Advances in Electronics and Electron Physics, Volume 18

ADVANCES IN ELECTRONICS AND ELECTRON PHYSICS VOLUME 18

This Page Intentionally Left Blank

Advances in

Electronics and Electron Physics EDITEDBY L. MARTON National Bureau of Standards, Washington, D. C .

Assistant Editor CLAIREMARTON EDITORIAL BOARD W. B. Nottingham T. E. Allibone E. R. Piore H. B. G. Casimir M. Ponte L. T. DeVore W. G. Dow A. Rose L. P. Smith A. 0. C . Nier

VOLUME 18

1963

ACADEMIC PRESS

New York and London

COPYRIGHT

@ 1963, BY AcAuvniic

P R E S S INC.

ALL R I G H T S R E S E R V E D N O P A R T O F T H I S BOOR MAY B E R E P R O D U C E D I N ANY FORM, B Y PHOTOSTAT, MICROFILM, O R ANY O T H E R MEANS, W I T H O U T W R I T T E N PERMISSION FROM T H E P U B L I S H E R S .

ACADEMIC PRESS INC. 111 Fifth Avenue, New York 3, New York

United Kingdorri E d i t i o n published by ACADEMIC PRESS INC. (LONDON) LTD. Berkeley Square House, London W.1

LIBRARY OF

CONGRESS CATALOG CARD NUMBER:

P R I N T E D I N T H E U N I T E D S T A T E S O F AMERICA

49-7504

CONTRIBUTORS TO VOLUME 18 MANFRED A. BIONDI,Physics Departnzent, University of Pittsburgh and Westinghouse Reseawh Laboratories, Pittsburgh, Pennsylvania

F. P. BROOKS, JR., International Business Machine Corp., Pouyhkeepsie, N e w Yorli DAVIDP. KENNEDY, International Business Afachine COTp., Poughkeepsie, New York F. LENZ,Institute of Applied Physics, University, Tubingen, Germany G. MOLLENSTEDT, Institute of Applied Physics, Unilrersity, Tubingen, Germany

F. E. ROACH,Central Radio Propagation Laboratory, National Bureau of Standards, Boulder, Colorado

V

This Page Intentionally Left Blank

For the best part of a year now your editor and associate editor have been in Europe, where many opportunities arose to establish new contacts and renew the old ones. The result is twofold: we gained new insight into contemporary European research in electronics and electrophysics and were able t o secure the collaboration of many colleagues to future volumes of Advances. A hearty welcome to our new contributors! As in the past years I should like to list here the authors of future reviews and the tentative titles of their contributions : G. Broussaud and J. C. Simon G. Birnbaum K. L. Bowles J. F. Dennisse M. Knoll and R. W. Schon J. L. Jackson and R. A. Piccirelli K. G. Emeleus R. G. Fowler L. S. Chernov S. H. Autler L. A. Russell J. W. Herbstreit J. Kistemaker and C. Snoek G. K. Wehner P. Grivet, and L. Malnar D. B. Medved M. Nalecz H. Raether D. de Klerk

Endfire Antennae Light Optical Masers Scattering in the Upper Atmosphere Radioastronomy Biological Effects of Atmospheric Ions Cooperative Phenomena Plasma Oscillations Electrons as a Hydrodynamical Fluid Microwavc Applications of Plasma Cryogenic Magnets High Speed Magnetic Core Memory Technology Tropospheric Propagation Atoms Produced in Sputtering Experiments Cathode Sputtering Weak Field Magnetometers Electron Ejection from Solids by Atom and Ion Impact Hall Effect and its Technical Applications Gas Discharge Phenomena High Magnetic Field

Other subjects, on which conversations are more tentative, comprise : magnetohydrodynamics, thermionic emission, noise in semiconductors, superconductivity, and others. I wish to express again my heartfelt thanks to all those whose collaboration makes these volumes possible.

L. MARTON

Sorbonne, Paris, July, 1963

vii

This Page Intentionally Left Blank

CONTENTS CONTRIBUTORS TO VOLUME 18.

.

.

.

.

.

.

.

.

V

FOREWORD . .

.

.

.

.

.

.

.

.

vii

.

.

.

The Nightglow F. E . ROACH

I . Definitions . . . . . . . . . . . . . I1. Units of Brightness . . . . . . . . . . . I11 General Spectroscopic Description of the Night Airglow IV . Nightglow Instrumentation . . . . . . . . . . V. Nightglow Observatories . . . . . . VI . Nightglow Heights . . . . . . . . . . . VII . The Hydroxyl (OH) Nightglow . . . . . . . VIII Oxygen 5577 . . . . . . . . . . . . . I X . Oxygen6300 . . . . . . . . . . . . . X . Sodium 1)in the Nightglow . . . . . . . X I . Nightglow from the O2 Molecule . . . . . . . XI1. Hydrogen Emission in the Nightglow . . . . . XI11. Excitation Mechanisms . . . . . . . . . . XIV . Concluding Remarks . . . . . . . . . . References . . . . . . . . . . . . .

.

.

.

.

.

.

.

1

. . . .

. . . .

. . . .

. . . .

. . . .

2 4 6 9

.

.

.

.

.

.

.

.

. .

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

9

.

.

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

13 14 22 28 29 29 29 42 42

Recent Developments in Computer Organisation F. P. BROOKS.JR. I . Introduction . . . . . . . . . . . I1. Metaprograms . . . . . . . . . . I11. Multiprogramming . . . . . . . . IV. The Content-Addressed Memory . . . . . V. The One-Level Memory . . . . . . . VI . Last-In-First-Out Register Stacks . . . . . VII . The Fixed-Plus-Variable-Structure Computer . References . . . . . . . . . . .

. .

. .

. .

. .

. .

. .

. .

.

.

.

.

.

.

.

. . . .

. . . .

. . . .

. . . .

. . . .

. . . .

. . .

.

.

.

.

.

.

.

.

45 46 49 52 55 59 62 64

Atomic Collisions Involving Low Energy Electrons and Ions MANFREDA . BIONDI List of Symbols . . . . . . . . . . . . . . . . . I . Introduction . . . . . . . . . . . . . . . . . . 11. Theoretical Developments . . . . . . . . . . . . . . I11. Low Energy Elastic and Inelastic Collisions . . . . . . . . . ix

67 68 72 75

X

CONTENTS

IV . Attachment and Detachment of Electrons . . . . . . . . . 116 V. Recombination of Positive Ions with Electrons and with Negative Ions . 137 References . . . . . . . . . . . . . . . . . . 158

Semiconductor Device Evaluation DAVIDP. KENNEDY

I . Introduction . . . . I1. The p-n Junction Diode I11. The Junction Transistor References . . . . List of Symbols . . .

.

.

. . . .

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

.

.

.

.

.

.

.

.

.

.

.

. 167 169 216 248 249

Electron Emission Microscopy

.

I. I1. I11. IV . V. VI .

G MOLLENSTEDT AND Introduction . . . . . . . . . Electron Optics of a Cathode Lens . . Photo Emission Microscopy . . . . Secondary Emission Microscopy . . . Ion Induced Emission Microscopy . . Thermionic Emission Microscopy . . . References . . . . . . . . .

AUTHORINDEX .

.

.

.

.

SUBJECT INDEX.

.

.

.

.

F. LENZ . . . .

.

.

.

.

. 251

. . . .

. . . .

. . . .

. . . .

. . . .

. . . .

. . . .

. . . .

. . . .

. .

. .

. .

. .

. .

. .

. .

254 262 283 298 . . 320 . . 326

.

.

.

.

.

.

.

.

. 339

331 .

.

.

.

.

The Nightglow F. E. ROACH Central Radio Propagation Laboratory, National Bureau of Standards, Boulder, Colorado Page ...

................................................ 111. General Spectroscopic Description of the Night Airglow. , . IV. Nightglow Instrumentation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................................... ....................................

glow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

IX. X. XI. XII. XIII.

XIV.

.................................... B. Statistical Distribution of 5577 Intensities C. Distribution of 5577 Intensity with Latitude.. . . . . . . . . . . . . . . . . . . . . . . D. Covariance of 5577 and other Radiations.. . . . . . Oxygen 6300 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. Midlatitude 6300 Arcs during Times of Magnetic Activity. . . . . . . . . . . . B. 6300 Activity in the Tropics .................................. Sodium D in the Nightglow. . . . ................................. Nightglow from the 0 2 Molecule.. . . . . . Hydrogen Emission in the Nightglow. . . ........................... Excitation Mechanisms.. . . . A. Photochemical Reactions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B. Excitation by Electrons Accelerated by C. The 5577 Nightglow-Aurora and Trapped Electrons.. . . . . . . . . . . . . . . . Concluding Remarks.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2 6 9 9 13

15 19 22 23 27 28 29 30

35 42 42

I. DEFINITIONS The word “airglow” was introduced by Elvey (1) in 1950, following a suggestion of 0. Struve, to designate optical emissions other than the polar aurora originating in the earth’s upper atmosphere. Subsequently, the word “nightglow” came to mean that part of the airglow emitted during the night. A t the time that the word “airglow” came into common usage, it was considered that the aurora was caused by particles (electrons or protons) proceeding from the sun to the earth’s dipole magnetic field, then spiraling down along the magnetic field lines to the upper atmosphere causing excitation and ionization en route with resulting optical emis1

2

F. E. ROACH

sion. The discovery of energetic particles in the exosphere trapped by the earth’s magnetic field has turned the attention of auroral theorists to problems involving the physics of trapped particles, their release from the magnetic tubes and their relationship with auroral excitation (see for example, Chamberlain, 2 ) . The center of attention has shifted somewhat from the interaction of moving charged particles with the earth’s magnetic field to the mechanism of trapping of charged particles and their release into the atmosphere. Since the original definition of the word “airglow” involves the idea of a n aurora by its exclusion, and, since auroral mechanisms are currently under debate, it is difficult to be precise in delineating just what should be included in a general discussion of the nightglow. The basic idea in the original concept was that the night airglow is due to resident properties and events in the upper atmosphere and that the aurora is due to extraneous imposed effects. I n the present discussion, we prefer not to be bound too tightly by this concept and will describe observed phenomena which seem a priori to be resident phenomena but which may later prove to be affected by extraneous events such as trapped particles. We exclude from this survey discussion of the twilight glow and the day airglow each of which is distinguished from the night airglow or nightglow by the fact that the direct sunlight is operative in the former cases and not in the latter.

11. UNITS OF BRIGHTNESS Two units of brightness or intensity will be used: (a) ergs . ~ r n - ~ (column) * sec-l and (b) rayleighs. I n a later section we shall discuss the absolute brightness of the several night airglow components. Here we shall mention a little of the history and usefulness of the rayleigh as a unit. I n 1930 ( 3 ) Lord Rayleigh2 performed a remarkable observational feat. Working out of a window in the cellar of his home in London, he observed the night sky with a photometer which had a n optical filter centered on the nightglow emission line a t a wavelength of 5577 A. He then turned the photometer around to catch the light of a standard lamp diffused by a magnesium oxide screen. His purpose was t o satisfy the urging of Sydney Chapman for a n estimate of the absolute intensity of the 5577 A night airglow line (at that time the phenomenon was not called airglow-many used the expression “permanent aurora”). Lord Rayleigh describes in his paper his calculations involving the calibration of the standard lamp, the properties of the magnesium oxide diffusing 1 Purely thermal emission from the lower atmosphere would not be included as airglow according to current usage. 1 The Lord Rayleigh referred to is R. J. Strutt, the fourth Lord Rayleigh.

3

THE NIGHTGLOW

screen, the correction for astronomical light coming through his filter in addition t o the upper atmosphere emission, and allowance for a correction of his reading from the slant angle by which he was forced to observe out of his basement window to what it would have been in the zenith. He announced that the absolute intensit>yof the 5577 A line was 1.81 X 1OI2 quanta . m e t e r 2 (vertical column) second-1

or

-

181 X lo6 quanta cm-2 (vertical column) second-).

It is of interest t o compare this classical measurement with current measurements. The median value for the zenith intensity of 5577 A based on 21,088 measurements during ICY-IGC is 254 X lo6 quanta * cm-2 (column) * sec-1 ( . b ) . For some time authors used the expression “megaquanta * cm-2 (column) . sec-I” in referring to nightglow iiitensities but this has now, by general acceptance, been called the “rayleigh.” The formal definition is as follows: “If the surface brightness, B, is measured in lo8quanta * cm-2 . sec-I . steradian-I then the intensity in rayleighs is 4aB” (see Hunten et al., 5 ) . Thus, the classical measurement by Rayleigh indicates a n intensity of the green 5577 nightglow line of 181 rayleighs and the IGY-IGC value is 254 rayleighs. A practical advantage of the unit is that the volume emission rate in the upper atmosphere can be estimated if the effective thickness of the emitting layer is known. I n many applications the thickness is approxiTABLEI.

R E L A T I O N S H I P BETWEEN THE R A Y L E I G I I AND

ERGS. CM-~(COLUMN) . SEC-1 Wavelength A 100 1,000 3,000 3,914 5,000 5,577 5,893 6,300 10,000 45,000

One rayleigh [in ergs cm-*(column) . sec - l ] 199 19.9 6.62 5.07 3.97 3.56 3.37 3.15 1.99 0.441

x x

10-6 10-6

X X

x

10-8

X

x

10-6

X

x X

10-8

F. E. ROACH

4

mately 10 km (los cm). Cancelling out the losin the definition thus leads to the useful approximation Intensity in rayleighs = the volume emission rate in quanta

*

CM-~

sec-’

A disadvantage of the unit arises in connection with discussions of energetics in that its energy content varies with wavelength. I n Table I some typical one-rayleigh energy fluxes are listed for several wavelengths. 111. GENERAL SPECTROSCOPIC DESCRIPTION OF THE NIGHT AIRGLOW As we shall see later, there are several “nightglows” occurring a t different atmospheric heights, and probably caused by different mechanisms. They have in common their origin somewhere in the earth’s upper

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

WAVELENGTH IN MICRONS FIG.1. Above: Distribution of intensities and wavelengths of the rotation-vibration bands of OH in the nightglow; observed to about 1.5 p and predicted for wavelengths longer than 1.5 p. Also, the absolute intensity of the thermal radiation from the lower atmosphere for a temperature of 275”K, a slit width of 0.1 p , and a n emissivity e of 0.3. Below: The transmission of the lower atmosphere versus wavelength.

atmosphere. As observed from the ground, they are affected by absorption and scattering from the lower atmosphere, The vertical transmission of the lower atmosphere a t sea-level is shown in Fig. 1. The thermal emission of the lower atmosphere is also shown for a band width of 0.1 micron. Figure 1 illustrates the spectral distribution of the by far most intense

5

THE NIGHTGLOW

nightglow feature (see Table II), the rotation-vibration bands of hydroxyl

(OH). . . We are restricted in our ground observations to a relatively small spectral region from about 3000 A to 25,000 A (0.3 p to 2.5 p ) with heavy absorptions near 1.4 p and 1.9 p. For wavelengths longer than 2.5 p the thermal emission from the lower atmosphere overwhelms even the very intense OH bands which extend out to 4.5 p (note the logarithmic scale for the upper part of Fig. 1). TABLE 11. NIGHTGLOW EMISSIONS Absolute zenith intensity Source

Wavelength

Rayleighs

0 . 3 8 to 4 . 5 I./ 8645 A G5G3 A 0300, 6364 A 5890, 5896 A

5,000,000 500 15 200 30 (summer) to ‘LOO (wintcr) 01 5577 A 250 4861 A 3 H I (HB) O2 (Herzberg Bands) 3000 to 4000 A 1500 N z+ 3914 (40).

OH O2 (0, 1 atm) H I (Ha) 01 NaI

Continuum (Nightglow) Continuum (Astronomical)

4000-7000 A

I500 (0.5R/.4 Mean) 4500 (1.5Rl.4 Mean)

Ergs . cm-2(column)

. sec-1

3.6 I . 1 x 10-3 4 . 5 x 10-5 6 . 2 x 10-4 1.0 X to G.8 X lo-‘ 8.9 x 1.2 x 8.8 x 2.0 x

10-4 10-5 10-8 10-6

x

10-3

5.0

1 . 5 X lo-*

a The presence of Nz+ 3914 A as a “nightglow” emission is uncertain. It is a prominent feature of the aurora.

A list of the observed spectral features from longer to shorter wavelengths is given in Table 11. It is apparent that the hydroxyl (OH) emission is energetically predominant. Historically, on the other hand, it is a latecomer. A partial chronological listing of nightglow discoveries including the identification of specific airglow emissions is given in Table 111. The reader is referred to Chapter 9 of Chamberlain’s ( 6 ) excellent book for a detailed description of the airglow spectrum shown both as a reproduction of original spectrograms and as microphotometer tracings. Such representations are invaluable to the specialist who is interested in details. 3 Recently a n Atlas of the Airglow Spectrum, XX3000-12,400 A ( 7 ) has been compiled by Krassovsky et al. It contains detailed listings of lines, microphotometer tracings and measured absolute intensities. Much of the material of Table I1 was taken from the Krassovsky Atlas.

6

F. E. ROACH

TABLE111. CHRONOLOGY OF SOME NIGHTGLOW DISCOVERIES Date

Author

Discovery

A. J. Rngstrcm

The green line, 5577, present in absence of visual aurora. 5577 present a t all times and in all parts of sky. 1895 W. W. Campbell Established existence of “Permanent aurora” or 1909 L. Yntema earthlight. 1919 V. M. Slipher Numerous spectrograms showing 5577. Demonstration of formula for increase of airglow 1921 P. J. Van Rhijn toward horizon (in absence of lower atmosphere). Interferometer measurement of green line in night 1923 H. D. Babcock sky. Wavelength = 5577.350; upper limit of width = 0.035 A. 1927 J. C. McLennan and Interferometer measurement of green line. J. H. McLeod Measurement of polarization of zodiacal light. 1928, 29 J. Dufay Midnight maximum of 5577. 1928 J. C. McLennan, J. H. McLeod and H. J. C. Ireton 6300,6364 (unresolved) and Na D line first recorded 1929 V. M. Slipher in nightglow spectrum. First absolute measurement of 5577 intensity. 1930 Lord Rayleigh Confirmed spectroscopic identification of green line. 1930 R. Frerichs Assigned it to atomic oxygen. Identified ‘Dzand ‘So levels of atomic oxygen. Predicted red lines: 6300, 6364 (‘Dz ‘ P z , ~ ) . Suggested that excitation of green nightglow (5577) 1931 S. Chapman is due to association of oxygen atoms via a 3-body collision. Quantitative separation of blue nightglow, zodiacal 1937 C. T. Elvey and F. E. Roach light and integrated starlight. 1941, 47 J. Dufay Identification of Heraberg bands of 0 2 in nightglow. 1943 P. Swings 1945, 47 D. Barbier Identification of strong rotation-vibration bands of 1950 A. B. Meinel hydroxyl (OH) in near infrarcd. Discovery of subvisual arcs of 6300 A in midlati1958 D. Barbier tudes. 1959 V. S. Prokudina Discovery of H a in the nightglow.

1868

-

1

IV. NIGHTGLOW INSTRUMENTATION The choice of instrument for the study of the nightglow is influenced by the absolute intensity of the phenomenon. T o illustrate, a comparison is made between the speed of a spectrograph widely used for nightglow (and aurora) research during the International Geophysical Year (IGY) and a birefringent type photometer used a t the Fritz Peak Observatory

7

THE S I G H T G L O W

for sevcral years. For convenience, comparative calculations will be shown for the recording of a n emission feature of 100-rayleigh intensity. Such a n intensity delivers a flux to the observer a t the surface of the earth of 108 F = - quanta cmd2 sec-I . steradian-I 477

- - lo* quanta - cm-2 . sec-I . (square degree)-'. 41,253

I n order to produce a spectrum line of photographic density 0.6 a total of 1.50 X 10'" quanta . cm-2 is r e q ~ i r e d . ~ TABLE Iv. COMPARISON

OF SPEEDS OF IGk' SPECTROGRAPH BIREFRINOENT PHOTOMETER

IGY spectrograph

AND

FRITZP E A R

Birefringent photometer

Aperture of lens: 6.0 in. = 15.24 cm Area of lens: 182 cm2 Field of view: Circular 5" diamcter = 10.6 square degrees. Transmission of system = 0.1 0.1 X 19.6 X 182 X lo8 F = 4.1253 X lo4 (12.8)2 = 8.65 X 105 quanta second-1 = 7.95 X l o 6 quanta * * sec-' Quantum efficiency = 0.1 1.5 X 1 O l o Exposure time for Electron flow 0.6 density = 7.95 x 106 = 8.65 X 104 electrons.second-1 = 1.89 X 104sec Let N = total number of electrons pro= 5.2 hr duced in time, 1 ; let p = precision of measurement = fi Precision of measurement of such a spectrum line = 2.5%

Slit width: 0.03 cm = 2" of sky focal length collimater = 12.8 Ratio: focal length camera Assunicd transmission of system = 0.5 F/cm2 of emulsion . , X lo8 - 0.5 X 22 X (0.03)* (0.03)2 4.1253 X lo4 X

-

-

~

N 1

0.2 0.1 0.018

8.65 1.7 8.65 1.62

X lo4 X lo4 X los X lo8

0.3 0.8 1.1 2.5

It is obvious from an inspection of Table IV that the two instruments, the spectrograph and the photometer, are useful in separate and complementary roles. For the study of spectroscopic details the long exposures 4 For a discussion of the properties of the photographic emulsion upon which this figure is based, the readcr is referred to Hiltner (8) and t o Baum (9).

00

TABLEV. IGY AIRGLOW STATIONS Geographic Number

1

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28

Name Thule Loparskaya Zvenigorod Bialkow Ondrejov Lomnicky-Stit Simferopol Rapid City Haute Provence Memambetsu Abastumani Fritz Peak Sendai Niigata Kakioka Gifu Maruyama Shodo-Jima AS0

Sacramento Peak Mount Abu Tamanrasset Poona Zamboanga City Lwiro Huancayo Camden Mirnyj

Country Greenland USSR

USSR Poland Czechoslovakia Czechoslovakia USSR USA France Japan USSR USA Japan Japan Japan Japan Japan Japan Japan USA India Sahara India Philippines Congo Peru Australia Antarctic

Latitude

Longitude

76"33' 68"38' 55'42' 51"29' 49"55' 49"12' 44"50' 44"02' 43"55' 43"55' 41 "45' 39"54' 38'06' 37"42' 36"14' 35"27' 35"Ol' 34"33' 32"53' 32'43' 24"36' 22"48' 18"31' 6"54' - 2"16' -12"03' -34'04' -66"33'

68'50'W 33'22'E 36"44'E 16'40'E 14'59'E 20'13'E 34'04'E 103"03'W 5'43'E 144'12% 30"50'E 105'29'W 140'33'E 138'49'E 140"ll'E 137"02'E 139'58'E 134"16'E 131"Ol'E 105"45'W 72'43'E 5"31'E 73"52'E 122'04% 28"49'E 75"20'W 150'38'E 93" E

Sheet Parameter L (250 km)

88 5.36 2.60 2.27 2.13 2.05 1.73 2.91 1.75 1.58 1.58 2.35 1.37 1.36 1.32 1.29 1.28 1.27 1.22 1.80 1.07 1.09 I .oo 0.97 1.07 1.08 1.91 20.18

Magnetic Latitudes -

Dip

soy9 66?3 54?0 49 ?2 47 :3 46'13 42?5 57?0 41 '10 37% 38'17 51'11 32 ?2 31 P7 30 ?O 29 y9 29 ?O 29?3 28?0 41 ?7 20 ?6 14'19 12?7 - 0?65 -16Yl - 1:3 -45P7 -64:s

Geomagnetic 88 ?l 63?7 51?1 50 ?9 49% 48: 1 41 '12 53Pl 4523

34?0

36?7 48?7 27?9 27P4 26:O 25PO 24% 23?9 22 ?O 41 ?6 15?5 25 ?4 9 P3 - 4:4 - 3?8 - OP6 -4236 -77:O

r m

*

THE NIGHTGLOW

9

required for the spectrograph in order to bring out faint details are not serious. However, for a rapid survey of variations of intensity over the sky the photometer5 is the better instrument. Recording spectrometers in which a photoelectric pickup is used behind a second analyzing slit have been useful in auroral and twilight research but are, in general, too slow for the lower intensities encountered in the nightglow. Some significant and useful work has been done with interferometers (see, for example, the classical measurement of 5577 A wavelength and width by Babcock, 12). V. NIGHTGLOW OBSERVATORIES During the IGY-IGC some twenty-eight observatories were active in the observation of the nightglow. They extended from Thule in the north to Antarctica (see Table V). The heaviest coilcentration of effort was on the green line (5577 A) for which more than 20,000 individual zenith observations were reported. A discussion of some of these results will be given in a later section. VI. NIQHTGLOW HEIGHTS Triangulation on nightglow patches by a method comparable to that used to determine heights of auroral features is not possible because of the generally amorphous character of the phenomenon. An exception occurs for some of the 6300 A features such as midlatitude or tropical arcs. The deduction of heights from measured emission temperatures on the basis of the upper atmosphere’s temperature-height profile has been used with some success. The direct measurement of airglow heights has been accomplished by filtered photometers on rockets. A summary of some measurements is shown in Table VI according to work done chiefly by NR L experimenters (13).

For many years efforts were made to estimate heights of airglow features from the general increase of intensities toward the horizon, the so-called Van Rhijn method. In principle, the method is sound, in practice the deduced height is strongly affected by many uncertainties so th a t the method may now be considered as of only historical interest. The reader interested in a critical discussion of this method is referred to Roach et al. (10). The formula introduced by Van Rhijn (14) although of limited practical usefulness in determining nightglow heights, is helpful in underA general description of the birefringent photometer is given by Roach et aZ. (10). The essential unit, the birefringent filter, is described by Dunn and Manring ( 1 1 ) .

10

F. E. ROACH

standing a prime observational fact, namely, the general increase of nightglow intensities from the zenith to the horizon. If h is the mean height of a nightglow layer above the earth's surface, R is the radius of the earth, z is the zenith distance,6 I0 is the intensity of the layer overhead, and I , is the intensity a t zenith distance x, we then have

V , " 1, I0

1

,/I

- (+)'sin2

x

The function V is listed in Table VII. Figure 2 illustrates how the function varies with zenith distance. TABLEVI. PROBABLE HEIGHTSOF NIGHTGLOW EMISSIONMAXIMA From model atmosphere ~~~

~

Number density Height" Temperature Eniission (km) (OK)

N?.

0 2

0

Total

1 . 0 0 (14) 4 . 4 7 (12) 2.34 (13) 6 . 9 5 (13) 2.04 (12) 3 . 5 5 ( 8)

3 . 9 8 (13) 1 . 4 1 (12) 9.55 (12) 4 . 4 7 (13) 4.57 (11) 5.75 ( 7)

3.80 (11) 1 . 5 1 (12) 9 . 5 5 (11) 4 . 2 7 (11) 1.12 (12) 2.63 ( 9 )

1.40 (14) 7.39 (12) 2.45 (13) 11.46 (13) 3 . 6 2 (12) 3 01 ( 9)

~~~~~

01% 5577

85 98 0 2 94 5893 a7 Continuum 103 6300 (250)

150 185 168 150 230 1210

From Packer (IS) excepting for 6300 which is estimated from correlation with F-layer parameters.

It must here be noted that the increase indicated in the left side of Fig. 2 refers to the case of no interference by an intervening lower atmosphere. Such a condition may be realized from a satellite or even from a balloon. The intervention of the lower atmosphere has two effects: (a) the line of sight pencil of light is absorbed causing a progressive weakening toward the horizon as greater air masses are traversed; (b) there is a general scattering (primarily molecular scattering) which increases toward the horizon. These two factors together with the increasing function, V , result in a distribution toward the horizon as shown in Fig. 2 (right side). The interpretation of such curves in terms of height t o the emitt)ing layer is strongly dependent on the assumed extinction (and scattering) The angle from the zenith toward the horizon along a vertical circle is called zenith distance by astronomers. It is the complement of the altitude.

THE NIGHTGLOW 1

TABLE VII. THEFUNCTION V = Ji

\h z \

0 20 40 50 60 70 75 83 85 90

11

-

(h)zsinzz

50

100

150

200

250

1.000 1.063 1.2'38 1.539 1.955 2.766 3.503 4.701 6.594 8,027

1.000 1.062 1.293 1.523 1.914 2.635 3.234 4.085 5.128 5.709

1.000 1.061 1.285 1.508 1.876 2.523 3 023 3.669 4.355

1.000 1.060 1.27'3 1.493 1.841 2.426 2.853 3,365 3.861 4.084

1.000 1.059 1.273 1.480 1.80'3 2.341 2.710 3.130 3.511 3.672

4.088

coefficients of the lower atmosphere. The spotty nature of the nightglow dictates the use of a large quantity of data from all parts of the sky and over a long period of time. Thus, effective coefficients with similar space and time coverage are needed. In practice the finesse with which these can be attained is a severe limitation on the precision with which the height can be estimated.

( 1 1 1 1 1 1 1 1 1 1

'0

20

40

60 80 0 20 40 ZENITH DISTANCE

60

80

100

FIG.2. Variation of nightglow intensities with zenith distance. Left: predicted from Eq. (1) for no lower atmosphere and three assumed heights. Right: Comparison of predicted (no lower atmosphere) and observed for 5577 from Fritz Peak. Difference betwecn curves illustrates the effect of the lower atmosphcre.

F. E. ROACH

12

TABLE VIII. CALCULATED VIBRATIONAL LEVELSOF OH Energy 0

0 1

2 3 4 5 6 7 8 9 10 ~

TABLEIx. LrST Wavelength X air (A) 3,816.6 4,172.9 4,418.8 4,640.6 4,903.5 5,201.4 5,273.3 5,562.2 5,886.3 6,168.6 6,256.0 6,496.5 6,861.7 7,274.5 7,521.5 7,748.3 7,911.0 8,341.7 8,824.1 9 ,373.0 9,788.0 10,010 10,273

~~~

OF

cm-1

ev

0 3,570 6,974 10,214 13,291 16,207 18,958 21,543 23,957 26,194 28,145

0.00 0.44 0.86 1.27 1.65 2.01 2.35 2.67 2.97 3.25 3.49

~

~

OH BANDSI N

Absolute intensity Transiin rayleighs tion (Chamberlain and (0’ - d’) Smith, 15) 0-0 8-0 9-1 7-0 8-1 9-2 6-0 7-1 8-2 5-0 9-3 6-1 7-2 8-3 4-0 9-4 5-1 6-2 7-3 8-4 3-0 9-5 4- 1

~~

0.023 0.12 0.73 0.71 3.8 11.o 4.4 22 57 33 110 130 310 520 280 710 930 1800 2800 3400 3100 3600 7600

~

ORDER OF WAVELENGTH

Wavelength X air (A) 10,828 11,433 12,115 12,898 13,817 14 ,336 15,047 15,824 16,682 17,642 18,734 19,997 21,496 28 ,007 29 ,369 30,854 32,483 34,294 36,334 38 ,674 41,409 44,702

Absolute intensity Transiin rayleighs tion (Chamberlain and (v’ - 0”) Smith, 16) 5-2 6-3 7-4 8-5 9-6 2-0 3-1 4-2 5-3 6-4 7-5 8-6 9-7 1-0

2-1 3-2 4-3 5-4 6-5 7-6 8-7 9-8

12,000 15,000 17,000 16 ,000 13,000 46 ,000 74,000 88,000 90,000 82,000 71,000 54 ,000 37 ,000 920,000 820 ,000 640 ,000 490,000 360 ,000 260 ,000 180,000 110,000 65,000

13

THE NIGHTGLOW

VII. THE HYDROXYL (OH) NIGHTGLOW The hydroxyl nightglow is quantally more than 1000 times as intense as all other known nightglow emissions. Energetically it corresponds to an aurora between IBC' I1 and IBC 111. If the hydroxyl emission were concentrated in the visual region of the spectrum, the night sky would glow like midtwilight, the Milky Way would be invisible and only the brightest stars would stand out against the competing background. TABLEx. THE S T R U C T U R E O F T H E 6-2 BANDO F OH (FROM (ASSUMEDTEMPERATURE: 225°K) R1

branch

Wavelength Intensity

R2 branch

K"

(A)

(R)

Wavelength (A)

1 2 3 4 5 6 7

8299.0 8288.7 8281.7 8278.3b 8278.5 8282.5 8290.4

87 101 77 44 21 8 2

8311.4 8296.8 8287.0 8281.5 8280.3 8283.5 8290.7

z

340

P I

Intensity (R)

Wavelength (A)

32 42 36 23 12 4 1

8399.3 8430.2 8465.4 8504.8 8548.6 8596.8

150

-

branch

CHAMBERLAIN,

6)a

PObranch

Intensity (R)

Wavelength (A)

Intensity (R)

155 179 136 78 36 14

8382.9 8415.7 8452.6 8493.6 8538.8 8588.1

57 75 64 41 20 8

598

265

a Q branch a t 8341.7; intensity 439 rayleighs; intensity of entire band = 1800 rayleighs. b Band head.

The hydroxyl nightglow bands are due t o rotation-vibration transitions in the lowest electronic state of OH, the 2?r state. The pertinent vibrational levels are listed in Table VIII. Transitions have been observed up to and including the ninth vibrational level. A complete list of all the bands either observed or predicted is given in Table IX together with the predicted absolute intensities from Chamberlain and Smith (15). The rotational structure of the individual bands may be illustrated by a specific example, the 6-2 transition (see Table X and Fig. 3). Three branches (P, R, and Q) can be identified. The P-branch has been nicely resolved and includes about six double lines extending toward longer wavelengths. The Q- and R-branches cannot be resolved with the resolution used in nightglow studies. 7 IBC refers to International Brightness Coefficient. The faintest visible aurora is IBC I and the steps go by powers of 10 t o IBC IV, the brightest.

14

F. E. ROACH

The intensities increase rapidly toward the infrared. I n the visible part of the spectrum the OH bands are relatively weak. However, it should be noted that the 9-3 band a t 6256 A (intensity 110 rayleighs) is a source of contamination in the case of observations of the 6300 A atomic oxygen line when coarse filters are used for isolating the line. Also the 8-2 band a t 5886 A (intensity 57 rayleighs) can cause trouble in the observation of the sodium-D lines a t 5890 and 5896 A especially in the summer

FIG.3. A portion of t h e nightglow OH spectrum showing in particular the 6-2 band. Compare with t h e detailed structure of the 6-2 band in Table X. The predicted position of the 10-5 band would place it in t h e same general region but sufficiently displaced to distinguish it from the 6-2 band. The absence of the 10-5 band and any other bands involving the 10th or higher vibrational levels is a n important observational fact. The original spectrogram is due to Meinel ( 1 6 ) .

when the D lines are extremely weak. The 7-1 band a t 5562 A is quite weak (22 rayleighs) and only a minor source of contamination in the observation of 5577 A (atomic oxygen).

VIII. OXYGEN5577 The three lowest spectroscopic levels of atomic oxygen are shown in Fig. 4. One of the prime observational facts that applies quite generally to the nightglow and also to some extent to the aurora is that the two radiations, 5577 (green) and 63008 (red) are independent of each other. This independence is apparent even to a casual observer after only a single night of observations. Characteristically, in midlatitudes, 6300 decreases rapidly in intensity in the early evening, reaehes a low value

* In general, we refer t o t h e 6300 emission and intend it to be understood t h a t 6364 is included. The latter is about 55 the intensity of the former.

15

THE NIGHTGLOW

then may rise slightly with the dawn. On the other hand 5577 only occasionally shows a twilight and/or dawn effect but frequently has broad periods of elevated brightness. The general behavior is illustrated in Fig. 5. The 5577 A nightglow has received a great deal of attention by observers, partly due to its early discovery and partly to the fact that its ev

J

0.74 SEC

-0

TERM

‘s

‘D

3P

FIG.4. The low lying energy levels of atomic oxygen.

wavelength is one that facilitates observations whether by photographic, photoelectric or visual methods. Out of the large body of published material on the emission, mention will be made of (a) evidence for cellular patterns in the 5577 nightglow, (b) statistical distribution of intensities, (c) geographical distribution of intensities and (d) covariance of 5577 with the Herzberg bands and the nightglow continuum.

A . Cellular Patterns The diurnal (or nocturnal) variations of the intensity of 5577 at a given observing station have been the subject of many investigations. A generalization is often found in the literature to the effect that, characteristically, there is a local midnight maximum of intensity. Although this seems to be statistically true, a maximum may actually occur at any time during the night. If the entire sky is under observation, there may be some

16

F. E. ROACH

800

I

I

20

21

I

I

I

I

22 23 0 I 105OW STANDARD TIME

2

3

4

I

I

I

700 600 rn I (3

5 G

500

(L

f

400

> k w

300

k

z 200

100

0 19

Fro. 5. Zenith intensity variations of the oxygen en?.hions, 5577 and 6300, at Fritz Peak during the night of September 6/7, 1961.

degree of simultaneity of intensity change over the sky. But there is also an element of independence especially for regions of the sky far from each other. The practical limit for observing is to a zenith distance of 80" (altitude lo"). For an emission height of 100 km this corresponds to a distance along the earth's surface of 466 km. In Table XI the distances correspondTABLEXI. DISTANCE ALONG EARTH'S SURFACE CORRESPONDINO TO ZENITH DISTANCE, z(h = 100 KM) z

Distance (km)

0 40 60 70 75

0

258 338

80

466

83 167

THE NIGHTGLOW

17

ing to other zenith distances are shown. The examples chosen in Table XI correspond to the zenith distances customarily used in the Fritz Peak observing. I n a systematic survey of the sky, it is thus possible to map the intensities over a region corresponding to a circle of radius 466 km (assuming a height of 100 km). The observations a t Fritz Peak, for example, result in an isophotal map over a region indicated in Fig. 6.

FIG.6. Extent of observational coverage for three assumed heights of the nightglow.

The discerning reader will here realize that there is a difficulty in making such isophote “maps.” The difficulty arises from the fact that there is a general increase of intensity toward the horizon [Eq. (l)] associated not with intrinsic changes of upper atmosphere emission but with the accident of observing from the earth’s surface. Numerical methods for eliminating this effect are discussed by Roach and Pettit (I&), and here it will suffice to say that reasonable approximations to local zenith intensities seem to be possible. An example of a series of isophote maps prepared in the manner indicated is shown in Fig. 7. It appears that there are distinct changes of structure through the night. Such maps have been made corresponding to close spacings of time (5 min). When they are projected by cinema techniques there is a strong impression of a large scale dynamical phe-

18

F. E. ROACH

nomenon rather suggestive of movements of the “weather” on successive weather maps. Thus, the idea of dynamical nightglow cells has developed. The estimation of the size of the nightglow cells is made difficult by the fact that they are frequently larger than the field of view from a single station. Using indirect methods, Roach et al. (17, 18) came to the conclusion that a typical cell has a size of about 2500 km ( ~ 2 . times 7 the observer’s field of view) and a speed of about 90 meters/second (200 miles/hr) . Smaller scale cellular structure can occasionally be detected on the records. It will not be surprising if it develops that there is a spectrum of

FIG.7. An example of hourly changes of 5577 intensity patterns a t Fritz Peak for the night of October 1/2, 1956. Darker shadings correspond to more intense regions of the sky.

cells from small scale turbulent irregularities to the gross phenomena mentioned here.

B. Statistical Distribution of 5577 Intensities We have indicated that the median intensity of 5577 for the IGY-IGC ensemble of data is 254 rayleighs. I n Table XI1 we show a statistical summary of the entire body of information. One of the general characteristics of all published statistical surveys of this radiation is that, when the intensities are plotted in histogram form they always show a positive skewness. This is not particularly surprising since on the low side there is a definite bound, namely zero intensity, whereas on the high side there is not necessarily a bound since a priori any intensity is possible.

19

THE NIGHTGLOW

TABLEXII. STATISTICAL DISTRIBUTION OF 55778 INTENSITIES Intensity in rayleighs Number of Lower observations decile

Station Airglow (25 stations) Mirnyj Thule (6) College (5) a

21,088 96 9,732 3,968

Lower quartile

Median

Upper quartile

Upper decile

176 300 490 1290

254 560 630 2400

360 820 812 6020

490 1,050 1 ,120 11,500

128 195 380 740

Taken from Yao, Table 8 (4).

w 2o 0

z

W

oz oz I>

0 0

0 10 I-

Z

W 0

200

400

600 800 1000

Q IN RAYLEIGHS

0

2

4

3sa

6

8

10

FIG.8. Statistical distribution of 5577 zenith intensities based on 21,088 observations during the IGY-IGC. Left: plotted with respect to t h e intensity. Right: plotted with respect to the cube root of the intensity.

The skewness in the distribution may be empirically removed by using a root of the intensity or its logarithm. The fact that the use of the cube root (Fig. 8) leads to an essentially “normal” distribution has led to the suggestion (Barbier, 19) that this is in support of the Chapman triple collision reaction as the source of excitation (see Section XIII, A ) . As examples of intensity distributions a t various locations, Fig. 9 shows some for Fritz Peak, Rapid City, College, and Thule-four stations ranging in latitude from outside, to and inside the auroral zone.

C . Distribution of 5577 Intensity with Latitude I n Table XI11 is assembled a large quantity of data on the absolute zenith intensity of 5577 for stations grouped according to latitude. Most

F. E. ROACH

20

8 lo z w

K K

3 0

0

0

0.5

%j w K

2 LOG

3

4

Q IN RAYLEIGHS

FIG.9. Distribution of 5577 intensities a t four stations: Rapid City, Fritz Peak, Thule, College.

TABLE XIII. COMPILATION OF OBSERVATIONAL MATERIAL FOR 5577

Number Q (5577) of obser- Rayleighs Station vations (median) I

I1

4932 5278 7252 3500

111 IV Yerkes Ithaca 0 Saskatoon Meanook College 3968 Mirnyj 96 Hallett 1374 0

0 0

Thule

9732

Lb for 100 km

Corresponding

x

Reference

220 235 280 315 250 600 1500 2000 2400 560 630

1.052 1.289 1.728 2.431 3.008 3.157 4.292 4.617 5.449 19.74 23.13

10"O 27"2 29"5 49"3 54"7 55"5 60Y90 62"3 64y42 76"s 77"O

630

87.81

83"3

Yao (4) Yao (4) Yao (4) Yao (4) Sandford (21) Sandford (21) Sandford (21) Sandford (21) Roach and Hees (22) Yao (4) M. A. Gordon (unpublished material) Roach et al. (23)

From spectrographic studies by Sandford (21). The absolute calibration for these four entries was obtained by forcing agreement between the spectrographic intensities a t Yerkes and the IGY photometric results for Rapid City. b L is the sheet parameter (in earth radii) of McIlwain (20); is the corresponding latitude (see text). 0

21

THE NIGHTGLOW

4

Ib

;0

$0 40

$0

sb

;0

eb gb

INVARIANT MAGNETIC LATITUDE

FIG.10. Distribution of 5577 intensities according to geomagnetic latitude (from Table XIII).

of the information comes from the IGY-IGC program with other sources as noted. A plot of the ensemble of data is shown in Fig. 10. Discussion of the interpretation of the observations is deferred until later.

D. Covariance of 6677 and other Radiations Barbier has been the leader in inve'stigations of simultaneous observations of several emissions. With his photometer a t the Haute Provence Observatory (France), he systematically observes in eight colors : 6700 (OH), 6300 (narrow, chiefly the 01 line), 6300 (broad including the 9-3 band of OH), 5893 (Sodium D),5580 [OIJ, 5260 (continuum), 4400, and 3670 (chiefly O2 Herzberg bands). On the basis of similar temporal changes in intensity, Barbier has grouped the emissions as follows: 5577

\

5260 4400 3670

[The 5580 group

!:::

1 )The 5900 group

6300 broad The quality of the correlations may be judged from Fig. 11 taken from Barbier (24). Of particular interest is the fact that the atomic oxygen emission, 5577, and the molecular oxygen emission (the Herzberg bands through the 3670 filter) are so closely correlated. This covariance supports

F. E. ROACH

22

/

900

700

36701

600

300

526-

f

20 0

100

I

0

1

500

I

1000 I(5580)

1 1500

FIG.11. Correlations between (a) 3670 (Herzberg bands) and 5580 (actually 5577 of atomic oxygen) and (b) 5260 (significant nightglow continuum plus astronomical components) and 5577. According t o Barbier (24) from observations a t Haute Provence.

the hypothesis that the atomic 557'7 and the molecular (Herzberg band) oxygen emissions result from a common excitation mechanism. IX. OXYGEN6300

It is extremely difficult to present a unified description of 6300 nightglow because of its many different manifestations. It has already been mentioned that there is no apparent covariance with 5577. From this fact we deduce: (a) after the emission of each photon of 5577 the oxygen atom must either emit a photon of 6300 or leave the lD state by collisional deexcitati~n~; (b) the lack of covariance between 6300 and 5577 shows that the second alternative is followed; (c) therefore, the 6300 emission that we do observe must be due to some mechanism not associated with 5577 and must be emitted at a n atmospheric height where collisional deexcitation is less than it is in the 100-km region where 5577 occurs. The emission of 6300 a t higher altitudes (say 250 km) and the nonemission of 5577 at these altitudes can occur only if the source of excitation is restricted to less than 4.2 ev-at least it must very strongly favor the 2.0 ev of the 'D state over the 4.2 ev of the 1X state. Barbier (25) has given a general summary of several morphological 6300 A features which he has observed and isolated a t the Haute Provence 9 It should be noted that the mean lifetime of the ID state is 110 see compared with less than 1 second for the IS state (see Fig. 4).

T H E NIGHTGLOW

23

Observatory (HP) in France and a t the tropical station a t Tamanrasset (T) in Sahara. These include the the the the the the

polar aurora (HP) twilight phenomenon (HP, T ) western sheet (HP) subpolar sheet (HP, T) tropical arc (T) “para” twilight phenomenon (T)

These phenomena are frequently superimposed photometrically aiid are distinguishable only by their concentration in particular directions or a t particular times. The 6300 A line has a very strong twilight and dawn enhancement caused by the direct action of sunlight on oxygen atoms in the upper atmosphere. The effect is especially prominent near the horizon in the azimuth of the sun but is also observable up to the zenith. There is no discontinuous change right at the moment of twilight although the intensity is rapidly decreasing. The twilight and night phenomena merge photometrically into each other. A logical discussion of the 6300 nightglow melange might hopefully be based on the excitation mechanisms, but such a criterion is iiot available to distinguish the several phenomena listed by Barbier. As a matter of fact, a definitely auroral phenomenon-midlatitude arcs which occur during times of magnetic activity-have been considered to be auroral in the morphological sense and possibly nightglow (photochemical origin) in the microscopic.

A. Midlatitude 6300 Arcs during .Times of Magnetic Activity During the IGY, a n interesting 6300 effect was discovered by Barbier (26). Almucantar sweeps revealed evidence for the existence of well-

defincd arcs going across the sky in a general east-west direction. They occur during times of significant magnetic activity. The properties of the arcs are here enumerated: (1) They are oriented along invariant latitudes,’O (Fig. 12). On one occasion, a t least, a n arc coincided in space and time with a region of high energy particles observed from a satellite (27) (Fig. 12). lo The invariant latitude, A, is deduced from the so-called sheet parameter, L, introduced by McIlwain (90) according to cos2 X = r / L where r is the geocentric distance to the emitting layer in earth radii. L is approximately the geocentric distance to the equatorial crossing of the pertinent magnetic line of force also in earth radii.

F. E. R O A C H

24

(2) They occur a t heights of about 400 km (Roach et al., 28; Moore and Odencrantz, 29; Rees, SO). (3) A typical cross sectional representation is shown in Fig. 13 (31). The great extent both horizontally and vertically is apparent.

6300A ARC

‘i

F. F?

FIG.12. A 6300 arc observed over western United States parallel to the locus of sheet parameter, L, = 2.5. Extension of arc coincides with region of maximum counts of high energy particles observed from Explorer VII.

0 2

0

2

I

’ NORTH

SOUTH

DISTANCE IN km

FIG.13. IsophotaI section of a typical 6300 A arc ($1).

(4) They have been frequently observed over ranges of some 3000 km in longitude. On occasion, they have been observed almost simultaneously in France and the United States suggesting that they may extend a t least one-third of the way around the world (32, 33) (Fig. 14).

FIG.14.6300 A arc of September 29/30, 1957, observed near the same sheet parameter, L (2.38), in Europe and t,he United States. Insert shows that the typical arc has a width approximately the size of the State of Colorado.

26

F. E. ROACH

12

I

I

I

I

I

I

I

I

I

I

-

$

+ 0

6

4

2

200

I50 v)

I (3

w

d

100

K

a” 50

0 350

I

I

I

I

I

1

I

1

I

I

20

21

22

23

00

01

02

03

04

05

300 E

Y

LL

r

250

200

-

I

19

06

HST, HOURS FIQ.15. Variation of 6300 A nightglow intensity over Maui (Hawaii) during the night of June 5/6, 1961 (center). Simultaneous variations of the ionospheric parameters foFe (upper) and h’F (lower).

27

THE NIGHTGLOW

( 5 ) There is evidence that there are conjugate arcs in both the northern and southern hemispheres (33). (6) They are significantly correlated with magnetic activity (Barbier, 34). (7) They have been observed predominantly in midlatitudes. (8) Two independent investigations indicate that radio frequency beams which traverse red arcs show strong scintillation effects (35, 36). (9) There is evidence that oblique radio echoes are reflected from the arcs (37).

B. 6300 Activity in the Tropics The temporal history of 6300 intensity in the tropics frequently exhibits a dramatic increase typically over a two-hour period (Fig. 15). 300

250

200 v)

I

i2

> a u

6

150

100

..

.

50

. ..t---INTERCEPT = 18 '

0

10

20

30

(foF2f exp

40

[-1-

50

60

FIG. 16. Observed intensity of 6300 A a t Maui (Hawaii) versus the function (foF2)*exp - [(h'F - 200)/41.3].

Associated with the increase is a concurrent change in the F-region of the ionosphere-the F-region increases its electronic density and/or moves to a lower part of the atmosphere. A semiempirical formula has been introduced by Barbier (38), and by A. and D. Delsemme (39) to describe the relationship between the absolute zenith intensity of 6300 and the

28

F. E. ROACH

parameters of fopzand h’F”

The quality of the correlation between Q and Eq. (2) is shown in Fig. 16. A possible significance will be discussed later a s we consider excitation mechanisms.

X. SODIUM D IN THE NIGHTGLOW The sodium D lines seem to be omnipresent in nature. The spectrochemist may inadvertently find them on his spectrograms due to contamination from a n operator’s hands. They occur in the spectrum of

JAN FEEI h

MONTHS

FIG.17. Mean seasonal variation of sodium D nightglow a t Cactus Peak (California) during period 1948-1951.

meteors as they become incandescent on entry into the upper atmosphere. They are prominent features of the spectrum of the sun,12 a s well as of many other stars. Interstellar lines of sodium were discovered years ago by astronomers. The sodium D lines flash up briefly during twilight and dawn. And finally they are present in the nightglow spectrum. The outstanding characteristic of the sodium D lines in the nightglow is their annual variation. As shown in Fig. 17 they display a maximum during winter and a minimum (close to zero, actually) during summer. At one time, it was conjectured that the maximum might be due to the passage of the earth through a meteoric cloud of material but the fact that the seasonal variations in the two hemispheres are six months out of I1 In ionosphere parlance f0F2 is the maximum frequency reflected by the F-layer and h’F is the lowest apparent atmospheric height from which the F-layer reflects. I2 The designation “D” lines was attached to them in the catalogue of prominent spectral features in the sun’s spectrum made by Frauenhofer in the 19th century.

29

THE NIGEIT(:LOW

phase does not support the idea. Another conjecture is that the source of the high atmosphere sodium is elevated sea-water salt. The covariance of the nightglow sodium D emission and OH emissions has been pointed out by Barbier (24). These two nightglow components seem to occur in approximately the same regions of the atmosphere.

XI. NIGHTGLOW FROM

THE

O2 MOLECULE

The following band systems of 0, have been observed in the nightglow : (a) The Herzberg bands ( A 3 2 , ++ X3&-). Most of the observed bands are in the 3600 A region. (b) The Atmospheric Sygtem (D'2,f + X3Z0-). The 0-1 band is a t 8645 A. The 0-0 band a t 7619 A is reabsorbed by the lower atmosphere. (c) Infrared Atmospheric System (ulAg+ X3Zu-). The 0-1 band is a t 1.58 p. The 0-0 band a t 1.27 p is reabsorbed; it should be observable from rockets. The total emission from these band systems is of interest. In Table I1 an estimate of 1500 rayleighs was made for the Herzberg bands. The 0-0 bands of the two atmospheric systems will have to be observed above the lower atmosphere (e.g., from rockets) in order to get reasonable measurements. Chamberlain (6) has estimated that the atmospheric system has a n intensity between 8000 and 30,000 rayleighs and the infrared atmospheric system not more than 50,000 rayleighs.

XII. HYDROGEN EMISSION IN

THE

NIGHTGLOW

Three separate hydrogen emissions are distinguishable in the light of the night sky : auroral, nightglow, and astronomical. The hydrogen lines Ha and HB, when of auroral origin, are broad and asynimetrical which has been interpreted as evidence for a significant radial velocity of incoming protons, which velocity is reflected in the movements of the hydrogen atoms after the protons have been neutralized by the acquisition of electrons. The nightglow and astronomical hydrogen lines are very narrow and quite faint. They can be disentangled from each other by the increase of astronomical hydrogen in the vicinity of the Milky Way.

XIII. EXCITATION MECHANISMS In Section 111we mentioned the absolute intensitics of some nightglow features. It is of interest to compare these with other energy fluxes in and through the atmosphere (Table XIV) as an orientation to a discussion of excitation mechanisms that may be responsible for the nightglow

30

F. E. ROACH

emissions. The very intense hydroxyl emission corresponds to a rate of temperature change of only 1.7 X 10-4"K second-' or 1°K in 6 X lo3 seconds (less than 2 hr). Such a change is possibly significant in the overall energy balance. The normal intensity of the 5577 radiation, on the other hand, is so low that its participation in the energy balance is trivial. It is necessary to keep in mind that there may be different types of excitation for the several nightglow species. The very fact that they occur a t different atmospheric heights strongly suggests such a conclusion. It is even possible that a given emission may have a multiple origin. In TABLEXIV. SOME ENERGY FLUXES Energy density, E , (erg . cm-8 . sec-l) Flux, F (for lo8 em thickness (erg . cm-a (col) sec-1) of layer)

-

Source Solar constant Nightglow OH (total) IBC I11 aurora (known optical radiations) Nightglow 5577 (250 rayleighs) 3 x 1Olo electrons . . sec-1 (7.5 kev each)

-

1 . 4 X lo6 3.2 18

3.2 X 1.8 x 10-6

0.0009 360

9 x 10-10 3.6 x 10-4

particular, 6300 A with its slow decrease in intensity during the post twilight period followed by other phenomena during the night suggests the possibility of multiple excitation mechanisms. Approaches to the general problem of nightglow excitation have included : (a) photochemical reactions, (b) electrical currents, and (c) release of magnetically trapped particles.13 These will be discussed in order.

A . Photochemical Reactions A listing of several photochemical reactions which are currently under discussion as possible contributors to the observed nightglow is given in Table XV. Historically, the first proposal of a photochemical origin for the excitation of nightglow is due to S. Chapman who in 1931 (40) suggested that the atomic oxygen in the upper atmosphere combining to form molecular oxygen constitutes a significant energy reservoir. The energy gained by the combining of two oxygen atoms into a molecule is 5.08 ev which is sufficient t o excite most of the observed nightglow features. 13 According t o present usage, excitation by release of trapped particles would be considered as a n auroral rather than a n airglow mechanism.

31

THE NIGHTGLOW

Chapman's suggestion that the energy of association of oxygen is responsible for the green line (5577 A) via a three-body collision has grown in general acceptance over three decades.

0

+ 0 + 0-t 02 + 0 ('Dl 0 (ID)+ 0 +-hv (5577 A) (IS)

Indirect evidence supporting the reaction is that it predicts covariance of 5577 and the Herzberg bands of molecular oxygen, in agreement with TABLEXV. SOMEPROPOSED PHOTOCHEMICAL REACTIONS Excitation energy (ev.) Reaction

Available

Required

+ +0

3.32 3.33

>3.25 but <3.49

(3) 0 + 0 + 0 - + 0 2 + 0 *

5.08

4.17

6.96 2.75

1.96

5.08

4.43

2.1 2.3

2.00 2.00

Emission OH v'

69

[OI] 5577 ID +- 1 8

(I) H .f O3-f OH* (2) Oa* H + OH*

+

(4){

[OI] 6300 3P +-ID O2 Herzberg bands AS&+ + XQ,NaI 5890, 96 2 s 6 2P

02*

+O+

+e+

(5) (6)

Ot+ NO+

(7) 0

+0 +X+

(8) NaH (9) NaH

+e

+

0 2

o* + 0 2 O* N

+0

+ O*

0 2 *

+X

+ 0 4 Na* + O H + H - +Na* + Hz

observation (Section X, D) ; also, the intensity of 5577 will, according to this reaction, be proportional to the cube of the atomic oxygen density, which is consistent with the normal distribution of 5577 intensities when the cube root of the intensity is used (see Section X, B and Fig. 8). Recently, measured rate coefficients have indicated, however, that the reaction proceeds too slowly to account for the observed nightglow intensity of 5577 ( 4 l 1 4 S ,43) and other mechanisms are now being actively sought. l 4 Reactions (5) and (6) have been much discussed as sources of 6300 nightglow, as well as the 6300 midlatitude and tropical arcs. It is to be noted that reaction (5) is energetically capable of exciting atomic oxygen 14 For a discussion of reactions (3) and (4) in Table XV the reader is referred to Barth and Putapoff (4%).

32

F. E. ROACH

so as t o produce both 5577 and 6300. On the other hand reaction (6) cannot produce the green line since the available energy is only 2.75 ev compared to 4.17 ev needed for the lS state leading to 5577 (see Fig. 4). Reactions such as ( 5 ) or (6) are consistent with the close correlation between the intensity of 6300 and the ionospheric parameters of foFz and h’F [Eq. (2) and Fig. 161. (foF2)2is proportional to the peak electron density in the F-region of the ionosphere and h’F determines the effective height of the F-region. As ( f o l ; “ 2 ) 2 increases the corresponding electron density increase favors reactions ( 5 ) or (6).lbAs h’F decreases the reaction is favored since the concentration of OZ+ [reaction ( 5 ) ] or NO+ [reaction (6)] increases. Thus, the strong correlation between the ionospheric parameters fop2 and h‘F [Eq. (2)] and the intensity of the red line (Fig. 16) is consistent with a photochemical origin for the emission. I n the case of the hydroxyl emissions we must first of all take into account a prime observational fact: Of all the possible bands none has been noted in which v’ is greater th an 9. For example, the band corresponding to v’ - v” = 10 - 5 should be a t a wavelength of 8400 A. It is clearly not present (see Fig. 3). It becomes necessary to find a reaction which is exothermic a t least t o 3.25 ev (v’ = 9) but not to 3.49 ev (v’ = 10). Two independent investigations have suggested the following reaction for the excitation of the OH radical (Herzberg, 44, Bates and Nicolet, 45). H 03’ OH* OZ* (3.32 ev available)

+

+

The fact that this so-called ozone reaction satisfies the condition that the available energy lies between 3.23 and 3.49 ev has caused considerable enthusiasm in its favor. Krassovsky ( 4 6 ) has criticized the ozone reaction and has proposed as a n alternative

02*+H+OH*+O The 02*refers to 0 2 excited to vibrational levels up to v = 2.5. For a detailed discussion of these two alternative reactions the reader is referred to Chapter 13 in Chamberlain’s book. No measurement of rate coefficients is available for either of the reactions. It is, therefore, not possible to judge whether either or both of the reactions contributes to the nightglow. Indirect evidence might be based on the height of the emission layer: the ozone reaction should be most effectivenear the 70-km level, whereas the excited molecular oxygen reaction favors a height in the vicinity of 100 km. Thus, the height evidence (Table VI) suggests that both reactions may contribute. 1 6 Reactions (5) and (6) are considered by ionospherists to be important contributors to the loss of ionospheric electrons by recombination.

THE NIGHTGLOW

33

T ha t the reactions listed in Table XV occur in the upper atmosphere cannot be doubted. The pertinent quant,itative questions are how rapidly they occur and how much they contribute to the observed nightglow intensities. In the absence of systematic reaction rate data, several authors have employed indirect arguments in support of particular reactions. A stimulating study has been made by Tohmatsu (47) who has attempted to rationalize reactions (3) or (4), Table XV, in terms of large scale physical inhomogeneities and movements in the 100-km region. For example, Tohmatsu suggests that regions of high 5577 intensity correspond to regions of a meteorological type downdraft. Conversely, low intensities are associated with updrafts.

B. E.rcitation by Electrons Accelerated by an Electric Field There have been frequent suggestions that the nightglow excitation might be the result of the heating, or acceleration, of ionospheric electrons by a resident electrical field. Th at there are large scale electron flows in the ionosphere is evident from the interpretation of synoptic magnetic records. According to Chapman and Bartels (48) there is a steady horizontal current between the equator and 40" latitude of about 40,000 amp. If this is evenly distributed over the 40" (-4 X lo8 cm) and has a thickness of about one scale height (-los cm) the current density is some 10-lo amp . cm-2. Recently a study has been made by Megill and Carleton (49, 50) of the basic physical principles of electron flow in the ionosphere with particular reference to the effect on excitation of the nightglow. Some of their results are shown in Table XVI. I n the example, conditions were chosen to yield a n absolute intensity of 5677 of 250 rayleighs. The high predicted value of 6300 intensity (>20,000 rayleighs) is meaningless because this radiation will be very strongly affected by collisional deexcitation during the 110-sec lifetime of the 'D state. It is of interest that the calculations of Megill and Carleton predict a n intensity for the Herzberg bands (420 rayleighs) of the same order as that observed (1500 rayleighs). Furthermore, changes of the electrical current will produce proportional changes in 5577 and the Herzberg bands in agreement with observation (Section X, 0). Since both the electrical current and the photochemical excitation hypotheses predict covariance of these two emissions, no choice between the mechanisms can be made on this basis. The predicted emissions of the 0 2 atmospheric systems are much lower than the estimates quoted in Section XI, but it must be recalled that there have as yet been no quantitative measures of these bands. The similarity in the numerical value of current density in the 100-km

34

F. E. ROACH

TABLEXVI. EXCITATIONOF THE NIQHTQLOW BY ELECTRONS ACCELERATED BY A N ELECTRIC FIELD(FROM MEGILLAND CARLETON, 60) (Assumed height = 100 km; assumed magnetic field, B, = 0.5 gauss)

E I R Field gradient, E (volts/cm)

