may be rewritten as

I1 = I 1 F I4 =

- a1

2(fZF/14F)14F

(4.12)

+ I4F

(4.13)

-a2111F

or in expanded form as 1'

= 'IF - c112[122/(122

14

= -

F

(4.14)

f I33)IZ4F

+ 14F.

(4.15)

=azl. Now by definition 1,,,/122= a12and Zzl/fl1 As shown by Ebers and Moll (53)these I's are related t o the respective saturation currents as follows Ill = 4 0 / ( 1

- %la,,);

4 2

I,,

= a12I20/(l - ~ 144 = 140/(1

= Z2O/(l - a 2 1 a 1 2 ) ; 2 1 ~ 1 2 ) ;

- %1%2)

I21

= (120

133

= 130/(1

- a21a12);

= '%1I10/(1 - a 2 1 c 1 1 2 ) ;

+ I30)/(1 - %lU12)

which on substitution into equations (4.14) and (4.15) become (4.16) (4.17)

315


and since I , ,

= I,,

for the symmetrical transistor E l 2 120 = @ 2 1 ~ 1 0 .

(4.18)

This shows that in the case of the p-n junction diode connected externally to the pnp transistor, no feedback factors are due to the diode and the basic relation (4.18) applies as in the case of one transistor as shown by Ebers and Moll (53). Now let us consider the case of two transistors with a common base substrate as may be seen in Fig. 26 (54). The internal feedback factors between

(b)

FIG.26. Two transistors with coninion base region.

316

GEORGE ABRAHAM

devices can no longer be neglected and must be taken into account. With S open, the input current equations for this configuration may be written as follows: (4.19)

I 1 =JIF-a12z2F-a1313F,

(4.20)

I2= - a 1 2 z l F - 1 2 F - a 2 3 1 3 F ~ I3

=

-cc31r1F

- a32r2F f

I3F.

(4.21)

For these equations, it is clear that the input currents 11,Z 2 , and I, are each due to three components. One is the forward current across a given junction and the other two are feedback components resulting from currents in the other two junctions of the device. As is shown in Fig. 26, if the switch S is closed,

L2 = ,I3.

I4 = I , + I 3 ,

Equations (4.19)-(4.21) may be combined into two equations because of the paralleling of the I2 and I, branches as follows: (4.22)

With two identical transistors (4.13) and (4.23) on a common substrate, the alphas are related because of symmetrical considerations as follows: = ax,

(4.24)

a31

= a 3 2 = UF,

(4.25)

a13

=a23 =MR.

(4.26)

a12 = a21

Where ex are the forward or normal alphas due to coupling between transistors and aF and aR are the conventional forward and reverse alphas of the transistors. Let

K1

=1 2 F / L

and

K2

= 13F/14F9

where Kl and K2 are current division factors between the devices, Eqs. (4.22) and (4.23) may now be rewritten in terms of the alphas of Eqs. (4.24)-(4.26). =IlF

14 = - ( T X

- Lax

+ UF)I1F f [(I

Kl

+ ccRK2114F

- @F)Kl

+ (I

- aR)K2]I4F*

(4.27) (4.28)


317

These equations are of the form (4.29) I,

=

- A 4 1 l I F + A44

(4.30)

Shown in Table I is a comparison of the A’s of Eqs. (4.29) and (4.30) for this two-transistor combination with those of Eqs. (4.14) and (4.15) for the diodetransistor circuit. The added effect of alphas due to coupling between the TABLE 1

COMPARISON OF THE COUPLING COEFFICIENTS FOR AN TRANSISTOR A N D THOSE OF Two INTEGRATED TRANSISTORS W I T H A COMMON BASE

~NTERCONNECTEDDIODE AND

Coefficient

Coefficient for interconnected discrete diode and transistor

A II

I

A14

~ L RKI

A41

ar 1

A44

Coefficient for two transistors with common base region

transistors in A,, and A,, terms and the more complex A,, term is indicated in the two-transistor configuration. The physical factors affecting czx will be considered next in the more complex case of integrated piipn diodes. In order for an integrated array of threshold devices t o operate multistably, several conditions must be met. A multistable circuit appropriate for integration should be selected. The integrated configuration must be designed to permit independent threshold operation of each device in its negative resistance, current and voltage saturation modes in a composite characteristic. This requires that either conventional isolation between adjacent devices be incorporated or that designed isolation be attained, for example, by electrical means. In any event, interactions and parasitics between devices in the common substrate should be minimized and. if possible, eliminated by built-in or designed isolation. Toward such an end, let us consider an array ofpiiprz devices on a common substrate as shown in Fig. 27 (55). These devices may be identical in which case external circuitry. for example, in thin film form, will be needed to provide interconnections and the necessary passive components (resistors) to provide a composite multistate characteristic. Alternately, the external circuitry can be minimized if the device’s negative resistance characteristics are

318

GEORGE A B R A H A M

appropriately graded across the array. In order to simplify the analysis, the interaction between two acljacent devices of the array will be investigated initially. Shown in Fig. 28 are two identical p/ip/i devices I and I1 integrated with common substrate regions P , and N2.Diodes P , N , and P , N , are serially connected independently to the common substrate via junctions J , and J , . The coupling between divices I and I1 is affected by a number of factors outlined in the following analysis as a basis for incorporating required isolation for multistate operation.

FIG.27. Monolithic avalanche array.

Fig. 29a shows two pnpn diodes and 29b the equivalent circuit. Since the two adjacent devices are part of an array that has been uniformly fabricated on a slice of silicon, in the equivalent circuit model it is assumed that the excess current distributions are uniform on the respective emitter and collector surfaces and that the respective emitter and collector current components cross these surfaces. On physical grounds as in (53) it will be assumed that linearity and reciprocity will hold at small applied voltages. The coefficients which are independent of junction voltages are shown in Fig. 29b. ax represents the effective alpha resulting from coupling between devices I and 11.

319


p2

I

J3

N2

V

I

P

P N

I

N

P

P

N

N

-

II

320

GEORGE ABRAHAM

P

P

N

N

- A

a X

12 2F

= a 1 R 2F

a 2 5 ~ 5 F =X aI

ZF

a 5313F = aF 13F

a2311FiaI F IF a2313F:a I F 3F

C (b)

FIG.29. Integrated dual pnpn diodes and equivalent circuit. (a) Integrated dual avalanchepnpn diode, (b) equivalent circuit.

32 I


In order to analyze interaction effects between thepnpn devices, let us consider the following equations which describe the equivalent circuit as shown in Fig. 29. I A = -11 = 1 l 1 A 1 - a 1 2 1 2 2 A z , (4.31) -IA=Iz=

Zc = Z3

+ ~ ~ 2 ~ 2 - ~ 2 3 1 3 3 ~ 3 + 0 - ~ ~ 5 (4.32) 1 5 5 ~ 5 ,

-a1211111

=0 -

= 14 = 0

ZZ2 22

+0 +0 +

- I ~ = 1 5 =O-a52122A2

With the substitution

ZMNAN

IA=I1 =

+ I,, A3 + 0 -

14FAA

(4.33)

a35155 2 5 ,

(4.34)

- a45 155 A5 >

-as313323

(4.35)

--54I4~14+155A5.

= I,, and since

-12,

4 = 13

-15,

1B = I4=

(4.36)

7

one obtains on substitution of (4.31) into (4.32) that

z1 = -1,

= (a12Q21 - l I Z Z F

+ a2313F + a 2 5 1 5 F .

(4.37)

1 -a21

Similarly on substitution of Eq. (4.34) into (4.39, 1, =

- 1)z5F.

- a5313F - ('45u54

-a5212F

(4.38)

1 - ff54

In view of relationships in Eq. (4.36), the terminal currents become (4.39) 1,

I,

= - a32

= u5212F ~

1 -a54

+ 1 3 F - @35z5F,

+-+-. I -

a5313F u54

(4.40) (4.41)

aZlz5F

1 - a54

The uMN coefficients may be expressed in terms of aF, aR, and ax as follows: a Z l= c

= UF

( =~ gs3 ~ =

=a32 =a35 =a45 =UR a25

= a 5 2 = ax.

On substitution of these coefficients into Eq. (4.39)-(4.41), one obtains

1, = a x 5 2 '2F 1 -afi

+ (&Jz3F

f

(

U+)z5F F ~ R-

I-u

(4.44)

322

GEORGE ABRAHAM

Equations (4.42)-(4.44)describe the dc characteristics of two coupled pnpn avalanche devices. Before carrying the analysis further, let us consider briefly the effect of the ax terms on the coupling between two devices. A case of particular interest occurs when one device is in a high conduction state and the other is in a low conduction state. The possibility of turning the second device on as a result of minority carrier injection by the first must be investigated. The effect of several relevant factors on interaction between the two devices will be considered, namely, ( a ) minority carrier transport, due to field in the base region, (b) carrier distribution in the base region of diffused structures, (c) recombination, (d) geometry, and (e) interaction between devices in a n asymmetrical multistable structure. If device TI is in a conducting state and device I is in an off o r high impedance state, junctions 4, 5, 6, will be highly forward biased ( Vj > KT/4). If device I is in a conducting state and device IT is in a n off o r high impedance state, junctions I , 2, and 3 will be highly forward biased ( Vj > > KT/q), junction 4 will be slightly forward biased ( Vj > KT/4),and junction 5 will be reverse biased (a potential collector of minority carriers from device I via base region P,).As a result, a n electric field will be established in base region P, from device I to 11. I n general, the electron and hole current densities in the base region P, for arbitrary variation of variable with position are

J, = - nq/i,Vq

+ qD,,V,

(4.45)

(4.46) 4DPV, where the first term on the right of each equation is the drift density and the second is the diffusion current density. In the horizontal direction, taken as the x-direction, the electron and hole current densities become Jp

J,,

= - PYP',VV -

= qp,nE,

+ qD,(dn/dx)

(4.47) (4.48)

where

(4.49) The partial derivatives indicate possible time variation. Since only the steady-state effect o f field on alpha is desired, such variation will not be applicable. I n order to maintain space charge neutrality, the drift and diffusion terms are equal in Eq. (4.48). Space charge neutrality implies equal excess majority and minority carrier concentrations ti1 and p1 and no and po are equilibrium values in region p z where electrons are minority carriers. By setting Jpx= 0 in Eq. (4.48),solving for Ex and substituting it into Eq. (4.47), one obtains, when the field is high I n/p)(3n,/dx J , , ~= ~ D , , ( +

= qD dtl,/ax

(4.50)

M ULTISTA BLE SEMICONDUCTOR DEVICES

323

where

is the effective diffusion constant as a result of the field (56). Since the N , emitter region is more highly doped than the P , base region (by approximately two orders of magnitude in most ptipn devices), the upper surface of the former can be treated as a n equipotential surface. Electrons injected from emitting junction J , are collected at the collector junction J,. An electron density gradient is established between these junctions in the P , region causing a corresponding electron current t o flow from emitter to collector. In order to maintain space charge neutrality in the P2 region, an equal hole density gradient is established in this region. T o obviate charge unbalance at high injection levels [56,571, a field is established in the P , base region in opposition to the hole density gradient thereby preventing hole flow to the collector o r center junction of device I. The field which I S directed toward the N, emitter induces minority carrier electron flow toward the collector. When the separation between devices is large compared to a diffusion length, the effects of recombination cannot be neglected. The survival of minority carriers in bipolar semiconductor devices is essential to their operation. The transport of such carriers between adjacent devices can also provide undesirable coupling between them. Electrons and holes may recombine with each other in two basic ways. One method is by the direct transition of an electron from the conduction band t o the valence band where it recombines with a hole. The second or more common method involves recombination of electrons and holes at recombination centers. Such recombination is the result of lattice defects. vacancies, or interstitials. The first process is dependent on properties of the semiconductor and the second process depends on its lattice imperfections. In transistors and pi7pn devices the second process is predominant. Typical field and impurity distributions are shown in Fig. 30. Minority carrier electrons injected by junctions J5 and J , as shown in Fig. 31 into region P , will be assumed to comprise the entire emitter current, I,,,. Those which survive transport across region P , t o reverse-biased junctions J , and J , make up the coupled collector current Icpz between the two devices. Some electrons are lost by volume recombination in region P,.The total number xq per second is called the volume recombination current I v p 2 . The number xq which are lost per second by surface recombination in region P , are called surface recombination current I s p 2 . These currents are related as follows: IEP2

= ICP2

+ I V P 2 + Is,,.

324

GEORGE ABRAHAM

x-a

i

E

(b)

FIG.30. Impurity and field distributions.

The effective base current would be the result of the recombination terms IBP2

= I"P2

+ ISPZ.

Considering npn transistor n3p2n2, ZEp2 represents the electron current due to injection into the P2 base region from junctions J2 and J,, and I p 2 is the collector current at reverse biased junction J , due to the electrons that survive transport across region P,.

325


The resulting coupled current gain is aF52

= f f 5 * P 5 Z Y2 M 5

where in the conventional sense a5* is the collector efficiency of junction J,, is the transport factor of the P2 region, y z is the emitter efficiency of J , , and M 5 is the avalanche multiplication factor of junction J 5 . As shown in Fig. 31 and the last term of Eq. (4.39), the n,pzn, transistor is in the grounded emitter configuration, the current ratio for which is p52

(%b)52

=~

(4.51)

- @F52

~ C / = ~ ’@ ~~ 5E2 / 1

As a result of the transverse geometry of region P2, its transport factor will effect current significantly. Under high level conditions /i’is affected by injection level and therefore by emitter current. Webster (56) has shown that variation of grounded emitter current gain can be described as a function

p52

Device I on

Device

FIG.31. Integrated avalanche devices.

n

off

326

GEORGE ABRAHAM

of emitter current, including the effects of volume, surface, and emitter recombination and emitter efficiency by the following relationship: (4.52) where,f(z) is known as a field factor and (4.53) as L,, = ( D P z p ) l i 2and L, = ( D,lt,)1/2.

(4.54)

In terms of the lifetimes, Eq. (4.52) becomes

where the low and high lifetimes are assumed to be comparable. In each of the terms of this equation clCb is inversely dependent on the first or higher powers on the base width. From a geometrical standpoint, if W > > L according to this relation uFS2will only be effective over short distances or at greater spacings the interaction between devices 1 and I1 will become negligible. As a result of its isolation from region P , by J , and the N, layer, junction J4 is not directly affected by the transport of carriers through region P,. As long as junction J , is reverse-biased, device I1 cannot be turned on. In order for the device to turn on its effective u p + aN = I . Typical values of a's for J , at low current are: u p R = 0.5 and with W >L,Ip2, u h F = 0.2. Hence, their sum is less than unity and the device will remain in an off condition unless the interaction with device 11 contributes sufficiently to the effective alpha of device I1 t o cause it to attain unity. Since L,, is of the order of a mil, spacings between devices of ten mils or more will reduce the transport factor and therefore uFZS or the coupling between devices I and I1 to a negligible value. The first term in Eq. (4.52) represents the surface recombination. When z is small,f(z) approaches unity. As the emitter current is increased, so does z , and f ( z ) approaches 1/2 at high levels of injection as the emitter current doubles. At high injection levels the field induced in the P, base region doubles the diffusion constant D, for minority carrier electrons, thereby reducing the loss of minority carriers by a factor of two. As a safeguard, the device in an on state should be operated at low level which will reduce the field term, diffusion constant, and transport factor. Let us consider next how diffusion or epitaxial growth (58, 59) can assist in providing isolation between adjacent devices on a common substrate through a builtin field. In the fabrication of diffused transistor structures an


327

important factor is the control of base width. For example, through the diffusion of p-type impurities, a semiconductor slice originally doped with a donor concentration, N,,, may be converted to p-type material near the surface and the geometry precisely controlled. At a distance Y below the surface, the concentration of acceptor impurites N if diffused from an infinite source is given by N , = N o erfc[ Y/2(D A f ) ' ' Z ]

(4.5%)

where N o = acceptor concentration at the surface, D, = diffusion constant of acceptor diffusant, t = time of diffusion. If one approximates the complementary error function by an exponential factor, exp ( - Y / L ) ,then N o = N , E N o exp ( - Y/L).The diffusion constant may be expressed as a function of temperature and activation energy E . D = Do exp( - E / K T )

(4.55b)

and the penetration depth can be accurately controlled as a function of the duration and temperature of diffusion. If all the acceptors are fully ionized, we have -&,

P

=

N , exp(

-E

KT I)

= N , = No e

xp(2).