E

0.013

0.002

~~

~~~

Current density (amp/cmz)

2.0

Predicted nightglow intensity in rayleighs O(1S) 5577 0 2 ( 1 2 ) (Atmospheric system) 02(*2)(Herzberg bands) Oz(lA) (Infrared atmospheric system) O ( l 0 ) 6300

x

10-10

4.2

x

10-9

250 160 420 1770 (21,000)"

250 250 420 650 (27,000)"

0.028

0.039

Electron loss rate by attachment (attachments . cm-8 * sec-1 . electron-') 0

II B

The intensities for 6300 ignore the effect of deexcitation by collision. I

I

I

I

I

1

IAO

260

360

700

\ \

2

I

W

I 200-

/

4

I

100-

I !'

160

2d0

360

b

400

FIG.18. Comparison of observed vertical photometric section of a 6300 A arc and (a) a photochemical excitation mechanism (SY),and (b) a horizontal electric current (61).

THE NIGHTGLOW

35

region for the E 1B case to that inferred for the ionosphere from magnetometer records is favorable to the hypothesis of excitation by electron acceleration in an electric field. The alternate possibility of the E 11 B case will be further explored in the next section. The physical conditions ohange significantly as one goes up in the ionosphere above the 100-km level. Recently, Megill et al. (51) have reported that the effect of a horizontal current flow in the upper atmosphere maximizes at a height of about 400 km. There is a rather striking agreement with the observed photometric cross section of a red 6300 A arc and the predictions of excitation by a current flowing under the influence of a field of 2 X volts/cm as shown in Fig. 18.

C . The 5577 Nightglow-Aurora and Trapped Electrons I n the previous section we called attention to a recent study of the excitation of some of the nightglow radiations by electrons accelerated by a n assumed1e electric field. The horizontal current density required for the excitation of nightglow emissions for the E IB case was shown in the previous section to be consistent with what has become a classical interpretation of the diurnal variations of magnetometer records in terms of ionospheric currents, The possibility that a current flow parallel to the geomagnetic field lines might be operative was left open. At midand high-latitudes such currents would approach the vertical. One can imagine a number of different conditions, all of which could be categorized as current flow. For example, there might be localized electrical fields say of the order of a scale-height (-10 km) in vertical extent. Or potential differences on a grand scale may exist between the 100-km region and the F-region above 200 km. Either the small scale or the large scale fields might serve t o accelerate charged particles such as electrons upward or downward. Such accelerations would lead to excitations as indicated in the previous section. Another possibility, in this same general category, is that charged particles are introduced into the extreme upper atmosphere and are decelerated en route to the 100-km region. Such a mechanism is reminiscent of most auroral theories from the time of Stormer to the present when there is much discussion about the escape of trapped charged particles from magnetic tubes into the ionosphere. I n this last section it is proposed to present a speculative discussion of such a mechanism with reference to possible excitation of both the 5577 nightglow and the 5577 aurora. lE In the discussions by Megill, Carleton, Rees, and Droppleman the matter of the origin and maintenance of an electric field is not discussed. They consider only the effects of a postulated field.

36

F. E. ROACH

Two hypotheses are considered : (1) The dumping hypothesis. The excitation is by energetic (-10 kev) trapped electrons which have been '(dumped" from their magnetic tubes a t altitudes well above 100 km, the excitation occurring during the deceleration in their downward path. (2) The local acceleration hypothesis. The trapped electrons are of low energy and, after release from their magnetic prison, th e y are accelerated downward presumably by a potential difference between the point of release and the general 100-km region.

D ............,..................,.,.,,,,. ...........,.....,.. .....,.........., ':W ...... ..... ..... ..... ..... . .. . . . . t

....

LATITUDE 20°

40°

55O

65'

FIG. 19. Idealized representation of magnetic tubes corresponding to different magnetic latitudes. Heights in the sketch are proportional to the length of a tube from the earth's surface to the equatorial crossing. The relative volumes with respect to unit terminal cross section are indicated.

I n Fig. 19 the tubes corresponding t o several magnetic latitudes are displayed with their curvature removed. The volumes with respect to a fixed end area are approximately in the ratio 1 (20' latitude), 10 (40'), 100 (55'), and 1000 (65'). The heights in the sketch correspond to the distance, I, along a geomagnetic line of force from the equatorial crossing to the earth's surface. The problem will be simplified by assuming that, in each tube, the charged particle (electron) density is uniform throughout and that the excitation is the result of the extrusion and/or persuasion of the charged particles out of the lower ends of the tubes. At the equatorial

THE NIGHTGLOW

37

crossing the electrons will have their greatest linear speeds parallel to the field lines. Since the largest volume of the tube is also a t the equatorial crossing, the mean density may, to a first approximation, be taken a s the equatorial density. 1. Symbols and Nomenclature. Let V = the volume in cm3 of a tubeI7 which ends in a 1 cm2 cross section near the earth, n = the mean density of the electrons in the tube in cn1-3, r = the rate of flow of electrons out of the tube in cm-2 sec-l, t = the time in seconds for the complete depletion of the tube on the assumption that there is no replenishment, I = length of the magnetic tube from the equatorial crossing point to the earth’s surface, 7 = the time for an electron of a given energy (hence a given velocity) to travel from the equatorial crossing point to the vicinity of the earth, L = the geocentric distance to the equatorial crossing point in earth radii, h = the height in km above the earth’s surface to the equatorial crossing point, h’ = the height in kni above the earth’s surface to the assumed end of the tube, ZJ = the velocity of the electron, Q = intensity of 5577. I n the general case, independent of the energy of the electrons, we have

For numerical applications, a relationship between auroral intensities (5577 A, in particular) and energetic electrons will be assumed according to Chamberlain (6). If Q is the inteiisity of 5577 A

Q

= =

3.3r quanta cm-2 sec-’ 3.3 X 10-9 rayleighs

(4)

for 10 kev electrons with a velocity of 6 X lo9 cm/sec. It will be assumed that Eq. (4) is applicable for either of the two hypotheses whether the 17 Throughout we shall refer to a “tube” as the half tube from the equator to the vicinity of the earth on the assumption that the auroral phenomenon is symmetrical in the two hemispheres.

38

F. E. ROACH

electrons leave the tube with approximately 10 kev of energy or acquire energy by acceleration subsequent to their extrusion; r may thus be eliminated from Eq. (4)yielding

t

=

3.3

x

10-6-

V.n

sec, (Q in rayleighs)

Q

1

= - sec.

T

2,

In Table XVII are assembled pertinent data on the magnetic tubes from the equator through the auroral zone. TABLEXVII. SOMEPROPERTIES OF GEOMAGNETIC TUBES

V (cm8)5 Latitude (for h’ = 500 (N km) 5 10 15 20 25 30 35 40 45 50 55 60 65 70

6.19 x 1.37 X 2.40 X 4.00 X 6.64 X 1.13 X 2.00 X 3.78 X 7.77 x 1.77 X 4.64 X 1.45 X 5.74 X 3.20 X

L (earth radii) 1 (cm)b

5.62 x 1.16 X 1.82 X 2.60 X 3.55 X 4.73 X 6.24 X 8.23 X 1.09 x 1.47 X 1O1O 2.02 X 10” 2.87 X 10” 4.28 X 10l2 6.88 X 107 10” lo8 lo8 lo8 lo@ lo@ lo0 100 101O

107 lo8 lo8 108 lo8 lo8 lo8 lo8 100 100 lo@ loB 10” los

(for h’ = 500 km) 1.087 1.112 1.156 1.221 1.313 1,438 1,607 1.838 2.157 2.610 3.278 4.314 6.038 9.220

h (km) log h (km) (for h’ = 500 (for h’ = 500 km) km) 553 714 993 1,410 1,994 2 790 3,868 5,337 7,370 10,260 14,510 21,110 32 090 52 360

2.742 2.853 2.997 3.149 3.300 3.446 3.588 3.727 3.867 4.011 4.162 4.324 4.506 4.719

0 V is computed from a modification of Eq. (7) in a paper by Hanson and Ortenburger (66). I is taken from Chapman and Sugiura (65).

2. The Dumping Hypothesis of Excitation. An examination of the dumping hypothesis is made for two bracketing assumptions concerning ~ the mean density, n, of energetic (10 kev) electrons: (a) n = 1 ~ r n -and (b) n = 10 cm-S. From Eqs. ( 5 ) and (6) we obtain the entries of Table XVIII some of which are shown plotted in Fig. 20. We use the condition t = r to correspond to a n approximate physical restriction since in a simple interpretation of the problem it is impossible to deplete a magnetic tube in a time, t, faster than the time, T , for an electron to move from the equator to the earth along a magnetic line of force, We note that this restriction pre-

39

THE NIGHTGLOW

cludes the possibility of a n IBC I11 aurora by dumping a t low latitudes (if n = 1 cm+) which is in rough agreement with experience. The value of t (second column of Table XVIII) for n = 1 cm-4 is 19 sec near the auroral zone (X = (35”). Thus, an IBC 111aurora in the auroral zone requires a replenishment of the reservoir of electrons in a short time. To maintain such an aurora for a significant time requires a steady input of energetic particles. As a matter of fact, it has been suggested by O’Brien and Laughlin (54) that the “trapped” particles may not be trapped a t all but are just in transit through the tubes. If we TABLE XVIII. THEDUMPINGHYPOTHESIS APPLIEDTO AN IBC I11 AURORA ENERGYOF ELECTRONS = 10 kev. (VELOCITY = 6 X lo9 CM S E C - ~ T = 3 x 10’’ CM-’ SEC-I)

t (secs) for n = 1 .r (sec) t/T Latitude [Eq. (5)] [fromEq. (6)] n = 1 5 10 15 20 25 30 35 40 45 50 55 60 65 70

0.002 0.005 0.008 0.013 0.022 0.037 0.066 0.126 0.26 0.59 1.45 4.79 19 107

0.009 0.019 0.030 0.043 0.059 0.079 0.104 0.137 0.182 0.245 0.337 0.478 0.713 1.147

0.22 0.28 0.27 0.30 0.37 0.47 0.63 0.92 1.43 2.41 4.30 10.0 26.6 93.3

t/.r

n

=

10

2.2 2.6 2.7 3.0 3.7 4.7 6.3 9.2 14.3 24.1 43.0 100 266 533

log Q (max) in rayleighs for t = T n = l 4.34 4.38 4.42 4.49 4.57 4.68 4.81 4.96 5.15 5.38 5.66 6.00 6.43 6.97

interpret t / r as the number of one-way transits over a half tube then only about 6 round trip oscillations of an electron could occur for n = 1 cm4 in the event of an IBC I11 aurora in the auroral zone, if dumping only is assumed. 3. The Local Acceleration Hypothesis. Even in the auroral zone bright auroras are the exception rather than the rule.’* Let us consider the general case for which the characteristic time, t, may be taken as 12 hr l 8 According to a study by Roach and Rees (22) of the distribution of zenith 5577 A intensities a t College, Alaska, near the auroral zone, the median value is 2400 rayleighs (an IBC I aurora) and the aurora IT1 or brighter intensity is observed only 0.4% of the time.

40 ( t = 4.32 X

F. E. ROACH

lo4 sec). Solving Eq. (5) for n yields n =

3

x

106Q . t

V

I n order to compare with observational results, we utilize the variation of Q median (5577) with magnetic latitude from Table XI11 from which a working plot yields entries of the second column of Table XIX. M A X I M U M POSSIBLE INTENSITY OF

W 0 5 -1

1

fBCIII, 10

,

I

, , ,

20 30 40 5 0 60 70

1

ao 90

MAGNETIC LATITUDE

FIG. 20. Predicted intensity of 5577 A intensity according to latitude for an electron density in the magnetic tubes of I 0111-3 according to Eq. (4).

I n Fig. 21 is shown a plot of the values of n deduced from Eq. (7) as a function of the height, h, above the earth’s surface to the equatorial crossing of the magnetic line of force (assuming that the tubes terminate a t a height, h’, of 500 km). An inspection of the plot of the n-values based on the observed points encourages a comparison with the values of equatorial n on the topside of the F-layer maximum. I n Fig. 21 the smooth solid curve is from a recent report by Bowles (55) and the dashed extrapolation is from a study by Lenchek et al. (56). The Lenchek et al., data were fitted to those of Bowles a t h = 6000 km. We recapitulate the assumptions implicit in the use of Eq. (7), namely, (a) Chamberlain’s value for the flux of -10 kev electrons re-

41

THE NIGI-ITGLOW

quired t o produce a 100 k R intensity, i.e., 3 x 10'" electrons cm-2 sec-I which led to Eq. (4);(b) the assumption of a 12-hr characteristic time; and (c) the assumpt!ion that the tubes end effectivelyat a height of 500 km above the earth's surface. TABLEXIX Latitude

Q (5577) (raylcighs)

log n (cm-9 [from Eq. (7)]

5 10 15 20 25 30 35 40 45 50 55 60 65

200 220 230 220 220 250 260 280 275 315 570 1300 2500

4.63 4.28 4.12 3.82 3.63 3.46 3.23 2.99 2.68 2.36 2.24 2.06 1.78

I

I

2

I

I

I

I

3

4

5

6

LOG ne ( ~ r n - ~ )

FIG.21. Comparison of observed equatorial thermal electron density and that predicted by Eq. (7).

We face a dilemma: The general argument is based on a flux of energetic (-10 kev) electrons, whereas, the estimate6 of equatmial electron densities refer to ambient and approximately thermal electrons (57). A solut,ion to the dilemma may be that the hypothesis of "dumping" of energetic electrons

42

F. E. ROACH

must be abandoned in favor of a mechanism based on local acceleration (possibly by atmospheric electric fields) of thermal electrons. For a critical discussion of some of the ideas presented in this last section, the reader is referred to recent papers by O’Brien (58),and by Roach (59). XIV. CONCLUDING REMARKS

A review article in a rapidly developing field probably never seems adequate to its writer. A quarter century ago the terrestrial component of the night sky which we now call nightglow was of only passing interest to a few investigators, many of them astronomers who were concerned with the blackening of their photographic emulsions on long exposures. Today there is a significant concentration of effort, and even a systematic listing of pertinent references over the past decade would be a sizable chore. It is the writer’s feeling that the questions have increased more rapidly than the answers. I n particular, it seems unfortunate not t o be able to make definitive statements on such a prime matter as the excitation mechanism responsible for the individual emissions. If the purpose of a review article is to encourage another writer a t some other time to fill in the gaps and do a superior job, then the present exposition of our vast ignorance surrounding our limited knowledge may be useful.

References 1. C. T. Elvey, Astrophys. J. 111, 432 (1950). 2. J. W. Chamberlain, Astrophys. J. 134, 401 (1961). 3. Lord Rayleigh, Proc. Roy. SOC.8129, 458 (1930).

4. I. G. Yao, in “Observations of the Night Airglow During the IGY-IGC” (F. E. 5.

6.

7. 8. 8. 10.

11. 12. 1s.

14.

Roach, ed.), Vol. 24 of the Annals of the International Geophysical Year. Pergamon Press, 1962. D. M. Hunten, F. E. Roach, and J. W. Chamberlain, J . Atmospheric Terrest. Phys. 8, 345 (1956). J. W. Chamberlain, “Physics of the Aurora and Airglow,” Intern. Geophys. Ser., Vol. 2. Academic Press, New York, 1961. V. I. Krassovsky, N. N. Shefov, and V. I. Yarin, “Atlas of the Airglow Spectrum 3000 to 12,400 A” Planetary and Space Sci. 9, 883, 1962. W. A. Hiltner, Trans. Intern. Astron. Union 9, 687 (1955). W. A. Baum, Trans. Intern. Astron. Union 9, 681 (1955). F. E. Roach, L. R. Megill, M. H. Rees, and E. Marovich, J . Atmospheric Terrest. Phys. 12, 171 (1958). R. B. Dunn, and E. R. Manring, J . Opt. SOC.Am. 46, 899 (1955). H. D. Babcock, Astrophys. J. 67, 209 (1923). D. M. Packer, Ann. Geophys. 17, 67 (1961). P. J. Van Rhijn, Pub. Astro. Lab. Groningen, No. 31 (1921).

THE NIGHTGLOW

43

J . W. Chamberlain, and C. A. Smith, J . Geophys. Research 64,611 (1959). A. B. Meinel, Astrophys. J. 111, 207 (1950). F. E. Roach, and H. B. Pettit, J . Geophys. Research 66,325 (1951). F. E. Roach, E. Tandberg-Hanssen, and L. R. Megill, J . Atmospheric T’errest. Phys. 13, 113 (1958). 18. F. E. Roach, E. Tandberg-Hanssen, and L. R . Megill, J . Atmospheric Terrest. Phys. 13, 122 (1958). 19. D. Barbier, Ann. Geophys. 16, 143 (1960). 80. C. E. McIlwain, J . Geophys. Research 66,3681 (1961). 81. B. P. Sandford, J. Atmospheric Terrest. Phys. 24, 155 (1962). 88. F. E. Roach, and M. H. Rees, J. Geophys. Research 66, 1499 (1960). 83. F. E. Roach, J. W. McCaulley, E. Marovich, and C. M. Purdy, J . Geophys. Research 66, 1503 (1960). 84. D. Barbier, in “The Airglow and the Aurorae” (E. B. Armstrong and A. Dalgarno, eds.), p. 54. Pergamon Press, New York, 1955. 86. D. Barbier, Ann. Geophys. 17, 3 (1961). 86. D. Barbier, Ann. Geophys. 14, 334 (1958). 87. B. J. O’Brien, J. A. Van Allen, F. E. Roach, and C. W. Gartlein, J . Geophys.

16. 16. 16a. 17.

Research 66, 2759 (1960). 88. F. E. Roach, J. G. Moore, E. C. Bruner, H. Cronin, and S. M. Silverman, J . Geophys. Research 66,3575 (1960). 89. J. G. Moore, and F. K. Odencrantz, J . Geophys. Research 66,2101 (1061). 30. M. H. Rees, J. Geophys. Research 68, 175 (1963). 31. T. Tohmatsu, and F. E. Roaoh, J . Geophys. Research 67, 1817 (1962). 38. F. E. Roach, and E. Marovich, J . Research Natl. Bur. Standards 63D,297 (1959). 33. F. E. Roach, D. Barbier, and R. A. Iluncan, Ann. Geophys. 18, 390 (1962). 34. D. Barbier, Ann. Geophys. 16, 544 (1960). 36. J. R. Roach, J . Research Natl. Bur. Standards 67D, 263 (1963). 36. J. W. Warwick, unpublished material. 37. G. A. M. King, and F. E. Roach, J. Research Natl. Bur. Standards 66D, 129 (1060). 38. D. Barbier, Compt. rend. acad. sci. 246, 1559 (1957). 39. A. Delsemme, and D., A n n . Geophys. 16, 507 (1960). 40. S. Chapman, Proc. Roy. SOC.A132, 353 (1931). 41. C. A. Barth, and A. F. Hildebrandt, J . Geophys. Research 66,985 (1961). 42. W. J. Schade, and J. Kaplan, Presentation a t IUGG Conf., Helsinki, 1960. 43. R. A. Young, and K. C. Clark, Phys. R e v . Letters 6, 320 (1960). 43a. C. A. Barth and M. Patapoff, Astrophys. J. 136, 1144 (1962). 44. G. Herzberg, J . Roy. Astron. Soc. Can. 46, 100 (1951). 46. D. R. Bates, and M. Nicolet, J . Geophys. Research 66, 301 (1950). 46. V. I. Krassovsky, Uspekhi Fiz. N a u k 47,193 (1952). 47. T. Tohmatsu, Rept. Ionosphere Research J a p a n 12, 253 (1958). 48. S. Chapman, and J. Bartels, ‘lGeomagnetism.” Oxford Univ. Press (Clarendon), London and New York, 1940. 49. N. P. Carleton, and L. R. Megill, Phys. Rev. 126, 2089 (1962). 60. L. R. Megill, and N. P. Carleton, Paper presented a t Gaseous Electronics Conf., Boulder, Colorado, 1962. 61. L. R. Megill, M. H. Rees, and LeAnn K. Droppleman, Planetary and Space Sci. 11, 45 (1963). 68. W. B. Hanson, and I. B. Ortenburger, J . Geophys. Research 66, 1425 (1961).

44

F. E. ROACH

63. S. Chapman, and M. Sugiura, J. Geophys. Research 61, 485 (1956). 64. B. J. O’Brien, and C. D. Laughlin, “Electron Precipitation and the Outer

Radiation Zone,” State University of Iowa, Iowa City, Iowa, Report SUI 62-9 (1962). 66. K. Bowles, Private communication; for similar curves Bee N B S Technical Note 169, March 16, 1963. 66. A. M. Lenchek, S. F. Singer, and R. C. Wentworth, J. Geophys. Research 66, 4027 (1961). 67. K. L. Bowles, G. R. Ochs, and J. R. Green, J. Research Natl. Bur. Standards 66D,395 (1962). 68. B. J. O’Brien, J. Geophys. Research 67, 3687 (1962). 69. F. E. Roach, J. Geophys. Research 68, 1015 (1963).

Recent Developments in Computer Organization F. P. BROOKS, JR. I B M Corporation, Poughkeepsie, New I-ork Page

I. Introduction., . . . . . . . . . , , . , . . . . . . . . . , . , . . . . . . . . . , . . . . . . . . . . . . . . . 45 11. Metaprograms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 A. Effect on Computer Organization.. . . . . . , . . . . . . . . , . . . , . . . . . . . , . . , 46 ,

B. Types of Metaprograms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111. Multiprogramming.. , . ......................................... A. What and Why.. , . ... ..... ................. B. Batch Multiprogramming. . . . . , . . . . . . . . . , . . . . , , , . C. Man-Machine Systems., , . . . . . . . . . . . . . . . . . . , . , , , . . . . . , . . . . . . . . D. Real-Time Multiprogramming. , . . , . , , . . , . . . . , . . . . . , . , , . , . . . . , . , E. Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IV. The Content-Addressed Memory, . , . . . , . . . . . . . . . . . . . , . . . . . . , . . . . . . . . A. What and Why . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B. Uses of Content-Addressing., . . . . . . . . . . , . . . . . . . , . . . . . , . . . . . . . . C. Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V. The One-Level Memory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. What and Why . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B. The Block Addressing System.. . .. , . . , . . . . . . , , . , ....,.... . ... . . C. Drum Transfers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D. Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ............ VI. Last-In-First-Out Register Stacks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. What and W h y . . . . . B. Advantages.. . . . , , , . C. Problems _ . . . .. , , , . , . . . . . . . . . , . . . . , . . . . . . . . . . . . . . . . ................... I). Evaluation. . . . . . . . . VII. The Fixed-Plus-Variable omputer . . . . . . . . . . . . . A. What and W h y . . . . . ................................. B. Results to D a t e . , . , , . . . . . , . . , , , . , . . . . . . . . . . . . . . . . . C. Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...... ...... References . . . . . . . . . _ . . , . , , . , . . . . . . . . . . . . . . . . . . . . . . . . . . . ,

,

,

, ,

,

,

47 49 50 51 52

52 52 53 54 55 55 56 57 58 59

62

64 64

I. INTRODUCTION The historical development and fundamental principles of computer logical organization were reviewed in this series by Lawless in 1959 ( I ) . Developments over the next two years were reviewed elsewhere in some detail by Beckman, the author, and Lawless in a 1961 paper ( 2 ) . It is the purpose of this paper to present and discuss the principal developments 45

46

F. 1’. BROOKS, JR.

since the writing of the 1961 paper, and to comment on the flowering of trends remarked then in the initial stages. The period has been marked more by consolidation and the widespread adoption of ideas introduced in earlier periods, than by the active introduction of new concepts. For example, such innovations as various forms of abbreviated addresses in instructions, concurrent operation of different computer sections, program interruption systems, etc., have been almost universally adopted during this period. Many forms, modifications, and embellishments of basic concepts have appeared, but these have reflected rather the various tastes and objectives of the large number of computer design teams now practicing, than the appearance of new understandings and concepts. The source of innovations in computer organization has substantially changed in recent years. Very few university groups are now building computers, partly because of the subtle and expensive technologies now used, partly because powerful and reliable machines are available to them a t reduced prices. A principal source of experimentation and thought on computer organization has thus diminished. Within commercial ranks, the compctition of an increased number of manufacturers has led to many innovations, which have, naturally, first appeared in the very large computers. Not only the source, but also the form of innovation has changed. Whereas new concepts used to be described in papers introducing the machine embodying the concept, now the concept is much more apt to be investigated theoretically and by computer simulation than by hardware modeling. This is a healthy development, for the evaluation of an organizational concept does not demand a model, and organizational ideas are earlier seen and more cheaply evaluated independently of technological innovations. Most of the recent developments to be described have not yet been embodied in operating machines; several probably will never be so embodied, due to lack of advantage over established techniques. 11. METAPROGRAMS A . E f e c t on Computer Organization No change in the use of computers has been more profound than the universal adoption of metaprograms (or programming systems, or software), which accept other programs as operands and/or produce other programs as results. As a consequence of this decade-long development, most users rarely concern themselves with the actual organization of a computer: they rarely see data represented in bits, rarely use actual addresses, and

RECENT DEVELOPMESTS I N COMPUTER ORGANIZATION

47

often use programming languages only indirectly related to elementary machine functions. Several important consequences follow :

(1) Computer organization iiced not be optimized for programmer convenience. ( 2 ) Rletaprogram operat>ionmay constitute 2-50% of the problem-solving cost,. (3) Computer organization nceds to be general and uniform so th a t similar functions are performed in similar manners, for metaprogram simplicity. (4) Operations often performed by metaprograms must be facilitated. This last consequence, in particular, serves as the principal motivation for most recent developments in computer organization. In order that these motivations be understood, we briefly review the elements of programming systems.

B . Types of Metaprograms 1. Supervisors. Much computer time can be wasted by a human operator who loads input-output devices for each job, starts and stops operation, logs time use, removes the program should errors or mistakes be detected, and removes the program when complete. This loss has been aggravated as computers have gotten faster, for typical job length has declined from hours to 1-5 min. A mrtaprogram called a supervisor (or monitor) is often used to perform most of the functions of the operator, other than loading and unloading input-output devices. The supervisor, as executed by the computer, loads the problem program, starts it, accounts for time, provides output indications for errors, ensures that the problem program does not exceed some specified time, etc. Some or all of the supervisor niay remain in the computer fast memory during problem program execution. In order to carry out these functions, the supervisor metaprograrn requires computer organization characteristics not provided on early machines: access to a clock, the ability to interrupt a problem program, protection of the supervisor itself from problem program faults, and others. 2. Input-Output Control Systems. Input-output devices and channels are the most difficult computer facilities to use-the more so i n modern machines, where they operate concurrently with and interlocked with the main program. Furthermore, the input-output functions desired by the user are peculiar to the devices available, not to the problem being solved.

48

F. P. BROOKS, JR.

An input-output control system (IOCS) is a set of programs and subroutines which permit a user to state his needs in broad terms (GET record, P U T record, etc.), and which handle the details of buffer storage assignment, i.-0. instruction initiation, handling of end and error conditions, grouping of records, labeling of tapes, etc. Much of the IOCS metaprogram will remain in memory during problem program execution. To carry out these functions, the IOCS requires a suitable set of interlocks, indications of events, ability to interrupt the main program, and full programmed control of input-output functions. 3. T r a n s l a t o r s A s s e m b l e r s and Compilers. A translator accepts a program stated in some specified language designed for programmer convenience and produces the same program stated in machine instructions. I n simplest form, the translator accepts a set of statements each of which corresponds to a machine instruction. It translates the operation from some convenient mnemonic specification to the code used in the computer. It also assigns storage space to or determines the earlier assignment made for the operands, specified by convenient symbols, translating the symbols t o the proper absolute addresses. Such a translator is called a n assembler. An assembler carries out its functions mostly through the construction of and reference to tables-e.g., tables of operator symbols, tables of storage assignment. A compiler is the most general form of translator. It differs from the assembler in possessing the following facilities to make the argument language easier to use: (1) Each elementary operation of the argument language may correspond to a multistatement program (a subroutine) in the function language rather than to a single elementary statement. This permits the definition and use of a virtually arbitrary set of elementary operations in the argument language. Functions such as sin 2, and loglo 5 can, for example, be incorporated as the elementary operations SIN and LOG. (2) The individual statements of the argument program may be compound in the elementary operations of the argument language. The programmer may use directly a compound algebraic statement such as x + u(v w SIN (z y ) ) . The burden of analyzing this into its elementary components is assumed by the metaprogram. (3) The representation used €or the operands is not constrained to a single pattern, but may vary widely. Consequently, the argument language must include declarative statements to specify the representations of the variables. Each imperative statement refers to each

+

+

RECENT DEVELOPMENTS IN COMPUTER ORGANIZATION

49

operand by a single name-the particulars of the representations are automatically considered in the analysis of the statement. Furthermore, the separation of the representation and the processing descriptions permit easier modification of each. (4) The imperative statements of the argument program are not constrained to be independent or independently translatable. The type of interdependence is usually limited as follows : certain control statements specify the sequence of execution of other statements, the values of certain of their parameters, or the formats of their operands. The span of a control statement (i.c., the set of statements controlled) may include other control statements. These compiler facilities not only make the argument language more useful; they also make the metaprogram more complex. To carry out these functions, a compiler needs not only table reference facilities but also facilities for scanning, character-by-character, argument language statements. It is also advantageous for the computer to furnish looping and data description facilities analogous to those of the argument language.

111. MULTIPROGRAMMING A . What and Why A fast computer may be time-shared among slow users or slow inputoutput devices, each of which has a separate program. This time-sharing among several programs is called multiprogramming. Since input-output time is often long with respect to computing time, a machine with several i.-0. channels and many devices can improve throughput by multiprogramming. If the set of problems to be run is known in advance, the multiprogramming supervisor can determine th a t schedule of time-shared execution which will minimize the total execution time for the batch. This is called batch multiprogramming. Far greater promise lies in the use of multiprogramming for several users, each operating the computer as if it were a single-machine, and participating in the solution of his problem. This real-time multiprogramming does not allow scheduling to tie done in advance, and thus poses new problems. Recent developments have thoroughly borne out the early expectations and give high hopes for the future of these developments. A batchtype multiprogramming supervisor has been written and run, and statistics on throughput improvement gathered. A real-time multiprogramming system has also been put into operation. Furthermore, other studies, done with one user on a machine, have demonstrated the great

50

F. P. BROOKS, JR.

improvement in problem-solving performance which can be realized by close man-machine cooperation. This is relevant, for such use of a powerful computer is only economically feasible through multiprogramming.

B. Batch Multiprogramming Several computers, including the Honeywell 800 ( 3 ) ,the Bull Gamma60 (4, and the IBM 7030 (Stretch) (5) have been so designed that multiprogramming could be done. So far as has been reported in the literature, experimentation and statistics-gathering has only been done for the 7030. Codd and a group of co-workers designed, wrote, and operated a multiprogramming supervisor which included a scheduler with various optional optimizing techniques (6-8). The principal results are : (1) On sets of eleven problems, each of which used tape extensively, the ratio of uniprogramming time to multiprogramming time was 1.5. (2) On a set of ten problems which used the CPU extensively, the disk moderately, and tape lightly, the ratio was 1.3. (3) On a 14-problem mixture of the first two sets, the ratio was 2.0. (4) The simple fact of multiprogramming accounted for most of the gain; the various optimizing techniques were only mildly effective. (5) On the average 2.7 programs were active at once. ( 6 ) The supervisor used the CPU on the average 12.4% of the multiprogrammed elapsed time. (7) Average time for processing an interruption was 1 . 8milliseconds. (8) The supervisor used some 14,000 words of core memory, which could be reduced in a second version.

C. Man-Machine Systems Many old-time scientific computer users have experienced the insight that comes through doing a numerical analysis calculation oneself, with a desk calculator. The same insight, to a lesser degree, is available to the user of a small computer, which can cheaply be made to stop and display intermediate results to the waiting user. There has been until recently no work at measuring or demonstrating the practical utility of the insight given by close man-machine interaction during problem-solving. Licklider and Clark, however, recently described several interesting experiments which demonstrate, but do not measure, this utility (9). I n the first set, a teaching machine was simulated by a small computer equipped with a display unit and a light-pen for input corresponding to

R E C E N T DEVELOPMENTS I N COMPTWEIt ORGANIZ.kTION

51

the display. The experiment indicated that fast, convenient response by the computer was crucial to the holding of the student’s interest. I n a second set of experiments, the graph of ail equation is continuously displayed while the student adjusts the coefficients. There is some indication that the immediate, convenient response stirs questions more effectively than other methods, and that the dynamic visual image conveys the relationships more effectively than other methods. I n a third set of experiments, the computer and display device have been used by hospital architects as visualizing and sketching tools. The computer analyzes and displays not only the layouts postulated, but also the patterns of traffic known for earlier layouts and calculated for the postulated one. The computer also straightens and aligns the users’ sketched-in alterations. The users of this tool attest to its power; no measurements have been made. Culler and Huff have reported on similar experiments (10). The Bardeen-Cooper-Schrieffer integral equation, nonlinear, hitherto unsolved for the cases a t hand, and not amenable to ordinary computer solution, was solved with the aid of a computer, a display console, a good physicist, and a set of simple programs giving the operator the desired manipulations of the solution paramcters. The paper indicates quite convincingly the peculiar effectiveness of the man-machine combination on such problems.

D. Real- Time Multiprogramming I n a recent paper, Corbato and his colleagues have reported the successful operation of a real-time multiprogramming system, designed to give the users of the M I T computer center simultaneous access to a n I B M 7090 ( 1 1 ) . A principal motivation is ease of program debugging; heavy use of the kind of problem-solving techniques described in Section 111, C above is also anticipated. The 7090 is modified to have the necessary functions: a clock, a memory protection system, a dynamic program relocation system, and supervisory program control over input-output operations. The supervisor now operating will allow three on-line computer users (the foreground) to be interleaved with each other and a background user, consisting of a conventional sequential supervisor with a batch of nonreal-time problems. The supervisor requires 5000 words of memory. The rest of memory is given entirely to one user a t a time, and users are swapped a t intervals of not less than 16 msec and are guaranteed a worsecase response time of 32 see. This gives a switching overhead on the order of 1%. Small or short programs get)better service, and the algorithm for scheduling is described.

52

F. P. BROOKS, JR.

E. Evaluation The new development in all areas of multiprogramming is actual experience, in place of the speculation and planning that have so long filled the literature and convention hall. No development could be more welcome. Furthermore, the experience has been encouraging. One expects that the throughput improvement from batch multiprogramming will rarely justify the effort, supervisory program space, etc., entailed, and that this approach will be used only on very large systems, if there. The techniques developed, however, apply in most cases to the real-time multiprogramming problem; and the experience in hand is both useful and instructive. Real-time multiprogramming as a means towards realizing closer man-machine coordination during problem solving is very promising. This development will probably constitute the next fundamental and widespread change in the way scientific computing is done. IV. THE CONTENT-ADDRESSED MEMORY A . W h a t and W h y Because an assembly metaprogram consists essentially of the translation of arbitrary symbols into storage addresses, and because similar operations arise in problem programs, it is often suggested that this function be built into computer hardware. The mechanism needed is a content-addressed (or associative) memory. Such a memory has at least some part (the key) of each word equipped so that the keys of all words can be simultaneously compared against a n argument key. Whichever word has a key matching that of the argument is then fetched or replaced. Double match may indicate error or may be resolved by priority rules. No match may indicate a n error or may control the allocation of an empty memory word to the new datum. The basic content-addressing function requires that each memory word undergo a comparison. For speed, a t least each word needs to be equipped with a comparator. If each bit of each word is so provided, the access time of the memory is somewhat, but not necessarily much longer than for a conventional memory built of the same technology. About two or three times as much equipment is required as in a conventional memory of the same capacity and technology. Small memories of this organization have been constructed in present-day technologies; fullsized ones constructed of cryotrons have been described in some detail, but not yet built (12). Petersen (13) and his associates have described a n N-word contentaddressed memory in which each of the N simultaneoua comparisons is

RECENT DEVELOPMENTS I N COMPUTER ORGANIZATION

53

performed bit-by-bit. This substantially reduces the amount of equipment, but the access time is raised by a factor of five or so, due to the serial nature of the comparisons. Beyond the equipment required for the comparisons, a content-addressed memory has extra equipment in the capacity required for storing the keys, which need not be stored in a coordinate-access memory. Content-addressed memories are usually equipped with conventional coordinate-addressing circuits as well, and these are used in handling duplicate entries, storing new entries in empty cells, etc. The utility and cost of a content-addressed memory are greater if the key field can lie anywhere in each word, i.e., if each bit of each word may be compared and if comparison is controlled by a mask word associated with the argument.

B. Uses of Content- Addressing Any memory serves as a symbol translation device. On a read operation, one furnishes a symbol of specified range, the address, and one receives the correspondent previously stored. On storing, one enters a symbol and a correspondent, and the symbol is redefined to the correspondent. A content-addressed memory augments this function in two important ways: (1) The symbols used are far less constrained; in particular, the range of the symbols may greatly exceed the capacity of the memory; ( 2 ) the same stored datum may be fetched with any of several key symbols. T o illustrate these two points, let us consider a memory of 212 (4096) words, each containing 64 bits, with full comparison. Within the word must be stored both the key or keys and any desired correspondent. If, for example, a correspondent of 22 bits is desired, a key of up to 42 bits may be used. Therefore, one may address such a memory with any set of 4096 42-bit symbols, each composed, for example, of seven alphabetic characters. This gives a far wider choice of address symbols than the corresponding conventional memory, where only the numbers 0 to 4095 may be used. The same content-addressed memory may be used to perform the inverse translation. Th at is, it may be referenced with a n argument correspondent of 22 bits, and the associated symbolic key will be fetched. Alternatively, such a memory word might contain several fields, such as an air traveler’s phone number (28 bits), date (9 bit,s), flight number (7 bits), destination (8 bits), and an address in a disk file where his name, etc., are stored. Then one may retrieve from the memory the record of a

54

F. P. BROOKS, JR.

particular passenger, or of passengers on a particular flight, or of passengers for a particular city, etc. Finally, a content-addressed memory may be used as a large comparison unit-a succession of arguments may each be quickly tested for the occurrence of any of a set of values.

C. Evaluation The outlook for content-addressed memories can be calculated by analyzing the uses, alternative means of accomplishing the same functions, and costs. One concludes that such memories will find numerous and important special-purpose applications, and that the principle is unlikely to be adopted for main memories of general-purpose computers. As a multiple comparator, the content-addressed memory is quite essential in some special-purpose devices, and will be used. As a symbol translator, the content-addressed memory is justified only when its special function is used most of the time, i.e., in onc or another special-purpose application. One such special application which will be widely copied occurs in the one-level memory to be described in Section V below, where a small content-addressed memory translates the highorder bits of each reference to main memory in the hlanchester-~errariti Atlas, a very large, general-purpose scientific computer. The special properties of a content-addressed memory are not needed for a high fraction of the operations required of a general-purpose computer's main memory, For example, even though the symbol translation function could eliminate most of the functions of an assembly program, this does not justify the added cost, for the symbol translation need be done only on human entry or inspection of a program-very rare events compared to"memory accesses. The content-addressed mcniory, however, pays the cost of translation in time or money each time a datum is accessed. When symbol translation is needed, the programmed methods are quick and efficient, requiring on the order of 10-40 memory references per translation. Similarly, fetch of a datum by different keys, the most powerful use of a content-addressed memory, occurs as only a minuscule fraction of all operations. To be sure, the existence of a content-addressing facility would increase the fraction severalfold, as a new highway builds total traffic. Nevertheless, the function itself is, and can be expected to remain, a minor part of all data processing operations. When it is needed, there are many programming techniques which give the function a t lower cost (when weighted by the frequency of use in general computation) than hardware mechanization.

RECENT DEVELOPMENTS IN COMPUTER ORGANIZATION

55

V. THE ONE-LEVELMEMORY A . What and Why A‘computer needs rapid access to memory and access to a large capacity of memory. Fast memory technologies cost more per bit than slow memory technologies. Moreover, in any program, the frequency of use of both instructions and operands is far from uniform; indeed, the frequency declines sharply and smoothly from the most-often to the least-often used instructions and data. These three facts have always dictated hierarchical memories of two or usually more levels-smaller, faster memories for frequently used data, and larger, slower memories for cheap accommodation of all the data needed. A hierarchy always poses addressing problems : one continuous address sequence versus several, allocatioii of levels to problem quantities, indexing within a n array only partly contained in fast memory, etc. The wide access-time gap between core memories (0.75-20 psec) and mechanical memories (5-1000 msec) has heretofore let the latter masquerade as input-output, with most of the hierarchy addressing problems ignored. Several contemporary trends have made this classical approach to the hierarchy problem obsolete. (1) Technology now makes more than two levels feasible and desirable. Registers, very fast local memories, 1000-word fast core memories, and large 3-dimensional core memories are already available a t costs appropriate for speed and capacity. (2) New memory approaches promise to bridge the cost-speedcapacity gap. With this bridging, the convenient dichotomy between “internal” and “external” memories disappears. Neither direct addressing nor the clumsy tape and disk addressing techniques will serve for a very large 200-psec memory. (3) Most important, the obvious economic advantages of memory hierarchies are offset by the considerable programming difficulties entailed in using such a n arrangement. Because efficient use is very difficult, inefficient use is very common; and this inefficiency partially offsets the performance/cost advantages of the hierarchy. Even so, the economics are so clear that hierarchies are here to stay. Inefficient or difficult use of them remains, therefore, as a principal problem to be solved by the computer-compiler architect. Users increasingly demand t ha t supervisors and compilers make various memory levels indistinguishable to the user, efficiently allocated among problem segments, and efficiently exploited during problem execution. In short, a physical

56

F. P. BROOKS, JR.

memory hierarchy must be made to appear as a one-level memory. This overwhelming task requires not only superb software, but also suitable computer architecture. Some attempts to devise effective memory-allocation and automatic memory-to-external-store transfer programs have been made (14). None of these is in common use. Kilburn and his associates a t the University of Manchester have attacked this problem frontally, carefully, and successfully in the design of the Atlas Computer (15). The complete hierarchy consists of registers, a 0.7 psec memory for 120 index registers, a main core store of about 16,000 words, a drum of about 96,000 words with rotation time of 12 msec. and data rate of one word each 4 psec, and magnetic tapes. The main core memory and the drum are together organized into a single central store, with built-in, automatic provisions for transfers between them and for allocating the main core store to the most often used data. The system also provides for locking problem programs out of specified memory areas. Further, it provides for automatic relocation of addresses in a program as it is executed, so that program and data may be independently placed in any blocks of core storage as they are loaded from the drum. This facility is especially useful in multiprogramming, for it permits several programs to share the machine without constraint as to their locations when they are executed.

B. The Block Addressing S y s t e m The Atlas central store is divided into blocks of 512 48-bit words each. I n the first copy of the machine, there are 32 blocks of core storage (called pages) and 192 blocks of drum store. The addresses used in instructions consist of 24 bits of which 3 are used to address word subdivisions and 1 distinguishes between the central store and various subsidiary stores. The high-order 11 bits of each central-store address serve as a block address, and 2048 different blocks are therefore addressable (a total of some one million words). Since the number of addressable blocks substantially exceeds the capacity of the machine, each of a set of various programs which might a t some time share the machine can be permanently assigned a set of block numbers for its exclusive use. A content-addressed memory consisting of 32 transistor registers is used to translate between the block number given as part of each address and the actual page of core memory currently containing that block. These Page Address Registers ( P A R ) each contain an 1l-bit key-the block number, and a 5-bit correspondent-the page number. Whenever an operand address is presented to the central store, its

RECENT DEVELOPMENTS IN COMPUTER ORGANIZATION

57

block number is compared against the PAR’s. If an equivalence is found, the page number is substituted for the block number presented. This accomplishes the automatic relocation function. The time consumed in this process is mostly overlapped with the execution of other instructions. Instruction addresses are not so translated before access is initiated; a special register holds the page number for the instruction counter. This is used to initiate the access, during which the block number is translated in the usual way and the result compared against the page number used. If it does not match, the instructions fetched are not executed. Each PAR also contains a lock-out bit which can be set by the supervisory program. This is used to accomplish memory protection between problem programs. If the PAR’s contain a match for the block number presented but the lock-out bit is on, the desired block is unavailable to this program, and the supervisory program is notified and put into execution. When the block number presented does not match any block number in the PAR’s, the desired data is not currently available in the main core store. The supervisory program is notified and put into execution. It fetches the desired block from the drum into an empty page position and stores some page onto the drum to free a page position for the next transfer.

C. Drum Transfers Computer delay due to transfers between the slow-access drum and core is minimized by four techniques: (1) The reading of a block is performed before the emptying of a page onto the drum, This requires that one page of core storage be always empty, hence wasted; but it permits the program calling for the drum block to recommence after one drum transfer, not two. (2) The transfer program can identify the angular position of the drum. It maintains a register showing the location of each block. It can therefore predict when the transfer will occur. After performing all the tasks incumbent upon transfer initiation, the transfer program passes the computer to the supervisor, which may proceed in executing some other problem program while awaiting the transfer of the accessed block. ( 3 ) The supervisor includes a learning program which keeps a record of the activity in each page. This is facilitated by a use bit in the PAR which is turned on by access to that page and is turned off when the supervisor reads it.

58

F. P. BROOKS, JR.

After the sought block has been put into a core page, the learning program compares the interval since last activity with the duration of the most recent previous inactivity. On this basis it selects the page “most likely” to be inactive and initiates its transfer to the drum. This frees a page position for the next read. I n simulation trials, this learning program was found in every case to minimize core-drum transfers as well as experienced programmers writing general problem programs. It did only moderately worse (16% in the case reported) than an experienced programmer writing specifically for one particular set of data array dimensions, etc. (4) The page transferred to drum is written in the first empty block position to minimize access time, and the transfer program accordingly updates its table of block locations on the drum.

D. Evaluation The Atlas system for the one-level store is devised with skill, careful economic analysis, and thorough integration of hardware and programming techniques (If?). It is a n excellent solution to the problems attacked, for, of course, the speed and cost objectives of the computer. The by-products of memory protection and program relocation are desirable in any event. As by-products, their realization is satisfactory in function, highly economical in equipment, and elegant and graceful in their integration in the memory system. The execution time invested in the one-level store function is surprisingly modest. This is, however, largely due to the high degree of overlap in instruction execution, a degree which would not be present in a less ambitious machine. The time inefficiency is also small because of the skill and care with which the function is integrated with the rest of the machine functions. The equipment required is hardly modest-the 32 PAR’s constitute most of it, but 576 bits of register, with 352 bits of it comparing circuitry, is quite substantial. The system also uses to good advantage the read-only memory and other supervisory program facilities; but these are hardly chargeable solely to the memory system. The drum plus the one-level memory are quite probably cheaper than the cost of 96,000 more words of core store, so the system is amply justified for Atlas. On a more modest machine, the same function could be accomplished through the use of the main memory for storing a t least the supervisory program, and, a t greater saving yet, the PAR’s as well. This would reduce performance by a factor of two, but this could be a mode of operation, used when the problem required more memory than the main memory attached.

RECENT DEVELOPMENTS I N COMPUTER ORGANIZATION

59

The learning program for optimizing transfers will undoubtedly be modified many times after the system is put into operation. The system is designed with sufficient flexibility that the necessary modifications should not prove too difficult.

VI. LAST-IN-FIRST-OUT REGISTERST.4CKS A . W h a t and Why Most high-speed computers contaiii several central registers, usually realized in transistors or other logical elements, used for holding immediately needed operands and intermediate results. The stack of these registers constitute the highest-speed part of the whole memory hierarchy. The number of such central registers has a pronounced effect on performance, and a good portion of any program is devoted to loading and storing them. Furthermore, a compiler which is to produce efficient object programs spends a substantial part of its compiliiig time in allocating these registers. A uniform register handling discipline is therefore needed when several similar registers are available. The study of compiler construction led several workers to the realization that Lukasiewicz’ parenthesis-free iiotation (17) is applicable to the analysis of compound arithmetic statements. The algorithm used in generating and evaluating Lukasiewica’ notation statements also suggested that a last-in-first-out discipline for operand registers offered several advantages. The same discipline had previously proved useful in list-processing programs. As a consequence, this coiicept has been embodied in several new computer designs, most notably the English Electric KDF-9 and later the Burroughs B-5000 (18). Conceptually, a last-in-first-out (LIFO) stack (or pushdown store) is treated as a set of registers arranged vertically. New operands from memory are entered into the top register, as the contents of each register replace those of the register just below. (The stack is conceptually infinitely deep.) Those arithmetic operators using two operands take them from the top two levels of the stack, and return the result to the top level, causing a one-level pushup. The top level may be stored in main memory, with or without pushup. I n practice, of course, the data is not shuffled from register to register. A short counter keeps track of the “top” register, advancing whenever a new entry is made (a “pushdown”) and diminishing when a value is stored or discarded (a “pushup”). When the counter advances completely around the stack and addresses a n occupied register, its contents are stored in main memory, per a memory list counter. Likewise, when the

60

F. P. BROOKS, JR.

register counter, upon diminishing, addresses a n unoccupied register, it is filled per the memory list counter.

B. Advantages The LIFO stack offers four chief advantages: (1) Main memory data references are minimized. Algorithms exist for converting ordinary compound algebraic statements into Lukasiewicz' notation such that during evaluation all intermediate results are properly stored in the stack for later use. Further, algorithms exist for minimizing the stack depth required for any arithmetic expression (17'). As a consequence, expressions in such a form can be evaluated with only the references required to load the operands, store the final result, and provide for a minimum number of overflows of stack capacity. (2) Subroutine management is sharply simplified. A subroutine can freely use registers without storing and restoring their contents; the LIFO mechanism accomplishes that as required. Furthermore, the operands needed by the subroutine may conveniently be left in the top of the stack, and it may conveniently leave its results there. Because a subroutine needs no temporary storage of its own, it may be used recursively, i.e., in its execution it may transfer control to itself. This property greatly increases the generality and power of subroutine techniques. (3) Compilation from a source language is simplified, due to both of the foregoing properties. The algorithm for the analysis of compound algebraic statements becomes simple. Register allocation is automatically handled and need not be programmed. The recursive definitions used in rigorously defining such source languages as ALGOL can be adopted almost directly into recursive subroutines. Tests for wellformation of source statements are readily made by checking stack depth before and after statement or subroutine evaluation. (4) Programs are shortened due to the elimination of most operand addresses, the bulkiest part of the conventional instruction. For example, consider the evaluation of

which can be rewritten in parenthesis-free form as uuxaxczx y + b X +dul+/

-.

RECENT DEVELOPMENTS IN COMPUTER ORGANIZATION

61

The program is: 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

Load u Load u

x Load a

x Load c Load z X Load y

+

11. 12. 13. 14. 15. 16. 17. 18. 19.

Load b

x

+ Load d Load v Load 1

+

/

-

C . Problems The advantages of the LIFO stack are accompanied by some offsetting disadvantages, problems, and perplexities :

(1) All computing is not arithmetic expression evaluation. It turns out that in general work the item coming to the top of the stack is not always that needed next. No data have been published as to the fraction of such “surfacings” that are immediately useful, but it may be as little as one-half. (2) One needs more than one kind of stack. A subroutine needs, for example, to store the calling instruction’s location somewhere, and to use it for return. If it places this value on the arithmetic stack, it lies on top of any parameter values left by the calling sequence, and it is covered by any final result calculated by the subroutine. The obvious solution-an address stack and a data stack-iterates to give many stacks. (3) The data to be placed in the stack is not always of the same length. When only floating point quantities are used, all is well. When addresses, variable-length fields such as arise in commercial computing, or single characters such as are encountered in scanning source-language statements occur, the desired stack register properties are neither uniform nor clear. (4) If most or all of the stack is in main memory, no real performance advantage is derived-the principal advantage comes from the presence of registers, however used. ( 5 ) The program shortening likewise comes from the truncation of addresses of register-held operands, not from the mechanization of the LIFO discipline. Both of these last two points may be exemplified by a program analogous to that in Section VI, B, 4, which used a stack depth

62

F. P. BROOKS, JR.

of 4. This program is for a conventional single-address machine with 3 central accumulators (CR1, CR2, CR3), addressed by two-bits. 1. Load CR1 2. X CRl 3. X CR1 4. Load CR2 5. X CR2 6. CR2 7. X CR2 8. CR1 9. Load CR2 10. Load CR3 11. CR3 12. / CR2 13. CR1

+ +

+

u u a c

z

y b CR2 d v 1 CR3 CR2

This program requires 6 fewer instructions than the LIFO stack program, makes no more main-memory references, requires 3 more operand addresses, and 26 more bits of instruction for the register designation. D. Evaluation

I n sum, the LIFO stack constitutes a useful innovation in computer organization. The advantages of the scheme are greatest, and the disadvantages fewest, when it is applied to scientific computers sufficiently large to contain several transistor registers. For such machines the LIFO stack offers a consistent register use discipline, advantageous in compiling largely because of subroutine simplification. One can expect the LIFO stack to become an accepted and widely-used technique, but it probably will not displace older techniques. VII. THE FIXED-PLUS-VARIABLE-STRUCTURE COMPUTER

A. What and Why Estrin in 1960 proposed a Fixed-I’lus-Variable-Structure computer organization (19) consisting of a conventional large scientific computer (the fixed part F of the structure) plus a n inventory of high-speed substructures (the variable part V ) which can be interconnected in various ways, and thus specialized to assist in various problems. Thus one can use on any problem a special-purpose machine whose cost, though not justifiable by the proportion of that problem to the total workload, is shared with other problems which use the same V-inventory in different configurations.

63

RECENT DEVELOPMENTS IN COMPUTER ORGANIZATION

B. Results to Date Estrin and his co-workers have published four papers describing the F V structure in general and as organized for each of three special applications (19-22). I n the first application, the V-structure is organized for the fast, independent generation of random numbers. A random number can be generated in about 8 ksec by a small serial unit which operates concurrently with the rest of the computer. The equipment consists of some 26 bits of registers, plus gates and simple control. (The F structure, a 7090, has the equivalent of some 164 bits of register in its data flow.) I n a program for Monte Carlo matrix inversion, independent random number generation improves speed by some 17.3%. I n a program for calculating gamma-ray diffusion, independent random number generation improves speed by 7.4%. I n a second application, the V-structure is organized for the calculation of In x: and ez by a quite efficient sequential table-lookup (STL) algorithm devised by the authors. The results are shown in the table:

+

In x Equipment a in data flow Cycles Fastest previous program STL algorithm as programmed STL algorithm as done inFfV

Ir

exp x

-

Words of storage

Cycles

Words of storage

164

178

46

140

48

164

85

880

80

1002

355

14

1037b

17.5

1037b

1 adder = l)h register. One bank of storage for both functions.

I n an ext,reme case, gamma-ray diffusion calculation, the independent and rapid calculation of logarithms and exponentials reduces computation time by 19% over calculation with the programmed version of the STL algorithm, The V-structure would often be set up to calculate random-numbers and logarithms and exponentials in the same problem. I n a third application, the V-structure is organized to assist in the computation of eigenvalues and eigenvectors of real symmetric matrices V structure in 7090 components solves by the Jacobi method. The F the problem about 4 times as rapidly as does the 7090. The V-structure incorporates the equivalent of some 424 bits of register, plus gates (compared again to 164 bits of register in the 7090).

+

64

F. P. BROOKS, J R .

C. Evaluation The case for the F V structure consists of a series of papers, each of which attempts to demonstrate that the V-inventory is justified for a t least one organization, in problems that use that organization. The totality of papers undertakes to show that the same inventory can be used in many advantageous configurations, so that its provision is justified even though no one organization of the V-structure is useful in all problems. This is a logically sound case; if the two points stated be shown, the V-structure is eminently justified. Estrin and his co-workers are to be congratulated for their direct and straightforward approach to the evaluation of the postulated structure. As it stands, however, the case is far from convincing. (The proposition may nevertheless be true.) I n no one of the applications does the performance gain substantially exceed the factor by which CPU equipment is increased. The same equipment invested in speeding up the fixed 7090 functions might therefore have resulted in similar performance improvement, without the effort required to design the suitable organization and microsequence of the V-structure peculiar to each problem. Furthermore, the applications so far described do not use the same V-inventory. This means that the justification for each must include the cost of the largest inventory ever used. The concept is by no means unthinkable. I t would seem unlikely that the scientific computing field will produce the best examples of the power of the approach. Combinatorial problems of all kinds would be expected to show much more dramatic improvements.

+

References 1. W . J. Lawless, Jr., Advances in Electronics 10, 153-184 (1959).

8. F. S. Beckman, F. P. Brooks, Jr., and W. J. Lawless, Jr., Proc. I.R.E. 49, 53-66 (1961). S. S. D. Harper, Proc. Comput. Data Process SOC.Canada, June, 1960, pp. 321-331. 4. P. Dreyfus, Proc. Western Joint Computer Conf. 13, 130-132 (1958). 6. W. Buchhole, ed., “Planning a Computer System.” Wiley, New York, 1962. 6. E. F. Codd, E. S. Lowry, E. McDonough, and C. A. Scalzi, Communs. Assoc. Computing Machinery 2, 11, 13-17 (1959). 7. E. F. Codd, Communs. Assoc. Computing Machinery 2, 347-351, 413-418 (1960). 8. E. F. Codd, Proc. Congr. Intern. Fed. Information Processing SOCS. Munich, 1968. 9 J. C. R. Licklider, and W. E. Clark, Proc. Spring Joint Computer Conf. 21,113-128 (1962). 10. G. J. Culler, and R. W. Huff, Proc. Spring Joint Cowlputer Conf. 21, 129-138 (1962). 11. F. J. Corbato, M. Merwin-Daggett, and R. C. Daley, Proc. Spring Joint Computer Conf. 21, 335-344 (1962). 12. R. R. Seeber, Proc. Eastern Joint Computer Conf. 18, 179-187 (1960).

R E C E N T DEVELOPMENTS I N COMPUTER ORGANIZATION

65

IS. J. R. Kiseda, H. E. Petersen, W. C. Seelbach, and M. Teig, I B M J . Research and Development 6, 106-121 (1961).

1.4. “Papers Presented a t ACM Storage Allocation Symposium,” Communs. Assoc. Computing Machinery 4, 416-464 (1961). 16. T. Kilburn, D. B. G. Edwards, M. J. Lanigan, and F. H. Sumner, I.R.E. Trans. on Electronic Computers 11, 223-235 (1062). 16. J. Fotheringham, Communs. Assoc. Coriiputing Machinery 4, 435-436 (1961). 17. K. E. Ivcrson, “A Programming Language,” pp. 163-174. Wiley, New York, 1962. 18. W. Lonergan, and P. King, Datamation 7, 28-32 (May 1961). 19. G. Estrin, Proc. Western Joint Computer Conf. 17, 33-40 (1960). 20. M. Aoki, G. Estrin, and T. Tang, Proc. Western Joint Computer Conf. 19, 157-172 (1961). 81. D. Cantor, G. Estrin, and R. Turn, I.R.E. Trans. on Electronic Computers 11, 155-163 (1962). 82. G. Estrin, and C. R. Viswanathan, J . Assoc. Computing Machinery 9, 41-60 (1962).

This Page Intentionally Left Blank

Atomic Collisions Involving Low Energy Electrons and Ions MANFRED A. BIONDI Physics Department, University of Pittsburgh and Westinghouse IZesearch Laboratories Pittsburgh, Pennsyluania Page 67 68 68 .......................................... 70 ........................... . . . . . . . . . . . . . . 72 111. Low Energy Elastic and Inelastic Collisions, . . . . . . . . . . . . . . . . . . . . . . . . 7 5 A. Elastic Collision of Electrons with Atoms and Molec . . . . . . . . . . . . . . 75 B. Inelastic Electron Scattermg Involving Rotational Excitation of Molccules . . . . . . . . . . ................................. 93 C. Inelastic Electron Scattering Involving Vibrational Excitation of Molecules.. . . . . ................................. 94 D. Scattering of Electrons by 10 E. Ion-Atom Collisions a t Low Energ .......................... 102 IV. Attachment and Detachment of A. Radiative Attachment and P 13. 13issociative Attachment and t . . . . . . . . . . . . . . . . 1'24 C. Thrce-Body Attachmcnt and Collisional Detachment. . . . . . . . . . . . . . . . . 128 1). Attachment to Co olecules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 E. I
List of Symbols b

impact parameter

D diffusion coefficient D(X Y ) dissociation energy e

electronic charge

E electric field intensity EA

electron affinity

f (e) scattering amplitude f nornialized electron velocity distribution function

I radiation intensity I ( e , 4) differential scattering crws section J current density 67

MANFRED A. BIONDI

momentum three-body rate coefficient three-body attachment coefficient three-body, neutral stabilized, ion-ion recombination coefficient three-body, neutral stabilized, electron-ion recombination coefficient three-body, electron stabilized, electron-ion recombination coefficient kinetic energy electron mass atom or ion mass particle density gas density gas pressure total collision cross section momentum transfer or diffusion cross section partial scattering cross sections, Qo, Q1, Q2, etc. cross section for rotational excitation, i -+ j charge transfer cross section photodetachment cross section radiative attachment cross section dissociative attachment cross section internuclear separation of atoms retarding potential difference temperature energy velocity; vibrational quantum number potential two-body electron-ion recombination coefficient dielectronic recombination coefficient mutual neutralization coefficient radiative recombination coefficient two-body rate coefficient radiative attachment coefficient collisional detachment coefficient ratio of initial central recombination rate to fundamental mode diffusion rate phase shift of lth partial wave wavelength of electromagnetic radiation characteristic diffusion length for j t h mode mobility collision or reaction frequency electromagnetic frequency electronic conductivity electronic wave function electromagnetic radian frequency

I. INTRODUCTION A . Scope and Background of Survey The present survey is concerned with recent advances in our knowledge of collisions of low energy electrons and ions with atoms or molecules

LOW ENERGY ATOMIC COLLISIONS

69

and with each other. I n general, the term “low energy” is intended to include the range from thermal energies, -0.03 ev, to a few ev. Thus, the survey iiicludes elastic scattering processes and low energy inelastic scattering of electrons involving excitation of molecular rotation and vibration states. Because of space requirements electronic excitation and ionization of atoms and molecules by electron impact have been omitted from the discussion. Recent studies of the attachment of electrons to atoms or molecules and the inverse, detachment, processes are discussed in some detail. Finally, a summary is presented of recent advances in our understanding of charged particle recombination processes, i.e., electron-ion and negative ion-positive ion recombination. The subject matter of this survey is such th a t it does not form a n extension of a particular previous survey. Instead, the material reviewed represents advances achieved since the publication of Massey and Burhop’s “Electronic and Ionic Impact Phenomena” (1) and Loeb’s “Basic Processes of Gaseous Electronics” ( 2 ) .The material in some cases extends and in other cases complements the recent surveys of “Electrical Discharge in Gases and Modern Electronics” by Goldstein (S), of “Negative Ions” by Branscomb (4), and of “Inelastic Collisions between Atomic Systems” by Hasted (ti). As the manuscript of the present review was nearing completion, the volume “Atomic and Molecular Processes,” edited by D. R. Bates (6)’ was published. The author gratefully acknowledges having received a preprint of the section on “Photodetachment” by L. M. Branscomb. Although many of the topics of the present survey are reviewed by authors in the Bates’ volume, it appears that sufficiently different emphasis and viewpoints have been taken that undue duplication has been avoided. I n general, a n attempt has been made to review the relevant experimental investigations of the last few years in terms of their contributions to our improved understanding of the various atomic collision processes. The author wishes to apologize for inadvertent omissions of relevant work which escaped his attention. I n many cases space requirements dictated that only a brief mention of a piece of research be made; it is hoped that the interested reader will refer to the original work cited in the references for more detailed information. As stated earlier, the present review is concerned largely with experimental advances; however, in Section I1 a brief outline is given of recent significant theoretical advances in subjects covered by the review. I n Section I11 the studies of elastic scattering of slow electrons by a variety of atoms and molecules, including recent atomic beam studies of atomic hydrogen and oxygen, are reviewed. Low energy inelastic scattering of electrons leading to rotational and vibrational excitation of the struck

70

MANFRED A. BIONDI

molecule are next discussed, followed by a review of the data for low energy electron-ion scattering in a plasma. Ion-molecule interactions are reviewed in terms of potential scattering, charge transfer, and ionmolecule conversion reactions. In Section IV, electron attachment and detachment are discussed in terms of the processes radiative attachment and photodetachment, dissociative attachment and associative detachment, and three body attachment and collisional detachment. A brief survey is made of some recent information concerning electron affinities for the various negative ions of oxygen. I n Section V, recent studies of electron-ion and ion-ion recombination are reviewed. Included in the discussion are the two body processes of radiative, dielectronic and dissociative recombination between electrons and ions and of mutual neutralization between negative ions and positive ions. Three body recombination is discussed in terms of reactions in which the stabilizing third body is a molecule, on the one hand, and a n electron, on the other. It will be apparent that the subjects of electronic excitation and ionization of atoms and molecules by electron impact have been omitted from the survey, in spite of the fact that significant progress in these fields has occurred recently. The development of techniques for producing electron beams of accurately known energy and small energy spread (7, 8) and of collecting with essentially 100% efficiency those electrons which are inelastically scattered (9) has provided the stimulus for a considerable number of significant measurements of excitation and ionization cross sections, especially in the interesting threshold region, during the last decade. The decision to omit these subjects was dictated by the fact that the review is already substantially longer than originally planned; fortunately, however, reviews of the omitted material by workers active in the field are under consideration.

B. Definitions I n the succeeding sections the various atomic collision processes will be discussed in terms of cross sections and two- and three-body rate coefficients. We shall, therefore, first define the various quantities which are used to characterize the processes under consideration. For a binary encounter (e.g., electron-atom scattering) one may introduce the concept of collision or reaction cross sections. For the case of scattering, if the scatterer is used as the origin of coordinates and the initial direction of the incident particle is taken as the polar ( x ) axis, then the differential scattering cross section, I(e, d ) , represents the cross section for scattering of the particle into “unit solid angle” a t the polar coordinate angles 0 and 4. If one has a beam of particles, then the total

LOW ENERGY ATOMIC COLLISIONS

71

cross section, &TI for scattering of particles from the beam by the scatterer is simply

The transfer of momentum from the incident particle to the scatterer requires a deflection of the particle; therefore, the weighting factor (1 - cos 0 ) appears in the definition of the momentum transfer (or diffusion) cross section, Qm:

Q,,,

=

lorh2rI(e, 4)(1

-

cos e) sin eded4.

(2)

In scattering theory involving spherically symmetrical potentials, V ( r ) ,a t large distances one has an incident plane wave of momentum k and a spherically symmetric scattered wave, i.e., the electron wave V

=

function is of the form:

-

+(r, e)

elkr

+ f(e)r-lP.

(3)

The quantity f(0) is the scattering amplitude of the scattered wave, the symmetry about the z axis having removed the dependence on the azimuthal angle 4. It can be shown that I ( 0 ) = If(e)lz. I n the method of partial waves, the total scattering cross section is represented as a sum of partial cross sections, Qt, i.e., QT =

2

(4)

QL

1 =o

This description arises from an expansion of the wave function in a set of partial waves involving the Legendre polynomials Pl (cos O), i.e.,

$(r, 0)

'c

-r

=

CIPl(cose)4&).

1 =o

Thus, one speaks of s-, p-, d- etc., waves corresponding to 1 = 0, 1, 2, etc. Associated with each partial wave is a phase shift, vr, which gives the asymptotic behavior of 4 according to the relation

&(r)

--1

k

sin (Icr - 17r/2

+ ql).

(6)

The partial cross sections are given in terms of the phase shifts by Qt

=

4r D-(21

+ 1) sins

vt.

(7)

72

MANFRED A. BIONDI

I n dealing with the rates of collisions or reactions of a n assemblage of particles of density n,, one may introduce the concept of a collision (or reaction) “frequency,” v, which provides a measure of the rate a t which the particle density is altered by collision or reaction, i.e.,

a -n -~ -vn,. at

If the process involves binary encounters between particles of types x and y, then the rate of collision (or reaction) depends on the density of each, i.e., - _ - -pnzny, (91 at where the two-body coefEcient P is related simply to the collision (or reaction) cross section for the process by

P

=

(Qv),

(10)

where v is the speed of relative motion between the particles and the averaging is carried out over the distribution in velocity of the particles in the assemblage. Thus, for two-body processes, v = On, = nu(Qv).

(11)

I n the case of three-body processes, involving three species x, y and z, one has - --

at

-KnZn,n,,

where the proportionality constant K is the so-called three-body rate coefficient. This coefficient is used to describe three-body encounters and, therefore, is related to the frequency of encounter (reaction) of species x by v = KnUn,.Although one sees discussions of three-body processes in terms of a n “effective cross section,” this concept is not meaningful since the “cross section” for the reaction of x and y is proportional to the concentration of 2. Instead, it is better to compare two- and three-body processes through their frequencies of occurrence, v. 11. THEORETICAL DEVELOPMENTS Although the present review deals primarily with recent experimental advances in atomic collision studies, it is appropriate to discuss briefly the related significant theoretical progress. [Excellent detailed reviews of some of the recent advances are to be found in articles by Gerjuoy ( I O U ) and by Borowitz and Smith ( l o b ) . ]Unlike the case of nuclear theory, all of the relevant interactions involved in the various atomic collision reac-

LOW ENERGY ATOMIC COLLISIONS

73

tions are known, and, therefore, one can formally set up the appropriate equations describing the processes; however, the equations, in general, are too complicated to permit exact solution. Thus, in only a few cases are quantitative predictions obtained, leaving the burden of determining many of the collision cross sections and reaction rates to experimental programs. The elastic scattering of low energy electrons by hydrogen atoms represents one of the simplest of atomic collision processes; however, as a three-body (proton plus two electrons) problem, it presents formidable difficulties in obtaining an accurate theoretical solution. The e-H scattering calculations have recently been greatly aided by the development, by Rosenberg et al. (11), of a method for determining bounds on the scattering and thus, in some cases, providiiig an estimate of the errors introduced as a result of the approximations used in the calculations. Prior to this, approximate calculations, such as the “effective range” theory introduced by Borowitz and Greenberg ( 1 2 ) for calculation of low energy electron scattering, could only look to consistency in the values of the s-wave phase shifts calculated by different methods for a n indication of the correctness of the theory. The weakness of this test was recently strikingly shown by the fact that, although the triplet’ phase shifts calculated by several different investigators using different techniques agreed very closely, they all exceeded the upper limit for zero energy scattering set by Rosenberg et al. (11). Currently, alternate methods of attacking the e-H atom scattering problem are being explored; for example, the “optical model” used extensively in nuclear collision theory is being investigated by Lippman el al. (13) for application to atomic scattering processes. A comparison of the theoretical values of e-H scattering with experimental measurements is made in Section 111, A , 1. Theoretical descriptions of various inelastic scattering processes involving low energy electrons and atoms or molecules have advanced in a number of areas. For example, the lowest energy excitation process, that of rotational excitation of a molecule by a n electron, has been treated by Gerjuoy and Stein (14) for the case of homonuclear diatomic molecules. Earlier work by Massey (15) showed that the excitation cross section for molecules which have a permanent dipole moment, e.g., HCl, is quite large. Morse (28) considered the case of the diatomic homonuclear molecule, which has no electric dipole moment, and concluded that the electron energy loss due to rotational excitation was small-of the order of the elastic collision energy loss. Gerjuoy and Stein reexamined the problem for Nz and for Hz, in which the electron couples to the molecule’s electric quadrupole moment to cause rotational excitation. They 1

Spin of incident electron plus atomic electron equals one.

74

MANFRED A. BIONDI

show that, a s a result of the long range character of the quadrupole field, appreciable interaction occurs with electrons capable of causing rotational excitation (those with angular momentum I > 0). Further, they justify the use of Born approximation a t low electron energies on the basis that the principal contribution to the excitation takes place a t large electron-molecule distances, where the wave function of the incident electron is only slightly distorted from a plane wave. Their calculations indicate that, while the electron energy loss in this case is smaller than for molecules with permanent dipole moments, it is still substantially in excess of the elastic losses, especially for Nz. These theoretical results are compared with experiment in Section 111, B. The general formalism for the calculation of the probability of radiative capture of a n electron by a positive ion (recombination) or by a neutral atom (attachment) predates the development of quantum theory, and both classical and quantum calculations have been shown to lead t o the same results (see for example Eddington, I r a ; Morse, 1%; Massey and Burhop, 1 ) . However, application to atoms or ions more complicated than hydrogen has suffered from the lack of knowledge of the appropriate wave functions. Recently, considerable effort has been devoted to the calculation of radiative capture of electrons by hydrogen atoms (or its inverse, photodetachment from H-), Here the original calculations of Bates and Massey (18), involving a plane wave representation of the free electron and an unperturbed hydrogen atom in its ground state, have been successively improved. The first improvement was made by Chandrasekhar arid colleagues (19), who modified the free electron wave function by the static Hartree field of the hydrogen atom. The bound state H- function in these calculations was determined through variational calculations involving energy minimization. More recently, John (20) has included electron exchange between the incoming and the atomic electron, with a n attendant improvement in the agreement with experiment (see the detailed description by Branscomb, 3'1; and see Section IV, A ) . An alternative free electron function has been variationally calculated by Geltman and Krauss (22)) using a linear combination of 1, 2, and 3 s hydrogenic wave functions a t short range, and results very similar to those obtained by Johns have been obtained. Internal consistency tests of these various theoretical calculations, involving use of the matrix element for the dipole moment in length, velocity, and acceleration forms (.%'I), indicate that there are still significant errors in the free and/or bound state wave functions in use, although the most recent calculations (22) indicate considerable improvement over the original work (18). Comparison of the various theories with experiment is made in Section IV, A .

LOW ENERGY ATOMIC COLLISIONS

75

Recently, calculations of three body recombination between a n electron and a positive ion in the presence of a second electron (the inverse of electron impact ionization of an excited atom) have been carried out for hydrogen (23-26) and for helium (27'). These calculations are of interest at rather substantial electron and ion densities (>, 1012 0111-9, where the three body recombination process begins to outweigh two body processes such as dissociative recombination (28). An electron in the vicinity of a positive ion makes a transition from the continuum into a bound state of the resulting atom following a collision with a second electron. Whether the electron is permanently captured or later reemitted depends on the rates of excitation and deexcitation of the particular level formed in this initial phase of the process. In addition to the spontaneous radiative decay from this level (if it is not metastable) there are excitations, ionizations, and deexcitations as a result of inelastic and superelastic impacts of other plasma electrons with the excited atom. On the basis of a number of simplifying assumptions (such as a Maxwellian energy distribution for the plasma electrons) and assumed values for the cross sections for excitation and deexcitation, calculations are made of the rates of loss of electrons i n hydrogen and helium plasmas. The results are compared with available measurements in Section V, C , 2.

111. L O W ENERGY ELABTIC A N D I N E L A S T I C COLLISIONS I n this section we consider the experimental determinations of collisions of slow electrons and ions with neutral atoms or molecules and with each other and compare the measurements with available theory. The classes of collisions covered here include elastic (no change of the internal state of the atom or molecule) and low energy inelastic collisions leading to rotational or vibrational excitation of the struck molecule.

A. Elastic Collision of Electrons with Atoms and Molecules i. Electron-Hydrogen A t o m Scattering. Although a number of theoret,ical calculations of the elastic scattering of low energy electrons by hydrogen atoms had been in existence for more than twenty years (,5'9), the formidable difficulties in producing a known density of hydrogen atoms had discouraged experimental investigations of this problem. I n 1957, Bederson, Malamud, and Hammer (BMH) (30) reported on atomic beam measurements of e-H total scattering cross sections for electron energies a t or below -10 ev. The hydrogen atoms were produced by means of a radio frequency discharge, and up to 65% dissociation of the molecular hydrogen was achieved. The hydrogen atoms in the beam were separated from the molecules by a Stern-Gerlach magnet. The angular resolution of the experiment was sufficient to determine the cross section

76

MANFRED A. BIONDI

for scattering through angles greater than 7". At the lower ( <10 ev) energies the results began to diverge markedly from the theoretically predicted behavior (31, 32), as indicated in Fig. 1. These discrepancies between theory and experiment stimulated new, improved calculations (33) of the singlet scattering cross sections, which were, however, unable

FIG.1. Total cross section for elastic scattering of electrons by hydrogen atoms. The experimental determinations of Brackman, Fite and Neynaber (BFN) and of Bederson, Malamud, and Hammer (BMH) are compared with several theoretical calculations (see text for explanation).

to account for the experimentally observed values if only s- and p-wave scattering contributions were significant. An independent experimental determination of the e-H scattering was provided by Brackman, Fite, and Neynaber (BFN) (34) who used a modulated atomic beam method of the type illustrated in Fig. 2 in this and later experiments. I n their initial work, electrons scattered into a cone whose axis was at right angles to the initial electron beam and had a half-apex angle of 45" were detected. In order to differentiate electron scattering by hydrogen atoms in the beam from residual gas scattering,

77

LOW ENERGY ATOMIC COLLISIONS

the atomic beam was modulated or “chopped,” and the scattered electron current synchronously detected and amplified. The degree of dissociation in the beam was determined by ionizing a part of the beam by electron impact and measuring the currents of H+ and Hz+ with a mass spectrometer. From the known ionization cross sections the relative H :Hs densities were deterained. Absolute densities were then determined by measuring ht and

Collecting

L

Spectrometer

Note: The slow-electron gun is rotated in plane at right angles to plane 01 drawing and normal to the beam

FIG.2. Modulated atomic beam apparatus for electron-atom scattering determinations. Using this type of apparatus, Gilbody, Stebbings, and Fite studied the angular dependence of electron scattering by hydrogen atoms.

the Hz+ current a t a dissociating oven temperature so low that the beam contained essentially Hz molecules only. I n order to relate the scattering of electrons into the observational cone to the total scattering cross section, Qr, BFN derived a n expression for their measured scattering in terms of the partial scattering cross sections, Qo,Q1,Qz, . . . (for the s, p, d, . . . waves) and retained only the s- and p-wave contributions. Their results were compared with theory on the assumption, first, that only s-wave scattering is important in determining the total scattering cross section (QT = Qo). I n the second case their results were interpreted in terms of both s- and p-wave scatter-

78

MANFRED A. BIONDI

+

ing (QT = Qo Q1).As indicated in Fig. 1, the results indicate slightly better agreement with the s- and p-wave calculation of Bransden, Dalgarno, John, and Seaton (BDJS) (53) (provided that their values of Q1 are used t o obtain QT from the measured scattering) than with the theory of Massey and Moiseiwitsch (32),in which only s-wave scattering is considered. Thus, a t first sight, it appears that the experiment of BMH (30) is in error, since apparent agreement between the measurements of B F N and theory is obtained. However, Temkin (35) suggested that, in view of the widely different detection angles of the two experiments, a substantial d-wave contribution could lead to sufficient forward scattering to give BMH’s large result and yet be completely missed in BE’N’s experiment (34). I n order to examine the nature of the scattering, Gilbody, Stebbings, and Fite (GSF) (56),using an apparatus of the type indicated in Fig. 2 in which the slow electron gun can be rotated about the atom beam axis while keeping the scattered electron detector fixed, measured the angular distribution of the scattered electrons. They found that their results were consistent with only s- and p-wave contributions to the scattering and tha t the p-wave contributions were substantially smaller than the values calculated by BJDS, being in better agreement with more recent calculations (37-40). A second approach to a direct experimental determination of the total scattering cross section was achieved by Neynaber, Marino, Rothe, and Trujillo (NMRT) (41), who used a modulated atomic beam from a n rf discharge and measured the absorption of electrons from a beam crossing the atomic beam at right angles. The electrons scattered from the electron beam by the modulated atomic beam gave rise to a n ac component in the collected electron beam which provided a measure of the scattering probability. I n this experiment, as in the angular distribution measurcments of GSE’ (39, the known cross section for electron scattering by molecular hydrogen (42) was used with the relative atom/molecule crosssection data t o obtain absolute values for the atomic scattering. The angular resolution in the electron collecting structure was such that only electrons scattered by more than approximately 25” were prevented from reaching the collector; thus the inferred total cross sections may be in error if there is a strong, small angle forward scattering component. Their results are shown in Fig. 3 as the solid curve, together with the recent calculations of McEachran and Fraser (37), Geltman (58),Smith (39),John (40), Temkin and Lamkin (ct?), and the previously cited work of BDJS (33). Excellent agreement ( < 10% discrepancy) over the measured energy range, 3-12 ev, is obtained with several of the calcula-

79

L O W E N E R G Y ATOMIC COLLISIONS

tions (37-40). I n addition, when the BFN points are recalculated with the smaller p-wave contributions (37) indicated by the angular distribution measurements (36) acceptable agreement is obtained between the two experiments. This agreement among the two experiments, BFN and NAIRT, and the recent theories, together with a recent theoretical argument by Gerjuoy and Krall (44)which rules out large forward scattering contributions, suggests that the large Scattering cross section observed a t low electron energies by BhlH (30) (see Fig. 1) is in error. However, to date, no experimental origin for the discrepancy has been uncovered, and 30,

I

I

I

I

I

I

I

Electron Energy fev J

FIG.3. Comparison of the total cross section for scattering of electrons by hydrogen atoms, as measured by Neynaber, Marino, Rothe, and Trujillo (solid curve), with theory and with the experimental values of BFN (see text for explanation). The vertical bars indicate tlie limits inside which half of NMRT’s data points lie.

additional measurements, in which the recoil of the H atoms is used to measure the scattering, are in progress (45). Before leaving the subject of crossed beam scattering studies, it should be noted that NMRT ( 4 1 ) first used their method to study IOW energy electron scattering by atomic oxygen in order to provide a comparison with a number of recent theoretical estimates (46). The experimental results, estimated to be accurate to approximately +_ 1070, are shown in Fig. 4, in comparison with the various theories. They lie between the results of Temkin (see 46) and extrapolations of the theories of Bates and Massey (47)and of Hammerling et al. (46)(NMRT added a p-wave contribution ( 4 1 ) to the s-wave calculations of all of these investigations). The theories included estimates or calculations of electron exchange and atomic polarization. Thus, it appears that at the present time experimental determinations of e-H total scattering and differential scattering cross sections are

80

MANFRED A. BIONDI

approaching an accuracy where they provide guidance in the choice of theoretical treatments of the problem. With future improvements in experimental technique it is to be hoped that a n even more rigorous test of the theories will be provided. 2 . Elastic Scattering of Very Low Energy Electrons. As is evident from the discussion of Section 111, A , I, even in the simplest electron scattering case (e-H) there are sufficient difficulties in the calculations a t low electron energies that extension to more complicated atoms or to molecules appears beyond the capabilities of present theoretical techniques. On the other hand, excellent measurements of the electron total scattering, ,

,

,

,

,

,

,

,

,

,

,

Hammerling, Shine, and Kivel

Robinson

5

0

10

Electron Energy ( e v )

FIG.4. Comparison of the total cross section for scattering of electrons by oxygen atoms, as measured by Neynaber, Marino, Rothe, and Trujillo (NMRT), with available theory (see text).

differential scattering and momentum transfer cross sections are available for a number of atoms and molecules ( I ) . These measurements fall roughly into two categories, electron beam and electron swarm studies.Z The electron beam scattering experiments have been limited to energies greater than several tenths of an electron volt ( I ) . Previous swarm experiments, such as electron mobility measurements, suffered from the fact that the electrons had a distribution of velocities determined in part by the temperature of the gas in which they moved and in part by the applied electric fields. Recent refinements in electronics-notably methods of measuring very small current signals, precise wave shaping circuitry, and microwaves-have permitted swarm measurements to be

(s

2 A third low energy 1 ev) technique, involving deduction of electron-atom scattering cross sections from measurements of the electrical conductivity of arcs, has bcen omitted from the present review. For a discussion, see W. Finkelnburg and H. Maecker, Electrische Bogen und thermisches Plasma, in “Handbuch der Physik” (S. Flugge, ed.), Vol. 22, p. 378ff. Springer, Berlin, 1956.

81

LOW ENERGY ATOMIC COLLISIONS

carried out under conditions where the electron swarm’s velocity distribution is Maxwellian, a t the temperature of the gas in which it moves. As will be seen shortly, this circumstance permits measurements of electron scattering a t very low energies, as low as -0.01 ev. The swarm experiments to be discussed fall into two categories, electron mobility measurements and microwave studies of the electron conductivity during the “afterglow” periods following creation of plasmas in various gases. A key assumption in these experiments is that it is possible to operate under conditions in which the electrons’ “temperature” is equal to the temperature of the gas in which they move. Unfortunately, in some of the microwave afterglow studies, this condition has apparently not been achieved, leading to substantial errors in the measurements (see Section 111, A , 2, d ) . (a) Basic equations. In the swarm experiments it is possible to relate the measured quantities to the scattering cross sections or related quantities through formulas obtained by solution of the Boltzmann transport equation (see for example Allis, 48). The momentum transfer cross section, Q,, is related to the momentum transfer frequency, Ym, by v,

=

N&,L!,

(13)

where N is the gas density and v the relative speed between electron and atom. The electron mobility, p, in an applied dc electric field, Elis related to V, and to the normalized velocity distribution of the electrons, f, by

(4a

where v d is the drift velocity in the field, e and m are the electronic charge and mass, respectively, and fo is the spherically symmetrical part of the distribution function (the first term in the usual spherical harmonic expansion of the slightly asymmetric velocity distribution). Margenau (49) has considered the response of electrons to a high frequency electromagnetic wave, arriving a t an expression for the complex conductivity, ue, of the electron gas of

where u p and ui are the real and imaginary parts of the conductivity, respectively, J is the current density, n is the electron density, and w is the radian frequency of the electromagnetic wave. Since u, is related to the complex (ac) mobility, p,, by uo = nepu,, it will be seen that Eq. (15) reduces to the dc mobility expression, Eq. (14), as w 0. --f

82

MANFRED A. BIONDI

The microwave measurements most conveniently measure (60) the ratio b,/(~i, which will be seen to be:

For ( v m / w ) << 1, the quantity ur/ua provides a weighted average of the momentum transfer frequency, over the electron velocity distribution. (b) Microwave conductivity measurements. Phelps, Fundingsland, and Brown (PFB) (50) developed the first quantitative techniques for determining Y, by microwave afterglow techniques. They used a resonant cavity method operating in the 3000 Mc/sec frequency range in which a discharge (plasma) was created in a gas sample within the cavity by a pulse of microwave energy. Following this the ionizing energy was removed and the plasma began to decay. After a sufficient time had elapsed for the electrons to “coo1 down” from their discharge energies and come to the ambient (gas) temperature ( T , = Tp,,), measurements were made of the quality factor, Q, and of the change of resonant frequency, A l , of the cavity a t various times in the post-discharge (afterglow) period. It can be shown that a suitably normalized ratio of Q to AJ is simply the ratio (ur/ul), where the conductivity components are averaged over the square of the electric field in the cavity. From this type of measurement, PFB obtained values of ur,’ul a t several different gas temperatures. They then adopted the scheme of comparing the observed ur/ua v s T , behavior with calculated temperature dependences assuming different simple models for the velocity dependence of Qm or vm, i.e., v, = avh, where integer values of h ranging from -2 through 0 to $2 were tried. Under conditions such that T , = T,,,, the electron velocity distribution, 10,is Maxwellian, and Eq. (16) can be evaluated for the various assumed velocity dependences of v,. Their preliminary results for nitrogen, which are discussed later in connection with Fig. 10, indicated a best fit for h = 2; i.e. a momentum transfer frequency which varies directly with electron energy. Some time later Anderson and Goldstein (AG) (51-53) reported on similar - microwave measurements (at a higher frequency, -9000 Mc/sec) of v, not only for electron-atom scattering but also for electron-ion scattering. I n their method the plasma, which essentially filled a portion of waveguide, was created by a pulsed dc hot cathode arc whose cathode and anode were, however, external to the guide. The propagation of a probing microwave signal through the plasma was measured in the presence of a second, intermittent microwave signal of sufficient intensity to alter the electrons’ conductivity by “heating” the electrons above gas temperature. From these measurements they were able to determine

x,

LOW E N E R G Y ATOMIC COLLISIONS

-

83

V, for electron-helium atom and electron-helium ion scattering (51, 53) and for electron-N* scattering (52). Other microwave conductivity studies of electron-molecule scattering have been carried out by Varnerin (54) (H2), Gould and Brown (55) (He), Gilardini and Brown (56) (Ne), Bekefi and Brown (57) (H2), and Takeda and Dougal (58) (Hg0). The results are discussed in Section 111, A , 2, d. (c) Electron mobility studies. Historically, electron mobility and diffusion measurements are among the oldest in the fields of gaseous electronics and atomic collisions (69). However, there have been recent refinements in these types of measurements which have, for the first time, permitted these techniques to be used to determine quantitatively the magnitude and energy dependence of electron-molecule scattering a t very low energies. The means for these new determinations has been provided by the advance of electronic technology, principally the development of precise wave shaping and timing techniques and of accurate means for measurement of very low currents. With these advances it is now possible t o measure the drift velocity of electrons through a gas under the action of such small electric fields that, even a t 77”K, the energy gained by the electrons from the field is negligible compared to gas tcmperature energies. Thus, the electrons maintain a Maxwellian distribution a t a temperature equal to the gas temperature, and therefore, a n analogous device to that described in the microwave conductivity studies can be used to determine the energy dependence of the electron collision frequency. I’helps ct al. (60), using a double grid tube of the type shown schematically in Fig. 5, have determined the mobility of thermal electrons in helium. A group of photoelectrons was produced a t the cathode by a short duration ultraviolet pulse and then moved under the action of a constant electric field through the two shutter grids to the collector. I n the various experiments the tube was operated in a number of different ways; in the “conventional” grid operation, bias voltages were applied to the alternate grid wires to cause them to collect electrons. These bias voltages were made zero for brief intervals delayed with respect to the uv pulse. The drift velocity was determined from the measured time difference in arrival of the electrons a t each of the two grids and from the known distance between the grids, d, thus minimizing errors due to injection and diffusion effects (61). An innovation (62), especially useful in the very low field measurements, involved operation of the grids with no bias voltage between alternate wires, i.e., in a transmitting condition, in order t o prevent disturbance of the drift field while the electrons move through most of the tube. Each grid was in turn made absorbing for a

84

MANFRED A. BIONDI

brief interval delayed with respect to the uv pulse by application of a bias voltage pulse to the grids. When a grid was made absorbing just as the electrons reached the vicinity of that grid, a decrease in collector current was noted. From the difference in times of absorption of electrons by grid no. 1 and by grid no. 2, the transit time between grids was determined. By the use of these techniques, measurements at very low values of E / p, the ratio of the drift field to gas pressure, were possible; in some cases values as small as (volts/cm-mm Hg) were attained. Thus, equality of the electron temperature with the ambient gas temperature was assured, as is illustrated in Fig. 6 for the case of helium. It will be seen that, Cothode

t--

Collector

FIG. 5. Schematic representation of an electron mobility tube employing two shutter grids, together with current vs. time patterns of currents leaving the photocathode and arriving a t the first and the second grids.

while the drift velocities a t higher values of E / p (> 10-l) merge for the various gas temperatures, as one goes to sufficiently low values of E / p the curves for the three temperatures separate, and the drift velocity becomes proportional to E/ p, indicating no further change in electron energy, from which one concludes that T, = T,,,. Room temperature studies by other investigators are shown for comparison. It will be seen that the recent mobility determinations by Bowe (63), who studied a number of gases, do not extend to sufficiently low values of E / p to permit accurate determination of the thermal mobility values. I n the analysis of the mobility measurements to determine the energy dependences of the collision frequency, v,, or cross section, Qm, for momentum transfer, the quantity ( l / v m ) appearing in Eq. (14) was expanded in a power series in the electron speed,

L O W ENERGY ATOMIC COLLISIONS

85

with integer values of j and constant coefficients, B,. By measuring electron mobilities a t a number of gas temperatures and a t sufficiently small values of E l p so that the electron energy distribution, fo, was accurately Maxwellian a t the gas temperature, it was possible to determine, with some confidence, the energy dependence of v, or through Eq. (13), of Qm.

The degree of fit of the calculated mobilities (using the assumed power series expansions for 1 / v m ) to the observed thermal mobility values is indicated in Fig. 7, in which the product p N , where N is the gas density,

10+

10-3

10'2

10-1

E/p (volts/cm-mm Hg)

FIG.6. Electron drift velocities in helium as a function of E / p and a t several gas temperatures. The recent measurements of Pack and Phelps are compared with earlier room temperature determinations by other investigators.

is plotted against the gas temperature. As detailed in the following section, different numbers of terms were used in the expansions for the different gases; in some cases several alternative expansions were tried. (d) Very low energy momentum transfer cross sections. The determinations of the very low energy scattering cross sections from microwave conductivity and from electron mobility measurements are compared in Figs. 8 to 12. It will be seen from Fig. 8 that, with the exception of AG's values (51, 65), there is good agreement among the microwave afterglow and mobility determination of Qm for helium. The early microwave work of P F B (50) was extended to higher energies by Gould and Brown (ii.') and to lower energies (less than room temperature) by the mobility studies of Pack and Phelps (PP) (69). A single term in the power series was found to be capable of accurately representing the mobility data over its range of application (0.003-0.05 ev). Thus, in the very low energy range Qm is found to be independent of the electron energy.

MANFRED A. BIONDI

>

I 0

100

200

300 T('K1

500

400

I0

FIG.7. Degree of fit of the thermal electron mobilities calculated from the assumed series expansions of the elastic collision frequencies in powers of the electron velocity (solid lines) with the experimentally determined values (points).

-

.k_ 9 -

Anderson 8 Goldstein

c

"

8-

(0

7-

$

$

-z

-

6-

P FB

ti 5 -

E

5

LGould Pock ond Phelps

4-

8

Brown

j-

5 2 I-

-

Y

.y

x 0

-

Electron Energy ( e v )

FIG.8. Momentum transfer cross section vs. electron energy for scattering of electrons by helium atoms. The values determined from mobility measurements by Pack and Phelps are compared with microwave determinations of PFB, Gould and Brown, and Anderson and Goldstein. The temperature values on the energy scale, placed so t h at kT, = u., give some indication of the range of the thermal measurements.

L O W ENERGY ATOMIC C O L L I S I O N S

87

For the case of neon, the microwave studies of Gilardini and Brown ev and indicate a cross section which increases at first rapidly from a value of -5 X lo-" cm2 a t 0.04 ev, becoming almost independent of energy a t -2 ev a t a value of -1.9 X lo-'" cm2,where the curve joins smoothly to the scattering measurements of Ramsauer and Kollath (see 59) and to the mobility determinations of Bowe (63). The low energy value is consistent with the measurements a t a single temperature (300°K) of PFB, who obtained a value Qm 1 x 10-l6 cm2 on the simplifying assumption that Qm is independent of electron energy in this region. (56) extend over the range -0.04-2

-

Z 6

Bekefi and Brown

Electron Energy i e v )

FIG.9. Experimental determinations of the momentum transfer cross section vs. electron energy for electron scattering by hydrogen molecules.

Considerably poorer agreement is obtained among the various determinations in hydrogen, Fig. 9. More recent microwave determinations by Bekefi and Brown (57) and the mobility studies of PP (69) lie substantially below P F B and Varnerin (64). I n this case PP used a two term series which gave a weak energy dependence for Qm. I n nitrogen, Fig. 10, the microwave value of P F B is in satisfactory agreement with the mobility analysis of PP, who used a two-term series for l/vm; however, these values are a factor of 4 to 7 below the AG values. I n addition, the P F B and PP cross sections increase with energy while AG found a decreasing cross section with increasing energy. It appears that in AG's experiments the electrons did not come into temperature equilibrium with the gas during the measuring interval (64). The heavier noble gases, such as argon, krypton, and zenon, exhibit a sharp minimum in electron scattering (Ramsauer effect, see 65) a t relatively low (-1 ev) electron energies. This minimum has been investigated

88

MANFRED A. RIONDI

in beam experiments from the high energy side; however, the failure of beam studies a t very low energies has left considerable uncertainty in the cross section behavior below the minimum. The recent microwave and low field mobility studies, in principle, permit detailed examination of the scattering behavior in this low energy region. The results of noble gas measurements are shown in Fig. 11. The dashed curves are the microwave results of PFB, obtained a t room temperature only, and analyzed on the simplifying assumption that Qn is independent of electron energy. The solid curves are the results of PP (62) and of Pack, Voshall, and Phelps (PVP) (66). The curves labeled

.s+ 20

Anderson 8 Goldstein

Electron Energy (ev)

FIQ. 10. Experimental determinations of the dependence on electron energy of the momentum transfer cross section for scattering of slow electrons by nitrogen molecules.

and u3 represent alternate power series expansions which fit the experimental mobility vs temperature data. For example, in argon, measurements were only obtained a t two gas temperatures; therefore, a two term power series was used to represent l / v m . For the observed mobility variation, three possible sets of j values in Eq. (17) can be used to fit the data; U I involves j = +1 and -2; u2 involves +1 and -3; u3 involves - 1 and - 2. The data for argon in Fig. 7 were fitted by the u1 expansion. It will be seen that, in spite of the uncertainty concerning the exact form of Q m l s energy dependence, it clearly increases with decreasing electron energy, reaching quite large values, in keeping with our expectation that, below the “transparency” region of the Ramsauer effect, the electron is scattered more strongly by the atomic field as its energy decreases. Finally, we include the deduced values of Qm for electron scattering by polar molecules, obtained from the mobility temperature dependences (TI, u2,

89

LOW ENERGY ATOMIC COLLISIONS

(66). These measurements permit a comparison with the recent theoretical treatment of Altshuler (67), who used Born approximation to predict the momentum transfer cross sections a s a function of electron energy for H2O and for NH3. The results of theory and experiment are compared in Fig. 12. It will be seen that, for HzO and NH3, the deductions from the experimental observations of I’VP, indicated by the solid

I

I

I

I

I

I

I

I

lines, are consistent with the energy dependence predicted by Altshuler from considerations of the long range scattering of the electron in the dipolar field of the molecule. However, the absolute magnitude of Qm is found t o be roughly twice the theoretical value in HZ0 and 60% greater than the theoretical value in NH,. The microwave results of Takeda and Dougal (TD) (58) for HzO are in fair agreement with PVP and approach their curve a t energies corresponding to room temperature (-0.03 ev),

90

MANFRED .4. BIONDI

suggesting that TD’s calculated electron energies in the presence of the second, heating microwave signal may be in error. Also included in Fig. 12 are PVP’s results for electron scattering in COZ and NzO. Theoretical calculations of Qm for these gases are not available. x 10-13

I

I

I

Io-I5c!

0.dl

0.22

I

I

I

I

0.24 0.25 a d 6 Electron Energy (ev)

0.d3

I

0.A

I

0.2,

9

FIG. 12. The energy dependence of the momentum transfer cross section for electron scattering by polar molecules. The solid curves indicate the values deduced from mobility measurements by Pack, Voshall, and Phelps; the short dashed curve the microwave values of Takeda and Dougal, while the long dashed curves indicate the theoretical values of Altshuler.

It will be seen from the foregoing discussion of very low energy electron scattering that the microwave conductivity and dc electron mobility studies as functions of gas temperature can provide quantitative determinations of Qm in this energy region. Of the two approaches, the microwave afterglow studies apparently suffer from a number of potential complications. It is not always correct to assume that the electrons come

LOW ENERGY ATOMIC COLLISIONS

91

into temperature equilibriuni with the gas during the afterglow, since excitation produced in the discharge (e.g., metastable atoms) may provide a n energy source during thc afterglow which keeps the electron energy substantially above gas temperature. Such effects appear to have occurred in the afterglow studies of ACT for the case of N z (52) and of PFB for A s (50), as suggested by Forniato and Gilardini (6l+),who found elevated electron temperatures during afterglows in nitrogen and in oxygen using microwave noise measurement techniques. By contrast, the dc mobility studies, with the relatively weak uv pulsed light source, can hardly heat the gas or produce excitations or chemical reactions in sufficient amounts to falsify the electron energy or introduce significant changes in the scattering atoms or molecules. It appears that by extending these techniques to include measurements a t a sufficient number and distribution of gas temperatures, much of the uncertainty in the deduced eiiergy dependences of Q7,, will be removed, since, to date, the several possible fits to the data indicated by the UI, 6 2 , C T ~curves have been the result of insufficient constraints, rather than a n inherent limitation of the method. It is also possible to extend greatly the high energy range of these determinations by experimental measurements of the average electron energy through the simultaneous determination of the electron diffusion coefficient D along with the electron mobility a t various values of E / p (see for example Townsend, Healey, Crompton et al., 68). When coupled with calculations from Boltzmann transport theory of the form of the energy distribution, accurate values of Qm over a n extended energy range can be obtained. Heylen (69) has demonstrated that, given average energy ( D / p ) determinations, the predicted electron mobility is rather insensitive to the form of the electron energy distribution, provided that Qm does not vary too rapidly with energy. Therefore, for many cases it should be possible to obtain accurate determinations of Qm over a wide range of electron energies from D / p arid p data analyzed on the assumption of a Maxwellian energy distribution. The solution of the Boltzmann transport equation and the determination of the transport coefficients have been discussed by Huxley and Cromptoii (70) for the case in which the variation of Qm is described by a single term of the form, 21)". Detailed machine calculations of the electron energy distribution and transport coefficients for a n arbitrary form of Qm have been carried out by Frost and Phelps (71) for the case of hydrogen. As discussed in the next subsection, such calculations lead to accurate determinations of Qm over a wide range of electron energies (-loF2 to -10 ev).

92

MANFRED A. BIONDI

B. Inelastic Electron Scattering Involving Rotational Excitation of Molecules Inasmuch as the rotational states of molecules are spaced 0.01 ev or less apart, the direct experimental determination of the cross section for excitation of the individual states by electron impact is beyond the present energy resolution capabilities of electron beam experiments (see, for example, Section 111, C). However, since rotational excitation plays a

E/N (volt - crn2 1

FIG.13. Comparison of calculated and experimentally determined values of the electron drift velocity and characteristic energy, D / p , in hydrogen as functions of E / N . The experimentally determined values of the various investigators are indicated by the various symbols, the values calculated from Boltzmann transport theory by the dashed and solid curves.

role in determining the rates of scattering and of energy loss of low energy electrons moving through a molecular gas, a detailed examination of the electron mobility and average energy data as functions of the applied electric field may provide information concerning the rates of such inelastic collisions. Two approaches to this analysis of experimental data have been made. Huxley (72) characterizes the rotational excitation by requiring the electron to have sufficient angular momentum and to approach the molecule sufficiently closely t o cause rotational excitation, then treats the electron’s velocity and impact parameter as adjustable parameters in his calculations in order to obtain a best fit to experimental mobility and D / p (average energy) data. Frost and Phelps (?‘I), on the other hand, use

93

LOW ENERGY ATOMIC COLLISIONS

the theoretical values of Gerjuoy and Stein (GS) (14) for rotational excitation and “best” estimates from experiment and theory for elastic scattering (and, in hydrogen, for vibrational excitation) in the Boltzmann transport equation to compute the electron energy distribution. From this they predict drift velocity and D / p values for comparison with measurements. Thcy then adjust the asfiumed cross sections until good agreement between their calculations and the measurements is obtained.

-

6

6

I

,

,

I

I

I

,

,

I

I l l

Bekefi ond Brown

v

0

I

4-

4-

.-P

& c

2-

0

X

u t:

c

10-178 -

6 -

T J

10-1

I

10

Electron Energy (electron volts)

FIG.14. Inferred elastic and inelastic cross sections for electrons in hydrogen. The cross sections for excitation and deexcitation of rotation states, i 4j, are indicated by the symbols Q , j . Also included are a lumped vibration excitation cross section, Q., and an electronic excitation cross section, Qe. The overall momentum transfer cross section for elastic and inelastic scattering is indicated by Qm and agrees with other experimentally deduced values indicated by the upper dashed curves. Using these cross section values in the Boltzmann transport theory, the degree of fit to experiincntal p and D / p values shown in the previous figure was attained.

The excellent agreement obtained between the Boltzmann transport calculations of Frost and Phelps and the observed drift velocity, W , and D / p data for hydrogen is indicated in Fig. 13. The dashed and solid curves are the calculated values a t 77 and 3OO0K, respectively. The experimental values obtained by a number of investigators are indicated by the points in the figure. The cross sections for rotational excitation and deexcitation of hydrogen, as well as the final over-all momentum transfer cross section required to obtain this fit, are shown in Fig. 14. The thresh-

94

MANFRED A. BIONDI

old energy and shape of the rotational excitation cross section of the GS theory are retained; however, the magnitude has been multiplied by a factor of 2.5 to obtain the agreement shown. The subscripts refer to the initial and final rotation states of the hydrogen molecule involved in the collision. The “superelastic” collision cross sections, e.g., Qzo, have been calculated by detailed balancing from the inverse, e.g., QOZ,processes. Rather good agreement is obtained between the calculated Qm values and those deduced by other investigators for more limited energy regions. It will be seen that, according to this calculation, the threshold for rotational excitation occurs a t -0.04 ev. Huxley, using his empirical method, obtained a threshold of -0.12 ev to fit the room temperature data. This value is much too high to be consistent with the 77°K observations. Thus, the analysis of Frost and Phelps is consistent with a substantial cross section for rotational excitation, ~ 1 O - l-~ lo-’’ cm2, as predicted by GS from consideration of the long range interaction between the electron and the molecule’s electric quadrupole moment. Some of the discrepancy between the GS theory and experiment may be removed by inclusion in the theory of polarization effects. I n addition, Dalgarno and Moffett (73) have suggested that, for hydrogen, there is a correction in the value of the quadrupole moment to be used in the calculation which reduces the discrepancy from a factor of 2.5 to 1.7. Similar analyses of rotational excitation have been carried out for nitrogen ( 7 l ) , although the closer spacing of the rotational levels requires inclusion of more rotational states, greatly increasing the computational complexity. In this case the best agreement between the calculations and the measured drift velocity and D / p data is obtained with rotational excitation cross sections which essentially agree with3 the theoretical values of GS.

C. Inelastic Electron Scattering Involving Vibrational Excitation of Molecules I n the previous subsection it was pointed out that, a s a result of the small energy spacing between rotational states of molecules, observation of the discrete excitations by electron impact was beyond present electron beam techniques. Thus, the little experimental information available concerning rotational excitation comes from a comparison of calculations based on Boltzmann transport theory with observables, such as 1.1 and D / F , obtained from swarm experiments. One may note from Fig. 14 that a n indication of the total vibrational excitation cross section is also There is a factor of two uncertainty in the theoretical values, owing to a factor of 2 discrepancy among the various measured quadrupole moments of nitrogen.

LOW ENERGY ATOMIC COLLISIONS

95

obtained from these analyses. I n addition to Frost and Phelps’ calculations ( 7 l ) , Heylen and Lewis (69) have carried out similar calculations for hydrogen, nitrogen, oxygen, and air and have obtained some indication of the over-all contribution of rotational and vibrational excitation to the total momentum transfer cross section in hydrogen. Fortunately, considerably more detailed experimental information concerning vibrational excitation by electron impact has recently been obtained by the use of the latest techniques for producing electron beams of very small energy spread (7, 8). Schulz (74, 7 5 ) and Schulz and Dowel1 lhpped -Elec t ron Current

FIG.15. (a) Schematic representation of the electrode configuration in the “trapped electron” tube. (b) Potential distribution on the beam axis of the tube.

(76‘) have studied vibrational excitation in nitrogen, carbon monoxide and oxygen using electron beams which, in effect, had half widths of -0.1 ev. Two methods were used, the “trapped electron” method (9) and a scattering measurement involving crossed electron and molecular beams (75). In the trapped electron method, Fig. 15, the effect of electrons of narrow energy spread is obtained by use of the retarding potential difference (RPD) scheme ( 7 ) , in which the electron distribution from the filament F is “chopped” by a retarding potential applied to plate Pz. By changing the retarding potential on Pzby a n amount AV,, the electron distributioii is “chopped” a t a new energy. If one observes the difference in effect of the electron beam traversing the collision region under these

96

MANFRED A. BIONDI

two conditions, one obtains a measure of the effectiveness of the electrons in a n energy band approximately AVr wide. After passing the retarding electrode the electrons are accelerated to the desired energy and enter the collision chamber. If the electron beam direction is taken as the z axis, then by application to electrode M of a sufficient potential, which partially penetrates the screen grid G, an electrostatic potential well is created in the z direction along the beam axis. A magnetic field is also applied in the x direction. If electrons from the beam, whose total energy in the tube is indicated by the double line and arrow in part (b) of the figure, make an inelastic collision and lose an amount of energy exceeding

I I

0

/

I

1

2

4

6

I 8

I

I

I I

1 0 1 2 1 4

Electron Energy, ev

FIG.16. Current of trapped electrons as a function of incident electron energy in nitrogen a t 300°K. The peak a t -2 ev energy corresponds to inelastic scattering of electrons which occurs well below the threshold for electronic excitation of the nitrogen molecules and corresponds t o a cross scction at the maximum of Qi,, 3 X 1 0 - 1 8 em*. N

V A ,they fall into the well and are “trapped,” in that they cannot reach the electron beam collector E, or the walls, G, but must diffuse radially across the magnetic field until they reach the trapped electron collector, M. This scheme has the great advantage that it provides essentially 100% ’ collection efficiency for the inelastically scattered electrons and hence can be used to observe rather small inelastic cross sections. Using the trapped electron method, Schulz was unable to observe vibrational excitation in hydrogen (9) by incident electrons whose energy lay between threshold value and -0.1 ev higher than threshold. From the known sensivity of the apparatus it was concluded that the cross section for excitation of the various vibrational states in the vicinity of threshold must be cm2. When the method was applied to studies of Nz and CO, however, a substantial (> cm2) cross section for inelastic scattering of electrons was found to occur well below the first electronic

L O W ENERGY ATOMIC COLLISIONS

97

excitation energy (see Fig, 16 €or the case of nitrogen). These results confirmed observations by Haas (77) who had previously found an inelastic process in Ng using a “swarm” technique of the Maier-Leibnitz type (see for example Massey and Burhop, 78). Since direct excitation of vibration is not expected to occur with such large cross sections (see 79), excitation via a temporary negative ion state, as illustrated in Fig. 17, was suggested as a possible explanation of the observations. Thus, the incoming electron requires a substantial energy (-2 ev) to reach the negative ion state. Since the state is unstable against autodetachment, after a short time (-10-13 sec) the electron is reemitted. Depending on

FIG.17. Schematic representation of inelastic scattering of electrons via formation of a temporary negative ion state. This process leads to vibrational excitation of the neutral Nz molecule.

whether or not the nuclei have time to move during the lifetime of the negative ion and on the overlap between the wave functions of the Nz- and N2 in the various vibration states, the molecule may be left in a vibration state other than v = 0, and an inelastic collision will have taken place. Schulz was able to demonstrate that vibrational excitation was indeed produced by these collisions by examining the energy losses of electrons traversing a molecular beam of N2 in an apparatus of improved energy resolution (75). An adaptation of the Marmet and Kerwin (8) double electrostatic analyzer was used to produce low energy electron beams of -0.1 ev half width. A particular electron velocity was selected from the velocity distribution produced by an electron gun by bending the electrons in a cylindrical electrical field. The selected electrons then crossed a molecular beam of nitrogen traversing a differentially pumped collision

98

MANFRED A. BIONDI

region. In one case, the forward scattered and, in the other, 60" scattered electrons were observed by passing them through a second electrostatic analyzer of the cylindrical electric field type. In this manner the relative number of electrons suffering a particular energy loss was determined. The observed forward scattered electron energy distribution is illustrated in Fig. 18, in which electron energy decreases to the right. The peak labeled v = 0 consists of unscattered or elastically forward scattered

-i

I

I

I

I

I

I

V

vlo

t

,I

t

-t-,I 1

I

2

I

3

Sweep Voltage, volts

FIG.18. Energy spectrum of forward scattered electrons in nitrogen. The incident electron energy is 2.6 ev. The peak labeled v = 0 consists of unscattered or elastically forward scattered electrons; the other peaks correspond to electrons which have lost energy in the amount indicated by their position relative to v = 0 on the sweep voltage scale.

electrons (in this case having 2.6 ev energy). It will be seen that, a t precisely the energy positions associated with excitation of Nz molecles t o v = 2, 3, 4, etc., states (go), peaks are observed in the electron energy s p e ~ t r u m By . ~ varying the incident electron energy it was possible to determine the relative cross sections for excitation of the various vibration states, as is shown in Fig. 19. The observed structure in the curves suggests that, as the incident electron energy changes, different negative ion states are reached and hence, the overlap of the Nz- wave function with respect to the various Nz vibration states changes. Finally, the sum of the cross sections for excitation to all of the 'The v = 1 peak is unobservable because of an instrumental effect, 8ee discussion in reference 75.

LOW ENERGY ATOMIC COLLISIONS

99

vibration states should equal the total inelastic cross section observed by Haas (7’7) and by Schulz in the trapped electron experiment (74). The various experiments are compared in Fig. 20, and good agreement concerning the energy of maximum cross section is found. It is believed that the appreciably narrower curve obtained by summing is largely the result of the smaller energy spread achieved with the electrostatic analyzer. Thus, it has been convincingly demonstrated that the rather large (peak cross section -3 X cmz) inelastic electron scattering observed at several ev energy in nitrogen results from vibrational excitation of the molecules, probably by an indirect process involving formation of a temporary negative ion. Similar studies of vibrational excitation in oxygen have been carried out by Schulz and Dowel1 (76). Since in this case the excitation cross sections are rather small, 10-ls > Q > cm2, the high sensitivity trapped electron method was used, a t some sacrifice in electron energy resolution. Figure 21 presents the cross sections for excitation of the various vibration states by giving their values at 0.16 ev above the threshold energy for each particular state. The absolute values of the cross sectioiis are &% only known within a factor of two; however, the 15 20 25 30 3 5 relative values are quite accurate. The symbols Electron Energy (ev) ]Ag and I&+ on the figure indicate the positions FIG.19. Dependence on of these electronic excited states on this scale electron energy of the relaand suggest rather small cross sections tive cross sections for indicm2) for excitation of these states a t 0.16 ev rect excitation of nitrogen above their threshold. molecules initially in the I n contrast to the case of nitrogen, where v = 0 state to various strong vibrational excitation was achieved by vibration states. electrons of several ev energy, oxygen exhibits rather small excitation cross sections, which, however, occur a t electron energies equal to the vibration threshold ( A z L ,= 0.2 ev). At present, it has not been possible to determine experimentally whether the vibration excitation in O2 is via a direct process or whether, as an intermediate state of a n indirect process, a vibrationally excited state of the 02ion is first formed. There is evidence from analyses of swarm experiments (81) that the total

id&

Electron Energy lev1

FIQ.20. Comparison of the several experimental determinations of the cross section for inelastic scattering of electrons by nitrogen molecules. The peak cross section, cma. determined in the trapped electron method, is ~3 X

10 x

9

*(: 7

Vibrational Quantum Number

FIG.21. Cross section, a t 0.16 ev above threshold energy, for electron impact excitation of the various vibration states (v = 1 , 2 , 3 , etc.) of oxygen molecules initially in the v = 0 state. The symbols 1~~ and %,+ indicate the positions on this “energy,’ scale of these electronically excited configurations of 02. 100

101

L O W ENERGY ATOMIC COLLISIONS

effective cross section for vibrational excitation of oxygen by electrons of mean energy -0.5 ev is of the order of lo-’’ cm2.

D. Scattering of Electrons by Ions The rate of scattering of slow ( T , ‘v 300’K) electrons by ions in a plasma has been deduced by Anderson and Goldstein (51) from their microwave conductivity measurements. By measuring the dependence of the average collision frequency of the electrons in a low pressure helium afterglow on the electron (ion) concentration they were able to separate the electron-ion scattering contribution from the electron-atom contribution. The values of the average electron-ion momentum transfer

Maximum Ion Density l ~ r n - ~ l

FIQ.22. Dependence of the average electron-ion collision frequency on ion (electron) density a t 7’. = Ti = 300°K, as determined from microwave conductivity measurements in helium.

collision frequency, V,,,,, deduced from their measurements are shown in Fig. 22. It will be noted that Cmr varies almost linearly with the electron (ion) density. Theoretical calculations (82-84) of electron scattering by ions in a plasma, which consider the Coulomb forces between the electron and ion cut off a t the Debye shielding radius, yield expressions for V,, of the form V,,

=

An,T,-” In [BTe3*/n,],

(18)

for the case T, = T,. Anderson and Goldstein deduce the values

A

=

3.6 ~ m ~ - ( ~ K ) % e c - ~and

B

=

3.7

x

lo3 C ~ - ~ - ( O K ) - $ ~

from their experiment. The calculated values of Ginsburg and Vilenski (82) are A = 3.59 and B = 3.32 X lo3, in excellent agreement with the

102

MANFRED A. BIONDI

experimental observations. The theory of Burkhardt et al. (83)gives substantially different values; namely, A = 2.25 and B = 8.4 X lo3, while Spitzer and Harm's (84) calculations also lead to a substantially smaller predicted value of the electron-ion collision frequency. Similar studies of mixed electron-atom and electron-ion scattering have been carried out by Lin et al. (85) using dc conductivity determinations in isothermal argon plasmas (10,000-15,000"K) a t rather higher degrees of ionization (> These measurements agree rather well with the dc conductivity predicted by Spitzer and Harm (84).

E . Ion-Atom Collisions at Low Energies I n this subsection we shall consider the collisions of low energy positive and negative ions with atoms or molecules insofar as such collisions lead to simple elastic scattering, charge transfer, and ion-molecule reactions. The experimental methods used for studying these processes involve largely ion mobility, ion beam, and afterglow-mass spectrographic apparatus. The means of determining the desired cross sections or reaction rates from the measured quantities are described next. 1 . Methods of Measurement. A principal means of determining the very low energy ( 5 0 . 1 ev) scattering or charge-transfer cross-sections is the ion mobility tube. For ions in thermal equilibrium with the gas in which they move (Ti = Tg,,) the Chapman-Enskog formula (86) gives for the ion mobility, p i ,

where e is the ionic charge, N the gas density, m7 the reduced mass of ion and atom, and E is a small correction to the first order mobility theory (86). The quantity is the momentum-transfer cross-section averaged over the Maxwellian velocity distribution of the ions and atoms. Thus, from ion mobility measurements carried out over a range of gas temperatures and in sufficiently small applied fields so that the ion energy is thermal, one can determine, in principle, the energy dependence of Qm. For simple potential scattering of the ion and atom, the momentum transfer cross section Qm is related to the differential scattering cross section, I ( @ ,as given in Eq. (2). However, for charge transfer processes of the symmetrical type, i.e.,

am

the original ion is neutralized and an identical new ion is formed. One may define a critical impact parameter, b,, inside which half of the ions colliding with atoms are neutralized and outside of which essentially no

L O W ENERGY ATOMIC COLLISIONS

103

charge transfer O C C U ~ S Viewed .~ in the center of mass system, for b < b,, the emerging ions are symmetrically distributed about the scattering angle 0 = go”, even if potential scattering takes place during the transfer collision. Thus, one can show (87) that the momentum-transfer crosssection appropriate to mobility measurements involving charge transfer is Q m ‘V nbC2 (21) Unfortunately, it appears very difficult to extend, by mobility measurements, the determinations Qm for potential scattering and for charge transfer to substantially higher energies than can be achieved in temperature studies of ion mobility. In the electron case, measurements of p and D / p a s functions of E / p were coupled with calculations of the electron velocity distributions to extend the cross section analyses well beyond the thermal range. However, ion velocity distributions, in even moderate electric fields, are extremely difficult to calculate. Wannier (88) has shown that, as a result of velocity persistence when ions collide with atoms, the velocity distribution becomes highly distorted in the applied field direction (he characterizes the velocity distribution a s “onion” shaped), and hence the spherical harmonic expansion to first order, which has been successfully applied to Boltzmann transport calculations of electron velocity distributions, breaks down completely. For nonMaxwellian distributions, only in the case of particularly simple ionmolecule interactions such as pure polarization attraction, have simple expressions equivalent to Eq. (19) been obtained (8,0), relating the mobility t o the interaction parameter (e.g., the atomic polarizability). A second means of studying the very low energy behavior of ions is provided by studies of electrons and ions during the afterglow following creation of a plasma in a gas. Often, the electron concentration during the afterglow is observed by microwave techniques (see for example Biondi, Rose, Goldstein et al., 90) while the ions are studied by monitoring, with a differentially pumped mass spectrometer, the currents of ions reaching a wall of the container boundiiig the plasma (91-95). During thermal equilibrium in the late afterglow, studies of the electron loss by ambipolar diffusion to the walls provide a means of determining the positive i o n diffusion coefficient D, (or mobility p l ), since the electrons’ ambipolar diffusion coefficient D , under these circumstances is simply,

D,

‘v

2Di

=

2p;kT/e.

6 Actually, the charge transfer probability oscillates rapidly between 0 and 1 as one decreases b below the value b,, and the transfer probability rapidly drops to zero outside of b,.

104

MANFRED A. BIONDI

Studies of the time dependences of the various ion currents reaching the wall of the plasma container permit deduction of the rates of the important ion-molecule reactions. Finally, ion beam apparatus has been refined to the point where it is possible to study ion-molecule collisions for rather slow ions ( 5 1 0 ev energy). I n some experiments the ion beam is made to cross a n atomic beam, permitting studies of collisions with atoms such as H and 0 (94). 2. Studies of I o n - A t o m Potential Scattering. In some cases measurements of the temperature dependences of thermal ion mobilities have provided a convenient, although not particularly precise, means of examining the low energy portions of the interaction potential curves between ions and atoms or molecules. I n general, the procedure followed in such studies has been t o assume a more or less realistic approximation to the long range attractive and short range repulsive interactions between ion and atom and then to calculate the variation of mobility with temperature for comparison with experiment. I n 1905 Langevin (95) pioneered in this area by calculating the mobility of a n ion colliding with polarizable atoms on the assumption that the long range attraction could be represented by a polarization interaction, V,( R ) = - cre2/2R4,where a is the atomic polarizability and R the internuclear distance between ion and atom, and that the short range repulsion could be represented by a rigid sphere behavior, i.e., V , ( R ) = 0 for R > Ro and V,(R) = 00 for R 6 Ro. Later, H a d and Cook (96)subsituted a softer repulsion term, V,(R) = C / R 8 ,for Langevin’s rigid sphere interaction. It has been recognized that these two forms for the repulsion bracket actual atomic behavior, the one being too hard, the other too soft, and the applicable experimental observations often lie intermediate between the predictions of the two theories (97’). Margenau (98) suggested the more complete form for the long range attraction,

A R

R C +-R6 ++.. R7

to include higher order interactions between ion and atom; however, from his estimates of the various coefficients it appears th a t the polarization term provides an adequate representation of the attractive potential in most cases. Meyerott (99) used a more realistic, exponentially falling repulsion term, V,(R) = C exp ( - cR), in his calculations of the mobility of Li+ in helium as a function of temperature, obtaining fair agreement with measurements. Recently, Dalgarno et al. (100) have given a n excellent survey of the theory involving potential scattering and the applicable experimental information up t o the year 1958. They show, for example, th a t a single

105

LOW E N E R G Y ATOMIC COLLISIONS

interaction, given in atomic units by

V ( R ) = 74.2 exp (-2.75R)

-

1.39/R4,

(23)

obtained by trial and error modification of Meyerott's interaction, satisfactorily predicts the observed values of mobility a s a function of temperature for Lif and Naf in helium ( I C I I ) , although the observations for Cs+ require a modification of the repulsive interaction coefficients. The substantial number of recent measurements of thermal positive and negative ion mobilities and diffusion coefficients (97, 102-108) have added little t o our knowledge of the applicable interatomic forces, although they have provided considerable information concerning the resonant charge transfer interaction (see Section 111, El 3 ) . Many of the studies were carried out at a single temperature and comparisons made with t,he mobility values predicted for a pure polarization attraction. Except in cases of highly polarizable gases, e.g., Ar, the agreement was found to be rather poor, as one might expect. However, in many of the temperature studies, e.g., Nez+/He, He+/Ne, Nez+/Ne, Ar2+/Ar (97, 106), the observed mobilities6 (see Table I) were TABLEI. EXPERIMENTAL VALUE6 O F THERMAL I O N MOBILITIES'I N U N L I K E ION/GAS CASESCOMPARED TO THE POLARIZATION (0°K) LIMIT.THE GAS DENSITY MOBILITIES ARE REFERRED TO A STANDARD OF

2.69

x

loi9 CM-3

Ion mobility (cni2/volt-sec) Ion/gas

0°K (theory)

77°K

195°K

300°K

Hez+/He Nez+/He He+/Ne Nez+/Ne Arz+/Ar

(19) (16.0) (12.2) (6.1) (2.1)

18.0 16.5 13.1 6.6 2.7

21.7 17.1 16.7 7.0 2.9

20.3 17.3 17.2

6.3 2.7

I,. M . Chanin and ht. A. Biondi, Phys. K P Z )106,473 . (1957); G. E. Courville and M. A. Biondi, J . Cheni. Phys. 37, Gl6 (1962). a

consistent with the low temperature limits determined by long range polarization attraction using the measured polarizabilities of the atoms. At finite temperatures the behevior often lay intermediate between the Langevin and Hass6-Cook theories, suggesting that a n interaction of the general form of Eg. (23) could be made to fit the observations by adjusting the repulsion parameters. 6 Beaty (105),has observed three distinct ion mobilities in argon at 300°K (PO = 1.5, 1.8, and 2.6). While the assignment of PO = 1.5 to Ar+ is probably correct, our conclusion t h a t the highest mobility ion is Ar2+ remains to be verified by mass analysis.

106

M A N F R E D A. B I O N D I

There are, however, two rather puzzling features which have emerged from these types of studies. For the case of Hez+in helium, the mobility a t 77°K has decreased from its 195°K value to a point where it is already below the pure polarization limit appropriate to T = O°K (97). Since corresponding effects are not observed in the more polarizable gases, neon and argon, it is difficult to see how “clustering” of Hez+ with helium to form a heavier ion complex can explain the results. Also, in studies of negative ion mobilities, e.g., 0 2 - and 0- in O2 (108), and low energy scattering cross section measurements for H- in He and in Ne ( l o g ) , scattering in excess of that predicted by the polarization forces is observed. Thus, a t 77°K the observed mobility of 0 2 - in 0 2 is 35% below the pure polarization limit, and a t energies of -10 ev and less the H- scattering by He and by Ne is roughly twice the polarization value and increases more rapidly with decreasing energy than for a pure polarization interaction. I n addition, studies a t 300°K of the thermal mobilities of negative oxygen ions in both atomic and molecular gases (107) yield values below the polarization limit, even if one assumes the ions are 0 3 - rather than OZ-. For scattering by atoms it does not appear that either addition of the higher order attractive terms or the partial cancellation resulting from consideration of the repulsive interaction can lead to the observed behavior.6a I n the case of molecular gases the inclusion of a longer range interaction resulting from the permanent electric quadrupole moment of the molecule may conceivably explain the observations (110). However, since the pronounced deviations in the negative ion scattering are observed in both atomic and molecular gases, it may be that the large extent of the negative ion wave function relative t o that of a positive ion is responsible for the additional interaction required to explain the negative ion observations. 3. Ion- Atom Charge Transfer. Processes of charge transfer, such a s

+ B-+ A + Bf C + D--+ C- + D, A+

and

involve the transfer of one or more electrons from one atomic species t o another a t a collision. Under certain circumstances-especially resonant charge transfer between identical atomic species, i.e., A+/A-charge transfer can be the dominant ion-atom interaction. I n this subsection 6* Note added in proof: S. Geltman (private communication, 1962) has pointed out that, for He2+/He,inclusion of the R-6 term in the interaction permits the mobility to rise from its value at 77°K to the pure polarization value a t 0°K. It seems doubtful that this added interaction term can similarly account for the 01-/0~,H-/He, and H-/Ne results.

LOW ENERGY ATOMIC COLLISIONS

107

we shall be chiefly concerned with single electron transfer froin neutral atoms t o singly charged positive ions for three different cases; (a) true resonance, (b) nonresonance, and (c) accidental resonance. (a) Resonant charge transfer. For the case of He+ in He, Massey and Mohr (111) (MM) calculated that the ion mobility a t ordinary temperatures and above should be determined largely by the charge transfer process rather than by the polarization attraction or short range repulsion interactions considered in the previous subsection. Unfortunately, owing to confusion of ion identity involved in contemporary (-1930’s) mobility measurements (112), MM’s calculation was considered to have overestimated seriously the charge transfer contribution, since it predicted a mobility half the observed value. Morc than a decade later the apparent discrepancy was resolved by the suggestion of Meyerott (113) that the mobility measurements had referred to He2+ in helium aiid by new diffusion ( l l 4 , 9 1 ) and mobility (103,115)measurements, which showed the presence of two ionic species in helium, one of which had the mobility predicted by M M for He+ in He and t8hcother of which agreed with earlier measurements ( 1 1 2 ) . More recently, the calculatioiis of ion mobilities in their parent gases under conditions where the charge transfer interaction dominates have been extended by Holstein (87) to other gases for which the wave functions a t large distances from the nucleus are reasonably well known. I n addition, the case H+/H has been calculated exactly by Bates (116), while the case H+/H* has been treated by Boyd aiid Dalgarno (117) for the excited state, n = 2. For the case of true resonance, A+ A + A A+, a t infinite ionatom separation the extra electron can occupy either ion core site with equal energy; however, as a result of the atomic interactions a t finite separation, the degeneracy is removed and a n energy difference, AIL, occurs between the two stationary states of the system. The frequency a t which the extra electron jumps back and forth between localization around each of the ion sites is simply v = Au/h. By calculating Au as a function of the internuclear distance of the ion cores, the critical impact parameter inside which the transfer probability during a collision has a n average value one half can be determined. Using Eq. (21) one can then calculate the momentum-transfer cross section. The theoretical treatments of ion mobilities in parent gases, together with comparisons with experimental measurements, have recently been reviewed by Dalgarno (118). In addition, a detailed review of calculations of charge transfer, with the notable exception of Holstein’s work, has been given by Bates and McCarroll (119). The observed temperature dependences of thermal ion mobilities for the resonant charge transfer case determined by Chanin and Biondi (9?’),

+

+

108

MANFRED A. BIONDI

together with their calculations using Holstein’s (87) theory, are given in Table 11. The lower temperature (77 and 195°K) theoretical values include appreciable contributions to the momentum transfer cross section by the long range polarization attraction. Agreement between experiment and theory is poorest for helium, which paradoxically should be the most accurately calculable case, since helium’s outermost shell is an s-shell, for which the Hartree-Fock wave functions used in the theory are applicable. One may investigate the general accuracy of the theory used in these calcuIations by comparing Holstein’s values with exact calculations of Bates OF THEORETICAL AND EXPERIMENTAL VALUES TABLE11. COMPARISON OF THERMAL IONMOBILITIES FOR ION/PARENTGAS CASES. THEMOBILITYVALUESARE REFERREDTO A STANDARD GAS DENSITYOF 2.69 x 1o’O CMV3

Ion Mobility (cm2/volt-scc) Temperature (OK)

TheoryG

Experiment*

77 195 300

17.1 13.8 12. 2

13.5 12.1 10.8

Ne+/Ne

77 195 300

5.5 4.6 4.1

5.2 4.5 4.2

Ar +/Ar

77 195 300

2.2 1.9 1.7

2.2 2.0 1.6

Ion/gas He+/He

a T. Holstein, J. Phys. Chem. 66, 832 (1952) and Research Report 60-94698-3-R9, Westinghouse Research Laboratories, Pittsburgh 35, Pa. (1955) unpublished. * L. M. Chanin and M. A. Riondi, Phys. Rev. 106, 473 (1957).

(116) for H+/H. It is found that, a t the critical interaction distances which determine the charge transfer cross section, the Au values computed by the two methods differ by only a few per cent, leading to even smaller differences in the computed mobilities. Thus, although better agreement between the experimental mobilites for He+ in He and semiempirical (118) or less exact theoretical (120) treatments has been obtained, one must regard the situation in helium as rather unsatisfactory. It turns out that the discrepancy between theory and experiment for both He+ and Hez+ ions in helium can be removed by using an atomic polarizability one third larger than the measured values; however, there is no apparent basis for such an adjustment of the long range attractive. interaction.

109

LOW ENERGY ATOMIC COLLISIONS

I n addition to the temperature dependence studies cited, measurements have been made a t 300°K for Kr+/Kr, Xe+/Xe (103, 104, 121, 122) and for Hg+/Hg (102). I n these cases the mobilities agree reasonably well with approximate, unpublished calculations by Bernstein (102, 103).

The charge transfer process has been investigated from moderate (-10 ev) energies to rather high energies (> lo3 ev) by ion beam techniques. Here the cross section for charge exchange is approximately the area (rrbC2)over which the probability for charge transfer oscillates between 0 and 1, multiplied by the average probability, %. Dalgarno (118) and, later, Sheldon (123) have shown that the theoretically predicted energy dependence (87) permits one to match the charge transfer cross section, Q C t , deduced from mobility studies a t very low energies ( <0.1 ev) to the measured values from beam experiments at higher energies (1.24) (1-1000 ev) for the cases Ar+/Ar and Xef/Xe. Equally good agreement is obtained using the absolute values obtained from Holstein’s theory for argon over the whole range (see calculations in Chanin and Biondi, 9‘7). The substantial amount of information concerning charge transfer obtained from ion beam experiments has been recently reviewed by Hasted (5).These studies, which. extend to energies as low as a few ev and as high as many kev, only partially overlap the “low energy” region of concern to the present paper; however, several of the more recent studies of resonant charge transfer will be briefly mentioned. Fite et al. (125) and Hummer et al. (1.26) have presented measurements of Q t for H+/H and H-/H, respectively, over the energy range -102-10‘ ev. They find that to over this range the H+/H cross section falls slowly from 3 X 1X cm2, while the H-/H cross section varies more rapidly, falling from 6 X 10-15 to <1 X 10-l6om2 in the same interval. These observations are in rather good agreement with theoretical calculatioiis (I27‘) made using the method of perturbed stationary states. There is not very much reliable information concerning charge transXt + fer cross sections a t very low energies for molecules, i.e., Xzf Xz X2+,largely because of uncertainties in ion identity in the relevant mobility studies. For example, it appears that, a t the gas pressures used in mobility measurements, a t thermal eiiergies the principal ion in nitrogen is N4+,as argued by Varney and co-workers (104, 128), in hydrogen it is HX+ (129, IS’O), and in oxygen it is 0 3 + (92). Prior to the last observation, Varney (104) and Dalgarno (118) suggested th a t in oxygen the single ion observed is 0 2 + and that the observation of a mobility of 2.3 cm2/volt-sec compared to the predicted polarization value of 2.9 is the result of a substantial charge transfer interaction, even in the molecular case. However, one should expect rather smaller thermal energy

+

+

110

MANFRED A. BIONDI

charge transfer cross sections for molecules relative to those for atoms, since, in most cases, the Frank-Condon principle requires th a t the nuclei of the molecular ion and of the neutral molecule be at similar separations for resonant electron transfer to take place a t long range. It is clear that mobility measurements involving mass spectrographic identification of the ions under study are needed to provide unambiguous determinations of the resonant charge transfer process in molecular gases. A t somewhat higher energies (>10 ev), some preliminary data from beam experiments have been presented by Stebbings and Turner (131) for the cases 02+/02, N2+/N2,and NO+/NO. These studies yield charge transfer cross sections at -100 ev of the order of 10-lb cm2, which are only slightly smaller than the values obtained for atomic species such a s Ne+/Ne and Ar+/Ar. (b) Nonresonant charge transfer. When the ionization energies of two atoms, A and B, are not equal, the charge transfer process, A++B-+A+B+,

(26)

is said to be nonresonant. If we denote the energy difference a t infinite separation between the configurations A+-B and A-B+ by Au,, then, according to the “adiabatic condition” (132), charge transfer will only take place if the collision between A and B is sufficiently violent tha t ( A u m ) ( R / v )< k , where R is a distance of atomic dimensions and v the velocity of relative motion of the colliding particles. Thus, one might expect that for sufficiently slow particles the charge transfer cross section becomes rather small in the nonresonant case. Hasted, in his review of high energy ( > 100 ev) processes ( 5 ) has demonstrated a rapidly decreasing cross section with decreasing velocity in the adiabatic region, i.e., Q,.t exp (-CAu,/v), for H+/We. Further, he has shown a striking correlation between the energy defect, Au,, of the reactions and the energy a t which a maximum cross section is observed, not only for charge transfer but also for ionization and excitation processes. Hasted points out that departures from the “adiabatic” energy dependence, yielding substantially larger cross sections a t low energies, are sometimes observed, possibly as a result of intrusion of other processes in the experimental measurement. It should be noted, however, that as one brings the two atoms A and B together, the energy difference between the two configurations A+-B and A-B+ may decrease, a s a result of differing polarizabilities of atoms A and B, to the point where (Au/ti)(R/v) does become small compared to unity. If, a t this separation, the charge transfer interaction is sufficient, transfer may take place with large probability, leading to the larger-than-expected transfer cross section. It is clear that in “nonresonant” cases no uniform predictions

-

111

LOW ENERGY ATOMIC COLLISIONS

can be made concerning the variation of the charge transfer cross section with energy. Unfortunately, the very low energy region, where the adiabatic condition should lead to small charge transfer, has not been investigated extensively experimentally, since ion beam techniques cannot reach these low energies and ion mobility studies cannot observe the drift velocity of A+ in B if A+ loses its charge to B by transfer. However, the technique of measuring the time dependence of mass analyzed currents of ions reaching the walls from the afterglows of plasmas (93, 133) has permitted the determination of two body rate coefficients and the corresponding averaged cross sections a t -0.04 ev (2’ = 300’K). Dickirisoii and Sayers (133) have studied charge transfer in He0 2 gas mixtures and obtain a value for the two body rate coefficient, P = 2.5 X lo-” cm3/sec, for the process Of

+

0 2 +

0

+ Oz+,

(27)

corresponding to Get1: 3 X cm2 a t an average energy of -0.04 ev. This cross section is more than an order of magnitude smaller than the values for resonant atomic cases such as Ne+/Ne and may involve a quite different process, i.e., atom, rather than electron, transfer (see Section 111, E, 4 ) . Fite et al. (93) obtain a value in this range from their measurements of afterglows in 0, and He-02 mixtures. However, very recent (134) studies by Langstroth and Hasted, using similar techniques, yield a n order of magnitude smaller value, P ‘v 1.8 X cm3/sec, for this process. The various studies are all in rather early stages, and it is not, as yet, possible to decide which is the correct value. Fite et al. (93) report a preliminary value for the transfer process,

-

Nz+

+ Oz+

Nz

+ Oz+,

-

act

(28)

which is rather large, P 2 X cm3 sec, corresponding to 3 X 10-15 cm2. These measurements, a t either a single afterglow temperature (300°K) or over a very narrow range of temperatures, do not permit deduction of the energy dependence of Q L I in the low energy region. However, these types of studies are first comiiig into extensive use (99, 93, 133, l&), and it is expected that information on energy dependences will be forthcoming. Recently, studies of nonresonant charge transfer and atom transfer reactions involving low energy ( < 1 ev) negative ions have been carried out in mass spectrometers employing “high” pressure ion sources (135, 136). Surprisingly large cross soctions, ~ 1 0 - < I ~QCt < lo-’* cm2 were observed for charge transfer reactions such as O-/NOz, SF6-/NOz,

112

MANFRED A. BIONDI

and C1-/N02, in view of the fact that substantial energy discrepancies exist if the reactions involve formation of NOz- without excitation of the internal degrees of freedom of the molecules. Some evidence for quite different behaviors in the variation of Qct with energy has been obtained in much higher energy (2100 ev) beam experiments (94, 131, 137, 138). It is found that the cross sections are of the order of cm2 and show only moderate energy dependences; QCt for N+/Oz, 02+/N2, and N2 +/N0 increases with decreasing energy around 100 ev; Qct for O+/Oz, N2+/02, O+/Nz and N+/NZ exhibits essentially no variation with energy in this range, while for Oz+/O and N2+/0 the cross section decreases with decreasing energy. (c) Accidental resonance charge transfer, If the ionization potentials of atoms A and B are very nearly equal, one has a n accidental resonance and “asymmetrical resonance” (159) charge transfer can occur. Bates and Lynn (119, 139) have argued that for sufficiently slow encounters the probability of charge transfer should be very small. Given that the energy difference a t very large separations of the two configurations A+-B and A-B+ is arbitrarily small, i.e., Au, ‘v 0, as the separation between A and B is decreased, the value of Au arising from the electrostatic potential interactions may become finite (for example, as a result of differing atomic polarizabilities for A and B), and hence electronic excitation will be required to change from the one molecular ion state to the other. Thus, unless the colliding particles have sufficient energy, the adiabatic condition rules out such transitions, and charge transfer will not occur. However, as a result of complexities in calculating the detailed shapes of the potential curves, Bates and Lynn do not provide a n estimate of the critical collision velocity below which charge transfer can no longer occur. One can obtain an estimate of the critical velocity by inquiring whether, before reaching a range Rp a t which the adiabatic condition rules out appreciable transitions between the two states, the total phase for charge transfer is already appreciable. If it is, then charge transfer occurs with high probability. To illustrate, a t a given relative velocity, v, the critical distance for appreciable charge transfer, R,, is given by (Auct/fi)(RJv)

-

1,

(29)

wherePAuct is the level splitting due to the charge transfer interaction in the absence of differing polarizabilities of A and B. The range R, a t which the adiabatic condition rules out, for the given velocity, electronic transitions between the molecular ion states split by the differing polarization interactions is given by

113

LOW ENERGY ATOMIC COLLISIONS

since, at the large values of R with which we are concerned, the polarization interaction is the only important c1ect)rostatic i n t e r a ~ t i o n .Since ~ AucLvaries much more rapidly (- exp - aR ) with separation than does Aupol there is a value of separation, R1, a t which the twosplittings are equal. For R < R1, we haveAurt > Au,,,Land charge transferoccursfreely, while for R > R1, we have nu,, < A U , , ~ ,that , ; is, the adiabatic condition inhibits charge transfer. For a given velocity, if Eq. (29) yields a value of the critical charge transfer distance, It,, which is less than R1, then the charge transfer is not inhibited. However, as the velocity is decreased, R, increases, until finally R, > R1 and we have reached the region in which the charge transfer cross section diminishes with decreasing velocity, a s discussed by Bates and Lynn. For the usual values of atomic polarizabilities, these velocities are very low, corresponding to energies <
-

QCt

He++

+ H --+

He+(2s, 2 p )

+ H+.

(81)

Here the electrostatic energy difference, AIL, between the two configurations, He++-H and He+-H+, is essentially completely determined by the coulomb repulsion between He+ and I%+.I n this case Auci(R1)

=

AuCoul(R1)

when the splittings are the order of volts and hence particle velocities of >lo8 cm/sec are required for a sufficiently violent collision to cause transitions between the two curves. The charge transfer cross section should therefore fall off below energies in the lo4 ev range. This is precisely the behavior observed by Stebbings el al. (94) in their He++/H measurements. 4. Ion-Atom Conversion Reactions. The subject of ion-atom (molecule) reactions is very broad. During the past decade significant advances have been made in the determinations of rates for a substantial number of the various reactions. A variety of techniques have been applied t o these This line of argument was dcveloped in conversations with T. Holstein.

114

MANFRED A. BIONDf

studies, ranging from thermal energy microwave afterglow measurements, in some cases with mass spectrographic identification of the reacting ions (91, 9d), to “high” pressure ion source and mass spectrometer techniques a t energies from -1 ev upwards. As the manuscript for the present review was nearing completion, the exhaustive review by Pahl (140) concerning recent advances in slow ion-atom studies was published. As a result, rather than attempt an abbreviated review of the whole subject, it appears more suitable to outline the classes of reactions studied and to limit detailed comments to a few cases bearing on material appearing elsewhere in the present review. Recently, Hasted ( 5 ) has reviewed atom transfer collisions of the type,

A+

+ BC

---f

(ABC)+ -+ (AB)+

+ C,

(32)

and has cited the relevant measurements a t greater than thermal energies. The very recent studies by Langstroth and Hasted (134), using mass spectrographic observations of a pulsed dc discharge, of the atom transfer reaction, O+ Nz--f NO+ N, have yielded a preliminary rate coefficient of -5 X cm3/sec a t 300”K, the same order of magnitude as for their 0 + / 0 2 “charge” transfer reaction (see Section 111, E , 3, b). During the last decade the existence or rates of a number of ion producing reactions involving excited atoms have been determined. These reactions may be illustrated schematically by

+

+

A* AM AM

+A+

Azf -I e,

+ B - t A + B+ -I- el + AM-+A + A+ -k el

Hornbeck and Molnar (161) postulated the associative ionization reaction (33) on the basis of mass spectrographic observations of molecular ion formation in low pressure noble gases. From the appearance potential of the ions it was concluded that the atom, A*, was in a very highly excited state, within -1 ev of the ionization continuum. The second, well known “Penning” ionizing reaction (34), involving a metastable atom, A, whose excitation energy exceeds the ionization energy of atom B, has been studied by the author (142) in microwave afterglows and by Shollette and Muschlitz (l43), using a low energy atomic beam apparatus, For the case of HeMionizing various atoms and cm3/sec molecules, two body rate coefficients in the range lo-” to are observed a t 300°K. Finally, observation of ionization in pure, single noble gas afterglows (142) led t o the conclusion that metastable-metastable ionizing collisions, reaction (35), occurred with a rather large cm3/sec) two-body coefficient (144).

115

LOW ENERGY ATOMIC COLLISIONS

Ion conversion (coalescing) reactions involve three-body collisions, i.e., A + + B + C + (AB)+ c. (36)

+

Phelps and Brown (91) used microwave afterglow aiid mass spectrographic techniques to study ambipolar diffusion of He+ and Hez+ions in helium. By analyzing the rate of loss of the electrons in the plasma they were able to show that conversion of the atomic ion to the molecular ion took place a t thermal energies (300’K) by the reaction, He+ 2He -+ He2+ He, with the three-body rate coefficient,

+

+

K

=

(6.2 f 1.4) X

cme/sec.

This analysis was supported qualitatively by the observed time dependences of the wall currents of He+ and He2+. From studies of electron density variations during microwave afterglows in helium-neon mixturefi, Oskam (145) deduced conversion of Ne+ ions to either Ne2+or (HeNe)+ with a total rate coefficient of -3 X lO-ao cm6/sec by the reactions Ne+ He Ne + Ne*+ He or (HeNe)+ Ne. Without mass analysis he was unable to evaluate the relative contributions of each branch. Oskam also postulated a charge transfer and dissociation process,.

+

+

He2+

+ Ne

--$

Ke+

+

+ He + He,

+

--f

(37)

from his afterglow mixture studies. Pahl and Weimer (146) confirmed this reaction by mass spectrographic studies of the positive column of a discharge tube. Although ion conversion reactions involving coalescence generally exhibit three-body pressure dependences, there is some evidence that, in more complex cases, the three-body process may saturate, leading to observation of a two-body dependence. Varney (1O4), in his ion mobility studies in nitrogen, was led to postulate the presence of two ions, N2+ and N4+, whose relative abundance changed with gas pressure and ion energy. Saporoschenko (128), using a relatively high pressure ion source and a mass spectrometer, found that the N4+/N2+ abundance ratio varied linearly with pressure, supporting Varney’s postulated 2-body formation mechanism, Nz+ Nz (N4+)*, (38)