Now (4.55c) As is constant throughout the base under equilibrium E, - Ef

=

KT( Y / L )

and E, must change with Y , creating an electric field in the base (see Fig. 30b). I n a p-type base the diffusion force on the holes is downward and the counterbalancing electric field is upward. If V is the electrostatic potential experienced by holes, then the electric field is given by (4.56)

Under an electric field the expression for electron current density becomes J, = q&niEx f

4D,(8fl1/8x>

(4.57)

328

GEORGE ABRAHAM

which by Einstein’s relation becomes

(4.58) When 17 = N,eKXlL the electric field aids the electron current (53)in t h e p base and thus for the same Jn requires a lower dn,/dY at the emitter junction. In the case of pnpn switches the anode and cathode regions are more highly doped than the inner floating regions by at least two orders of magnitude, for example IOl7 versus I O l 5 impurities per cubic centimeter. Hence a greater number of minority carrier electrons will be injected into the P , region from N , than from N , . For integrated pnpn devices which have been fabricated for diffusion from above, the built-in field E, Which is directed upward is shown as in Fig. 31 aids minority carrier electron flow downward. AS was shown previously, the transverse drift field E, in the P, region induces electron flow in opposition to it so as to localize them in a conducting device I. Hence, the combined influence of the fields on electrons injected by forward-biased junctions J , and J3 is downward t o the left. The resultant field causes these carriers to be directed toward the P , N , interface where surface recombination is high. This will reduce the transport of electrons from device I to IT, further decreasing the effective value of a x S 2 .In addition, for the case of a pnpn switch, Lin (60) has shown that in order for the device to have a high lateral alpha, the lateral collector to the base current gain must be high and the base sheet resistivity low. Additional electron isolation between devices I and 11 is also affected by multistate circuit design. For example, if device I is selected o r designed to break down at a lower applied voltage than device IT, then the sum of the effective a’s of the p n p and npn transistors, representing device I are lower than those of device I1 when operated as a composite structure. At low positive biases the initial portion of the multistate characteristic is due to the current saturation regions of the two devices in parallel as shown in Fig. 3 1. As the applied potential is increased, device I1 will turn on when its breakover voltage is reached. At higher voltages following the negative resistance portion of the contribution of device I to the composite characteristic, device I1 will fire. Thus, device TI will always be off until after device I has been turned on. Accordingly, device I which fires first is not dependent for turn-on upon the state of device I1 and conversely. Hence, multistable state operation provides additional built-in isolation between devices. In view of the isolation provided by geometry, recombination, and built-in fields due to drift and diffusion, the term c x 5 , is negligible compared to aF. Thus Eq. (4.44) becomes (4.59)


329

Now if Eq. (4.42) is multiplied by aR and Eq. (4.43) is multiplied by - 1)/( 1 - aF) and added, one obtains

(c(FcLR

(4.60) Similarly, multiplying Eq. (4.60) by subtracting yields

CI,

and Eq. (4.59) by (2aFaR - 1) and

Using the substitutions K1 = 1 2 / 1 3 and K2 = 15/13, Eq. (4.61) becomes

(4.62) from which

may be obtained

where 2 is a constant equal to the bracketed expression. In order to determine 13F,substitute Eq. (4.63) into Eq. (4.59) and solve for 13,: (4.64) where A is a constant that also includes the term y. I , , may now be determined by substitution of y and A into Eq. (4.40)

I,

= K2I3

=

- c ( R / Z F + A13 - aRy13

(4.65)

or I , , = [(A - K2aR,l)/aR]13= P I 3 where p is given by the bracketed term and includes A and y. By subsititution of Eq. (4.65) into Eq. (4.31) we may obtain I , , 11, = (Ki aRfi)13=

+

330

GEORGE ABRAHAM

where A includes explicitly the factor fl and implicitly A and y. Similarly by substitution of Eq. (4.63) into Eq. (4.34) can be obtained

I,,

=

(K,

+ a,y)Z,

= EZ,

(4.66)

where E includes the factor y. By rearrangement the diode self-currents may be expressed in terms of constants A , fl, A, E , and y and the current I , as follows:

Equations (4.67)-(4.71) can be rearranged to give the voltages across the five junctions as follows: (4.72)

(4.73)

(4.74)

4

(4.75)

(4.76) In the on-state A13/Z11 > 1 and Vl is positive. When f i I 3 / Z 2 2 > 1, V , must be negative. In order for devices I and I1 to be in conducting states V , and V5 must be forward biased. In this event, the total voltage across each device becomes (4.77)


33 I

and

(4.78) where the current division coefficients are included in the A , p, A, E , and y factors. In homogeneous substrate material z X z 5= r x 5 2and, as outlined above, are negligible compared to aF at spacings greater than a diffusion length. Switching of an avalanche transistor or pizpn device depends not only on the dc voltage applied to the device, but also on rate of change of the applied voltage. When the device is in an off-state, the transition capacitance of the device, primarily that of the center junction, cannot be neglected (61, 62). In the off-state the outer junctions are forward biased and the center junction reverse biased. The depletion layer capacitance of the center junction is shunted by a high junction resistance, usually larger than a megaohm. When the applied voltage increases at a slow enough rate that the current through the junction capacitance is negligible, breakdown occurs when the dc current increases until the effective alpha of the device equals unity. When the applied voltage Vchanges rapidly, the voltage across the junction capacitance changes at a rate dV,/dI and the current due to the parallel capacitanceacross the junction conductance adds to the total p r p diode current, thereby increasing the effective voltage across the center junction. For high rates of change of voltage breakover and switching occur at a lower applied voltage than before. For example, in a device with a 0.001 /IF effective value ofjunction capacitance, voltage rates of change of the order of hundreds of volts per microsecond can result in appreciable reduction of necessary switching voltage. The upper limit of the rate effect is determined by the time needed for redistribution of stored charge in the two base regions of the pnpn device to keep its outer junctions forward biased. Accordingly, at high frequencies consideration must be given to the rate (dz1,ldl)at which the applied voltage rises determine the breakover point where switching occurs in a pnpn device. In large area pnpn devices the rise of local current (di/dt)is another factor that must be taken into account (63, 64). This factor determines the lateral rate of spread of current with time over the junction. When the junction area is subdivided into an array of multiple devices, the di/df factor is limited to individual small-area devices and therefore becomes less significant than in large-area silicon controlled rectifiers and similar devices where the spread of current with time can be appreciable. Care must also be taken to avoid the effects of second breakdown in avalanche devices (65,66).This effect is thermally related and may be destructive when a transistor or pnpn device is biased into its active region. Second breakdown can be avoided by device design and by limiting the current density required to initiate the process.

332

GEORGE ABRAHAM

V. MULTISTABLE CIRCUITS In Section I1 it was seen that composite multistable characteristics may be obtained from appropriate interconnections of negative resistance devices. Depending on whether the negative resistances are open or short circuit stable, the form of the composite characteristic of their combination will be uniquely determined. For example, the serial connection of short-circuit-stable negative resistances can be made to result in a composite characteristic that is short circuit stable. Analogously, the parallel connection of multiple opencircuit-stable negative resistances can lead to a composite charcteristic that is open circuit stable. Let us next consider the implications of multiple negative resistance elements in further detail. A . Multistable Short-Circuit-Stable Negative Resistances in Series

When short-circuit-stable or 5’-type negative reistances are connected in series they may be made to operate multistably. In order to accomplish this, the load line of the active negative resistance devices must intersect one or more negatiye resistance regions and the bounding positive resistance regions. Let us consider first multistable operation of hole storage bipolar diodes and transistors as shown in Fig. 32. SOURCE OF

FIG.32. Serial connection of two hole storage S-type negative resistancesto give three stable states.

DYNAMIC

B+

As used in the present configuration dynamic B f is defined as a pump or periodically varying potential applied to a selected nonlinear device to store energy and to enable the device function as an amplifier and/or to exhibit a negative resistance characteristic. For example, a source of dynamic B f shown may be any source of recurring signals so long as the frequency or repetition rate of the recurring signals is greater than the reciprocal of the


333

lifetime of injected electrical charge carriers and provided that one element of each variable impedance device is driven positive with respect to another element of the variable impedance device during each cycle of operation. A multistable circuit is provided wherein a source of dynamic B+ is connected in series with a plurality of variable impedance devices to inject electrical charge carriers into a plurality of variable impedance devices at a rate greater than the electrical charge carriers decay due to recombination to maintain a steady state of stored electrical charge carriers in the variable impedance devices. The stored electrical charge carriers are used to obtain a composite negative resistance curve having a plurality of regions in which stable states of operation may be located (67). The number of these regions will be one more than the number of variable impedance devices connected in series with the source of dynamic B + .

FIG.33. Equivalent circuits.

The upper circuit of Fig. 33 represents the equivalent circuit of the collector-base junction of the transistor before dynamic B + is applied. The middle circuit of Fig. 33 represents the equivalent circuit during the application of dynamic B + and the lower circuit represents the equivalent circuit immediately after the dynamic B + has been removed from the transistor. In Fig. 34 is shown the composite negative resistance 1-V characteristic of the variable impedance devices for the circuit of Fig. 32. B. Modification of Coniposite Characteristic to Provide f o r Multistate Triggering

In order to provide triggering from a source of unipolar signals of constant amplitude a composite device characteristic generally has to be modified (68, 69). This is necessary in order to provide overlapping negative resistance

334

GEORGE A B R A H A M

.(

23

FIG. 34. I- V characteristic.

regions required for triggering. Let us consider a multistable circuit of the short-circuit-stable type which is to be so triggered. In Fig. 35 the multistable circuit shown comprises a high-frequency energy source, or source of dynamic B + V , , connected in series with variable impedance devices Q,,, Q l r , and Q13, variable resistor R,,, and a source of direct current voltage V15. Control knob 17, which is connected t o the source of dynamic B + V,,, may be employed to vary manually such parameter of the source of dynamic B+ as frequency, phase, duration, and magnitude. The output of the multistable circuit may be connected across variable resistor R , , as shown. A source of input signals 16 is connected to a selected element

FIG.35. Modification of I-V characteristic with passive components.

L J FREO.

335


,.

of variable impedance device Q , It is, of course, understood that the source of input signals 16 could be connected, with proper polarity, to another element of variable impedance device Q I 1 or to a desired element of variable impedance devices Q12 and/or Q 1 3 . The variable impedance elements R, R, 2a, and R , 3 J are shown connected in shunt with the variable impedance devices Q1,. Q l z ,and QI3,respectively, for reasons which will become apparent. The variable impedance devices Q , , . Q l z , and Q 1 3 may be any devices capable of exhibiting a short-circuit-stable negative resistance characteristic, for example, semiconductor devices such as active diodes or transistors. The electrical charge carriers may be any positive o r negative minority carriers such as electrons o r holes. I

20

21

22 23

I

FIG. 36. Unmodified characteristic of Fig. 35.

From a composite device standpoint, bariable impedances R , l;,, R l z a ,and R I 3 ; may , be considered as a part of the variable impedance devices Q,,, Q I 2 . and Q , J. respectively. for purposes of the operationaldiscussion which follows. The number of electrical charge carriers stored in the steady state is dependent in part upon the value of the load impedance and consequently may be varied by changing the value of load impedance. Hence, in Fig, 38 the magnitude of the steady state may be controlled. for example, by variable resistor R1-V

The number of electrical charge carriers stored i n the steady state will affect the shape of the composite voltage-current characteristic curve of variable impedance devices Q',, Q I 2 , and Q 1 3 when the magnitude of the dynamic B + applied to the transistors is zero. In Fig. 36, curve 21 represents

336

GEORGE ABRAHAM

the composite voltage-current characteristic when a relatively small magnitude of dynamic B+ is applied and curves 22 and 23 represent the voltagecurrent characteristic when the relative magnitude of dynamic B+ is increased to the magnitude of dynamic B + applied to obtain curve 22. It is noted that as the magnitude of dynamic B+ is increased, the conductivity of variable impedance devices Q l l , Q12,and Q13 increases, i.e., the current flow through the variable impedance devices per unit of voltage applied increases. This, in effect, is regenerative feedback and is attributed to the storage of electrical charge carriers. Thus, in the circuit shown in Fig. 35, as the magnitude of the dynamic B+ is increased, the number of stored electrical charge carriers is increased and curve 20 assumes the position of curve 22. It should be noted that curve 23 depicts the selected case where the device impedances of the transistors Q l l , Q12.and Q13 are substantially the same. Thus, the portion of curve 23 from 0 to B may be attributed primarily to the buildup of electrical charge carriers in transistor Q l l and the portion of curve from B to D may be attributed primarily to the buildup of electrical charge carriers in transistor Q I 2 ,etc. As the magnitude of the dynamic B+ applied to the circuit shown in Fig. 38 inreases and the proportion of the voltage across device Q l l increases, regeneration causes a part of curve 22 to assume the position of portion OA of curve 23. As the voltage across device Q1 increases further, regeneration is increased until with sufficient regeneration negative resistance appears in the vicinity of point A between A and B on the curve 23. Thereafter, increased voltage across variable impedance device Q l l will form the negative resistance portions of curve 23. Essentially the same curve-forming process will reoccur as the voltage across variable impedance device Q 1 2increases to cause a part of curve 22 to assume the position of the portion CD of curve 23. Thus, it is seen that variable impedance devices Q l l . Q l z as well as Q 1 3 have in general different dynamic impedance levels. The curve 23 in Fig. 36, the curve 24 in Fig. 37 , the curve 25 in Fig. 38, and the curve 26 in Fig. 39 each depict a composite voltage-current curve having a characteristic which is generally termed in the art as an S-type, " voltage-controlled," or " short-circuit-stable negative resistance characteristic. Referring to Fig. 38, a composite voltage-current characteristic curve of the multistable circuit depicted in Fig. 36 is shown which is similar to curve 23 in Fig. 37, but differs in the relative position of the several portions thereof with respect to one another. In particular, the negative resistance regions A-B, C-D. E-F overlap at a selected current level. It has been found that by control of the relative internal impedances of the several devices Q1,, Q l z , and Q , 3 , by various techniques to be described subsequently, the position of the portions of the composite current-voltage characteristic curve representative of the respective devices Q l l , Q 1 2 ,and Q 1 3 may be shifted such that "


337

V

FIG.37. Quadristable load intersection.

negative resistance and positive resistance regions of each portio will verlap similar regions of the other portions and therefore may be intersected by a common positive load resistance. For example, it has been found that the assembly of selected devices Q1I . Q l 2 ,and Q I 3having substantially identical internal impedances provides a composite voltage-current characteristic curve such as that shown in Fig. 36 wherein negative resistance regions do not overlap. By the assembly of selected devices QI1, Q I 2 , and Q I 3 having substantially nonidentical internal impedances, however, a composite voltage current characteristic curve of the type shown in Fig. 37 may be obtained. A single load line is drawn on each of the composite voltage-current characteristic curves 24, 25, and 26 of the multistable circuit shown in Figs. 40-42 respectively. Each of these load lines is drawn through a point on the voltage ordinate that is determined by the bias applied to variable impedance device Q I 1 by the source of dc voltage V , , at an angle 0 whose cotangent is equal to the sum of resistance R,4and the impedance of variable impedance devices Q I 2and Q , 3 ,i.e., the sum of the impedance load on variable impedance device Q I I ,assuming other impedances in the circuit, such as the imped-

Y

V

FIG.38. S-type bistable load intersection.

-I

E

FIG.39. S-type tristable load intersection.


FIG.40. Mulitstable connection of N-type negative resistances

23

21

FIG.41. Uncompensated coniposite characteristic.

27 I

I FIG. 42. Quadristable composite characteristic.

339

340

GEORGE ABRAHAM

ance of the dynamic B + are negligible. Each of the load lines ,'A Y , and 2 in Figs. 37-39, respectively, is shown intersecting the composite voltagecurrent characteristic curves 24, 25, and 26 at several points, in regions where the slope of the curve is negative as well as where the slope of the curve is positive. The points of intersection in the positive slope region P,,P,,P,, etc. represent stable points of operation for the multistable circuit shown in Fig. 35. On the other hand, the points of intersection in the negative resistance region N , , N , , etc. of Fig. 37 and 38 do not represent points of operation for values of load resistance greater than that of the negative resistance. As will be discussed subsequently in connection with Fig. 39, the points of intersection in the negative resistance region, N , , N Z ,etc., may be points of operation for values of load resistance less than the negative resistance. I n Fig. 37 the curve 24 is so adjusted relative to the load line X to permit bistable, tristable, etc., operation, depending upon the number of negative resistance regions available between selected levels, dependent upon the value and polarity of the input pulse signal applied to the circuit via the variable impedance device Q I 1by the source of input signals 16 in the circuit of Fig. 35. Considering bistable operation of the device of the basic circuit under the conditions of characteristic curve 24, a normal bias voltage E maintains the device in a stable condition, for example, in its first stable region 0-A, at point P,.Thereafter, an input pulse from input source 16 of E, value and negative polarity with respect to bias voltage E will move the circuit to switching condition at point A whereupon switching to the next stable region B-C to point A', will suddenly occur. After this pulse is applied the device will remain in the second stable region B-C, at P, (a) until an input pulse of value AE, and of positive polarity is applied which will move the circuit to switching condition at point B whereupon switching to the first stable region 0-A to point B' will suddenly occur or (b) until an input pulse of value AE, and of negative polarity is applied which will move the circuit to switching condition at point C whereupon switching to the third stable region D-E, to point C', will suddenly occur. Again the voltage E will maintain the circuit in its stable state at point P, of the region 0-A, or at point P , of the region D-E until another input pulse of selected value and polarity is applied. In Fig. 38 the curve 25 is so adjusted relative to the load line Y to permit bistable operation in the first and second stable regions and to permit monostable operation in another region dependent upon the value and polarity of the voltage applied to the circuit via the variable impedance device PI, by the source of input signals 16 shown in Fig. 35. Bistable operation in the first and second stable regions of characteristic curve 25 is identical with that just described in connection with characteristic curve 24. Since the load line Y does not intersect either the second negative


341

resistance region or the third stable region, a different type of operation generally termed “monostable” occurs in the second and third stable regions BC and DE, respectively. Thus, when the device is being maintained in its second stable region B-C, at point P,, because of the normal bias voltage E, and an input signal of value AE, and of negative polarity is applied to the circuit, the device is moved to switching condition at point C whereupon switching to the third stable region D-E, to point C” will suddenly occur. As long as the input signal remains, the device will stay in the third stable region at point C” but as soon as the input signal is removed, the device moves to switching condition at point D whereupon switching to the second stable region B-C, to point D”, will suddenly occur. Again the voltage E will return and maintain the device in its second stable region B-C, at point P,, until another input signal of selected value and polarity is applied to the circuit. In Fig. 39, the curve 26 is so adjusted relative to the load line Z to permit bistable operation in the first and second stable regions and to permit astable operation in another region. Again, the bistable operation in the first and second stable regions of characteristic curve 26 is identical with that described in connection with characteristic curve 24. In this instance the load line Z intersects the second negative resistance region at N 2 , does not intersect the third stable region D-E. and intersects the third negative resistance region at N , . Thus, when the device is being maintained in its second stable region B-C, at point P,, because of the normal bias voltage E and an input pulse of value A E , and negative polarity is applied to the circuit, the device is moved to switching condition at point C whereupon switching to the third negative resistance region. to point C”’. will suddenly occur. At point C”, assuming sufficient reactance in the circuit, oscillation begins. It will be appreciated that for the short-circuit-stable type of negative resistance, the reactance in the circuit must be inductive. As long as the input signal remains, oscillation continues at point C”‘ and when the input signal is removed the normal bias voltage controls and oscillation continues at point N , . Thereafter, an input pulse from input source 16 of value AE will move the circuit into the stable region D-E and into switching condition at point D whereupon switching to the next stable region B-C, to point D, will suddenly occur. Again the voltage E will maintain the circuit in ’stable region B-C, at point P,, until another input pulse of selected value and polarity is applied. While bistable operation involving switching between adjacent stable regions has been described in connection with Figs. 37-39, it will be appreciated that switching between other stable regions may be obtained, employing comparable circuitry. by the application of input pulse signals of greater value. In such instance, of course. a correspondingly greater output signal may be obtained.