+ *

where the vibrationally or rotationally excited (N4+)* is subsequently deexcited by collisions before auto-dissociating. Preliminary afterglowmass spectrometer studies by Fite et al. (93) of the time dependences of ion currents reaching the wall of the discharge tube confirm the two-body pressure dependence over the pressure range 0.1-1 mm Hg and yield a

11G

MANFRED A. BIONDI

very tentative rate coefficient for the reaction of -5 X cm3/sec, cm2. It is, however, corresponding to an average cross section of rather surprising that a t low pressures (-0.1 mm Hg) the collisions which stabilize the (N4+)*complex can occur rapidly compared to the autodissociation time, which should be rather short for such a relatively “simple” molecule. For the case of hydrogen, the reaction observed by Stevenson and Schissler (147) in studies of low energy (-1 ev) ion conversion in the ion source of a mass spectrometer, i.e.,

Hz+

+ Hz-+ H3+ + H,

(39)

has been suggested (129) as important at thermal energies in determining the ion present in mobility experiments, with Confirmation of the large abundance of H3+ in drift tubes by Barnes et at. (130). Gioumousis and Stevenson (148) have analyzed the kinetics of the ions in the ion source, where the ion energy is determined by the applied repeller field, and find that the experimental observations are consistent with a conversion cross section which varies inversely with ion velocity for ion energies 5 1 ev. The associated two body conversion coefficient is rather large, cm3/sec. For the case of negative ions, there has been a great deal of speculation (149, 150) concerning ion identity in various laboratory measurements and in ionospheric analyses. For example, in the case of oxygen, reactions of the types, 0- f 202 -+ 0 3 0 2 (40) (02-)* 0 2 -+ 030, (41)

+

+

+

have been postulated to account for 03-production in the laboratory experiments and in the upper atmosphere. At the present time there are no measured values for reactions (40) and (41); in fact negative ion-atom reaction rate determinations are quite scarce (135, 140).

IV. ATTACHMENT AND DETACHMENT OF ELECTRONS I n this section we review recent studies of the attachment of low energy electrons to atoms or molecules to form negative ions and the processes by which the electron is detached from the negative ion. A brief discussion is presented of some new information concerning the electron affinities, i.e., the binding energy of the electron to the atom or molecule, associated with these processes. Emphasis is placed on negative ion formation and destruction processes in oxygen, because in recent years a considerable number of researches have centered on this gas, with a n attendant improvement in our understanding of the relevant processes,

117

LOW ENERGY ATOMIC COLLISIONS

and also because electron attachment to oxygen atoms or molecules is of great importance in the ionosphere. In addition, the types of attachment and detachment processes which have been found to be significaiit in oxygen are illustrative of most of the important reactions for other electronegative gases. The general subject of negative ions and the attachment and detachment processes have been reviewed recently by a number of authors. Since Massey’s (151)monograph on negative ions appeared in its second edition in 1950, Branscomb has discussed progress in negative ion studies up to 1958 (4) and very recently has reviewed the subject of photodetachment of electrons from negative ions (21, 152). In addition, in discussing charged particles in the upper atmosphere, Dalgarno (150) has reviewed the attachment and detachment processes of possible relevance to the ionosphere. The studies of the various attachment and detachment processes have been carried out in the laboratory by electron drift tube, microwave afterglow, electron beam, and mass spectrographic techniqucs of the type already discussed in earlier sections. In addition, crossed negative ion and photon beam apparatus and spectroscopic studies of electric arcs have been used to investigate the properties of negative ions.

A . Radiative Attachment and Photodetachment The process of radiative attachment and its inverse, photodetachment, may be represented for oxygen atoms and molecules by the reactions, O+eGO-+hv (42) 0 2 c 02hv. (43)

+

+

I n the capture process the transition of the electron from a free (continuum) state to a bound state of the resulting negative ion is accompanied by the emission of a quantum of radiation (the affinity spectrum). Thus, for a single negative ion bound state, the radiative attachment spectrum for atoms exhibits a minimum frequency, vInln, corresponding to the transition of a n electron of zero kinetic energy, and extends to higher frequencies in accordance with the relationship, hv = E A ue, where EA, the electron affinity, is the binding energy of the negative ion, and ua is the kinetic energy of the initially free electron. As in the case of radiative recombination between electrons and positive ions, the intensity distribution in the affinity spectrum depends not only on the transition probability for each electron energy but also on the kinetic energy distribution of the electrons taking part, in the radiative attachment process.

+

118

MANFRED A. BIONDI

To date it has not been possible to detect radiative attachment by measuring the loss rate of free electrons; however, the affinity spectrum of H- was first observed in the laboratory by Lochte-Holtgreven (153) in studies of a water stabilized hydrogen arc. More recently Weber (154), in shock tube experiments at Kiel, has obtained agreement between his observed intensity distribution and the expected H- affinity spectrum distribution, on the assumption of local thermodynamic equilibrium. I n studies of reaction (42) Boldt (155), also a t the Kiel laboratories, has observed the 0- spectrum from a higher temperature atmospheric pressure arc. Using the measured temperature profile of the arc and assuming local thermodynamic equilibrium he was able to separate the intensity of the affinity spectrum from the other sources of radiation. Using Kirchhoff’s Law he then deduced the inverse (photodetachment) rate and obtained satisfactory (-30 %) agreement with the measured values of Smith and Branscomb (156) (see later discussion in this subsection). Since the most general deductions of the coefficients for the radiative capture of electrons by atoms have been made from the photodetachment studies rather than from the affinity spectrum observations, we shall discuss the attachment rate determinations after describing the photodetachment measurements. Smith and Branscomb (15‘7) and their colleagues have developed a crossed beam apparatus with which they have determined the photodetachment cross sections as a function of photon energy for a number of atoms and molecules. I n principle, a beam of negative ions is crossed by photons capable of causing photodetachment, the detached electron current signal providing a measure of the photodetachment probability. I n practice, rather formidable problems must be overcome in order to obtain a n accurately measurable detached electron signal. Considerable effort went into the design of a negative ion source and mass selector to give a reasonably high beam current of negative ions (-loF7 amp at -300 ev) with a low noise characteristic. Further, a very intense photon beam was generated by means of a high intensity carbon arc and a n fj’l.5 optical system. The desired wavelength bands were isolated by means of absorption and interference filters, resulting in approximately 1 watt of the desired radiation crossing the negative ion beam. I n order to detect the weak signal of detached electrons in the presence of surface photoelectrons and scattered ions, a combination of weak electric and magnetic fields was used to collect the detached electrons and suppress the other currents. Finally, the signal-to-noise ratio was improved by a narrow-band, phase-sensitive detector locked to the modulated photon beam. The absolute photodetachment cross sections were, in general,

119

LOW ENERGY ATOMIC COLLISIONS

obtained by comparing relative measurements as a function of wavelength for a particular negative ion with measurements for H- and 0-, whose absolute integrated cross sections had been measured by Branscomb and Smith (156, 158). I n these absolute measurements the photon flux was determined radiometrically and an absolute accuracy of k 10% obtained. The measured photodetachment cross section, Q p , , , for H- as a function of photon wavelength is indicated in Fig. 23. The experimental points

1

0

0

0.2

0.4

0.6

0.8

1.0

a( PJ

1.2

1.4

1.6

1.8

2.0

FIQ.23. Cross section for photodetachment of electrons from H- ions as a function of photon wavelength. The solid dots represent the experimental measurements of Branscomb and Smith; the long-short dashed curve is the theoretical calculation of Chandrasekhar and Elbert, the short dashed curve that of Chandrasekhar, the solid curve that of John, and the long dashed curve that of Geltman and Kraus (see text for details).

are indicated by the dots, together with several theoretical calculations using dipole velocity matrix elements and a Hart-Herzberg twenty parameter bound-state wave-function (see Section 11).The experimental points have been adjusted within their _ + l o % accuracy range by normalizing to the theoretical curve of John (20) a t X = 0.,53 p. The long-short dash curve represents the static central field calculations of Chandrasekhar and Elbert (169);the short dashes, the plane wave calculation of Chandrasekhar (160); the solid line, the exchange central field calculations of John (20);and the long dashes, the variational calculation of Geltman and Kraus (26). The agreement between experiment and the

120

MANFRED A. BIONDI

theories of John and of Geltman and Kraus is good for X < 1 p. The deviations at longer wavelengths (approaching threshold) may result from the failure to include in the theories the long range effects of atomic polarization by the free electron. While the photodetachment cross section for H- is important in considerations of stellar opacities, the photodetachment of electrons from 0- and 0 2 - is of interest in considerations of free electron behavior in the ionosphere. The measurements of 0- and 02- detachment cross sections [Eqs. (42)and (43) going to the left] have been reported in various papers by Branscomb, Burch, Smith, and Geltman (156, 161-163). I

7

I

I

x 10-18

I

-I -

65 I

I

-

I

Photon Energy lev)

FIG.24. Experimentally determined photodetachment cross sections for 0- and 0,- as functions of the photon energy.

The results for the photodetachment cross section in 0- shown in Fig. 24 were obtained from absolute determinations of the integrated cross section and a successively improved set of relative measurements in the vicinity of the threshold energy. These relative measurements were made to fit a predicted threshold law increasing roughly as (hv - hvrnin)" for approximately 0.3 ev beyond threshold (dashed section of curve). This procedure permitted a n accurate determination of the minimum photon energy capable of causing photodetachment of electrons from the negative ion beam, ( h ~ ) ,=~ 1.465 i~ 0.005 ev. The relationship of this value to the electron effinity of 0 is discussed in Section IV, E. The small additional bump in the curve just below the main threshold results from a small contribution from the 2Pf6configuration of 0-, lying slightly above the 2Py6 state.

121

LOW ENERGY ATOMIC COLLISIONS

I n the case of photodetachment from 02-,a number of complications relative to atomic ions may arise. First of all, since the photon does not carry appreciable momentum, the photodetachment transitions between 0 2 - and O2 are governed by the Franck-Condon principle, which requires that the molecular internuclear separation remain essentially unchanged during the transition. Thus, if the equilibrium internuclear separations of 02-and of 0 2 are appreciably different, the photodetachment of 0 2 in the u = 0 vibration state will lead to a vibrationally excited O2 molecule. I n addition, the various thermally excited rotation and vibration states of the negative ion will, in general, involve slightly different photon threshold energies, leading to a smearing out of the photodetachment cross section in energy. The photodetachment cross section for 02-was measured by Burch et al. (168)for photons of energies between 0.5 ev and 3 ev (see Fig. 24). No threshold energy was found, as might be expected in view of the above mentioned smearing out effects and the fact that the threshold law for the 02-(2a,) state is expected (21) to have a leading term of the form (hv - h v m , J ~ . The solid curve through the data points is based on the expected threshold law starting a t a threshold value of 0.15 ev. As recognized by the authors (163), this choice of threshold energy is rather arbitrary, since in general the threshold law behavior for other ions (e.g., 0-) extends over a much more limited energy range. This point is discussed in more detail in Sections IV, C , and IV, E. Before discussing the radiative attachment rates inferred from these measurements, it should be noted that photodetachment from C-, S-, OH-, OD-, C1-, Br-, and I- have also been studied. I n the case of C- (164)a curve resembling that obtained for 0- was obtained, with a threshold photon energy of 1.25 & 0.03 ev and rising to a maximum cross section of -1.4 X lo-’’ ,me a t 1.5 ev. Slight evidence for an excited metastable state, possibly C - ( 2 D ) , was indicated by a weak photodetachment signal a t lower photon energies. Studies of S- (165) also yielded a curve similar to 0- and a threshold energy of 2.07 0.09 ev. I n studies of photodetachment from OH- and OD- ( d l ) , the observed threshold photon energy of 1.78 ev has becn indicated to be the electron affinity for the u = 0 to o = 0 transition, since no difference in threshold energy for OH- and OD- was detected. Very recently, Berry et al. (166) have studied the absorption spectra of the halogen negative ions C1-, Br-, and I-. They find two distinct absorption steps in the cases of C1- and Br-, corresponding to the two possible ground configurations, ZP$$and 2P,i, of the halogen atoms produced by the photodetachment. Preliminary values of the corrected threshold photon energies are found to be 3.65 ev (Cl-), 3.39 ev (Br-)

+

122

MANFRED A. BIONDI

and 3.07 ev (I-), in reasonable agreement with values of electron affinities deduced by other means (21). The photodetachment measurements as a function of photon energy can be inverted, by the use of detailed balancing, to yield the radiative attachment rates for transitions connecting the particular end points to which the photodetachment studies refer, In some cases, when coupled

l

o

-

l

4

r

Electron Energy (ev)

FIG.25. Radiative attachment coefficients for electron capture by H, 0, and 0 2 as functions of the incident electron energy. These curves werc deduced by inversion of the photodetachmcnt data. For the case of 02,several predicted curves are shown, depending on the value chosen for the electron affinity (see text).

with auxiliary information, these calculations can be regarded as giving a quantitative measure of the over-all radiative attachment coefficient a t each electron energy. The predicted (21, 152) two-body radiative attachment coefficients, &ad, for reactions of the type (42) and (43) are given in Fig. 25 for H, 0, and 0 2 . For the case of hydrogen, involving attachment into an s state, the threshold law predicts a linear increase of &ad with electron energy, while for oxygen atoms, involving formation of a p State, a finite value of orad at zero energy is expected, and a relatively small change with energy is predicted from the inversion of the

LOW E N E R Q Y ATOMIC COLLISIONS

123

photodetachment data. Thus, even with the averaging effect of a distribution in energy of electrons, quite different temperature dependences are to be expected for radiative attachment leading to s state and p state formation. The predicted Brad values for €I and 0 obtained from the photodetachment measurements can be regarded as quantitative indications of the actual radiative attachment coefficients. For the case of H, we have agreement of the predicted photodetachment coefficiei;ts with theory (ZO), on the one hand, and with the shock tube determinations of the affinity spectrum radiation ( I S 4 ) , on the other. For the case of 0, where it is conceivable that there is a lower lying negative ion state than one with 1.47 ev binding energy (see Section IV, E ) , we are assured, by the agreement of the photodetachment observations with the determinations from arc studies of the affinity spectrum radiation (155), that radiative transitions to such a state are less important and therefore, the predicted radiative attachment rate is essentially correct. For the case of 0%) no such statements can be made. It is not clear in what electronic or vibration state (or states) was the 0 2 - beam used in the photodetachment studies. Since there have been no affinity spectrum determinations for the case of O2 to assure us that radiative capture of electrons by 0 2 molecules in predominantly the v = 0 state leads to essentially the inverse of the observed photodetachment spectrum, the curves of Fig. 25 for 0 2 can neither be regarded as an upper nor a lower limit to the radiative attachment coefficient. The several curves, labeled 0, 0.2, and 0.5 ev, show the effect on the deduced b r a d values of different choices of the value of the electron affinity. The photodetachment work originally used the value 0.15 ev for the affinity, while collisional detachment studies suggest a value of 0.44 ev (Section IV, C). If the radiative capture of electrons by O2 (v = 0) molecules leads predominantly to the formation of negative ions in the state in which they were formed in the beam of the photodetachment apparatus, then the curve of Fig. 25 with the appropriate binding energy for this state of 02-provides the desired Brad values. However, if, for example, the equilibrium spacings of O2and of 02are significantly different, and the photodetachment beam consisted of 02(v’ = 0) ions, then the photodetachment studies apply to transitions of the type 0 2 - (v’ = 0) + 0 2 (v > 0), while for the attachment rate we are interested in transitions of the type 0 2 (v = 0) -+ 0 2 - (v’ > 0). In the latter case, the radiative transition probabilities bear no direct relationship to the inversion of the photodetachment process and may be larger, smaller, or the same in value. It appears, therefore, that direct measurements of the radiative attach-

124

MANFRED A. BIONDI

ment process in 0 2 are required, although if the capture cross section for thermal electrons is of the magnitude suggested b y the inversion of the photodetachment data cm2 < o r a d < 10P5cm2),the experimental problems for such a determination will be formidable.

B. Dissociative Attachment and Associative Detachment The radiationless electron capture process of dissociative attachment and its inverse, associative detachment may be illustrated, for the cases of oxygen molecules and ozone, by the reactions, 0 2

+ e * (O2-Iunst.

O3

+e

and

$ (&-),,*st.

+ 0, so- + + + 0. 0-

0 2

02-

(44) (45a) (4513)

Here the potential curves of the neutral molecule and negative ion are such that a n electron of a particular kinetic energy collides with a molecule to form a n unstable state of the molecular negative ion (see Fig. 26, which represents hypothetical potential curves for 0 2 and 0 3 made t o conform to experimental measurements, 108, 167, 168). The negative ion begins to dissociate, and in a short time reaches a separation (e.g., E , in Fig. 26a) where autodetachment of the electron can no longer occur, and the dissociation goes to completion. Recently, Dunn (169) has again pointed out that, as a result of the dependence of transition probability on orientation of the internuclear axis with respect to the direction of the incoming exciting electron, preferential directions of dissociation with respect to the electron direction may result. Since dissociation times are short compared to rotational periods, if the exciting electrons have a definite direction in space (as in an electron beam experiment), for certain molecular configurations of the states involved in the reaction, the dissociation will take place predominantly with the fragments moving parallel to the beam, while for others the reaction proceeds predominantly with fragments moving perpendicular to the beam. For the usual mass spectrometer sources and Lozier-type tubes used in many of the dissociative attachment studies, where particles moving parallel to the beam are not detected, substantial errors in the interpretation of results may occur when the molecular configurations of the states involved are not accurately known. Reaction (44) has recently been restudied by both electron beam (170-173) and electron swarm techniques (108, 167, 174, i75). The electron beam studies of Buchelnikova (171) have indicated that the threshold electron energy for the reaction is -4.6 ev and that a peak attachment cross section, &diss = (1.3 k 0.2) X 10-l8 cm2, is attained

125

LOW ENERGY ATOMIC COLLISIONS

a t -6.2 ev. Craggs et al. (170) and Schulz (172) obtained substantially identically shaped cross section curves, as indicated in Fig. 27; however, Craggs et al. reported a peak cross section of 2.3 X lo-’* cm2. Schulz carefully redetermined the peak cross section in his narrow-energy-spread beam tube and obtained a value of 1.3 X lo-’* cmz, estimated to be accurate to k 15%. In the same tube Schulz also determined the ionization cross section of 0 2 molecules by electrons of 30 ev energy and obtained excellent agreement with the value of Tate and Smith (17‘6), la) I

I

7 -

6 -

-s

5 -

P e

4 -

Y

I ,

I

I

02 + 0

!= m

t

3 2 -

-1

I

0

2 I I 2.0 3.0 0-0Internuclear Separation IAngstroms) I

1.0

~

02 - 0 Internuclear Separation

FIG. 26. Hypothctical potential energy curves for oxygen molecules and ozone based on available spectroscopic and negative ion measurements. In part (b), the curve for 03-,for which a n electron affinity of 2 3 ev is indicated, is not drawn to the scale of the rest of the figure.

while Craggs et al. did not obtain such agreement in their work. Thus it appears that Buchelnikova’s absolute cross section determination is correct. Dissociative attachment in ozone has been investigated by Curran (1SS), who observed 0- and 0 2 - formation as a result of the two branches, reactions (45a) and (45b). From the electron energy a t which each ion first appeared, he concluded that the potential “curves” (obtained by holding the internuclear separation of the diatomic fragment fixed during the reaction) must exhibit crossings of the type shown in Fig. 26b. The information concerning electron affinities of O2and Oa obtained from the electron beam studies of dissociative attachment is discussed in Section IV, E.

126

MANFRED A. BIONDI

I n addition t o oxygen molecules, dissociative attachment in Iz and SFa has also been extensively studied. By combining the results of microwave afterglow and mass spectrographic techniques, Biondi and Fox (17'7) have determined the absolute cross section as a function of electron energy for I- formation. The microwave studies were made in

Electron Energy. w

FIG.27. Comparison of experimental determinations of the r..ape of the electron capture cross section curve as a function of electron energy for the reaction 0 2 e -+ 0- f 0. The data of Schulz leads to a value at the maximum of &di&s = (1.3 5 0.2) X 10-18 cma.

+

iodine vapor with 3 mm Hg pressure of helium "recoil" gas to assure that the electrons in the afterglow were a t T, = 300°K. The measurements yielded a n average attachment cross section &dias. =

3.9

x

10-15 cm2

over the Maxwellian electron distribution a t 300°K. The mass spectrograph studies, using the RPD method to obtain a narrow effective

LOW ENERGY ATOMIC COLLISIONS

127

energy spread, yielded relative values of the attachment cross section from 0-1 ev. Ry a computer solution of the integral equation relating the averaged cross section to the actual cross section and the known electron energy distribution in the RPD experiment, the variation of the cross section with electron energy was determined. An absolute scale for this cross section was established by averaging over a thermal (300°K) electron distribution and comparing with the microwave value. It was found that the cross section increased rapidly with decreasing cm2)a t low (-0.1 ev) electron energy, reaching very large values (> energies, in contrast to the conclusions of Buchdahl (178), who found a decrease in cross section with decreasing energy below 0.2 ev. Thus it appears that, in contrast to the case of 0 2 , a repulsive branch of the Izcurve crosses the I2curve a t its minimum, leading to a maximum capture cross section for zero energy electrons. Hickam and Fox (179) studied electron attachment processes in SF6 and found that dissociative attachment to form SF5- occurred with maximum probability for electrons of -0.1 ev energy. The cross section at this energy appeared to be 10-l6 cm2 or larger, the uncertainty stemming from problems of determining the detection sensitivity for ions with dissociation kinetic energy. A rather large number of dissociative attachment reactions have been recently measured or remeasured, in general using Lozier type apparatus or mass spectrometers, in some cases with the RPD electron sources. I n water vapor, no attachment of very low energy (thermal) electrons was found (171, 180, I S l ) , although a t higher ( >6 ev) energies appreciable negative ion formation was observed. I n mass spectrographic studies of H-/H2 (182), Cl-/HCl (183), O-/NOz (284), and F- and C1-/CC13F (185) dissociative attachment was found to occur only a t higher (>>1ev) electron energies. Similarly, Lozier apparatus studies of 0-/CO (186) and O-/COz (187) indicate appreciable attachment cross sections, 3 X and 5 X cm2, respectively, only a t higher (-10 ev) electron energies. On the other hand, Curran (188) observes the attachment process F-/SFe to occur a t essentially zero electron energy. However, the identical shape of the F- cross section to the SF6- formation cross section may indicate that the F- is formed by the occasional spontaneous decay of the internally excited SF6- ion (Section Iv, 0). I n the same vein, mass spectrometer (189) and trapped electron (190) studies of O-/NOz indicate formation of 0- for electrons of zero energy and upwards. A peak in the cross section a t -0.7 ev is evidently associated with the usual dissociative attachment process, while Schulz (190) presents evidence that a second peak a t -2.2 ev results from spontaneous decay of a

128

MANFRED A. BIONDI

temporary negative ion state of N 2 0 into 0- and N2 in various vibration states (see the discussion of temporary negative ion states, Section 111, 6). When the dissociative attachment studies include precise determinations of the electron energy and the kinetic energies of the dissociating fragments, information concerning electron affinities (Section IV, E ) can be obtained. The process of associative detachment, i.e., reactions (44) and (45) going to the left, is included in this review-largely to indicate the need for measurements of this potentially important process. Dalgarno (150) argues that rate coefficients as large as 10-lo cma/sec for this two-body detachment process are possible. As will be seen from Fig. ZGb, the process 02- 0 --+ 0 3 el is exothermic and may, therefore, be a n important detachment process in the mixed 02-0 region of the upper atmosphere.

+

+

C. Three-Body Attachment and Collisional Detachment

As in the case of dissociative attachment, three-body attachment involves the collision of an electron with a molecule to form a n unstable negative ion; however, in this case the negative ion is not able to dissociate but must transfer energy to a third body in order to be stabilized. For the case of low energy (51 ev) electrons in 0 2 , experimental evidence suggests t hat a slightly modified form of the process originally proposed by Bloch and Bradbury (191) accounts for the electron capture. Referring to Fig. 2Ga, an electron of the proper energy can be captured by an 0 2 (YZ2,-) molecule in the v = 0 state to form a n unstable, vibrationally excited negative ion,

+

(OZ),=O e

(0~-)~=~,

(46)

where in the absence of accurate knowledge of the vibration spacing in the negative ion it is not possible to assign a precise value for m. If, before the reaction reverses by autodetachment, a collision with a third body reduces the vibrational excitation, then a stable negative ion is formed. If all of the vibrational excitation is removed a t this collision, we have

+

(02-),=, X

, "(O2-),,0

+ X + energy.

(47)

If the third body, X, is an atom, then the energy must appear a s translational motion; if it is a molecule, then the energy can also appear as internal vibration. I n over-all effect the attachment process obeys a three-

LOW ENERGY ATOMIC COLLISIONS

129

body equation, (OZ),,O

+ e + X * (O~-),=O+ X + energy.

(481

Recently, there have been a number of studies of the attachment of low energy electrons in oxygen using drift tube (108, 167), ionization chamber (192), and microwave afterglow techniques (195-196). The results of these studies fall into two categories. Two of the microwave discharge-afterglow studies (194, 195) confirmed the results of a n earlier, preliminary microwave study (197) by the author in which, a t thermal (300°K) electron energies, a rather small rate of electron loss was found which gave a n apparent two-body attachment process with a cross section of em2. On the other hand, extensive measurements from electron drift tube (108, 167), ionization chamber (192), and microwave afterglow studies of a plasma produced by a high energy electron pulse (195) all conclusively show that the attachment of low energy (0.01-1 ev) electrons is by a three-body process of the type illustrated in reaction (48). We shall discuss shortly the reasons for the low electron loss in the niicrowave dischargc-afterglow measurements. The recent demonstration that the thermal electron attachment accurately obeys a three-body pressure dependence over a pressure range from 0.01 mm Hg (198) to greater than 150 mm Hg (193) removes a longstanding difficulty in the Bloch-Bradbury explanation of Bradbury's data. Presumably as a result of experimental difficulties in the 1930's in making low energy measurements, Bradbury concluded that the low energy attachment process obeyed a two-body pressure dependence over the pressure range of his studies ( 35 mm Hg). This required that the stabilization reaction (47) proceed with such rapidity that every excited ion be stabilized before autjodetachment (reaction (46) going to the left) could occur. Even if an incredibly large stabilizing cross section, -10-12 mi2,was taken, a very long autodetachment time, -1O-l" sec, was required. The new measurements are consistent with more realistic values of these quantities (108). In the drift tube studies of Chanin, I'helps, and Biondi (CPB) (108, 167), a fraction of the photoelectrons ejected from the cathode became attached t o oxygen molecules t o form negative ions on passing through the drift tube. By observing the time dependence of the arrival of the negative ions at the collector, the attachment coefficient as a function of E / p was determined. The attachment coefficient as a function of the average electron energy in the swarm was then obtained from published values or' average energy as a function of E / p . It was possible to carry the measurements t o sufficiently low E / p values to permit reasonable extrapolation of the data to thermal electron energies at each gas temperature.

130

MANFRED A . BIONDI

The energy dependence of the three body attachment coefficient,

K(Oz), obtained by CPB is shown in Fig. 28. I n order to facilitate the measurement a t small drift fields, helium was added to the oxygen to lessen diffusion effects. The effect of helium as a stabilizing agent has been evaluated separately and is discussed shortly. It will be seen that a t both gas temperatures, 77 and 300"K, the attachment coefficient reaches a maximum a t an average electron energy of -0.1 ev, suggesting that this is the energy required to reach the unstable, vibrationally excited negative ion state (see Fig. 26a). A t 300°K a thermal (ti, 'v 0.039 ev) attachment coefficient of somewhat less than 3 X

Average Electron Energy ( e v )

FIG.28. Dependence of the three body attachment coefficient, K(Oz), on average electron energy at gas temperatures of 77°K (dashed curve) and 300°K (solid curve).

cm6/sec is obtained, while a t 77°K (tia N 0.01 ev) a thermal value of cma/sec is indicated. At T = 195°K the thermal value is found < t o be 1 X cme/sec. The microwave studies of van Lint (193) yield similar 195-300°K values, but indicate that a minimum value is attained at -170°K and that with further decrease of temperature the K values cm6/sec is attained. increase, until a t 77°K a value of > 2 X The effectiveness of various gases acting as the third body, X, in stabilizing the reaction has been determined from mixture studies. The energy dependences of K(Oz), K(N2) and K(He) obtained by CPB are shown in Fig. 29. It will be seen that the K(N2) values are in reasonable agreement with the measurements of Bortner and Hurst (192) which do not extend to quite as low energies. (The K(Oz) measurements of Bortner and Hurst, obtained in nitrogen-oxygen mixtures at 300"K, are, however, -40% lower than the values a t >0.3 ev given in Fig. 28.) It will be seen that nitrogen and helium are substantially less effective than O2in stabilizing the attachment reaction. It is not surprising that

131

L O W ENERGY ATOMIC COLLISIONS

for helium, where the vibratiollal energy of the 0 2 - must be converted to energy of translation between He and 0 2 - , the stabilization is less efficient than for oxygen, where both vibration transfer and possibly charge transfer may deexcite the negative ion. (There is some indication

/ Hurst and BortnerT

-

\

-- 77°K 300°K

0

'0b:b I

0.1

.O

Average

Electron

Energy (ev)

FIG.29. Comparison of the stabilizing offects of 02,N,, and Hc acting as third bodies in the attachment of electrons to 0,. The dashed (77°K) and solid (3OO"li) curvcs are the data of Chanin, Phclps and Biondi, which are comparcd with the values a t higher energies of K(N3) measured by Hurst and Bortner.

that the vibration spacing in 0 2 - may be rather close to that of 0 2 . ) For nitrogen, the absence of resonance with 0 2 - in vibration spacing may account for the decreased stabilizing efficiency. I n addition, stabilization by charge transfer is not possible in this case. The thermal (3OOOIi) values

132

MANFRED A. BIONDI

of van Lint (193) are in the ratio K ( N Z ) / K ( O 2= ) 0.06, in reasonable agreement with CPB,’* and in the ratio K(He)/K(02) = 0.04, in strong disagreement with CPB. The accuracy of the mixture data in both experiments is rather poor, and therefore, substantial errors in the deduced K values may result; however, the difference between the two K(He) measurements is unexpectedly large. In view of the more extensive data presented in CPB’s determinations of K(He), these values are, for the present, given more weight. Earlier in this subsection it was noted that studies of the decay of electron density following creation of a microwave discharge in oxygen (194, 195, 197’) yielded a smaller, apparently two-body attachment loss quite inconsistent with the above results. This apparent contradiction may be removed by the following considerations, Suppose some active species, capable of causing detachment of the electron from the negative ion [e.g., reaction (48) going to the left], is created in substantial numbers in the microwave discharge. The electron density during the afterglow then quickly decays by negative ion formation until the rate of detachment by the active species just balances the rate of attachment. If the active (excited) species is itself predominantly deexcited by collisions with neutral molecules, then as the density of the excited species dccreases, the quasi-equilibrium concentration of free electrons follows. Thus, the final electron decay is controlled by the excited species decay, which by our hypothesis obeys a two-body (varies linearly with neutral density) destruction law. Nicholls and Hopwood (199) suggested that the excited entities were vibrationally excited neutral molecules. It is estimated, however, th a t the lifetimes of the v 3 3 vibration states necessary to cause detachment are far too small t o be consistent with the observed decay time scale (see discussion in CPB, 108). It is possible that this attractive hypothesis may be rescued by substituting the metastable, alA, state, lying about 1 ev above the ground 3Z,- configuration of 0 2 , a s the excited species. However, no data are available concerning collisional destruction rates for this state. Although the above hypothesis can not be quantitatively checked, it does provide a n explanation for the observation of the proper three body attachment coefficients in microwave studies of electron decay froin a plasma created by irradiation of a gas with Mev electrons (193). Here, with ionization and excitation caused by electrons decaying in energy, the population of low-lying excited states relative to ionized molecules 78 Note added in proof: Hasted and co-workers (private communication, 1962) have obtained a value, K ( N 2 ) = (1.4 f 0.2) X 10-30 cmC/sec, from microwave afterglow studies a t 300°K, which is considerably larger than the values of CPB or of van Lint.

LOW E N E R G Y ATOMIC COLLISIONS

133

and electrons is much smaller than in a conventional microwave plasma, in which electrons slowly gain energy in the field until they make exciting and, much less frequently, ionizing collisions. Before leaving the subject of three body attachment by very low energy electrons, it should be noted that Hammond et al. (LOO) have obtained preliminary evidence of very rapid attachment of thermal electrons in NOz, although a simple three body attachment process is not sufficient t o explain the observed pressure dependence.

Temperature

(OK)

FIG.30. Thermal energy values of the three body attachment coefficient, K ( O ? ) and of t h r collisional detachment coefficient, )!?deb, as functions of the gas temperature.

The inverse of the three body attachment process is collisional detachment of the electron from the negative ion. At temperatures of 300 and 370°K, CPB were unable to detect any detached electrons in the drift tube. Phelps and Pack (201) made extensive studies a t higher temperatures, 42O-58O0Ii, and obtained values for the two body detachment coefficient, Pd(.t. ranging from to cm3/sec over this temperature range (see Fig. 30). Using detailed balancing on the reaction, 0 2

+e + * 0 2

02-

+

02,

(49)

one has a t equilibrium, K [ 0 2 ] 2 [ e=] P d e t . [ 0 2 ] [ 0 2 - ] , where the brackets are used here to denote particle concentrations. From the law of mass action one then has

K/Pdet. = CT-9: exp [ e ( E A ) / k T ] ,

(50)

where the coefficient C involves statistical weight factors and funda-

134

MANFRED A. BIONDI

mental constants. From the extrapolated thermal K values shown in Fig. 30 and the measured @dp?t. over the temperature range 420-580°K, Phelps and Pack obtain a value EA = 0.44 0.02 ev for the affinity of 0 2 . (See, however, discussion in Section IV, E.) These studies of thermal attachment and detachment in oxygen considerably modify previously proposed values for the ionosphere (see for example Bates and Massey, 202). If attachment to trace constituents of the ionosphere is unimportant, as is generally believed, then attachment to O2via the three body process is dominant to altitudes of -90 km, where radiative attachment to oxygen atoms begins to become important. In addition, the small detachment rates observed in laboratory studies require substantial readjustments in the model used to infer electron lifetimes in the D-region from polar cap blackout observations (203).

D. Attachment to Complex Molecules An additional, radiationless electron capture process which can occur with great efficiency involves a complex molecule such as SFa. Here the initial capture process is apparently of the form

(SFd

+ * (SFB-)~*,~., e

(51)

where the energy released in transferring the electron from the free to the bound state appears as excitation of the internal degrees of freedom of the complex molecule. It is argued that, as a result of the great number of ways in which this energy can be distributed among the internal modes, the time for the molecule to come back to the configuration necessary to eject the electron by autodetachment is very long sec). Thus, stabilization by collision with a third body might easily show a saturation a t rather low pressures (-1 mm Hg), indicating that essentially every excited negative ion is stabilized before autodetachment can occur. Hickam and Fox (179) have studied negative ion formation in SFs using an R P D electron gun to obtain a narrow electron energy distribution. They find that the maximum capture cross section for reaction (51) occurs a t an electron energy of 0 f-0.05 ev and that the capture process exhibits a sharp, “resonance” characteristic with a half width of a t most a few hundredths of an ev, the uncertainty in these values stemming from the fact that the effective electron energy distribution used in these studies had a half width of -0.1 ev. They estimate that the peak of the capture cross section is in excess of cm2. Also, from the time of flight through their mass spectrometer it can be shown that the lifetime of (SFs-) * against autodetachment or dissociation must exceed sec. mm Hg) used in their ion source, collisional At the low pressures ( 5 stabilization of the excited ions is not expected.

LOW ENERGY ATOMIC COLLISIONS

135

It is interesting to note that Curran (188)observes that the F- formation in SF6 also exhibits a sharp, “resonance” characteristic with maximum cross section at zero electron energy, but with approximately f i o o the magnitude of the SFs- curve. Thus, the F- may result from the excited st‘6- occasionally achieving a configuration in which dissociation into SFs and F- becomes possible. E . Electron Afinities There is a considerable body of information concerning the electron affinities of the various atoms and molecules. Fortunately, there have been a number of surveys, from 1953 to 1962, by Pritchard (204), Branscomb (4, Sl), and Buchelnikova (205) which thoroughly cover most of the available data on the affinities of atoms and molecules derived from a variety of chemical and physical measurements. I n the present review, essentially only new information, obtained from R P D electron beam and from collisional detachment measurements, will be discussed. With the advent of techniques for producing beams of accurately known energy and narrow energy spread (7, 8), it has become possible to obtain accurate values for the electron affinities of negative ions formed by dissociative attachment from molecules whose dissociation energies (206) are accurately known. If one uses a Lozier-type tube in which the kinetic energy of the negative ion formed by dissociative attachment can be determined by retarding potentials applied to the ion collecting structure, then it will be seen, using Fig. 2Ga as an example, that the electron affinity is given by EA(X)

=

D(XY)

- [u. - IIE(X-) - KE(Y)],

(52)

where D(XY) is the dissociation energy of the molecule (206), ue is the electron energy, IZE(X-) is the kinetic energy of the negative ion and KE(Y) is calculated from KE(X-) and the principle of conservation of momentum. However, account must be taken of possible anisotropy in the dissociation directions, as pointed out in the discussion of Section IV, B, in order to obtain accurate values of the dissociation kinetic energies. Use of this technique (172)has recently called into question the generally accepted value for the affinity of the oxygen atom, EA(0) = 1.47 ev, obtained from photodetachment studies (16.2). Support for this value was obtained by Randolf and Geballe ( l Y S ) , who determined the affinity by the above meiitioned procedure applied to three reactions, O2 On

+ e + 0- + 0 (dissociative attachment), + e + O+ + 0 + 2e (dissociative ionization),

(53) (54)

136

and

MANFRED A. BIONDI

O2 + e -+ O+ + 0-

+ e (ion pair formation).

(5.5)

Using the appearance potential of SF6- to set the zero of their electron energy scale, they obtained values of EA(0) = 1.5 _+ 0.1 ev from these measurements. Schulz (l72),on the other hand, has carried out very careful measurements in which he has checked his experimental method by first determining EA(H) from H-/HZ and H-/H20. I n the same apparatus he finds EA ( 0) = 2.0 ev from studies of the dissociative attachment reactions, 0-/02 and O-/COz. He further cites studies of O-/NzO, O-/NOz, and O-/SOz which support this value, although the less certain values of D for these molecules do not permit comparable accuracy in the affinity determination. Schulz’ value supports the earlier determinations of Hagstrum (207) (ion pair formation) and Tozer (see 208) (dissociative attachment and ion pair formation), who used electron distributions of broader energy spread. Craggs and Tozer (186), also using a somewhat broader electron energy distribution, obtain a value

EA(0) = 1.75 f 0.1 ev from 0-/CO studies. There is evidence accumulating that experimental difficulties in establishing accurate electron energy scales and in obtaining good negative ion retarding curves may be the source of these discrepancies among the various experiments. For example, it appears th a t the use of SF6 to establish the zero of the electron energy scale may lead to significant errors ($09). As pointed out earlier, the existence of a state of 0- lying -2 ev below the ground state of 0 need not contradict the photodetachment and affinity spectrum observations, provided that one accepts the existence of a long-lived excited state of 0- lying -0.5 ev above this state. (Recall that evidence for a weakly bound, metastable excited state of Cwas presented in connection with the photodetachment measurements.) It is only necessary that radiative transitions from the continuum to the excited state be substantially stronger than transitions to the ground state t o explain the affinity spectrum observations, and it is necessary that the negative ion beam used in the photodetachment studies have a substantial population of this excited state, Further evidence for the existence of two states of 0- is provided by Schulz’ observation ( l 7 2 ) , in one series of ion retarding curves, that some of the 0- from the dissociation reaction reached a state 1.5 ev below the ground state of 0. However, these measurements were difficult to carry out and are regarded as preliminary in nature.

LOW ENERGY ATOMIC COLLISIONS

137

In contrast t o the case of oxygen atoms, for which there are abundant (and somewhat conflicting!) determinations of the electron affinity, the value of EA(02) has been a matter of considerably greater speculation. The photodetachment threshold fit (163) a t hvmin = 0.15 ev has been used as a tentative value of the electron affinity in some ionospheric analyses. However, the recent collisional detachment determinations of Phelps and Pack (201) show rather conclusively that the 0 2 - in the drift tube experiment lies 0.44 k 0.02 ev below the ground state of 0 2 . O n the other hand, Curran (168), from studies of 0 2 - / 0 3 , has obtained a value EA(02) 3 0.58 ev. One possible explanation for the difference between these values lies in the assumption th a t in the electron beam studies the 02-is in the v = 0 vibration state and that in the drift tube studies i t is in the v = 1 state. However, it is then necessary that the v = 1 state of the negative ion not be deexcited by the more than lo8 collision with neutral 0 2 molecules that occur during ion transit across the tube (210). A final point, bearing on recent observations in rocket soundings of the ionosphere of a preponderance of NO*- ions (211), comes from studies by Curran (136), who used a high pressure ion source in conjunction with a mass spectrometer to study charge transfer among very low energy negative ions (see Section 111, E 3 b). He finds that NO2 molecules capture electrons from slow 0-, SFB-, SFs-, and C1- negative ions l ~ ~ 1 O - cm2. l ~ Also, from with cross sections ranging between ~ 1 0 - and the largest affinity of the initial ion (i.e., C1-) he concludes that EA(NO2) > 3.8 ev. Thus, the NO2- formation in the ionosphere may be via charge transfer from the more usual negative ions initially formed (e.g., 02-),rather than by free electron capture. V. RECOMBINATION OF POHTIVE IONSWITH ELECTRONS .AND WITH NEGATIVE IONS The processes of positive ion-electron and positive ion-negative ion recombination determine the mutual neutralization of charge carriers in ionized gases. Unfortunately for the purposes of this review, our state of knowledge of the various recombination processes is in some areas rather sketchy, while in others it is confused by conflicting experimental evidence. A contributing factor to this unsatisfactory state is the difficulty in making quantitative determinations of recombination rates, owing t o the fact that, unlike attachment or scattering rate measurements, knowledge of the absolute density of each charge carrier is required. In addition, to date essentially only a single class of measurements has been successfully used to observe the recombination-that involving measurements in a plasma or its afterglow. Thus, there are

138

MANFRED A. BIONDI

no alternative methods of measurement, such as crossed ion and electron beams, to provide much needed comparisons with the plasma observations. As in the case of attachment reactions, recombination between charge carriers may be either a two- or a three-body process. I n some of the reactions, a n intermediate, unstable excited atom or molecule is formed and must be stabilized by dissociation or collision with a third body. At the higher plasma densities it will be seen that this third body may be a charged particle, viz., an electron. Concerning two body recombination processes, we shall consider recent information relating t o radiative capture of electrons by ions, dielectronic recombination, and dissociative electron-ion recombination. I n the case of ion-ion recombination, some evidence for mutual neutralization of positive and negative ions has been obtained, although the particular capture mechanism has not been determined. The three-body recombination processes are discussed in terms of recent work on electron stabilized, electron-ion recombination, and the more familiar, atom stabilized, Thomson process for both electron-ion and ion-ion recombination. An extensive survey of experimental work relating to electron-ion recombination has recently been made by -4nderson (212). Most of the experimental studies refer to measurements during the afterglow following ionization of a gas. I n those experiments in which the recombination is determined from observations of the electron or ion density decay, Langmuir probe, microwave, or rf conductivity measurements have been used to obtain the required absolute charge densities. Other recombination studies involve spectroscopic determinations of absolute afterglow radiation intensities or of relative intensity variations with time in the afterglow, but these optical measurements must be coupled with a determination of the density of the recombining charged particles at some point to yield the magnitude of the recombination coefficient. A. Equations Governing Particle Behavior during the Afterglow The various recombination measurements have been carried out with widely different values of the experimental parameters, e.g., plasma density, neutral gas density, and container geometry. I n each case it is necessary to insure that proper account is taken of the various charged particle creation, destruction and transport processes in order to obtain meaningful data. Let us illustrate this point by considering the case of the afterglow of a low density plasma in which two body electron-ion recombination is important, and yet charge production, loss, and diffusion processes must be considered. The equation governing the time variation

LOW ENERGY ATOMIC COLLISIONS

139

of the electron density may be written in the form,

where the term Pe(r, 1) represents electron creating processes such a s metastable-metastable ionizing collisions (14W), and Le(r,t ) lumps volume electron removal processes other than recombination, e.g., negative ion formation. The next term represents ambipolar diffusion loss of electrons in the preseiice of several possible positive ion species, each having a n ambipolar coefficient D,k (91). In the last term, ffk represents the two body recombination coefficient of electrons with the particular positive ion of density n+k. If one further considers that the positive ions also are created and destroyed by a variety of ionizing and conversion reactions, e.g., A + + A2+, it is not surprising that it is difficult to assess precisely the experimental conditions under which observations of electron or ion decay or of afterglow radiation provide unambiguous determinations of the desired recombination rate. It is often essential to know the rates of these other atomic collision processes and to measure a s many of the experimental quantities as possible in order to obtain meaningful results. Experiments on recombination have been analyzed in terms of several highly simplified models of the afterglow. On the assumptions that only one positive ion species is present and that the only significant process is recombination of electrons with these ions, i.e., dne/at = -cine2, one has the usual “recombination” solution, l/ne = [l/ne(0)1

+

at.

(57)

If, on the other hand, only one positive ion species is present and only diffusion loss is significant, one has the “diffusion mode” solution, e2

n,

=

2

aj

exp (- Dut/Aj2),

j= 1

where the Aj’s are characteristic diffusion lengths for the various diffusion modes obtained by setting n, = 0 on the plasma’s bounding walls. The lowest, or fundamental, diffusion mode has the largest value of A and therefore, in the absence of production, is approached after a sufficient time lapse in the afterglow. If, with only one positive ion species, fundamental mode ambipolar diffusion and a small volume recombination loss are the only significant processes, then Eq. (56) may be approximated (114) by

140

MANFRED A. BIONDI

anelat N - (Da/A12)ns -- me2, whose solution is of the form

An important contribution to the analysis of afterglow recombination experiments has been provided by the numerical solution of the equation,

an,/&

=

DaV2n,- me2,

(60)

applicable t o a n afterglow in which only one positive ion species is present and for arbitrary diffusion and recombination losses, provided that other processes are absent. Gray and Kerr (923) have obtained these solutions for the infinite cylinder and the sphere, thus extending and enlarging upon earlier work by Oskam (145), who treated the case of infinite parallel planes. The limitations of these various approximations, together with the errors introduced in analyses of certain experiments by their use, are discussed in the succeeding subsections.

B. Two-Body Recombination Processes 1. Radiative Recombination. The process of radiative recombination is analogous to the previously discussed radiative attachment, except that the neutral atom is replaced by a positive ion, i.e.,

+

+

H+ e H* hv, (61) where H* indicates that the neutral atom may be formed in a n electronically excited state, and the free-bound electronic transition is accomplished by the emission of a quantum of radiation. It will be seen that if u,denotes the kinetic energy of the initially free electron, then hv = ue (ui - ul), where ui and u, refer to the ionization and the excitation potential energies of the atomic states involved in the reaction. Thus, for a distribution of electrons one expects the radiation to occur as a continuum on the short wavelength side of the series limit of a particular level. With the advent of quantum theory, exact calculations of the recombination coefficients were made for the case of hydrogen, and approximate values were obtained for more complicated atoms. Mohler (924) made the first (and essentially the only) quantitative determination of the absolutc magnitude of the radiative capture probability to a particular excited level. He measured the coefficient for recombination of electrons of -0.3 ev average energy into the Gp level of Cs by spectroscopically determining the absolute intensity of the continuum radiation associated with this transition and simultaneously measuring n, and IZ,with a

+

LOW ENERGY ATOMIC COLLISIONS

141

Langmuir probe. The intensity distribution I ( v) exhibited the proper dependence on t i e and varied as ne3, as is to be expected in a plasma containing principally one positive ion species, so that n+ 'v n,. His value, a ( 6 p ) 'v 5 X cm3/sec, is the same order of magnitude as the value predicted for radiative capture of electrons by protons. Until quite recently Mohler's work provided the only direct, quantitative determination of radiative recombination. However, theory indicates that a n appreciable fraction of the recombination events involve capture into the ground state of the atom. Thus, a good order of magnitude estimate of the total radiative recombination coefficient can be obtained by inverting the data for photoionization (215) of ground state atoms [reaction (61) going to the left]. The values so obtained are in reasonable agreement with available theory for a number of atoms. Studies of the absolute intensity of the continuum radiation associated with the Balmer lines of hydrogen have recently been carried out by Fowler and Atkinson (216) for a hydrogen plasma generated in a shock tube. The plasma density was determined from stark broadening of the Hb line and the electron temperature bracketed by noting that, if all the radiation over the wavelength range 2600-4200 A were the result of the affinity spectrum radiation, then a temperature varying between 54004200"11 would be required to fit, the spectrum, while if recombination is the source of the radiation in this wavelength interval, a temperature varying from 3900-4400°K would be required. For some reason no attempt was made to add the predicted contributions of affinity and recombination radiations a t each temperature and thus determine the temperature which best fitted the observations. On the assumptions th a t Te = 4500°K and that all the radiation is the result of recombination, a coefficient of cm3/sec is obtained, in reasonable agreement with theory. Earlier work of the same type by Olsen and Huxford (217) apparently has led t o erroneous predictions owing to neglect of the effects of an applied electric field on electron production and on the electron energy during the measurements (216). Thus, because of experimental difficulties, there has been little detailed testing of theoretical calculations of radiative recombination, although no one doubts the validity of the quantum mechanical formulation. In spite of uncertainties involved in calculations for more complex ions than H+, theory must be regarded as the primary guide in estimating the order of magnitude of radiative capture until more experimental work is forthcoming. For the case of radiative recombination of electrons with molecular ions, a Frank-Condon condition is imposed, forbidding appreciable change of internuclear separation or velocity during the radiative transition, a s

142

MANFRED A. BIONDI

in the case of radiative attachment to molecules. As a result of this added complication, in which detailed knowledge of the molecular potential curves is required, quantitative theoretical calculations are at present not available. 2. Dielectronic Recombination. A second, indirect form of radiative recombination is possible for ions having more than one ground configuration, so that the excited states of the atom converge to different ionization limits, e.g., Vil and Vi2. If Viz > V,I, then some excited levels of the configuration 2 lie above the continuum of configuration 1. The process of dielectronic recombination (1) involves as a first step the radiationless transition, 1Xf e 2X*, (62)

+ *

where the ion in configuration 1 captures an electron of the proper energy to form the excited state of configuration 2 without change in total energy of the system. The excited state may decay by autoionization [reaction ((32) going to the left] with a lifetime of lO-'4 sec, or it may be stabilized against autoionization by a radiative transition to a level below Vil, i.e., zX* + zX'* hv. (63) However, since radiative lifetimes are considerably longer (210-lo sec) than autoionization times, there is only a small probability of stabilizing the initial recombination event. The little experimental evidence concerning the importance of this process comes from studies of the inverse, photoexcitation, process. For example, Pery-Thorne and Garton (218) have measured the far uv absorption of krypton. They find a series of strong, broad lines (Beutler lines) corresponding to transitions from the ground state to excited states between the 2P$aand 2P56series limits of krypton. The breadth of the lines is the result of the short excited state lifetime against auto0.04), they ionization. From the measured f-values of these lines (f were able to show that a n earlier estimate by Garton et al. (219)for argon of (Ydiel. 1O-l" cm3/sec at T , = 300°K is considerably too large, perhaps by two orders of magnitude. I n the earlier work a value off 1 had been assumed, leading to the high estimate. Thus, it appears that dielectronic recombination, for the noble gas ions a t least, is somewhat less important than ordinary radiative recombination. 3. Dissociative Recombination. The previous discussion has pointed out that electron capture by radiative and dielectronic recombination processes leads, a t T , = 300°K, to values of a < lo-" cm3/sec. The inference from ionospheric measurements and the observations in microwave afterglow studies of electron-ion recombination coefficients of the

s

+

-

<

-

LOW ENERGY ATOMIC COLLISIONS

143

order of 10-8-10-6 cm3/sec led to the suggestion by Bates and Massey (28) of a very efficient,, radiationless capture process, dissociative recombination between electrons and molecular positive ions, as the explanation of these very large coefficients, At the present time there is considerable controversy concerning interpretation of the laboratory measurements; therefore, we shall review experiments designed to investigate the nature of the recombination process, as well as experimental determinations of the two-body recombination coefficients for various gases. We adopt this procedure since, as the discussion which follows shows, the process of dissociative recombination is sufficiently complex that theoretical calculations arc a t present very qualitative ; thus, heavy reliance is placed on the experimental deterininations of the rate coefficients. As in the analogous case of dissociative attachment, the dissociative recombination process involves the formation of a n intermediate, unstable molecular state, which then dissociates. Using neon as a n illustration, we have Ne2+ e (Ne2*)unst.S Ne* Ne. (64)

+ +

+

I n order t o carry out quantitative calculations of the rate of this type of reaction i t is necessary to have detailed knowledge of the molecular potential curves, especially in the vicinity of the crossings of the molecular ion and the excited molecule states, and of the autoionization time of the unstable excited molecule. Such detailed knowledge is not a t present available, either from theoretical calculatioris or from experiment; however, Bates (28) was able to present plausibility arguments suggesting that a coefficient of -lo-’ cm3/sec is not an unreasonable value for this process. More recently Bauer and Wu (220) have attempted to calculate dissociative recombination between Hz+ and electrons, while Gibbons (221) has adapted some of their procedures to the case of NO+. Neither calculation can be regarded, a t present, as more than qualitative; however, each suggests the possibility of large electron capture values for the dissociative process. On the experimental side, the large two body recombination loss was discovered in microwave afterglow studies of the electron loss from thermal ( T , = Ti = T,,,) plasmas by Biondi and Brown (292).Following studies of helium afterglows (114), in which, a t low pressures, the predominaiit loss process [see Eqs. ( 5 6 ) and (58)]was found to be ambipolar diffusion of helium ions and electrons, attempts were made to study diffusion loss in neon (222). It was found that neither the pressure nor the temporal dependence of the electron decay was appropriate for diffusion loss; instead, recombination between the electrons and a single ion type appeared to dominate. For this case, Eq. (57) fit the observed

144

MANFRED A. BIONDI

decays over a substantial range of electron density and the curves exhibited essentially no dependence on neutral gas density at T , = 300°K. The coefficient, a = 2 x cm3/sec, seemed a t the time inexplicably large ;however, confirmation of this large recombination loss was provided by Holt and his colleagues (223), who had been making optical radiation studies of helium and neon afterglows. When they added microwave techniques to provide electron density values, they obtained similar large values of a from the intensity decay curves, on the assumption that I ne2for this simple recombination case. IJnfortunately, there has been a tendency to infer the existence of recombination or t o attempt t o deduce values of a for cases in which terms in Eq. (56) other than recombination contribute significantly during the measurements. For example, Persson and Brown (224) have shown that for a sufficiently asymmetrical initial electron density distribution in the plasma container, the subsequent diffusion decay of the various modes, Eq. (58), can, for a limited time interval, appear t o follow the recombination solution, Eq. (57), leading to a completely unjustified inference of a recombination loss. I n addition, even in those cases where care has been taken to assure a symmetrical initial density distribution, the presence of appreciable fundamental mode diffusion can lead to serious errors in the estimates of recombination rates. Using the criteria developed by Gray and ICerr (21.3) it is possible to show th at for many of the experiments, e.g., helium (114, 225) the recombination rates may have been overestimated by a n order of magnitude. I n these cases the values of a were determined from a limited electron density range fit to Eq. (57) under conditions where the ratio of initial recombination loss to fundamental mode diffusion loss, y = a A ~ ~ n , ( 0 ) / Dwas , , not large compared to unity. An equally questionable method of determining recombination coefficients is to carry out measurements where diffusion is quite important and to attempt t o analyze the data in terms of Eq. (59). Faire and Champion (226) have used this procedure for low pressure nitrogen afterglows. Although they obtain internally consistent values of the diffusion and recombination coefficients, the sensitivity of this analysis to the presence of higher diffusion modes (even the symmetrical ones) and the fact that recombination loss generates these higher spatial modes cast serious doubts on the accuracy of the deduced a values. When the Gray and Kerr criteria are, however, applied to studies of such gases as neon and argon (222, 223, 22?’), where large values of y( >, 100) were attained, one finds that the actual recombination coefficients lie rather close to the values deduced from a n analysis in terms of Eq. (57). Additional evidence th at the electron removal is by volume

-

L O W ENERGY ATOMIC COLLISIONS

145

recombination has been provided by the observation of the phenomenon of “afterglow quenching” in neon (228) and in helium (227, 229, 230). Here it is observed that, when the electron eiiergy during the afterglow is momentarily increased slightly by application of microwave energy to the plasma, the afterglow (recombination) radiation intensity decreases, and the loss rate of electrons decreases. Both of these observations are consistent with recombination control during the afterglow, since recombination rates generally decrease with increasing energy, while atomic excitation processes and ambipolar diffusion loss arc both expected to increase with increasing electron energy. Attempts have been made to determine whether these large recombination coefficients observed in microwave afterglows are indeed the result of the dissociative process by examining two of its characteristic features. Referring to reaction (G4), it will be seen that (a) a molecular positive ion is required, and (b) the excited atom formed a s a result of this process has a n additional kinetic energy of dissociation over the usual thermal eiiergy of the ions and atoms in the plasma. The first of these points has been investigated (227, 231) by studying electron loss during afterglows where first molecular positive ions (Arz+) and then atomic ions (Ar+) are expected to dominate. At moderate (p 10 mm Hg) pressures in pure argon the afterglow ions are all converted to Arz+ in a time short compared to the measuring In this case the “recombination” solution, Eq. (57), is followed over a n electron density range of a factor of 40, and a value of a ‘V 7 X lop7cm3/ sec is obtained. If, on the other hand, a small amount (1 : 1000) of argon is added to pure helium, then Ar+ is the predominant ion, formed by the Penning ionizing reaction, HeM Ar + He Ar+ e. On the time scale of the measurements, appreciable conversion to Arz+ does not occur, since the Ar atoms necessary for the coilversion are present in such a small concentration. I n this case, after an initial afterglow period showing evidence of the Penning ionization process, the final decay is by fundamental mode diffusion [Eq. (58) with a, = 0 for j # 11 over the measured pressure range, 2-7 mm Hg, and a t electron densities equal to the values attained in pure argon. Analysis of scatter in the data indicates that if recombination is present in this case, it must occur a t < times the rate it did in pure argon. Thus, the large two body recombination requires the presence of molecular positive ions. The second point, that dissociative recombination leads to the

-

+

+

+

8 Mass spectrographic studies of microwave afterglows in noble gases, e.g., references 91 and 93, have confirmed the predominance of the molecular ion at moderate pressures.

146

MANFRED A . BIONDI

formation of excited atoms with kinetic energy of dissociation, has been investigated by Rogers and Biondi (23W),who examined the shapes of the afterglow lines for excess Doppler broadening. Although, as the discussion a little later will make clear, the evidence for the large two body recombination loss in helium is confused by conflicting experimental evidence, this gas was chosen for the line broadening studies because, a t low pressures, the afterglow lines are well separated in the spectrum and some of the lines originate from states of short lifetime. The former consideration is of value in the low-intensity, high resolution Fabry-Perot interferometric techniques (233) used in these afterglow studies; the latter point is required in order that the fast atoms radiate a broadened line before they either transfer their excitation to a slow atom or dissipate their excess kinetic energy in collisions. At the low pressures at which the afterglow radiation consists predominantly of the helium line spectrum, the electron and ion loss is diffusion controlled; however, the temporal dependence of the late afterglow radiation has been found to be consistent with the predicted behavior of the product, ne n(He2+), considering the fact th a t the early afterglow ions are He+, and the He2+is formed by three body collisions of He+ and two helium atoms. I n addition, the line is very slightly broader than thermal (2' = 30OoIi) during the discharge, decreases t o thermal width during the early afterglow and then increases in width during the late afterglow, when the radiation is expected to originate from recombination. This observation should be considered rather convincing proof that dissociative capture is the origin of the observed, large recombination coefficients; yet the inferred dissociation kinetic energy of the excited atom is rather smaller (-0.1 ev) than originally expected. Also, one wishes the line broadening had been observed for a case, such as neon, where the recombination loss is well established, rather than for helium, where considerable uncertainty exists. As a result, the problem has been reexamined for neon, and it appears that the necessary conditions for observing line broadening can be met; therefore studies are presently underway. Having established that the dissociative process is probably the cause of the observed recombination, it is still difficult to state the dissociative recombination coefficients for the noble gases and some of the diatomic gases, since one finds large variations in the detail with which a given gas has been studied and in the degree to which the obstacles to achieving quantitative determinations have been avoided. The case of helium is particularly puzzling since, following the early preliminary recombination studies, there have been several detailed studies (229, 230, 232) whose results are, to some degree, conflicting. The line broadening studies (23.2)

L O W E N E R G Y ATOMIC COLLISIONS

147

described earlier, although carried out in a diffusion controlled region, were consistent with a recombination coefficient for helium in the range 10-9-10-* cm3/sec. Chen, Leiby, and Goldstein (CLG) (Zd9), working a t rather high (-30 nun I-Ig) pressures in a long cylinder 1.G4 cm in diameter, achieved a value of y > 10, which from Gray and Kerr’s analysis should lead t o reasonably accurate (-25%)) determinations of a from the slopes of the l/n, vs t curves. The corrected value of a obtained from their data is cm3/sec, essentially independent of pressure over the -7 X range 15-30 mni Hg. Both CLG and Iierr and his students (230)’who carried out painstaking studies of helium afterglows, observed a proportionality between the emitted afterglow intensity and ne2at high ( > 15 mm Hg) pressures, indicating recombination contr01.~However, it appears that CLG’s inference, by the use of narrow band interference filters, that thc high pressure afterglow radiation consisted of lines such as A5876 and A3889 is incorrect, since spectographic studies ($30, 23.2)indicate that, a t these pressures, the radiation is almost entirely band spectra of Hez*. Kerr and co-m-orkers (280) have carried out very careful absolute intensity measurements of the various helium bands, which all decay with the same time dependence, and find that, by summing th e contributions within the spectral range of their apparatus, a > 7 X cm3/ sec, with a n absolute accuracy of a factor of two. Further, they find that a t late (12-40 nisec) times in the afterglow a t 15 mm Hg pressure the decay is exponential in character, i.e., diffusion controlled. I n the intermediate (-4-12 msec) region a more rapid decay than by diffusion alone is observed, and on the assumption that a solution of the form of Eq. (59) gives a n upper bound on CY they estimate a 2 < X lop9 cm3/sec. However, in this same time interval, other of their curves a t the same pressure indicate non-negligible metastable-metastable ionization, which, if also present in the analyzed curves, could lead to a substantial underestimation of a. Thus, it is not clear whether I<err and co-workers’ results contradict CLG’s early afterglow value of a ‘v 7 X cm3/sec. Even if Kerr et al. have not underestimated the later afterglow value of a, it may be that the decay time of vibrational excitation of Hezf, which is estimated to be rather long (231), perhaps of the order of several milliseconds, leads 9 It should be noted that a t the high electron densities, ~ 1 0 e/cc, ” used by CLG the predicted magnitude of the three-body (ion plus two electron) recombination rate is the same as the observed value, except that a quite different time dependence for the t4ectron loss is predicted. In addition, the afterglow intensity should not be proportional to ns2 if this process is of importance (see discussion in Section V, C, 2).

148

MANFRED A. BIONDI

to a progressive diminution of a with afterglow time. It is reasonable t o assume that the Hez+ is most probably formed in a high vibration state as a result of the three body conversion from He+. If, as a result of the curve crossing in the dissociative recombination process, reaction (64), the higher vibration states He2+ exhibit larger values of a, then the required dependence of a on time in the afterglow can result. Even granting the foregoing hypothesis to bring the two high pressure helium studies into harmony, we are unable to account for the dissociative process leading to emission of Hez* band radiation. There have been no serious proposals that He3+ ions are sufficiently stable to occur in appreciable concentrations in the afterglow studies1° and so permit dissociative recombination to form He2* He. If we start from He2+,the excited states of He* formed by recombination are expected to decay by emission of radiation long before conversion to Hez* by three body collisions can occur. Thus, in spite of painstaking studies of helium afterglows, we are unable to satisfactorily account for a number of the observations in terms of a unified set of atomic collision processes; in particular, the precise nature of the recombination process and its magnitude have not, as yet, been determined. Of the other noble gases, only neon, and to a lesser extent argon, have been studied in sufficient detail and under well enough controlled experimental conditions to permit quantitative conclusions concerning the magnitude of a. I n neon (145, 223, 227), the afterglow spectrum consists only of line radiation and the emitted intensity is accurately proportional to me2. These observations, coupled with the fact that measurements were carried out in a recombination dominated region (y >, loo), suggest that the value given in Table I11 is a reasonably accurate measure of recombination between electrons and Nez+ ions, presumably in their ground vibration state (231). I n argon, for which it is somewhat more difficult to obtain or prepare extremely pure gas samples, the afterglow radiation studies are less complete, although once again I ne2 is found (231). I n addition, measurements of a are carried out in y > 100 regions, so that accurate values are obtained. Although the noble gases krypton and xenon have been recently restudied by Lemon and Sexton ( 2 3 3 , substantial impurities of the one gas in the other, together with rather poor ranges of linear l/n, vs t data, especially for the case of krypton, prevent quantitative conclusions 2 X cm3/sec, in agreement being drawn. For xenon a value of a

+

-

-

lo The appearance of mass 12 ions in maw spectographic studies of helium afterglows is usually under conditions where C+ is a readily suspected impurity (234, 236). To clarify this point studies using the mass 3 isotope of helium are contemplated.

149

LOW ENERGY ATOMIC COLLISIONS

with earlier work by Richardson (237), who had similar impurity problems, is obtained. The quantitative determinations of recombination coefficients in the diatomic gases are even more sparse, as a result of the fact that, unlike noble gases where a diatomic ion is the most complex expected, polyatomic molecular ions are known to occur. At present, the technique of simultaneous mass analysis of the ions reaching the walls of the microwave afterglow cavity, together with the usual electron density determinations, is just coming into extensive use. A preliminary report of studies of recombination of electrons with nitrogen ions and with oxygen ions has been given by Kasner, Rogers, and Biondi (KRB) (92). I n these microwave afterglow studies, using a differentially pumped, Boyd-type rf mass spectrometer to monitor the ions reaching the wall of the microwave cavity, it was observed that, at pressures > mm Hg, N3+ and N4+ions in nitrogen and Oaf in oxygen became significant. Thus, earlier studies (222, 226) of these gases do not, in all probability, refer to N2+and Oz+ ions, as originally supposed. I n order t o reach a recombination controlled region (y > loo), K R B added a relatively high (-20 mm Hg) pressure of neon to the nitrogen and the oxygen to reduce diffusion loss to a negligible value. Ionization of O2 and N2 by neon metastables assured that the neon remained “inert,” with only oxygen and nitrogen ions appearing in significant quantities during the afterglows. Recent extensions (234) of the N2-Ne mixture studies, with improved determinations of time-resolved afterglow ion currents and use of the most recent Gray and Kerr correction factors, lead to a value of CY

=

(3 f 1) x

cm3/sec

for N2+ ions and electrons a t 300°K. I n these studies, gated photomultiplier scans of the spatial distribution of afterglow radiation in the rectangular microwave cavity showed no vertical or lateral asymmetries. On the assumption that I ( s , y, z ) [n,(z, y, z)12 the inferred electron distribution appears to be slightly more centrally concentrated than for a fundamental diffusion mode distribution. However, in the high y region attained in the studies, the resulting higher diffusion modes have orily a small effect on the deduced recombination value. If the Nz+ ions under study are produced by the reaction NeM N Z + Ne Nez+ el then energy considerations require that they be in a vibration state, v 6 3, while if they are produced by electron impact on ground state, v = 0, N z molecules, the Frank-Condon principle requires that they be in the v = 0 state. At higher nitrogen partial pressures in the N2-Ne mixtures the N4+ion, together with some N3+, predominates. Here

-

+

+

+

150

MANFRED A. BIONDI

-

a tentative value a(N4+) 1 x crn3/sec is obtained. It is interesting to note that this value is approximately the same as the corrected value obtained from the earlier work (222). A preliminary value for Ozf ions, obtained a t low (-lop3 mm Hg) partial pressures of oxygen in neon and for y > 100, is a =

(1.7 5 1) X

cm3/sec (92, 234).

The oxygen studies have not proceeded sufficiently far to assign the vibration state of the Oaf ion, nor has a value of a! for the 0 3 + ion been obtained. Results for other diatomic gases are not presented, since there is contradictory evidence from the various microwave afterglow studies, many of which have not been carried out in recombination controlled regions, and all of which have omitted mass identification of the ions under study. For example, for hydrogen it is not a t present possible to reconcile Persson and Brown’s (224) “higher diffusionmode’’ explanation of electron decay from their short duration (-1 psec), asymmetrically distributed plasmas with the results of Varnerin (54),who obtained a value of a cm3/sec at high (>40 mm Hg) pressures, where y 3 10 was attained. Since H3+ ions, rather than Hz+ ions have been found to predominate in moderate pressure (greater than a few mm Hg) hydrogen afterglows (235) it is clear th at mass analysis of the ions is one of the essential steps in the study of recombination and other afterglow processes in diatomic gases, and is of considerable assistance in studies of noble gases and their mixtures. I n this review, many of the studies of recombination carried out in the last decade have been omitted from consideration because of space requirements and because some of them failed to meet the conditions for quantitative recombination determinations. I n most of the studies for which recombination coefficients are presented, the experimental conditions have been such that the assumption that T , = TgBs= 300°K during the measuring interval should be valid. There is little reliable information concerning the dependence on electron energy of the recombination coefficients. For reasons which by for now should be obvious, the quoting of an energy dependence of l’-o.8 hydrogen from the early studies (222) is not valid, while from the same paper the finding of essentially no dependence on temperature over the range 77°K T , 410°K for electron-ion recombination in neon should be reliable. Here the electron temperature was varied by changing the gas temperature. Chen et al. (229) studied the energy dependence of a a t higher pressures in helium, using microwave energy to heat the electrons and gauging the effect on the recombination rate by the decrease in

-

<

<

LOW ENERGY ATOMIC COLLISIONS

151

afterglow intensity. This study is essentially a n extension of earlier work by Anderson (258), who measured the dependence of light intensity on electron energy in the negative glow of a dc discharge in helium. In each case a n approximate variation of a as Te-’ j was found, over the range 300°K < T , < 1500°K in CLG’s studies. Subject to the qualification that the origin of the helium band radiation does not fit our simple picture of dissociative recombination, such a temperature dependence can be explained by the dissociative process. From the predicted dependence (28) of a on the rate processes controlling reaction (64) it can be shown that it is only necessary that the time required for stabilization against autoionization by the increase in separation of the dissociating atoms be long compared to the autoionization time. (Refer to Fig. 26 and the analagous discussion of dissociative attachment.) For a n autoionization time of -10-15 sec and a sufficiently ‘(flat” repulsive curve, this condition can occur. By the same token, depending on the relative values of the autoionization and stabilization times and on the point a t which the repulsive excited molecule curve crosses the molecular ion-curve, as one inrreases the electron energy, a n initially increasing or constant value of a may occur. Thus, the neon results are by no means inconsistent with the dissociative process. The experimentally determined values of the dissociative recombination coefficients between electrons and positive ions are presented in Table 111. Only those values are included for which the ion identity is reliably determined or at least inferred with some confidence and which have been measured over a sufficient electron density range in a recombination controlled region. Even so, a factor of two modification of these values would not be surprising in view of the difficulty in specifying the effect of such relevant factors as the vibration state of the molecular ion. 4. Mutual Neutralization. The two-body recombination process leading to the mutual neutralization of a positive and a negative ion may be illustrated schematically by the reaction

x++ IT-+ x*+ Y,

(65)

where X and Y may refer to atoms or molecules and the asterisk indicates that the positive ion may be neutralized by electron capture into an electronically excited state. There are a number of modes by which any excess energy of the reaction may be absorbed, the previously mentioned electronic excitation, vibrational or rotational excitation if one or both reactants are molecules, and kinetic energy of relative motion of the neutralized particles. As in the case of dissociative recombination, except for a case such as H+ and H-, thcre is little hope of obtaining quantitative theoretical estimates of the rate of reaction (65), since de-

152

MANFIEED A. BIONDI

tailed calculations of the potential curves for the reacting species as a function of their separation are required. However, the available theoretical estimates (239) suggest that in favorable cases, as a result of the long range coulomb interaction between the positive and negative ion, the curve crossing between the X+-Y- and X*-Y states of the system may occur at large internuclear separation, leading to very large recombination cross sections, > 10-14 cm2. TABLE rrr. DISSOCIATIVE RECOMBINATION COEFFICIENTS O F THERMAL (300°K) ELECTRONS WITH VARIOUS POSITIVE IONS Ion

Reference

Remarks

227

This value, believed accurate to a factor of 2, is given in preference to earlier work, ref. 222, as a result of larger y values and higher purity gas samples. The ions should be in a low, possibly v = 0, vibration state.

227

The argon samples used contained a very small nitrogen impurity, whose effect is believed t o be unimportant.

-2 X 10-8

236, 237

The effect of the krypton impurity, with its higher ionization potential, may be small.

x 10-7

92, 234

The N2+ ions should be in a low, probably v = 0, vibration state.

X 10-8

234

The effect of Na+, which appears during the afterglow in appreciable amounts, has not been assessed.

1 . 7 X 10-7

92, 234

These studies are less complete than for the Nz+ ion. The vibration state of Oz+ can not be specified.

01

(cm3/sec)

Ne2+ 2.4 X 10-7

7

Arz+

Xez+

N ~ +

N4+

02+

3 -1

x

10-7

There is little experimental evidence concerning the value for a for the mutual neutralization reaction. A study of charge removal from afterglows of iodine and bromine was made by Yeung (240). Following creation of a plasma, the afterglow electrons very quickly disappeared by attachment to form negative ions. Thus, during a major portion of the afterglow, essentially only positive and negative ions were the charge carriers, and it, therefore, was feasible to determine their densities by an rf dielectric constant measurement, analagous in many respects to the microwave measurements of electron densities. A coaxial geometry was

LOW ENERGY ATOMIC COLLISIONS

153

employed, and, by operating a t low (-0.1-1 mm Hg) vapor pressures, the ion collision frequency was kept small compared to the probing rf angular frequency. The values of a were deduced from the slopes of l/n, vs time curves measured over a very limited ion density range (a factor of 2). Thus, the reliability of these determinations is called into question by the considerations discussed in the previous subsection. No variation of the slopes of these curves was observed for a factor of >10 variation of vapor pressure. This is somewhat surprising since, from the data presented, it appears that volume recombination loss a t charge densities of < 2 X 10” ions/cm3 only slightly outweighed fundamental mode diffusion loss, leading to values of y which were not always large compared to unity. Thus, one must consider the possibility that higher mode diffusion was responsible for much, or all, of the inferred recombination. Yeung quotes values of the mutual neutralization coefficient a t = 1.5 X lo-* cm*/sec for iodine “molecular” ions and -290°K of aI1put. aneut. = 1.9 X lop8 cm3/sec for bromine and assigus a n uncertainty of - 5 % . I 1 However, these values should be considered as indicating the possible order of magnitude of this process, rather than accurate determinations, in view of the criticisms raised in the previous paragraph and also of a n absolute ion density error of 50% stemming from a mass assignment error. It is known that I- is formed in the thermal electron attachment reaction, rather than Iz-, as Yeung assumed (see, for example, 177). This work, while as yet hardly definitive, represents a very important step in positive ion-negative ion studies, avoiding a s it does the ambiguities of probe determinations of charged particle densities. These techniques, together with mass analysis of the ions reaching the walls of the afterglow container, should be of value in the study of mutual neutralization reactions iiivolving 0 2 + and &-, Nz+ and 0 2 - , etc., which are of considerable interest for ionospheric analyses.

+

C. Three-Body Recombination Processes 1. Neutral Molecule Stabilized Recombination. The excess energy of recombination between a positive ion and a negative ion or a n electron 11 In the recently published chapter on “Ionic Recombination” in Atomic and Molecular Processes, ref. 6 , Sayers points out that, in a continuation of Yeung’s work, Greaves has found a serious error in an electronic calibration which suggests that a ten timcs larger value of CY is to be inferred from the data. The value of y, however, remains unchanged and the criticisms in the text, remain valid, even with these larger a values.

154

MANFRED A . BIONDI

may be removed by a neutral atom or molecule acting as a third body, i.e.,

+ +N+X*+Y+N + + N + X * + N.

X+ YX+ e

(66) (67)

There is not a great deal of experimental information concerning these three body processes. However, for ion-ion recombination, reaction (66), the classical theories of Thomson (241) for medium and low pressures (51 atmosphere) and of Langevin (242) for high pressures ( > 1 atm) have been, for many years, regarded as providing adequate treatments of the capture probability. For the low pressure case, one calculates the probability of occurrence of a collision with a neutral molecule which removes sufficient kinetic energy from the positive or negative ion to cause the orbit in the coulomb field of the other charged particle to become closed. I n this region the capture probability increases linearly with increasing neutral particle density so that one may assign a three body coefficient to describe the capture rate. I n the high pressure case, where the necessary energy removing collisions occur frequently, the recombination rate is limited by the speed with which the one ion can drift toward the other under the attraction of its field. This mobility limited motion, therefore, varies inversely with gas density. Quite some time ago Machler (243) investigated ionic recombination in air a t high pressures (>>1 atm) and found the pressure dependence of the Langevin theory. Sayers (244) investigated the range from tenths of an atmosphere to a few atmospheres and found a t first the increase in recombination with pressure predicted by Thomson theory, followed by a decrease with further pressure increase above -1 atm. Natason (245) recently developed a single treatment valid over the whole range from low pressures to very high pressures and obtains excellent agreement with Machler’s and Sayers’ data. I n the low pressure range Sayers’ data and the Natason theory lead to a three-body ionic recombinatlion coefficient for air a t 300°K of K,i N 3 X cm6/sec. Similar values were obtained in studies by Gardner (246) of pure oxygen over the pressure range 100-760 mm Hg. These large coefficients suggest that a t pressures of 2 1 0 mm Hg the three body process becomes more important than the mutual neutralization process. An alternate process leading to three body ionic recombination has been examined theoretically by Fueno et al. (247). Here the recombination occurs via a two stage process,

+ N 5 (XN)+, (XN)+ + Y-+ X Y + N. Xf

followed by

LOW ENERGY ATOMIC COLLISIONS

155

An alternate process involving formation of a weakly bound complex with the negative ion rather than the positive ion may also be possible. On the assumption that formation and decay of the complex by reaction (68a) is essentially in equilibrium, while reaction (68b) is highly exothermic, they calculate the over-all three body coefficient for the process. For “air” ions they obtain a value a t 2 I ) O O I i of K,, 1 X 1 O V 6 cm6/sec, with values for other gases such as 0 2 , CO, COZ, NzO lying within a factor of two, except for Hz, whose value is -4.5 times larger. It thus appears that this process is more than a n order of magnitude less effective in causing ionic recombination than the Thonison process. However, the authors compare their calculated values for the most part with very old ( > 50 years) measurements, which suffered from serious impurity effects and measuring problems, and conclude that their calculated values are in satisfactory agreement with measurements. There is even less information concerning neutral atom stabilized, electron-ion recombination, reaction (67). Massey and Burhop ( 1 ) have modified the Thomson ion-ion theory by considering the fact that, unlike a negative ion, a n electron loses only a very small fraction of its kinetic energy on making a momentum transfer collision with a neutral atom. Thus, the electron-ion recombination coefficient is reduced by a factor of the order of (m/2M)fh, where m is the electron and n l the ion mass, relative to the corresponding ion-ion process. They point out that, if the third body is a molecule rather than an atom, the total energy loss per collision, including losses to rotational and vibrational excitation, replaces the usual 2 m / M factor in the calculations. Using the measured energy loss and collision cross sectioii data for air, they calculate a value, K,, 11 6 X cm6/sec at 300°1i, approximately 50 times smaller than the ion-ion value. Unfortunately, there appear to be no measurements of the neutral stabilized, electron-ion recombination to which the theoretical values can be compared. 2. Electron Stabilized Recombination. Recently, in order to explain volume loss of electrons and positive ions from moderate and high density plasmas, a three body recombination process has been invoked which is essentially the inverse of ionization by electron impact on excited atoms. Using hydrogen as an example, one has

-

H+

+ e + e S H * + e.

(69)

Since the process does not require the presence of molecular ions, it can lead to recombination rates in excess of radiative values when only atomic ions are present, provided that the plasma charge densities are sufficiently high. D’Angelo (24) has proposed this process to explain electron-ion re-

156

MANFRED A. BIONDI

combination rates greater than the radiative values and has calculated the rate of reaction (69) for 10I2 < ne < loL3e/cm3 and 1000°K < T , < 10,OOO"K on the assumption th at radiative cascading to lower levels stabilizes the recombination. Bates and Kingston (25), McWhirter (26), and Hiniiov and Hirschberg (27) have improved on these calculations for hydrogenic ions and for He+ by inclusion of the effect of superelastic electron collisions on the stabilization. An important point stressed in these calculations is the fact th a t simple capture of a plasnia electron into a high-lying state of H* does not 14.

I

I

I

1

I

x Conductivity kT in ev A

m

c

-

-0

.

2

rn -

Spectroscopic kT in ev

--- Calculated kT in ev

13

.

12

11

c

A

--

0

I

I

I

1

2

3

Time lmsecl

h

-2

FIG.31. Decay of electron density and electron temperature during the afterglow in a helium plasma. The experimentally determined values are indicated by the symbols; the dashed curve is the predicted decay of electron temperature obtained from the measured electron density decay and the theory of electron stabilized, electron-ion recombination.

assure permanent recombination, since other plasma electrons may collisioiially excite the H" into higher bound or even continuum states before radiative transitions or superelastic electron collisions bring it to a lower state. Thus, it is shown that only when the bound state reached obeys the condition ( u i - u,) >> lcT, is one assured of a "permanent" recombination event. The experimental studies bearing on this process, which in fact probably inspired some of these calculations, were carried out a t the Princeton Plasma Physics Laboratory on the B-1 stellerator-a long torus with magnetic field wiiidings to reduce charged particle losses from the plasma to the walls (27, 248, 249). Motley and Kuckes (249) and Hinnov and Hirschberg (27') have determined the variation of electron density and of electron temperature, using millimeter microwave, d-c conductivity and spectroscopic techniques, during afterglows in hydrogen and helium at low pressures (-1 - l o p Hg). Hinnov and Hirschberg (27) have calculated the expected three body recombination coefficients for H+ and He+,

1Ti7

L O W E N E R G Y ATOMIC COLLISIONS

obtaining good agreement with the calculations of Bates, Kingston and McWhirter (26, 260) but rather a stronger dependence of the recombination rate on electron density and electron temperature than calculated by D'Angelo (24). It is found that the three body recombination coefficients, K,,', inferred from the observed decay of charge density and of electron temperature agree very closely with the calculated values for both hydrogen and helium afterglows over electron densities ranging from -loL2 - 6 X 1013e/cm3. The degree of agreement is illustrated in Fig. 31,

-131

1

8

I 9

I

10

I

11

I

12

I

13

I

14

1

15

I

' 9 0 "e

FIG.32. Calculated total recombination coelficient as a function of electron density and electron temperature for two-body radiative, and three-body electron stabilized recombination between electrons and positive ions.

in which the calculated electron temperature required to give the observed electroii density decay via the three-body recombination process agrees well with the observed values. The three-body recombination coefficient for low electron temperatures (IcT, 5 0.25 ev) is given by

Kre' = 5.6 X 10-27(kT,)-4.5cm6/sec,

(70)

when (kT,) is expressed in electroii volts. This recombination is in addition t o the usual two-body radiative process, so th a t one has a total effective recornbination coefficient of the form, a =

-k Kre'ne.

(71)

The values of CY calculated by Hinnov and Hirschberg for lo7 < n, < 1 O I 6 e/cms and 0.03 < kT, < 1 ev are shown in Fig. 32. It will be seen that, in studies of thermal, k!!', = 0.026 ev, plasmas at high elect,ron densities, n, 3 10" e/cc, the three-body process contributes as much to electron loss by recombination as a two-body process with a coefficient

158

-

MANFRED A. BIONDI

cm3/sec. Thus, care must be taken in analyzing volume electron loss in terms of two-body recombination processes in such investigations as those of Chen et al. (229), which are in this range (see discussion of their work in Section V, B, 3 ) . It has been suggested (24, 251) that some of the early recombination studies in arc afterglows (252, 253) a t rather high electron densities and moderate electron temperatures (determined by Langmuir probes) may have actually referred to this three body process; however, dissociative recombination of electrons in a plasma containing both molecular and atomic ions could also lead to the observed loss rates; the experimental data are too sparse to choose between the two mechanisms. From the foregoing discussion it appears that, while our understanding of such recombination processes as radiative capture and electronstabilized capture of electrons by ions is satisfactory, if limited, there are other areas, such as dissociative recombination and mutual neutralization, where considerable improvement in our state of knowledge is desirable. Fortunately, the necessary experimental techniques are available, and the interest in these subjects is sufficiently great that it is to be expected that considerable progress in these areas will be forthcoming in the next few years. a!

ACKNOWLEDGMENTS The author is greatly indebted to his colleagues, especially T. M. Donahue, T. D. Holstein, A. V. Phelps, and G. J. Schulz, for their many suggestions and criticisms which have been of great value in the preparation of this review.

References 1. H. S. W. Massey and E. H. S. Burhop, “Electronic and Ionic Impact Phenomena.” Oxford Univ. Press, London and New York, 1952. 2. L. B. Loeb, “Basic Processes of Gaseous Electronics.” Univ. of California Press, Berkeley, California, 1955. 3. L. Goldstein, Advances in Electronics and Electron Phys. 7, 399 (1955). 4. L. M. Branscomb, Advances in Electronics and Electron Phys. 9, 43 (1957). 6. J. B. Hasted, Advances in Electronics and Electron Phys. 13, 1 (1960). 6. D. R. Bates, ed. “Atomic and Molecular Processes.” Academic Press, New York, 1962. 7 . R. E. Fox, W. Hickam, 11. J. Grove, and T. Kjeldaas, Rev. Sci. Znslr. 26, 1101 (1955). 8. P. Marmet and L. Kerwin, Can. J. Phys. 38, 787 (1960). 9. G. J. Schulz, Phys. Rev. 112, 150 (1958). 10a. E. Gerjuoy, Revs. Modern Phys. 33, 544 (1961). l o b . S. Borowitz and S. J. Smith, Phys. Today 16, No.4, 30 (1962). 11. L. Rosenberg, L. Spruch, and T. F. O’Malley, Phya. Rev. 119, 164 (1960). 12. S. Borowitz and H. Greenberg, Phys. Rev. 108, 716 (1957). 13. B. A. Lippmaon, M. H. Mittteman, and K. M. Watson, Phys. Rew. 116, 920 (1959).

LOW ENERGY ATOMIC COLLISIONS

159

E. Gerjuoy and S. Stein, Phys. Rev. 97, 1671 (1955); 98, 1848 (1955). H. S . W. Massey, Proc. Canabridge Phil. SOC.28, 99 (1932). P. M. Morse, Phys. Rev. 90, 51 (1953). A. S. Eddington, “The Internal Constitution of the Stars.” Cambridge Univ. Press, London and New York, 1926. 17b. P. M. Morse and E. C. G. Stueckelberg, Phys. Rrv. 36, 116 (1930). 18. D . R. Bates and H. S. W. Masscy, .4strophys. J . 91, 202 (1940). 19. S. Chandrasekhar, Astrophys. J . 102, 223, 395 (1945); S. Chandrasekhar and D. D. Elbert, zbid. 128, 633 (1958). 20. T. L. John, Astrophys. J . 131,743 (1960); Monthly Notices Roy. Astron. Sac. 121, 41 (1960). 21. L. M. Branscomb, i n “Atomic and Molccular Processes” (D. R. Bates, ed.), p. 100, Academic Press, New York, 1962. 22. S. Geltman and M. Krauss, Bull. A m . Phys. Soc. I21 6, 339 (1960). 23. R. G. Giovanelli, Australzan J. Sn‘. Research Al, 275, 289 (1948). 24. N . D’Angelo, Phys. Rev. 121, 505 (1961). 26. D. R. Bates and A. E. Kingston, Nature 189, 652 (1961). 26. R. W. P. McWhirter, Nature 190, 902 (1961). 27. E. Hinnov and J. G. Hirschberg, Phys. Rev. 126, 795 (1962); Proc. 61h Intern. Co7bf. on Ionization Phenomena i n Gases, Munich, 1961 p. 638 (1962). 28. D. R. Bates and H. S. W. Massey, Proc. R o y . SOC.8187, 261 (1946); A192, 1 (1947); D.R. Bates, Phys. Rev. 77, 718 (1950); 78, 492 (1950); 82, 103 (1951). 29. J. McDougall, Proc. Roy. SOC.A136, 549 (1932); P. M. Morse and W. P. Allis, Phys. Retj. 44, 269 (1933). 30. B. Bederson, H. Malamud, and J. M. Hammer, Bull. Am. Phys. SOC.[2] 2, 122 (1957); also Tech. Report No. 2, Electron Scattering Project, College of Engineering, New York University 1957, unpublished. 31. S. Chandrasckhar and F. H. Breen, Ast7ophys. J . 103, 41 (1946). 32. H. S. W. Massey and B. L. Moiseimitsch, PTOC.Roy. Sac. 8206,483 (1951). 33. B. H. Bransden, A. Dalgarno, T. L. John, and M. Seaton, Proc. Phys. Soc. (London) 71, 877 (1958). 34. R. T. Brackmann, W. L. Fite, and R. H. Neynaber, Phys. Rev. 112,1157 (1958). 35. A. Temkin, Phys. Rev. 116,358 (1959). 36. H. B. Gilbody, R. F. Stebbings, and W. L. Fite, Phys. Rev. 121, 794 (1961). 37. R. P. McEachran and P. A. Fraser, Can. J . Phys. 38, 317 (1960). 38. S. Geltman, Phys. Rev. 119, 1283 (1960). 39. K. Smith, Phys. Rev. 120, 845 (1960). 40. T. L. John, Proc. Phys. Sac. (London) 76, 532 (1960). 41. R. H . Neynaber, L. L. Marino, E. W. Rothe, and S. M. Trujillo, Phys. lieu. 123, 148 (1961); 124, 135 (1961). 42. E. Bruche, Ann. Physik. [4] 82, 912 (1927), C. E. Normand, Phys. Rev. 36, 1217 (1930); C. Ramsauer and R. Kollath, Ann. Physik. [5] 12, 529 (1932). 43. A. Temkin and J. C. Lamkin, Phys. Rev. 121, 788 (1961). 44. E. Gerjuoy and N. A. Krall, Phys. Rev. 119, 705 (1960); N. A. Krall and E. Gerjuoy, ibid. 120, 143 (1960). 45. B. Bederson, Private communication, 1962. 46. L. B. Robinson, Phys. Rev. 106, 922 (1957); P.Hammerling, W. W. Shine, and B. Kivel, J . A p p l . Phys. 28, 760 (1957); A. Temkin, Phys. Rev. 107, 1004 (1957); M. M. Klcin and K. A. Brueckner, ibid. 111, 1115 (1958). 47. I). I t . Rates and H. S. W. Massey, Proc. Boy. SOC.819’2, 1 (1047).

14. 15. 16. 17a.

160

MANFRED A. BIONDI

48. W. P. Allis, i n “Handbuch der Physik” (S. Flugge, ed.), Vol. 21, p. 383ff. Springer,

Berlin, 1956. H. Margenau, Phys. Rev. 69, 508 (1946). A. V. Phelps, 0, T. Fundingsland, and S. C. Brown, Phys. Rev. 84, 559 (1951). J. M. Anderson and L. Goldstein, Phys. Rev. 100, 1037 (1955). J. M. Anderson and L. Goldstein, Phys. Rev. 102, 388 (1956). J. M. Anderson and L. Goldstein, Phys. Rev. 102, 933 (1956). L. J. Varnerin, Jr., Phys. Rev. 84, 563 (1951). L. Gould and S. C. Brown, Phys. Rev. 96,897 (1954). A. L. Gilardini and S. C. Brown, Phys. Rev. 106, 25, 31 (1957). G. Bekefi and S. C. Brown, Phys. Rev. 112, 159 (1958). 58. S. Takeda and A. A. Dougal, J. Appl. Phys. 31, 412 (1960). 69. L. B. Loeb, “Fundamental Processes of Electrical Discharges in Gases.” Wiley, New York, 1939. 60. A. V. Phelps, J. L. Pack, and L. S. Frost, Phys. Rev. 117, 470 (1960). 61. J. J. Lowkc, Australian J . Phys. 16, 39 (1962). 62. J. L. Pack and A. V. Phelps, Phys. Rev. 121, 798 (1960). 63. J. C. Bowe, Phys. Rev. 117, 1411, 1416 (1960). 64. D . Formato and A. Gilardini, Proc. 4th Intern. Conf. on Ionization Phenomena i n Gases, Uppsala, 1959 p. 99ff. (1960); Proc. 6th Intern. Conf. on Ionization Phenomena in Gases, Munich, 1961 p. 660ff. (1962). 65. H. S. W. Massey and E. H. S. Burhop, “Electronic and Ionic Impact Phenomena,” Chapter 1, Section 4. Oxford Univ. Press, London and New York, 1952. 66. J. L. Pack, R. E. Voshall, and A. V. Phelps, Phys. Rev. 127, 2084 (1962). 67. S. Altshuler, Phys. Rev. 107, 114 (1957). 68. J. S. Townsend and V. A. Bailey, Phil. Mag. [6] 43,873 (1921); 44, 1033 (1922); 46, 657 (1923); R. H. Healey and J. W. Reed, “The Behaviour of Slow Electrons in Gases.” Amalgamated Radio, Sydney, Australia, 1941; R. W. Crompton, L. G. H. Huxley, and D . J. Sutton, Proc. Roy. SOC.A218, 507 (1953). Very recent, accurate determinations h a w been made by R. W. Warren and J. H. Parker, Jr., Phys. Rev. 128, 2661 (1962). 69. A. E. D. Heylen and T. J. Lewis, Proc. 4th Intern. Conf. on Ionization Phenomena in Gases, Uppsala, 1969 pp. 156-163 (1060); A. E. D. Heylen, Proc. Phys. Soc. (London) 76, 779 (1960); 79, 508 (1962). 70. L. G. H. Huxley and R. W. Crompton, in “Atomic and Molecular Processes” (D. R. Bates, ed.), p. 336, Academic Press, New York, 1962. 71. L. S. Frost and A. V. Phelps, Proc. 6th Intern. Conf. on Ionization Phenomena in Gases, Munich, 1961 pp. 102-202 (1962); Phys. Rev. 127, 1621 (1962). 72. L. G. H. Huxley, Australian J. Phys. 9, 44 (1959); J. Atmospheric Terrest. Phys. 16, 46 (1959). 73. A. Dalgarno and R. J. Moffett, Proc. Symposium on Collision Processes, 1961. 74. G. J. Schulz, Phys. Rev. 116, 1051 (1959). 75. G. J. Schulz, Phys. Rrv. 126, 239 (1962). 76. G. J. Shulz and J. T. Dowell, Phys. Rev. 128, 174 (1962). 77. R. Haas, 2. Physik 148, 177 (1957). 78. H. S. W. Massey and E. H. S. Burhop, “Electronic and Ionic Impact Phenomena,” pp. 75-78. Oxford Univ. Press, London and New York, 1952. 79. H. S.W. Massey and E. H. S. Burhop, “Electronic and Ionic Impact Phenomena,” p. 454ff. Oxford Univ. Press, London and New York, 1953.

49. 60. 51. 52. 53. 54. 55. 66. 57.

L O W ENERGY ATOMIC COLLISIONS

161

80. G. Herzberg, “Molecular Spectra and Molecular Structure.” Van Nostrand, Princeton, New Jersey, 1950. 81. L. G. H. Huxley, J. Atmospheric Terrest. Phys. 16, 46 (1959); A. V. Phelps, Private communication, 1962. 82. V. L. Ginsberg, Zhur. Fiz. 8,253 (1944); I. M. Vilenski, Zhur. Bksptl. Teortlt. Piz. 22, 544 (1952). 83. G. Burkhardt, Elwert, and unsold, Z. Astrophys. 26, 310 (1948); G. Brlrkllartlt, Ann. Physik [6] 6, 373 (1950). 84. L. Spitzer and R. Harm, Phys. Rev. 89, 977 (1958). 86. S. C. Lin, E. L. Resler, and A. Kantrowitz, J . A p p l . Phys. 26, 95 (1955). 86. S. Chapman and T. G. Cowling, “The M:tthematical Tlicory of ?;on-Uniform Gases.” Cambridge Univ. Press, London and New York, 1939. 87. T. Holstein, J. Phys. Chem. 66, 833 (1952); Research Report 60-94698-3-R!), Westinghouse Research Labs., Pittsburgh Pennsylvania, unpublished. 88. G. Wannier, Bell System Tech. J . 32, 170 (1053). 89. G. Wannier, Phys. Rev. 83, 281 (1951). 90. M. A. Biondi, Rev. Sci. Instr. 22,500 (1951); D. J. Rose and S. C. Brown, J . :I p p l . Phys. 24, 1053 (1954); L. Goldstcin, M. A . Lampert, and J. Geiger, Elec. Conimun. 29, 243 (1952). 91. A. V. Phelps and S. C. Brown, Pk!/s. Rw. 86, 102 (1952). 92. W. H. Kasner, W. A. Rogers, and M. A. Biondi, Phys. Rat. Letters 7, 321 (1961). 93. W. L. Fite, J. A. Rutherford, W.R . Snow, and V. A. J. Van Lint, Report N o GA-2824, General Atomic, 8an Diego, California, 1962, unpublished. 94. R. F. Stebbings, A. C. H. Smith, and W. L. Fite, Report No. GA-2783 General Atomic, San Diego, California, 1962, unpublished; also work submitted to Proc. Roy. SOC. 95. P. Langevin, A n n . Physik [4] 8, 245 (1905). 96. H. R. Has& and W. R. Cook, Proc. Roy. SOC.8126, 196 (1929); Phil. Mag. [7] 12, 554 (1931). 97. L. M. Chanin and M. A. Biondi, Phys. Itev. 106, 473 (1957). 98. H. Margenau, Phys. Rev. 66, 1000 (1939); Phil. Sci. 8, 603 (1941). 99. R. Meyerott, Phys. Rev. 66, 242 (1844). 100. A. Dalgarno, M. R. C. McDowell, and C. Williams, Phil. Trans. Roy. SOC.A260, 411 (1958). 101. A. F. Pearce, Proc. Roy. SOC.8166, 490 (1936); I(. Hoselitz, ibid. 8177, 200 (1941). 10.9. M. A. Biondi, Phys. Rev. 90, 730 (1953). 103. M. A. Biondi and L. M. Chanin, Phys. Rev. 94, 910 (1954); L. M. Chanin anti M. A. Biondi, ibid. 107, 1219 (1957); M. A. Biondi and L. M. Chanin, ibid. 122, 843 (1961). 10.4. R. N. Varney, Phys. Rev. 88, 362 (1952); 89, 708 (1953); E. C. Beaty, ibid. 104, 17 (1956); F. R. Kovar, E. C. Beaty, and R. N. Varney, ibid. 107, 1490 (1957). 106. E. C. Beaty, PTOC.6th Intern. Con$. on Ionization Phenomena in Gases, Ilfunich, 1961 p. 183fT. (1962). 106. G. E. Courville and M. A. Biondi, J. Chem. Phys. 37, 616 (1962). 107. E. W. McDaniel and H. R. Crane, Rev. Sci. Instr. 28, 684 (1957); and E. W. McDaniel and M. R. C. McDowell, Phys. Rev. 114, 1028 (1959). 108. L. M. Chanin, A. V. PhelpR, and M. A. Biondi, Phys. Reu. 128, 219 (1962). 109. T. L. Bailey, C. J. May, and E. E. Musehlitz, J. Chem. Phys. 26, 1446 (1957). 110. A. M. Arthurs and A. Dalgarno, Proc. Roy. SOC.A266, 540, 552 (1960).

162 111. 118. 113. 114. 115. 116.

MANFRED A. BIONDI

H . S. W . Massey and C. B. 0. Mohr, Proc. Roy. Soc. 8144, 188 (1934). A. M. Tyndall and C. F. Powell, Proc. Roy. SOC.8134, 125 (1931). R. Meyerott, Phys. Rev. 70, 671 (1946). M. A. Biondi and 8. C. Brown, Phys. Rev. 76, 1700 (1949). J . A. Hornbeck, Phys. Rev. 83, 374 (1951); 84, 615 (1951). D. R. Bates, M. Ledsham, and A. Stewart, Phil. Trans. Roy. SOC.A246, 215

(1953). 117. T. J . M. Boyd and A. Dalgarno, Proc. Phys. Soc. (London) A72, 694 (1959). 118. A. Dalgarno, Phil. Trans. Roy. SOC.A260, 426 (1958). 119. D. R. Bates and R. McCarroll, Advances in Phys. (Phil. Mag. Suppl.) 11, 39 (1962). 120. N. Lynn and B. L. Moiseiwitsch, Proc. Phys. SOC. (London) A70, 474 (1957). 121. R. J . Munson and A. M. Tyndall, Proc. Roy. SOC.8177, 187 (1941). 126. E. C. Beaty, Phys. Rev. 104. 17 (1956). 123. J. W. Sheldon, Phys. Reu. Letters 8, 64 (1962). 124. B. Ziegler, 2.Physik 136,108 (1953); R. M. Kushner, B. M. Palyukh, and L. A. Sena, Zzvest. Akad. Nauk S.S.S.R. 23, 1007 (1959). 115. W . L. Fite, R. F. Stebbings, D. G. Hummer, and R. T. Brackmann, Phys. Rev. 119, 663 (1960). 116. D. G. Hummer, R. F. Stebbings, W. L. Fite, and L. M. Branscomb, Phys. Rev. 119, 668 (1960). 127. A. Dalgarno and H. N. Yadav, Proc. Phys. SOC.(London) A66, 173 (1953); A. Dalgarno and M. R. C. McDowell, ibid. A69, 615 (1956). 128. M. Saporoschenko, Phys. Rev. 111, 1550 (1958); R. N. Varney, J. Chem. Phys. 31, 1314 (1059). 129. R. N . Varney, Phys. Rev. Letters 6,559 (1960). 130. W . S. Barnes, D. W. Martin, and E. W. McDaniel, Phys. Rev. Letters 6, 110 (1961). 131. R. F. Stebbings and B. R. Turner, Report No. GA-2768, General Atomic, San Diego, California, 1961, unpublished. 132. H. 8. W. Massey and E. H. S. Burhop, “Electronic and Ionic Impact Phenomena,” Chapter VIII. Oxford Univ. Press, London and New York, 1952. 133. P. H. G. Dickinson and J. Sayers, Proc. Phys. SOC.(London) 76, 137 (1960). 134. G. F. 0. Langstroth and J. B. Hasted, Discussions Faraday SOC.33, 298 (1962). 135. A. Henglein and G. A. Muccini, J. Chem. Phys. 31, 1426 (1959). 136. R. K . Curran, Phys. Rev. 126, 910 (1962). 137. R. F. Stebbings, W. L. Fite, and D. G. Hummer, J. Chem. Phys. 33,1226 (1960). 138. M. A. Fineman, A. C. H. Smith, R. F. Stebbings, and B. R. Turner, Report No. GACD-2991, General Atomic, San Diego, California, 1962. 139. D. R. Bates and N. Lynn, Proc. Roy. SOC.A263, 141 (1959). 140. M. Pahl, Ergeb. exact. Naturwiss. 34, 182 (1962). 141. J . A. Hornbeck and J. P. Molnar, Phys. Rev. 84,621 (1951). 142. M. A. Biondi, Phys. Rev. 88,660 (1952). 143. W. P. Shollette and E. E. Muschlitz, J. Chem. Phys. 36,3368 (1962). 144. A. V. Phelps and J. P. Molnar, Phys. Rev. 89, 1202 (1953). 145. H. J. Oskam, Philips Research Rept. 13, 335, 401 (1958). 146. M. Pahl and U. Weimer, 2. Naturforsch. 13a, 50 (1958). 1.47. D . P. Stevenson and D. 0. Schissler, J . Chem. Phys. 29,282 (1958). 148. G. Giomousis and D. P. Stevenson, J. Chem. Phys. 29, 294 (1958). The units for the reaction coefficient in Table I should be cm3/5 rather than m3/a.

LOW E N E R G Y ATOMIC COLLISIONS

163

149. D. S. Burch and R. Geballe, Phys. Rev. 106, 183, 188 (1957); H. Eiber, Proc. 5th Intern. Conf. on Ionization Phenomena i n Gases, Munich, 1961 p. 1334ff. (1962). 150. A. Dalgarno, Ann. geophys. 17, 16 (1961). 151. H. 5. W. Massey, “Negative Ions,” 2nd ed. Cambridge Univ. Press, London and New York, 1950. 152. L. M. Branscomb, Proc. 5th Intern. Conf. on Ionization Phenomena in Gases, Munich, 1961 p. Iff. (1962). 153. W. Lochte-Holtgreven, Naturwi8senschaften 38, 258 (1951). 154. 0. Weber, 2 . Physik 162, 281 (1958). 165. G. Boldt, 2. Physik 164,319 (1959). 156. S. J. Smith and L. M. Branscomb, J . Research Natl. Bur. Standards 66, 165 (1955). 157. S. J. Smith and L. M. Branscomb, Rev. Sci. Instr. 31, 733 (1960). 158. L. M. Branscomb and S. J. Smith, Phys. Rev. 98, 1028 (1955). 159. S. Chandrasekhar and D. D. Elbert, Astrophys. J . 128,633 (1958). 160. S. Chandrasekhar, Astrophys. J . 128, 114 (1958). 161. L. M. Bransconib and S. J. Smith, Phys. Rev. 98, 1127 (1955). 162. L. M. Branscomb, D. S. Burch, S. J. Smith, and S. Geltman, Phys. Rev. 111, 504 (1958). 163. D. S. Burch, S. J. Smith, and L. M. Branscomb, Phys. Rev. 112, 171 (1958); 114, 1652 (1959). 164. M. L. Seman and L. M. Branscomb, Phys. Rev. 126, 1602 (1962). 165. L. M. Branscomb and S. J. Smith, J . Chern. Phys. 26, 598 (1956). 166. R. S. Berry, C. W. Reimann, and G. N. Spokes, Bull. A m . Phys. Sac. [2] 7, 69 (1962). 167. L. M. Chanin, A. V. Phelps, and M. A. Biondi, Phys. Reu. Letters 2 , 344 (1950). 168. R. K. Curran, J . Chem. Phys. 35, 1849 (1961). 169. G. H. Dunn, Phys. Rev. Letters 8, 62 (1962). 170. J. D. Cragg, R. Thorburn, and B. A. Tozer, Proc. Roy. Sac. 8240, 473 (1957); J. D. Craggs and B. A. Tozer, ibid. A247, 337 (1958); 8264,229 (1960). 171. I. S. Buchelnikova, Zhur. Eksptl. Teoret. I’iz. 36, 1119 (1958); translation, Soviet Phys-JEl’P 36, 783 (1959). 172. J. G. Schulz, Phys. Rev. 128, 178 (1962). 173. P. L. Randolf and R. Geballe, Tech. Rept. No. 6, Dept. Phys. Univ. of Washington, Seattle, Washington, 1958, unpublished. 174. M. A. Harrison and R. Geballe, Phys. Rev. 91, 1 (1953). 175. A. N. Prasad, Proc. Phys. Sac. (London) 74, 33 (1959); A. N. Prasad and J. D. Craggs, ibid. 77, 385 (1961). 176. J. T. Tate and P. T . Smith, Phys. Rev. 39, 270 (1932). 177. M. A. Biondi, Phys. Rev. 109,2005 (1958); R. E. Fox, ibid. p. 2008; M. A. Biondi and R. E. Fox, ibid. p. 2012. 178. R. Buchdahl, J . Chem. Phys. 9, 146 (1941). 179. W. E. Hickam and R. E. Fox, J. Chem. Phys. 26, 642 (1956). 150. G. J. Schulz, J . Chem. Phys. 33, 1661 (1960). 181. A. N. Prasad and J. D. Craggs, Proc. Phys. Sac. (London) 76, 223 (1960). 188. G. J. Schulz, Phys. Rez:. 113, 816 (1959). 183. R. E. Fox, J . Chem. Phys. 26, 1281 (1957). 184. R. E. Fox, J . Chem. Phys. 32, 285 (1959). 185. R. K. Curran, J . Chem. Phys. 34, 2007 (1961).

164

MANFRED A. BIONDI

J. D. Craggs and B. 2. Tozer, Proc. Roy. SOC.A247, 337 (1958). J. D. Craggs and B. Z. Tozer, Proc. Roy. SOC.8264, 229 (1960). R. K. Curran, J. Chem. Phys. 34, 1069 (1961). R. I<. Curran and R. E. Fox, J . Chem. Phys. 34, 1590 (1961). G. J. Schulz, J . Chem. Phys. 34, 1778 (1961). F. Bloch and N. E. Bradbury, Phys. Rev. 48, 689 (1935). T. E. Bortner and G. S. Hurst, Healfh Phys. 1, 39 (1958). V. A. J. Van Lint, Report No. GA-1168, General Atomic, San Diego, California, 1959, unpublished. 194. M. C. Sexton, M. J. Mulcahy, and J. J. Lennon, Proc. 4th Intern. Conf. on Ionization Phenomena in Gases, Uppsula, 1969 p. 94 (1960). 195. E. H. Holt, Bull. A m . Phys. SOC.[2) 4, 112 (1059). 196. P. J. Chantry, J. S. Wharmby, and J. B. Hasted, Proc. 5th Intern. Conf. on Ionization Phenomena in Gases, Munich, 1961 p. 630 (1962). 197. M. A. Biondi, Phys. Rev. 84, 1072A (1951). 198. G. J. Schulz, Bull. Am. Phys. SOC.[2] 6, 387 (1961). 199. J. D. Craggs, Proc. 3rd Intern. Conf. on Ionzzatzon Phenomenu zn Gases, Venice, 1967 (Italian Phys. SOC.,Oct. 1958), p. 207ff., unpublkhed. 200. R. H. Hammond, J. Pares, V. A. J. Van Lint, and D. Zumwalt, Report NO. GACD-2009, General Atomic, San Diego, California, 1961, unpublished. 201. A. V. Phelps and J. L. Pack, Phys. Rev. Letters 6, 111 (1961). 202. D. R. Batcs and H. S. W. Massey, J . Atmos. Terrest. Phys. 2, 1 (1952). 203. D. I<. Bailey, Proc. I.R.E. 47,255 (1959). 204. H. 0.Pritchard, Chem. Rev. 62,529 (1953). 205. N. 8. Buchclnikova, Uspekhi Fiz. Nauk. 66, 351 (1958); translated by A. L. Monks, Report No. AEC-tr-3637, Oak Ridge National Laboratory, Tennessee. 206. S. Gaydon, “Dissociation Energies.” Chapman & Hall, London, 1953. 207. H. I). Hapitrum, Revs. Modern Phys. 23, 185 (1951). 208. R. Thorburn, “Applied Mass Spectrometry.” Inst. Petroleum, London, 1954. 209. G. J. Scliulz, Private communication, 1962. 210. J. L. Park and A. V. Phelps, Bull. Am. Phys. SOC.[2] 7, 131 (1962). 211. I. G. Y. Rocket Report No. I, Natl. Acad. Sci., Washington, D. C., 1958, unpublished. 212. J. M. Anderson, Report No. 61-RL-2817G, General Electric Research Lab., Schenectady, N. Y., 1961, unpublished. 213. E. P. Gray and D. E. Kerr, 4 n n . Phys. (N . Y . ) 17, 276 (1962). 214. F. L. Mohler, J . Research Bur. Standards 10, 771 (1933). 215. See, for example, G. L. Weissler, i n “Handbuck der Physik” (S. Flugge, ed.), Vol. 21, p. 3046. Springer, Berlin, 1956. 216. R. G. Fowler and W. R. Atkinson, Phys. Rev. 113, 1268 (1959). 217. H. Olsen and W. Huxford, Phys. Rev. 87, 927 (1952). 218. A. Pory-Thorne and W. R. S. Garton, Proc. Phys. SOC.(London) 76,833 (1960). 219. W. R. S. Garton, A. Pery, and K. Codling, Proc. 4th Intern. Conf. on Ionization Phenomena i n Gases, 1969 p. 206 (1960). 280. E. Bauer and T. Wu, Can. J . Phys. 34, 1436 (1956). 261. J. J. Gibbons, Abstr. D.A.S.A. Reaction Rate Conf. (N.B.S.), Boulder, Colorado, 1961 unpublished. 222. M. A. Biondi and S. C. Brown, Phys. Rev. 76, 1697 (1949). 823. R. B. Holt, J. M. Richardson, B. Howland, and B. T. McClure, Phys. Rev. 77, 239 (1950).

186. 187. 188. 189. 190. 191. 192. 193.

LOW E N E R G Y ATOMIC COLLISIONS

294. 296. 226. 227. 228. 229. 2SO. 231. 232.

233. 234. 236. 236. 237. 238. 239.

240. 2.41. 24%'. 243. 244. 246. 246. 247. 248. 249.

260.

165

K . B. Persson and S. C. Brown, Phys. Rev. 100, 729 (1955). M. C. Sexton and J. D. Craggs, J . Electronics and Control 4, 493 (1958). A. C. Faire and I<. S. W.Champion, Phys. Rev. 113, 1 (1959). M. A. Biondi, Phys. Rev. 129, 1181 (1963). L. Goldstein, J. M. Anderson, and G. L. Clark, Phys. Rev. 90,486 (1953). C. L. Chcn, C. C. Leiby, and L. Goldstein, Phys. Rev. 121, 1391 (1961). C. S.Leffel, M. N. Hirsh, and 1). E. Kerr, Ann. Phys. ( N . Y . ) to be published; D. E. Kerr and C. S. Leffel, zbid. to be published. M . A. Biondi and T. Holstein, Phys. Rro. 82,962 (1951); M.A. Biondi, zbzd. 83, 1078 (1951). W. A. Rogers and M. A. Biondi, Bull. Am. Phys. SOC.[a] 2, 87 (1957); W. A. Rogers, Ph.D. Thesis, University of Pittsburgh, 1958, unpublished; W. A Rogers and M. A. Biondi, Phys. Rev. to be published. M. A. Biondi, Rev. Sci. Instr. 27, 36 (1956). W. H. Kasner and M. A. Biondi, to be published. A. V . Phelps, Sc.D. Thesis, M.I.T., Cambridge, Massachusetts, 1951, unpublished. J. J. Lennon and M. C. Sexton, J . Electronics and Control 7, 123 (1959). J. M. Richardson, Phys. Rev. 88, 895 (1952). J. M. Anderson, Phys. Rev. 108, 898 (1958). D. R. Bates and T. J. Lewis, Proc. Phys. SOC.(London) 868, 173 (1955); n.R. Bates and T. J. M. Boyd, ibid. A69, 910 (1956). T. H . Y . Yeung, Proc. Phys. SOC.(London) 71, 341 (1958). J. J. Thomson, Phil. Mag. 161 47,337 (1921). P. Langevin, Ann. chim. phys. [7]28, 433 (1903). W. Machler, 2. Physik 164, 1 (1936). J. Sayers, Proc. Roy. SOC.A169, 83 (1938). G. L. Natason, Zhur. Tekh. Fiz. 29, 1373 (1959). M. E. Gardner, Phys. Rev. 63,75 (1938) T. Fucno, H. Eyring, and T. Rce, Can. J. Chem. 38, 1693 (1960). A. F. Kuckes, R. W. Motley, E. Hinnov, and J. G. Hirschberg, Phys. Rev. Letters 6, 337 (1961). R. W. Motley and A. F. Kuckes, Proc. 5Lh Intern. Conf. on Ionizntzon Phenonienn i n Gases, dlunich, 1961 p. 651 (19F2) D. R. Bates, A. E. Kingston, and R. W. P. McWhirter, Proc. Roy. Soe. A267,

297 (19B'L). 651. S . Byron, R. C. Stabler, and P . Bortz, Phys. Rev. Letters 8,376 (1962). 652. C. Kenty, Phy.9. Rev. 32, 624 (1928). 253. F. L. Mohler, J . Research Bur. Stundardn 19,447, 559 (1937).

This Page Intentionally Left Blank

Semiconductor Device Evaluation DAVID P. KENNEDY International Business Machine Corporation Poughkeepsie, New York

I. Introduction.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11. The p-n Junction Diode.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B. Unstable Reverse Characteristics.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C. Reverse Current.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D. Reverse Breakdown.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E. Forward Characteristics, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . F. Transient Characteristics. . . . . . . . . . . . . . . . . . . . . . 111. The Junction Transistor, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B. Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C. Steady-State Characteristics, . . . . . . . . . . . . . ..................... L). Small-Signal Parameters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E. Stored-Charge Characteristics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . List of Symbols.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Page 167

170 175 196

225 23 1 240 248 249

I. INTRODUCTION Since Shockley’s classic article on the theory of p-n junctions (1) semiconductor devices have undergone a continuous process of study and evaluation. I n his paper Shockley presented basic mechanisms of operation associated with diodes and transistors although only elementary structures were considered in a n oversimplified mode of operation. Subsequent laboratory experiments established many inadequacies in these initial concepts. Elementary theory provides only the basic electrical characteristics of semiconductor devices and cannot, in most situations, properly explain many of the important details, Since that time1949-semiconductor component evaluation has become intimately concerned with the development of theoretical models characterizing the operation of diodes and transistors. hiodern literature on the subject contains many new and subtle methods for measuring fundamental component parameters and, using analytical models suggested by such rneasurements, provides theoretical studies which contribute significantly to our knowledge of component operation. The inherent difficulties of 187

168

DAVID P. KENNEDY

this problem have made progress very slow but, on the other hand, constant effort has yielded a substantial amount of information th a t is of fundamental importance to the field. At this point we might ask why the evaluation of semiconductor components is so intimately concerned with the study of theoretical mechanisms pertaining to their operation. The answer is quite simple. Unless we fully understand how a semiconductor device should operate, it is indeed difficult to correctly evaluate its electrical characteristics and to judge its merits or its deficiencies. I n the author’s opinion, projects which are established to evaluate semiconductor components, eventually become deeply involved in device theory; this indicates our present knowledge of the subject is inadequate for many practical purposes. The device designer, for example, tries t o attain specific electrical characteristics although there is insufficient theoretical information to guide his efforts. Similarly, the application engineer is seldom able to predict the operation of semiconductor devices in a new circuit without actual laboratory experience. Although the device designer and application engineer often use empirical methods to solve their respective problem, this technique is extremely difficult for the component manufacturer who is concerned with problems of reliabiIity and reproducibility. These inadequacies in our knowledge of semiconductor device operation has resulted, in part, from the accelerated development program that has taken place during previous years. Industrial requirements emphasized the design and development of new and novel devices rather than obtaining a better understanding of available units. Furthermore, manufacturing techniques were generally “brute force” in nature requiring a minimum of process control-low manufacturing yield and poor reproducibility were economically acceptable as long as everybody had the same type of problem. Today this situation is rapidly changing. Economic and technical requirements upon modern semiconductor devices make i t increasingly difficult to design and manufacture by empirical methods. A greater effort is therefore being applied to the evaluation of semiconductor components; this effort should lead to a better Understanding of their operation and also to improved experimental techniques for establishing their electrical properties. The preceding remarks provide a basis of understanding for the apparently divergent directions th at have been taken in the evaluation of semiconductor components. The device designer, for example, uses a number of experimental techniques which are intended to provide information pertaining to fundamental parameters of component operation. Application engineers, on the other hand, often use entirely different methods to establish the same component parameters; this situation

SEMICONDUCTOR DEVICE EVALUATION

169

indicates the inherent difficulties of this problem and, furthermore, it often results from the fact that no particular method of evaluation has proven superior. Both the device designer and application engineer have one common goal-to establish methods whereby we can accuratcly evaluate the properties of semiconductor devices. From laboratory measurements upon a complete device it is necessary to establish physical mechanisms contributing to its electrical characteristics, to obtain a reasonable estimate of its properties when used in a large variety of applications, and to also recognize units which may not exhibit a satisfactory degree of reliability. The intent of this paper is to revicw the subject of semiconductor component evaluation. We shall discuss the experimental techniques used to establish important physical properties of these devices and also the theoretical models associated with such cxperiments. For brevity, it is indeed necessary to limit the types of devices considered in these discussioiis and, furthermore, to limit the number of topics pertaining to each device. We shall, therefore, place principal emphasis upon the problems of p-n junction diodes and transistors. Although the importance of other semiconductor devices-varactors, photo devices, etc.-is fully recognized, many of their evaluation problems are similar to the more common semiconductor diode and transistor. Furthermore, in this review we shall consider topics which are either not adequately discussed in the literature-or have been considered, in part, in individual papers without having been integrated into a single topical presentation. Clearly, little is to be gained by reiterating nicthods of measuring transistor smallsignal parameters, for example, since this aspcct of transistor evaluation has been adequately considered in numerous books and papers on the subject. A few of the evaluation methods to be presented are, in the author’s opinion, becoming a laboratory tool rather than a subject of intensive investigation-satisfactory agreement has been demonstrated between theory and experiment so that the method will reliably establish particular device characteristics. 11. THE p-n JUNCTION DIODE

A . General

A p-n junction diode is indeed an elementary semiconductor device and yet the problem of evaluating its electrical characteristics can become exceedingly difficult. This evaluation usually consists of both static and dynamic-or switching-type measurements although the latter is often restricted to high speed computer components. In static type measurements we are concerned with the diode current resulting from a n applied

170

DAVID P. KENNEDY

biasing potential-in both the forward and reverse direction. Under conditions of reverse bias the magnitude of this current, and also its degree of saturation, are important. I n addition, semiconductor diodes must also exhibit a stable reverse current over long periods of time-this stability is often established a t both room temperature and at a n elevated temperature. Another determining factor in the evaluation of a diode is its reverse breakdown characteristics; satisfactory components usually exhibit a very abrupt reverse breakdown which is repeatable a t a given voltage. The basic problem when evaluating this type of semiconductor device is to establish that its electrical properties are dictated by known concepts of physics and not by unknown or undesired mechanisms. Laboratory instrumentation for the evaluation of diodes can be kept relatively simple for some types of measurements while for others it must, of necessity, be very complicated. Static measurements, for example, can be made with a controlled source of biasing potential and current measuring instruments. This type of equipment, although satisfactory, is not particularly convenient when large numbers of devices are to be evaluated. Many laboratories, therefore, use commercially available instruments which apply a low frequency sweep voltage to the diode and present its volt-ampere characteristics upon a cathode-ray oscilloscope-this sweep rate is sufficiently slow to be presumed a static condition. Similarly, commercial instruments are also available which can establish the transient switching properties of a p-n junction diode although this equipment is rapidly becoming inadequate for the measurement of modern units operating in the low-nanosecond range. For the measurement of very high speed components, therefore, it is often necessary to engage in an extensive instrumentation program using a pulse sampling oscilloscope and a high speed pulse generator,

B. Unstable Reverse Characteristics Initially, semiconductor devices were presumed capable of operating for a n indefinite period of time without “wearing-out.” Fundamental mechanisms of operation predict that a p-n junction diode, for example will not exhibit a measurable change in its crystallographic properties due to the application of either a forward or a reverse biasing potential; this, of course, assumes no damage is incurred through such mechanisms as excessive heating. Unfortunately, experience shows that all semiconductor components exhibit a finite lifetime and, furthermore, that this problem becomes exceedingly serious in large electronic systems where reliability is a n important factor. Because theory predicts th at normal operating conditions should introduce a negligible physical change within semiconductor com-

SEMICONDUCTOR DEVICE EVALUATION

171

ponents, we can only assume their present “end-of-life” results from surface contamination. This problem, in fact, represents one of the most difficult aspects of component evaluation and yet it is probably the least understood. Experimentally, a significant degree of similarity is observed in the deterioration pattern of such devices when subjected to life tests. The p-n junction diode, for example, often exhibits a substantial increase in reverse current while, a t the same time, its reverse breakdown voltage

CURRENT

FIG.1. Illustration of current hysteresis in a p-n junction diode.

decreases and becomes “soft,” (i.e., the diode exhibits a large dynamic breakdown resistance). Characteristics of this type could be classified a s a form of long-term instability within the junction. If this instability remains undetected it can, in some applications, lead to a n excessive reverse current which is capable of destroying the semiconductor device and, sometimes, other associated components of the system. Frequently, a n extremely unstable p-n junction diode exhibits a shortterm instability that can be readily observed in static or low frequency measurements of its volt-ampere characteristics. Although exaggerated for illustrative purposes, Fig. 1 is a sketch of the oscilloscope pattern for such a condition of short-term instability. I n this example, a n increasing reverse biasing voltage produces a substantially different reverse current than when this voltage is decreming; characteristics of this type are often called a reverse current hysteresis.

172

DAVID P. KENNEDY

I n this discussion, unstable reverse characteristics have been attributed only to a p-n junction diode although they are also observed in the collector of junction transistors. This problem, in fact, is encountered in all phases of semiconductor component development and manufacturing. As previously stated, most situations involving instability in semiconductor diodes can be assumed to result from surface contamination, b u t beyond this little can be said about its cause or its cure. Each diode represents a new and completely different problem. I n one situation, a diode may have been improperly dried prior to encapsulation; in another, inadequate encapsulating techniques may provide a leak path to the atmosphere. The gravity of this problem has caused many semiconductor manufacturers to search for a “magic elixir” which will yield adequate protection for a semiconductor surface. From the use of a dry oxygen ambient to coating the device with a mixture of red lead and “glimp,” one usually finds t hat any foreign material on the semiconductor surface will itself degrade the electrical characteristics of a junction. Although new protection techniques have been recently developed, these methods are not, as yet, used extensively throughout the industry and therefore the problem of instability in semiconductor devices remains with us today. It is appropriate, a t this time, to discuss some recent developments relating t o the subject of surface protection and encapsulation of silicon diodes, For many years surface passivation has been a n ultimate goal for workers in this field. Using both physical and chemical techniques, attempts have been made to provide an environment for a silicon junction in which no contaminant could alter its electrical characteristics. Physical me.thods have included encapsulation in a wide variety of plastics and glasses ; these have never proven entirely satisfactory. Chemical passivation methods have been directed toward the formation of a thick oxide layer on the silicon surface. This oxide coating-with a n additional protective material on the oxide-has provided a substantial improvement in the stability and reliability of these semiconductor devices. An important development in this direction was reported by Perri et al. ( 2 ) where a three-micron glass layer was bonded to a n oxide-coated surface, thereby providing excellent protection for the semiconductor. Diodes of this type were subjected to a large number of humidity and temperature tests without significantly altering their electrical characteristics. Although short-term instabilities are usually caused by a n extreme amount of surface contamination, they are often the easiest type t o eliminate. In such situations the source of Contamination is relatively obvious and furthermore, since the instability can be observed within a short period of time, results of a n cxperiment can be readily evaluated. Long-term instabilities, on the other hand, represent a far more difficult

173

SEMICONDUCTOR DEVICE EVALUATION

problem from both an engineering and evaluation point of view. Component deterioration is usually caused by a small contamination source and can take place over hundreds-and sometimes thousands-of hours; a significant part of the problem is simply determining whether a particular engineering change has resulted in an improved stability. To this end, component designers have searched for methods which provide a n accelerated aging process. N o single method has been found “fool-proof” although one extremely successful technique, in the author’s opinion, is to operate a device a t an excessive temperature for extended periods of time.

WORKMANSHIP

i

Surface Cleaning Joints And Connections Atmosphere Control

a

I

DESIGN -4

Thermal Cycling Fatigue

0

: :

Atmosphere Specification Seal And Mechanical Structure

I) 1)

.;

/

::

-\

\

\

APPLICATION High Mechanical Mechanical Stresses Stresses High High Power-Cycling Stresses

High Temperatures Circuit -Design Margins

V FAILURE

C O N S T A N T RANOOMFAILURE RATE

DEGRADATION FA IL UR E

TIME

FIG.2 . Generalized transistor failure-rate pattern with major influencing factors (from C. H. Zierdt, Elec. Mfg. p. 166, April 1960).

A silicon p-n junction diode, for example, can be biased near breakdown in a n elevated ambient temperature; operation in this manner will often detect many potentially unstable devices. Recent investigations have been made into the problems of accelerating the aging process in semiconductor devices (Zierdt, 3 ; Howard and Dodson, 4). I n these investigations the component failure pattern is assumed to consist of three regions, Fig. 2, where each region results from substantially different failure mechanisms. Early failures are frequently caused by inadequate component design or workmanship and will often result in a catastrophic situatioii-an open or short circuited devicewhich is easily recognized and corrected. Degradation trype failures, on the other hand, occur only after a n extensive period of time. Although

174

DAVID P. KENNEDY

these studies were conducted upon junction transistors, the results are in qualitive agreement with previous statements on high temperature operation. Zierdt (3)recognized the contribution of surface contamination to the degradation of p-n junction characteristics and also the use of high temperatures to accelerate this contamination process. For many years component manufacturers used high-temperature storage as a standard process to accelerate possible junction contamination in a semiconductor

FIG.3. Acceleration curves for fifty per cent failure of past and present production (from Howard and Dodson, 4).

device. Initially this method was satisfactory because of the severity of the problem; this situation was quickly modified by improved methods of construction. High temperature storage no longer provides a satisfactory aging process. Extrapolating the failure-time curve of devices subjected to high temperature storage can indicate satisfactory operation for a period of hundreds of thousands of hours-in contrast, a n unsatisfactory one thousand hour failure rate could be exhibited by the same devices

SEMICONDUCTOR D E V I P E EVALUATIOX

175

when used in an actual circuit. If, on the other hand, semiconductor coinponents are placed in operation during this high temperature test, units previously passing high temperature storage will often fail in a relatively short period of time. It appears that high temperature storage does not accelerate many of the contamination mechanisms encountered duriiig a n operation type of life test, and therefore it cannot be considered a satisfactory method. Furthermore, there is substantial evidence that high temperature operation accelerates several contamiiiation mechanisms simultaneously, thereby providing a more accurate method of component evaluation. Operating assorted diodes and transistor in a n oven for a sufficient period to attain a 50 % failure rate, Howard and Dodson ( 4 ) could detect differences between two groups of devices which were encapsulated by different methods (Fig. 3). Clearly, high temperature operation provides a n important improvement in the technique of accelerating the aging process in semiconductor devices. Unfortunately, this method is frequently unpopular because it often leads to a large failure rate. Although arguments prevail that a practical device is never operated in this manner, sufficient experimental evidence is available to establish that it leads to an improved component stability.

C . Reuerse Current When evaluating the reverse current characteristics of a p-n junction one finds general agreement with elenientary theory (1) but there are many details which remain unexplained. I n magnitude, this current is usually greater than theoretical considerations predict and, furthermore, many devices do not exhibit a well-defined saturation region-where the reverse current is essentially independent of biasing voltage-which has been proposed as a fundamental junction characteristic. Elementary theory describes the volt-ampere properties of a p - n junction by a n expression of the form I = 18(eqt/kT- 1 ) (1) When deriving this expression, the parameter IS--or saturation currentis presumed to result from the thermal generation of hole-electron pairs within neutral semiconductor material adjacent to the space charge layer. This mechanism, therefore, should introduce a n apparent saturation of the reverse characteristics with a magnitude proportional to the generation rate-and hence the recombination rate-of minority carriers,

176

DAVID P. KENNEDY

Silicon p - n junctions usually exhibit a reverse saturation current that is orders of magnitude greater than predicted by Eq. (2). Furthermore, this type of semiconductor device will seldom saturate in a manner prescribed by Eq. (1)-the reverse current frequently changes three orders of magnitude between a low reverse biasing potential and breakdown. Germanium p-n junction diodes, on the other hand, are generally in better agreement with elementary theory-limited, of course, by our knowledge of L,, L,, rP, T,, etc. This statement is not intended to imply that all germanium junctions are well-behaved-they can offer as many difficult problems as a silicon device. From measurements of this type it is necessary to establish whether the excess diode current represents a fundamental semiconductor characteristic or, instead, it results from undesirable mechanisms such as surface leakage. If excess current is a characteristic of the semiconductor material, we can sometimes extract information pertaining to the physical properties of a diode; this type of information is invaluable to a device designer. If, on the other hand, excess current results from surface leakage, contamination mechanisms are probably present which may alter the reliability of the device. I n many situations it is not a n easy task to distinguish between the two types of mechanisms. Many similarities are found between the excess current characteristics of a device resulting from the semiconductor material and resulting from surface leakage. I n 1957 several papers were published on the subject of excess reverse current in a p-n junction diode; each paper attributed this current t o substantially different mechanisms. Sah et al. ( 5 ) applied the ShockleyRead theory of carrier recombination (8)to explain both the excess current and also the lack of saturation observed in silicon junctions. This theory assumes the presence of trapping levels within a semiconductor material through which all carrier generation and recombination takes place. Further, this theory also shows an increased generation rate within the space charge layer of a silicon p-n junction thereby contributing to its total reverse current. Germanium junctions, on the other hand, are shown to be substantially free of space charge generation and therefore their excess current is presumed to result predominantly from surface leakage. I n contrast, other workers have proposed that excess diode current results from surface contamination in the vicinity of the p-n junction (Cutler and Bath, 7; Erickjsen et at., 8). Surface contamination introduces two, fundamentally different, mechanisms by which an excess reverse current can be exhibited. Earlier investigations have conclusively established that some contaminents on the surface of a semiconductor induce an inversion layer-or channel-on one side of the p-n junction (9). This surface channel effectively modifies the junction area and also its electrical

SEMICONDUCTOR DEVICE EVALUATION

177

characteristics by providing a conduction path from one side of the device. In addition, these contaminants can also contribute to the reverse junction current when they appear as a condensable vapor and in sufficient quantity to form a coherent conduction path across the structure. In many silicon diodes, therefore, the true cause of an excess reverse current is probably a combination of the above mechanisms. The Shockley-Read theory of carrier recombination ( 6 ) assumes the presence of recombination-generation sites, or traps, with energy levels which reside within the energy gap of a semiconductor material. These recombination sites are assumed to be caused by defects in the lattice structure as would result from dislocations, impurity atoms, etc. Figure 4

FIG.4. The basic processes of carrier generation arid recombination by trappirig (a) electron capture, (b) electron emission, (c) hole capture, (d) hole emission (from

Shockley and Rcad, 6).

illustrates the manner in which holes and electrons may be generated or recombined. Any trap is assumed to be in either one of two states, differing by one electronic charge; the trap can be either negative or neutral. If the trap is neutral, it can capture an electron from the conduction band, Fig. 4(a)-the electron gives up its energy to heat or light (or both) -and the trap acquires a negative charge. A neutral trap may also acquire a negative charge by capturing an electron from the valence band, Fig. 4(d), thereby leaving a hole at this location. A charged trapping site can become neutral by emitting an electron to the conduction band, Fig. 4(b), or to the valence band, Fig. 4(c); the latter is equivalent to a mechanism of hole capture. A limitation is assumed upon the rate a t which carriers can be recombined during this trapping process; this limitation results from the availability of holes and electrons. I n a heavily doped n-type semiconductor, for example, electrons will occupy all trapping sites and hole trapping implies immediate recombination. I n a lightly doped n-type material, on the other hand, these trapping sites are only

178

DAVID P . KENNEDY

partially occupied by electrons and therefore hole capture does not imply immediate recombination. If a n unoccupied trap in n-type material captures a valence electron, within a specified time the hole will be emitted without undergoing recombination. Using these concepts, an analytical investigation was conducted upon the generation-recombination process in a semiconductor. Assuming these trapping levels are single valued and residue a t the mid-gap of a semiconductor, this analysis provides a steady-state generation-recombination expression of the form .

I n a heavily doped n-type material, Eq. (3) reduces t o the familiar expression

If, on the other hand, Eq. (3) is applied to a junction space charge layer where pn << ni2we obtain (5)

which implies a very large carrier generation rate. The physical processes associated with space charge layer generation can be readily visualized by a n elementary example; this is essentially equivalent to the example presented by Sah et al. ( 5 ) . At the edge of a p-n junction space charge layer-under conditions of reverse bias-the minority carrier concentration is held near zero. If, a t this location, we assume the n-type and p-type semiconductor material have equivalent lifetimes (7, = T~ = TO) and impurity atom concentrations ( p , = n,) the saturation current is, from Eq. (4),given by

I,

=

2qAn,Lo/ro

(6)

do,., d G .

where Lo = = I n elementary junction theory ( I ) , Eq. (6) is combined with Eq. (1) to characterize the volt-ampere characteristics resulting from a n applied biasing potential. Clearly, from this mechanism we would expect any junction to exhibit a well defined reverse current saturation. If, on the other hand, the space charge layer is recognized as a depletion layer, the Shockley-Read theory (6) predicts a minority carrier generation rate, from Eq. ( 5 ) , given by

a = - -n,

270

(7)

SEMICONDUCTOR DEVICE EVALUATION

179

Using Eq. (7) we therefore have a reverse current componeiit resulting from space charge generation of minority carriers,

I?,,.ch

=

qAnn,w/rO

(8)

This current exhibits substantially differentcharacteristics than described by Eq. (6)-it increases with space-charge-layer width and hence will depend upon the junction biasing potential. Comparing the magnitudes of diode current resulting from carrier generation within essentially neutral material, Eq. ( G ) , and from generation within the space charge layer, Eq. (8) provides important information pertaining to the evaluation of these devices. For silicon junctions it is not unusual to find the space charge generated component of reverse current to be three orders of magnitude above the bulk generated componeiit; this situation implies a qualitative explanation for many observed characteristics. A germanium diode, on the other hand, exhibits substantially different theoretical properties. I n typical examples, the space charge generated component of reverse current is usually a n order of magnitude below the bulk-generated component and therefore elementary theory should adequately approximate the reverse characteristics of this type of device. I n addition, Eq. (3) has been rigorously applied to a calculation of the space-charge-generated reverse current of a silicon junction (5). Equation (3) was written in terms of the energy levels of a one-dimensional structure, and the total current was established by integrating this expression across the junction depletion layer,

I,,,

rh, =

yAJ’&(z)dz

(9)

Clearly, in this type of calculation it is difficult to compare experiment and theory because many physical constants remain unknown. To alleviate such difficulties the calculated volt-ampere curves have been fitted to experimental characteristics of a diode; this has been done for both reverse and forward bias, although the latter will be discussed a t a later time. Figure 5 illustrates that satisfactory agreement can be obtained between theoretical and experimental results and such agreement is always a very strong argument. Through this analysis the reverse current of a silicon junction is shown to be dependent upon its depletion layer width and hence this current should exhibit a V’? or V55 dependency-in accordance with its impurity atom profile. Unfortunately, this situation is not unique because similar characteristics are predicted when surface leakage is the predominant cause of the excess current. Recognizing this difficulty, Sah

180

DAVID P. KENNEDY

et at. ( 5 ) separated the mechanisms of bulk and surface-generated excess current by constructing two types of junctions-one with a large and the other with a small area-to-circumference ratio (Fig. 6). Although little is mentioned about the results of these experiments, conclusions are drawn which indicate that freshly etched devices appear to exhibit an excess current resulting predominantly from space charge generated minority carriers. lo2

!I 4

2 v

2>

)

I

W

0

a

5

B 10-1

10-2

I0-3 lo-“

10-10

I O - ~ CURRENT AMP.

10-8

I 0-7

FIG.5. Silicon p-n junction characteristics (from Sah et al., 6).

Having considered the mechanism of minority carrier generation within a junction space-charge layer, we shaIl next discuss the characteristics of surface leakage. Initially, surface contamination of semiconductors was first considered by Brattain and Bardeen (9). In their study they established that n-type material, for example, when subject to certain contaminants, could exhibit a thin p-type skin-or surface “channel.” This thin skin of inverted semiconductor material can attain a thickness of cm, and thus introduce an independent channel of surface con-

SEMICONDUCTOR DEVICE EVALUATION

181

duction that is shielded from the bulk semiconductor by a potential barrier. When present on a p-n junction (Fig. 7), this inversion layer provides a path of electrical conduction from the p-type material thereby extending the junction. Additional refinements have been added to this

t

t P+

N-TYPE

P+

(a)

(b)

FIG.6. Geometry for separating surface and bulk currents: (a) large junction area t o circumference ratio; (b) small junction area to circumference ratio (from Sah el al., 6). X- I

SURFACE BARRIER

RECTIFIER BARRIER

Fro. 7. Diagram of the model for surface leakage (from Cutler and Bath, 7 ) .

theory in which many semiconductor properties are explained in terms of surface states and other related phenomena; these studies have been particularly concerned with the behavior of a semiconductor surface under the influence of different ambient gases, for example, and not neces-

182

DAVID P. KENNEDY

sarily their influence upon the electrical properties of a p-n junction diode. I n 1957 Cutler and Bath (7) presented a n analysis of the surface leakage in p-n junctions using a very elementary analytical model; this analysis, although approximate in nature, agrees reasonably well with experiment. One side of the structure is assumed to contain a n iiiversion layer that is in electrical contact with the other side, Fig. 7; this layer provides a n electrical barrier between the bulk semiconductor material and its surface. For simplicity the inversion layer conductivity is assumed constant and also the elementary diode equation, Eq. (l),is assumed to characterize all current flow. In this analytical model the surface barrier is, in effect, a n extension of the rectifying junction, although it contains substantial series resistance and hence it is riot uniformly biased, Using this simplified analytical model, the change in voltage drop, V(z), within the inversion layer is given by Ohm's law,

-dV_ dx

-Z(.E)/uw

where Z(z) is the cumulative current, u is its two dimensional, leakage path, conductivity and w is the path width. Further, the elementary diode equation is used to describe the change in Z(z) resulting from current flow across this surface barrier,

where I, b is the saturation current for the surface barrier. Solving these equations, subject to appropriate boundary conditions, one obtains

where Isb

kT

= 2UW2Is-

Q

The parameter 11 in Eq. (12) represents the total leakage current of the diode occurring at a n applied biasing voltage 8. Combining this leakage current expression with the elementary junction equation, Eq. (I), we obtain a relation characterizing the total diode current = Z,j{evv/kT -

11

reb{

p l k T

- I

q171

-Ic T

(1.2)

The positive and negative signs, respectively, characterize a forward

183

SEMICONDUCTOR DEVICE EVALUATION

and a reverse biased diode. Further, the parameter I a j represents the junction saturation current. Qualitative information is readily obtained from Eq. (14) which is of fundamental importance in the evaluation of practical devices. If, for example, arbitrary constants are properly selected in Eq. (14), large reverse biasing potentials yield the proportionality 1 cc

v54

(15)

From this relation it appears that both surface leakage and also spacecharge generation in an abrupt silicon p - n junction can exhibit a reverse

I0,OOO

I.000 I

v)

a

-3

I00

0

10

0,

X

U

1.0

0.1

'

0.01 0.01

I 0.1

I

I

I

1.0 V (VOLTS)

10

I00

FIG.8. Experimental points and theoretical curve for a silicon p-n junction diode at room temperature. The theoretical curve is calculated from Eq. (14) where 1.j = 5.7 X

and

Zab

=

10-10

(from Cutler and Bath, 7).

diode current that is proportional t o V. Although this proposed model for surface leakage is an approximation, it indicates the possibility of confusion between these proposed models when only the reverse-current characteristics are used to evaluate a particular device. Figure 8 illustrates a comparison between the measured characteristics of a silicon p-n junction and the proposed relation of Eq. (14). Recognizing the simplicity of this model for surface leakage, a satisfactory agreement is obtained between theory and experiment although the observed discrepancies clearly indicate the need of further refinements. Here, nevertheless, we find another mechanism capable of contributing to the experimentally observed reverse characteristics of a p-n junction. The first mechanism-space charge generation-is not particularly desirable in a silicon junction although from a practical point of view it does

184

DAVID P. KENNEDY

not seriously influence component reliability. Surface leakage, on the other hand, indicates the presence of contaminating agents, which are usually unstable, and can result in an instability of reverse junction current. I n a similar investigation of surface induced excess current, Eriksen et al. (8) integrated Eq. (10) with the addition of a spatially varying channel conductance. These workers also considered the problem of surface leakage through condensed vapors on the semiconductor surface. The first part of this effort-improved integration of Eq. (10)-provides little advantage over the above conclusions except to show that the proportionality I m V$+is not always correct; this leakage current is shown to be a n approximately logarithmic function of voltage and dependent upon the material conductivity. The assumption of a “channel” a t the semiconductor surface does not, in fact, explain a largc number of experimentally observed electrical properties of the p - n junction and therefore a n additional leakage current has been postulated within a coherent liquid film a t the semiconductor surface (8).Unfortunately experimental information is insufficient to adequately confirm the existence of this proposed mechanism although it is probably safe to assume its presence in many p-n junction diodes.

D. Reverse Breakdown I n the early stages of p-n junction development the mechanism of reverse breakdown was a subject of investigation for many workers. In 1951 McAfee et al. (10) proposed that internal field emission could explain why-upon reaching a critical biasing potential-junction current rapidly increases with voltage. The mechanism associated with this characteristic-which is frequently called “Zener breakdown”-was first suggested by C. Zener (11) to explain similar properties encountered in electrical insulators; he postulated a field induced electron tunneling from the valence band to the conductance band. Applying a modified form of Zener’s theory t o a semiconductor junction, qualitative agreement was obtained between the experimentally determined breakdown properties of a device and its theoretically determined properties. Although we now know junction breakdown is more complicated than initially suspected, this preliminary investigation represented a starting point for many years of study on this and related subjects. Today, our understanding of breakdown mechanisms exceeds many other aspects of semiconductor component operation and, furthermore, it is used extensively in their evaluation. Figure 9 illustrates the breakdown characteristics of two fundamentally different p - n junction diodes. The general properties of these

SEMICONDUCTOIt DEVICE EVALUATION

185

devices are quite similar as they both exhibit a low reverse current when the applied potential is below their respective breakdown voltage; above this potential they exhibit a low dynamic resistance and a rapidly increasing reverse current. Although Fig. 9 is exaggerated for illustrative purposes, the breakdown of a high voltage junction should be exceedingly sharp-a small increase in bias voltage results in a large increase in reverse diode current. Low voltage p-n junctions, on the other hand, should exhibit a “soft” breakdown characteristic implying the presence of a

CURRENl

FIG.9. Illustrative breakdown characteristics of a high-voltage and a low-voltage p-n junction diode.

different breakdown mechanism. Additional differences between two such units can be observed in the temperature coefficient of their critical breakdown voltage. High-voltage p-n junctions exhibit a positive temperature coefficient-breakdown voltage increases with an increase of temperaturewhich is in contrast t o the negative coefficient of a low voltage unit. Furthermore, junctioiis with an intermediate breakdown voltagebetween the well defined high-voltage and low-voltage units-can exhibit a very low, and sometimes zero, temperature coefficient; this is assumed to result from a combination of two different mechanisms with opposite temperature coefficients,

186

DAVID P. KENNEDY

I n 1953 McKay and McAfee (12) demonstrated that p-n junction breakdown is not confined to the previously proposed mechanism of internal field emission. Using newly developed experimental methods they measured a large carrier multiplication in p-n junctions when biased near their critical breakdown potential. Furthermore, they also proposed that this carrier multiplication is essentially the same as a Townsend ionization process (IS) that was previously used in the theory of gaseous conduction. I n brief, electrons will gain energy upon entering the spacecharge layer of a reverse biased junction and will lose energy by lattice collisions. Carrier multiplication occurs when these lattice collisions result in a generation of hole-electron pairs-this implies that the electron energy must be sufficient for pair production. Here we have a fundamental difference between the two units illustrated in Fig. 9. High voltage junctions can withstand a sufficient biasing potential to achieve pair production without a large electric field within its space charge layer; carrier multiplication is thus the predominant breakdown mechanism. Low voltage junctions, on the other hand, exhibit a very large space charge electric field a t low magnitudes of reverse bias; this type of device will therefore exhibit a Zener type breakdown before electrons can attain sufficient energy for pair production. If only a simple electron multiplication process is considered in the breakdown of p-n junctions, we cannot account for many of its experimentally observed properties. The rapid increase of junction breakdown current, for example, is more characteristic of a regenerative type mechanism within the semiconductor material; a comparable situation occurs in gaseous conduction. Townsend (see 13’) proposed a similar regenerative mechanism in gaseous conduction by assuming positive ions introduce an additional ionization mechanism when traveling from anode t o cathode-this process is frequently called a “Townsend avalanche.” Although this proposed role for the positive ion is now known to be incorrect, its concept is immediately applicable to the electrical breakdown of a reverse-biased junction. Under the influence of a space-charge-layer electric field, electrons gain sufficient energy to produce a hole-electron pair when in collision with the lattice; these holes move back through the space charge layer, undergo pair-producing lattice collisions and thereby generate more electrons. Assuming a process of this type, it is possible for a single electron to enter the space-charge layer of a junction and, through lattice collisions, generate an infinite number of additional charge carriers. Through an application of Townsend’s avalanche mechanism McKay ( I 4 ) developed a particularly simple expression characterizing the breakdown of a p-n junction. If ai and pi represent the number of ionizing col-

187

SEMICONDUCTOR DEVICE EVALUATION

lisions per cm by a n electron and a hole, respectively, carrier multiplication is readily characterized for a junction of plane-parallel geometry, Fig. 10. Assuming no electrons are initially injected into a space-charge layer of width w; if n1 ionizing collisions occur in the space 0 < x < x1 and n2 in the space ( 2 1 dx) < x < w,the number of electrons leaving a t z = w is 72 = no n1 nz (16)

+

+ + Ikt he r m or e , in the space x1 < z < (xl + dx) we have nl + no electrons entering a t x1 and n2 holes entering a t + d s ) ; therefore the number of electrons generated in x1 < x < (xl+ dx), by collision, is given by (21

Assuming the ionization rates for holes and electrons are equal,

r-- - -

0

JUNCTION-----

xx+dx

LYI =

Pi,

7

W

Frc. 10. The geometry assumed for the calciilrttion of avalanche multiplication (from McICay, 14).

Eq. (17) is readily integrated with the boundary conditions a t x = 0 and n = no n1 a t x = w,

+

1- 1 =

n1

=

0

[a,dx

where M = n/no-which is the carrier multiplication factor. When this integral becomes unity an unstable regenerative multiplication can be assumed within the space charge layer since M = 00 ; this situation is assumed t o represent an avalanche breakdown. The above analysis suggests many fundamental questions pertaining to current multiplication and avalanche breakdown in a p-n junction. As a mathematical simplification, equal ionization rates have been assumed for holes and electrons; the validity of this assumption remains unconfirmed. Furthermore, it is also necessary to establish the energy threshold for pair production-for both holes and electrons-since this parameter determines the minimum junction voltage at which avalanche breakdown can take place.

188

DAVID P . KENNEDY

Figure 11 illustrates the experimental circuit used to determine the multiplication properties of a p-n junction ( 1 5 ) .I n very shallow deviceswith a junction depth of 2 to 3 p from the surfaceminority carriers can be generated by a “chopped” light source. Pulses of junction photocurrent are amplified, then rectified, and the resulting dc component used to drive one coordinate axis of an X-Y recorder. The other coordinate axis of

X-Y RECORDER

FIG.11. Circuit used for obtaining the multiplication characteristics of p-n junctions (from Chynoweth and McKay, 1 5 ) .

this recorder is driven by the external biasing potential applied to the junction. Using this method, a continuous increase of junction bias voltage also traces out the resulting photocurrent and hence the threshold of carrier multiplication can be readily observed. Using this experimental arrangement Chynoweth and McKay [ I 51 first established the threshold energy for hole-electron pair production by an electron in a silicon junction. Upon illumination, minority carriers (electrons) are generated within the p-type material of a p-n junction, which exhibits a total potential due to its internal-built-in-potential, Vi, and also an externally applied bias, V,. Electrons, upon entering the

189

SEMICONDUCTOR DEVICE EVALUATION

space-charge layer, gain energy from the electric field and lose energy by lattice collisions; if before leaving the space charge-layer they attain , pair production, current multiplication is readily sufficient energy, V Ofor observed. I n this experiment the onset of multiplication is assumed to occur when the electron has attained this threshold energy, VO, just before it leaves the space-charge layer of width w.Assuming VOois the applied bias voltage a t the first observation of carrier multiplication, we have (Vd J’J = 1’0 VLO (19)

+

+

where V L O is the energy lost by a n electron when acquiring the eiiergy VO. If VLOis assumed to be zero when w is zero, a plot of (V,O V,) vs. 20 for many junctions will yield V Owhen extrapolated to w = 0; the deplction-layer width w a t an applied junction voltage can be established from capacity measurements. Using this experimental technique, the threshold energy for pair production, V O by , an clcctron in a silicon junction was found to be 2.25 It 0.10 ev. It thereforc appears that avalanche mechanisms cannot take place in junctions exhibiting a breakdown voltage below 2.25 volts, and will generally require a greater voltage to overcome energy losses by lattice collisions, VLO. Later, in 1958, the ionization rate was determined for holes and electrons in a silicon p-n junction (16). It was first established that the devices used in these experiments were of the linear-graded type; this was accomplished by determining the dependence of junction capacity upon applied voltage. Having verified this junction property the following relations were assumed to hold between the depletion-layer electric field, E , the junction potential, V , the depletion-layer width, w,

+

(20)

where 8,is the maximum electric field and w1is a width constant. Using Eq. (20) to change variables in Eq. (18) one obtains

,

u 1n

,

From Eq. (21) Chynoweth (16) obtained a n approximation for the ionization rate of both electrons, ai,and holes, Pi, in a silicon p-n junction. Using photocurrent measuring equipment of the type illustrated in Fig. 11, measurements were made of the carrier multiplication, M , upon

190

DAVID P. KENNEDY

actual devices. I n addition, from these measured values of M , an empirical polynominal was developed to describe this characteristic and therebyrprovide a means of integrating Eq. (21). Devices used in this experiment were selected to exhibit either a long electron lifetime or a long hole-lifetime ; this assured that the multiplication process was initiated by a single type of charge carrier. Figure 12 illustrates the results 5.5