342

GEORGE ABRAHAM

For example, in Fig. 37 switching may be accomplished from point P, of the first stable region to point P, of the third stable region by the application of a pulse of negative polarity having a value AE3 and returned to point P , of the first stable region, if desired, by the application of a pulse of positive polarity having a value AEz. It will be appreciated that the pulse values listed above are the minimum values required for the switching actions and that the value of the pulse is not critical so long as it attains the required minimum and does not exceed the minimum requirement for the next adjacent stable region. It will be seen that by proper orientation of the characteristic curve relative to the load line, the input voltages AEl and AEz, for example, may be of equal value so that a switching action for bistable operation may be obtained by a reversal of the polarity of the input signal. Similarly. by proper orientation, the negative input voltages AEl. AE,, etc., for example, may be in any selected relation such as A E , = nAE, or AE, = AE, + nk where n is an integer and k is a constant. Thus, the device will produce an output representative of the input signal applied and may be employed as a pulse counter. In addition to its multistable operation, the device may be adapted for monostable or astable operation if desired. C. Multistable Open-Circuit-Stable Negatiire Resistances in Parallel In order to facilitate fabrication monolithically on a common semiconductor substrate, let us consider a conveneint multistable circuit consisting of a plurality of devices each capable of exhibiting an open-circuit-stable type of negative resistance characteristic. The devices are connected in parallel [70] across an output circuit to form a composite characteristic with alternate negative resistance regions separated by regions of positive resistance over selected voltage increments and means are provided for increasing or decreasing the negative resistance or active region of each device. The multistable circuit thus obtained may be triggered to a desired stable region several ways, i.e., by varying the relative amplitude, phase, or width of pulses applied to a selected element of the variable impedance devices, etc. For example. triggering from a first stable region to a second stable region may be accomplished by applying a pulse of proper amplitude, polarity, width, and shape, for a given load line t o a desired element of a selected variable impedance device and a pulse of reverse polairty which may be similar in other respects will trigger the multistable circuit from the second to the first region. In Fig. 40, such a composite circuit is shown comprising a plurality of variable impedance devices Q1,, Q 1 2 , Q i 3 , and Q14,connected in series with variable resistances R , Rlla, R13a,and R l s , ,respectively, and in shunt with another across variable impedance R , and battery V , in series connection.


343

As shown in this figure, the battery V16 reverse biases each of the variable

impedance devices. The output of the multistable circuit may be taken across variable impedance R,,, as indicated. A source of input signals 18 is connected to a selected element of variable impedance device Q , The variable impedance devices Q l l , Q 1 2 ,PI,,and Q14 may be any semiconductor devices capable of exhibiting an open-cricuit-stable negative resistance characteristic. For example, npn-type transistors or silicon-controlled rectifiers may be utilized. The variable resistances R l f d ,RlZarR13a, and R14= are provided to insure that the effective parallel impedances of identical devices Q l l , Q l Z rQ,, and Q I 4 and their serially connected variable resistances, respectively, R, l a , R , Za, RI3=,and R14a,are appropriately nonidentical. Where the junction impedances of the devices Q 1 , , Qlz, Q13, and Q14 are designed to be selectively different, the variable resistances Rlla, Rlz,, R13,, and R14a are not essential and may be eliminated. As shown in Fig. 41, it has been found that the characteristic curve for an assembly of open-circuit-stable devices in parallel is dependent upon the resistive impedance relation between devices. In the rare circumstances where the devices are identical in resistive impedance, the characteristic curve takes the form of an extended n-type negative resistance as shown at 21, due to the fact that all devices turn on and off simultaneously. Normally the resistive component of the device impedance, which is the principal portion at low frequencies, differs in each device to a slight extent in the case of devices of a similar variety selected at random. This slight difference in resistive impedance will provide a composite characteristic curve of the type shown at 23 due to the successive reaction of each device. It will be noted that in the composite characteristic curve 23, the negative resistance regions A-B and C-D do not overlap. That is, the difference in resistance impedance is inappropriate to effect a significant overlap such that portions of at least two of the negative resistance regions overlap within a selected voltage range. The curve 23 in Fig. 41, the curve 24 in Fig. 42, the curve 25 in Fig. 43, and the curve 26 in Fig. 44 each depict a composite voltage-current curve having a characteristic of the open-circuit-stable type. Referring to Fig. 42, a composite open-circuit-stable voltage-current characteristic curve is shown which is similar to curve 23 in Fig. 41 but differs in the relative position of the several portions thereof with respect to one another. In particular, the negative resistance regions A-B, C-D, and E-F overlap at a selected voltage level. It has been found that by control of the relative internal impedances of the several devices Q l l , Q12, Q13, and Q14 by various techniques to be described, the position of the portions of the composite voltage-current characteristic curve representative of the respective devices Q l l , Q 1 2 , Q 1 3 ,and Q I 4 may be shifted such that negative resistance

344

GEORGE ABRAHAM

V

FIG.43. N-type bistable load intersection.

and positive resistance regions of each portion can be located so as to fall within similar voltage ranges of the other portions of the composite characteristic and therefore may be intersected by a common positive resistance load. Fig. 45 depicts another variation of the circuit comparable in many respects t o the arrangement of Fig. 42 wherein the variable impedance devices Q I 1 , Q 1 2 . Q I 3 , and QI4 are associated on a common two-layer junction structure of semiconducting material indicated at 19, in a single complex variable impedance device. In this configuration devices of the four-layer variety are shown wherein additional p-/I junction semiconductor regions are added epitaxially or by diffusion to the initial p-n junction slice, as indicated at A , , A , , A , and A,, to form a multiple junction structure, as indicated. As was pointed out, it is essential for multistable operation that the relative inipedances of the devices of QI1. Q 1 2 , Q13,and Q1, be appropriately different. Therefore. i n the instance when the devices are substantially identical some means for altering the impedance of the parallel branches such that they will differ is essential. In Fig. 45, the series resistances R l l a , R12,, R13a.and R14a serve this function. These series resistances need not be variable, as shown.

FIG. 44. N-type tristable load intersection.


345

Hence fixed resistances may be substituted if desired in a given multistable design. In Fig. 45 as in Fig. 40, variable load impedance R,, and dc source V16 are connected across the parallel connection of variable impedance devices and the output is taken across the load impedance R 1 5 .With the dc source V,, polarityas shown, each device would constitute two forward-biased junctions separated by a reverse-biased center junction. It will be noted that a single load line is drawn on each of the composite voltage-current characteristic curves 24, 25, and 26 of a multistable circuit shown in Figs. 42-44, respectively. Assuming other impedances in the circuit are negligible, it will be noted that each of the load lines 27, 28, and 29 in Figs. 42-44, respectively, is shown intersecting the composite voltage-current characteristic curves 24, 25, and 26 at several points, in regions where the slope of the curve is negative as well as where the slope of the curve is positive.

FIG.45. Integrated multistable device.

The points of intersection in the positive slope region represent stable points of operation for the multistable circuit, P,,P,,P,, etc. On the other hand, the points of intersection in the negative tesistance region N , , N 2 , etc. (Figs. 42 and 43), do not represent points of operation for values of load resistance greater than that of the negative resistance. As will be discussed hereinafter in connection with Fig. 44, the point of intersection in the negative resistance region N , may be the point of operation for values of load resistances less than the negative resistance. In Figure 42, the curve 24 is so adjusted relative to the load line to permit bistable, tristable, etc., operation, depending upon the number of negative resistance regions available between selected current levels, dependent upon the value and polarity of the input pulse signal applied to the circuit via the variable impedance device Q I 1 by the source of input signals 18 as shown in Fig. 40.

346

GEORGE ABRAHAM

D. Midtistable Characteristic with One Direct and One Innoerted Negatii,e Resistance By means of phase inversion it is possible to convert one kind of negative resistance characteristic to its complementary type [71]. In order to achieve this, let us consider a semiconductor device having a least two p-n junctions, preferably a transistor type structure, where each of the junctions are back biased and the device itself subjected to dynamic B + , such that both N- and S-type negative resistance curves are generated. The output taken between appropriate terminals results in an additive combination of the two dissimilar negative resistance characteristics, one of which has been converted in kind now like the other, producing either a double S-type or a double N-type negative resistance characteristic of three stable states. The phase inversion properties of the transistor structure have thus been utilized to convert one kind of the negative resistance characteristics to the other.

4 FIG.46. Circuit for one direct and one inverted negative resistance.

This is illustrated in Fig. 46 where a source of dynamic B + , V12,is applied across the collector-emitter terminals of transistor Q , In this configuration push-pull injection is realized. Push-pull injection occurs when a source of dynamic B + is applied across a pair of junctions connected back to back in a semiconductor device, so that the minority electrical charge carriers are injected into the regions bounding each junction during the portion of the cycle of operation in which the junction is forward biased. With such twofold injection, it is possible to generate an S-type negative resistance characteristic at both the collector-base and the emitter-base junctions. Capacitor C, 3 , employed between the source of dynamic B+ and the collector of transistor Q,,, serves as a means of connecting the source of dynamic B+ to this semiconductor device. Bias sources V15 and V16 serve to back bias both the emitter-base and collector-base junctions, and, although not shown, are by-

,.

M ULTISTABLE SEMICONDUCTOR DEVICES

347

c

$13 I, 1I

DYNAMIC

B t

I, FIG.47. Alternate circuit.

passed by capacitors. A load resistor R , , , across which the output voltage of the circuit is realized, is connected across the emitter-base junction. The circuit of Fig. 47 is similar to that of Fig. 46 except that the source of dynamic B + , V ,2 , is connected across the collector-base junction of transistor Q , , *and the output load resistor R,, is connected across the collector-emitter terminals. Referring to Fig. 48 in conjunction with Fig. 46, Fig. 48a shows an N-type

;I-_'

++ C-B JUNCTION

(a)

E-8 JUNCTION (C)

E - B JUNCTION

(h)

t - E .IUNCTION

(d)

FIG.48. I- V characteristics of circuit of Fig. 46.

348

GEORGE ABRAHAM

negative resistance characteristic generated at the collector-base junction, which is caused by increasing the bias V15, a reverse bias to this junction, until the avalanche breakdown threshold is reached. This showing is prior to the application of dynamic B f . At this time, Fig. 48b shows a normal diode characteristic exhibited by the emitter-base junction. Figure 48d shows the emitter-base junction subjected to dynamic B + and the resulting S-type negative resistance characteristic. The curve would be as shown, but in the absence of any other negative resistance occurrences, i.e., without the avalanche breakdon at the collector-base junction. What actually appears across the emitter-base junction, as seen across load resistor R,,, is the double S-type negative resistance characteristic, as shown in Fig. 48d. The curve here is the composite of the direct S-type curve generated at the emitter-base junction and the reflected N-type curvegeneratedat thecollectorbase junction. The reflected N-typecurve results from phase inversion, common to three terminal devices. This inversion is shown in Fig. 48a by interchanging the voltage and current axes and observing the shape of the curve as it appears in the third quadrant, while maintaining the voltage axis as the ordinate with the current axis as the abcissa. This affords 180" phase shift or complete signal inversion, and the N-type now appears as an S-type negative resistance characteristic. The N-type negative resistance associated with avalanche breakdown thus occurring at the collector-base junction is viewed as an S-type characteristic, looking into the emitter-base junction. Fig. 48e shows a double N-type curve at the collector-base junction, consisting of the N-type avalanche negative resistance characteristic generated there and the reflected S-type negative resistance characteristic which is generated at the emitter-base junction. In other words, the double S-type negative resistance characteristic seen at the emitter-base junction in Fig. 48d appears as a double N-type negative resistance characteristic when viewed from the collector-base junction. It should be understood that the normal transistor is not symmetrical and the curve shown is the ideal curve which would be realized from a symmetrical or double-collector type semiconductor device.

E. Tristable Operation Employing Single Negatioe Resistance Devices A simple ternary memory element makes possible radix three computers with their greater data handling capabilities. Ternary logic computers have not been considered practical due t o the unavailability of devices having a three stable state switching capability to complement o r replace widely used bistable switching devices employed in contemporary computer systems. A method for achieving tristability in a single avalanche semiconductor junction device is with multiple avalanche interactions (72, 73). This is shown in the circuit of Fig. 49 for interacting depletion layers illustrated in Fig. 50


349

t

JFIG.49. Multiple avalanche circuit.

23

24

I'

25

FIG.50. Interacting device depletion layers.

( 7 4 ) . The resulting tristable negative resistance I-V plot is shown in Fig. 51. An experimental example of a coupled tristable avalanche oscillator is shown in Fig. 52. The three V-l traces in the upper photograph are for (a) the bistable case, and as shown (b) and (c) are tristable cases for two different values of resistance, R , . The circuit diagram is shown in Fig. 52c. Sine wave oscillation resulting from avalanche interaction is illustrated in Fig. 52b. In Fig. 53, tristability with a gallium arenside tunnel diode (S-type negative resistance) is demonstrated. The static bistable V-1 characteristic is shown in 53a, the static tristable V-I characteristic due to coupled avalanche, in 53b, and the circuit diagram is given in Fig. 53c. Experimentally the serial

FIG.51. Tristable coupled avalanche.

FIG.52. Tristable coupled avalanche oscillator. (a) R;= 2.0 K (bistable), fuse = 1.25 mHz; (b) R; = 5.0 K (tristable), foSc = 1.25 mHz; (c) R ;= 8.0 K (tristable). Vertical scale 15 V/cm, horizontal scale 0.25 mA/cm, Rz= 3.0 K,R,= 5.5 K, E2 = 45 V, R ;varied. (d) Sine wave oscillation during avalanche interaction. Vertical scale 5 V p-p, horizontal scale 1 pecicm, R ; = 8.0 K, R2= 3.0 K, R, = 5.5 K,Ez = 45 V, f,,, = 1.66 mHz.

FIG.53. Tristability in a gallium arsenide tunnel diode. (a) Static bistable characteristic, (b) static tristablecharacteristic. Vertical scale 5 mA/cm, horizontal scale 0.1 V/crn. (c) Tunnel diode (GaAs-ZJ61).


35 1

Fig. 54. Quadristability in a GaAs tunnel diode. (a) Quadristable mode, (b) quadristable oscillatory mode A, (c) quadristable oscillatory mode B. Vertical scale 5 mA/crn, horizontal scale 0.1 V/cm.

352

GEORGE ABRAHAM

FIG.5 5 . Integrated multistablepripn avalanche I- Vcharacteristic. (a) Bistable characteristic (single device). Vertical scale 0.3 mA/cm, horizontal scale 4 V/cm, R, 20 R.(b) Tristable characteristic (two devices in parallel on common substrate). Vertical scale 2 rnA/cm, horizontal scale 2 V/cm, R, = 20 R.(c) Five stable state characteristic (four devices in parallel on common substrate). Vertical scale 10 rnA/div, horizontal scale 5 V/cm, R, = 200 R. :


353

resistor, R,, was selected so that R,l > IR , ( , where R,,is the negative resistance of the tunnel diode, to result in the bistable V-1 characteristic of Fig. 53a. The parallel resistor, R , , , was then varied to provide the desired form of the static tristable V-I characteristic of Fig. 53b. I n Fig. 54 several quadristable modes, two of them oscillatory in (b) and (c) of the figure, are shown for a gallium arsenide tunnel diode. Shown in Fig. 55 are the voltage-current characteristics of integrated multistable avalanche devices (N-type negative resistances) on a common substrate. Shown in (a) of the figure is the bistable switching characteristic of a single device. In Fig. 5% the tristable characteristic of two devices connected in parallel on a common substrate are shown. Figure 5% shows the V-I characteristic of four parallel avalanche array pnpndiodeson a common substrate with five stable states resulting. The multistrate serial connection of ten tunnel diodes (S-type negative resistance) and the resulting V-l characteristic with eleven stable states is shown in Fig. 56.

(b)

FIG.56. Multistate serial connection of tunnel diodes. ( a ) Circuit, (b) I-Vcharacteristic.

354

GEORGE ABRAHAM

FIG.57. Multistate tunnel diode, characteristic serial connection. Vertical scale 0.1 mA/div, horizontal scale 50 rnVidiv.

Figure 57 is an oscilloscope photograph of the V-I characteristic. A V-I photograph is shown in Fig. 58 for seven tunnel diodes fabricated monolithically in parallel by alloying on a common substrate. A variable resistor was employed across each diode to compensate for individual variations in their characteristics (75-77). Due to the parallel connection of S-type negative resistance elements (which is not the preferred connection for this type of negative resistance as shown in Section I1 the peak-to-valley ratio was slightly greater than unity. This is due to the shunting effects of S-type negative resistances connected in parallel and to parasitic coupling in the high conductivity substrate material. This provided experimental verification that the serial connection of 5’-type negative resistances is the preferable form.

FIG. 58. Multistate monolithic tunnel diode, characteristic parallel array. Vertical scale 20 rnA/div, horizontal scale 100 mV/div.


355

F. Ititegrarrtl Deilices Three-quarter inch diameter commercially obtained silicon wafers were used in this investigation t o fabricate multiple avalanche negative resistance elements on a common substrate. Three epitaxial layers were grown on (100) silicon to provide a total of four regions (pnpn) following which the top and bottom surfaces were plated (by evaporation) with a gold film to give an overall thickness of approximately .002 mils. Silicon pnpn slices with 20 V breakover characteristics were employed for monolithic fabrication of up to 200 individual devices on a common substrate. Resulting devices were made in various areas from 2 mils square to 8 mils

FIG. 59. Experimental nionolithicpnpn array mounted in 14 lead flat pack.

square and in various configurations and spacings. Each new device has essentially the same breakover voltage as its large-area counterpart. The composite structures were mounted in a 14 lead flat package (see Fig. 59). T o d o so, the common cathode structure was bonded to the insulating header substrate, the common cathode, and the anodes were individually thermocompression bonded to the header pins with 2 mil gold wire. Experimental arrays of pripri diodes which were fabricated by a combination of diffusion and expitaxial growth techniques with an H-geometry on a common substrate as shown in Fig. 60 were also operated multistably. For the fabrication of integrated tunnel diodes on a common substrate a LO mil thick slice of (100) germanium doped with I O l 9 donors per cubic centimeter and with a resistivity of 0.0007 R-cm was scribed into 20 mil square dice. The anodes were made of indium pellets offrom 0.5 to 3 mils in diameter. The pellets were alloyed into the germanium substrate by quadruple focused

356

GEORGE ABRAHAM

FIG.60. Array of H-geometry prrpri devices integrated in Si.

infrared sources under vacuum of approximately 50 p at a temperature of 300°C for approximately I0 seconds. The process produced multiple tunnel diodes with an average peak current and peak-to-valley ratio of 7 to I . From the large yield of diodes on the germanium substrate, seven were selected with similar characteristics. The base material was connected to the header which served as a cathode. Anode connections were made by thermocompression bonding with 2 mil gold wire to the alloyed indium pellets which served as anodes (see Fig. 61). Although diodes of similar characteristics were selected, it was necessary to employ a variable resistor across each diode to compensate for individual variations in their characteristics. To this point the multiple N + I stable states generated due to the serial or parallel connection of appropriate multiple S- or N-type negative resistances were with linear loads. Negative resistance interactions due to negative resistance devices with interacting negative resistance loads will be discussed in the next section. VI. NEGATIVERESISTANCE INTERACTIONS In the graphical analysis of a device characteristic (1-3) the load is generally considered to be single valued if not linear at least in the vicinity of the operating point. In this section we shall consider the interaction of composite


357

N- and S-type negative resistances with negative resistance loads. As was shown in the previous section, the composite S or N characteristic may have N + 1 stable states where N is the number of negative resistance devices. With negative resistance interactions the additional number of stable states that result increases the radix and therefore the total amount of information that may be stored. This facilitates a reduction in the number of active devices necessary to attain a given radix.