5.0

B

4.5

1

d J

4.0

a 5 z

9 t-

2-

3.5

z P

P

:: 3.0 2 5

2.0 RECIPROCAL OF ELECTRIC FIELD IN CM VOLT"

xto-6

FIG.12. The field dependence of the ionization rates for holes and electrons in silicon (from Chynoweth, 16).

of this experiment. A significant difference is observed between the ionization rate of holes and electrons-curves A and B, Fig. 12-although an identical ionization rate was a fundamental assumption in the derivation of Eq. (21). Using a more rigorous formulation of Eq. (21)-assuming the hole and electron ionization rates are not necessarily identicallittle change is observed in curve A of Fig. 12-the ionization rate for holes. For electrons, on the other hand, the ionization rate more nearly approached a straight line; this change occurring a t large magnitudes of electric field-curve B, Fig. 12. From these experiments the ionization

SEMICONDUCTOR DEVICE EVALUATION

191

rate of electrons, for example, is readily described by the relation ai =

a exp (- b /E)

(22)

which is also found in gaseous conduction. From Eq. (18) and Eq. (22) we obtain a particularly simple analytical criterion for avalanche breakdown in a p - n junction, 1= a

lo8exp ( - b / ~ ( x ) ) d x

(23)

where the integration is conducted across the entire space charge layer. Although this expression does not take into account differences in the ionization rate of holes and electrons, Maserjian (17) assumed they were present in approximately equal numbers a t breakdown and therefore experimentally established average values for the constants in Eq. (23) : a b

Ge 1.2 X lo7 1.4 X lo6

Si 9 x 105 1.8 X los

Using these parameters, breakdown voltages were calculated for lineargraded and abrupt type structures. Further, Kennedy and O’Brien (18) similarly established the avalanche breakdown conditions for diffused p - n junctions; this device frequently exhibits a breakdown voltage which is between the abrupt and linear-graded type of structure. From the foregoing discussion it is clear that avalanche breakdown is a well defined property of p - n junctions, The critical breakdown voltage can be readily calculated for both an abrupt impurity profile (17) and a diffused device (18) with accuracy adequate for most practical situations. Devices not in satisfactory agreement with these calculations often have physical parameters that differ Substantially from their presumed magnitudes, or else the breakdown occurs from undesired mechanisms such as surface contamination. Evaluating the reverse breakdown properties of a high voltage p - n junction is therefore both a quantitative and a qualitative process. The critical breakdown voltage should agree substantially with its calculated value otherwise we should immediately suspect trouble, Furthermore, avalanche breakdown should provide an exceedingly “sharp” characteristic and not a well defined “soft” region where the reverse current is a comparatively slow function of reverse biasing voltage. In contrast with the breakdown mechanisms of high voltage p - n junctions, an insignificant amount of carrier multiplication is observed in low voltage devices. Unless reverse breakdown occurs substantially above the forementioned threshold for pair production-approximately

192

DAVID P. K E N N E D Y

2.25 volts for silicon (15) and 1.5volts for germanium (19)-an avalanche process cannot take place. In silicon p-n junctions, for example, this transition takes place in the vicinity of 3 to G volts. Silicon junctions that undergo reverse breakdown below approximately 3 volts will exhibit a very small amount of carrier multiplication; reverse breakdown is thus presumed to be caused by field emission. The large electric field within low voltage p-n junctions results in the generation of hole-electron pairs-these mobile charge carriers are swept clear of the space-charge layer without undergoing multiplication. It is for this reason that we can easily observe fundamental differences in the reverse breakdown characteristics of high voltage and low voltage devices, Fig. 9. Unfortunately, a substantial difference exists between our knowledge of avalanche multiplication and of field emission. Since the experiments of McKay and McAfee (IZ), in 1953, establishing the mechanism of carrier multiplication, this subject has been under constant investigation. Zener breakdown-which is no less important-has been seriously neglected; most experiments have been directed toward the problem of separating avalanche and field emission currents with no further investigations into the latter. This situation now appears to be changing. Figure 13 diagrammatically illustrates the breakdown process due t o internal field emission. I n the absence of a reverse biasing potential, Fig. 13(a), the bottom of the conduction band and the top of the valence band can be made t o appear a t approximately the same energy level; this is accomplished by introducing a large impurity concentration into the n-type and p-type material. If the junction space charge layer is sufficiently narrow, carrier transitions will take place between the valence and conduction band-requirements of equilibrium will assure this net junction current is zero in the absence of a reverse bias. Upon the application of a reverse biasing potential, Fig. 13(b), a greater number of empty conduction band energy states reside opposite the valence band electrons than empty valence band states opposite conduction electrons; a net electron current flows from the valence band to the conduction band. Chynoweth and McKay (20) studied the breakdown properties of p-n junctions constructed from high conductivity p-type silicon ( = 0.007 ohm cm). These were diffused devices with junctions residing a t 2 to 3 1.1 from the surface which exhibited a scatter of breakdown voltages centered around 3 t o 5 volts. Carrier multiplication was measured on these devices using the same methods illustrated in Fig. 11; they exhibited characteristics consistent with the previous high voltage junction investigation. Little or no carrier multiplication could be observed a t bias voltages below 1.0 volt yet a significant breakdown current was present. Furthermore, some of these devices exhibited exceedingly soft reverse

SEMICONDUCTOR D E V I C E EVALUATION

193

characteristics and a reverse current which appeared to increase from zero junction voltage. Junctions of the p-n type used in these experiments could not be classed as exhibiting a predominant breakdown mechanism due to either field emission or avalanche-actually they exhibited both types of breakdown mechanisms. ilt low reverse bias potentials-where 211 << 1-the

CONDUCTION BAND

VALENCE BAND

(a) EOUlLlBRlUM

CONDUCTION BAND VALENCE BAND

( b ) REVERSE BIAS

FIG.13. Illustrative energy band diagram for a low-voltage p-n junction.

devices clearly exhibit a field emission mechanism; as the bias is involt-ampere characteristics creased-to approximately 3.5 volts-the change and avalanche mechanisms are encountered. It has been suggested that the field emitted carriers attain sufficient energy to exceed the threshold of pair production thus causing an avalanche process. Through this combination of breakdown mechanisms the junction exhibits a soft breakdown characteristic a t low voltages but-as the regenerative mechanisms of avalanche breakdown occur-the breakdown becomes sharp. Recently, studies were made on the breakdown characteristics of p-n

194

DAVID P. KENNEDY

junctions with breakdown voltages between 0.1 and 8.0 volts. I n these low voltage junctions internal field emission was the predominant cause of breakdown because insufficient difference of potential was present for carriers to attain the threshold energy for pair production. Figure 14 illustrates the forward and reverse characteristics of these devices. A relatively sharp breakdown is observed in the two higher voltage units which probably results from avalanching; the lower voltage units,

10

8

6

4

2

1.4

1.2

1.0 0.8 0.6 0.4 BIAS IN VOLTS

0.2

0

0.2 0.4

0.6 0.8

FIQ. 14. Room temperature current-voltage characteristics for typical examples of Ge and Si diodes made from materials of different resistivities (from Chynoweth et al.,

21).

on the other hand, clearly demonstrate a soft, field emission, type of breakdown. I n early investigations into the avalanche process a mechanism of instability-noise-was also observed to take place in p-n junction diodes (14). When viewed upon an oscilloscope, this noise has a unique appearance, Fig. 15, with a magnitude proportional to the breakdown current. At low current these noise pulses are relatively short in length, occur in a random fashion, and the interval between each pulse is comparatively long. Increasing the breakdown current substantially alters their appearance as pulses of breakdown current become longer until the device appears to be in its high current mode of operation most of the time. A

195

SEMICONDUCTOR DEVICE EVALUATION

further increase of breakdown current first decreases the magnitude of these short low current pulses and then a new series is established. Going through several minima and maxima of this type, with a n increasing breakdown current, these noise pulses finally disappear when a junction is biased well into its breakdown region. The mechanism causing noise generation in a n avalanche breakdown process remains unknown. Although experiments pertaining to the emission of visible light from a junction a t breakdown ( 2 2 ) have provided information from which a noise generation mechanism is postulated, insufficient attention has been given to the subject. Observations of light

5 W

K

n

3

0

I 0

I

0.5

I

I

1.0 1.5 TIME IN MICROSECONDS

I

2.0

FIG.15. “Noise” pulses of junction current a t onset of breakdown in silicon (from McKay, 14).

emission indicate that breakdown occurs a t very small spots on the junction face; this has led to a conclusion that associated electric fields constrict avalanche breakdown t o a very small junction area. This constriction, if present, is assumed to introduce a large series resistance thereby producing instability until a sufficient external biasing potential is applied t o the device. The discovery of a light emission a t avalanche breakdown has led to other conclusions which are important to the future evaluation of p-n junctions. This light-which appears as small visible spots throughout the depletion layer-exhibits a distribution which is similar t o lattice dislocations through the junction and thus suggests th a t breakdown occurs a t these sites (23). This postulate was confirmed in 1960 when Batdorf et al. (24) studied the avalanche breakdown process within experimental junctions that were essentially free of dislocations. When biased to breakdown, light was emitted from the entire depletion layer of these devices rather than from small spots and, furthermore, the device was essentially free of noise. Although these experimental units were not entirely free from lattice imperfections, the results are adequately convincing to establish the location of avalanching within the space charge layer. These experiments upon diglocation-free diodes indicate that previ-

196

DAVID P. KENNEDY

ous investigations into the avalanche breakdown process were probably conducted upon junctions containing lattice dislocations within their space charge layer. Many fundamental avalanche parameters-carrier ionization rate, ionization threshold, etc.-were therefore measured up0 n these idealized devices ($5) to determine whether previous conclusions had been influenced by the presence of such dislocations. From these measurements, one difference was observed-carrier multiplication is enhanced in the vicinity of lattice dislocations; this implies that the arbitrary constants a and b of Eq. (23) are probably applicable, only when dislocations are present, If in the future, dislocation-free junctions are of frequent usage, a new set of constants will probably be required for avalanche breakdown calculations. Measurements of reverse breakdown upon a p-n junction provide both quantitative and qualitative information relating to its mechanisms of operation. In most situations the avalanche breakdown voltage can be calculated to within ten percent of its experimentally determined value; this provides a means of verifying many of the physical parameters characterizing a particular device. If, for example, the breakdown voltage of a diode is not in substantial agreement with its calculated value, basic differences are implied between its assumed physical parameters and their actual value. For an alloy type of structure this situation could indicate an incorrect impurity atom density within the base semiconductor material. Similarly, for a diffused p-n junction any lack of agreement between its experimental and calculated avalanche breakdown voltage would imply the possibility of erroneous conclusions pertaining to the physical parameters associated with either its diffusion process or its base semiconductor material. In addition to a direct comparison between the theoretical and experimental breakdown voltage of a p-n junction, a substantial amount of information is obtained from a qualitative observation of its breakdown characteristics upon an oscilloscope. If a relatively “soft” breakdown characteristic is observed when avalanche mechanisms should predominate, one can be relatively certain that surface contamination is present and, furthermore, that the device will be unsatisfactory from a reliability point of view.

E. Forward Characteristics I n the evaluation of semiconductor diodes, significant differences can be observed between the forward volt-ampere characteristics of devices constructed from silicon and germanium. Silicon diodes, for example, require a larger magnitude of biasing voltage-to attain a specified forward current-than equivalent germanium devices. I n addition, both silicon and germanium diodes exhibit a substantially smaller forward

SEMICONDUCTOR DEVICE EVALUATION

197

current-for a given bias voltage-than predicted by elementary theory ( I ). Although qualitative explanations have been given for these experimentally observed properties, there is little quantitative information on the subject; this results from inherent difficulties of the problem from both an experimental and a theoretical point of view. Elementary p-n junction theory makes use of marly simplifying assumptions which do not accurately represent a n actual device in its normal mode of operation. A more rigorous investigation of the subject, on the other hand, leads to mathematical difficulties which can only be overcome by introducing suitable approximations-this approach, nevertheless, provides a n extensive amount of qualitative information. Similarly, the problem is equally difficult from a n experimental point of view. Only a limited number of laboratory techniques are presently available which can provide the required information pertaining to p-n junction operationthese are usually destructive type measurements which are not particularly suited to component evaluation. Such comments are not intended to imply that this aspect of semiconductor evaluation has been neglected. The practical advantages of a n optimized p-n junction diode are sufficiently obvious to stimulate most component designers toward this goal although of necessity, their methods have been mostly empirical. Figure 16 illustrates the forward volt-ampere characteristics of a typical p-n junction diode. Ideally, elementary theory predicts that Eq. (1) should adequately approximate this curve. Experience, on the other hand, shows that relatively poor agreement is obtained between theory and experiment; this can be observed in both the magnitude and slope of Fig. 16. Actually, the magnitude of diode current is a very difficult parameter to correlate with theory since it depends upon many fundamental semiconductor parameters which cannot be accurately measured. Minority carrier lifetime, for example, is one of these parameters. I n contrast, the slope of this volt-ampere is easily correlated with Eq. (1) since the logarithm of diode current should exhibit a straight line relation to applied voltage-this, of coucse, assumes the device is baised well above 0.025 volts. Furthermore, this slope should be independent of these undetermined semiconductor parameters previously mentioned. At low magnitudes of junction current this slope is usually q/kt-which is in substantial agreement with Eq. (1)-while a t large currents it frequently changes t o q / 2 k t ; this situation is illustrated in Fig. 16. Furthermore, in practical junction diodes we must also contend with series resistance which alters the high current characteristics of a device. Evaluating the forward conduction characteristics of a semiconductor diode, therefore, becomes a problem of establishing inherent component parameters which limit the total junction current, I n addition, we are often confronted with

198

DAVID P. KENNEDY

two diodes-presumed to be identical-which exhibit a substantially different forward current at the same applied voltage; from the foregoing type of measurement we must establish the source of difficulty. Several mechanisms contribute to the forward volt-ampere characteristics of a p-n junction diode. Biasing a junction in the forward direction

10-2 cn -.

W

a

W

n

r

=I I-

10-3

z W

a a

3

V 0

a

10-4

U

s

B

I 0-5

0-

0.2 0.4 0.6 0.8

1.0 1.2 1.4 FORWARD VOLTAGE

1.6

1.8

2.0

FIG.16. Junction rectifier characteristic showing the effects of leakage conductance, series resistance, and self-heating (from Saby, 27).

lowers its “built-in” potential barrier and thereby provides an excess number of minority carriers at each junction face. Further, by drift and thermal diffusion these excess carriers move away from the junction and undergo recombination within the bulk semiconductor material; this motion constitutes an electric current. By assuming a n insignificant number of excess charge carriers are associated with these nonequilibrium mechanisms, elementary theory has substantially over-simplified the problem and thus neglected a large number of important properties associ-

SEMICONDUCTOR DEVICE EVALUATION

199

ated with diode operation. These neglected properties] in fact, can be used t o explain many fundamental differences between the theoretical and experimental volt-ampere characteristics of actual semiconductor devices. When excess minority carriers are injected into a semiconductor, charge neutrality is approximated by the introduction of additional majority carriers; these excess carriers modify the junction injection characteristics and also the mechanisms of minority carrier transport throughout the structure. At low diode current these excess carriers represent only a small perturbation upon the equilibrium concentration and therefore can be ignored without introducing a serious analytical error. At large magnitudes of diode current, on the other hand, this excess concentration of charge carriers is not necessarily negligible and will frequently introduce fundamental changes in the static volt-ampere characteristics. The inherent mathematical difficulties associated with a rigorous solution of the minority carrier transport problem have been recognized for many years. This solution must consider both the influence of drift and diffusion mechanisms upon the motion of holes and electrons. Furthermore, consideration must also be given to the charge distribution which may result from spacial deviations from charge neutrality. This physical system-in one dimension-is frequently approximated by the following differential equations:

J , = -u,(n~

+ -kQT dx

To solve this problem of minority carrier transport in a semiconductor it is necessary t o simultaneously solve these six differential equations-subject to the boundary conditions imposed by a practical device. This problem has been studied extensively and, by introducing simplifying assumptions into Eqs. (24), many fundamental properties of minority carrier transport can be established (26).

200

DAVID P. KENNEDY

Saby (27) conducted investigations into the forward volt-ampere characteristics of p-n junctions in which he classified the assorted mechanisms causing deviations from elementary theory, Fig. 16. At low magnitudes of forward current, Fig. 17(a), deviations from a n ideal device are assumed to be caused by leakage current; this is not inconsistent with qv/kT

qjiilqv/2k MODULATED REGION exp (qv/EkT) TRANSITIONAL INFLEC- [VESTIGIAL UNMODULATED REGION exp (qv/kT)

EXCESS (LEAKAGE) CONDUCTION

I (a)

SELF HEATING REGION

(IR DROP)

CONSTANT

SERIES R CONSTANT

OHMIC REGION

FORWARD VOLTAGE (LINEAR SCALE 1

FIG.17. Nonideal junction rectifier characteristics (from Saby, 27).

the assumption of a surface inversion layer-or “channel”-which was previously suggested to result in a n excess reverse current. Throughout the useful operational range of a diode, Fig. 17(b) the forward voltlow currentampere characteristics first exhibit a slope of q/kt-at and a slope of q/2lct a t higher currents. A further increase of diode current, Fig. 17(c) introduces a region where the predominant limitation upon the device results from its series resistance (ohmic). Beyond these frequently

SEMICONDUCTOR DEVICE EVALUATION

20 1

encountered characteristics of the junction diode a sufficient amount of heating is obtained to cause thermal runaway, Fig. 17(d)-this situation is dependent upon the environmental conditions under which such measurements are made. Saby (27) applied a simplification of Eqs. ( 2 4 ) to the forward biased p-n junction-he assumed local charge neutrality must be maintained throughout the semiconductor material. From this assumption a n electric field-and hence a difference of potential-is readily shown to exist in the region adjacent the junction space charge layer. Upon calculating the magnitude of this voltage and subtracting it from the available junction potential, the resulting volt-ampere characteristics are in reasonable agreement with experiment. This proposed mechanism-which is frequently called conductivity modulation-can be readily understood by the following example : Assume a forward biased p-n junction in which the forward current is a consequence of only one type charge carrier-holes in the n-type semiconductor material. Large magnitudes of forward bias upon this type structure results in a substantial concentration gradient of holes within the n-type material and-because charge neutrality must be maintained everywhere-we must also have a similar distribution of electrons. Since the total electric current due to the diffusion and drift of electrons is given by (25)

the presence of a substantial electric field is readily seen when J, = 0. Further, upon integrating this electric field across the entire n-type semiconductor material, k = JE(z)dz (26) we obtain the potential drop resulting from conductivity modulation. Upon combining this potential with the elementary expression of a p-n junction, Eq. (l),Saby ( 2 7 ) analytically established a mechanism which yields the previously described volt-ampere slope of q/2kt. Assuming a potential drop within neutral semiconductor materialdue t o conductivity modulation-introduces a n important addition to elementary junction theory-direct proof of this mechanism is indeed difficult. I n 1958 Harrick (28) provided this proof by using infrared absorption techniques (29) to measure the concentration of excess carriers throughout the body of a semiconductor diode. Theoretical verification of these experiments was obtained through a modified form of Boltzmann type relations characterizing the injection of minority carriers by a p-n junction. Further, by using an expression for high level minority carrier

202

DAVID P. KENNEDY

transport in a semiconductor (30)-which is often called ambipolar diffusion-theoretical confirmation was obtained for the observed relation between minority carrier concentration and total diode current. Although additional work on this problem is necessary, measurements by infrared absorption provide a direct verification of conductivity modulation in a forward biased p-n junction diode. I n addition, it was also suggested that fundamental modifications should be observed in the minority carrier injection characteristics of a p-n junction due t o conductivity modulation (28). At low injection levels Boltzmann type relations can be used to establish the relative magnitude of holes and electrons on each side of a junction,

Further, we can also assume the total hole and electron concentrations (np;n,; p n ; p p ) each consist of a n equilibrium component (no;P O )and also a non-equilibrium component (an; 6p) due to the applied bias potential v. Introducing these quantities into Eq. (27) we obtain

If in Eqs. (28) charge neutrality is assumed at each junction face (6np= 6pp; 6n, = 6p,J one of the 6 terms can be eliminated yielding the relation

Similarly, an equivalent expression can be established for 6n,. If we now compare Eq. (29) with elementary junction theory, substantial agreement is obtained at low magnitudes of biasing voltage; this implies that a small number of excess carriers are present. At large applied junction voltages, on the other hand, Eq. (29) indicates that significant changes should be observed in the injection properties of the p-n junction. I n addition to the introduction of a modified Boltzmann type relation for the p-n junction Harrick (28) also used a charge free approximation for the ambipolar diffusion equations (SO) to relate the total diode cur-

203

SEMICONDUCTOR DEVICE EVALUATION

rent to the density of excess minority carriers appearing a t each junction face,

The parameters u, and u represent the electron conductivity (un = npp,) and total conductivity (u = nqcl, -I- p q p p ) at the junction face. The remaining parameters-diffusivities and diffusion lengths-are ambipolar quantities which are related to the drift field associated with this diffusion 0

-20

-40

-60

-80 -100

-50 0 50 CURRENT DENSITY (rno/cm2)

I00

FIG.18. J - 8 p and J-V characteristics for highly doped p-n junction. The dashed curve is experimental while the solid curve is calculated (from Harrick, 28).

process. Upon combining Eq. (29) with Eq. (30), a more general voltampere relation can be obtained for the semi-infinite p - n junction diode; this general relation provides an extension to the low level junction properties characterized by Eq. (1). Using infrared absorption, a quantitative comparison has been made between the diode current and the magnitude of excess carriers, 6p, a t the junction face. This comparison indicates that the calculated value of 6p is in agreement with the measured value to within a factor of two; considering the associated experimental problems, this is excellent agreement. It should be noted a t this point that to attain agreement between theory and experiment it was necessary to consider the change in conductivity and lifetime for both sides of the p - n junction since both hole and electrons contributed to the total diode current. Figure 18 illustrates

204

DAVID P . KENNEDY

a comparison between theory and experiment for a typical diode used in this investigation. From the foregoing discussion it is readily seen that inadequate information is presently available to properly evaluate the forward voltampere characteristics of a p-n junction diode. Qualitatively, we can identify when a diode is operating in its low level mode of operation and also when high level mechanisms-conductivity modulation, for example-become a dominant factor. Furthermore, we can also determine when the series resistance (ohmic) within a device is seriously limiting its maximum forward current; this is frequently a difficult measurement since heating can occur thereby masking other mechanisms. Beyond this type of evaluation procedure, many fundamental questions arise pertaining to both the physics and the characterizing parameters of a particular device. From an analytical point of view, we have not, as yet, developed a satisfactory model to describe a forward biased semiconductor diode. Clearly, ambipolar diffusion mechanisms must be considered in any new analytical model along with appropriate modifications for the high level injection properties of the p-n junction. If, on the other hand, we had a satisfactory method to calculate the volt-ampere characteristics it is doubtful that it could be used in the quantitative investigation of actual devices; instead, its principal value would be to provide a more detailed qualitative understanding of diode operation. Fundamental semiconductor parameters-mobilities, minority carrier lifetimes, etc.-are usually required in calculations of this type and they are not readily established for a finished semiconductor device.

F. Transient Characteristics In 1950 Michaels and Meacham (31) reported the observation of a large transient current spike in point contact diodes when they are rapidly switched from their high current to their low current mode of operation. The implications of this observation were readily seen by many workersa semiconductor diode could not be considered an indefinitely fast switching device. In high speed switching applications, for example, when a diode is rapidly switched from its forward to its reverse bias condition, a substantial reverse current is observed before the device can attain its Iow current mode of operation. This diode characteristic places fundamental limitations upon their application in high speed computer circuits, hence transient recovery has become a popular measurement in the evaluation of semiconductor components. In addition to these application difficulties, investigations of the subject have been stimulated by its inherent usefulness as a laboratory measurement tool. In 1953 Pel1

SEMICONDUCTOR DEVICE EVALUATION

205

(32) suggested that transient measurements could be used to establish the minority carrier lifetime within a completed semiconductor device. Although the initially suggested methods for measuring carrier lifetime were not particularly convenient, other workers have introduced refinements which substantially simplify the procedure. I n their initial investigations Michaels and Meacham (51)postulated a mechanism explaining this reverse transient characteristic. It was suggested that a forward biased p-n junction would inject minority carriers into a semiconductor material and thereby establish a stored charge within the structure. Upon rapidly reversing this biasing potential, the junction-which was previously a source of minority carriers-becomes a sink and “gathers in’’ excess holes remaining in the semiconductorthey assumed n-type material. A reverse biased junction, therefore, will exhibit a large reverse transient current until all stored holes are eliminated either by their transition across the junction or by recombination processes. I n these initial experiments a substantially different recovery time was observed for each device-this probably resulted from differences in minority carrier lifetime or possibly from inadequate reproducibility in the injection properties of a point contact rectifier. Since some devices exhibited a very long transient recovery period while others were very short, it was believed that an understanding of the associated mechanisms could lead to the design of high speed switching diodes. The fundamciital mechanisms associated with reverse diode recovery are conceptually very simple, but from an analytical point of view many mathematical difficulties are encountered. To overcome such difficulties, analytical investigations of the subject have been accomplished by introducing approximations which place restrictions-both geometrical and electrical-upon the applicability of each analysis and also upon the experimental methods used in these transient measurements. Unfortunately, many persons engaged in component evaluation conduct such measurements without considering the implied restrictions and thus misinterpret the results. An example of this situation was recently brought to the author’s attention. Using transient recovery techniques, the minority carrier lifetime was being measured upon a n epitaxial type device containing a high conductivity layer in the immediate vicinity of the junction. Since mathematical investigations are usually conducted upon analytical models of semi-infinite geometry, the resulting theoretical (recovery time)-(lifetime) relations are of questionable applicability to the transient properties of epitaxial devices. Similar arguments can be presented for diffused p-n junction diodes containing a “built-in” drift field; this is also a modification upon the usual analysis. I n a n attempt to discourage such applications w0 shall discuss the theoretical aspects of

206

DAVID P. KENNEDY

transient recovery measurements thereby establishing many experimental restrictions implied by a lack of analytical generalization. One of the first analytical investigations into the reverse transient characteristics of p-n junctions was in conjunction with the measurement of minority carrier lifetime ( 3 2 ) . Assuming a square wave of voltage is applied t o a diode, Fig. 19, the resulting current is found to consist of three regions-two of these regions (A and B, Fig. 19) have magnitudes which are determined by series resistance within the circuit. The third region-region C-exhibits a decaying reverse current resulting from the loss of stored minority carriers by diffusion and recombination, It is from this third region that the minority carrier lifetime can be established. Ge DIODE

:R

FOR WARD

FIG. 19. Pulsed characteristic of Ge diode. The generator (G) supplies a square wave of voltage (V,) which produces the current, i, through the circuit shown (from Pell, 3.2).

To relate carrier lifetime within a semiconductor diode to its reverse transient characteristics the hole distribution is calculated throughout an entire transient period. This distribution is readily obtained by solving the time-dependent differential equation

Equation (31) implies a number of approximations in this analysis. The device, for example, is assumed to be operating a t a very low minority carrier injection level and, furthermore, the carrier lifetime, rP, is assumed constant. The required minority carrier distribution is obtained by solving Eq. (31), subject to the boundary conditions p(x)=O p(x) = p ,

x=o; O
(32)

SEMICONDUCTOR DEVICE EVALUATION

207

and also the initial condition p(x)

=

(PO- pll)e--z/Lp

+p,

(33)

Before considering the solution of Eq. (31), and its relation to the minority carrier lifetime, we shall first discuss implications resulting from the assumed boundary conditions, Eq. (32). These boundary equations require the junction to represent an ideal minority carrier sink throughout an entire transient period and, furthermore, that equilibrium is maintained only at infinity. Clearly, these equations imply a semiinfinite region of homogeneous semiconductor material with a minority carrier sink located at one end (x = 0). In this analysis, and in others, it is important to remember that the resulting theoretical (1ifetime)-(recovery time) relations are only applicable to a semi-infinite structure; from a practical point of view, this means that the region under consideration must be a t least several diffusion lengths long. I n addition to these implied restrictions, another is encountered when these boundary equations are considered in conjunction with the assumed initial condition of the problem, Eq. (33). Under forward bias-just prior to initiating the transient-Eq. (33) establishes a hole distribution for this structure assuming a constant density of excess carriers (PO- p , ) at one end (z = 0). At the instant a reverse biased is applied, Eq. (32) requires the hole concentration a t x = 0 to instantaneously change from PO to zero; this, of course, could only occur if the diode current became infinite. From Fig. 19, series resistance will obviously limit the total transient current-region B-and therefore we cannot experimentally satisfy this analytical requirement-usually, the series resistance is sufficiently small so that it will limit diode current for only a small part of the total recovery period. Recognizing the inherent limitations of this analysis, we can show the hole distribution is given by

Since only diffusion mechanisms are assumed, the reverse transient current of this diode is obtained from (jP (35) iP = - s 4 & when evaluated a t the junction face (x = 0). Equation (35) reduces to a particularly simple expression if only a small portion of the initial tran-

208

DAVID P. KENNEDY

sient period is considered-this portion should be much shorter than the lifetime of excess minority carriers,

Using Eq. (36) Pel1 (32) established the minority carrier lifetime within a semiconductor diode. Although inconvenient, it was suggested that a n oscilloscope templet could be made upon which the rate of transient current decay is calibrated in terms of the carrier lifetime. I n addition t o this analysis, and also in addition to this method of measuring carrier lifetime, investigations were also made into the influence of a n ohmic contact-of both infinite and zero recombination velocity-upon the transient recovery time. It was coiicluded that the ohmic contact would indeed modify the trsnsient characteristics of a diode if it was located less than a minority carrier diffusion length from the junction. An alternative method of measuring minority carrier life-time was suggested by Lederhandler and Giacoletto (33). This method differs substantially from previous discussions; it is a n open circuit measurement -zero diode current-rather than a closed circuit measurement where a large diode recovery current is permitted, Using a cathode ray oscilloscope, a post-injection junction potential-Fan (34)-can be observed across the diode for a short period after its forward bias has been removed. This voltage results from excess minority carriers remaining a t the junction face and has an amplitude given by v

k 7’

= - Ln

4

(E)

(37)

Equation (37) is based upon a n assumption th a t only one type of charge carrier (holes) is stored within the structure. Upon removing the forward biasing potential from a diode, Fig. 20, this post-injection voltage is found t o decay in a manner which can be related to the lifetime of minority carriers. The inherent simplicity of this open-circuit type of transient measurement can be seen by an approximate analysis of the associated mechanisms. Upon removing the forward biasing potential, diode current reduces to zero and a large concentration of minority carriers remain a t the junction face. Neglecting the mechanisms of diffusion and drift, these excess carriers are lost t o bulk recombination and the device returns to equilibrium in a manner prescribed by

SEMICONDUCTOR DEVICE EVALUATION

209

If we now combine Eq. (37) and Eq. (38) we obtain AT Y

v = - -(f/Tp)

(39)

which describes the post injection voltage when 6p >> p . ~ . From Eq. (39), a region should be observed in this transient measurement where the junction voltage decreases linearly with time; this occurs when the density of excess holes exceeds their equilibrium value. Upon

VOLTAGE AT a-a’

(APPLIED PULSE)

VOLTAGE AT b-b’ n l i

(OPEN ClRCUlTED JUNCTION WAVEFORM)

FIG.20. Circuit illustration for applying constant current pulse t o emitter-base junction and observing a n open-circuited junction voltage upon termination of pulse (from Lederhandler and Giacoletto, 38).

locating this region, a measurement of its slope should provide a n accurate determination of the minority carrier lifetime. The simplicity of this proposed method is deceiving since many experimental problems arise in the laboratory. We frequently find, for example, that the decay characteristics of a device are exccedirigly dependent upon its forward current prior to this open circuit measurement. When the current is too low we cannot satisfy the requirement dp << p,, and therefore a linear region will not be found. Similarly, this region of linear decay is also modified by a n excess forward current since conductivity modulation will be present. Further difficulties arise when this lincar region is not encounteredregardless of the forward current-or it may exist for so short a period of time that measuring its slope becomes impossible. Because of these experimental difficulties open circuit transient measurements are no longer used

210

DAVID P. KENNEDY

extensively for determining the minority carrier lifetime in a p-n junction diode. Figure 20 illustrates a typical oscilloscope pattern which is obtained during an open-circuit measurement of these transient recovery characteristics. Upon removing the forward bias, a rapid decrease occurs in diode voltage due to ohmic resistance within the structure; the remaining is the junction post-injection potential, Vj. At this time we shall consider the rapidly decreasing component. In previous discussions, series resistance was shown to introduce fundamental limitations upon the forward volt-ampere characteristics of a diode and therefore it is an important parameter when evaluating such devices. Using static type measurements to determine this series resistance often results in excessive heating and thereby modifies fundamental diode properties during the experiment. An open-circuit transient measurement, on the other hand, can be used for this measurement with a negligible amount of heating. Using a low “on-off” duty cycle, this abrupt voltage decrease, a t the termination of forward bias, is proportional in magnitude to both the series resistance of the device and its forward current. An important modification of the previously described closed-circuit diode recovery measurement was presented by Kingston (35) and also by Lax and Neustadter (36). Kingston (35) investigated the transient recovery characteristics when a large reverse biasing potential is applied to the diode through an external series resistance, R, Fig. 2l(a). Instead of requiring an infinite diode current a t the start of this transient, the reverse bias, V,., and the load resistance R, are adjusted to maintain a constant magnitude of reverse current. At the instant a device is switched from its high current to its low current mode of operation, two sources of potential exist within the circuit: the external bias, V,, and also the junction post-injection voltage Vj. I n this experiment, if V , >> Vj, an essentially constant reverse current will be observed since

Furthermore, this constant current condition can be maintained for a substantial period of time, Fig. 21(b), since the junction cannot become reverse biased until the post-injection voltage is zero. An analysis of this closed circuit transient is obtained by solving the previously considered minority carrier continuity equation, Eq. (31), with slight modifications in the associated boundary conditions. Instead of assuming a rapid loss of excess minority carriers a t the junction face is coincident with the start of this transient, a constant current is intro-

21 1

SEMICONDUCTOR DEVICE EVALUATION

duced with an amplitude of V J R . Furthermore, it is also assumed that this constant current is continued until the junction post-injection voltage becomes zero-excess carriers are removed from the junction face. I n this manner a particularly simple expression is obtained to relate the

PHASE

I

4:b+L PHASE Ill-

t

t'

(b) FIG.21. (a) Illustrative diode switching circuit. (b) Idealized transient recovery of a p-n junction diode (from Kennedy, 88).

minority carrier lifetime, rP, to the length of time, t', the diode can maintain a constant reverse transient current, ( 3 5 ) ,

This problem has also been investigated in a more rigorous fashion using time dependent boundary conditions in place of the above approximation method (36).An important result of this work is to show that the

212

DAVID P . KENNEDY

constant current approximation is, in fact, a reasonable mathematical simplification when used in the analysis of this diode recovery problem. The illustrative recovery waveform in Fig. 21(b) shows the inherent simplicity of this measurement. Rather than measuring a rate of decay, which is always inconvenient and difficult, this technique uses the length of time, t’, a particular device can maintain a constant current. From Eq. (41) another advantage is readily seen. Since recovery characteristics are inherently dependent upon both the forward and reverse diode current, the ratio I ? / ] , can be adjusted so that this constant current period greatly exceeds the carrier lifetime-thereby simplifying problems of instrumentation-or is substantially shorter than the carrier lifetime. I n many laboratories the current ratio I r / I f is conveniently adjusted so that this constant current period is equal to the minority carrier lifetime. As previously mentioned, measurements of minority carrier lifetime have been restricted to devices of semi-infinite geometry and also to situations where a low minority carrier injection level is maintained. From a practical point of view the latter restriction is not particularly serious. The influence of a high injection level upon the transient properties of diodes is easily detected-remaining below this level does not impose any particular difficulty. Minority carrier lifetime measurements can be made upon a single device throughout a wide range of forward current, I f ;this should introduce no change when the ratio I r / I f is maintained constant. If, on the other hand, a modification is observed in the transient recovery time, this forward diode current should be reduced until it is no longer a n influencing factor. I n addition t o these restrictions, theoretical (lifetime)(recovery time) relations have been established only for devices which are free of a n internal minority carrier drift field thereby eliminating the well-known diffused junction diode. The influence of this drift field has been qualitatively established but this information is inadequate for accurate laboratory measurements. Analytical investigations into the recovery mechanisms of a diode become exceedingly complicated if they are carried beyond these elementary forms which have been presented. I n most situations a n electronic computer is required to solve the associated mathematical equations and to interpret the results in terms of diode operation. Two examples of this are presently found in the literature-Iglitsynz et al. (37) and Kennedy (58).Iglitsynz et al. (37) calculated the influence of high level minority carrier injection upon the transient response of p-n junctions when measured in a circuit of the type illustrated in Fig. 21. A time dependent solution was obtained for the zero-charge ambipolar diffusion equations, permitting a determination of the minority carrier distribution throughout a n entire transient period. I n addition to the resulting minor-

SEMICONDUCTOR DEVICE EVALUATION

213

ity carrier drift field which is associated with high level mechanisms, they also introduced into their analysis the mechanism of minority carrier recombination through a single mid-gap trapping level. Although a limited amount of information was given by the authors, their conclusions are extremely important; they conclude that the high level minority carrier recombination rate can be established by reverse transient measurements upon a p-n junction diode. Presently, a computer is required to calculate the lifetime associated with a particular recovery time when measured a t these high levels of minority carrier injection. In 19G2 Kennedy (38)conducted a qualitative investigation into the influence of a minority carrier drift field upon the reverse transient recovery characteristics of a p-n junction diode. Assuming a drift field of constant magnitude, Fourier methods were used to establish the distribution of excess minority carriers throughout the entire transient period. E’urthermore, in this analysis au ohmic contact of arbitrary recombination velocity was assumed a t a finite distance from the p-n junction. An important conclusion of this investigation was the large variation in diode recovery characteristics that can result from the presence of a drift field, Fig. 22. An aiding field, for example-one directed to move minority carriers away from the junction-will substantially decrease the constantcurrent portion of this transient recovery while only a small decrease is observed in the asymptotic region. I n contrast we find a n opposing minority carrier drift field-one directed to move carriers toward the junctionsubstantially increases the constant-current portion of this transient but also decreases the asymptotic portion. Figure 23 illustrates the minority carrier distribution resulting from a “built-in” drift field within the semicoilductor material. From these illustrations we can obtain a physical picture of mechanisms associated with the theoretical recovery characteristics preseiited in Fig. 22. When the drift field within a structure is dirccted to enhance the motion of minority carriers away from a junction-aiding field-Fig. 22(a), a decrease is observed in the time required to clear them from the junction face. I n a transient recovery measurement we therefore would expect a n aiding field to substantially decrease tjhe constant current region, Fig. 22, and to somewhat decrease the decay time since a greater number of carriers are lost to bulk recombination mechanisms. I n contrast, a n opposing drift field-directed to force carriers toward the junction-introduces an opposite effect. Throughout the entire transient recovery period the field moves carriers from the bulk material to the junction face; it therefore requires a substantially longer time to remove carriers from this location. I n this situation we find an increase in the constant current region, Fig. 22, with a very abrupt termination; this rapid asymptotic

ln L

-J

-11P -

214

215

SEMICONDUCTOR DEVICE EVALUATION

I.oo

0.75

I

0.025-

Pix;t)

- 0.50 c

II

t'/rp ~ 0 . 1 2 5

Pe

0.25

I 00

0 75 P(x 1 ) 0.50 Pe 0 25

01

02

03

X/W

04

05

06

07

FIG.23. Minority-Carrier distribution during transient period of a typical diode (from Kennedy, 88).

decay of recovery current results from the few remaining excess carriers within the bulk semiconductor material. From the foregoing it is seen that transient recovery measurements of a p-n junction represent an important tool for component evaluation. The closed circuit type of measurement, in particular, provides a means of obtaining a reasonably accurate determination of minority carrier lifetime. For this measurement, caution should be used to assure other

216

DAVID P. KENNEDY

factors are not introduced which can result in a substantial error. The device, for example, should be of sufficient length-with respect to a minority carrier diffusion length-to be presumed infinite. Furthermore, recognition should also be given to the fact that Eq. (41) may not be applicable to the recovery characteristics of a diffused type structurefurther analysis is required to establish the correct mathematical formula.

111. THEJUNCTION TRANSISTOR A . General For transistors more than diodes, important differences should be noted between component characterization and component evaluation. Characterization and classification of a transistor according to its electrical properties is a natural result of the inherently poor reproducibility encountered in most manufacturing processes. Component evaluation, on the other hand, is principally directed toward the physical mechanisms contributing to these observed electrical characteristics; this type of information is important to the design, development and application of transistors. In many situations, measurements used for transistor characterization are identical to those used for transistor evaluation but, on the other hand, in many other situations, they are quite different. Characterization measurements are frequently on a “go or no-go” basis, where the current gain, for example, must reside within a given set of boundaries. In contrast to this situation, to properly evaluate the operation of a transistor it is first necessary to obtain extensive quantitative information pertaining to its physical and its electrical characteristics. From both a n experimental and a theoretical point of view, evaluating the electrical characteristics of a transistor can be an exceedingly difficult task. Inadequate information is presently available-in most situationsto accurately relate its electrical characteristics to its physical mechanisms of operation. Furthermore, direct experimental investigation of these mechanisms is usually very difficult-if not impossible. Experiments pertaining to the evaluation of transistor mechanisms are usually conducted in such an indirect fashion that their interpretation is often subject to question. It is not surprising, therefore, that transistor evaluation has, in itself, become a subject of intensive investigation. A number of very subtle measurement techniques have been developed which provide an extensive amount of information on the operation of a transistor. In addition, these measurements have also introduced many new questions which cause further confusion into an already difficult problem. There remains one encouraging fact; transistor evaluation is presently receiving more attention than it has in previous years. A large number of investiga-

SEMICONDUCTOR DEVICE EVALUATION

217

tions are being made into the factors influencing transistor reliability, high and low frequency mechanisms of operation, and also into their ever-important switching properties. In a very general manner transistor measurements can usually be cataloged into one of three catagories (39)-static, dynamic-small signal, and dynamic-switching. Static measurements are basically intended to establish the low-frequency volt-ampere characteristics although, in practice, their usefulness extends beyond this elementary requirement, In a dynamic-small signal type of measurement the transistor is held a t some particular operating point and its response is determined to a small sinusoidal voltage-or current. Small signal measurements are, in most situations, used to establish the operating characteristics of a transistor in a linear amplifier type of applications. The last catagory of transistor measurements-dynamic-switching-is directed toward large-signal, high-speed switching properties of this semiconductor device. Although when evaluating a transistor w0 should, in theory, be concerned with all aspects of its operating mechanisms, in practice this is seldom a true situation. Transistors intended for low-frequency audio amplifier applications, for example, are seldom evaluated in terms of their switching characteristics. Evaluation of semiconductor devices is usually restricted to their eventual application. Frequently, modes of operation are encountered in a switching circuit which are not found in a linear transistor amplifier and therefore high speed switching transistors offer evaluation problems which are not common to other types of devices. Using very primitive laboratory instruments, static volt-ampere characteristics can be established on a “point-by-point” basis. I n most practical situations this technique is very time consuming although it offers practical advantages-sufficient accuracy of measurement is readily obtained to provide quantitative information on a specific device (Carlson, 40). Using a small amount of additional instrumentation, static volt-ampere characteristics of a junction transistor can be plotted on an X-Y recorder thereby reducing the time consuming nature of a “point-by-point” method yet retaining its inherent accuracy. One word of caution is appropriate at this time. Frequently we encounter heating in a transistor during this type of measurement which can seriously influence its applicability. When a large number of devices must be measured, neither the “pointby-point” nor the X - Y recorder technique is appropriate. To satisfy this requirement, most laboratories use commercially available transistor measuring instruments which provide an increased speed but, a t the same time, do not maintain the same measurement accuracy. Instruments of this type apply a low frequency sweep voltage to the transistor and pre-

218

DAVID P. KENNEDY

sent its volt-ampere characteristics upon a cathode-ray-oscilloscope ; this frequency is sufficiently low to be presumed a static condition. In addition, situations arise when the volt-ampere characteristics of a transistor must be established at high operating power levels where heating becomes a serious problem. To overcome such difficulties, measurements can be made on a pulse basis (Cooper, 41) where the “on-off” duty cycle is adjusted to result in an adequately low power dissipation-consistent with other limitations of the system. The problems associated with small-signal measurements of junction transistors have been discussed extensively in the literature (4%’). I n principle, these measurements are the same whether for a low performance alloy transistor or for a modern diffused type of structure; instrumentation requirements for these measurements, on the other hand, are often substantially different. When evaluating a junction transistor its small signal parameters are often required at both low (zero) frequency and a t a frequency which approximates cutoff for the device. This requirement introduces many instrumentation difficulties because substantially different laboratory equipment is needed to perform such measurements at, for example, 1 kc and a t 1 kMc. For this reason the problem of instrumentation for small signal transistor measurements is usually an important part of any component evaluation program. Throughout the past few years the large-signal transient response of junction transistors has been a subject of intensive investigation. The fundamental purpose of this effort is to establish physical properties of a transistor that influence its “turn-on” and “turn-off” switching characteristics. In this investigation, recognition is given to the stored charge within the base and other regions of a transistor, and, furthermore, a change from one mode of operation to another is assumed to occur only when appropriate modifications are introduced into this stored charge. This technique of investigation, although providing only a gross picture of transistor mechanisms, has successfully established many fundamental properties of a device which influence its switching characteristics.

B. Stability Since their inception, junction transistors have suffered from inadequate electrical stability. Both storage and operational life tests indicate the electrical properties of a transistor often exhibit a long term degradation which, like the semiconductor diode, is attributable to surface contamination. This problem, in fact, is encountered more often in transistors than in diodes since the former is substantially more susceptible to surface contamination. Furthermore, from a component evaluation

SEMICONDUCTOR DEVICE EVALUATION

219

point of view, it is often very difficult to detect the presence of surface contamination in a junction transistor; only a small amount is required to seriously alter many of its small-signal parameters-current gain, for example. This difficulty is partiaularly enhanced by the fact that a transistor is not an exceedingly reproducible device. A number of components, which can be assumed identical, often exhibit wide variations in their electrical characteristics; this is sometimes attributable to manufacturing process control (43) but a t other times it is caused by surface contamination which is inadvertently introduced during constructioninadequate cleaning, etc. Conventional methods of quality, or process, control cannot separate the two causes of poor reproducibility-process variation and surface contamination. I n most situations an extensive amount of life testing must be used in order to detect the presence of contamination mechanisms which usually lead to instability. The degradation mechanisms previously outlined for a semiconductor diode are, in most situations, encountered in junction transistors. The collector junction, for example, is subject to the same reverse current instability due to surface contamination but, in addition, the transistor also provides other indicators for detecting the presence of contamination mechanisms. The first of these indicators is certainly the low frequency current gain. Contamination a t the periphery of a n emitter junction, for example, will often increase the minority carrier surface recombination velocity which, in turn, reduces current gain. Further, the presence of an inversion layer-which was previously associated with the junction diode-can provide a conduction path between the emitter and collector in many transistor configurations; this mechanism, in fact, has been frequently found to contribute to transistor instability. Surface contamination can exist in the immediate vicinity of a collector junction without altering many electrical properties of a transistor. A reduced collector junction breakdown voltage, for example, can be exhibited by a device that otherwise performs in a satisfactory manner. I n this transistor-like the junction diode-collector junction breakdown becomes “soft,” and reverse current hysteresis is frequently observed. Although such a transistor may exhibit adequate current gain it could not be considered any more reliable than a diode with similar characteristics-it would probably have a very short useful life. It is important to note that surface contamination of a junction transistor must be evaluated in terms of the diode properties of both its collector and emitter junctions and also in terms of its transistor characteristics when the entire device is in operation. Only in this manner is it possible to properly evaluate the influence of contamination mechanisms. In many geometrical configurations sufficient isolation exists between the emitter

220

DAVID P . KENNEDY

and collector so that surface contamination of one junction will not change the electrical properties of the other. Current gain in a junction transistor is particularly sensitive to surface contamination in the immediate vicinity of its emitter junction. Only a small increase is required in the surface recombination velocity to substantially decrease the base region transport efficiency and thereby degrade the current gain (44). Consistent with this viewpoint, Gartner and Boxer (45) have proposed a method of qualitatively evaluating this surface recombination velocity and thereby provide some insight into the mechanisms causing gain degradation during life tests. I n a common emitter connection, the small signal current gain of a transistor, p, is determined by the base region transport efficiency and by the emitter junction injection efficiency. From previously considered mechanisms, a large base region minority carrier injection level introduces changes in both of these parameters which consequently modifies the current gain. Increasing the base region minority carrier densitydue to an increased emitter current-enhances carrier motion from the emitter to the collector junction thereby decreasing the influence of surface recombination (46, 47). Simultaneously, a loss of emitter injection efficiency is also observed a t large carrier injection levels (Misawa, 48) which competes with the increase of base region transport efficiency. In combination, the two mechanisms-increased base region transport efficiency and decreased emitter injection efficiency-result in an initial increase in current gain with emitter current; this gain reaches a maximum and thereafter decreases with an increase of emitter current. In an investigation of this problem, Gartner and Boxer (45) compared the theoretical and experimentally determined characteristics of current gain, p, vs. emitter current, I,, for a number of transistors, before and after life testing. From this investigation, a qualitative indication was obtained for the degree of change occurring in the surface recombination velocity during component operation. Although this technique provides one of the few ways we can evaluate surface recombination mechanisms upon a completed transistor, the subject has received insufficient attention and therefore requires further study. I n this investigation, the following approximate relation is used to describe the dependence of current gain, 8, upon emitter current, I,, for a p n p transistor: 1 - a = HMz) d(z)g(z)l (42)

+

where H represents the base regin recombination from both bulk and surface induced mechanisms,

SEMICONDUCTOR DEVICE EVALUATION

and

K

22 1

is given by K

=

H-'(Dnnoew/DppodA)

(44)

The parameters g ( z ) and f(z) introduce the high injection level effects,

+ P/l + 21' +p z = 2 P - Ln(1 + P ) = J,w/qn,D,

g(z) = 1 f(z>g(z) = 1

where

(45) (46)

Upon normalizing Eq. (44) in terms of its magnitude at zero emitter current, we obtain

BlPO

= (1

+ 4 {g(z> +

Kf(Z)dZ)

1

(47)

which has the independent variables K and z, Fig. 24. There are two important properties of this expression which can be used to evaluate an actual device; the maximum value of p/po vs. K and also the value of z at this maximum, for each value of K-these are illustrated in Fig. 25. From experimentally measured values of /3 vs. I,, a maximum can be determined thereby establishing the magnitude of K-and hence the magnitude of z. Having this information before and after life tests, for example, one can calculate the resulting changes in surface recombination velocity and emitter injection efficiency. Using the foregoing methods, characteristics have been studied for transistors subjected to various life tests (45). Upon completion of these tests, some devices exhibited an increased surface recombination velocity while others, in contrast, exhibited a decrease. I n addition to detecting changes in base region surface recombination velocity, some transistors were found to undergo a change in emitter junction injection efficiencythe mechanism causing this change remains unexplained. The experimental results of this effort clearly indicate a need of further investigation but, a t the same time, in its present elementary form this method provides a technique for detecting small changes in surface recombination occurring during the life testing of transistors. Additions and refinements of the present theory-in conjunction with further experimentscould yield a valuable tool for the evaluation of surface recombination mechanisms upon a completed semiconductor device. I n addition to changes in the surface recombination velocity, other modifications are often found upon close investigation of junction transistors. Experiments indicate that a major contribution to transistor instability results from the formation of an n-type inversion layer-or channel-across the p-type base region (Zierdt, 3). This layer, in effect, provides a conduction path between the emitter and collector. Channel

222

DAVID P. KENNEDY

formation across the base region of a transistor is not a particularly new phenomena; it was first observed in grown junction transistors. With the advent of alloy type structures, channeling became a relatively insignificant problem because of the long surface path-and hence low channel

FIQ.24. The characteristic function of Eq. 47 plotted with (from Gartner and Boxer, 46).

K

as a parameter

conductance-between its emitter and collector. Today we again find that channeling is an important consideration in the operation of junction transistors. A number of modern diffused devices have geometrical configurations which provide a large channel conductance; these are as susceptible to channeling as the earlier grown junction transistors.

223

SEMICONDUCTOR DEVICE EVALUATION

r

0.005 0.01

0.02

0.05

0.2

0.1

0.5

0.1

---K

(a)

0.004

0.01

0.05

0.02

0.1

0.2

0.5

I

-K

(b)

FIG.25. Boxer, 46).

(a) (p/p0) as a function of K ; (b) Z,,

as a function of

K

(from GBrtner and

224

DAVID P. KENNEDY

To illustrate this mechanism, Fig. 26 presents the basic structure of a grown and a n alloy type transistor. The grown junction transistor, Fig. 26(a), has a n inherent base region surface path length-between its emitter and collector junctions-of one base width; this situation assures a large channel conductance. Furthermore, at the time this device was in popular use, cleaning and encapsulation techniques were primitive and thus surface channeling was a serious and difficult problem. Although essentially the same processing was applied to alloy transistors, Fig. EMITTER BASE

T

I

EMIT TER ;BASE COLLECTOR

BASE

I

EMITTER A

I

---------

EMITTER

1 I

COLLECTOR

(b) FIG.26. Basic geometrical-configuration; (a) grown junction transistor; (b) alloy transistor.

BASE +

----- --COLLECTOR

(b) FIG.27. Illustrations of diffused mesa transistors.

26(b), they are not influenced by channel formation to the same degree as a grown junction device. The geometrical configuration for this type of transistor assures that a base region inversion layer will have a very small emitter-collector conductance. I n alloy transistors, therefore, surface contamination introduces electrical changes in the emitter and collector diodes although these are seldom as devastating as encountered in grown junction transistors. Figure 27(a) illustrates a diffused mesa transistor which, like a grown transistor, has a short surface path length between its emitter and collector. When constructing this type of device, SiO is selectively evaporated upon the silicon prior t o a n emitter diffusion; this determines the basic configuration of a completed unit. Particular technological difficulties are encountered in this technique with regard to the alignment of evaporation masks. To simplify this mask alignment problem the geometrical configuration of Fig. 27(a) is frequently adopted. Here, a n

SEMICONDUCTOR DEVICE EVALUATION

225

emitter junction appears on one side of the mesa thereby maintaining an emitter to collector surface path length of one base width-this is in contrast to centering the emitter and thus lengthening this path, Fig. 27(b). Detection of surface channeling in modern transistors is substantially more difficult than in previous years; this situation results from improved cleaning techniques. Previously, a grown junction transistor, for example, exhibited sufficient degree of surface contamination to permit a floating potential measurement upon its emitter junction. Today a device which eventually will have a surface channel might be completely satisfactory a t the start of operational life tests. In this type of transistor, channeling appears to result from a redistribution of ionic contaminants due to the collector junction electric field. Furthermore, upon forming this channel during an operational life test, it can be annealed out if the transistor is subjected to high temperature storage. This characteristic is presumed to result from contaminate scattering in the absence of a large electric field. I n summary, the electrical stability of a junction transistor, like a semiconductor diode, is intimately associated with the problem of surface contamination. Through mechanisms of surface leakage, channel formation, and modifications of the surface recombination velocity, junction transistors are subject to all the unstable properties previously attributed to a diode and, in addition, will frequently exhibit a substantial degree of instability in its current gain. Evaluating the inherent electrical stability of a transistor invariably implies the extensive use of life testing which can be a time consuming task-previously described accelerated ageing methods are applicable.

C . Steady-State Characteristics The use of static volt-ampere curves represents one of the earliest methods of evaluating the electrical properties of transistors. Although a number of more subtle evaluation methods are presently available, the static technique remains an important laboratory tool; it provides a rapid qualitative characterization of a device throughout its entire range of operation. Furthermore, if quantitative measurements are required, these static characteristics can be established on a point-bypoint basis-although this introduces a number of additional problems which can influence measurement accuracy. Thermal dissipation, for example, will change extensively throughout the entire evaluation range thereby modifying the transistor temperature and hence, its volt-ampere characteristics. In addition to the traditional st,atic methods of transistor evaluation, other, less conventional, methods are often used although they are

226

DAVID P. KENNEDY

seldom discussed in the literature. These special evaluation techniques are not generally applicable to all devices; they are often directed toward a specific device having a particular geometrical configuration. This class of evaluation technique usually results from experimental observations in the laboratory where a correlation is observed between a particular electrical characteristic and one or more of the physical transistor properties. Initial steady state evaluation of a junction transistor is concerned with the diode characteristics of both its emitter and collector junctions. I n principle, these junctions are equivalent EMITTER BASE COLLECTOR to individual semiconductor diodes of the type previously considered ; basic differences will lie in possible interaction mechanisms due to their close proximity. The (a) collector junction, for example, can exhibit a punch-through to the emitter junction (4.9) which is readily observed in these volt-ampere characteristics. Upon applying a reverse biasing potential to the I I collector-assuming the emitter is a t zero I Y bias-space-charge widening can occur (b) I SPACE I until the collector space-charge region just CHARGE LAYER reaches the emitter, Fig 28(b). Increasing the collector biasing voltage beyond this point results in a penetration of the emitter space-charge layer by the collector space-charge layer; this, in effect, forward I I biases the emitter junction and can be (c) as a change of emitter to base detected CHARGE LAYER potential, VBB,Fig. 29. It should be noted FIG. 28. Transistor punchthat applying a reverse bias potential to through characteristics: (a) device at equilibrium; (b) collector junc- the emitter-base junction will increase tion punch-through; (c) emitter (not decrease) the measured value of junction punch-through. collector punch-through voltage. Assuming, for example, a collector biasing~. potential of V1 is required for punch-through to an equilibrium emitter, a reverse bias of Vz upon the emitter junction will increase the measured Vz. collector junction punch-through voltage to Vl Similarly, junction transistors can also exhibit an emitter punchthrough mechanism where the emitter junction space charge layer penetrates to the collector junction, Fig. 28(c). For alloy type structures we can presume the emitter punch-through and collector punch-through

m

+

227

SEMICONDUCTOB DEVICE EVALUATION

occur at the same magnitude of junction potential; this situation is not characteristic of diffused type structures. I n a diffused transistor, colIector junction space charge widening is usually greater into the collector region than into the base and therefore a relatively large voltage is required for collector punch-through. Contrasting with this situation, an emitter junction will usually have an exceedingly large impurity atom concentration on one side-the emitter region-and thus space charge widening occurs predominantly into the base. For the diffused junction transistor, therefore, it is not unusual to experience collector junction punch-through a t 30 volts and an emitter junction punch-through a t 12 volts. Calculating the collector punch-through potential of a double-diffused transistor (49) is accomplished by solving Poisson's equation, d2\E _ - QP(X> dx2 Keo

(48)

p y 2+VBE

VBC

where p(x) represents the charge distribution within the space-charge layer. Using FIG.29. Illustrative circuit approximations adopted from the elemen- for punch-through measuremerits. tary theory of a reverse biased p-n junction (f), the charge distribution p ( z ) can be represented by the impurity atom distribution equation

From Eq. (48), therefore, the junction potential associated with a given collector junction space charge layer width is given by

Setting in Eq. (50) (x, - a,)-the collector junction space charge layer edge within the base region-at the same location as the space charge layer edge of the equilibrium emitter junction, a punch-through voltage is readily calculated. I n most situations, calculating the punch-through voltage of a doublediffused transistor is a difficult task which must be accomplished upon a high speed electronic computer. Figure 30 illustrates this type of calculation which was conducted for a transistor assumed to have a given bulk impurity atom distribution and also a fixed impurity atom profile for the collector junction diffusion. This graph illustrates the manner in which

228

DAVID P. KENNEDY

the collector punch-through voltage, Vcp,changes for different emitter junction diffusion profiles. When discussing the punch-through mechanism it was tacitly assumed that the breakdown voltage for each junction was greater than 3

Ioo

10'

v,

I02

p (volt s)

FIG.30. Collector punch-through voltage for a diffused junction transistorr(frorn Kennedy and O'Brien, 4 9 ) .

their respective punch-through voltage; this is not always a true situation. For the emitter of a diffused transistor, in fact, punch-through to the collector junction is seldom observed because of emitter junction breakdown. In contrast, it is often a design variable for the diffused collector

SEMICONDUCTOR DEVICE EVALUATION

229

junction; for essentially the same transistor characteristics either collector junction breakdown or punch-through can establish the maximum collector voltage. Furthermore, it should be noted that advantages are obtained when the collector punch-through can be readily observed in the electrical characteristics of a transistor. From a n experimental point of view it is an exceedingly difficult task to physically measure the base width of a transistor-by staining, probing, etc. The punch-through voltage, on the other hand, provides a very sensitive electrical measurement for this and other small changes which can occur in the base region of a transistor. Assuming that both the emitter and collector junctions undergo a breakdown mechanism before punch-through, they should, individually, exhibit the reverse characteristics of a conventional p-n junction diode. Collector junction breakdown, for example, should be exceedingly abrupt, as previously attributed to an avalanche process. An emitter junction, on the other hand, will often exhibit substantially different breakdown characteristics-particularly in a diffused transistor. Base and emitter region conductivity grading usually results in an emitter breakdown voltage of 4 to 6 volts; this implies that a large amount of its breakdown current can be caused by field emission. For this reason it is not unusual to experience a relatively soft emitter breakdown characteristic in diffused junction transistors. I n addition to the usual breakdown characteristics of an emitter junction, some devices exhibit a double emitter breakdown as illustrated in Fig. 31(a); this situation is attributable to the particular transistor, its geometrical configuration, and also its processing. Here we have an example of one type of highly specialized evaluation method often used in a component development laboratory. I n this particular situation, the double breakdown is a qualitative indication of an excess base resistance due to overetching. Contrary to the breakdown characteristics of a typical emitter junction, the exaessive base resistance-due to overetching the periphery of the emitter, Fig. 3l(b)-is observed above emitter breakdown-6 volts in this illustrative example, Fig. 31(b). Assuming the collector-to-base potential at B-B’ is zero, sufficient emitter bias voltage can be applied to attain collector junction breakdown at A-A’; this, of course, results from an excessive resistance between A-B. After breakdown, the collector junction represents a low resistance path in parallel with the large base resistance. This evaluation method, although very qualitative, provides a means of immediately eliminating developmental devices which are obviously in serious difficulty. I n addition to the foregoing steady state measurements, it is frequently necessary to detect the formation of a surface channel across the

230

DAVID P. KENNEDY

base region of a junction transistor. I n previous years this was a relatively simple task. It was only necessary to reverse bias the collector junction and measure the emitter floating potential; sufficient channel conductance was usually present to result in an emitter floating potential equal to the collector bias. Today, channel formation occurs over many hours of operation and is therefore detectable as a shift in the characteristics of a device. Leaving the base lead open, a biasing voltage between the emitter

t

f

EMITTER

COLLECTOR (b)

FIG.31. Double breakdown of emitter junction due to over-etching: (a) emitter volt-ampere characteristics; (b) illustration of over-etched device.

and collector results in a collector current which is proportional to both the transistor gain and the collector junction saturation current. If a substantial change occurs in the transistor operating point, channeling can be suspected-it is not unusual to experience an order of magnitude increase in collector current due to channel formation. This experiment, in conjunction with previously described characteristics of a base region inversion layer, is often an adequate evaluation technique. Although the static volt-ampere characteristics of a junction transistor can be presented in many forms (40) the common-emitter connection, Fig. 32, is frequently used for component evaluation. By visualizing-or

231

SEMICONDUCTOR DEVICE EVhLUATION

measuring-incremental changes occurring about a given operation point, an estimate is quickly obtained for the variation of small signal parameters throughout the entire transistor operating range. Figure 32 illustrates how many of these small signal parameters can be derived from such a set of volt-ampere characteristics. This analytical technique, a t best, is only a crude approximation although it represents one of the quickest ways to obtain an over-all view of the electrical properties of a transistor. Because the details of this subject-transistor evaluation in terms of CUTOFF REGION

,rc

r

@+Arbb' (

Ic-~c~-vc~~c

I

UI

[SATURATED L REGION

1

1

LI I

+;

= o LOCUS GIVEN BY

FIQ. 32. Common-emitter output characteristics with V B as parameter (from Carlson, @).

their volt-ampere curves-has been given extensive coverage in the literature (40, @), a reiteration would be of little value a t this time.

D. Small Signal Parameters The small signal parameters of a transistor, as the name implies, characterizes the device in terms of incremental voltage-or currentvariations about some quiescent operating point. Actually, this is a linear characterization of a fundamentally nonlinear device; any substantial change of operating point results in a large change in the measured values of its small signal parameters. For this reason the measurement is presumed to be made a t sufficiently small signal levels to assure that these parameters remain constant. In many situations it becomes necessary,

232

DAVID P. KENNEDY

therefore, to measure the small signal parameters of a transistor a t two or three operating points which have been selected to enhance particular component characteristics. We could, for example, measure the current gain a t two or three different magnitudes of collector current-small, intermediate, and large-thereby obtaining a complete picture of how this parameter is influenced by various fundamental mechanisms of transistor operation. I n addition to the inherent problems associated with obtaining a truly small signal measurement, the frequency of measurement introduces an additional difficulty. A large portion of the evaluation process is accomplished a t relatively low frequencies where few instrumentation problems arise. I n addition, it is also necessary to evaluate the small signal parameters of some devices to frequencies beyond the kilomegacycle range which, in itself, is often a major task (42). An extensive amount of the semiconductor literature has been devoted to the subject of small signal characterization of transistors and the associated problems of instrumentation. For this reason it would be of little value to present the interrelation between transistor H and Y parameters, for example, or to describe the multitude of approximation equations which have been proposed to characterize the change in small signal parameters resulting from their dependence upon frequency or current. Instead, we shall discuss a relatively new approach taken in the evaluation of transistors; obtaining a correlation between theory and experiment thereby explaining, in part, some of the physical properties influencing transistor operation. Initially, theoretical concepts of transistor operation were developed to provide a semi-quantitative explanation in a form which was mathematically tractable. Often this approach is very successful and yields results which are in substantial agreement with experiment. There are situations, on the other hand, where this approach is particularly unsuccessful and, in fact, yields incorrect results in both magnitude and basic concept. Today, many workers are eliminating such difficulties. More rigorous analytical studies are being made on fundamental mechanisms of transistor operation; although numerous mathematical difficulties are encountered, these difficulties are being overcome and, wherever necessary, large scale electronic computers are used, Junction transition layer capacitance is one small signal parameter which greatly influences the high frequency properties of any transistor, In addition, from a component evaluation point of view, this capacitance also represents a parameter which will reflect changes occurring in the physical constants of a particular device. I n the construction of a diffused junction transistor, for example, many important physical constants

SEMICONDUCTOR DEVICE EVALUATION

233

-impurity atom concentrations, junction depths, etc.-are experimentally determined by techniques which are often subject to question. Further, when manufacturing such devices, these physical constants will often change due to inadequate process monitoring techniques. Capacitance measurements of the reverse biased collector and emitter junctions provide a check upon such difficulties. For both the alloyed and diffused junction transistor, substantial agreement should be obtained between the calculated junction capacitance and its experimentally determined magnitude before any degree of confidence can be placed in our knowledge of the impurity atom distribution. In 1949 Shockley (1) presented equations which characterize the capacitance of an alloy (abrupt) type of p-n junction under all conditions of reverse bias. I n addition, he also studied the capacitance-voltage characteristics of a p-n junction containing a linear graded impurity atom distribution; this device was found to exhibit the proportionally C V-)$. Since experiment established a similar capacitance-voltage relation for the diffused p-n junction, it was presumed that this structure could be approximated by a linear graded impurity distribution. Additional theoretical investigations of the subject have shown that this is not always a true situation (18). Diffused junctions of small impurity atom concentration gradient are, indeed, equivalent to a linear graded structure up to their avalanche breakdown voltage. If, on the other hand, a diffused junction has a large impurity atom concentration gradient, the linear graded approximation is only appropriate a t a small reverse biasing voltage. At high voltages, this type of device can exhibit a capacitancevoltage proportionality of the form C 0: V-r4 which is characteristic of an abrupt junction, Unfortunately, it is not obvious where the dividing line lies between the two types of diffused junctions and therefore a detailed capacitance calculation is required in the evaluation of many junction transistors. For computational purposes, the collector junction of presently available diffused junction transistors can be assumed independent of the emitter junction at small reverse biasing potentials. This situation greatly simplifies the problem of calculating the collector junction capacitance since it is often identical to a diffused p-n junction diode. If, instead, collector junction capacitance must be calculated for a large reverse collector voltage-when its space charge layer penetrates near the emitter-several additional independent variables must be introduced. For the diffused p-n junction diode, Lawrence and Warner (60) have calculated space charge layer capacitance and, furthermore, have reduced the results of these calculations to a very useful graphical form of the type illustrated in Fig. 33. Using many of the approximation Q:

TOTAL DEPLETION LAYER THICKNESS IN CENTIMETERS

SEMICOXDUCTOR DEVICE EVALUATION

235

methods applied to abrupt and linear graded structures ( I ) , the junction space charge layer width-and hence its capacitance-is related to the total junction potential through Poisson’s equation

This, of course, presents a difficult computational task and therefore has been accomplished on an electronic computer. For the emitter junction, the problem is substantially more difficult since two diffusions are involved; this cannot be reduced to a simple graphical form and must be computed for each transistor. Using essentially the same methods applied to the analysis of a diffused diode, Kennedy and O’Brien (49) calculated the capacitance associated with an emitter junction when Poisson’s equation is assumed to have the form

Because this type of structure is restricted to small values of reverse bias, it is first necessary to determine a space charge layer width yielding the equilibrium junction potential,

where C ( x ) is the impurity atom distribution, X i is the junction center and up,a,, represent the space charge layer edges. This equilibrium potential, Eq. (53), is then subtracted from all solutions of Eq. (51) to obtain the capacitance-voltage characteristics of the emitter junction. Again, as in the case of the collector junction, this calculation must be conducted on a large scale electronic computer. Figure 34 illustrates a typical computation of the equilibrium emitter junction capacitance assuming a fixed collector junction impurity atom profile. Another transistor small signal parameter of particular importance is the common emitter current gain; this parameter, for the moment, will be considered a t low (or zero) frequency. Probably the most frequent occurrence in the design and development of transistors is to complete the construction of a new device only to find it has either a very small current gain or, a t best, has insufficient gain to satisfy a particular set of specifications. Often, in this situation, the individual emitter and collector junctions have excellent diode characteristics thereby implying the device should work in a satisfactory manner. At this point two mechanisms are questioned-the emitter injection efficiency and also the

W N

U a

FIG.34. Emitter junction capacity at potential equilibrium (from Kennedy and O’Brien, 4.9).

SEMICONDUCTOR DEVICE EVALUATION

237

base region transport efficienoy. One, or both of these fundamental parameters is usually at fault when inadequate current gain is encountered in a transistor although there are no experimental techniques whereby they can be individually measured. For many years this type of situation has been solved on an empirical basis. Upon constructing a large number of devices, each of narrower base width and hence of greater base region transport efficiency-by modifications in the collector and the emitter diffusions-a formula is obtained which produces devices of adequate current gain. I n contrast, an analytical approach can be applied to such problems and thereby successfully separate out the fundamental difficulties. This method assumes that either the emitter injection efficiency or the base region transport efficiency, or both, are contributing to the loss of current gain. Unfortunately, in most devices we do not actually know the base region minority carrier diffusion length otherwise current gain could be calculated. Instead, using a “best guess’’ for this parameter, both the base region transport efficiency and emitter injection efficiency are calculated for a one dimensional model. In most situations one of these contributing parameters is often found to be substantially below the other thereby indicating a source of difficulty. Further, by properly selecting a new value of minority carrier diffusion length, agreement is readily attained between theory and experiment. Having the necessary physical constants, a new diffusion process can now be calculated which represents an essential modification of the defective device and, in theory, will provide an adequate current gain. Using this analytical evaluation technique one can quickly locate sources of inherent difficulties in a junction transistor design with a minimum of laboratory experimentation and, in addition, establish the necessary changes to correct the situation. In 1962 Kennedy and Murley developed methods for calculating both the emitter injection efficiency (51) and the base region transport efficiency (59) of double diffused junction transistors. Assuming both drift and diffusion contribute to the transport of minority carriers within the base and emitter regions of a transistor,

the “built-in” drift field, due t o conductivity grading, can be readily

238

DAVID P. KENNEDY

approximated by a Taylor series. This field, in analytical form, is given by

where C ( x ) is the impurity atom distribution of the particular device under consideration. By substituting Eqs. (54) into appropriate expressions for hole and electron continuity,

we obtain a pair of differential equations-one for the base and one for the emitter-which are readily solved by series techniques. Using this method, equations are obtained for the base and emitter region minority carrier distributions which satisfy appropriate boundary conditions at the depletion layer edges of the emitter junction and the collector junction, and, furthermore, satisfy a given surface recombination velocity a t the emitter ohmic contact. From these minority carrier distribution equations, both the emitter region and base region minority carrier current can be established thereby obtaining the emitter injection efficiency and base region transport efficiency. From a practical point of view, calculating the base region transport efficiency and emitter injection efficiency is sufficiently difficult to require a large-scale electronic computer. Figure 35 illustrates the theoretical emitter characteristics for a device in which the base width is held constant and the emitter junction depth is permitted to change. In this illustration Pr represents the transistor current gain assuming the base region transport efficiency is unity. This technique of transistor evaluation uses both experimental and theoretical information to detect the source of specific difficulties within a device, To verify the impurity atom distribution, theoretical and experimental agreement should be obtained for such parameters as junction breakdown voltage, punch-through, and junction capacitances. Furthermore, theoretical calculations of common emitter current gain can be used for a qualitative evaluation of additional mechanisms pertaining to transistor operation. Assuming, for example, static measurements and junction capacitance measurements upon a device are in substantial agreement with theory, current gain calculations can be used to indicate whether this device should, in fact, exhibit a satisfactory current gain.

N ul

00

s

P 0

To

ul ul

-

o g r Pn

g

0 0

0 0

Y

0

0

0

-J

g

P

ul

0

b 0

0

0 0

g lo

FIG. 35. Current gain flu for a constant physical base width (from Kennedy and Murley, 61).

240

DAVID P. KENNEDY

E. Stored-Charge Characteristics From the foregoing discussions, the steady-state volt-ampere curves of a transistor provide a limited evaluation of its large signal characteristics, Many fundamental problems arise if we attempt to extend this information into the domain of large-signal, high-speed, switching; this would require the introduction of many small-signal transistor parameters which are current dependent and therefore undergo substantial change throughout the switching process. Actually, it is possible t o deduce many large-signal switching properties if the static volt-ampere curves are used in conjunction with appropriate families of small-signal parameters-this technique, in general, cannot be considered satisfactory. To determine even relatively simple large-signal switching characteristics of a particular device, it is first necessary to conduct a large number of small-signal measurements-the method is too laborous to become a useful laboratory tool. In an attempt to simplify this problem, many workers have proposed methods of measurement which represent an extension for existing small-signal techniques. Although these methods have improved the situation, it is relatively clear that a new approach is required; this new approach should account for both the large-signal and high speed aspects of the problem. The high speed electronic computer provides an application for junction transistors in which their large-signal switching characteristics are of principal importance. I n most computer circuits the transistor must be driven between cut-off and saturation; this requires the device to be capable of rapid transitions between these limiting regions of its operating characteristics. Further, the large-signal switching properties of a particular transistor must be described in terms which can be related to its operation in an actual circuit-even though there exists a vast number of possible circuits. We must, for example, evaluate the rate at which the junction transistor can be switched from an “off” state t o “saturation” and, in addition, this evaluation must be in terms which describe the switching rate when using an arbitrary source and an arbitrary load. Clearly, this problem of component evaluation is very difficult. The problem, in fact, is so difficult that an adequate solution has never been obtained. In many situations the evaluation of a transistor-in terms of its applicability in a particular computer circuit-is established in an experimental circuit which closely resembles its intended use in the computer; this technique is indeed empirical although it is necessary in view of our present knowledge of transistor operation. I n 1957 Beaufoy and Sparks (63) proposed an evaluation method for the large-switching properties of a transistor which more nearly satisfies

SEMICONDUCTOR DEVICE EVALUATION

24 1

the requirements of device designers and also the requirements of computer engineers. They proposed that the junction transistor could be considered a charge controlled device in that a specific electric charge must enter the transistor when turning it “on” and that a similar charge must be removed before it is returned to its “off” state. Furthermore, in this proposal, i t was suggested that the electric current entering and leaving through the transistor base contact was essentially a measure of this charge. Although it is now realized that many problems must be solved before we can fully apply this method in the large-signal investigation of junction transistors, the method does have sufficient promise to stimulate extensive activity in the field of component evaluation. From the point of view of a component designer, the charge control method provides a n important relation between the large-signal switching properties of a transistor and the fundamental physical mechanisms of its operation. Similarly, this method is equally valuable to the circuit designer since the switching characteristics of a transistor are presented in a form which can be related t o specific circuit requirements. The basic concepts of this analytical approach are based upon a n assumption that space charge neutrality must always be maintained within the base region of a junction transistor (26). Upon applying a forward bias t o the emitter junction of a p n p transistor, excess holes enter the base region thereby upsetting charge neutrality-to maintain neutrality excess electrons enter the base region through its ohmic contact. Fundamental to this evaluation technique is a n ability to measure the additional base region charge which has been effectively neutralized by the excess electrons; this is established by integrating the transient component of base current, i b ( t ) ,

(57) Similarly, turning a transistor “off” is presumed to be described by substantially the same type of mechanism. Assuming the transistor switching time is shorter than the base region minority carrier lifetime, the integrated transient base current represents the total base region charge Q B that must be eliminated before an “off” condition can exist. I n a practical junction transistor the number of holes within the base region is not exactly equal to the quantity of electrons entering through the base contact (Sparks, 54). When applying a forward bias to the emitter junction it is also necessary to charge up the emitter junction depletion layer capacitance. I n this situation the emitter junction space charge layer becomes narrower since many base region electrons are used to neutralize the charge upon donor atoms. Similarly, a n equal number of

242

DAVID P. KENNEUY

acceptor atoms are neutralized by holes on the emitter side of the junction. This charge associated with the emitter junction space charge layer, Q V E , depends upon the voltage swing applied to the emitter junction during “turn on” and is a component part of the total base charge, Qn, encountered in this transient process. I n a n identical manner Q V E is also the charge removed from the space charge layer when this external biasing voltage is removed; in the base region this appears as additional base current leaving the device through its ohmic contact. It is importaiit to note that the emitter junction charge Q V E is often a small part of the total base charge QO but, unfortunately, in many high speed switching devices this situation is not satisfied.

=t P

W -I

0

I

EMITTER

COLLECTOR

FIG.36. Base region minority carrier distribution in the active mode of operation.

Using this charge control approach for the large-signal characteristics of junction transistors, many parameters can be established which are fundamental to the transistor switching process. Assume, for example, the emitter and collector junctions are planer, abrupt, and parallel. I n addition, if we assume the collector junction is reverse biased while the emitter junction is forward biased, Fig. 36 illustrates the base region minority carrier distribution for a transistor of reasonabIy large current gain. Here, the emitter to base minority carrier current can be assumed constant and given by 1 = qAp(z)+) (58) where p ( z ) is the minority carrier (hole) distribution and ) dz/dt we obtain transport velocity. Substituting ~ ( z =

U(T) is

their

therefore

The parameter T~ represents the minority carrier transport time between

SEMICONDUCTOR DEVICE EVALUATION

243

emitter and collector while Qs is the total base region charge which is stored in the form of excess minority carriers (holes). Clearly, if the emitter junction capacity is neglected, Q6 = Qn, Eq. (57), and the base region transport time, n, equals a parameter which is often called the collector time constant, T,, [54] 7

QH

= -

(61)

I,

Inherent difficulties arise in the charge control method of compoiient analysis (54). The technique is generally applicable to the evaluation of alloy type structures where a large base region charge is encountered, I n a diffused junction transistor, on the other hand, the base width is very narrow and therefore only a small base region charge is associated with its switching process. This small charge makes the measurement problem more difficult and, furthermore, the charge associated with the emitter junction, Q V E , can no longer be assumed a small part of the total charge, Q B , entering the base contact. An experiment was performed by Shveiken (55) which appears to be in substantial agreement with the above concepts. I n this experiment, the base region charge, Eq. (I), was used to determine the alpha cutoff frequency, 5&,of alloy type transistors containing a homogeneous base region. The base region transport time, T ~ ,was assumed essentially , therefore equivalent to the collector time constant, T ~ and

I,

,fa = 0.193 (J n

(62)

It should be noted th at Shveiken’s alloy transistors had a maximum cutoff frequency-based upon small signal measurements-of approximately 8.0 Mc thereby implying the presence of relatively large base widths and hence a relatively large stored charge. In this situation less than 10% difference was encountered between the cutoff frequency established by Eq. (62) and by appropriate small signal measurements. An inherent advantage of this charge control method arises from the fact that many characterizing parameters are relatively insensitive to the operating point of a transistor. The previously defined collector time constant, T ~ establishes , the base region charge per unit of current when the collector junction voltage is held constant. Since the emitter depletion layer capacitance contains a charge, Q V E , proportional to the emitter bias voltage-hence the collector current, I,-and further, since Q V E is a component part of the total base charge, Q B , it follows that this base charge Q B is slightly dependent upon I,. I n addition to the emitter junction charge, QVE,conductivity modulation encountered a t a high minority carrier injection levels will also result in a variation of T~ with collector

244

DAVID P. KENNEDY

current. This mechanism was investigated by Meyer (56) in which he has related the stored base region charge, Q8, to the collector current of a transistor having a base region transport efficiency of unity,

where Iew AqDpNd

z=-

Since ~t

=

&./Ic we have, from Eq. (63), (65)

Figure 37 illustrates Eq. (65) throughout a large range of emitter current; this graph shows that the emitter-collector transport time, T ~ ,will decrease by a factor 2 between low and high emitter injection levels. This, I.o

09 a0

a7 0.6

0.5

.oI

0.I

1.0

z

10

FIG.37. Normalized intrinsic collector time constant, 7 , and ~ (from Sparks, 6 4 ) .

I00

vs. 2 (theoretical)

' - 1

of course, is consistent with the fact that the ambipolar diffusion constant of minority carriers will double a t high injection densities. I n addition t o a decreasing collector time constant, T., due to conductivity modulation, Kirk (57) has proposed another mechanism which also reduces T. at a n increased colIector current. This mechanism will, in effect, increase the base layer width by modifying the space-charge layer edge a t the collector junction. At large collector current densities the mobile charges within the collector junction space-charge layer can no longer be assumed to have a non-negligible influence upon the spacecharge potential distribution. Actually, the space-charge boundary

245

SEMICONDUCTOR DEVICE EVALUATION

adjacent the neutral semiconductor material is displaced toward the junction center; this situation is equivalent to a n increased base width. Computation of this characteristic has been made assuming the frequency ff (where h,, is unity) is given by

where re is the emitter junction time constant

Q V E / I b , T~ is

the base region

I0,OOO

5000 2000

-9-

LATED PLOT EXPERIMENTAL PLOT

1000 0)

$

500

v

+ v !

200 100

50

.5

2

5

10

IC

20

50

100

200

(ma)

FIG.38. Experimental and calculated plots of Transistor (from Kirk, 67).

fi

vs. I, for the 2N 796 MADT

transport time, and rz is the collector junction space-charge layer transit time. Individually these time constants are given by expressions of the form

Figure 38 illustrates a comparison between the theoretically determined magnitude of Eq. (66) and its measured value throughout a wide range of collector current. Agreement bekween experiment and theory is indeed

246

DAVID P. KENNEDY

satisfactory and therefore this mechanism must be considered in the evaluation of switching transistors. Although the collector time constant, rc,has been defined in a manner that prevents a collector capacitive charge from influencing the measurement of base charge, Q B ; the parameter r, is, nevertheless, dependent upon the collector junction voltage. Since the collector junction space charge layer width-and thus the base width-is dependent upon the collector biasing voltage, a t a given emitter current the total number of stored minority carriers decreases with an increase of bias voltage thereby decreasing rc. For this reason, measurements of rEare conducted a t a

4

I I

W

J

EMITTER

DISTANCE

t

b

COLLECTOR

FIG.39. Base region minority carrier distribution in the Saturation mode of operation.

specified emitter current and also a t a specified magnitude of collector biasing voltage. I n many situations the collector time constant is measured a t zero collector voltage thereby implying the transistor is a t the edge of saturation; this parameter has been defined (54) as roo =

Q B / ~ ~

(68)

So far we have only discussed the collector time constant, r,, which, by definition, is only applicable throughout the active region of a transistor’s operating characteristics. In addition to this parameter, it is also necessary to define a time constant associated with the base charge of a junction transistor when driven into saturation. Saturation implies that both the emitter and collector junctions of the transistor are forward biased thereby forming a base region minority carrier distribution as illustrated in Fig. 39. Initially we will assume that no minority carriers are injected into the collector region and thus the transistor contains a base charge Q S S in excess of that required to just drive the device to the edge of saturation. From this excess base charge, we have a saturation time constant given by 7. = Q B S / I B S (69) where IOS is the excess base current required to drive the device into

SEMICONDUCTOR DEVICE EVALUATION

247

saturation. I n theory Q B S represents the excess base region charge th a t must be removed from a transistor to take it out of saturation. The charge control parameters are intended to represent the base region charge which must be injected or removed to switch a device from one mode of operation to another-to switch, for example, from saturation cutoff. I n this concept of transistor operation the switching speed is directly proportional to the rate a t which this base charge is injected or removed. Practical transistors, when in saturation, are often not found t o follow this simple relation. Diffused junction transistors, for example, will frequently exhibit a very large saturation time constant, and furthermore, will switch out of saturation a t a rate essentially independent of the rate base region charges are removed. This characteristic implies t ha t base region charge storage is not the predominant charge storage mechanisms. A diffused collector junction, unlike the alloy structure, injects minority carriers into its collector region when forward biased; a t the same time this junction also injects minority carriers into the base region. Like the p-n junction diode (37) minority carriers become stored within the collector region and this junction cannot be returned to zero bias-the edge of saturation-until they have been removed from the collector junction face. I n this situation, stored minority carriers are fed to the collector junction a t a rate faster than they can be removed by base current thereby keeping the transistor in a state of saturation. Although we have neglected consideration of the base charge th a t is used in the collector and emitter transition capacities, the basic concept of the charge control approach is presented. This method is particularly powerful since it provides a conceptual simplicity which is not always available in such complex problems. Essentially, the minority carrier transport time, between the emitter and collector, is defined in terms of the base region stored charge and the collector current. Since transistor switching speed is intimately related to this transport time, the charge control method provides a particularly simple method of viewing transistor operation. An example of the advantages of this method was demonstrated in 1959 by Varnerin (58);in this investigation the qualitative effects were established for complicated base region donor distributions upon the base region transport time. Assuming a specified collector punch-through voltage and emitter junction capacitance, it is shown that a retarding base region drift field will actually provide a minimum base region transport time-and hence a maximum switching speed-since smaller base region thicknesses can be attained. Although this investigation was qualitative, it is clear that the charge control technique has a n inherent simplicity enabling us to investigate new approaches to increasing the switching speed of junction transistors.

248

DAVID P . KENNEDY

References 1. W . Shockley, Bell System Tech. J . 28, 435 (1949). 2 . J. A. Perri, H. S. Lehman, W. A. Pliskin, and J. Riseman, Electrochem. Senziconductor Svmposium, Detroit, 1961. 3. C. H. Zierdt, Jr., Solid State J . 2, 21 (1961). 4. B. T. Howard, and G. A. Dodson, Bell Lab. Record 40, 8 (1962). 6. C. T. Sah, R. N. Noyce, and W. Shockley, Proc. I.R.E. 46, 1228 (1957). 6. W. Shockley, and W. T. Read, Jr., Phys. Rev. 87, 835 (1952). 7. M. Cutler, and H. M. Bath, Proc. I.R.E. 46, 39 (1957). 8. W. T. Eriksen, H. Statz, and G. A. DeMars, J . Appl. Phys. 28, 133 (1957). 9. W. H. Brattain, and H. Bardeen, Bell System Tech. J . 32, 1 (1953). 10. K. B. McAfee, E. J. Ryder, W. Shockley, and M. Sparks, Phys. Rev. 83, 650 (1951). 11. C. Zener, Proc. Roy. Soc. 8146, 523 (1934). 12. I(. G. McKay, and K. B. McAfee, Phys. Rev. 91, 1079 (1953). 13. L. B. Loeb, “Basic Processes in Gaseous Electronics.” Univ. of California Press, Berkeley, California, 1955. 14. K. G. McKay, Phys. Res. 94, 877 (1954). 16. A. G. Chynoweth, and K. G. McKay, Phys. Rev. 108, 29 (1957). 16. A. G. Chynoweth, Phys. Rev. 109, 1537 (1958). 17. Maserjian, J . Appl. Phys. 30, 1613 (1959). 18. D . I?. Kennedy, and R. R. O’Brien, I.R.E. Trans. Electron Devices ED-9,478 (1962). 19. J. Tauc, J . Phys. Chem. Solids 8, 219 (1959). 20. A. G. Chynoweth, and K. G. McKay, Phys. Rev. 106, 418 (1957). 21. A. G. Chynoweth, W. L. Feldman, C. A. Lee, R. A. Logan, G. L. Pearson, and P. Aigrain, Phys. Rev. 118, 425 (1960). 22. A. G. Chynoweth, and K. G. McKay, Phys. Rev. 102, 36’3 (1956). 23. A. G. Chynoweth, and G. L. Pearson, J . Appl. Phys. 29, 1103 (1958). 24. R. L. Batdorf, A. G. Chynoweth, G. C. Dacey, and P. W. Foy, J . Appl. Phys. 7, 1153 (1960). 66. A. G. Chynoweth, J. Appl. Phys. 31, 1161 (1960). 26. W. Van Roosbroek, Bell System Tech. J . 29, 560 (1950). 27. J. 5. Saby, Phys. SOC.Rept. Meeting on Semiconductors, Rugby (1956). 28. N. J. Harrick, J . Appl. Phys. 29, 764 (1958). 29. N. J. Harrick, Phys. Rev. 109, 1173 (1956). 30. W. Van Roosbroek, Phys. Rev. 91, 282 (1953). 31. S. E. Michaels, and L. A. Meacham, Phys. Rev. 78, 175 (1950). 32. E. M. Pell, Phys. Rev. 90, 278 (1953). 93. S. R. Lederhandler, and L. J. Giacoletto, Proc. I.R.E. 43, 477 (1955). 34. H. Y . Fan, Phys. Rev. 76, 1631 (1949). 36. R. H. Kingston, Proc. I.R.E. 42, 829 (1954). 36. B. Lax, and S. F. Neustadter, J . Appl. Phys. 26, 1148 (1954). 97. M. I. Iglitsynz, Iu. A. Kontsevoi, and K. V. Temko, Radiotekh. i elektronika 6, 508 (1960). 38. D. P. Kennedy, I.R.E. Trans. on Electron Devices 9, 174 (1962). 39. I.R.E. Standards on Methods of Testing Transistors, Proc. I.R.E. 44, 11 (1956). 40. A. W. Carlson, Semiconductor Products 2, 31 (1959). 41. B. J. Cooper, Electronic Eng. 30, 440 (1958).

SEMICONDUCTOR DEVICE EVALUATION

249

43. E. J. Rymaseewski, and D. F. Singer, “Handbook of Semiconductor Electronics,” 2nd ed. (L. P. Hunter, ed.). McGraw-Hill, New York, 1962. 43. D. P. Kennedy, J . Research and Development 6 , 331 (1961). 44. D. P. Kennedy, Solid-state Electronics 3, 215 (1961). 45. W. Gtlrtner, and V. Boxer, Proc. Transistor Reliability Syniposium, New York, page 73, 1966. 46. W. M . Webster, Proc. I.R.E. 42, 014 (1954). 47. E. S. Rittner, Phys. Rev. 94, 1161 (1954). 48. T. Misawa, J. Phys. SOC.Japan 10, 362 (1955). 49. D. P. Kennedy, and R. R. O’Brien, J. Electronics and Control 11, 303 (1961). 60. H. Lawrence, and R. M. Warner, Jr., Bell System Tech. J . 39, 389 (1960). 61. D. P. Kennedy, and P. C. Murley, I.R.E. Trans. on Electron Devices 9, 136 (1962). 68. D. P. Kennedy, and P. C. Murley, J . Appl. Phys. 33, 120 (1962). 53. R. Beaufoy, and J. J. Sparks, A.T.E.J. 13, 310 (1957). 64. J. J. Sparks, Proc. I.R.E. 48, 1690 (1960). 66. V. I. Shveikin, Radiotekh. i elektronika 6 , 1158 (1960). 66. N. I. Meyer, J. Electronics and Control 4, 305 (1958). 67. C. T. Kirk, Jr., I.R.E. Trans. on Electron Devices 9, 164 (1962). 58. L. J. Varnerin, Proc. I.R.E. 42, 523 (1959).

LIST OF SYMBOLS A A. A.

= area = surface area = emitter junction area C = junction capacity Con = surface concentration of impurity atoms Cb = impurity atom density within bulk semiconductor D, = hole diffusion constant

D,,= electron diffusion constant D , , D I = impurity atom diffusion constant E = electric field Em = maximum electric field in a p-n junction I = electric current I. = junction saturation current I . = transistor emitter current I, = transistor collector current J = flux J, = hole flux J , = electron flux L = diffusion length L, = hole diffusion length L, = electron diffusion length M = carrier multiplication factor N D = donor atom density N A = acceptor atom density QB = transistor base charge Q ~ = E emitter junction charge Q, = total charge entering base contact R = steady state electron or hole recombination rate

250

DAVID P. KENNEDY

T

temperature (abs.) voltage Vi = internal “built-in” junction voltage V , = applied junction voltage V o = electron energy for pair production Va0 = applied junction voltage at start of carrier multiplication V L =~energy lost by an electron due to lattice collisions Vj = junction post-injection voltage Vr = reverse junction bias voltage V,, = collector punch-through voltage u p = junction space-charge width in p-type material a,, = junction space-charge width in n-type material & ( t ) = transistor transient base current k = Boltzmann’s constant n = density of electrons in conduction band no = equilibrium density of electrons in conduction band noe = equilibrium density of electrons in emitter region p = density of holes in valence band p o = equilibrium density of holes in valence band p O b= equilibrium density of holes in base region p = electron charge s = surface recombination velocity 1 = time v = electron transport velocity w = width CY = transistor common-base current gain CY; = ionization rate for electrons p = transistor common-emitter current gain pi = ionization rate for holes t o = free space permittivity K = dielectric constant u = electrical conductivity 7, = hole minority carrier lifetime 7% = electron minority carrier lifetime T~ = collector storage time constant 7e = emitter storage time constant ~~0 = collector storage time constant a t edge of saturation sr = base region transport time = potential

V

= =

Electron Emission Microscopy G. AloLLENSTEDT

. ~ N D F. LENZ

Institute of Applied Physics, University, Tubingen, Germany Page

I. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11. Electron Optics of a Cathode Lens.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. Principal Setup.. ........ , , . . . . . . . . . . . . . . . . . . . . B. System without an Aperture Diaphragm. . . . . . . . . . . . . . . . . . . . . . . . . C. System with an Aperture Diaphragm.. . . . . . . . . . . . D. The Diffraction Limit.. . . . . . . . . . . . . . . . . . . . . . . . . E. Consequences for the Design of Cathode Lenses,. . . . . . . . . . . . . . . . . . . . 111. Photo Emission Microscopy. . . . . . ................................ A. ResoIution Limit. . . . . . . . . . . . . ........................... B. Photoemissive Sensitivity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C. Instruments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D. Factors Influencing Emission,, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E. Applications.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IV. Secondary Emission Microscopy. ............................... A. Physical Basis.. . . . . . . . . . . . , ................................. B. Secondary Emission Microscopy Using Imaging Lenses. . . . . . . . . . . . . . C. Scanning Electron Microscopy with Secondary Electrons . . . . . . . . . . . . V. Ion Induced Emission Microscopy ............................... A. Factors Influencing Image Qua ............................ B. Instruments. . . . . ................................... C. Applications. , , . . .................................... VI. Thermionic Emission Microscopy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. Current Density and Energy Distribution of Electrons in the Case of Thermionic Emission ................................ B. Instruments and Applications, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .............................................

255

262 262 262 264 265 274 280 283 283 285

291 298 298 310 315 320 321 323 326

I. INTRODUCTION The high resolving power of the transmission electron microscope cannot be directly applied to the study of solid surfaces because the optimal thickness (“transparency thickness”) of specimens in the transmission type electron niicroscope is very small. It is of the order of the mean free path of the transmitted electrons between two successive elastic scattering acts which corresponds to a mass thickness of the order of gm/cm2. A number of successful methods to overcome this limitation of the transmission microscope have been devised to get 251

252

0. MGLLENSTEDT ANl) F. LENZ

direct electron microscopical information about surface structures. These are : (1) replica methods; (2) reflection electron microscopy; (3) electron mirrar microscopy; (4) emission microscopy. I n replica methods a thin foil of transmissible thickness is prepared which contains some information about the geometrical arrangement of structure details but in most cases little or no information about the physical properties and chemical composition of the original specimen surface. Another method for the direct observation of specimen surfaces is the rejlection electron microscopy in which a primary electron beam is directed onto the solid specimen surface. The back scattered electrons most of which have suffered only small or even no energy losses, can be focused by lenses to an electron optical image as in the case of the transmission microscope. Another method is the electron mirror microscopy in which the electron beam is directed towards the solid specimen surface which is held on a potential slightly negative with respect to the cathode. Thus the electrons cannot reach the specimen and turn back a t a point very near to the specimen surface. On their way back they are reaccelerated, and an image is formed which contains information about the electric or magnetic field distribution immediately in front of the specimen surface. All these methods have in common that the imaging electrons are produced by a separate electron gun and that the interaction with the specimen takes place far away from this gun. Emission microscopy, in contradistinction to these methods, is characterised by the fact that the imaging electrons are emitted by the specimen itself, and the concepts “cathode” and “specimen” have identical meaning. There are various methods by which a solid surface can be induced to emit electrons. Those which are of importance for emission microscopy, are (1) photoemission, (2) secondary electron emission, (3) electron emission under ion, atom or molecule bombardment, (4) thermionic emission, ( 5 ) TF-Emission, (6) field emission, The instruments can be classified according to these types of emission. In the four first types the specimen is usually a plane surface, and the electron optical magnification and image forming system is practically the same in all four cases. I n this article we shall be mainly concerned with this first group of instruments. In the emission microscopes with TF- and field emission the cathode is usually a hemisphere with a very small radius of curvature, the operating voltage is smaller, and the requirements for good vacuum are more stringent. We shall not treat field emission in this article since it has been treated exhaustively elsewhere. I n contradistinction to transmission microscopy where the image contrast is produced by the scattering of the imaging electron beam from the atoms of the specimen, the factors determining the contrast in emission

ELECTRON EMISSION MICROSCOPY

253

images are different: the variations of current density in the image may be caused by (1) variations of the eniissivity in the specimen surface in consequence of the characteristic properties of the surface matcrial such as its work function; (2) variations of the directional distribution of the emitted electrons due to the crystallographic orientation of grains or to the local surface orientation with respect to the optical axis of the imaging system; (3) variations of the emissivity of the specimen surface depending on the angle of incidence of the primary radiation releasing the electrons; (4) electric and magnetic microfields near the cathode surface due to variations in the contact potential or the magnetization of the surface elements.

The first electron emission images were taken by Goldstein (1) in 1878 with a very simple experimental arrangement. These images were however, not focused, and had a magnification of the order of unity. Further they were not used to study the qualities of the cathode but rather the nature of electron rays, and Goldstein does not call his imaging system a n emission microscope. Only half a century later when one had learned from Busch’s ( 2 ) theoretical paper that the magnetic concentration coils that were hitherto used mainly with Braun tubes, had imaging qualities in the optical sense, a detailed contribution to geometrical electron optics by Knoll and Ruska ( 3 ) was submitted on September 10, 1931, in which electron emission images of marks on the surface of a gas discharge cathode were shown, imaged by 50 kev electrons using a magnetic lens. Already in this investigation, the interchangeability of the magnetic lens by an electrostatic one (spherical condenser) was also shown. Even the use of a n aperture diaphragm to intercept off-axis rays was already shown to be advantageous. A slightly modified arrangement was used by Knoll et al. (4) for a special investigation of the distribution of the electron emission from a theriiiionic cathode. Instead of setting the electrons free by ion impact, therniionic emission was now used to image the surface. A higher magnification was attained by using a magnetic projector lens, and the electron image was recorded by photography from outside. Practically at the same time with the work performed by Knoll and his co-workers in the high voltage laboratory of the Technische Hochschule Berlin, a purely electrostatic cathode lens (“immersion objective”) was developed by Bruche (5) in collaboration with Johannson (6) in the

254

G . MOLLENSTEDT AND I?.

LENZ

AEG Research Institute in Berlin which later attained great importance in practical emission microscopy. 11. ELECTRON OPTICSOF

A

CATHODE LENS

A . Principal Setup The principal setup of a cathode lens as used in present day emission microscopy is shown in Fig. 1. The electrode distances and voltages vary in different instruments, and not all make use of a limiting aperture. I n literature, such lenses are often referred to as “immersion objectives” because the electron optical index of refraction, i.e., the electric potential, Cathode

Limiting Aperture

FIG.1. Potential distribution and ray paths in an electrostatic cathode lens.

is different on both sides of the objective lens, as in an optical immersion objective. There are, however, some principal differences between the optical immersion objective and the electron optical cathode lens: I n an optical immersion objective the refraction index at the specimen position is larger and of the same order of magnitude as in image space, and it is not essential for the imaging procedure itself but serves only to improve the resolution limit by a factor of the order of unity. In electron emission microscopy, however, the refractive index at the specimen surface is practically equal to zero, and it is an essential condition for the image formation that the refractive index in image space is greater by several orders of magnitude. For the following theoretical discussion of the resolving power of the emission electron microscope we shall first discuss a system with a cathode whose surface is considered to be an equipotential plane a t zero potential. Though in real emission systems the cathode surface is neither exactly plane nor an equipotential, and in fact much of the contrast in a n emission micrograph is due to deviations of the specimen surface from such idealizing assumptions, the results of the calculation will show the influence of the energy spread of the emitted electrons, of the electric and

ELECTRON EMISSION MICROSCOPY

255

magnetic field directly in front of the surface, and the effect of a suitably arranged small aperture on the resolving power. The most important part of the lens field with respect to the aberrations limiting the resolving power is the region immediately in front of the cathode where the energy of the electrons is still small compared with their final energy e U A to which they are accelerated by the potential difference UA between cathode and anode. Only in this region the inclination of the electron rays with respect to the optical axis is comparatively large, while in all other parts of the optical system the rays can be considered a s paraxial, so that these other parts give no essential contribution to the aberrations. For this reason we may at first restrict ourselves to a n investigation of the course of rays in the near vicinity of the cathode surface where the electric field is practically homogeneous and parallel to the optical axis.

B. System without an Aperture Diaphragm I n homogeneous electric and magnetic fields in axial (z-) direction the equation of motion for a n electron is

a

- (mv) = -eE

at

- e[vB],

where E and B are the electric and magnetic field, e is the charge, m the mass of the electron and v its velocity. Written in components

m x = -eyB mji = exB mi! = ejEl may be integrated to

Herein, the integration constants have been determined from the initial conditions that for t = 0 x = y = z = 0, and xo, yo, 5 0 are the initial velocity components. It follows from Eq. (3) that each electron is refocused to the axis a t 2nm tl = (5) eB ~

An electron, emitted with i o= 0, has a t this time reached the plane

25G

G . MOLLENSTEDT

AND F. LENZ

This plane z = z1is reached by an electron with i o# 0 a t a time tl' given by 2

(7) We obtain its distance from the axis in this plane if we insert t i , from Eq. (7) for t into Eq. ( 3 ) and form the absolute value

I n Eq. (8), we have introduced r = d m , PO = d m - . If i o is small compared with IEI/B, i.e., in the limiting case of a weak magnetic field, Eq. (8) yields

In Eq. (9) we have introduced i o = v o sin a ;io = vo cos a,where a is the angle between the initial velocity and the optical axis. If in Eq. (9) a is varied from 0 to 90' we find the maximal distance from the axis for (Y = 45". This means that all electron rays starting from an object point with an initial velocity v o cross an image plane a t z = z1within a circle of radius

if e = %muo' is the initial kinetic energy. A similar expression for the resolution limit has first been obtained by Recknagel (7). In the other limiting case that io is large compared with IEI/B, we have from Eq. (8)

From this it might appear (8) that the resolution limit may be reduced arbitrarily by a sufficiently strong magnetic field but practically this is not so. For if electrons are emitted with io >> IEI/B, there are also other electrons in the beam with smaller i odown to zero. Among these there will also be electrons, e.g., with i o= (3r/2)(IEI/B).For these, the sine function on the right hand of Eq. (8) becomes equal to one. This means that all electron rays leaving the cathode with velocities smaller than v o cross the image plane z = z1 within a circle of radius

257

ELECTRON EMISSION MICROSCOPY

smaller than the theoretical value &I = 10V cm In order to make hagn = 1 ev and \El = lo5volts/cm following from Eq. (10) with E = (m/2)vO2 a magnetic field of more than 6.7 * lo6 gauss would be necessary. Since the strongest magnetic fields that can be produced with conventional methods are of the order of several lo4 gauss, an improvement of the resolving power of the emission microscope by the application of a strong axial magnetic field does not seem very probable. For this reason we may leave aside the magnetic field in the following considerations. For the estimation of 6,1 it would have been still more advantageous not to use z = z1 as image plane but a neighbouring plane

where Az << 21. I n this case we have instead of Eq. (9)

r =

sin

mvo2 elEl

a

)

cos a - eB ~ z s i n a 2rmv0

If a is varied from 0” to 90” we obtain the smallest circle of least confusion if we choose

Its radius is

For the interpretation of these results it is irrelevant whether the electron rays are really focused in the plane Eq. (6) or Eq. (13) and whether the magnetic field B vanishes or not. Any lenses or other imaging systems which form a real or virtual image of the plane Eq. (6) or Eq. (13) in any other plane do not affect the resolving power if they are arranged in a region where the electron velocity is large compared with vo. This is also true for the following discussion of the effect of an aperture. For the definition of the resolving power, we have so far used the “circle of least confusion,’’ i.e., the circle within which all geometrical rays cross an image plane. A more detailed theory must take into account the distribution of the momentum (absolute value and direction) of the emitted electrons, calculate the intensity within the circle of least confusion corresponding to one fixed value of vo and then superpose all such circles for all occurring values of vo with their statistical weights. Such calculations have been made under various assumptions for the momentum distribution which dependtl on the type of electron emission, the

o.

258

MOLLENSTEDT AND F. LENZ

nature, energy, and direction of the incident particles, and of the cathode temperature. The results are similar to the expressions Eq. (10) and Eg. (16), i.e., they are proportional to t/elEl with varying factors of the same order of magnitude where B is the mean, most frequent or maximal energy in the initial momentum distribution (7, 9-16).

C . System with an Aperture Diaphragm Boersch (16) has suggested and quantitatively discussed an improvement of the resolving power of the electron emission microscope by using a narrow aperture diaphragm arranged in a plane where all rays leaving the cathode with zero velocity cross the optical axis. For a discussion of

20

4

f

FIQ.2. Definition of the rays s ( z ) and w(z), and of the back focal plane z j .

the effect of such a diaphragm we consider a purely electrostatic system (Fig. 2). The plane z = zo’ is chosen so that the field between zo and 20’ may be considered to be homogeneous, and the electron velocity in this plane is already large compared with vo. In Fig. 2 the field is symbolized by a lens which stands for any potential distribution 4 ( z ) on the axis of a field of axial symmetry between xo’ and zf. I n this case the electron rays in the region > zo’ are paraxial, and follow the paraxial ray equation

If we define two linearly independent solutions (17) by ~(20’) =

1;

~’(20’)

=

0;

~(20’) =

s(z) and

0;

~’(20’)

we can express the general solution r ( z ) in the region z

r(z)

=

r(zo’)s(z)

+ r’(zo’)w(z)

> zo’

w(z) of Eq. =

1,

(18)

by (19)

259

ELECTRON EMISSION MICROSCOPY

If we define the plane of diaphragm z

=

zf by

we have can be expressed in terms of the initial velocity components a t the cathode using Eq. ( 3 ) and (4). I n the case B -+ 0 we have

~’(2;)

r

=

Pot;

z = iot

e(E( + __ t2 2m

Since i is large compared with i oin the plane z = zo’, we have

If we insert Eq. (23) into Eq. (21), we have

It follows directly from Eq. (17) and (18) that the Wronski determinant is (2.5) (s(z)w’(d - w(z)s’(z>> = d r n

l/m

If we put z

=

z f , we have

and Eq. (24) can be written as T(Zf) =

f i.0

Vf

where vf denotes the electron velocity in the plane z focal length defined by

=

zf and f is the

260

G. MOLLENSTEDT AND F. L E N 2

From Eq. (27), it can be directly Been that a narrow aperture diaphragm of radius rf will intercept all rays for which r(z,) > rf, i.e., i o

Vf

>f rf;

e, =

m

2 Po2

> e4(zf)

If, for example, r f = 10 p, 4(z,) = 40 kv, f e,

> 40 kev . 4

=

=

5 mm, all rays with

0.16 ev

(30)

are intercepted. Thus a considerable gain in resolution may be attained, but of course, the image intensity is greatly reduced. If the initial velocity v o of an electron is smaller than v,(r,/j),it will pass the aperture with any initial direction a. If, on the other hand, vo exceeds vf(rf/f), only such electron rays can pass for which sin a is smaller than sin a.

=

V f Tf

-vg

f

The solid angle within which all rays with initial velocity aperture leave the cathode is given by 2ir

Lao

sin ada

=

27 (1

- d1 - @

DO

passing the

7)')

For v o > vf(rf/f), this solid angle decreases rapidly with increasing vo. This means that the aperture has a strong filtering effect, and we can, for an estimation of the resolution limit, replace v o in Eq. (10) by v,r,/f. Thus we obtain

With 4(zf) = 40 kv, /El= 100 kv/cm, rf = 10 p, and f = 5 mm, we cm = 160 A. have 6,1 = 1.6 There is experimental evidence (17, 18) for the effectivity of the filtering action of the aperture diaphragm. The experiments show that, if a very narrow diaphragm is used, the width of the velocity distribution of the electrons passing the aperture becomes practically independent on the initial velocity distribution at the cathode [Eq. (33) does not contain c!]. Other suggestions to reduce the width ofithe energy distribution by a filter lens or an electron mirror (19) have also been made but so far no successful realization of such suggestions has become known.

ELECTRON EMISSION MICROSCOPY

261

D . The Difraction Limit Diffraction effects set a fundamental limit to an arbitrary reduction of resolving power by using correspondingly narrow apertures. It can be deduced from Eq. (3) and (4) that the inclination with which an electron ray is crossing the axis after being accelerated by the potential difference U , is given by (34)

m

If by use of an aperture at anode potential [uf = 4 ( 2 e / m ) U , ] , f o is limited to values below r f u f / f [see Eq. (29)], we have (35)

It is irrelevant for this discussion whether a real image is formed in the plane z = z1 or only a virtual image which is projected by a lens or lens system to any other recording plane. The limitation of aperture expressed by Eq. (35) will result in a limitation of resolving power by a diffraction disc of radius XI 6~ = 0.61 r/

(36)

where h =

2/2emU,

(37)

is the electron wavelength in the space at anode potential. For this reason it is of no use to make rl smaller than a value

for which 6el from Eq. (33) and 60 from Eq. (36) become equal. For U , = 40 kv, A = 0.06 A, E = lo5 volts/cm and f = 5 mm, the optimal aperture radius becomes 5 p . In this case, 6,l as well as 60 have the value

If we assume that the resolutiou limit is of the order of the sum of 6,1 and 60, we obtain for our example 6 = 80 A.

262

G . MOL L E NS T E DT AND F. L E N 2

It must, however, be kept in mind that this result has been deduced assuming a plane equipotential cathode surface, which may be an unrealistic assumption. Some theoretical investigations have been made on the reduction of the resolving power resulting from field perturbations by an uneven cathode surface, variations of surface potential (e.g., contact potentials), space charge etc. (8, 10, 20-22). Another advantage of a narrow limiting aperture is the increase in depth of focus which is reciprocal to the effective opening angle of the beam contributing to the image formation. Bartz (23) has demonstrated that in his secondary emission microscope the depth of focus is about 5 times superior to that obtained in an optical microscope. E. Consequences for the Design of Cathode Lenses From the results of the above considerations we see that the shapes and potentials of the electrodes of a cathode lens should be chosen such as to make the field in front of the cathode as strong as possible and to produce the back focal (“crossover”) plane z = zf behind the anode where a fine limiting aperture can be arranged and adjusted. The optimal choice of the lens parameters has been treated in a number of theoretical and experimental papers (24-2Sa). For cathode lens systems consisting of cathode, Wehnelt electrode, and anode which produce a real image of the cathode without using an additional lens the following general rule may be stated (27): If UA is the voltage applied between cathode and anode, the field strength in front of the cathode is always smaller than UA/cm. Since the field strength in front of the cathode is limited by electric breakdown, some authors have used high voltage pulses of a few microseconds duration for the operation of their emission microscopes (25, 28-30). 111. PHOTO EMISSION MICROSCOPY

A . Resolution Limit As shown in Section I1 the resolution limit 6,1 of a cathode lens is approximately given by 61, = e/elEl if no limiting aperture is used. Herein, e is the most probable initial energy, and E the electric field strength immediately in front of the specimen surface used as cathode. Lukirsky and Prileiaev (31) have measured the energy distribution of the photoelectrons emitted from a polycrystalline silver surface under ultraviolet irradiation with X = 2537 A. It is shown in Fig. 3. I n horizontal direction the relative kinetic electron energy is plotted in units of the maximum photon energy following from Einstein’s relation for the photoelectric effect. I n vertical direction the energy distribution

263

ELECTRON EMISSION MICItOSCOPY

function N ( e ) is shown where N ( E ) & is the relative number of electrons with energies between e and e dt. Figure 3 shows that for a thick t,arget the most probable value is about 0 . 4 ~ , , , ~This ~ . result is not only found with silver but also with all other studied target materials (-41, Zii, Cu) and different wavelengths of uv irradiation, i.e., different values of tmnX. Icor emission microscopy with photoelectrons it is interesting to note t h a t for a foil 100 A in thickness the niovt probable ~ ~ ~ higher. energy of about 0 . 6 is~somewhat The reason is evidently that in a thin foil the primary photoelectric effect can oiily 1 0 025 050 075 occur near to the surface so that on their E/Emor way to the surface the electrons have less FI(+.3 . Energy distribution opportunity to lose energy than electrons of photoelectrons eniitked under which have beeii excited in deeper layers of iiltraviolet irradiation with A = a thicker target. Since most emission micro- 2537 A from ( 1 ) a thick silver scopic specimens are thick, the most proha- target, and ( 2 ) froin a silver foil ble emission energy to be used in the expres- 100 A in thickness (Sf). sion for the resolution limit is t = 0 . 4 E i n j x . If hv is the photon energy of the exciting uv radiation, and hv, the average work futictiott of the target,, we have, according to Einstein’s relation for the photoeffect

+

t

-

hv

=

hv,

+

or where A, = C/V, is the cutoff wavelength. For a polycrystalline zitic surface A, corresponds to the average value of the work functions of the various crystallites forming the surface. This value depends most sensitively on the surface roughness, gas adsorption and surface oxidation, but according to experience the practical cutoff wavelength for zinc is about X, = 3000 .I. If an extreme pressure mercury lamp (HBO 107 of Osram, West Germany) is used, the uv radiation behitid a Hcrasil quartz lens which is used to focus the electric arc otito the specimen has a spectrum with a shortest wavelength A, = 2400 A. If we insert this value for X into Eq. (41)’ we have with hc = 1.24 . lo-‘ ev C I ~ =

0.4hc

(k k) -

=

0.4 ev

264

G. M6LLENSTEVT A N D F. LENZ

The electric field streiigth in front of the cathode in the lens used by Koch (32) was determined from measurements in the electrolytic tank to 15 kv/cxn. From this a theoretical resolution limit of (43)

would follow. A more optimistic and more realistic value of &I = 16.50 11 results if we use the wavelength of the strong line X = 2630 A i n the LIV spectrum instead of the short wavelength limit where the irltellsity is very low. Indeed, Koch (36) has, with a Zn cathode and using the HBO 107 lamp, reached a resolution limit of 61, = 2000 A even without using a limiting aperture. A considerably improved resolution of about 1000 A was attained, however, by inserting an aperture 30 I.C i n diameter in the back focal plane of the cathode lens. IJnfortunately, it has not yet been possible t o use a much smaller limiting aperture down to the optiinal diameter of about 15 I.C because of the low intensity of the uv radiation, though according to Eq. (39) this would lead to a theoretical resolution liniit helow 200 A. It seems, however, possible to increase the field strength in front of thc cathode, and to reduce the difference between X, arid X by using rorresponding uv filters. The latter measure would mean a great reductioii of intensity, so that it does not seem practicable a t the preseiit performance of uv sources. An optimistic estimation of the results of an increase of field strength, however, makes it seem possible that a limit of about 250 A should be attainable with the present methods, provided that suitable specimens with a plane surface are used.

B. Photoemissive Sensitivity The photoemissive sensitivity i.e., the ratio of emission current and incident electromagnetic power is a function of wavelength which, for most metallic cathode materials, is increasing with increasing quantum energy, see Fig. 4. C. Instruments The principle of the photo emission microscope was first described and tested by Briiche (34). Mahl and Pohl (35) constructed a microscope of improved performance and applied it to studies of a number of metallic and nonmetallic surfaces after various mechanical, chemical, and thermal surface treatments. Though the iiistrumental design arid the applications contain many most interesting features we cannot got into much detail since this review article shall mainly cover recent developments not older than 10 years,

E1,ECTHON EM1SSIC)N MICROSCOPY

3

-R

2'755

' A

2480

10-4

40

*

265

2255

I

* C d of 8 3 ' K

io

X C d af293'K

-k

5 5

A / at 293 ' K

0 Zn a/ 293' K

s;'c I

C

0

Y

u 1C

4

4.5

-

5.0

Av

cv 5.5

FIG.4. Nornial photoemissive sensitivity verniis wavelength of incident radiation (33).

kv

Frc:. 5 . I<. L. Huguenin's photo emission rnicsroscope (36): (1) microscope head; ( 2 ) cathode; (3) ion gun; (4) projector; ( 5 ) niagnctic deflection; (6) fluorescent screen and camera.

266

o.

M ~ L L E N S T E D TAND F. LENZ

1. E . I,. Huguenin, 1957 (36). Huguenin’s paper contains many experimental details and theoretical considerations. His microscope is electrostatic, aiid a projector lens is devised for a maximuni electroil optical magnification of 200. The acceleration voltage can be varied between 15 and 30 k v ; mostly 25 kv is used. With a mercury pump “Normavap

FIG.6 . Micurowope head with an externally adjustahle racok for specimen displacement in rtxial clircc*tion ($6).

60” (C.G.R.) a vacuum of

to lop6tor is maintained. Figure 5 shows a schematic representation of the arrangement. Two interchangeable microscope heads were constructed. The one shown in Fig. 6 allows a displacement, of the specimen of about 60 mm in axial direction. This displacement is required in order to be able to arrange an ion gull or a cathode sputtering device below the specimen, if the specimen surface is to be etched by ion impact under vacuum before observation.

ELECTRON EMISSION MICROSCOPY

267

The microscope head shown in Fig. 7 is used if a therriial treatment of the specimen is required. It caii be heated either by rlectroii bomhardrnent from behind or by direct contact with a small steatite furnace (Fig. 8). The cathode lens consists of the specimen, a Wehiielt electrode a t cathode potential, and a grounded anode. The electroil optical properties were calculated following Hepticr's theoretical paper (27).A distance of G mm betweeii specimeii and Wehiielt electrode was chosen i n order to simplify the uv irradiation. The bore diameters of the Wehiielt electrode and the anode were 13 a d 10 mm respectively, the distalice betwceti Wehnelt electrode aiid anode 12 mni, the thickness of the Wehnelt electrode X.5 mm. In this case the field strength at '"B-A the cathode surface was 2400 volts/cm a t an acceleratioii voltage of 25 kv. N o liniitFro. Mic.roscopc,hrnci fur iiig aperture in the back focal plane was specilllcn lleatlIlg ( ~ 6 ) :Aused. anode, \ { , and \V\;-\Vehnelt The uv sotlrce (high pressure me.rc1lr.y elertrodes, C-s~eci~lle~l;1'lamp) was llot Iiionochroliiatic, but in the fila11lent; S-ln51llatinR Inaterid case of a zinc specimen a great deal of the eniission is due to the 27.50 A line. ]Tor A, =. 3000 A, this corresponds to - (I,%<) = 0.3 I-', i.e., to a resolution limit of 0.6 p and a useful niagnification of about 200 if the resolutioii limit of the screen (or of thc photographic plate) is about 100 p. Alumina

Steatite specimen

FIG.8. Resistanre fiwnare for sprc*inienheating (36). 111 some of the best images a resolutiori of this order was observed. In other pictures the resolution limit is restricted by speciineii contamination under the influence of the ion irradiation, electric instabilities, flashover aiid surface charging phenomena. As the cutoff wavelength depends

208

C . MSLLENSTEDT AND F. LENZ

sensitively on the surface material and its state of oxidation, contaminntioii etc., the resolution limit varies from specimen to specimen. The arrangement for specimen irradiation is shown in Fig. 9. The Philips extreme pressure mercury lamp SI’ 500 was used as uv source. At a total power input of 500 watts a luminous flux of 15,000 lumen is emitted into a colic of 80” aperture, arid the power emitted by the niost iiiteiise 3650 A line is about 10 watts. From a zinc specimen an emission current density of 2 pamp/cm2 was attained. This correspoiids to ail exposure time of about two seeoiids a t a inagiiification of 60, if a Guillemiiiot “collodium No. 4” film is used. An advantage of this simple arrangement is that thc uv source as well as the optical focusing lens can be arranged outside the microscope tube, I

1-

i

I

_1

..

Fro. 9. Illrimintition for photoelectric clecstrori crriission (.%) : ( I ) sprcirntm; ( 2 ) p r o t c 4 v e ring; (3) Wehrielt electrode; (4)anode.

and enough space is left inside for a barium evaporation device and a n ion gun. Surface embossment, polishing grooves, grain boundaries and dust particles are imaged with good contrast. The local variations of the surface inclination relative to the illumiiiatiiig beam and shadow effects give a plastic and brillaiit iinpression. 2. Iy. Koch, 1958 (36). The photo emission microscope used by ICoch (36) is represented in Fig. 10. The light optical systeni coiisists of two quartz lenses L which focus the extreme pressure mercury arc of a n Osram HBO 107 lamp H on the specimen. This lamp emits lo5 sb at a power dissipation of 100 watts. The shape of the Wehnelt electrode 2 allows a n opening aiigle of the light beam of 30”. The distances aud bore diameters of the cathode lens were chosen much smaller than in Huguenin’s microscope (36) in order to obtain high inagiiification and resolving power. In most cases, a voltage of -40 kv was applied to the cathode, and about -36 kv to the Wehrielt electrode. With this choice of the Wehnelt potential and a cathode-Wehiielt distance of 2 mm, the focal length

ELECTRON E M I S S I O N MICIZOSCOPY

289

became 9 mni, mid the back focal plane was in a position behind the anode bore whwc the aperture could be arranged. The specimen X is fixed by a screw cap to a heatable holder 0. The cathode assembly I< is arranged in a large disk insulator V. A flexible menibraiic ;\I and supporting balls N allow a displacement perpcridicular to the axis in spite of the big croBs sectioii on which the pressure difference is acting. The other opeiiing 0 which is iiicliiied by 15’ with respect to the axis can be used for visual inspection, for a sc~conclradiation source, an ion

FIG.10. Cross section through Koch’s photo (mission microscope with I I V irrittliation (.32): A-anode; B-tipertrrres; (1 arid tJ---aperture :djustment; F and 0--wintlows; H-rncrcwry lamp; I and V---insulators; J-adjusting screws; K-cathode assembly; I,--lensrs; M--flexildc nrwihrane; N-httll-bearing ; 0-spec.irnen holtler; S-guard cylinder; T-ariodc holtlrr ; X-spwimon: %--Wehnelt, electrode.

gun, a vacuum abrasion rnechaiiism or a sniall evaporator. A bending of the optical axis as used in some earlier photo eniissioii microscopes is not necessary since iiiost, of the uv radiation scattered from the cathode is intercepted by the limiting aperture and the additional apertures T, C, and R. Below the cathode letis, at1 interinediate tube and an electrostatic projector lens is arranged. Th r filial image oil the fluorescent sween can be observed through a powerful eyepirce tube with 20-fold magnification. A photographic camera can he separatcd from the rrst of the vacuum space by a slidr valvc. The vacuum of about tor was pumped with an oil diffusion pump. In order to study the efTect of a short wavelength on the photo emission

270

G . MOLLENSTEDT AND F. LEN2

and the image quality, the mercury lamp was compared with hydrogen lamps. When a Philips hydrogen lamp with a power dissipation of 24 watts or a “Point Source Hydrogen Arc HF 7” of Manufacturers’ Supply Company Kent was used, the photo emission was about 50 tinies lower. Since a great deal of the short wave end of the uv spectrum is absorbed by the windows and lenses, a gas discharge lamp of the Lyman type burning inside the microscope column without optical focussing elements was constructed. Figure 11 shows some details of this lamp. The open discharge canal is arranged inside a capillary tube K of quartz glass 50 nim in length with 0.85 mm inner diameter. It is sealed to another quartz tube containing a high voltage electrode H whose cross swtion is larger because of the great heat production. I ts inside borc leaves the gas through and serves for a visual alignment of the capillary tube with respect to the specimen. The quartz tube is tightly enclosed by a water jackct 1\1. The flange F is sealed to flexible bellows so that a n easy adjustinelit is possible. The opening B is arranged as near to the specinien as possible. The electrode V facing the cathode lens system is made of high-polish V2A steel. It consists of the interchangeable aperture B(0.4 or 0.6 mm in diameter) and the proper discharge electrode R which is made of aluniiiiuin as the opposite electrode H in order to keep the sputtering rate low. The vacuum seal between quartz tube and water jacket &I and high voltage electrode holder consists of gasket rings. A viriidur tube R between the gasket rings serves to reinforce the fragile quartz tubc. On the front side the lamp is closed by a n adjusting window J. The gas inlet can be controlled by a gas throttle screw G. The radiation spectrum of this hydrogen discharge is extended into the short ultraviolet. In the Schuman region (ca. 1200-1850 A) it eniits mainly the Lyman a line (1216 A) and a number of lines near 16.50 A. It is interesting t o note that the photoelectron yield is much higher for short-wave uv than in the long-wave region (33, 37). This increase in yield, however, is reduced by the lack of a focusing system and the necessity to keep the voltage stable by a distance of a t least about 50 inin between lamp and cathode. This reduction is important, though the angular cinissiori characteristic has a sharp maximum in direction of the capillary axis. Within the microscope column some phosphorus peritoxide was arranged in order to remove water vapor which has a very high absorption cross section for short-wave uv radiation (%), and the hydrogen from a Kipp apparatus was predried. The discharge could be operated with a n alternating voltage of 2 kv or with 1 kv direct voltage. I n order to exclude the discharge plasma from the microscope column a LiF window 0.4 mm in thickness was arranged in front of the aperture B, which also absorbed some of the uv radiation. Compared with the Hg extreme pressure lanip

Frc,. 1 1 . Hydrogen discharge lamp ( 5 2 ) : B-aperture: 1)-gas int:ikca: E, H, V-electrodes; throttle, J-window; K, &--quartz tube; M-cooling jacket; R-insiilntor tube; S-gaskets.

F-flange;

C,-

272

Q. MOLLENSTEI)T

A N I ) 1'. L E N Z

(4.4amp) the exposure time rorrespondirig to the same optical density in the photographic plate was 30 to 60 tinies longer with the hydrogen lamp. There was no significant diffcreiice in image quality or intensity between the operation with alternating current (about 80 ma) and direct current (with electrode H negative). Only if the high voltage electrode H was positive, the inteiisity was considerably reduced. Figures 12(a) and 12(b) show the influence of the uv source on the image of a zinc surface. In (a) where the Hg lanip is used, there are great

FIG.12. Photo emission image of a polished zinc siirftice ( 3 2 ) : (a) with a mercury rxtreme pressure lamp IlRO 107; (b) with the hydrogrn lamp shown in Fig. I I .

local differences in electron emission. The image shows a grained structure, aiid its lines are interrupted because otily uv quanta from the shortwave end of the Hg lanip spectrum have sufficient energy to emit electrons from all parts of the surface. Figure 12(b) shows the same specimen irradiated by the hydrogen lamp, It gives a more uniform distribution of emission, and the image is more brilliant arid plastic. The same influerice of the photon energy could be observed with Ti, Zr, and some steel specimens. 3. H . Rethge, H . Egyert, and K . Herbold, 1958 (39). An interesting combination of photo emission and ion induced electron emission realized

ELECTHON EMISSION MICROSCOPY

273

by Hethge and his co-workers is stiocw in lcig. 13. The ~ i radiatioli v froin a Iiiercury rxtrenle pressure lamp HBO 107 is focused by a quartz leiis 7 onto the specilnen 1 through a quartz window 10. From the opposite side, the speciiiieii surface is bombarded by ions froin a canal ray tube a t a n

FIG.13. Combination of uv irradiation and ion bombardment (39):(1) specimen; (2) Wehnelt electrode; (3) anode; (4)objective aperture with adjusting mechanism (5); (6) quartz window for IIV radiatiorl; (7) quartz lens, focal length 25 mm, (8) canal ray discharge tube: (9) adjusting rnerharllsm for the specimen; (10) specimcLn heating.

angle of incidrnce of 2So, in order to etch the surface and to enlit electrons. The acceleratiou voltage (variable froiii 5 to 20 kv) for the ions is supplied by a second high voltage generator. 0 1 1 the cathode side it is connected with the high voltage generator for electron acceleration, and the positive

274

C;. MOLLENSTEDT AND

F. LENZ

terminal gives the anode voltage for the ion source. The temperature of the specimen can be varied by meaiis of ail electric heater 10. The vacuum is about tor. The intermediate image is magnified to a total magnification of 450 by means of a projector lens. The micrographs are recorded photographically inside the column. A mechanism allows a precise adjustment from outside of an aperture diaphragm in the back focal plane of the cathode lens during observation. -4resolution limit of 1000 A could be attained. I). Factors Influencing Emission 1. Surface Layers with Detrimental Eflect. a. Oxides and other compounds with the specimen material. Specimens prepared in air usually

FIG.14. Inrrcasc of photo emission from a einc surface by abrasion under vacuum ( 3 2 ) . Abrasion in air and subsequent immediate introduction into vacuum has nearly the same effect. Magnification 75-fold.

are poor emitters, presumably owing to surface layers of oxides or other compounds or gas adsorption. By abrasion in air or under vacuum such layers can a t least partially bc removed and the emission increased (Fig. 14). I n poor vacuum, especially a t high temperatures, the oxide layers gradually grow again. Huguenin (56) has studied the effect of several solvents on freshly abraded zinc surfaces, and found that distilled water, alcohol, benzene, arid trichlorethylene reduced the emission but pure ether

ELECTRON EMISSION MICROS(‘0PY

275

arid acetone had no detrimental effect. Inipurc solveiits Ieavo a film twhind which stops the emission c.omplctcly. The emissioii from some spccinieii inaterials (l’t, Ni, Ag, Z i i , ‘iu) could h r much increased by an admisfiion o f air (36, 40). h. Contamination by organic polymers. 17ndcr the influence of uv, electron or ion radiation, a polymer layer is formed owing to the presence of organic molecules it1 the residual gas which iiorinally reduces the image contrast. In the case of a crystnllinc gold surface, however, IIuguenin

FIG.15. Selective contaniinatiori

oil H

gold siirfaw :it

Inrdliirii

ion currents (36‘).

(36) has found that this contarnination may even enhance the contrast (Fig. 15) between different grains. This rffect is ascribed to a selective contaiiiiiiatioii 011 different crystal facw. After bombarding the speciinen for several iniiiutes with the central part of an intense fine beam (about 1 pa) of argoii ions produced in a discharge tube a t a distance of about 35 ~ i i mfrom the cathode with a discharge voltage of 25 kv and a total current of 100 pa, an excelleiit photo emission is obtained from Au, Ag, Zn, Cu, Xi rtc., aiid the grains become visible with good contrast (36). After a few minutes of uv irradiation the emission is reduced again.

276

G. MOLLENSTEDT AND F. LENZ

With some specimens the intensity of the ion source was iiot sufficient to remove the unwanted surface layers. Therefore the effect of ail intense

Lcm,

FIG.16. Discharge tube for clcariing t h r surface by intense ion bonihardnlent (36').

gas discharge was studied (36). I n the discharge tube shown in Fig. 16 pressure of 0.05 tor was used, aid the voltage could be varied from ,500 to 8000 volts. With Ag, the best results were obtained with 2000 volts and 2ma, with Au, U, A1 8000 volts and 3 ma. After this treatment an additional ion bombardment from the ion source was performed (as above), in order to clean the surface from the atoms which were rediffused to the surface from gas during the discharge process. This procedure made the crystal structure of Ag arid Au well visible, but satisfactory results for Z n and Cu were iiot obtained. I n order to obtain a direct effective surface cleaning without the unwanted rediffusion process which occurs in the low vacuum of the gas FIG.17. High inten- discharge, another ion source with a working sity Ar ion source, work- voltage of 10 kv and a discharge current of 3 ma ing voltage 10 kv, ion was constructed (J6) which is represented in current 2 to 3 ma, staMizing resistance 100 Fig. 17. After bombardment of 2 to 15 minutes with kQ (S6).

ELECTHON EIIIIHKION MTCIlOKCOPY

277

argot1 ions froin a distance of 18 m n with an ioii current density of 10 niajcni2, the grain structures of -2g, L Zn, l~ Cu~ became , well visible, but the results with A1 and l l g spwinicns w r e still unsatisfactory. I t seems that the varuiitn must be considerahly iniproved i n order to prevent the formatioil of oxide layers. An additional increase of the ioii current was found to be of no USP because i n this rase the resulting surface roughness would prevent thc observatioti of the grain contrast.

Fic:. 18. Retlirc*tion of cmntamirintion liy increased temperature. Photoemivsion from R polislied zinc surface after I,:{ arid 10 iiiiri i i v radiation at (a) 20"C, (h) 100Y: (32).

Koch (:?a)has found that the contamination call be prevented by increasing the temperature of the specimen (see Fig. 18). If the speciriieti is kept at normal temperature, the contrast is greatly reduced by surface contarnination after a few minutes while a surface kept a t 100" can be observed over a much longer period before the contamination effect begins to play an important role. 2. Increasc (tf Emission b g Lay(>rs Intr~ntionallyEuaporatd onto the Burjacc. Gross and Seitz (40) rvaporated thin active layers of varying thickness onto the surfaces. ,4e with clean metals heated to thermionic etnissioii, they obtained crystal structure images from nickel surfaces by depositing barium atid heathg. The barium was selectively vaporized

278

G. MOLLENSTEDT

AND F. LENZ

from different crystal surfaces,’ and a contrasted thermionic emission image of the heated cathode was obtained, The good contrast remained even in the photo emission after cooling to room temperature for some time but then disappeared again. When the specimen was heated again, the good contrast could be restored. Spivak et al. (41) have evaporated thin Sb-Cs layers on ferromagnetic material. The work function of Sb-Cs layers is so low that radiation

FIG.19. Top: ThF4wedge with n thin carbon film on a aluminized glass plate (4%’). Bottom: Nodes and antiriodcs of standing uv wave, inadc visible by the variation of photo emission in the emission microsrope (42).

from the visible part of thc spectrum can be used to emit photo electrons. More details will be given in the following paragraph on applications. h46llenstedt et al. (42) have used a modification of Wiener’s classical experiment who has demonstrated standing light waves in a very thin photographic layer inclined by a small angle with respect to a reflecting surface. They have evaporated a wedge-shaped ThFI layer onto a reflecting surface. There is a strong variation of radiation intensity on the wedge surface owing to the formation of standing electromagnetic waves. Figure 19 explaius the procedure.

ELEC'THON EMISSION MICROSCOPY

279

On ail ordinary mirror glass plate, ail aluminum layer about 1000 A in thickness and a ThF, wedge of continuously increasing thickness are evaporated. By honihardment with 40 kcv ions a t a current density of lo-' amp 'cni? and a vacuum of .5 . lo-&tor, a thin layer of hydrocarbon polymers a few i n thickiiess is formcd 011 the wedge surface. This layer has low emission but it can be used as a probe film. Ultraviolet irradiation from a Hg HRO 107 source with an aiiglc of incidence of about GO" with respect to thc surface rioriiial forms a standing wave pattern in the

FII:.20. -4goltl lager evaporated on glass is (*overedwith a T h F , distarice layer of constant, thickiiess corrcqonding to a i l aritiriode of the standing wave on its surface. On the TIIF, layrr gold strps of 0 , 5 . 1 0 , 20 nlid 45 A thickness are evaporated. From the photo emission image tlic t,hickrirss depeiidenc~eof the emission can be determined. The iiiaximal emission ia obtained from the gold step 10 A iii thickness (42).

wedge (4.2). The dependence of photo emission on the wedge thickness can well be obscrved in the emissioit inicroscope, as Fig. 19 shows. From the distance of the maxima and minima in the emission pattern an effective wavelength of 2.5.50 A\can b(>calculated. Shorter waves are not effectivc because of the ahsorption by the optical system made of quartz, and longer waves ar(b iiot effective since the cutoff wavelength is 2700 h correspondiiig to a work fuiictioii of 4.5 ev of the polymer layer. From the distance of the first emission maximum from the aluminum substrate a reflexion phase shift of 124" can be calculated.1 Gold and aluminum were a k o used as photo emission probes. A probe thickness of 10 A gold (see Fig. 20), atid of 40 -4aluminum (possibly

280

C;.

M6LLENSTEDT .4ND F. LENZ

partly oxidized) was fourid to give maximum emission. Compared with the emission without) a distance layer, the emission from gold was increased by the factor 2.5, from aluminum by 3. Koch is continuing his iiivestigations under considerably improved vacuum conditions of the order of 10-* tor to make use of this effect to increase the photoclectric yield aiid to obtain contrasted images of surfaces by the different reflexion phase shifts of different phases and different crystal faces of the same material. Koch (J2) has obtained a series of iiiiages of polished zinc surfaces onto which a ziiir layer was evaporated under vacuum. The preferential depositioii a t some germination centers gives a decoration effect.

E . Applications

111this review we can only mention a few characteristic examples for the great number of possible applications of photo emission microscopy. H uguenin (J6) mentions photo emission images of surfaces of uranium aiid Ag-Cu alloys, arid he compares the photo emission image of a silver siirfacc with an optical micrograph arid ail emission picture in which the electrons are emitted under ion bombardment. A reversal of contrast hc3tween photo emission aiid ion induced emission is observed. Figure 21 shows a cleavage surface of a zinc. monocrystal cleaved a t licluid air temperature (32). The horizontal deep groove was evidently formed during the cleavage process. Starting froin the edges of this groove there are some narrow stripes of much lower emission, parallel to each other and inclined a t 60' with respect to the groove. If the liiniting aperture i n the focal plane of the cathode lens is a little displaced in lateral direction, a reversal of contrast is observed, and the dark stripes become bright. This indicates that the angular distribution of the emitted electrons has a preferential direction. By optical interference measiirc.ments it was found that the corresponding parts of the surface are inclined with respect t o each other, and by X-ray diffraction they could be identified as twins. Spivak and his co-workers (41) have observed the domain structures of poly- aiid mouocrystalline cobalt in a photo emission microscope of very simple construction. The cobalt specimen is covered with an extrririely thiii Sb-Cs layer, though which the magnetic inicrofields can penetrate. Since the Sb-Cs layer has a very low work function the photo elcctrons can he emitted by visible light from an incandescent bulb. A shielded magnetic lens is used to magnetize the specimen and t o image its surface. The magnetic field strength amounts to GOO or 800 gauss, the cathode voltage is 6 to 8 kv, arid a vacuum of 5 . lo-? tor is used. Oil vapor is frozeii out by a liquid nitrogen trap. If the sensitizing cover

oii the ferromagnetic is thin enough, a sufficieiit iniagr inodulat ion by the riiicrofields is attaiucd at a 60-fold electron-optical iiiagiiification. With inversion of thc direction of the iiiagiietizitig field the iinage contrast is reversed, too. It is supposed that thc imagcx contrast is due not oidy to the influeiicc of the niicrofields on the electroil rays within the cathodc leiis

FIG.21. Cleavage siirfare of a zinc nionorrystal ( J 2 ) . 1 )ark sagittiform regions beronie Ixight if the liiuiting aperturc: is tlisplaced. This irit1icatc.s a prcfrrential direction in t h e photo cniission from rrionoc,rystnlliiIc surfaces.

but possibly also to a dependence of the work fuiiction 011 the iiiagiictic. field strength. I’igure 22 shows iLti emission iiriagc of thr domaiii structure of a monocryst,alliiie cobalt surface. The light-optical powder iiiethod g i i w the sanir pattern. Thc authors state that the photo emission iiiethod giws electron-optical iinages of the local distrihutioii of magnetic microfields on the surface which art’ equivalent to light-optical images aiid hctter than former rmission iiiicrographs with sc~oridaryrlrctroii rmission. The c.lcctroii optical methods

282

G. MOLLENSTEDT AND F . LENZ

give more iiitense and contrasted images of magnetic microfields than magneto-optic methods using the Kerr effect whose intensity is hardly sufficient for visual observat,ion and which requires long exposure times for photographic recording. Bethge and co-workers (39) found that a freshly polished and etched nickel surface which was directly brought into the vacuum showed a similarly strong contrast as in the optical microscope. On the other hand, an emission micrograph of the same surface iiiiaged with electrons released by air ions, showed much less contrast hut increased plasticity,