FIG.61. Monolithic tunnel diode arrays.

358

GEORGE ABRAHAM

A . S-S Interaction

Let us consider next the interaction of an S-type negative resistance with an S-type negative resistance load. Such an interaction is shown in Fig. 62. The device characteristic in this case is represented by 0-1-6-5. The load at the first switching point I is given by negative resistance L-L. Switching occurs along this line, namely from 1-2-3-4, where the line segment 2-3 is an additional stable state. As the device characteristic is further traversed at higher negative voltages by the load, the operating point proceeds from 4-5,

0

I

'L '

'L FIG. 62. S-S negative resistance interaction and switching sequence.

returning along this line to point 6 as the sweep voltage decreases. Switching occurs along line L'L' namely from points 6 to 7 from which the operating point returns to the origin as the sweep voltage goes to zero. Experimental examples of S-S interaction are shown in Fig. 67 for multistable hole storage diodes connected in series. B. N-N Interaction

In Fig. 63 an idealized N-type avalanche negative resistance is represented by the segments 0-1-6-5. [ts load is also an N-type negative resistance along

359


L

0 -

L'

L'

\

L

FIG.63. N-N negative resistance interaction and switching sequence.

which switching occurs via segments 1-2-3-4. Segment 2-3 is stable and segments 1-2 and 3-4 are unstable. As the original N-type negative resistance is further traversed by the load, the operating point proceeds from 4 to 5. On the return sweep, it goes to 6 via 4. At point 6 switching occurs to point 7. From this point on, the operating point returns monotonically to the origin along 7-0 as the voltage is reduced to zero. Experimental examples of N-N interactions for avalanche transistors are shown in Figs 68 and 69.

C. S-N Interaction In the case of S-N interaction annihilation may occur. The sweep sequence is shown in Fig. 64 before and after annihilation. Prior to annihilation the switching sequence is shown on the composite S-N characteristic in (a) of the figure. The sequence before annihilation is 0-1 -2-3-4-5-6-7-8-9-0. Following annihilation of the negative resistances, the sweep sequence bebecomes 0- 1-5-6-0 over the remaining characteristic which is essentially linear. If a voltage-controlled negative resistance characteristic is made to interact with that of a current controlled-negative resistance, annihilation of a portion of the composite characteristic may be possible. In order to accomplish this, the range or one or both of the negative resistance elements should be variable so to as to extend to the energy range of its counterpart. This may be

3 60

GEORGE ABRAHAM

V

FIG.64. (a) Composite S-N characteristic. (b) S-N negative resistance annihilation.

readily accomplished if appropriate S- and N-type negative resistances occur in the same device. Let us consider a piip transistor in which an N-type negative resistance occurs due to avalanche at the collector-base junctions. If the junction is also parametrically excited by a high-frequency energy source or dynamic B + as shown in Fig. 65 to inject carriers at a rate high compared to the reciprocal of the effective lifetime of minority carriers in the high resistivity side of the junction, a voltage-controlled negative resistance will also appear in the composite characteristic. This is shown in Fig. 66b. The switching device shown in Fig. 65 has different impedance values in each of the regions indicated as I, IT, and I11 in the typical open-circuit-stable characteristic curve of Fig. 66a. In region I the resistive impedance is relatively


361

I RA D I AT I0N

61 ALTERNATE CONTROL ENERGY SOURCE N

V35,.

DB

+ 19&

N 46

FIG.65. Schematic for S-N negative resistance annihilation. V

V

FIG. 66. S-N negative resistance annihilation. (a) N-type avalanche negative resistance with pump off, (b) S- and N-type negative resistances noninteracting,(c) annihilation.

362

GEORGE ABRAHAM

high and is measured in megohms, region II is the regionofnegativeresistance, and in region I11 the restrictive impedance is relatively low and is measured in ohms. Thus, when the switching device Q31is energized by dc source V33 in the absence of radiation from source p34,the resistive impedance is relatively high. When the switching device Q 3 1is excited by radiation from source p34, however, the open-circuit-stable characteristic curve shown in Fig. 66b is changed and a typical short-circuit-stable characteristic curve begins to develop at the point of origin. That is, at low values of current and voltage, a region VI having a relatively low impedance,comparable to that of region 111, a second negative resistance region V, and region VI having a relatively high impedance, comparable to that of region I, are generated as part of the characteristic curve. In addition, the resistance at avalanche breakdown is changed, as shown by the alteration of the negative resistance region 11. This phenomenon is portrayed in Fig. 66b. The short-circuit-stable or S-type negative resistance characteristic generated is the result of the exposure of the semiconductor to the electromagnetic radiation. If the frequency of the radiation source is high compared to the reciprocal of the effective lifetime of the minority carriers of the semiconductor, minority carriers will accumulate, lowering the impedance of the device, resulting in a regenerative condition, and leading to a negative resistance characteristic. As the energization from source is increased, such as by movement of the device toward a maximum portion of the antenna radiation pattern, (a) a greater number of stored minority carriers results, (b) avalanche breakdown potential is reduced, and (c) the open-circuit-stable negative resistance increases. Thus, the region IV is extended as shown in Fig. 66b as the intensity of radiation from source is increased until the region III of the open-circuitstable portion and the region IV of the short-circuit-stable portion meet. At this meeting the N-type avalanche characteristic and the S-type minority carrier storage characteristic have annihilated each other and the resistive impedance of the switching device is relatively low, in the order of ohms. Solid-state switching over several bands of frequencies has been obtained utilizing both diodes and transistors with a resultant high back-to-forward impedance ratio. In one particular instance, at X-band frequencies, a 100 W cw transmitter was employed to radiate via a horn antenna and a beaded N-type, 5i2/cm, semiconductor was installed in the field of the antenna as the solid-state switching element. The assembly provided an impedance variation from megohms without applied field to a few ohms with applied field. Similar results were obtained with other semiconductor switching elements including tunnel diodes, four-layer avalanche diodes, and bipolar transistors.

v34

r334

MULTISTABLE SEMICON I>UCTOR DEVICES

363

FIG. 67. lnteraction of two voltage-controlled negative resistances. (a) Four stable states due to negative resistance interaction, DB+ = 2 Vat 150 mHz; (b) tristablecharacteristic, DBT -= 2 V at 150 mHz; (c) two negative resistances at different energy ranges, DB 1 = 2 V at 150 mHz; (d) static characteristic, DB t 0. Vertical scale 5 mA/cm, horizontal scale 15 V i m . :

This method of negative resistance annihilation has been employed* to provide a fast-acting long-life duplexer (high-low power switching device) for use at a variety of frequencies. Such a device changes from a high impedance to a low impedance upon the interaction and annihilation of the negative resistance characteristics exhibited in the composite characteristic. In Figs. 67-69 are shown examples of S-S and N - N interactions in bipolar semiconductor devices. Examples of S-N interactions in avalanche devices are shown in Figs. 70-72 at excitation frequencies of 10. 210, and 10,000 MHz, respectively.

* US. Patent No. 3,333,196 dated July 25, 1965, issued to George Abraham.

FIG. 68. N-N negative resistance interactions due to parallel connections of two avalanche transistors. (a) No interaction, (b) no interaction, tristable, (c) quadristable, one interaction, (d) quadristable, one interaction, (e) interaction, tristable Vertical scale 5 V/cm, horizontal scale 0.5 mA/cm, R1 varied, R3 and R, = 50 R, R, = 500 R.


365

FIG.69. N-N negative resistance interactions due to parallelconnectionof fiveavalanche transistors. (a) NO interaction, (b) first interaction, (c) second interaction, (d) third interaction, (e) fourth interaction, (f) fifth interaction.

366

GEORGE ABRAHAM

FIG.70. S-N interaction in avalanche transistor. (a) S- and N-type negative resistance in single device characteristic, (b) negative resistance switching (noninteracting), (c) partial interaction, (d) negative resistance annihilation. Horizontal scale 20 mA/cm, vertical scale 7 V/cm, R,= 10 K, D B frequency = 10 mHz.

+

D . Increased Number of Stable States due to Negative Resistance Interactions

The maximum number of stable states with interactions that can be realized with M interacting negative resistance elements of a given type is as follows : As was shown in Sections TI and V, the total number of noninteracting stable states is M + 1. In addition, there will be ( M - l)! ;interactions, if each negative resistance element is allowed to interact with each other one in its composite characteristic. This gives us a total number of possible states of:

stable states where r represents a gamma function. Since M T ( M ) = T ( M + l),

which is the maximum number of stable states that can be realized for an S-S or an N-N interaction.

MULTISTABCE SEMICONDUCTOR DEVICES

367

FIG.71. S-N negative resistance annihilation in integrated multistable double avalanche device. (a) DB+ = 1.40 V, (b) DBS = 1.29 V, (c) static characteristic ( D B + = 0 V). Horizontal scale 0.3 mA/cm, vertical scale 1 V/cm, DB frequency = 210 mHz.

+

FIG. 72. S-N negative resistance annihilation at X band in experimental transistor. (a) Annihilation, (b) partial annihilation, (c) partial anihilation, further avalanche reduction, (d) reduced avalanche voltage, (e) avalanche breakdown, (f) static characteristic. Horizontal scale 0.15 mA/cm, vertical scale 5 V/cm.

369

MULTISTABLE SEMICONDUCTOR DEVlCES

VIT. MULTISTABLE DYNAMICS The Ebers-Moll model of the transistor and the pnpn device is nonlinear. The model may be employed t o determine the transient response of integrated circuits incorporating such devices. However, for large-signal switching circuits numerical analysis is often used when the transient response cannot be obtained in analytic form. Negative resistance circuits generally imply extreme device nonlinearities when logic functions are performed. Though the transient response of such logic circuits may be described by nonlinear differential equations, their solutions generally d o not appear in closed form. An alternate approach is to employ piecewise linear techniques in order to obtain an analytic solution for nonlinear circuit equations. This method is also commonly used for analysis of such linear circuits as the small-signal transistor model. In the case of Ebers-Moll equations the piecewise linear model is obtained by merely replacing the exponential functions of these equations by their linear approximations. Piecewise linearization gives a circuit approximation to a nonlinear model suitable for switching analysis. A . Notilitienr Atialysis

In order to apply the foregoing t o the analysis of the multistable characteristic of Fig. 73 one can replace this by the first-order approximation shown in Fig. 74. I n this figure the composite characteristics consist of three linear

-1

Fic;. 73. Tristable voltage-controlled negative resistance

3 70

GEORGE ABRAHAM

positive resistances r l , r 3 , and r5 separated by two linear negative resistances r2 and r4. In each of the regions I through V the relationship between current and voltage is assumed to be linear. In order to display the composite multistable characteristic, the applied dc potential V and the external load resistance RL, must both be of sufficient magnitude. In fact, the value of RL is so chosen to intersect the composite characteristic at points I , 2, 3, 4, and 5.

I

FIG. 74. Piecewise linear equivalent approximation of tristable voltage-controlled negative resistance.

Accordingly the resistance of the load must be greater than that of each of the negative resistances r2 and r4. I n regions 1, TII, and V the variational resistances are positive; an approximate analysis can be carried out by replacing the actual negative resistance characteristic by its linear counterpart. The latter is a first-order approximation of the multistabledevice characteristic. In Fig. 75 we have a basic circuit employing parametric storage of minority carriers in semiconductor diodes or transistors which are so connected to produce a tristable negative resistance characteristic of the voltage-controlled type. In Fig. 76 the active devices are replaced by voltage-controlled negative resistances R,, and Rn2.These elements are shunted by a passive external circuit consisting of capacitance C in parallel with a resistance R and an inductance L.

37 1

MULTISTABLE SEMICONDUCTOR DEVICES L

DYNAMIC 0-c

FIO.75. Tristable circuit.

At any point along the r~onlinear composite device characteristic the variational resistance is r = de/c/i. In regions 11 and IV, the slope, and therefore the variational resistance is negative. The equivalent circuit may be described by the following equations: L(diR/dt)

+ R,iR + + eNl

t)N2

-E =0

wheref(eN, + e N z )has the din~ensionsof current. The other symbols are as shown in the equivalent circuit of Fig. 76. Under steady-state conditions stable modes exist when simultaneously = RLiRS

and iR, = f i ( e N I \

+ eN2S

f eN~S

+

(7.2) eNzS)

=

iNS.

When the currents iRs= iNs the current i, through the capacitance branch is zero, namely, at singular points I , 2, 3. 4. and 5 of Fig. 77. The subscripts S represent a singularity. For small changes in voltage e and current i we have, as a singularity is approached iR - iRs= i and (7.3) eNI eN2 - e N I S- e N I S = e.

+

RL

T eN I

tFIG.76. Equivalent circuit.

372

GEORGE ABRAHAM V

FIG.77. Tristable transient dynamics, voltage-controlled negative resistance with three stable nodes and two saddle points.

Substituting Eqs. (7.3) into (7.l), we have

L d f ( / d f f) L(diRs/dt) + RL i

+ RL + e N I S f eN2S f e - E = 0. iRS

In view of (7.2) dildt = - (RLi - e ) / L

(7.4)

where R consists of all the resistance external to the device under consideration. Similarly

By the method of Liapounoff (78) equations ofthe first approximation are to be obtained i n which terms higher than the second may be neglected. Hence we have . f ( e N l f eNz) + f ( e N I S

+ eNzS)


+ eN2)

Jf(eN,

f

(3(eNl

eNl)

373

- -1 (CNIF+CN~S)

‘

Hence

The ratio of Eqs. (7.5) to (7.4) is

Equations (7.4) and (7.5) are first-order simultaneous equations which represent the operation of the tristable system to a first approximation. These equations are linear and are of the form

+ bi i = cc + cli

6

and

= ac

(7.7)

where a = -l/rC; C =

-l/L;

b = IjC d = -R/L

the characteristic equation is of the form ( 2 , 3) a-S

b

c

n-s

( I / r C )- s

When expanded this becomes

(7.8) where S represents the roots of the characteristic equation (7.8). The roots S,. S 2 of this quadratic equation are

These roots of the characteristic equation determine the phase representation of the nonlinear system.

374

GEORGE ABRAHAM

Analysis of the roots of characteristic Eq. (7.9) as applied to the five regions, I-V, will determine the nature of the singularities at the points of intersection of the load line with the composite negative resistancecharacteristic. Several possible types of singularities must be investigated (81). For example, the solution will be a node if the roots are real and of identical sign. The node will be stable if the roots are negative, and unstable if positive. Real roots of opposite sign will result in a saddle point. Complex roots will define a vortex when pure imaginary, and a focus when complex conjugates. As was the case for nodes, foci will be stable when their real parts are negative and unstable when their real parts are positive. From Eq. (7.6)it is apparent that the slope of the root will be zero along the load line, namely, d / d e = 0 when R = -e/i. Correspondingly the slope of the root will be infinite along each negative resistance region, namely di/de = 00, when r = ei. This applies to both negative resistance regions I1 and IV for which the load R,I R,,,, R,,, . In each case, both roots are real and of opposite sign resulting in two saddles at points 2 and 4. In regions I, 111, and V where the composite characteristic has resistances r l rr 3 , and r 5 , respectively, the roots are negative. Accordingly in these regions stable nodes or foci will occur at points I , 3 , and 5 . These are the points of system stability or stable states of the multistable circuit. In the case of the stable nodes the solutions are parallel to the nil axes near the nodal points, namely, for large values of time following a disturbance. Triggering of the multistable circuit may be effected by appropriate external stimuli, for example by a change i n applied voltage. The curves of Fig. 77 show how the voltage and current through the composite negative resistance characteristic vary following changes in energy of the system. Figure 78 shows the tristable dynamics for the current-controlled case. The switching solution curves are shown in the figure where the arrows represent the direction of increasing time. In order to represent the equilibrium states, for example, in the R - r plane (78-80, 82-84). We can proceed as follows, noting that the complex portion of the roots (7.9) under the radical is L - (R,rC)’ - [2r(CL)’i2]2.

(7.10)

This quantity must be less than zero for the roots to be complex.Thecomplex roots are bounded by the factors of (7.10) respectively set equal to zero, hence L - RLcr + 2r(LC)”’

=0

L - RLcr - 2r(LC)li’ = 0.

(7.1 I )

These may be rearranged respectively as follows

r[R, - 2(L/C)li2= ] L/C r [ R , 2(L/C)’/’]= L/C

+

(7.12)

Equations (7.12) are those of equilateral hyperbolas in the R - r plane as

375


v I

FIG.78. Tristable transient dynamics current-controlled negative resistance with three stable nodes and two saddle points.

shown in Fig. 79 when both hyperbolas A and B are asymptotic to the R-axis and to horizontal lines R = 2 ( L / C ) ’ i 2respectively. , Similarly, to obtain and differentiate between the stable and unstable foci, we set the real part of the roots equal to zero, i.e., - R,r = L/C. (7.13) This is also the equation of an equilateral hyperbolic curve C (Fig. 79) with r and R as asymptotes. Here r must be a negative resistance as L , R, C are positive. The unstable foci are between curves B and C, and to the right of their intersection, P. This represents the region in which the composite device characteristic is negative and where oscillations or unstable equilibrium is possible. The saddle points are determined when the roots of the characteristic equations are real and of opposite sign. This occurs where R + r < 0; R + r = 0 is the equation of line OP in Fig. 79. Since R is positive, r must be negative in this region. The point P of intersection of the curves B and C is that through which the saddle point boundary line OP passes. P is a point of bifurcation for the types of equilibrium discussed and shown in Fig. 79. This analysis applies directly to the voltage-controlled multistable device characteristic. Each negative resistance region is bounded by positive resistance regions as shown in Fig. 77. The equilibrium states as plotted in the R - r plane of Fig. 79 apply to each successive bistable region of the composite multistable characteristic.

376

GEORGE ABRAHAM R

STABLE NODES

lSADDLE POINTS

FIG.79. Equilibrium states in R

-r

plane.

In triggering from a stable state in one region t o another (see Fig. 77 and 78) the time involved during transition is dependent upon the reactive elements of the circuit (85, 86). The reactances also include internal device reactances and parasitics present in external wiring (87). B. Multistable Negative Resistance Sw'itching and Oscillation A variety of techniques for triggering multistable switching circuits are available with varying degrees of complexity. When considering possible ways of triggering the conventional flip-flop, for example, three distinct methods

377

M ULTISTABLE SEMICONDUCTOR DEVICES

immediately present themselves. First a triggering source consisting of positive and negative pulses can be applied to appropriate input trigger terminals of the flip-flop, each successive pulse changing the state of the device. A second method effects triggering by positive or negative pulses applied to appropriate set-reset terminals of the circuit, successive pulses causing set and reset respectively. The third possibility employs a steering circuit to trigger the circuit on and off with pulses of one polarity. The steering circuit directs alternate pulses to each side of the flip-flop. These methods provide satisfactory triggering. Certain disadvantages. however, are inherent in each method. The first method requires both positive and negative pulses. The second requires connection to both sides of the flip-flop. The third requires additional circuitry to accommodate the unipolar pulses that are applied. Greater simplicity in achieving multistable triggering is desirable and could be effected from a single one-polarity source without use of a pulsesteering circuit. This can be achieved with a single source of unipolar pulses applied at a single input terminal, making use of the internal negative resistance characteristics of the active devices involved. Such an alternate method of triggering multistable elements free from the above limitations of triggering techniques is as follows. Using a negative resistance device as the active element, the internal device parameters are utilized together with an input capacitor and a load resistor of preselected values to realize unipolar pulse switching from a single source without the use of pulse steering. Referring to the figures in which the reference characters refer to similar componeilts, there is illustrated in Fig. 80 a four-layer avalanche diode Q 1 2 , 131

Ctl

32\

FIG.80. Multistable pnpii switching circuit.

,

the active element of this multistable switching circuit. Capacitor C, connects the source of input or triggering pulses applied to terminal 31 to the diode. The positive side of the power supply or bias source V13 is applied to the avalanche diode via the output impedance resistor R , , at the output 32 of this circuit, with the negative side connected to common 33. The output voltage Eo is realized across resistor R , 4 . The multistable circuit of Fig. 81 utilizes a transistor as the active element. Multistable operation is obtained by biasing the transistor so that it operates in the avalanche mode, i.e., positive side of bias V,, is grounded here while

378

GEORGE ABRAHAM

FIG.81. Multistable transistor switching circuit.

the negative side is connected to the output terminal via the output resistor R , , . The additional element in this circuit not shown in Fig. 80 is the variable resistor R16. This resistor, often supplemented by an additional bias in the emitter-base circuit of the transistor, serves to lower the steady output voltage of the negative resistance characteristic so that it more nearly resembles the more practical curve of the four-layer diode as shown in Fig. 84. Fig. 81 shows another variation of the multistable switching circuit in which a tunnel diode Q , is the negative resistance active element. The negative resistance characteristic of the tunnel diode is of the S-type or voltagestable as opposed to the N-type or current stable negative resistance characteristic realized with an avalanche diode, as shown in Fig. 80. The S-type curve would appear to be similar to that shown in Fig. 77 if the ordinate axis represented current instead of voltage and the abscissa were voltage instead of current. The S-type curve of tunnel diode Q L 7 connected , across the emitterbase junction of transitor Q l s , appears as an N-type negative resistance characteristic, as seen across the output impedance R I 4 which is connected to the collector and emitter terminals via the bias V13. The normal 180” phase shift realized by a signal applied to the base of a transistor for a small signal amplification, as seen at resistor R14 in the collector circuit of the grounded emitter configuration is responsible for this inversion. Resistor R , , , connected in series with the tunnel diode serves merely to limit the current through that device. Except for the negative resistance characteristic, inversion discussed above and the bias V , , , which as in Fig. 80, is again connected negative to common and positive to output 32 via resistor R14, this multistable

FIG.82. Multistable tunnel diode-transistor switching circuit.

379


I

I

I

I

I

I

1

I

I

INPUT I

I

1

I

I

I I

h I I

n I I

FIG.83. Input and output pulse waveforms.

switching circuit of Fig. 82 provides the same circuit function as those of Figs. 80 and 8 I . Figures 83 and 84 will be used to describe this operation. To provide a multistable switching circuit capable of being triggered by a single source of one-polarity pulses consistently applied to the input terminal, certain operating parameters must be specified. I n order for positive pulses applied at the input terminal 31 of the switching circuits to cause the negative resistance device to switch from one state to the other, from off to on, for example, it is necessary for the pulses to be differentiated. Figure 83 shows single-polarity pulses, positive in this figure. as applied to the multistable switching circuit, the pulses being labeled input '* in the figure. Differentiation of these pulses "

I"

I

I

I

FIG.84. Graphical representation of N-type negative resistance triggering.

380

GEORGE ABRAHAM

is occasioned by series capacitor C,, and the shunt resistance of the negative resistance device. The requirements for differentiation in this typical series C, shunt R differentiation circuit is that the value of R be very small compared with the capacitive reactance of the capacitor. It thus becomes apparent that the internal characteristics of the negative resistance device chosen determine in part the value that must be selected for the capacitor C,, in the multistable switching unit. Fig. 84 is used to illustrate this essential relationship between the capacitor C, and the resistance of the negative resistance device necessary for differentiation. Before the application of the first pulse, the negative resistance device is in the off (or high impedance) state, having quiescent point Q, as its position of stability. The slope of the curve at this point, it should be noticed, is close to the ordinate axis which if parallel thereto would represent an infinite impedance. The actual impedance realized is thus in the order of megohms. At the application of the first pulse, the amplitude of which must be greater than AV,, the voltage change necessary to trigger the negative resistance device to the second stable state Q 2 , switching takes place. Here at Q 2 ,the resistance is low, in the order of ohms, and the relationship between the negative resistance device and the capacitive reactance of capacitor C, I necessary for differentiation is realized. The second pulse applied to this R-C network is thus differentiated. As shown in Fig. 83 the rise of the second pulse appears as a positive spike which has no effect on the negative resistance device since it it already in the “ o n ” state. The decay of this pulse appears as a negative spike. The negative spike needs only to present a negative-going change in voltage greater than A V , , the increment of voltage necessary to trigger the negative resistance device back to the “off” state at Q,. Several observations can be made at this point. In Fig. 83 the pulse labeled ‘‘ output,” the output voltage of the multistable switching circuit, evidences what has just been described as having taken place. The output voltage rises at the instant of the rise of the first input pulse and returns to the off state with the spike occasioned by the differentiated decay of the second input pulse. Also, while not shown in this figure, negligible differentiation takes place at the instance of the first pulse due to the presence of the series capacitor and the shunt resistor. For the purposes here, this small amplitude differentiated pulse has .no effect on the operation, and was therefore shown as an absence of differen.’3tion. The amplitude requirement of the input pulses has been shown to be that needed to overcome the positive peak of the negative resistance characteristic, as shown in Fig. 84. The pulse width is also critical. The duration of the pulse must be short compared to the response time of the negative resistance circuit. If this requirement were not observed, the very pulse that turns the device on would also be differentiated and turn the device off.

,


38 1

The necessary relationship between the output resistance R,,, the input pulses and the negative resistance characteristic is shown in Fig. 84. The line 21 is the load line occasioned by this resistor. Output resistance R,4 must be less than the negative resistance devices for bistable operation. The exact value of this resistor designates the position of the quiescent points Q , and Q2 (Fig. 84) for a specified value of bias. Having these points of stability specified, the amplitude of the input pulses required for triggering is determined. To obtain triggering of a mutt istable switching circuit from a single source of unipolar pulses connected to only one set of terminals of the circuit, the interrelationships between the elements of circuit and the operating conditions must be carefully selected (88).Examples of multistable triggering are shown in Figs. 91 and 92. In Fig. 85 is shown the three basic switching modes of an emitter-shortedto-base avalanche transistor. The basic circuit may be seen in (d) of the figure. Untriggered astable oscillation is shown in (a). Tn (b) of the figure the monostable output of the triggered avalanche circuit is shown. Bistable unipolar triggering, as described in the preceding paragraphs is seen in (c) of this figure. Figure 86a, b, and c shows the I-V oscilloscope traces of an experimental coupled-semiconductor avalanche device. The circuit diagram is shown in (c) of the figure. Figure 86a is the noninteracting case with the switching sequence 0-1-2-3-4-5-6-7-8-9-0 shown at the left of the photographic trace. I n Fig. 86bpartial annihilation has occurred eliminating the return trace 6-7-8-9. The partial interaction that remains is shown in the oscilloscope photograph and the sequence at its left, namely 0-1-2-3-4-5-4-1-0. The triggering modes of coupled avalanches are illustrated in Fig. 85. in Fig. 87 subharmonic generation is shown with the avalanche trigger circuit of Fig. 90. In Fig. 87a a bistable output is shown with no countdown. In(b)of the figureisrepresented a countdown ratio of 1 : 2 for a pulse-to-trigger ratio of I : 4. Finally, in (c) of the figure the oscilloscope photograph of a 1 : 3 countdown ratio is shown. The following Fig. 88 shows an additional feature of the multistable circuit, namely the combination of subharmonic generation and astable oscillation, for no countdokn in (a) of the figure and for 1 : 2 countdown in (b). In Fig. 89 the upper oscilloscope photograph is that of an untriggered astable oscillation of the multistable avalanche circuit of Fig. 90. The second trace shows bistable triggering of the astable oscillator. In (b) of the figure inonostable triggering of an astable oscillation is depicted. Tristable countingwith the avalanche circuit of Fig. 90 is shown in Fig. 91. The (a) trace shows the untriggered ground state. Triggering to the first state is shown in trace (b) and to the second state in trace (c). Finally in the upper trace (d) is shown tristable counting which occurs cyclically in this case from state 2 to 1 to 0. A similar set of multistable counting waveforms from states 0 to I to 2 are

382

GEORGE ABRAHAM

FIG.8 5 . Modes of operation of avalanche transistor multivibrator. (a) astable mode, (b) monostable mode, ( c ) bistable mode. Horizontal scale 300 pec/cm, vertical scale 12 V/cm. (d) Transistor multivibrator.


383

FIG. 86. Coupled semiconductor avalanche. (a) Noninteracting, (b) partially interacting, (c) circuit diagram.

384

GEORGE ABRAHAM

FIG.87. Avalanche subharmonic generation. (a) No countdown ( I : 2 pulse-to-trigger ratio), (b) 1 : 2 countdown (1 : 4 pulse-to-trigger ratio), (c) 1 : 3 countdown (1 : 6 pulse-totrigger ratio). Vertical scale 1 V/cm, horizontal scale 600 pseclcrn, pulse repetition rate 1250 Hz.

Fic. 88. Avalanche astable subharmonic generation. (a) Astable triggering, no countdown, (b) astable triggering, 1 : 2 countdown. Vertical scale 1 V/cm, horizontal scale 600 pseclcm, repetition rate 1250 Hz, astable oscillation frequency 120 kHz.

FIG.89. Multistable triggering modes of avalanche multivibrator. (a) Astable triggering of tristable multivibrator (astable frequency 95 kHz), (b) monostable triggering of tristable multivibrator. Vertical scale 1 Vicm, horizontal scale 600 pseclcni, repetition rate 1250 Hz.

GEORGE ABRAHAM

GENERATOR

FIG.90. Tristable avalanche transistor multivibrator circuit.

FIG. 91. Triggering of tristable avalanche rnultivibrator. (a) Tristable counting, (b) triggering to second state, (c) triggering to first state, (d) no trigger (ground state). Vertical scale 1 V/cm, horizontal scale 600 pseclcrn, trigger 4psec at -2 V, 1246 Hz.

MULTISTABZE SEMICONDUCTOR DEVICES

387

shown in Fig. 92 for the quadristable tunnel diode circuit of Fig. 93. I n traces (a) and (b) of the latter figure are shown the V-Icharacteristic of three tunnel diodes in serial connection. The (a) trace is magnified along the ordinate axis. Fig. 93c shows three astable frequencies that were obtained from the circuit as the voltage was swept through the three negative resistance regions of the composite characteristic. Each frequency could be tuned independently of those due to the other tunnel diodes comprising the composite V-I characteristic.

VItI. CONCLUSION It has been shown that radices higher than binary are now achievable with present-day technology. For example, multistable circuits can readily be built from unipolar and bipolar semiconductor negative resistance building blocks. The complementary features of voltage-controlled and current-controlled negative resistance devices allow versatility in the design of multistate circuits. Examples include the serial connection of voltage-controlled or the parallel connection of current-controlled negative resistances which can result in composite characteristics with one more state than the number of negative resistances involved. With S-S or N-N negative resistance interactions additional states occur, whereas with an S-N interaction, annihilation of the S and N negative resistance regions is effected. Reduction in circuit complexity results directly from tristable and quadristable operation with single devices. By device design or electrical modification of device characteristics the value of negative resistance and the spacings between stable states can be varied to accommodate triggering. provide desired output voltage levels, or result in operation in several digital and analog modes. The semiconductor junction devices employed lend themselves effectively to monolithic array integration utilizing integrated circuit technology. When active devices such as transistors or pnpn devices are fabricated monolithically in a common substrate. parasitic effects become a problem. For example. when active devices are embedded in the substrate, parasitic capacitances appear. Parasitic resistances occur when contacts are made on the monolithic surface. There are two commonly used methods to isolate monolithic and active devices from each other. Dielectric isolation may be provided with the use of SiO, ro isolate transistors from each other and the substrate. An alternate approach is the use of p-n junction isolation. In this case the substrate is heavily biased to minimize transistor action parasitically. With negative resistance multistable monolithic circuits such isolation procedures are not necessary as isolation is built in electrically. This offers the advantage over conventional isolation techniques that no additional processing steps are required.

388

GEORGE ABRAHAM

FIG.92. Tunnel diode tristable triggering. (a) Bistable triggering, (b) tristable triggering, (c) tristable triggering(180”phase shift). Vertical scale 0.3 V/crn, horizontal scale 30psec/crn.


389

FIG. 93. Tunnel diode rnultifrequency oscillator. (a) Voltage-current characteristic. Vertical scale 1 rnA/div, horizontal scale 0. I V/div. (b) Voltage-current characteristic. Vertical scale 20 mA/div, horizontal scale 0.1 V/div. ( c ) Multifrequency output. Vertical scale 0.3 V/div, horizontal scale 0.4 psec/div. (d) Circuit configuration.

390

GEORGE ABRAHAM

There is still further work to be done in the area of the research. For example, as the radix increases the contraints on the effects of noise, composite device triggering, load linearity, and power supply, regulation requirements become more stringent and therefore impose more critical integrated circuit design requirements. There is also a parallel need for the further development of higher order logic as an extension of Boolean logic. This is needed to describe the operation of specific multistate devices and circuits in order to increase their compatability with existing binary systems.

APPENDIX : CURRENT BUILDUP DUE TO PARAMETRIC EXCITATION The change in conductance of semiconductor materials and devices due to injection of excess minority carriers has been the subject of extensive study (89-92). Reversal of forward bias originally applied to a p-n junction results in continued conduction until the injected minority carriers decay due to recombination. Carrier lifetimes are customarily determined by the change in conductance caused by excess minority carriers. Recovery of the junction appears as a reverse transient during which time the back resistance of the device increases to a specified value. The recovery time of diodes and transistors due to minority carrier storage normally invokes a limit on their signal speed characteristic. Long recoverytimes are generally considered detrimental. In this investigation we shall utilize the effects of recovery in the development or multistable storage and other computer functions. When the forward voltage applied to a p-n junction is either removed or reversed in polarity, a transient may be observed across the junction. The stored minority carriers are removed by recombination. Steele (93)has shown that the current of a single reverse transient may be evaluated from the diffusion equation subject to the transient boundary conditions for a p-n junction. A one-dimensional analysis is employed in which a slab of n-type germanium of thickness Lo has an abrupt junction at x = 0 and an ohmic contact at x = L o . The following assumptions are made: (a) the hole density ( p ) deviation from equilibrium varies from an injected value (po) at the junction to a value (p = 0) at the ohmic surface when the diode is conducting, (b) all the current in the diode is carried by holes, (c) all t.he voltage drop occurs across the p-n junction resulting in no electric field in the bulk germanium. Subject to these conditions the hole density in the germanium is described by the diffusion equation 8~ - _ - - - P+ D - a2P at

z

ax2


39 1

where T is the lifetime and D is the diffusion constant for holes. When steadystate conditions are attained under forward bias p / T = 0.

subjecttotheaboveboundaryconditions,namelyp = p o I x = oa n d p = O l x = L o , the steady-state solution of the diffusion equation is of the form =

sinh[(L, - x)/L] sinh(L,/L)

where L is the diffusion length for holes, Lo is the pellet thickness, and x is the distance from the junction. Subject to the transient boundary conditions at

p=O

x=O

and

p=O

at

x=Lo,

the transient solution for holes is

The current density which is given by Jp = -4D(dp/3~)

For the case where Lo < L Jp

=

-29p0 D/Lo exp -

[5 (9’1

This is of the exponential form multiplied by a constant. We shall use this in the following analysis. If we consider a train of reverse transients such that each successive transient occurs before the previous one has decayed to a small fraction of its peak value. then the train can be represented as shown in Fig. A . I . In (a) of this figure is shown the input driving function and in (b) the current response of the individual transients is indicated without superposition. As the period

392

GEORGE ABRAHAM

'M-nnn-

DRIVING FUNCTION INPUT

TIME

'

CURRENT RESPONSE WITHOUT SUPERPOSITION

1

CURRENT RESPONSE WITH

t

- - - -- -- - - - - - - --.- ,_--.--d

---

4

FIG.A.l. Response due to parametric excitation of semiconductor diode.

FIG.A.2. Hole storage response.

TIME

393


of the driving function has been selected to be short compared with the transient response time, successive reverse spikes overlap causing a buildup in their amplitude. Such response may be approximated by superposition as is shown in Fig. A.lc. It is assumed that minority carriers that have been injected by a previous driving pulse continue to recombine at the same rate during and after the arrival of successive driving functions and their reverse transients. Superposition of the latter results in a buildup of the injected minority carrier current to a steady-state value as will be shown. Referring to Fig. A.2 we let

where the symbol [r/T]denotes the largest integer which is less than or equal to [t/T].Also let f

- [t/T]T= u

(A.2)

where u is a periodic function o f t with period T. Now suppose that [ f / T ]= N . Then

Cf

=

( +~n T )

n=O

where n = ( N - K ) . Let us assume that the series f ( u + n T ) converges uniformly in the interval (0,T ) and denote the sum by G(u) and the remainder by RN(u). Then if E is an arbitrary positive number, an integer M can be found such that whenever N > M

lT=O

N

G(u)-

1 .f(u + ! I T )= 1 R N ( u I)
= ( l / A ) g ( f )

and -e-lN+

I)pl

e d t ) = I - e-l’T For 6

=e-pT

g(t).

where the entire function of time F ( t ) is given by F ( ! )= G ( t )

+ Ph(t)

and G ( t )is a periodic function of period T. then e N ( t= ) -(d”+ ‘/A)g(t).

(A. 16)

When N = O e o ( t )= (ii/A)g(t)

and

G ( t )= ( I / A ) g ( t ) then

+

F ( t ) = G ( t ) e,(t)

=(

I

-

d/A)g(f).

In terms of an exponentially decaying transient whose initial value is normalized to unity, Fig. A.3 gives a geometrical representation of A and S as a function of time. Steady-state operation is obtained when the transient term approaches zero (i.e.. approaches a n infinitesimally small value). In order to

396

GEORGE ABRAHAM

FIG.A.3. Decrement due to carrier storage.

make a numerical evaluation, say for a transient reduction to 1/100 of its initial value at A = 1/2 we have, using Eq. (A.16) - ~ 5 ~ + ' g (= t )Ae.(t)

or e,(t)/g(t) = d N f ' / A

so (I/2)N+1 = 1/100

whence N + 1 = 6.67 and N = 5.67. For this example it will take 5.67, say 6, exponential transients for the nonperiodic part of (A.14) to fall off to 1/100th of its initial value. Using the analogy of separation of plates in a condensor, we have seen that energy is added each time the plates are separated. This energy would build up indefinitely if the separation of the plates continued at the same amplitude. As more minority carriers are stored a greater field builds up


397

between the capacitor plates requiring greater force t o separate them. Hence, for a given pump amplitude the number of minority charge carriers that can be stored is limited t o a finite level o n a steady-state basis. Physically this is determined by such factors as surface and volume recombination and by the avalanche breakdown voltage. The latter establishes an upper bound o n the number of minority carriers that can be stored.

FIG.A.4. Buildup of minority carriers in hole storage diode due to parametric excitation. (a) Excitation frequency 25 kHz, (b) excitation frequency 100 kHz, (c) excitation frequency 250 kHz, (d) excitation frequency 10 mHz. Vertical scale I .5 V/cm, horizontal scale 50 pseclcni, dc bias current 2.5 mA, excitation voltage 6 V.

In Fig. A.4 is shown the build up of minority carriers in a hole storage diode when parametrically excited at various frequencies by a pump. As the frequency is increased from 25 kc t o 10 mc, the time that the diode reaches a steady-state condition due t o storage of niinority carrier decreases.

ACKNOWLEDGMENTS This research was completed under the Navy Edison Program at the University of Maryland. The experimental work was carried out at the Naval Research Laboratory, Washington, D.C. Appreciation is gratefully expressed to Dr. R. D. Myers for his helpful comments, to Dr. H . C . Lin for his critical review of the manuscript, and to Dr. H . E. Tompkins for his interaction on device modeling.

398

G E O R G E ABRAHAM

REFERENCES 1. H. 2. H. 3. R. 4. K.

Nyquist, Regeneration theory. BeN Syst. Tech. J . 11, 126 (1932). S. Black, Stabilized feedback amplifiers. Tran.7. AfEE. 53, 114 (1934). S. Mackay, Negative resistance. Amer. J . Phys. 26, 60 (1958). G. McKay, Avalanche breakdown in silicon. Phys. Rev. 94, 877 (1954). 5. S. L. Miller, Ionization rates for holes and electrons in silicon. Phys. Rev. 105, 1246 (1957). 6. J . L. Moll and R. Van Overstraeten, Charge multiplication in silicon p-n junctions. Solid-state Electron. 6, 147 (1963). 7. D. P. Kennedy and R. R. O'Brien, Avalanche breakdown characteristics of diffused silicon p-n junctions. lEEE Trans. E1ectron Devices 9, 874 (1966). 8. T. Misawa, Negative resistance inp-n junctions under avalanche breakdown conditions, Parts I and 11. fEEE Trans. Electron Devices, 13, 136 (1966). 9. L. Esaki, New phenomena in narrow germanium p-rr junctions. Phys. Rev. 109, 603 (1958). 10. N. Holonyak, LA. Lesk, R. N. Hall, J. J. Tiemann, and H. Ehrenreich, Direct observation of phonons during tunneling in narrow junction diodes. Phys. Rev. Lett. 3, 167 (1959). 11. R. L. Batdorf, G . C . Dacey, R. L. Wallace, and D. J. Walsh, Esaki diode in InSb. J . Appl. Phys. 31, 613 (1960). 12. J. F. Gilbert and F. A. Trambore, Electron mobilities and tunneling currents in silicon. J . Appl. Phys. 32, 131 (1961). 13. R. G . Shulman and M. E. McMahon, Recovery currents in germanium p-n junction diodes. J . Appl. Phys. 24, 1267 (1953). 14. B. Lax and S. F. Neustadter, Transient response of a p-n junction. J. Appl. Phys. 25, 1148 (1954). 15. S. R. Lederhandler and L. J. Giacoletto, Measurement of minority carrier lifetime and surface effects in junction devices. Proc. I R E 43, 477 (1955). 16. H . N. Baker, J . M. Goldey, and I . M. Ross, Recovery time ofpnpn diodes. IRE Wescorz Rer. 15, 43 (1959). 17. S. R. Hofstein, Minority carrier lifetime determination from inversion layer transient response. IEEE Trans. Electron Devices 14, 785 (1967). 18. G. Abraham, Electrical switching circuit. U.S. Patent No. 2,964,654 (1960). 19. P. R. Prince, Paralleling avalanche transistors. Proc. IEEE 53, 304 (1965). 20. W. Shockley and W. T. Read, Jr., Statistics of the recombination of holes and electrons. Phys. Rev. 87, 835 (1953). 21. W. T. Eriksen, H. Statz, and G. A. DeMars, Excess surface currents on germanium and silicon diodes. J . Appl. Phys. 28, 133 (1957). 22. C . Zener, A theory of electrical breakdown of solid dielectrics. Proc. Roy. Soc., London 145, 523 (1934).

23. K. B. McAfee, E. J. Ryder, W. Shockley, and M. Sparks, Observation of Zener current in germanium p-n junctions. Phys. Rev. 94, 877 (1954). 24. G. Abraham, Variable gain tunneling, U.S. Patent No. 3,327,136 (1967). 25. R. Williams, Avalanche and tunneling currents in gallium arsenide. RCA Rev. 27 (3), 336 (1966).

26. K. G. McKay, Avalanche breakdown in silicon, Phys. Rev. 94, 877 (1954). 27. J . S. Townsend, " Electricity in Gases." Oxford Univ. Press, London and New York, 1915.


399

28. K. G . McKay and K. B. McAfee, Electron multiplication in silicon germanium. Phys. Rev. 91, 1079 (1953). 29. P. A. Wolff, Theory of electron multiplication in silicon and germanium. Phys. Rev. 95, 1415 (1954).

30. A. G. Chynoweth, Ionization rates for electrons and holes, in silicon. Phys. Rev. 109, 1537 (1958). 31. B. M. Wul and A. R. Shotov, Multiplication of electrons and holes in p-n junctions, Solid State Phys. Electron. Telecomrnun., 1, 491 ( I 960). 32. J. L. Moll and R. van Overstraeten, Charge multiplication in silicon p-n junctions, Solid-State Electron. 6, 147 (1963). 33. S. L. Miller, Avalanche breakdown in germaniuni. Phys. Rev. 99, (4), 1234 (1955). 34. S. L. Miller, Ionization rates for holes and electrons in silicon. Phys. Rev. 105, 1246 (1957). 35. A. G. Chynoweth and K. G. McKay, Internal field emission in silicon p-ti junctions. Phys. Rev. 106, 418 (1957). 36. G. A. Baraff, Distribution functions and ionization rates for hot electrons in semiconductors. Phys. Rev. 128, 2507 (1962). 37. W. Fulop, Calculation of avalanche breakdown voltages of silicon p-n junctions. Solid-State Electron. 10, 39 (1967). 38. J. Maserjian, Determination of avalanche breakdown in p-n junctions. J . Appl. Phys. 30, 1613 (1959). 39. W. Shockley, Problems related to p-n junctions in silicon. Solid-state Electron. 2 ( l ) , 35 (1961). 40. C. D. Root, D. P. Lieb, and B. Jackson, Avalanche breakdown voltages of diffused silicon and germanium diodes. IRE Trans. Electron Deoices 7 , 257 (1960). 41. D. P. Kennedy and R. R. O’Brien, Avalanche breakdown characteristics of a diffused p-n junction. IEEE Trans. Electron Devices 9 (6), 478 (1962). 42. R . K. Kokoska and R. L. Davies, Avalanche breakdown of diffused silicon p-n junctions. IEEE Trans. Electron Devices 13 (12), 874 (1966). 43. T. Misawa, Negative resistance inp-n junctions under avalanche breakdown conditions, Parts I and 11. fEEE Trans. Electron Deuiccs 13, ( I ) , 137 (1966). 44. S. L. Miller and J. J. Ebers, Alloyed junction avalanche transistors. Bell Syst. Tech. J . 34, 883 (1955). 45. J. J. Ebers and S . L. Miller, Design of alloyed junction germanium transistors for high speed switching. Bell Sysr. Tech. J . 34, 761 (1955). 46. J. S. T. Huang, Study of Transistor switching stability in the avalanche region. fEEE J . Solid-State Circuits 2 (l), 10 (1967). 47. R. W. Aldrich and N. Holonyak, Jr., Multiterminal PNPN Switches. Proc. IRE 46 ( 6 ) , 1236 (1958). 48. W. Fulop, Three terminal measurements of current amplification factors of controlled rectifiers. IEEE Trans. Electron Deuires 10, 120 (1963). 49. F. E. Gentry, Turn-on criterion for p-n-p-n devices. IEEE Trans. Electron Devices 11 (2), 74 (1964). 50. J. J. Ebers and J. L. Moll, Large signal behavior ofjunction transmitters. Proc. IRE42, 1761 (1954). 51. J. F. Gibbons, A critique of the theory of PNPN devices. IEEE Trans. Electron Devices 11 (9), 406 (1964). 52. 1. M. Maclntosh, The electrical characterization of silicon P-N-P-N triodes. Proc. IRE 46, 1229 (1958).

400

GEORGE ABRAHAM

53. J. J. Ebers and J. L. Moll, Large signal behavior of junction transistors. Proc. IRE 42 (12), 1761 (1954). 54. R. F. Rutz, Two collector transistor for full binary addition. IBM J. Res. Develop. 1, 212 (1957). 55. E. F. Kovanik, Circuit applications of stepping transistors. Int. Solid-State Circuits Conf. Dig., 1956 36 (1959). 56. W. M. Webster, On the variation of junction-transistor current amplification factor with emitter-current. Proc. I R E 42, 914 (1954). 57. S . Wang and T. T. Wu, On the theory of the D.C. amplification factor of junction transistors. IRE Trans. Electron Devices 6 , 162 (1959). 58. K. G. Breitschwerdt, Characteristics of diffused PN junctions in epitaxial layers. IEEE Trans. Electron Devices 12 (I), 13 (1965). 59. H. Kroemer, Zur theorie des diffusions und der drift-transistors. Arch. Elec. Ubertragung 8, 223 (1954). 60. H. C. Lin, D.C. analysis of multiple collector and multiple emitter transistors in integrated structures. IEEE J. Solid-State Circuits 4, 20 (1969). 61. Rate effect, the voltage-current characteristics of four-layer diodes at high frequencies. A D Note, No. 3, Shockley Transistor Corp. (1969). 62. C. W. Haase, A study and analysis of the problems involved in triggering a P-N-P-N silicon diode pulse counting circuit. M.S. Thesis submitted to George Washington University (1962). 63. T. Misawa, Turn-on transient of a pnpn triode. J. Electron. Contr. 7 , 523 (1959). 64. S. Ikeda and T. Araki, The di/dt capability of thyristors. Proc. IEEE 55, 1301 (1967). 65. A. C. English, Mesoplasmas and second breakdown in silicon junctions. Solid-state Electron. 6, 511 (1963). 66. H. A. Schaff, G. H. Schwuttke, and R. L. Ruggles, Jr., Second breakdown and crystallographic defects in transistors. IEEE Trans. Electronic Deuices 13, 738 (1966). 67. J. W. Horton and A. G. Anderson, A full binary adder employing two negative resistance diodes. LBM J. Res. Develop. 2, 223 (1958). 68. R. A. Johnson and C. 0. Harbourt, Static combinations of negative resistance devices. Proc. Nat. Elect. ConJ 16, 427 (1960). 69. C. A. Renton and B. Rabinovici, Composite characteristics of negative resistance devices and their applications in digital circuits. Proc. IRE 50, 1648 (1962). 70. George Abraham, Multistable Circuit Employing Plurality of Parallel-Connected Semiconductor Devices Each Having More Than One PN Junction. U.S. Patent No. 3,200,266, (1965). 71. George Abraham, Multistable Circuit Having One Direct and One Inverted Negative Resistance. U.S. Patent No. 3,315,093 (1967). 72. K. Weiser, Interaction of two avalanche layers in GaAs. Solid-state Electron. 10, 109 (1967). 73. R. H. Haitz, Microplasma interaction in silicon P-N junctions. Solid-state Electron. 7, 439 (1964). 74. George Abraham, Multistable Avalanche Device. U.S. Patent No. 3,328,605 (1967). 75. L. P. Hunter, Graphical analysis of transistor characteristics. Proc. IRE38, 1387 (1950). 76. H. J. Reich, J. G . Skalnik, and H. L. Kraus, “Theory and Applications of Active Devices.” Van Nostrand-Reinhold, Princeton, New Jersey, 1966. 77. J. F. Gibbons, “Semiconductor Electronics.” McGraw-Hill, New York, 1966. 78. A. M. Liapounoff, Probltme gkneral de la stabilite du movement. Ann. Fac. Sci. Toulortse (1907). Princeton Univ. Press, Princeton, New Jersey, 1947.


40 1

79. A. Andronow and C . E. Chaikin, “Theory of Oscillations.” Princeton Univ. Press, Princeton, New Jersey, 1949. 80. W. J. Cunningham, “Nonlinear Analysis.” McGraw-Hill, New York, 1958. 81. H. Poincare, ‘‘ Les MCthodes Nouvelles de la Mkcanique Celeste.” Gauthiers-Villars, Paris, 1892. 82. N. Minorsky, “Nonlinear Oscillations.” Van Nostrand-Reinhold, Princeton, New Jersey, 1962. 83. N. Kryloff and N. Bogoliuboff, ‘’ Introduction to Non-Linear Mechanics.” Princeton Univ. Press, Princeton, New Jersey, 1949. 84. S . Lefschetz, “Contributions to the Theory of Nonlinear Oscillations.” Princeton Univ. Press, Princeton, New Jersey, 1950. 85. William G. Oertel, The monostable tunnel diode trigger circuit. Proc. IEEE 54, 936 (1966). 86. B. G. Farley, Dynamics of transistor negative resistance circuits. Proc. IRE 40, 1497 (1952). 87. H . Madani, Graphical derivation of trajectories for transistor-tunnel diode logic circuits. Radar Eng. (London) 113, 225 (1966). 88. George Abraham, Negative Resistance Multistable Switching. U.S. Patent No. 3,293,453 (1966). 89. Von. Th. Einsele, Uber die Tragheit des Flutzleitwerts von Germaniumdioden, Zeit. Angew. Phys. 4 , 183 (1952). 90. R. G. Shulman and M. E. McMahon, J. Appl. Phys. 24, 1267 (1955). 91. E. M. Pell, Phys. Rev. 90, 229 (1953). 92. S . R. Lederhandler and L. J. Giacoletto, Proc. IRE43, 477 (1955). 93. E. L. Steele, J. Appl. Phys. 25 (7), 918 (1954).


Author Index Numbers in parentheses are reference numbers and indicate that an author’s work is referred to although his name is not cited i n the text. Numbers in italics show the page on which the complete reference is listed. A

Bitzer, D. L., 235, 237(31), 239, 240(34), 241(31), 242, 258(30), 263(55), 266, 26 7 Black, H. S., 274(2), 398 Blackstock, A. W., 183(108), 190 Blais, R. N., 15, 17, 18, 19, 24(29), 25(29), 26(29), 85 Bleckrode, R., 106(43), 187 Boeschoten, F., 92(17), 107, 117, 119, 126(6I), 129(61), 130, 135(17), 144(17), 186, 188 Bogoliuboff, N., 374(83), 401 Bonin, R. V., 248, 267 Boulassier, J . C., 92(13), 117, 186 Bouwknegt, A., 183, 190 Boyer, E. L., 107, 117, 187 Breitschwerdt, K . G., 326(58), 400 Brown, F. H., 248(43), 263, 267 Brown, S. C., 117, 138(52), 140(52), 187 Brunet, A., 107, 153, 155(39), 156(39), 187 Burgers, J . M., 15, 57, 85 Burkhart, J. A., 92(30), 183(30), 186 Burlaga, L. H., 4(18), 85 Burton, G. F., 92(29), 180(29), 186 Busygin, E. G., 184(115), 190

Abraham, G., 284(18), 290(24), 342(70), 346(71), 349(74), 381(88), 398, 400, 40 I Abraham, H., 63(67), 86 Acton, J. R., 201, 203, 266 Ahsmann, G. J . , 92(12), 104(12), 107, 117, 126(12), 186 Albright, N. W., 83, 86 Aldrich, R. W., 302(47), 399 Aldridge, R. V., 92(19), 117, 127(51), 129, 130, 137, 145, 186, 187, 188 Allis, W. P., 60(68), 61, 86, 174(89), /8Y Anderson, A. G., 333(67), 400 Andoh, S., 240, 241, 254(37), 267 Andronow, A., 374(79), 401 An’shakov, A. S., 184(113), 190 Araki, T., 331(64), 400 Aroa, B. M., 258, 263(55), 267 Atkinson, W. R., 31(40), 85

B Baker, B. O., 184(114), 190 Baker, H. N., 275(16), 398 Bandel, H., 61, 86 Barach, J . P., 53, 54, 55, 86 Baraff, G . A., 293(36), 399 Batdorf, R. L., 275(11), 398 Beams, J. W., 2, 3, 4(8), 5(23), 6(23), 7(23), 42(23), 84, 85 Bennett, W. H., 117, 184( 117), 188, 190 Bickel, W. S., 185(119), 190 Bird, R. B., 153(84), 189 Bishop, M. S., 157, 267

C

Cano, R., 92(14), 111(14), 112, 117. 126(14), 142, 186, 188 Ceglio, N. M., 137, 188 Chaikin, C. E., 374(79), 401 Chen, Y. S., 231(27a), 232, 266 Chester, A. N., 156(83), 189 Chodil, G. J., 231(27), 232, 260, 262, 266, 267 403

404

AUTHOR INDEX

E

Christian, R. H., 34, 85 Chung, K., 92(15), 107, 117, 121, 123, 124(15), 126, 127, 128, 129(64), 133, 134, 138, 140(62), 142, 143, 144(41), 186, 187,188 Chynoweth, A. G., 292(30), 293(35), 399 Clark, M., 124(49), 187 Cravath, A. M., 124(58), 188 Clement, M., 92(13), 117, 186 Coates, W., 263, 267 Cole, H. C., 184(118), 190 Coleman, W. E., 263, 267 Cox, J. L., 184(117), 190 Criscimagna, T . N., 255, 256, 267 Cunningham, W. J., 374(80), 401 Curtiss, C. F., 153(84), I89 Cuvellier, J., 92(13), 117, 186 Cziky, G . A., 180(101), 181(101), 189

D

Ebers, J. J., 301(44, 45). 303, 314, 315, 318(53), 328(53), 399, 400 Ecker, G . , 131(66), 163, 167(66), 188 Edmonds, P. H., 179(93), 189 Ehrenreich, H., 275(10), 398 Einsele, Von., Th., 390(89), 401 Elste, G., 20, 85 English, A. C., 331(65), 400 Eriksen, W. T., 290(21), 398 Ernsthausen, R. E., 248, 267 Esaki, L., 275(9), 398 F Farley, B. G., 376(86), 401 Fearn, D. G., 92(29), 180(103), 180(29), 181, 186, 189 Ferreira, C. M., 175(90), 189 Findeisen, B., 220, 266 Flannery, D. L., 117, 138(52), 140(52, 74), 187, 188

Dacey, G. C., 275(1 I), 398 Dagai, M., 92(13), 117, 186 Davies, R. L., 293(42), 399 Day, B. P., 92(29), 180(29, 99, 104), 186, 189 Day, R. A., 19, 21, 50, 85 de Boer, J. Th., 228, 231, 266 DeHeer, F. J., 20, 85 de Jule, M. C., 231(27), 232, 260, 262, 266, 267

Delcroix, J. L., 91(4, 5, 6, 7, 8, 9, lo), 92(6, 9, 25), 93(33), 96, 97, 98(5), 99, IOO(8, 34), 101, 102(35), 103(6), 107, 108(7), 110(6), 113, 114(6, 33), 145(7), 147(6), 148, 149(6), 156(6), 158, 170(33), 174(9, 87), 175, 176, 177(7), 178, 179(25), 184(9, lo), 185(6), 185, 186, 187, 189 Demars, G. A,, 290(21), 398 Demeter, L. J., 92(17), 107, 117, 119, 126(61), 129(61), 130, 135(17), 144(17), 186, 188 Dick, G . W., 255, 267 Dietrich, J. R., 2, 4(8), 5(23), 6(23), 7(23), 42(23), 84, 85 Druyvestyn, M. J., 61, 86

Forman, J., 225(24), 233, 266 Fowler, R. G., I(]), 3(12), 4(20), 15, 16(30), 17, 18, 19, 24(29), 25(29), 26(29), 33, 34, 35, 39(51), 40(51), 42, 43, 44(51), 45, 46, 47, 48, 57, 58(1), 60,71, 77, 84,85,86 Fradkin, D., B. 183(108), 190 Frank, J., 56,86 Frost, R. S., 76(76), 86 Fukui, H., 231(27A), 232, 266 Fulop, W., 293(37), 303, 399

G

Gardner, A. L., I16(47), 187 Gaur, J. P., 263, 267 Gender, R. W., 259, 267 Gentry, F. E., 303(49), 399 Gerardo, J. B., 35, 85 Gerry, E. l., 103(37), 107, 117, 179(93), 184(37), 187, 189 Giacoletto, L. J., 275(15), 390(92), 398, 401 Gibbons, J. F., 306, 309, 354(77), 399, 400 Gibbons, R. A,, 115(44), 187 Gilbert, J. F., 275(12), 293(12), 398

405

AUTHOR INDEX

Golden, D. E., 61, 86 Goldey, J. M., 275(16), 398 Goldstein, L., 35, 85 Goldstein, R., 92(28), 180(28), 181, 186 Gowar, J., 184(114), 190 Gregory, R., 257, 267 Grieni, H. R., 33, 85 Grigori Yants, V. G.. 184(115), 190 Gritzmacher, T. J., 107, 117, 187 Grosse, F. A., 3, 85 Gunshor, R. L., 106(45), 131, 132, 133(45), 135(45), 187 Guntherschultze, A., 89, 109(1), 110(1), 111(1), 114(1), 115(1), 185 Guthrie, A,, 138(72a), 139, 188

Holt, J. F., 107, 117, 187 Holz, G. E., 212, 213, 218, 219, 220, 224, 226, 266 Hood, J. D., 33, 34, 85 Horton, J. W., 333(67), 400 Hoskinson, J. H., 263, 267 Huang, J. S. T., 299(46), 301(46), 399 Huang, K., 142, 143, 188 Huchital, D. A., 92(24), 179, 186, 189 Hudis, M., 92(15), 117, 121, 123, 124(15), 126, 127, 128, 129(63), 140(62) 141, 186, 188

Hunter, L. P., 354(75), 400

I H Haase, C. W., 331(62), 400 Haberstich, A., 6, 9, 10, 11, 12, 13, 14, 17, 18, 34, 42(25), 85 Haitz, R. H., 348(73), 400 Hales, R. H., 3, 32, 33, 85 Hall, L. S., 116(47), 187 Hall, M. S., 259, 267 Hall, R. F., 205(9), 206, 208. 209, 210, 213, 218, 221, 222, 223, 228, 266 Hall, R. N., 275(10), 398 Hamawi, J. N . , 118, 120, 187 Hamberger, S. M., 36, 38(52), 86 Harbourt, C. 0..333(68), 400 Harm, R., 125(59), 188 Harman, W. J., Jr., 209, 224, 266 Hastings, S. R., 180(99, 104). 189 Hauksbee, F., I , 84 Hendricks, C. D., 35, 85 Hirose, T., 250, 251, 254, 267 Hirschfelder, J., 153(84), 189 Hoehn, H. J., 246, 247, 249(41), 250(41), 26 7

Hoffman, G. R., 223, 228, 266 Hofstein, S. R., 275(17), 398 Holonyak, N., Jr., 275(10), 302(47), 398, 399 Holt, E. H., 92(26), 98(26), 106(45), 117, 131, 132, 133(55), 135(45,55), 136,138. 139, 140(55), 141, 142(55), 144(55), 179, 186, 187, 188

Ibadov, S., 182, 190 Ikeda, S., 331(64), 400 Ishizaki, H., 263, 267 Isler, R. C., 35, 85 Isogai, F., 262, 267

J Jackson, B., 293(40), 399 Jackson, R . N., 211, 212, 215, 216, 217, 218, 223, 224(14), 228(17), 231, 232, 234, 266 Jahn, R. G., 3, 85 James, J., 2, 84 Janning, J. L., 263, 267 Jennings, W. C., 92(26), 98(26), 179, 186 Jobe, J . D., 20, 85 Johnson, A. W., 36, 38(52), 86 Johnson, K. E., 208, 209, 210, 211, 212, 213, 215, 216, 217, 218, 221, 222, 223, 224( 14), 266 Johnson, R. A., 333(68), 400 Johnson, R. L., 237(31), 241, 242, 263(62), 26 7

Johnson, W. E., 249,250, 251, 255,267 Jolly, J., 92(27), 104(38), 179(27), 186, 187 Josephs, J . J., 206(10), 220, 266 Josephson, V., 3, 32, 33, 85 Jurahashi, K., 263, 267

406

AUTHOR INDEX

K Kadomtsev, B. B., 135, 136(67), 188 Keen, B. E., 92(19), 117, 127(51), 129, 130, 137, 145, 186, 187, I88 Kennedy, D. P., 275(7), 293(41), 398, 399 Kerr, D. E., 35, 85 Kiteava, V. F., 178(92), 179(96), 189 Kochin, N. E., 74(74), 86 Kokoska, R. K., 293(42), 399 Kolb, A. C., 33, 85 Koltypin, A. E., 184, 190 Koopman, D., 4(21), 50, 51, 52, 85 Koslov, V. V., 184(113), 190 Kovanik, E. F., 317(55), 400 Knauer, W., 180(105), 190 Kraus, H. L., 354(76), 400 Kretschmer, C. B., 92(17), 107, 117, 119, 130, 135(17), 144(17), 186 Kroemer, H., 326(59), 400 Kryloff, N., 374(83), 401 Kurahashi, K., 262, 267

L Lamar, E. S., 60(68), 61, 86 Latimer, I. D., 19, 21, 50, 85 Lax, B., 275(14), 398 Lederhandler, S. R., 275(15), 390(92), 398, 401 Lefschetz, S., 374(84), 401 LeMoine, J., 63(67), 86 Lenard, W. M., 259, 267 Leonard, S. L., 106(53), 117, 187 Lesk, I. A., 275(10), 398 Liapounoff, A. M., 372, 374(78), 400 Lidsky, L. M., 91, 93(11), 107, 117, 118, 120, 129(63) 137, 141, 144, 145, 158, 184(78), 179(93), 186, 187, 188, 189 Lieb, D. P., 293(40), 399 Liewer, K. W., 183(108), 190 Lin, H. C., 328, 400 Liou, P., 38, 86 Loeb, L. B., 56(59), 57, 86 Lorente-Arcas, A,, 92(20), 107, 153, 155(42), 156, 160, 161, 186, 187 Lubin, M. D., 152(82), 179(94), 189 Lubin, M. J., 35, 36, 31, 58, 85, 86

Luce, J. S., 89, 91(2), 185 Lustic, C. D., 220, 266

M McAfee, K. B., 290(23), 292(28), 398, 399 McCormick, G. K., 117, 188 MacIntosh, 1. M., 309, 399 McKay, K. G., 275(4), 291, 292(28) 293(35), 398, 399 Mackay, R. S., 274(3), 398 Mackin, R. J., 91, 93(11), 107, 115(44), 117, 158, 186, 187 Maclean, E. A,, 33, 85 McMahon, M. E., 275(13), 390(90), 398, 40 I MacNair, D., 180(98), 189 Madani, H., 376(87), 401 Magnuson, G . D., 125(60), 188 Mahadevan, P., 125(60), 188 Manus, C., 92(13), 117, 186 Markin, J., 231(27), 232, 266 Markus, H. L., 206(1 l), 233, 266 Martel, R. A., 246, 247, 248, 249(41), 250(41), 267 Maserjian, J., 293, 399 Mattioli, M., 92(14), 111(14), 112, 117, 126(14), 142, 186, I88 Mayer, W. N., 248, 267 Meek, J. M., 56, 86 Michelson, C., 91, 93(11), 107, 117, 158, 186 Miller, F. L., 20, 85 Miller, J. W. V., 248, 267 Miller, S. L., 275(5), 293(33, 34), 294, 301(44, 4 9 , 398, 399 Mills, J. I., 19, 21, 35, 39(51), 40(51), 42, 43, 44(51), 45, 46, 47, 48, 50, 85, 86 Minoo, H., 91(3, 4, 5 , 6, 7, 8). 92(6, 22, 25, 31), 93(31), 96, 97, 98(5, 31), 99, lOO(8, 34), 101, 102(35), I03(6), 106(31), 107, 108(7), 110(6), 113, 114(3, a), 115, 137, 138, 139, 145(7), 146, 147(6), 148, 149(6, 31), 152, 153, 155(80), 156(6), 158(31), 175, 176, 177(7), 178, 179(25), 185(6), 185, 186, 187, 189 Minorsky, N., 374(82), 401

407

AUTHOR INDEX

Misawa, T., 275(8), 294, 331(63), 398,399, 400 Mitchell, F. H., 5, 7(24), 85 Modeki, T., 248, 267 Moiseivitsch, B. L., 20(34), 85 Moll, J. L., 275(6), 292(32), 293(6), 303, 314, 315, 318(53), 328(53), 398, 399, 400

Montgomery, R. W., 131(65), 188 Moore, D. W., 206(1 la), 223, 230, 266 Moreton, G. E., 4(16), 85 Morosov, A., 92(23), 186 Morse, D. L.,92(16), 117, 118(16), 127, 128, 186 Morse, P. M., 60(68), 61, 86 Moustafa Moussa, H. R., 20, 85 Murase, K., 263, 267

P Pack, J. R., 76(76), 86 Paschen, F., 56(57), 86 Pawlick, E. V.,92(28), 180(28, 102), 181, 186, 189

Paxton, G. W., 4, 57, 60, 85 Pell, E. M., 390(91), 401 Penning, F. M., 57, 86 Petty, W. D., 243, 245, 259, 260, 261, 267 Phelps, A . V., 76(76), 86 Philip, C. M., 180(100, 103), 181(100), 189 Pipkin, A. C., 51, 86 Poeschel, R. L., 180(105), 190 Poincart, H., 374(81), 401 Popovici, C., 91(8), lOO(8, 34), 101, 102(35), 103(36), 110(36), 131(36), 185, 187

N

Prince, P. R., 287(19), 398 Pugh, E. R., 34, 85 Pye, J. W., 180, 181(103), 189

Nakano. G., 61, 86 Nakayama, N., 240, 241, 248, 250, 254(37), 26 7

Naraghi, M., 35, 39(51), 40(51), 42, 43, 44(5 I), 45, 46, 47, 48, 86 Nasser. E., 57, 86 Nastyakha, A. I., 184, 190 Ness, N. F., 4(18), 85 Neustadter, S. F., 275(14), 398 Ngo, D. T., 260, 267 Nolan, J. F., 245, 267 Noon, J. H., 92(26), 98(26), 106(45), 1 17, 131, 132, 133(55), 135(45, 5 9 , 136, 138, 139, 140(55), 141, 142(55), 144(55), 179, 186, 187, 188 Nyquist, H., 274(1), 398

0

Oberg, P. E., 253, 267 O’Brien, R. R., 275(7). 293(41), 3Y8, 399 Odintsov, A. N., 178(92), 189 Oertel, W. G . , 376(85), 401 Ong, R. S. B., 83, 86 Osawa, M . , 250, 267 Osipov, Yu. I., 179(96), 189 Owaki, K., 254, 267

R Rabinovici, B., 333(69), 400 Raether, H., 57, 86 Rawlin, V. K., 180(102), 189 Read, W. T., Jr., 290(20), 398 Reich, H . J., 354(76), 400 Renton, C. A,, 333(69), 400 Relser, E. J., 35, 36, 37, 85 Richard, A., 91(9), 92(9), 174(9), 184(9), 186

Rigden, J. D., 92(24), 179, 186, 189 Roberts, A. S., Jr., 117, 184(117), 188, 190 Roehling, D. J., 183(108), 190 Rogowski, W., 56, 86 Root, C. D., 293(40), 399 Roquet, J., 4(19), 85 Rose, D. J., 91, 92(8, 15, 1 0 , 93(11), 103(18, 37), 104(18), 107, 117, 121, 123, 124(15, 49). 126, 127, 128, 129(64), 133, 134, 140(62), 142, 143, 144, 145(79), 156(82), 158, 184(18, 37, 78), 186, 187, 188, 189 Ross, 1. M., 275(16), 398

408

AUTHOR INDEX

Rothleder, S. D., 91, 93(11), 107, 117, 158, 186 Rubin, P. L., 179(96), 189 Ruggles, R. L., Jr., 331(66), 400 Russell, G. R., 35, 85 Rutz, R. F., 315(54), 400 Ryder, E. J., 290(23), 398

S Sabolev, N. N., 179(96), 189 St. John, R.M., 20, 85 Salerno, J. A., 61, 86 Salop, A., 61, 86 Sautter, G. F., 253, 267 Sazonov, M. I., 184(113), 190 Schaff, H. A,, 331(66), 400 Schlich, R., 4(19), 85 Schlutter, J., 20, 85 Schmersal, L. J., 249, 250, 251, 255, 267 Schmidt, H. A,, 117, 133(55), 135(55) 136, 138, 139, 140(55), 141, 142(55), 144(55), 188 Schonland, B. F. J., 3, 85 Schreffler, R.S., 34, 85 Schwuttke, G. H., 331(66), 400 Scott, F. R., 31, 85 Scott, R. P., 53, 86 Selzer, E., 4(19), 85 Sharp, C. M. H., 131(65), 188 Sharpless, G. T., 208, 209, 210, 213, 218, 221, 222, 223, 266 Shelton, G. A., 15, 71, 77, 85, 86 Shimizu, M., 254, 267 Shockley, W., 290(20, 23), 293(39), 398, 399 Shotov, A. R., 292(31), 293(31), 399 Shulman, R. G., 275(13), 390(90), 398, 401 Silk, J . K., 117, 188 Sivinski, J. A,, 53, 54, 5 5 , 86 Skalnik, J. G., 354(76), 400 Slottow, H. G., 235, 237(31), 239, 240(34), 241(3 I), 242, 243, 245, 248(44), 250, 258(30), 259, 260, 261, 263(55), 266, 26 7 Small, J., 127, 128, 129, 140(62), 188 Smirnov, P. A,, 184, 190 Smit, J. A., 61, 86 Smith, J., 218, 228, 266

Smith, P. T., 74, 75(75), 86 Smith, R. C., 263, 267 Smith, S. L., 20(34), 85 Snoddy, L. B., 2, 4(8), 5(23), 6(23), 7(23, 24), 42(23), 84,85 Sobel, A., 214, 266 Sobolev, N. N., 178(92), 189 Sovie, R. J., 18, 85 Sparks, M., 290(23), 398 Spitzer, L., 125(59), 188 Statz, H., 290(21), 398 Steele, E. L., 390(93), 401 Stratton, T. F., 183(108), 190 Stredde, E., 233, 263, 266 Swift, J. D., 201, 203, 266 Szili, Z., 92(25), 179(25), 186

T Thompson, J. P., 206(11), 233, 266 Thomson, G. P., 70,86 Thomson, J. J., 2, 70, 84, 86 Tichmarsh, J. G., 240, 267 Tidman, D. A., 83, 86 Tiemann, J. J., 275(10), 398 Toba, T., 254, 267 Tottori, H., 262, 267 Touzeau, M., 91(9), 92(9), 174(9), 184(9), 186 Townsend, J. S., 56, 291, 86, 398 Trambore, F. A., 275(12), 293(12), 398 Travis, A. J., 184(118), 190 Trindade, A. R., 91(3, 4, 5, 6, lo), 92(6 21, 25), 96, 97(32), 98(5, 32). 99(21), 100, 103(6), 107, 108(7), 110(6), 113, 114(3, 6), 124(32), 131(21), 145(7), 147(6), 148, 149(6, 21, 32), 151, 152(21), 154(21), 156(6, 21), 158, 165(21), 169(21), 170(21), 171, 172(21), 173, 174, 175, 176, 177(7), 178, 179(25, 97), 184(10), 185(6), 185, 186, 189 Trofimov, A. V., 92(23), 186 Trogdon, R. L., 255, 267 Tsuruta, N., 262, 267 Turcotte, D. L., 83, 86 Tynan, E. E., 247, 267

409

AUTHOR INDEX

U Umeda, S., 250, 251, 254, 263, 267

V

Van Benthem, W., 92(12), 104(12), 106(43) 107, 117, 126(12), 186, 189 Van der Kooi, A. G., 183, 190 Van der Sijde, B., 110(46b), 111(46b), 114(46a, b, c), 117, 118(46b), 119, 121, 122, 124(46b), 126(46b), 187 Van Houten, S . , 215, 218, 223, 228(17), 231, 232, 234, 266 Van Overstraeten, R. 275(6), 292(32), 293(6), 398, 399 Van Winkle, G . L., 206(1 I), 233, 266 Veron, H., 240, 267 Von Hippel, A., 56, 86 Von Zahn, W., 2 , 8 4 Voorhies, H. G., 31, 85 Vriens, L., 159(85), 160(85), 189

Weiser, K . , 348(72), 400 Welber, B., 247, 267 Wen, L. C . , 92(28), 180(26), 181, 186 Westburg, R. G . , 26, 27(38), 28(38), 29(38), 85 Weston, G. F., 201, 205(9), 215, 218, 221, 223, 228(17), 231, 232 233, 266 Weymann, H. D., 3, 85 Wheatstone, C., 3, 8 4 Wild, J. P., 4(17), 85 Williams, M., 183(108), 190 Williams, R., 290(25), 298(25), 398 Willson, R. H., 239(32), 240(33), 252(33), 253, 258, 263(55), 267 Wilson, C. T. R., 3, 85 Winn, W. P., 29, 30, 31, 85 Witting, H. L., 184(116), 190 Wolff, P. A., 292(29), 293(29), 399 Woo, J. C . , 92(18), 103(18), 104(18), 144(79), 145, 184(18, 78), 186, 189 Wu, T. T., 323(57), 400 Wul, B. M., 292(31), 293(31), 399

Y W Wakerling, R. K., 138(72a), 139, 188 Wallace, R. L., 275(1 I), 398 Walsh, D. J., 275, 398 Walters, F., 211, 218, 228, 266 Wang, C. C., 240, 267 Wang, S . , 323(57), 400 Wanless, D., 170(86), 186 Weber, L. F., 258(56), 259(56), 263(62), 267 Webster, W. M., 323(56), 325, 400 Weil, R., 257, 267

Yapor, I. P., 184(115), 190 Yoshikawa, S . , 91, 93(11), 107, 117, 140, 142, 143, 158, 186, 188

z Zanfagna, B., 92(14), 111(14), 112, 117, 126(14), 186 Zayac, M. T., 248(43), 263, 267 Zener, C., 290(22), 398 Zeyfang, E., 182, 190

Subject Index A

Ac arrays, 235-264 see also Ac displays; Ac panels characteristics of, 239-245 electron beam and optical address methods for, 257-263 sine-wave methods in, 252-254 square-wave methods for, 254257 state changes in, 242-245 switching characteristics of, 241-245 wall voltage for, 237-238, 243 Ac drive systems, square-wave, 255-256 Acoustic speed, of electrons, 4 Acoustic waves, nonlinear acoustic, 1-84 Ac panels color in, 263-264 construction techniques for, 245-248 crossbar address methods in, 252-257 development of, 245-252 electrical and light output characteristics for, 249-250 electrode geometry for, 247 “gray-scale” operation of, 259-263 operation of as gas-discharge display, 235-237 other measurements in, 250-252 Active zone, in hollow cathode arcs, 158-1 66 Alfvkn wave, slow, 136 Annihilation, in S-N interaction, 359-363, 367 Antiforce wave, 5-1 9 electron density profile for, 26 peak temperatures vs. gas pressure for, 45 time-temperature data for, 24-25 wave-speed studies and, 4 1 4 3 Arc discharge studies, 91 see also Hollow cathode arcs Argon antiforce waves in, I 1, I3 potential distribution plots for, 27 proforce wave in, 14

Astable circuits, 274 Avalanche, electron, 56-57 Avalanche array, monolithic, 31 8 Avalanche breakdown see also Breakdown waves ionization coefficient in, 293 negative resistance and, 274 in p-n junctions, 289-294 in transistors, 294-307 Avalanche circuit multiple, 349 multistable, 319 Avalanche devices integrated, 312-331 physics of, 289-31 2 second breakdown in, 331 Avalanche multiplication, 309-31 2 Avalanche multivibrator, 385 Avalanche subharmonic generation, 384-385 Avalanche transistor, 296 interaction in, 366 Avalanche transistor multivibrator, 382,386 B Bar-matrix displays, ac discharges in, 263-264 Bar-matrix multiple tubes, 193 Bar-matrix operation, planar numerical displays and, I92 Baryon flux, 60 Bipolar devices, breakdown in, 289 Bistable load intersection, 338 Bistable operation, in first and second regions of characteristic curve, 340-341 Branching, in avalanche theory, 57 Breakdown waves, 4-26 see also Avalanche breakdown electrical, 1-2 excitation process in, 21 generation of by stray electrostatic fields, 36

410

41 1

SUBJECT INDEX

Breakdown waves (cont.) from negative electrode, 5 potential at wave front, 8-10 proforce and antiforce types, 5-1 5 resolution of, 83 secondary, 26-31 secondary wave velocities in, 31 tertiary, 53-55 wave potential decrements in, 12-1 3 wave speeds of, 15 wave velocity decrements in, 9-1 I C Cathode, hollow, see Hollow cathode Cathode voltage drop, in hollow cathode arcs, 149-1 52 Cathotron, 102 Collisional ionization processes, 51 Collisional operators, electron equations and, 61-62 Collision probability averages, 62-68 Color dc displays, 233-234 Crossbar address methods, for ac displays, 252-257 D Dc arrays, 204-235 see also Dc displays basic structures in, 205-209 basic switch in, 213-215 clamping in, 21 3-21 5 color in, 233-234 cyclic mode of operation in, 215-216 leakage resistance in, 209-21 I priming in, 21 1-213 pulsed storage mode in, 21 8-220 scanning function in, 234-235 sputtering and leakage resistance in, 209-2 I 1 storage mode of operation in, 217-218 switching considerations in, 21 3-220 Dc discharge cells characteristics of, 195-1 98 light output from glow discharge cells and, 201-203 “ o n ” and “off” transitions in, 198-201 sputtering of cathode in, 203-204 two modes of operation in, 215

Dc displays see also Dc arrays dot-sequential operation in, 21 5 glow transfer type, 224-227 halftone, 230-233 internal resistor panels and, 228-230 practical types of, 220-233 pulsed storage panel for, 230 scanned data, 221-224 storage type, 227-230 Digital computer, memory store and, 270-272 Diode, transistor and, 313-31 8 see also Tunnel diode Doppler shift, 2 Dot-matrix characters, 194 Drift waves coexistence with ion acoustic waves, 135 hollow cathode arcs and, 133-1 35

E

Electrical breakdown wave, 1-2 Electric field in avalanche breakdown, 275-216 ionization coefficient and, 293 Electric propulsion systems, ion sources for, 180-1 82 Electric shock tube microwave studies of, 35 multisegmented, 36-38 precursor-free, 39 precursor-producing, 40 Electric shock tube precursors, 31-50 one-dimensional equations and, 58-60 Electromagnetic T shock tube, 33-34 Electron($ acoustic speed of, 4 collision probability averages for, 62-68 free diffusion of, 3 Electron acoustic waves electric shock tube precursors of, 31-50 first observation of, I laboratory experiments in, 4-55 laser precursors and, 50-52 nonlinear, 1-84 slow proforce waves and, 53 theories of, 56-83 see also Breakdown waves

412

SUBJECT INDEX

Electron avalanche, 56-57 Electron beam methods, as arrays, 257-263 Electron current density, in avalanche devices, 327-328 Electron density of hollow cathode arcs, 1 16-1 I9 for proforce waves, 46 Electron density measurement techniques, 36- 37 Electron distribution, Maxwellian, 160-1 61 Electron equations collision operators and, 61-62 for proforce waves, 72-83 Electron wave, one-dimensional, 57 External plasma, in hollow cathode arcs, 116-126

F Faraday dark space, 201

G Gas discharge displays, 191-265 see also Ac arrays; Dc discharge cells cathode sputtering in, 203-204 characteristics of dc discharge cells in, 195-204 color in, 233-234 dynamic electrical characteristics of, 198-201 plasma panel in, 235 self-priming, 21 1 Gas-filled diode ignition and maintaining of potentials in, 198 “off” state in, 195-196 “ o n ” state in, 197 secondary effects in, I98 static voltage-current characteristic of, 195-1 98 transistor state in, I97 Gas flow rate, in hollow cathode arcs, 114-116 Geissler discharges, 2 Glow discharge cells, light ouput from, 20 1 -203 Glow transfer displays, 224-227

“Gray-scale“ operation, of ac panels, 259-263

H Halftone displays, 230-233 HCA discharge, see Hollow cathode arc discharge Heavy particle equations, 70-72 Helium antiforce waves in, 10, 13, 17 optical cross sections for, 22-23 proforce waves in, 12, 17 Hole storage diode, 397 Hole storage response, 392 Hollow acoustic arc, slow Alfven wave in, 136 Hollow cathode, geometry of, 89-90 Hollow cathode arcs, 87-1 85 “active zone” in, 158-1 66 ac operation of, 183-1 84 anode in, 103 applications of, 175-1 84 arc ignition in, 105 arc rotation in, 127-1 31 cathode assembly for, 103 cathode channel pressure drop in, 152-1 57 cathode pressure drop in, I55 cathode region in, 145-157 cathode voltage drop in, 149-1 52, 157 cathode wall radiation in, 164 current balance in cathode region of, 166-1 70 current-vol tage characteristics for, 109-1 I6 discharge vessel and, 104 discharge voltage in, 109-1 10, 157 drift waves and, 133-1 35 electron density in, 116-1 19 experimental requirements for, 103-104 experimental results for normal range in, 109-1 57 external plasma and, 116-1 26 gas-flow rate in, 97, 114-1 16 gas pressure in, 116 H C ion laser and, 177-1 80 high pressure (HP) regime in, 99-103 homogeneous conditions in, 159

413

SUBJECT INDEX

Hollow cathode arcs (cont.) improved theoretical approach to, 174-1 75 incoherent noise in, I38 internal positive column in, 97 internal positive column (IPC) ionization term in, 164-166, 170-174 ion acoustic waves and, 131-136 ion bombardment in, I62 ionization term in, 164-1 66, 170-1 74 as ion sources for electric propulsion systems, 180-1 82 ion temperature and, 123-125 IPC (internal positive column in), 97, 164-1 66, 170-1 74 Joule heating in, 163-164 low-current (LI) regime in, 98-99 low gas flow operation (LQ regime) in, 98 low-pressure discharges of, 102-103 low-pressure operation for, 103-1 08 low-pressure regimes for, 106-108 magnetic field in, 110-1 14, 122 magnetoplasmadynamic arc thrusters and, 182-1 83 maximum wall temperature in, 96 Maxwellian electron distribution in, 160-161 metal-to-gas heat conduction in, 164-165 metastable bombardment in, 163 multichannel, 175-1 77 neutral gas density and, 152 noise in, 138-144 nonlinear wave mixing and, I37 in normal regime, 93-97 in N region, 95, 157-175 operating conditions for, 103-108 oscillations and noise in, 126-145 particle temperatures in, 119-126 photon bombardment in, 163 power dissipation in, 146-149 quiescent plasma machine and, 144145 relevant parameters in, 116 thermionic emission in, 164 vessel pressure and, I14 wall temperature and, 93, 96, 101, 114 n., 145-146 wall temperature distribution in, I57 working regimes of, 92-103 Hollow cathode effect, 91 Hollow cathode glow, 91 Hollow cathode ion laser, 177-1 80

I Incoherent noise, and hollow cathode arcs, 138 Integrated devices, 355-356 Internal positive column (IPC), in hollow cathode arcs, 97, 164-1 66, 170-1 74 Internal resistor panels, 228-230 Ion acoustic waves coexistence with drift waves, I35 identification of, 131-133 Ion diffusion regime, change in, 141 Ionization coefficient, electric field and, 293 Ionization processes collisional, 51 shock-fronted, 51 Ionizing wave, 3 Ion radical flux, enhanced, I39 Ion temperature, 125

J Joule heating, in hollow cathode arcs, 163-1 64 K Kerr cells, 2 Kirchhoff’s law, 60

L Laser precursors, 50-52 Lichtenberg branching, 57 Lightning, study of, 3 Load intersection, S-type bistable and tristable, 338 Low cathode arc, ion current and, 99

M Magnetic field effect, in hollow cathode arcs, 110-1 I4 Magnetohydrodynami c (MHD) drives, 100 Magnetoplasmadynamic (MPD) arc thrusters, 182-1 83 Marx circuit impulse generator, 4

414

SUBJECT INDEX

Massachusetts Institute of Technology, 91 Matrix displays, 192 Memory capacity, increasing of, 270 Mercurial phosphorous, 2 Minority carrier storage, negative resistance and, 277-289 Monostable circuits, 274 Moving striations, 2 Multichannel cathodes, 175-1 76 Multiple avalanche circuit, 349 Multistable avalanche circuit, 319-320 Multistable characteristic, with direct and inverted negative resistance, 346 Multistable circuits, 332-356 Multistable device, integrated, 345 Multistable dynamics, 369-387 nonlinear analysis of, 369-376 Multistable negative resistance switching and oscillation, 376-387 Multistable semiconductor devices, 269-397 annihilation in, 358-363 parametric excitation of, 390-397 Mu1tis table states generation of, 272-289 negative resistances in, 272 Multistable switching circuits, triggering of, 316-377 Multistable transistor switching circuit, 377-318 Multistage triggering, 333-342 Multivibrator avalanche transistor type, 382 minority carrier storage power type, 288 silicon power transistor hole type, 286 Multivibrator circuit, tristable avalanche transistor type, 386

multistable short-circuit stable, in series 332-333 in multistable states, 272, 332, 342 in series, 287, 332-333 S-type, 282-285 tristable operation with, 348-354 tunnel diode and, 276-277 voltage-controlled, 278-279, 336 Negative resistance annihilation, 360-361, 367-368 Negative resistance interaction, 363-368 Negative resistance switching, multistable, 376-387 Negative resistance triggering, N-type, 379 Neon lamps, as gas discharge lamps, 191-1 92 Neutral gas density, calculation of, 153-1 54 Nitrogen, secondary wave velocities in, 30 N-N interaction, 358-359 Noise, in hollow cathode arcs, 138-144 Nonlinear electron acoustic waves, 1-84 npn transistor, 31 0 N-type negative resistance triggering, 379 Numerical indicator tube, 192

0

Oak Ridge National Laboratory, 91 One-dimensional analysis, fundamental equations for, 58-72 Open-circuit-stable voltage-current characteristic curve, 343 Optical address methods, in ac arrays, 257-263 P

N Negative resistance avalanche breakdown and, 275-276 current-controlled, 281 -282 interaction in, 363-365 internal generation of, 274 minority carrier storage and, 277-289 multistable connection of, 339 multistable open-circuit stable, in parallel, 342-345

Panels, ac see Ac panels Parametric excitation, current buildup due to, 390-397 Particle temperatures, in hollow cathode arcs, I 19-1 26 Paschen’s law, 56 Photopreionization, 51 Photoionization-avalanche theory, 57-58 Planar numerical displays, 192 Plasma, external, in hollow cathode arcs, I 16-1 26

415

SUBJECT INDFX

Plasma-acoustic shock, 33 Plasma-acoustic shockwave, 53 Plasma panel, see Ac panel Plasma physics, 3 Plasma precursor, 3 P-n junctions, 289 avalanche breakdown in, 289-294 in four-layer configurations, 344 reverse-biased, 31 2 Pnp transistor, negative resistance in, 360-362 Pnpn devices, 289, 3 I0 see also Pnpn diodes applied voltage change and, 331 on common substrate, 317-318 integrated, 355-356 lattice imperfections and, 323 model of, 369 radius of curvature for, 31 0-3 I2 switching vs. curvature of, 31 I Pnpn diodes, 3 18 avalanche array of, 353 integrated, 320 Pnpn switching circuit, multivariable, 377 Potential waves, 2 Preionization, in plasma physics, 3 Priming, in dc array design, 211-213 Proforce wave, 5-7 electron density profile for, 26, 46 electron equations for, 72-83 slow, 53 time-temperature data for, 24-25 wave-speed studies in, 41-43 Pulsed laser, explosion of, 4 Pulsed storage mode. in dc arrays, 21 8-220, 230

Q Quiescent plasma machine, 144-145

R Radial diffusion direct measurement of, 143 noise and, 138-1 39 Radices, higher-order, in memory capacity, 210-271

Random access memory elements (RAMS), 222-223 Read only memory (ROM), 222 Regenerative circuits, three types of, 274 Resistance negative, see Negative resistance total device, 307-310 Return stroke ionizing wave, 3

5

Scanned-data displays, 221-224 SELF-SCAN display, 224-227 Semiconductor avalanche, coupled, 383 see also Avalanche Semiconductor devices, conductance change in, 390 Semiconductor diode, parametric excitation of, 392 Shock tube, electric, 3 Shock tube diffusion precursor, 51 Short-circuit-stable negative resistances, 332-333 Slow proforce waves, 53 S-N interaction, 359-366 Square-wave drive systems, 254-256 S-S interaction, 358 “Starfish” test, Johnson Island, 4 Steady profile waves, internal conditions for, 63-70 Storage displays, 227-230 Storage panels, in dc arrays, 217-218 Striations, moving, 2

T Television display system, 232 Tertiary breakdown waves, 53-55 Total pnpn device resistance, 307-310 Townsend avalanche, 56-57 Transistor see also P-njunction; pnpn devices avalanche breakdown in, 294-307 collector characteristics of, 297 conducting state and, 306 Ebers-Moll model of, 369 Transistor-diode operation, 31 3-31 8

416

SUBJECT INDEX

Transverse magnetic field electron temperature along, 47 wave velocity through, 48 Tristable avalanche multivibrator, 386-387 Tristable coupled avalanche oscillator, 350 Tristable load intersection, 338 Tristable operation, with single negative resistance devices, 348-354 Tristable transient dynamics, 375 Tunnel diode monolithic arrays of, 357 multistable monolithic, 354 multistate serial connection of, 353-354 negative resistance for, 276-277 voltage-controlled, 284 tristability and quadristability in, 350-351 Tunnel diode multifrequency oscillator, 389 Tunnel diode-transistor switching circuit, 378 Tunnel diode tristable triggering, 388

U

Ultraviolet photopreionization, 51

V Vessel pressure, hollow cathode arc and, 114

W Wall temperature in hollow cathode arc, 93, 101, 114, 145-146, 157-158 longitudinal profile of, 95 maximum, 96 Wave-speed studies, for proforce and antiforce waves, 41-43

Z Zener breakdown, 290 Zener emission, in avalanche breakdown, 216 Zener tunneling, 291

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