FIG.22. Photo emission image of the domain structure on the surface of polished monocrystnlline cobalt ( 4 1 ) .

and some grains were brighter than in the case of photo emission. It is interesting to note that directly after the ion bombardmeiit the photo emission image had also considerably changed its appearance. TCvidently, some residues from the etching process are removed from the pits by the sputtering action of the ioiis, so that some formerly dark regioiis became bright. When the temperature was increased to 150" a t a vacuum of lo-* tor, the brightness of the grains was reduced, presumably in consequence of oxidation. I n some photo emission micrographs with a resolution of about 1000 A a surprisingly good reproduction of very small details was obtained (39). Photo emission micrographs of cerium metal surfaces (39) contain more image information for the metallographer than optical micrographs

ELECTILON E M I S S I O N MICItOSCOPY

283

because of the distinct difference ill emission from different materials. With iiicreasiiig temperaturcl, the contrast a t the grain boundaries beconies stronger, but regions which w c w bright a t 20”C, showed greatly reduced emission already a t 150°C. This is attributed to oxidation in the comparatively poor vacuuni of 1 0 P tor.

1Lr.

SEC‘OY l).iItY

li:M IShIOU

AIICHOS(’0PY

. I . I’hysical Hasas 1. Etwrgy DistriLutzoii o j Sccondnry Electrons. The energy distribution of secondary electrons emitted from the surface of thick specimens under the influence of slow (100 to 2000 ev) primary electrons is well

FIG.2 3 . Cornnion representation of t he encrgy distributions of secondary electrons from various targets (Ta, 310, W, Ag, Zn,N g , brass, Be on %lo,NiFe, CuFe, CuBe) nicasured by Kolluth ( $ 4 ) . .411 experiniental points tire situated in the hatched region.

known from precisc measure~i~ents b y inany authors. Figure 23 shows a common representation of the energy distributions measured with various target materials ( 4 4 ) . Recent measurenieiits with ail c.lec.trostatic high-resolution analyzer (18) in which primary electroils with an energy of 5 and then 30 kev penetrated thiii foils have shown that the energies of the secondary electrons emitted 011 the exit side of the foil had practically the same distributions as shown i l l Fig. 23. Figure 24 shows the energy distributions related to their maximum values for various foil substances (IiCl, C, Al, Ag, Xi, foil thickncss 500 A). KC1 has the smallest, aiid Ni the widest distribution. The iiiost probable energy is about 1.2 ev. There was no significant diff‘erence between the distributions measured a t primary energies of 5 aiid of 30 kev. The energy distributions of secondary electrons from the surfaces of thick targets were not measured for fast primary electrons hut we suppose that they are similar t o those shown in Fig. 24.

G . MOLLENSTEDT mi) F. LENZ

2 . Drpenrlmce sf EmissionL 011 Target illat~rial.The electron yield 7 which is defined as the ratio of the number of secondary electroils per incideiit primary electron depends on the target material. Figure 25 (45) shows the energy dependence of the clectroii yield for various materials. The maximum yield is attained for primary energies of the 0 2 4 6 B e v 10 order of several hundred ev. For the niateEnergy rials shown in Fig. 25 it varies between 0..5 FIG.24. Energy distribu- and 1.8. For higher primary energies the tion of secondary electrons yield decreases below one but there are f r o ~ nKC1, C, Al, Ag, and N i still sigiiificarit differences between various foils 500 A in thickness released materials (46). by 5 kev primary rlectrons in 3. InJEumcp of thp i l n g l ~of Incidence of tritnsmisaiori (18). the Primary ElPctrons. The dependence of the secoiidary clcctroii yield 7 on the angle of incidence a bctweeii the directioiis of iiicideiice and the iiorinal to the surface was mcasiired (4'7). For not) too large 01 it can be approximated by

If wc cstiinate the resolutioii limit by iiisertii~gthe most probable energy of 1., cvifor c in 1431. (16) with a field strength of E = 50,000 voltsjcm i n 1.8

1.4

11.0

2

1 0.6

0.2

0

4 00

8 00

Primary energy E p

1200

1600

2000

__c

FIG.25. Secondary electron yield versus primary energy for various target niatcrials (46).

ELECTRON EMISSION MICROSCOPS

285

front of the cathode we obtain 6,.t = 0 . 6 c ’ r E = 1800 A. If an optimal limiting aperture correspoiidirig to Eq. (:JS) is used, a coiisiderably reducrd t heorctical rcsolviag power of about 80 A would result. Iikperimental work of Huaiig (48) c;oiifiriiis, that the width of thc eiicrgy distribution of the iniage-forming electroils is really reduced by a liiiiitiiig aperture. A s thc secotidary electroil yield at, high priitiary energies (e.g., 13 k t v ) tiepelids 011 the target iiiatwial, a distitic.tioii of differelit materials in the specimeii surfarc of a secondary emission microscope is to be expected if the surface coiitarriiiiatioii by polymers caii he suppressed. Since the sec+otidaryelectroil yield dcpeiids on the aiiglc of i ticidetice of the primary electrons, plastic images of cnil)ossed bpeciiiiens are to 11c caxpected i n coiisequriice of the variations of iticideiicr anglc and ail sdditioiial shado ,ving effect, if aii oblicluc. aiigle of iiicideiice is chosen. This iiieaiis that the coiiditiotis for a sccoiidary etiiissioti niicroscopy arc fulfilled which iti some respect” is superior to optical surface microscopy. 4. S ~ r o n d n r yField I?rmission(dlaltcr f$ffoct). A special type of srcondary electron ciiiissioii, the so-called llalter effect (49) was used hy 1Iahl (,TO) to form eniissioii itiiages. 111 this case, the secondary electroii yield is very high (100 to 1000), a i d the rtiiitted electroils are delayed up to several minutes. Siiicr the riicrgy tlistrihtioti of the eliiitted electroiis is c~omparativrlywide atitl there are stroitg fluctuatioiis of thc loral einissioii, the image cluality is iiot very good, hut JIahl’s cinissioti niicrosc~)pic investigat,ioti has contributed to a hrtter utidcrstatiding of the rf‘f coiifiriiied 1lalter’s explanation of its physical nature.

B. Spcotd ar y Ern ission il I icrosco p!j I ‘siny Ima!l in y h r w s 1. Imtrrhm(>nts. a. W. Bayh, 1058 ( , ! I ) . The arrangement of thc cathode leiis is shown in Fig. 2(i. 1:roiii an elcctroii gun of the Stc~igerwaltl type (;a),a fiiie electron beam strikes the target under an obliclue aligle of about 20”. To the cathode K of thc primary clectroti gun, a I oltage of -60 kv is applied, aiid its anode A has thc sam’ poteiitial as the specimen 0, i.e., -43 kv, so that the priniary elcctmtis strike the target with ail cilergy of 1 5 kcv where they releasci seco~idaries.A part of the intermediate image is again magnified by iiiraiis of an rlcctrostatic projector lens to a total electron optical niagnificatioii of 1000. The filial iniagc is recorded photographically iiiside the inicroscope colum~l.The spcciiiieii temperature can be varied by ineaiis of rrsistaiice heating. The filial image can be directly observed on a fluorescent screeii through a powerful Zeiss eyepiece with 20-fold magriificat ion.

286

G . MOLLENSTEDT

AND F. LEXZ

b. G. Bartz, 1958 ( 5 3 ) . Figure 27 is a schematic representatiorl of Bartz’ surface microscope. The primary electrons are produced i n a n adjustable electron gun with a magnetic condenser lens. The angle of incidence is about 20’. The Wehnelt electrode which encloses the specimen like a Faraday cage is on cathode potential. I t is ail advantage of this construction that, the primary beam proceeds in a practically field free space and is consequently not much deflected. For this reason it is possible to use small primary energies (e.g., 2 kev) for which a beam deflection occurs only immediately in front of the cathode. At a primary

FIG.26. Arrangement arid alectrir rircuit of a cathode lens and primary electron source in Bayh’s secondary electron emission miczroscopc ( 5 1 ) . 0-specimen; G and W-Wehnelt electrodes of rathodc lens and primary gun, respectively; E and Aanodes of cathode lens and primary gun, respectively; K-cathode; RI-limiting aperture; I-insulator.

energy of 2 kev the secondary electron yield is not much smaller than its maximum value (see Fig. 2 5 ) . According to Bartd nieasurenients in the electrolytic tank, he attains 60 kv/cm and a focal length of 5 . 2 mm for a n acceleration voltage of 40 kv. According to Eg. ( I G ) this corresponds to a resolution limit of about I500 A when no limiting aperture is used. With a limiting aperture of optimal dimensions, a theoretical resolution limit of about 80 A should be attainable. c. U. Decker, 1961 (54). Decker’s microscope has, in addition to the primary electron source, an ion source on the opposite side. A voltage of about -40 kv is applied to the specimen. Ariothcr high voltage source supplies +30 kv for the canal ray ion gun, so that the air or argon ions which clean and etch the specimen have an energy of 70 kev. The pri-

ELECTRON E M I S S I O N MICllOBCOPY

287

Fit:. 27 I3artx' secondary electron etnission rriirrosc~ope (,55). Primary elec*trori gun: (1 1 vathode; ( 2 ) IVehnrlt elect,rodr; (3) anode; (4) niagnetir condenser lens, cbathode I c n h ; (5) sperirnrn; (6) insulator; (7) \Vrhrielt elertrotle; (8) coritart spring; (5)) uiiode; (10) liiniting :tperturr; (1I ) projector lens; (12) fluorewent screen; ( 1 3 ) speviinrn holder with precision mec*linnisin for spccinien displacement in axial and perpeiitlicwlar dirrcntion.

5.

+

FI~:.28 I k c k c r ' s niicroscope ( 5 4 ) . Besides the electron soiircc EQ, a canal ray ion soiirce IQ is iisetl in order to clean and cktcli thc spccimcn surface.

288

G. MBLLENSTEDT A N D F. L E N 2

inary electrons hit the target with an eiiergy of 20 kev. With a n electrostatic projector lens a final magnification of 700 is attained on the fluorescent screen. The photographic recording method is the same as in Bayh’s and Bartz’s microscopes. In order to prevent contamination, the speciinen is heated to about 200’. A resolution of 1000 A is attained. 2. I’rrsent I’Prformancc. a. Dependence of image quality 011 the liniitiiig aperture. In order to surpass the resolving power of the optical microscope, a liniiting aperture in the back focal plane of the cathode lens must be used. There is experimental evidence that by such a limiting aperturr thr width of the energy distribution of the image-forming electrons is coiisiderably reduced (see Section IT, B ) . Of course, thc image intensity is greatly reduced if a n aperture of small diameter is used, but Bayh has recorded ail image a t a niaguification of 850 with an rxposurc’ time of 10 src, and a limiting aperture 8 p in diameter. In order to reduce

I00

FIG.29. Improvement of iruage quality with decreasing aperture diitrrictcr (a) p, (I)) 30 p , 1.5 p, ((1) 8 11. The electron optical inagnification was 850 ( , T I ) . ((8)

the effect of lens aberrations it is important that the aperture is exactly adjusted in axial and perpendicular direction, so that the axis of the imaging beam goes exactly through the center of the aperture. The variation of iniage quality with aperture diameter is denioristrated by Fig. 29 which shows a serirs of images of the same perlitic steel specimen. With an aperture diameter of 100 p some details are poorly defined, but with reduced aperture diameter the definition of the image is gradually improved. Aperture diamrters below 8 p have also been used, arid there would still be enough iiiteusity to record the micrographs but the difficulties of precise alignment cause much trouble, and a further irnprovenient of image quality was not observed. From theoretical coilsiderations (see Section 11, C) such an improvement is not t o be expected, since for aperture diameters of this size, diffraction effects begin to play an important role. b. Resolutioii test. On two micrographs of the same specimen taken a t high electron optical magnification pairs of points are selected which appear separated on both pictures. This separation, however, is in most

ELECTRON JCMIHSION MICIWSCOPY

288

cases to be found oiily i n oiiti dirrrtion siuce the image sulfers from astigniatism. I t is not yet clear whethrr this astigmatisni is a coiisequriirc of thr preferential direction of the primary heani, of the aberratioils of the cathode leiis, or of an esceatricity of thc limiting aperture. Anyway, an improvement of iniagc qualitry may be espected froin the correcting action of a stigmator. c. Dependence of emission on cathode inaterial. The differelice in emission froin various specimen materials is sigiiificaiit only when the surface is clean. If the varuuni is of the order of tor, and there are organic vapors in the residual vacuum, the contrast of a plane specimen consisting of different materials, is greatly rcdueed after a few seconds if the specimen is held a t room teniperature. A s in the case of photo ernission, the original coiltrast can be iiiaintaiiied for some minutes if the specimen is heated to temperat,ures of about 150°C.

F I ~ 30. . Srcmtlary rlcctron emmioil micrograph of a spec*inienconsisting of A), CU, and Fe ( 6 4 ) : (a) freshly cleaned wrfarc, (h) after I nim irradiation; (I-) after bombardment with Ar ions.

After an intense irradiation with hr ions froni a canal ray source the original contrast is restored even a t room temperature. I n some casrs surprisingly high contrast appears i l l secondary eniission micrographs. As a n example, Fig. 31 shows oriented growth on austeiiitic steel. d. Xonconducting specimen surfaces. Since on a tionconducting surface the primary electron beam would produce unwanted surface charges, which would impair the image quality, nieasures must be taken to prevent such charges. Hartz (53) has evaporated a platinum layer 50 A in thicktiess on poorly conducting speoiniens such as erythrocytes, poorly coritiuctiiig coal sections and diatoms. This inethod gives a good representation of the surface embossment but a distiiiction of the substrate inaterials by their specific emission is not possible because the mean path of t>he secondary electrons is shorter than the thickness of the platiniini layer. The formation of image contrast is only detcrmined by the secondary rniission from platinum and the shadow rffert of the prirnary electrons which hit under a n oblique angle.

290

((;.

G. MOLLENGTEDT A N D F. L E N 2

FIG. 31. Austcnitic steel; orientrd growth during cooling from 1000 to 700°C Ihrtz).

FIG. 32. Nonconducting, thermally etched A1203 surface with a carbon layer 50 A in thickness (U. Decker, specimen from L. Cartz, Morganite Development and Research Ltd. London).

ELECTRON EMISSION MICROSCOPY

29 1

Recent, hitherto uiipublished results by Decker show that a carbon layer about 50 A in thickness, evaporated on a non-conducting surface by iiieans of Bradley's procedure removes the surface charges and allows t o distitiguish different materials by their specific secoiidary emission. Apparently this is due to the low secondary electron yield from carbon and the comparatively long mean path length of secondary electrons in carbon. Inclusions i n glass becoiiie well visible if a carbon layer is used, and that there is no disadvantageous effect of surface charges. Another application of this niethocl is shown in Fig. 3%where a thermally etched surface of sintered A1,0, was covered with a carbon layer 30 A in thickness. e. Iniagiiig of magnetic micro fields. We have mentioned in Section 111, 11, 2 that the magnetic domains i n a ferromagnetic material can be made visible in the photo eiiiission microscope (41). Spivak and his co-workers (S,j) have also observed such specimens with secondary electrons but the results were inferior to those obtained i n (41). Decker (see :?G) has imaged the local niagiietic fields on the surface of a iiiagnetic tape 011 which a souiid frequency of 2-200 cps was recorded. ('. Scan niny Electron A1 icroscopy with SPcondary Electrons 1. G'cncral liemarlis. In scanning niicroscopy, the specimen surface is scanned with a very fine elcctroii brain, arid the emitted secoiidary electrons are used to control the intensity of a synchrouized writing bean1 scitnnitig the scrceii of a viewing tube. This procedure whose performailre a i d applicability has heeii coiisiderably i m p r o v d by the British working group i n Cambridge i n the latest years, is not ail imaging met#hotlin the optical sense, but since the iniage is formed by secondary electrons, a i d the resolution h i i t is clearly beyond that of optical microscopy, it should be nieiitioiicad i l l a review article on emission electroii microscopy. 1:igurc 33 scrves to explain the imaging principle. In all other hitherto irieiit io1ic.d ctiiission riiicroscopical tnethods a coniplete iniage of the cathode surface is fornied i l l every rnolnetit by int'ans of the cathode lens on a fluorcscent screen or a photographic emulsion. In scanning niicroscopy, however, no lenses are used to focus the complete iniage but the procedure is similar to that used in television viewing tubes. The object surface which may be regarded as subdivided into small eleinerits whose diameter is eclual to the resolution liniit of the instrument, is scaiined by a fine electron beam with a cross section approximately equal to that of one of the elements. As the beam sweeps over a particular element, this emits a number of secondary electrons, depend-

iiig on its physical properties. These clectroiis may, by a number of ways, he employed to form i n synchronism with the beam scanning the object, a magiiified image of the object. If tJhe line distance is equal to the beam diameter, both are equal to the resolution limit. The widening of the scariiiing electron spot by diffusion of the electrons in the specimeii may be iieglected since most of the emitted secondary electrons come from the point of impact, because electroiis excited ill deeper regions have much less chance to reach the surface aiid to be emitted. The magnification V = h/a i n electroil scaiiiiing microscopy is equal to the ratio of line lengths on the viewiiig screen aiid thc scarined lilies of the specinieii. 2. Instruments. a. 1\1. IGioll, 1933 (57), aiid M.Knoll and R. Theilc, 1939 (n‘8).This type of iniagc production was first technically realized by Synchronized Scanning Beams

dB L object - 0 -A

14’1(..

It

- b Image

---

3 3 . Image foriiiation by inems of scanriiiig

Knoll and Theilc (57, 68) and by von Ardeiine (59).Von Ardennc’s instrument, however, was not used to produce images using slow secondary clectrons alone but together with fast scattered electrons, and he recorded the iniagc by a mechanical device with a rotating drum, and not on a viewing screen. We shall not describe it in more det,ail, though von Ardenne’s paper contains a number of original and interesting ideas. The principles of operation of Knoll’s first scanning microscope are explained in Fig. 34. The specimen 0 whose surface is to be scanned, is arranged in a n evacuated tube on a metallic signal plate M. If the specimen consists of a conducting material, a signal plate is not required. The electron gun S in the scanning system containing the specimen produces a very fine electron beam. By a magnetic or electric deflection system A this beam is deflected in two perpendicular directions by means of sawtooth sweep voltages or currents with two appropriate frequencies in the same way as iii a television viewing tube. By this scanning procedure

the iniage is analyzed, aud the inforinat ion ahout the secondary cmissioll froin surface elemetlt~ssituated along a scanning line is trallsmitted during consecutive time elemcnts. l’hr smaller sweep frequency corresponding to t,he tiiimber of times the complete image. is writtc~rin titiit time, is called the image freque1ic.y. 111 order to give the humaii eye thc iriipressioii of a contitiuous image, a11 image frequency of about 60 sec-1 is sufficient. The higher sweep frequcncy c*orresponditig to thc numbcr of lines scanned iri unit time is callcld lint. frc~lueucy.The ratio of both frequencies is th(3 line number which should hc chosen sufficic~iitlyhigh in order to utilize completely the resolviiig power permitted by the scanning beam diameter.

The primary electron beam releases sccoiidary electrons at thc momcutary point of impact. They arc drawn to thc c.ollcctor electrode I< which is held at a positive potential l Y pof about 10 volts with respect to the signal plate, atid the secondary ernissioii current flows through the signal resistance I?,. The voltage difierence between the ends of this resistance is the signal contaiiiiiig the itiformation 011 the secontlary emission factor of the surface c~leniciits.I t is ainplified i i i a L\ itlr-hat~dainplificr V atid used to control the einissioti of the elcctroii gull in the viewitig tube B in which the electron beam is swept over the viewiiig scrc‘eti i n synchronism with the primary beani in the spwimeli tube. Hereby the tiine modulation of the signal voltage is retransduccd to a brightness niodulation of the corrcspondiiig image elements. The resulting image cat1 he recorded photographically with a powerful optical systetn. The brightness of the image elemeiits depeiids 011 their secondary electron yield and the amplification factor. The secondary electron yield

294

c.

MOLLENSTEUT

AND F. LENZ

itself depends on the surface material, the angle of incidence and the vrlocity of the primary beam. Grooves in a surface give a n increased brightness a t thrir cdges where the inclination angles a are large, since the emission is proportional to cos-' a. Knoll and Theile have also obtained images of insulating specimens usiug an additional continuous wide-angle electron beam. In this case each surface element forms a small condenser with the sigiial-plate which is slowly charged by the additional wide-angle beam to ail equilibrium potential and suddenly discharged by the scanning primary beam. This condenser discharge current pulse which is proportional to the charge stored by the image element between two passages of the scanning brain, is used as image signal. Similar methods are now widely used in image storage tubes. b. V. I<. Zworykin, ,J. Hillier, and It. L. Snyder, 1942 (60). As we have seen, the resolution limit of the scaiinirig method is mainly determined by the diameter of the fine beam scanning the sprcimrn. In Knoll's and Theile's instrument the beam diameter was of the order of 100 1.1 since the beam was produced by a conventional electron gun without demagnifying lenses. Zworykin et al. (60) improved the perforniauce of the scanning electron microscope by the following measures : (1) The crossover of a n electron guii was demagiiified in a two-stage electrostatic leiis system to a fine prohe about 500 A in diameter. I n order to provide space for the deflection coils as well as for the fluoresceiit screen and multiplier, this fine probe was imaged once more by an additional long-focus electrostatic lens with approximately unity magnification onto the fixed specimrn. (2) The primary electrons hit the specimen with a n energy of 800 ev so that the secondary electron yield and the difference in the secondary emission currents from different parts of the specimen are high. The secondary electrons are accrlerated to a fluorescent screen which they strike with a n energy of approximately 9000 ev. The radiation emitted from this screen, whosr intensity is proportional to the secondary emission current, is collected hy a powerful lens to a photomultiplier. If t h r spectral emission of the fluorescent substance is matched to the spectral sensitivity of the multiplier photo cathode, a gain in signal may be attained as compared with a system in which the secoridary electrons from the specimen fall directly on the first electrode of a multiplier. By the employment of a photomultiplier as preamplifier, the thrrmal resistor noise can be reduced considerably. (3) The primary beam is modulated by a 3000 cps square wave, and the output of the multiplier is amplified and filtered, and eventually, clipped so as to accentuate the differences in signal between different

ELECTHON EMISSION MI(!ILOHCOPY

295

elements of the surface, increasing corrcspondingly the contrast in the final image which is recorded by a facsiniile printer. In this instrument, a magnification of GO00 was used, and the resolution limit was estimated to be of the order of 500 A. Vine details in the embossment of metal surfaces were made visiblc. c. The Cambridge team (61-66). Research and development work on scanning electron microscopy conimenced a t the Engineering Laboratory, University of Cambridge in 1948. This team attained a n cwmitial improvement of the signal-to-noise ratio and of the resolving power. They first employed the new type of direct electron multipliers with beryllium-copper dynodes hut in the most recent type a combination of scintillator, light-pipc and photomultiplier is used for the collection of secondary electrons. 3. Fundamental LimitatiorLs. In order to improve the resolving power it is neccssary to reduce the diameter d of the scariniiig primary beam. For a given “Richtstrahlwert” R (G’i’), i.c., current density per unit solid angle, a reduction of the beam cross section is necessarily connected with a n iiicrease of the angular aperture of the heam according to the equation Id = 2- j (45) rcr

The maximum value of the “Richtstrahlwcrt” is given by (68)

if U is the acceleration voltage and j , the current density a t the cathode surface of the primary electron gun. It follows from 14ki. (45) and (46) that the number N of primary electrons striking a surface element of area ( r / 4 ) d 2is given by Rt N = a j d 2 4 = d2rcr2 (47) 4 e 4 e if t is the effective time during which secondary electrons from each surface element are collected. If the electron optical system focusing the primary beam suffers from spherical aberration, we have d

=

2c,cY3

(48)

if C, is the spherical aberration coefficient of the focusing system. This means that N is proportional to d%. If the size of the scanned specimen and the total scan period is kept constant, t is proportional to d2, hence N proportional to d’+*; if, on the other hand, the number of image ele-

PHOTOMULT

ERS E

ES

SPECIMEN/APERTURE STAGE 0 I I _ L _

1

APERTUREANODE 0

SCANNING

ELECTRON MICROSCOPE SEM-3 5 CHEMATIC

DIAGRAM

+ 500 V

- 20 K V

FIG.35. Schematic diagram of the scanning electron microscope (6'6).

ELECTRON EMISSION MICROSCOPY

297

meuts is kept constant, N is proportional to d S S . This sets a fuiidaiiielltal iare of thp numhcr limit to a reduction of tl sitice the n i e a ~ ~ - s ( ~ ~fluctuation of primary electrons striking a s1irfac.e elemetit is eclual to d V $ 5 , alld the contrast, i.e., thc relative variatiou of secoiidary emission froin different surface elenients can only be observed if it is largc as compared with the fluctuation contrast N-35. The practical limit attained by the Cambridge team is about 100 A when a n image of 2 lo4resolved elenierits is recorded in 5 min. A further improvement of resolving power might be attained by increasing the recording time, by reducing the number of resolved image elemelits or by increasing the Richtstrahlwert. Receut?iiivestigations (69-71) show that a considerable increase of the liichtstrahlwert may be expected, whell point cathodes are employed in the primary electron gun. 4. dpplications. Two great advantages of the scanning method are the high resolving power and the possibility to image surfaces of very irregular shape. Eveti such parts of the specimen surface which are situated i l l thc blind space as seen froin the multiplier appear illuminated since the secondary electrons can reach the dynode along indirect paths. I‘igure 36 shows a tungsten chisel-edged whisker in contact with an etched silicon surface. Smith arid Oatley h a w shown (63) images of a tuiigsten-germaniurn point contact before and after a condenser discharge through the contact. The process was carried out while the contact was under observation, and the electrical rectification characteristics could also bc measured. RIcd4uslan and Smith (72) have reported on a study of the slow chemical decomposition of siiiglp crystals of explosive materials such as silver aeide and lead styphriate by heat. Potential differences as small as one volt between adjacent areas of a specimen surface can produce strong “voltage coiitrast,” as Everhart Pt al. (64) have demonstrated in scanning images of reverse-biased p-n junctions. Similar voltage-detection experiments have been perfornied with biased polycrystalline gallium phosphide specimens. A great number of other interesting examples has been published, among these images of nonconducting specimens covered with thin layers of gold-palladium in order to reniove unwanted charging processes. Insulator surfaces can also be imaged if a low primary voltage, e.g., 1.5 kv is used. In this case, the effective secondary emission coefficient is unity, and the picture contrast is coiltrolled only by collector modulation. The reduction of Richtstrahlwert a t low voltages is largely cornpensated by t)he increase in secondary emission, so no change in recording time is necessary: Coiitrast due to surface films is enhanced a t low voltages because differences in secondary emission coefficients are more

298

G . MOLLENSTEDT AND F. LENZ

pronouiiced and penetration effects are reduced, the range of 500 volt electrons in alumiriurii being roughly 30 A. 5. Contamination. Contamination is not usually a serious problem in high voltage scanning microscopy if the exposure time is less than 30 niin. In the case of iiisulating surfaces, Thornley (&5) has found that during cxamiiiation at high voltages, a contamination layer is formed rapidly,

FIG.36. Tungsten chisel-cdgcd whisker in contact with an etched silicon sinface.

but if it is then examined with a low voltage beam a t approximately the same current density, the deposit is completely removed in about 30 sec., and prolonged examination a t low voltage produces no further change on the surface.

V. IONINDUCED EMISSION~L~ICROSCOPY A . Factors Influencing Image Quality 1 . Energy Distribution of Emitted Electrons. From early experiments it was known that most of the electrons extracted from a gas discharge

ELECTRON EMISSION MlCKOSCOPY

299

electron source (voltage 4-25 kv, pressure <0.1 tor) had energies corresponding to the total voltage applied to the discharge (’73).This was also confirnied by the resolutioii limit of about 25 A of the Truh, Tauber electron transmission microscope in which a gas discharge electron gun was used (‘74). Because of the chromatic aberration of the electron lenses, such a resolution could only be obtained if tthe energy distribution of the imaging electrons was of the order of 1 or 2 ev. hkllenstedt and Duker (76) have measured the energy distribution from an air discharge source of the Induiii type (74) in an electrostatic velocity analyzer (‘76).The results are shown in Fig. 37.

Energy

FIG.37. Energy distribution of elrrtrons from an air discharge electron source. Discharge voltage: 40 kv.

The energy distribution had a rnaximurn (most probable energy) a t about 1.25 ev, and a half width of about 2 ev. It was found to be iiidependent of the cathode material but it, was recogiiisecl later that, this independence was due to polyiner contai~ii~latio~i layers formed on the surface, and that the energy distribution from cleaii cathode surfaces actually depends on the cathode material. Praclal and Simon (‘7’7) have found that the energy distribution of electrons passing through the narrow limiting aperture of a cathode lens uiider argon ion bombardment could be described by an equation of the form

CEI

=

constant. exp

[ - ($1

(49)

if the ion current density is sufficiently high to remove the contamination layer. I n Eq. (49) d l is the contribution of the energy interval dt tJot,he

electron current, and T an effective emission temperature charact,eristic for the cathode material. Froni Eq. (49) it follows that log ( d I / d t ) is a linear function of c and that the characteristic temperature T can be determined froin the slope of the correspouding straight lines in a log ( d I / d e ) v. E diagram (Fig. 38). An energy distribution of the form Eq. (49) is to be expected hehirid the limiting aperture if the energy distribution of the electron current

FIG.38. Energy distribution of electrons emitted under argon ion bombardment from various targets (77).

density j emitted from the cathode is a Maxwell distribution (compare Section VI, A ) (78) (50)

The most probable energy kT in this distribution varies from 3 to 10 cv for the investigatcd cathode materials and does not depend significantly 011 the primary ion voltage. Dietrich and Seiler (18) have fourid a dependence 011 foil material in the energy distribution of electrons emitted from the hack surface of thin foils bombarded with 57 kev lithium ions (Fig. 39). It is interesting to note that the electron energy distributioii from KCX foils was much narrower than that from the other foils. I t appears prob-

30 1

ELECTRON EMISSION MICROSCOPY

able that the electron energy distributions from the front side of thick targrts are similar to those showii in Fig. 39. 2. Dependence of Emission ori Specimen I 0.5 Matcm’al, T y p c of I o n s and Primary Ion hhergy. The following diagrams show the 0 dependence of the ratio I s / I pof the srcondKCI C Al Ag Ni ary electron current to the primary ion cur0 2 4 6 der10 rent on the primary ion energy, the cathode Energy material and the type of ions, measured in FIG.39. Energy d i s t r i h a vacuum of tor (79, 80). tion of clrrtrons emitted from It follows from these experimental results the back surface of thin foils that specimens consisting of different mate- bombarded with 57 kev lithirials should show sufficient coiitrast to dis- um ions 118). tiiiguish them. Further, the increase of electron emissioii with increasing primary ion energy suggests to choose a high ion energy. Gaukler (81) has made some measurements of matcrial dependence of emission with a gas discharge ion source of the type used in practical emission microscopical work. I n this case the ions have a wide energy distribution, while in (80) tho ions were more monochromatic. For a judgement of Gaukler’s results it is further iniportaiit to consider that the ion current density on the specimen surface may vary with the chosen

0

20

40 60 80 100 Vt (total goy, voltage in h v )

F I ~40. . Secondary electron eniission as target material. Positive ions He+ (79).

3

120

140

160

function of ion energy showing effect of

302

G. MOLLENSTEDT A N D F. LEN 2

ALUMINIUM

I

20

I

40

I

60

I

eo

I

roo

I

120

a

VI (total gap voltage in k v l

FIG.41. Secondary electron emission from aluminum as a function of the energy of several types of positive ions (79).

discharge gas even if the discharge voltage and the discharge current are kept constant. For his measurements Gaukler has replaced the projector leiis of the instrument described in Section V, B, 2 by a Faraday cage enclosed by another grounded cage in order to exclude errors due t o secondary electrons from the Faraday cage walls. Emission measurements were made for 18 targct materials and 6 ion types suitable for practical eniissioii microscopical work. The results are given in Table I. These results show that the highest cmission is obtained from the light metals Mg, Be, and Al. If we compare the discharge gases O2 and N z (or air), we see that in one group of target materials ( N g , Re, Al, Fe, C, Ta, Mo, Ag, Au, Cu) both yield about the same emission. Another group (Zr, Co, Ti, Zn, Ni, RIu metal) emits more strongly if O2 ions are used. This is probably due to oxidation. Platinuni emits more strongly under N2 bombardment (&?), an effect which is not yet understood. The emission under bombardment with Ar ions is in most cases a little lower than in the case of N2. 5 10 20 30 All metals, however, show a considerable increase FIQ. 42. Electron of emission if Hz or CzHz is used as discharge gas emission coefficients as compared with N2. from various metallic Figure 43 demonstrates the image contrast due surfaces in the ion to a variation of emission from silver and tungsten energy range from 5 to 40 kev. Positive ions for different types of ions (81). If the residual vacuum contains too much A+ (80).

TABLE I. ELECTRON EMISSION FOR

VARIOUS T.4RGET SfATERIdLS A X D ION

DISCHARGE VOLTAGE25

TYPES(81);D I S C H A R G E

CURRENT

50 Fa,

KV

Electron current in

amp MU-

Mga

Be

,41a

170 310 230 170 1i 0 170

125 200 145 110 125 125

90 160 155 57 90 105

Zr

Fe

Zn

C

54 100 90 66 52 60

39

26 62 35 16 24 30

24.5 40 5% 28 23 23

* Emission enhanced by oxide layer.

35 50 17 28 28

Ti

Ta

Pt

20 38 46 23 17.5 28

18 28 38 17 17 19

18 46 51 16 17 10

Mo

__ 17 31 49 15 16 17

Co metal

W

.4g

Xi

16 28 55 12 15 18

15 24 55 13 14 14

13 31 35 10.5 13 13

25 50 11.5 12 50

17a 31 50 12 14 41

Au

lia 1 0 . 5

25 29 7 10.5 11

cu

-_

10.5 24 37.5 11 10.5 11

304

G. MOLLENSTEDT .4ND F. LENZ

FIG.43. An example for the variation of image contrast in dependence on the type of ions (82).(a) Tungsten foil with evaporated silver squares. Ions from (h) HP, (c) C,H2, (d) air discharge.

20 30 Accclcroling Voltage in k v

40

FIG.44. Relative image current density as function of accelerating voltage (81). All values measured with different target materials and different discliargc gases are situated between the two outer curves.

ELECTRON EMISSION MICIlOSCOPP

308

oxygen, some materials are oxidized. If the vacuum is of the order of tor, and the ion current densities are weak as in Gaukler's experimetits, these oxide layers cannot bc rmioved by boinbardniellt with an inert gas. Figure 41 shows the results of s o n i ~nicasureiiieiits (81)of the dependeiicc of electron intensity on the accelerating voltage in the imaging system. The image brightness increases with incrcasing acceleration voltage.

FIG.15. Perlitic steel (a) 20", (b) 2" angle of incidence (85). The rough stnirture of the perlitic grains is visible most clearly in (a) while the fine structure in the ferrite grains conies out only in (b).

3. DPpc.ndance o j Corttrast on the Orientation of the Ion Ream. The oblique incidence of the ion beam produces a shadow effect similar to the shadowing technique well-known from transmission electron microscopy. Hereby, a roiitrasted visualization of the surface embossment is possible. For this reason it is desirable that, the angle of incidence of the ion beam can be varied. For the visualization of a relatively rough surface embossment, an angle of about 20" is appropriate. If on the other hand the surface elevations are very small, a smaller angle is preferable. The effect of the angle of incidence is demonstrated in Fig. 45. I n most cases angles in the range 5 to 10" are most mitable.

306

G . MOLLENSTEDT A N D F. LENZ

Fert el al. (84) have found that the electron emission under ion bombardment is not a monotonic function only of the angle of incidence but that it depends strongly on the orientation of the ion beam relative to the crystallographic axes. It was shown (84) that variations of the angle of incidence as well as of the azimuth of the plane of incidence may result in considerable variations of contrast. Reversal of contrast between adjacent grains was demonstrated in emission images of mumetal, iron, and copper, and twins became visible or invisible according to the orientation of the ion beam (85). For a quantitative measurement (86) of the variation of emission with azimuth, the emission microscope described in Section V, B, 4 was used. This instrument was modified by using a new ion gun and an improved vacuum system. The specimen can now be rotated under vacuum and applied voltage about a n axis perpendicular to the studied surface. The mechanical and electron-optical conditions are defined so that during rotation the image of one point of the specimen surface remains in the center of the plane of observation. The angle of incidence is between 30 and 40'. Over the fluorescent screen, a diaphragm defining a beam of enmuth (degm4 Fro. 46. Dependence of electron given cross section can be arranged, and emission on the azimuth of thc the current of this beam can be continuously recorded. Figure 46 (85) shows plane of incidence (86). some of the results of such measurements, Sharp minima of the electron emission occur if the plane of incidence is a plane of great atomic density. 4. Contamination and Cathode Sputtering. a. Contamination. In most emission microscopes the relatively poor vacuum of the order of tor contains residual organic molecules. If the surface is to bombarded with ions a contamination layer is formed much faster (87) than under a n electron bombardment of the same energy. Such contamination layers reduce the definition of contours and the contrast due to the variation of emission from different materials. This unwanted effect can be slowed down considerably if the specimen is kept a t a temperature of about 150°C (see also Section 111, D , I , b). Figure 47 shows the results of measurements by Speidel (87). ~

ELECTRON E M I S S I O N MICROSCOPY

307

Another method to remove contamination layers is to use high ion current densities for which the cathode sputtering rate equals or exceeds the contamination rate. I n the modern emission microscopes described in the following chapter on instruments, this method is generally used. Still another method to prevent contamination is to improve the vacuum conditions essentially or to cool the surroundings of the specimeii (“negative oven”). The latter method has already been used successfully in electron transmission microscopy (88). b. Cathode sputtering. Ions striking the specimen surface produce the cathode sputtering effect well known from gas discharges, i.e., particles of atomic size are ejected so that specimen surface layrrs are vfA/min) -60 -50

-100

-50

0

/on Current Dcnsi/y j : 1.4 10-7Amp/cm2

50

roo ;F’

47. Temprrature dcpexidence of cwntamination rate (8‘7)

gradually removed (see also Section 111, L), 1, b). This effect may be used to remove polymer contamination layers which reduce image contrast or t o etch the surface (89). This method of ionic etching is recently much used (90). I n the emission niicroscope ionic etching can be perforrned under observation with a resolving power beyond that of the optical microscopti. Figure 48 gives an example for the ioii etching effect. l‘onts et al. (91) have measured the sputtering rate of copper by n number of ion types (Fig. 49) by weighing the target before and after. Thus we see that a high ioii energy is advantageous not 011ly with respect to high electron yield but also in order to reduce a n excessivr destruction of the specimen by cathode sputtering. We quote from Yonts (91): “Sputtering ratios for copper have hecn determined in the energy range 5-40 kev for bombardment by Ar+, He+, and D+. Argon values range from 8.48 a t 5 kev to 9.25 at 27.5 kev, deuterium from 0.048 a t 10 kev to 0.023 a t 4-2 kev, and helium from 0.23 a t 15 kev t o 0.075 a t 40 kev. Preliminary data are included for 30 kev sputtering of copper by Hf ( O . O l l ) , Df (0.03), He+ (0.13), N+ ( 5 . 2 8 ) , Nef (3.61), Arf (9.02), Cu+ @.GO), Kr+ (I.5.15), and U+ (20.!4). Also in-

308

G . MOLLENSTEDT AND F. LENZ

FIG.48. Emission image of a Ag surface (56): (a) before and (1)) after ionic etching.

ION ENERGY ( k c v l

FIG.40. Sputtering of copper by helium ions (91). The sputtering rate (numher of sputtered atoms per incident ion) decreases with increasing ion energy.

cluded are sputtering ratios a t 30 kev for Arf on T a (2.7), hIo (3.31), and A1 (2.38). M o s t of these data are the result of a single measurement, and require further verification.” These sputtering ratios were measured for perpeiidicular ion incidence. It is well known, however, for low ion energies (92) that the sputtering

309

KLECTHON EMISSION MICROSCOPY

ratio increases with decreasing angle of incidence, and it is highly probable that the same applies to higher energies, but the exact dependence is not yet known. If it is ititended to keep the sputtering ratio low, the use of light ions is advisablc. Another influencc~of thc ion brain 011 the specimen consists in the fact that a great many of the bombarding ions are trapped i n the cathode material whic'h may suffer structural changes. Gaukler has studied cathotlc sputtcritig i n an emission microscope by measimiiig the t inie required to destroy a layer about 5000 A iii thickness TABLE 11. T I M E ( I N S E C ) REQUIRED TO D E S T R O Y A L A Y E R 5000 A I N THICKNESS BY SPUTTERINO FROM A N IONSOURCE; 1 ) I S C H A R G E V O L T A G E 24 K V (81)

.4ir Hydrogcm ilcetylenc Argon

Silver

CkJltl

Copper

185 1500 10.5 70

305 2700 200 100

310 2520 190 107

TABLE 111. NUMBER OF SPUTTERED ATOMS PER EMITTED ELECTRON FOR D I F F E R E N T TARGET l[ATERIkI,S A N D I I I S C H A R G E GASES (82) -~ ~ ~

Silver Air Hydrogen Acetylene Argon

6 0 3 19

0 3 0

5

~

_

_

_

Gold 4 (i 0 2 2 5 21

_

~

Copper 6.5 0.35 3 0 18

which had bccn evaporated on a glass substrate. This time can easily be determined by ohservatioii in the emission microscope. Table I1 shows the results of such nieasuremcnts. Further experimeiits (82) showed that the sputtering rate from a gold target with ions from an air discharge did riot depend on temperature in the range 20°C to 500°C. I7or emission microscopic application low values of the ratio $ / y of the numbcr of sputtrred atoms and the number of emitted electrons, i.e., little sputtering a t high image brightness are desirable. Table I11 shows some experiniental results. 6. Depth of Focus and Stcrco Ilficrogmphs. As we have seen a t the end of Section 11, R the depth of focus is improved if a narrow limiting aperture is used. Figure 50 demonstrates t,hat under such conditions the

310

G. MOLLENSTEDT

AND F. LENZ

depth of focus is sufficient to obtain well defined stereo micrographs. The micrographs in Fig. 50 were taken with a limiting aperture 35 p in diameter, and the specimen was inclined by 3" on either side with respect to the optical axis. As in transmission microscopy, the image contrast can undergo considcrable variations if the image is slightly defocused. R'lahl (94) has found that in some cases the image contrast could be accentuated or even reversed hy a deviation from the exact focusing conditions.

FIG.50. Stereo emission images of a steel surface with crossing scratches (93).

B. Instruments 1. H . Mahl, 1938 (94). I n early emission micrographs (95, 96') in which the electrons were released by the ions from a gas discharge, the image quality was limited by the scattering of the imaging electrons from the gas molecules because a gas pressure of the order of 2 t o 10 * tor was necessary to obtain sufficient intensity in a conventional gas discharge electron gun (94). Mahl used a longitudinal magnetic field in order to increase the ion production in his gas discharge so th a t he got sufficient intensity even when the pressure was low enough to reduce the unwanted scattering of the imaging electrons to a negligible value. He attained a resolution limit of about 1 or 2 p. He further observed different electron yield from different specimen materials and described cathode sputtering effects in the emission images. 2. G. Mollenstcdt and H . Dulcer, 1963 (97, 98). The ions were produced in a separate gas discharge source from which a n ion beam was emitted through a narrow aperture onto the cathode surface under a n oblique angle of incidence. Thus it was possible to keep a vacuum of about tor in the cathode lens while the ions were produced in a gas discharge of

ELECTRON EMISSION MICROSCOPY

811

about tor. An electrode of the Briiche-Johannson type (5, 6 ) with small electrode distances atid a high acceleration voltage was used in order to attain a higher field strength in front of the cathode than in Rlahl’s instrument. A narrow limiting aperture was arranged in the back focal plane of the cathode lens in order to increase the resolviiig power (see Sectioii 11, C). Further developments of this instrument with respect t o the physiral and nictallographical requirements have been described in resolution limit of 500-600 A is attainable. (98-100). 3. The “Jletioskop” (101). This is a commercial instrument of Trub, TBuher, Ziirich, Switzerland, whose development is a direct continuation of the Mollenstedt-lliiker instrument described in the preceding paragraph. Apart from several manufacturing details, the most important improvements are the following: magnetic projector lenses were used in order to improve the spark-over stability, the temperature range of the specimen was considerably increased, and at1 automatic control system was ititroduccd. l’hv instrument which is already in use iti several laboratories in various countries, is showii in Fig. 51. The “Metioskop” con s of an operating console, containing all electrical aiid vacuuiii equipmrwt, and the microscope tube. The cathode head (1) coiitaiiis the specimen holder aiid its adjustment. The high voltage supply ( 2 ) (up to 15 kv) is during operation covered by a metal hood. When the specimen is changed, the hood is opened, and the cathode head is detached. The specimen (1) (see separate section ill douhle scale) consists of a metsllic ground-in joint 15 mm in diameter and 0.3 to 3 . 5 mm in thickness on whose 1)ackside a heat conducting pivot (s),7..5 mm i n diameter, is fixed. A thermocleinetit in this pivot is conducted directly to the backside of the specimen. Specimens which arc available in small size only are pressed or soldered into a metal piece of appropriate shape. The lead wires, together with those for the heating coils which simultaneously serve as high voltage supply, are potiducted through the cathode head (1) atid its high voltage supply lead ( 2 ) into an insulated high vokage box in the operating consoIc, i n which storagtx batteries for the cathode heating, anti a mirror galvanometer for the temperature measurement are arranged. The light pointer of the gal\ranoineter is projected onto the temperature scale. The specimen temperature can be varied between room temperature and 1000”(~.After reiiistallmeiit of the cathode head thc specimcn can hc adjusted by inf’aiis of the specimen control (8). The Wehnelt electrode (9) is coiinccted through its high voltage supply head (10) with the high voltage box i n the console. The grounded anode ( I 1) is alignahle (12). A most important imaging element is the limiting aperture (13) which can be aligned (11) in horizontal and vertical direc-

FIG.51. Soction through the microscope tube of the “Metioskop” (101): (1) cathode head; (2) specimen high voltage supply; (3) metal hood, hinged; (4) spccimen; (5) heat contlurting pivot; (6) heating coils; (7) teniperature scale with light pointer; (8) specinitln control; (9) Weliiielt clecatrotle; (10) Wehnclt high voltage supply; (1 1) anode; (12) anode alignnient; (13) limiting aperture; (14) aperture alignnient; (15) ion b oiirw ; (16) gas intake for ion source; (17) alignment and angular atljiistinent of ion gun; (18) magnetic projectors; (19) eyepiece; (20) fluorescent screen; (21) optical niicroscope; (23) plate lock; (24) plate magazine. 312

tioii. An exact alignment of aiiode and Wehiidt elertrode is iniportant, because otherwise aberrations are produced. The exact vertical adjustment of the limiting aperture is important, because otherwise the monochromatizing effect treated in Section 11, C cannot be achieyecl simultaiieously for the whole specimen surface. The correct alignment of all imaging elemelits is tested by observing the image cluality 011 the Auoresceiit screen. The practically attainable resolution is determined by the deviations of the specimen surface from an ideal plane. *in attaiiirneiit of the theoretical resolution limit is to be expected only if these deviations are extremely small. The ioti source ( 1 5 ) is usually operated with voltages het\vc.cn 20 and 45 kv. This voltage cau be tapped from a potentioiwter in the opcratiiig console. If necessary, a second high 1.oltage source of +45 kv can hc joined in scrips so that an ion energy of up to 80 kv caii tie used. The ion source can be aligned, and its angle of incidence varied in the rangc from 0 to 20" (17). Through the controllable gas intake ( I G ) many different types of ions can be used for etching and electron emission in order to extend the range of application of the instrument. The primary electron image is magnified by two magnetic projector lenses (18) whose current is supplied from storage batteries or highly stabilized transistorized socket-power units. The current supply aiid a magnification indicator scale are contained in the operating console. The final magnification can be varied in the range from 500 to 1500 diameters. The observation chamber has 3 eyepieces (19) to observe the fluorescent screen ( 2 0 ) . The final image can be observed through a powerful optiral microscope (21) with 10 or 20-fold magiiification. Below the screen i i i whose level a table plate of plexiglass is fixed, a photographic camera is arranged. I t has a plate lock (23) aiid contains a magazine with 5 plates 6.5 X 9 mi3. The microscope tubr is evacuated through two high vacuum coiiiiectioiis by an evacuatioii system consisting of a backing pump with a pumping speed of 5 meters3/hr and a three-stage fractionating oil diffusion pump with 200 liters,/sec. Another forepunip with 1 metcr3/hr serves for the separate evacuation of the plate lock. This is necessary if the plates must br chaiiged when the specimen is 011 a high temperature. The working vacuum is of the order of several 10k5 tor. The complete vacuum control is niaiiaged by niagiietic tiid motor valves. The indicator scales on the operatioil console serve to rwntrol thc cathode and ioii currents, the projector and heating currents and voltages. The high voltage is produced hy a Zeiss high freyueiicy unit. 4. Ch,. Fcrt and R. Simon, 1956 (102, f03).Figure 52 shows a scc.tional view of the upper part of EIert's and Simon's emission micro,zcope. A n interestiiig feature of the cathode lens is that no Wehiielt electrode is

314

G. MOLLENSTEDT

A N D F. L E N Z

used. This means that the cathode field strength can be madc practically equal to the quotient of acceleration voltage and cathode-anode distance, i.e., much stronger than in lenses with a Wehnelt electrode. Septier (27) has already proposed to use such au arrangement but he had difficulties with its practical realization. Such a cathode-anode systeni alone does not produce a real image of the cathode but in combination with a subsequent magnetic lens it has the required imaging properties. A narrow limiting aperture is arranged in the back focal plane. The intermediate image is further magnified by a magnetic projector lens. I n the strong

FIG.52. Sectional view of tlic uppcr part of t h e instrument (103).

field of 100 to 150 kv/cm the ion heam suffers a strong deflection. In order to strike the center of the specimen with the ion beam, the axis of the ion source is arranged iu oblique downward direction. With this cathode lens a very high resolving power has heen attained. Fcrt and Simon state a resolution limit of 250 A. 5. 13. B. Bas, 1961 (104). A special feature of this instrument is its universality. An ion source for ion energies up to 70 kev, and an electroil source for electron energies up to 5 kev can be used. Besides, a quartz window in the microscope tube is provided in order to make possible also photo emission by uv irradiation. The arrangement of electrodes i n the electrostatic cathode lens is similar to those shown in Figs. 13 and 28

IZLECTRON E M I S S I O N M I C R O S C O P Y

315

but the ion bcam is focused onto the specinien by an electrostatic condetisrr lens. Even thermal emission cat1 be used because the specimen can be heated up to temperatures of 2230°C. Two types of heaters i n which the specinicii is heated by electron bornbardinelit are described. The lens system is purely electrostatic. 6. I I . Dih7cr and A . Illenherger, 1962 (105). Duker and llleriberger have also realized a cathode lens without a Wehnelt electrode (Fig. ,%),

iz

F I ~ :5. 3 . TIw c*athodr lens of 1)itkc.r and Illenbergrr (106).

i n which the anode bore diameter is small compared with the cathodeanode distance. With an accelwation voltage of 30 kv and a distance of about cm bctween cathode aiid anode, the field strength is about 150 kv/ctn. The real image is formed by a subsequent electrostatic lens. Duker has obtained a resolution limit of about 700 A even without using a limiting aperture.

r.

,Zpplications

The field of applications of the emission microscope with ion induced emission is still i i i c\-olutioii. 1. Jletnllir Specimens. Most applications refer to iroii, steel, and other metals aiid alloys. The elenleiits in different structures of steel and iroii surfaces such as perlite (78, 106) or martensite (93) appear with brilliant contrast due t o variations of emissioii from structure elements of different chemical composition and to variation of the angle of ion incidence in consequence of surface elevations. The difierent crystal surfaces in FeCr-Ni mixed-crystal alloys (78, 106) are also imaged with good contrast due to the variation of eniissioii with crystal orientation. In such pictures thc formation of twiiis can oftcti be observed. Caukler (81) has observed structural changes in metallic surfaces in coiisequriice of temperature variations, especially collective crystalli-

31(i

G . MOLLENRTEDT AND F. LEN2

eatiori of silver in the temperature range 300-000°C. In this investigation he foiind great variations of contrast in the grains. Kellcr (93) has studied structural chatigrs in a n rtched surface of tempered niartciisito in the temperature range 150-850°C. He observed

FIG.54. Variation of emission from platinum surfaces a t increased temperatures undrr oxygen ion homhardrnent (106): (a) 200°C; (b) 300°C; ( c ) 500°C; (d) 350°C.

the coagulation of originally fine dispersed particles to a less emissive coarser structure. Investigations by Duker (100) show that a contrasted observation of the crystalline structure of y-iron is possible at temperatures as high as 950°C. Adsorption layers from preparatory treatment were observed (100) at) 2GO"C, and their removal by ion bombardment a t 660°C. Other inter-

ELECTRON EMISSION MICROSCOPY

317

FIG.55. Dendritic structures in a surface of I;ranium with 8%] Mo and 2% A1 (100).

esting phenomena were observed on iron surfaces after cooling from 930 to 460°C and from 800 to 170°C. An interesting behavior of a platinum surface under iritense bombardment with oxygen ions a t high temperatures was found (82, 106). At 150°C the emission is uniform over the surface (Fig. 54a) as in the case of

318

G . MOLLENSTEDT

A N D F. LENZ

a n inert discharge gas. At temperatures above 200°C, dark (i.e., less emitting) spots are formed under intense oxygen ion bombardment, in most cases starting from the grain boundaries and gradually growing with increasing ion current density. If the current density is reduced, they disappear, and if it is increased they grow until the total surface is covered.

FIG.56. Srtfflorite cmbeddetl in calcite (108).

The rate of growth depends on temperature. This reversible formation of dark spots can only be observed in the temperature range between about 200 and GOO'C. It cannot be observed on specimens which have once been heated beyond G5O'C. Similar effects were also found with iridium, rhodium, and palladium. A satisfactory explanation is still missing.

ELECTRON EMISSION MICROSCOPY

319

FIG.57. I’olyrrystalline aliiiriiiie under H 2 + ion bombardment. The diffuse apprarance of sonic of the grains may be axcriticd to local space charge clouds in front of thc surface limited by the grain bountlarics (100).

320

G. MOLLENSTEDT

A N D F. LENZ

Duker (107) has devised a camera for taking 16 mm-motion pictures under vacuum with which he has observed transformations of steel and the oxidation of iron. Interesting phenomena observed under oxidizing and reducing conditions could be explained by different solubility of oxygen in CY and y-iron, respectively. 2. Nonconducting Specimens. Cevales (108) has first used the emission microscope with ion induced emission to study ores. Since most ore miiierals aiid their dross dilutions are poor conductors, he had a t first difficulties with surface charges. In order to overcome these difficulties, he protected a square of about 4 mm2 in the center of the specimen with a collodion foil before covering the whole surface with a silver layer about 1000 A in thickness. After the evaporation of the silver layer the collodion square was removed again. This procedure allowed taking pictures of many poorly conducting minerals. Figure 56 gives a typical example. An application of Cevalcs’ (108) method to reduce charging-up phenomena to ceramic materials is described in (109) where images of several polycrystalline alumina and thoria specimens are shown. A special feature of these images is the charge localized on single grains. It is found that some of the grains are covered by diffuse charge clouds while other grains give a well defined image (see Fig. 57). VI. THERMIONIC EMISSION MICROSCOPY

A. Curreiit Density and Energy Distribution of Electrons in the Case of Thermionic Emission

If a phase-space density nc(r,v) is defined such that ne(r,v)dr dv is the nuniber of electrons in a volume element dr = dxdydz in configuration space with velocity vectors whose end points are situated in a volunie elcnient dv = da,dv,du, in velocity space, we have (110) inside the emitter of absolute temperature T the Fermi distribution n,(r,v) =

(;>” [1 + tanh (&- g)]

Here E F is the energy of the Fermi level, measured from the bottom of the conduction band. If the surface of the emitter is a plane perpendicular to the x-axis, the electrons must not only have a total energy sufficient to Overcome the potential barrier, but mvZ2/2alone must be sufficiently large. For such electrons for which mv2/2is large compared with E F and liT, Eq. (51) may be approximated by the Maxwell distribution

74r,v) = 2

(T)~ cxp (G) exp (- g,) +

(52)

If only such electrons are emitted for which rnvz2/2 > l i p E+ ( E , is the work function), we can calculate the current density of electrons

emitted from t,he rinitt,er surfacc by integrat>ioiio w r t,hc velocity spacc

This is the Richardson-Dushnlarl formula for the niaxirnuin thcrinionic emission current density.

7

FORBIDDEN BAND

F I ~ ,58. . Ihergy bands in a mctalli(~ertiittcr: E F = Fcrmi lcvt4; E+ = mork Eriiwtion.

The initial velocity components of an emitted electron which before emission had the velocity components t i z , I I ~ ,z':, are

J- : ~

Ljz,

p,,

21z1

=

11-2

_

-

~_ _ ~_ _ _

-

(If'i p

+ IS,$)

The contribution of electrons in the initial velocity interval dvzdi~,clv,~to the total current density is

322

(2.

MOLLENHTEDT A N D F. LENZ

Tho contribution of all electrons whose initial velocities have an absolute value between arid v ~ I J , to the current density is

+

We obtain the contribution of all electrons with initial eiicrgies between and e & by substituting 6 = mv2/2 in Eq. ( 5 5 )

+

djj3= 4rmr -exp

hY

6

(- 3)exp (- 6)

€(it

If we divide by j , from Eq. (53) we have the relative contribution of'

1

2

3

4

5

6 E kT

-c-

FIG.5!1. 1listril)ution of initial energies for thcrniionic- ernission.

is the fraction of the total emission current carried by electrons with initial energies between e and e de. ( 2 / v ' i ) d\/c/kTexp ( - e / k T ) d ( e / k Z ' ) is tho contrilirition of an energy interval de t o the cliargc density inside t,he emitter.

+

electrons with initial energies between 6 and distribution

E

+ dc, i.e., thc initial energy

I t should he noted that the contribution of an energy interval rlt to t,he emission current density is different from the contribution of an energy interval de to the charge density in ail electron gas with Maxwell distribu-

ELECTRON EMISSTOX MICROSCOPY

323

(58)

The most probable energy in the distribution Eq. (57) is

Thus we see that a relatively high resolutioii may be attained in thermal emissioii microscopes even if no limitiiig aperture is used. If for example, T = 1300°1<, IEl = 3 . 10: volt c i r ' , Eq. (10) yields (ti0)

'I'ADI.E I\'. EMISSION FROM BASENETAI.S BELOW1000°C ( B .4 F'O RM A T E a ( T I V A T ( ) R ) Good

Poor

Fe

Ti

Ni

Si

C:U

Zr W

C'r c;o

'ra 310

~

Promoters

a

Poisotis

Little effect

Most effective.

B. Instruments and -4pplication.q The first thermionic emission micrographs were published in 1932 (4, 6). Their rcmlutioa limit was of tJhe order of 10 p but it was soon irnproved to 3 p by Bruche and Iiiiecht (111) who obtained some images of

well polished polycrystalline nickel surfaces. The light-microscopical limit was surpassed in 19-42. With an acceleration voltage of 30 kv and a field strength of 30 kv cin-', Boersch (112) attained a resolvable distance of

t I

FIG.60. Thermionic emission microscope (Philips).

700 A in micrographs of thoriated molybdenum. Mecklenburg (113) produced images of pasted Ba-Sr-cathodes in which 400 A were resolved, with an acceleration voltage of 20 kv and a field strength of about 40 kv/cm. Heidenreich (114) described an electrostatic emission microscope operating with an acceleration voltage of 10-25 kv, patterned closely

ELECTRON EMISSIOK MICllOHCOPT

FI~:.61. 6tci.1 surface, activated with BaC,’O:,, at about !JOO°C‘. 1,h.tron optk-al magnification 1300. The lines in one of the grains are vrystal steps w 1 i i i . h aiqwar during observation, presumably in consequence of thermal or vaporization etching (118).

326

G. M6LLENSTEDT A N D F. LENZ

after that of Meckleiiburg (113). The magnification can be varied from 250 to 4000, and the resolution limit is better than 1000 A. A very interesting application of the thermiotiic emission microscope is the observation of transformations in metals and alloys. Grain growth, (125, 116) recrystallization and other structure changes can be continuously observed, and impressive motion-pictures of such processes can be taken. Surface roughness and variations in chemical composition give also strong contrast. Rathenau and Baas (117) have published interesting pictures showing grain growth in NiFc and FeSi alloys, transformations in eutectoid steel from austenite into pearlitc and vicc versa, the influence of chemical treatments on staiiiless steel and other metallographic applications. They have activated the specimen surface by evaporation of barium or cesium or both onto it. By this activation thc work function is reduced. Furthermore, image contrast is obtained since absorption of activator atoms depends on the exposed lattice plane. Therefore grains of identical composition but different orientation emit different current densities. According to Heidenreich (114),the iron group metals caii be activated easily using a solution of barium formate rather thaii evaporated Ba or Sr. Tables I V and V give a qualitative description (114)of the emission from some base metals below IOOO'C, and the effect of metallic additives to barium formate activator on iron and steel (below 1000°C). Heidenreich (114) has studied the A , and A , transformations in plain carboii steels in his thermioriic emission microscope, and drawn some interesting conclusions coiiceriiing the types of reaction occurring during such transformations. An instrument, specially designed for thermionic emission microscopy is shown in Fig. 60. A new instrument in which the image from the cathode lens is magnified by an electrostatic projector lens, has been described by Panzer (118). The specimen can be vertically and horizontally adjusted and tilted under operation. ,4 limiting aperture in the objective back focal plane is used. Figure 61 shows an example of its performance. References 1. 14:. Goldstcin, Ann. Physzk [3]

11, 832 (1880).

9. H. Busch, 4 n n . Physzk [4] 81, 974 (l!U6). 3. M . Knoll, and E. Ruska, Ann. Physzk [5] 12, 607 (1932). 4. M. Knoll, F. G. Houtermans, and W. Schular, 2. Physzk 78, 340 (1932). 6 . E. Bruche, Naturwissenschaften 20, 49 (1932). 6. E. Bruche, and H. Johannson, Naturwissenschaften 20, 353 (1932). 7. A. Rccknagel, 2. Physzk 117, 689 (1941). 8. (2. V. Spivak, and V. I. Lyubchenko, Izvesl. Akad. Nauk S S.9.R , Ser. F i z 23, 697 (195'3).

ELECTRON EMISSION MICROSCOPY

327

A. Recknagel, 2. Physik 120,331 (1943). A. Septier, J . phys. radium 16,573 (1954). A. Septier, Compt. rend. acad. sci. 240, 1200 (1955). L. A. Artsimovich, Zzvest. Akad. Nauk S.S.S.R., Ser. Fiz. 8, 313 (1944). K. Si-men, Acta Phys. Sinica 13, 339 (1957). 1 4 . Chuan-de Wu, Acta Phys. Sinica 12,419 (1956). 16. Chuan-de, Wu, Sci. Sinica (Peking) 6, 381 (1957).

9. 10. 11. 12. IS.

16. H. Boersch, 2. tech. Physik 23, 129 (1942). 17. F. Pradal, and R. Simon, Compt. rend. acad. sci. 244,2150 (1957). 18. W. Dietrich, and H. Seiler, 2. Physik 167, 576 (1960). 19. Yu. V. Vorobyov, Doklady Akad. N a u k S.S.S.R. 120, 751 (1958); Zzvest. Akad. Nauk S.S.S.R., Ser. Fiz. 23, 694 (1959). 80. F. Bertein, J. phys. radium 14,235 (1953). 8f. Yu. V. Vorobyov, Zhur. Tekh. Fiz. 26, 2269 (1956); 29, 589 (1959). 22. D. P. Vinogradov, lzvest. Akad. N a u k S.S.S.R., Ser. Fiz. 20, 1120 (1956); 28, 722 (1959). 89. G. Bartx, Optik 17, 135 (1960). 24. A. Septier, Compt. rend. acad. sci. 236, 652, 1203 (1952); 236, 58 (1953). $6. I. N. Prilezhayeva, V. V. Livshits, and G. V. Spivak, Zhur. Tekh. Fiz. 26, 97 (1955). 26. E. Hahn, Optik 16, 500 (1958); 16,513 (1959). 86a. E.-A. Soa, Jenaer Jahrbuch 1969 I, 115. 27. A. Septier, Ann. radiodlec. 9,374 (1954). 88. G. V. Spivak, and Ye. M. Dubinina, Doklady Akad. N a u k S.S.S.R. 88, 673 (1953); Vestnik Moskov. Univ., Ser. Fiz.-Mat. i Estestven. Nauk 8, 27 (1953). 89. Ye. M. Dubinina, G. V. Spivak, and I. A. Pryamkova, Zzvest. Akad. N a u k S.S.S.R. 23, 762 (1959). SO. J. Gardez, Cowipt. rend. acad. xi.249, 2034 (1959). Sf. P. Lukirsky, and S. Prilefiaev, 2. Physik 49, 236 (1928). 32. W. Koch, 2. Physik 162, 1 (1958). 3s. H. Simon, and R. Suhrmann, “Lichtelektrische Zellen und ihre Anwendungen.” Springer, Berlin, 1932. 34. E. Briiche, 2. Physik 86,448 (1933). 36. J. Pohl, 2. tech. Physik 16, 579 (1934); H.Mahl, and J. Pohl, 2. tech. Physik 16, 219 (1935); H. Mahl, Mineral. u.petrogr. Mitt. 46, 289 (1935). 36. E. L. Huguenin, Compt. rend. mad. sci. 239, 404 (1954); Ann. phys. [13] 2 , 214 (1957). 97. N. Wainfan, W. C. Walker, and G. L. M’eissler, J . Appl. Phys. 24, 1318 (1953). 98. K. Watanabe, F. Marmo, and E. C. Y. Inn, Phys. Rev. 90, 155 (1953). S9. H. Bethge, H. Eggert, and K. Herbold, Proc. 4th Intern. Conf. on Electron Microscopy, Berlin, 1968 p. 217 (1960). 40. H. Gross, and G. Seitx, 2.Phyrik 106, 734 (1937). 41. G. V. Spivak, T. N. Dombrovskaya, and N. N. Sedov, Doklady Akad. Nauk S.S.S.R. ll3,78 (1957). 42. G. Mollenstedt, R. Speidel, and W. Koch, 2. Physik 149,377 (1957). 43. H. E. Ives, and T. C. Fry, J. Opt. SOC.Am. 23,73 (1933); K.Deutscher, Nalurwissenschaften 44, 486 (1957); 2. Physik 161, 536 (1958). 44. R. Kollath, Ann. Physik 161 1, 357 (1947). 46. R. Kollath, in “Landolt-Bornstein Zahlenwerte und Funktionen,” Vol. 11, Part 6, p. 1008. Springer, Berlin, 1959.

328

G. MOLLENSTEDT

AND F. LENZ

J. G. Trump, and R. J. Van de Graaff, Phys. Rev. 76, 44 (1949). H. 0. Muller, 2. Physik 104, 475 (1937). L. Y. Huang, 2. Physik 149, 225 (1957). L. Malter, Phys. Rev. 60, 48 (1936). H. Mahl, 2. tech. Physik 18, 559 (1937); 19, 313 (1938). 51. W. Bayh, 2. Physik 160, 10 (1958). 6% K. H. Steigerwald, Optik 6,469 (1949). 55. G. Bartz, Proc. 4th Intern. Conf. on Electron Microscopy, Berlin, 1958 p. 201

46. 47. 48. 49. 50.

(1960).

64. U. Decker, Physik. Verhandl. 12, 144 (1961). 65. G. V. Spivak, M. G. Kanavina, I. S. Sbitnikova, and T. N. Dombrovskaya, Doklady Akad. N a u k S.S.S.R. 106, 706 (1955). 66. G. Mollenstedt, Proc. European Reg. Conf. on Electron Microscopy, Delft, 1960 p. 8 (1961). 67. M. Knoll, 2. tech. Physik 16, 467 (1935). 58. M. Knoll, and R. Theile, 2. Physik 113, 260 (1939). 69. M. von Ardenne, Z . Physik 109, 553 (1938). 60. V. K. Zworykin, J. Hillier, and R. L. Snyder, A S T M Bull. 117, 15 (1942). 61. D. McMullan, Proc. Inst. Elec. Engrs. (London) 100, 245 (1953). 62. C. W. Oatley, and T. E. Everhart, J . Electronics 2, 568 (1957). 63. K. C. A. Smith, and C. W. Oatley, Brit. J . A p p l . Phys. 6, 391 (1955). 64. T. E. Everhart, K. C. A. Smith, 0. C. Wells, and C. W. Oatley, Proc. 4th Intern. Conf. on Electron Microscopy, Berlin, 1958 p. 269 (1960). 65. R. F. M. Thornley, Proc. 4th Intern. Conf. on Electron Microscopy, Berlin, 1968 p. 173 (1960).

66. K. C. A. Smith, Proc. European Reg. Conf. on Electron Microscopy, Delft, 1960 p. 177 (1961). 67. B. von Borries, and E. Ruska, 2. tech. Physik 20, 225 (1939). 68. D. B. Langmuir, Proc. I.R.E. 26, 977 (1937). 69. S. Maruse, and Y. Sakaki, Optik 16,485 (1958). 70. M. Drechsler, V. E. Cosslett, and W. C. Nixon, Proc. 4th Intern. Conf. on Electron Microscopy, Berlin, 1958 p. 13 (1960). 71. S. Krause, and W. D. Riecke, Mikroskopie 17, 31 (1962). 72. J. H. L. McAuslan, and K. C. A. Smith, PTOC.Stockholm Conf. on Electron Microscopy, 1966 p. 343 (1957). 73. L. Fauldraht, Dissertation, Berlin (1942/43). 74. G. Induni, Helv. Phys. Acta 20, 463 (1947). 75. G. Mollenstedt, and H. Duker, 2. Naturforsch. 8a, 79 (1953). 76. G. Mollenstedt, and F. Heise, Physik. BZ. 6, 80 (1949); G. Mollenstedt, 2. Naturforsch. 7a, 465 (1952); Optik 9,473 (1952). 77. F. Pradal, and R. Simon, Conipt. rend. acad. sci. 247, 438 (1958). 78. C. Fert, in “Trait6 de microscopie 6lectronique” (C. Magnan, ed.),Vol. I, p. 306. Hermann, Paris, 1961. 79. H. C. Bourne, R. W. Cloude, and J. G. Trump, J. Appl. Phys. 26, 596 (1955). 80. P. Cousini6, N. Colombie, C. Fert, and R. Simon, Compt. rend. acad. sci. 249, 387 (1959). 81. K. H. Gaukler, 2. Metallk. 61, 463 (1960). 88. K. H. Gaukler, Diplomarbeit, Tubingen, 1959. 83. W. Bayh, 2. Physik 161, 281 (1958). 84. C. Fert, N. Colombie, B. Fagot, and P. van Chuong, “Le bombardewient ionique.”

ELECTRON EMISSION MICROSCOPY

329

Colloqzies Internationaux du Centre National de la Recherche Scientifigue, N o . 113/67, Editions du C N R S , Paris, 1962. 86. B. Fagot, and R. Santouil, Compt. rend. acad. sci. 264, 2147 (1962). 86. C. Fert, Lecture on 5th Intern. Congr. for Electron Microscopy, Philadelphia, 1968 1, A-7 (1962). 87. R. Speidel, 2. Physik 164, 238 (1959). 88. S. Leisegang, Proc. 3rd Intern. Conf. on Electron Microscopy, London 1954

p. 184 (1956). 89. W. Feitknecht, Helv. Chini. d c t a 7, 825 (1924); T. Braun, Z. Physik 40, 686

(1927). 90. R. L. Cunninghani, P. Haymann, C. Lecomte, W. J. Moore, and J. J. Trillat,

J . A p p l . Phys. 31, 839 (1960); F. L. Anderson, and V. F. Holland, ibid. p. 1516; G. D. Magnuson, B. B. Meckel, and P. A. Harkins, ibid. 32, 369 (1961); T. K. Bierlein, and B. Mastel, Rev. Sci. Instr. 30, 832 (1959). 92. 0. C. Yonts, C. E. Normand, and D. E. Harrison, J. A p p l . Phys. 31,442 (1960). 98. G. Wehner, and I). Rosenberg, J. A p p l . Phys. 31, 177 (1960). 98. M. Keller, Diplomarbeit, Tiibingen, 1954. 94. H. Mahl, A n n . Physik [5] 31, 425 (1938). 96. M. Knoll, and E. Ruska, Z. Physik 78, 318 (1932). 96. E. Westermann, Arch. Elektrolech. 30, 109 (1936). 97. G. Mollenstedt, and H. Diiker, Physik. Verhandl. 3, 104 (1952). 98. G. Mollenstedt, and H. Duker, Optik 10, 192 (1953). 99. G. Mollenstedt, and M. Keller, Proc. 3rd Intern. Cmf. on Electron Microscopy, London, 1954 p. 390 (1956). 100. H. Diiker, 2. Metkllk. 61, 314 (1960). 101. L. Wegmann, Nezie Zurich. Zty., Beilage Tech. no. 1266, April 13, 1960. 102. C. Fert, and R. Simon, Compt. rend. acad. sci. 243, 1300 (1956). 103. C. Fert, F. Pradal, R. Saporte, and R. Simon, Proc. 4th Intern. Conf. on Electron ?dicroscopy, Berlin, 1968 p. 197 (1960). 104. E. B. Bas, Vide 16, No. 96, 30:3 (1961). 106. H. Diiker, and A. Illenberger, Proc. 5th Intern. Congr. for Electron Microscopy, Philadelphia, 1968 1, D-5 (1962). 106. G. Miillenstedt, and M. Keller, Rev. univ. mines 12,415 (1956); Radex-Rundschau p. 153 (1956). 107. H. Diiker, 2. Metallk. 61, 377 (1960); Radex-Rundschau p. 406 (1960). 108. G. Cevales, Z. Erzbergbau Metallhuttenwesen 14, 159 (1961). 109. L. Cartz, G. Mollenstedt, and A. Septier, Trans. Intern. Ceramic Congr., Copenhagen, 1968 p. 21 (1962). 110. P. A. Lindsay, Advances in Electronics and Electron Phys. 13, 198 (1960). 111. E. Briiche, and W. Knecht, 2.Physik 92, 462 (1934). 112. H. Boersch, NaturtuSssenschaften 30, 120 (1942). 118. W. Merklenburg, Z. Physik 120,21 (1943). 114. R. D. Heidenreich, J . A p p l . Phys. 26, 757 and 879 (1955). 116. S. R. Rouze, and W.L. Grube, Proc. 5th Intern. Congr. for Electron Microscopy, Philadelphia, 1969 I, CC-6 (1962). 116. J. Nutting, and S. It. Rouse, Proc. 6th Intern. Congr. for Electron Microscopy, Philadelphia., 1962 1, CC-7 (1962). 117. G. U '. Rathenau, and G. Baas, Physica 17, 117 (1951); Acta Met. 2, 875 (1954); Mdtauz (Corrosion-Inds.) 29, No. 344, 1 (1954). 118. It. Panzer, Physik. Verhandl. 10, 197 (1959).

This Page Intentionally Left Blank

Author Index Numbers in parentheses are reference numbers, and are inserted to enable the reader to locate a reference when the authors’ names are not cited in the text. Numbers in italic indicate the page on which the full reference is cited.

A

Beckman, F. S., 45, 64 Bederson, B., 75, 78(30), 79(30), 169 Bekefi, G., 83, 87, 160 Berry, R. S., 121, 163 Bertein, F., 262(20), 327 Bethge, H., 272, 273(39), 282, 327 Bierlein, T. K., 307(90), 329 Biondi, M. A., 103(92), 104(97), 105(102,

Aigain, P., 194(21), 248 Mis, W. P., 81, 160 Altshuler, S., 89, 160 Anderson, F. L., 307(90), 329 Anderson, J. M., 82, 83(51, 52, 53), 85(51, 53), 91(52), 101, 138, 145 (228), 151, 160, 164, 166 Aoki, M., 63(20), 66 Arthurs, A. M., 106(110), 161 Artsimovich, L. A., 258(12), 327 Atkinson, W. R., 141, 164

103, 106, 108), 106(108), 107(103, 114), 109(92, 102, 103), 111(92), 114(92, 142), 124(108, 167), 126, 129(197), 132(108, 197), 139(114, 142), 143(114), 144(114, 227), 145 (227, 231), 146(233), 147(231), 148 (227, 231), 149(222, 234), 150(92, 222, 234), 153(177), 161, 162, 163,

B Baas, G., 326, 329 Babcock, H. D., 9, 42 Bailey, D. K., 1340203), 164 Bailey, T. L., 106(109), 161 Bailey, V. A., 91(68), 160 Barbier, D., 19, 21, 22, 23, 24(33), 27(33), 29, @

Bardeen, H., 176(9), 180, 248 Barnes, W. S., 109(130), 116, 162 Bartels, J., 33, 43 Barth, C. A., 31(41), 43 Barts, G., 262, 286, 287, 289, 327, 328 Bas, B. B., 314, 329 Batdorf, R. L., 195, 248 Bates, D. R., 32, 43, 69, 74, 75(25, 28), 79, 107, 108, 112, 134, 143, 151, 152 (239), 156, 157, 169, 162, 164, 166 Bath, H. M., 176, 181, 182, 183, 248 Bauer, E., 143, 164 Baum, W. A., 7, 42 Bayh, W., 285, 286, 288, 305(83), 328 Beaty, E. C., 105(104), 109(104, 22), 161, 162

Beaufoy, R., 240, 249

164,166

Bloch, F., 128, 164 Boersch, H., 258(16), 324, 327, 329 Boldt, G., 118, 123(155), 163 Borowits, S., 72, 73, 168 Bortner, T. E., 129(192), 130, 164 Borts, P., 158(251), 166 Bourne, H. C., 301(79), 302(79), 328 Bowe, J. C., 84, 87, 160 Bowles, K. L., 41(57), 44 Boxer, V., 220, 221(45), 222, 223, 249 Boyd, T. J. M., 107, 151(239), 162, 166 Brackmann, R. T., 76, 78(34), 109(125), 169, 162

Bradbury, N. E., 128, 164 Brandsen, B. H., 76(33), 78, 114(33), 169 Branscomb, L. M., 69, 74, 109(126), 117, 118, 119, 120, 121(21, 163, 164, 165), 122(21, 152), 135(162), 137,168,162, 163

Brattain, W. H., 176(9), 180, 248 Braun, T., 329 Breen, F. H., 76(31), 169

331

332

AUTHOR INDEX

Brooks, F. P., Jr., 64 Brown, S. C., 82, 83, 85, 87, 91(50), 103(90, 91), 107(91, 114), 114(91), 115, 139(91, 114), 143(114), 144 (114, 222), 149(222), 150(222), 160, 161, 162,164, 166 Bruche, E., 78(42), 169,253,264,311,323, 326, 327, 329 Brueckner, K. A., 79(46), 159 Bruner, E. C., 24(28), 43 Buchdahl, R., 127, 165 Buchelnikova, I. S., 124, 127(171), 135, 163, 164 Buchhols, W., 50(5), 64 Burch, D. S., 116(149), 120, 121, 135 (162), 137(163), 163 Burhop, E. H. S., 69, 74, 80(1), 87(65), 97, 110(132), 142(1), 155, 168, 160, 162 Burkhardt, G., 101(83), 102, 161 Busch, H., 253, 326 Byron, S., 158(251), 165

Codd, E. F., 50, 64 Codling, K., 142(219), 164 Colombie, N., 301(80), 302(80), 306(84) 328 Cook, W. R., 104,161 Cooper, B. J., 218, 248 Corbato, F. J., 51, 64 Cosslett, V. E., 297(70), 328 Courville, G. E., 105(106), 161 Cousinie, P., 301 (80), 302(80), 328 Cowling, T. G., 102(86), 161 Craggs, J. D., 124(170, 175), 125, 127 (186, 187), 132(199), 136, 144(225), 163,164, 166 Crane, H. R., 105(107), 106(107), 161 Crompton, R. W., 91,160 Cronin, H., 24(28), 43 Culler, G. J., 51, 64 Cunningham, R. L., 307(90), 329 Curran, R. K., 111(136), 124(168), 125, 127(185,189), 135,137,162,163,164 Cutler, M., 176, 181, 182, 183, 248

C

D

Cantor, D., 63(21), 66 Carleton, N. P., 33, 34, 43 Carlson, A. W., 217, 230(40), 231, 248 Carts, L., 319(109), 320(109), 529 Cevales, G., 318(108), 320, 399 Chamberlain, J. W., 2, 3(5), 5, 12, 13, 29, 37, 4% 43, 44 Champion, K. S. W., 144, 149(226), 165 Chandrasekhar, S., 74, 76631), 119, 159, 163 Chanin, L. M., 104(97), 105(97, 103, 108), 106(97, 108), 107(103), 109 (103), 124(108, 167), 129, 132(108), 161, 163 Chantry, P. J., 129(196), 164 Chapman, S., 30, 33, 38, 43, 102, 161 Chen, C. L., 145(229), 146(229), 147,150, 158,165 Chuan-de, Wu, 258(14, 15), 327' Chynoweth, A. G., 188, 189,190, 192(15), 194, 195(22, 23, 24), 196(25), 248 Clark, G. L., 145(228), 166 Clark, K. C., 31(43), 43 Clark, W. E., 50, 64 Cloude, R. W., 301(79), 302(79), 328

Dacey, G. C., 195(24), 248 Daley, R. C., 51(11), 64 Dalgarno, A,, 76(33), 78, 94, 104, 106 (110), 107, 108(118), 109(127), 114 (33), 116(150), 117, 128, 159, 160, 161, 162, 163 D'Angelo, N., 75(24), 155, 157, 158, 159 Decker, U., 286, 287, 289(54), 328 Delsemme, A,, 27, 43 DeMars, G. A., 176(8), 184(8), 248 Dickinson, P. H. G., 111, 162 Dietrich, W., 260(18), 283(18), 284(18), 300, 301(18), 327 Dodson, G. A,, 173, 174, 175, 248 Dombrovskaya, T. N., 278(41), 280(41), 282(41), 291(41, 55), 327, 328 Dougal, A. A., 83, 89, 160 Dowell, J. T., 95, 99, 160 Drechsler, M., 297(70), 328 Dreyfus, P., 50(4), 6'4 Droppleman, LeAnn K., 34(51), 35(51),

45 Dubinina, Ye. M., 262(28, 29), 327 Duker, H., 299, 310, 315, 316(100), 317 (loo), 320, 338, 329

333

AUTHOR INDEX

Duncan, R. A,, 24(33), 27(33), 43 Dunn, G. H., 124, 163 Dunn, R. B., 9(11), 42

E Eddington, A. S., 74, 159 Edwards, D. B. G., 56(15), 65 Eggert, H., 272, 273(39), 282(39), 327 Eiber, H., 116(149), 163 Elbert, D. D., 119, 159, 163 Elvey, C. T., 1, 42 Elwert, 101(83), 102(83), 161 Eriksen, W. T., 176, 184, 648 Estrin, G., 62, 63, 66 Everhart, T. E., 295(62, 64), 297, 328 Eyring, H., 154, 165

F Fagot, B., 306(84, 85), 329 Faire, A. C., 144, 149(226), 166 Fan, H. Y., 208, 248 Fauldraht, L., 299(73), 328 Feitknecht, W., 307(89), 329 Feldinan, W. L., 194(21), 248 Fert, C., 300(78), 301(80), 302(80), 306 (86), 313, 314(103), 315, 368, 329 Fineman, M. A,, 112(138), 162 Fite, W. L., 76, 78(34), 79(36), 103(93), 104(94), 109(126), 111, 112(94, 137), 113(94), 115, 159, 161, 162 Forniato, D., 87(64), 91, 160 Fotheringham, J., 58(16), 65 Fowler, R. G., 141, 164 Fox, R. E., 70(7), 95(7), 126, 127(183, 184, 189), 134, 158(7), 158, 183, 164 Foy, P. W., 195(24), 648 Fraser, .'1 A., 78, 79(37), 169 Frost, L. S., 83(60), 91, 92, 94, 95, 160 Fry, T. C., 279(43), 327 Fueno, T., 154, 165 Fundingsland, 0. T., 82, 91(50), 160

Gktner, W., 220, 221(45), 222, 223, 249 Gardez, J., 262(30), 327 Gardner, M. E., 154, 165 Gartlein, C. W., 2 3 ( 2 7 ) , 4?? Garton, W. R. S., 142, 164

Gaukler, K. H., 301,302(81,82), 303(81), 304(81), 305, 309(82), 315, 317(82), 328 Gaydon, S., 135(206), 164 Geballe, R., 116(149), 124(173, 174), 135, 163

Geiger, J., 103(90), 161 Ckltman, S. 74, 78, 79(38), 119, 120, 135(162), 159, 163 Grrjouy, E., 72, 73, 79, 93, 168 Uiacoletto, L. J., 208, 209, 248 Gibbons, J. J., 143, 164 Gilardini, A. L., 83, 87(64), 91, 160 Gilbody, H. B., 78, 79(36), 159 Ginsberg, V. L., 101, 161 Gioniousis, G., 116, 162 Giovanelli, R. G., 75(23), 159 Goldstein, E., 253, 326 Goldstein, L., 69, 82, 83(51, 52, 53), 85(51, 53), 91(52), 101, 103, 105(3), 145(228, 229), 146(229), 147, 150 (229), 158(229), 158, 160, 161: 166 Gould, L., 83, 85, 160 Gray, E. P., 140, 144, 164 Green, J. R., 41(57), 4 Grecnberg, H., 73, 158 Gross, H., 275(40), 277, 367 Grove, D. J., 70(7), 95(7), 135(7), 158 Grube, W. L., 326(115), 329

H Haas, R., 97, 99, 160 Hirm, R., 101(84), 102, 161 Hagstrum, H. D., 136, 164 Hahn, E., 262(26), 327 Hammer, J. M., 75, 78(30), 79(30), 169 Hammcrling, P., 79, 159 Hammond, R. H., 133, 164 Hanson, W. B., 38, 4 Harkins, P. A., 307(90), 329 Harper, S. D., 50(3), 64 Harrick, N. J., 201(29), 202, 203, 248 Harrison, M. A., 125(174), 163 Harrison, D. E., 307(91), 308(91), 329 HassB, H. R., 96, 161 Hasted, J. B., 69, 109, 110, 111(134), 14, 129(196), 158, 162, 164 Haymann, P., 307(90), 329 Healey, R. H., 91, 160

334

AUTHOR INDEX

Heidenreich, R. D., 324, 326, 319 Heise, F., 299(76), 328 Henglein, A., 111(135), 116(135), 162 Herbold, K., 272, 273(39), 282(39), 397 Hersberg, G., 32, 43, 98(80), 161 Heylen, A. E. D., 91, 95, 160 Hickam, W. E., 70(7), 95(7), 127, 134, 135(7), 168, 163 Hildebrandt, A. F., 31(41), 43 Hillier, J., 294, 328 Hiltner, W. A., 7, 49 Hinnov, E., 75(27), 156(249), 169, 166 Hirschberg, J. G., 75(27), 156(249), 169, 166 Hirsh, M. N., 145(230), 146(230), 147 (230), 166 Holland, V. F., 307(90), 329 Holstein, T., 103(87), 107, 108, 109(87), 145(231), 146(231), 148(231), 161, 166 Holt, E. H., 129(195), 132(195), 144, 148 (223), 164 Hornbeck, J. A., 107(115), 114, 162 Hoselits, K., 105(101), 161 Houtermans, F. G., 253(4), 396 Howard, B. T., 173, 174, 175, 248 Howland, B., 144(223), 148(223), 164 Huang, L. Y., 285, 328 Huff, R. W., 51, 64 Huguenin, E. L., 265, 266, 267(36), 268, 274, 275(36), 276(36), 280, 327 Hummer, D. G., 109(125), 112(137), 162 Hunten, D. M., 3, 42 Hurst, G. S., 129(192), 130, 164 Huxford, W., 141, 164 Huxley, L. G. H., 91(68), 92, 160

I Iglitsynz, M. I., 212, 247(37), 248 Illenberger, A., 315, 329 Induni, G., 299, 328 Inn, E. C. Y., 270(38), 327 Iverson, K. E., 59(17), 60(17), 66 Ives, H. E., 279(43), 327

J Johannson, H., 253, 311, 326 John, T. L., 74, 76(33), 78, 79(40), 114 (33), 119, 123(20), 169

K Kanavina, M. G., 291(55), 328 Kantrowitz, A., 102(85), 161 Kaplan, J., 31(42), 43 Kasner, W. H., 103(92), 109(92), 111(92), 114(92), 149(234), 150(92, 234), 161, 166 Keller, M., 310(93), 315(93, 106), 316 (106), 317(106), 329 Kennedy, D. P., 191, 211, 212, 213, 214, 215, 219(43), 220(44), 226(49), 227 (49), 228, 233(18), 235,936,237, 239, 2.49 Kenty, C., 158(252), 166 Kerr, D. E., 140, 144, 145(230), 146(230), 147, 164, 166 Kerwin, L., 70(8), 95(8), 97, 135(8), 168 Kilburn, T., 56, 66 King, G. A. M., 27(37), 34(37), 4.3 King, P., 59(18), 66 Kingston, A. E., 75(25), 156,157,169,166 Kingston, R. H., 210, 211(35), 248 Kirk, C. T., Jr., 244, 245, 249 Kiseda, J. R., 52(13), 66 Kivel, B., 79(46), 169 Kjeldaas, T., 70(7), 95(7), 135(7), 168 Klein, M. M., 79(46), 169 Knecht, W., 323, 329 Knoll, M., 253, 292, 293, 310(95), 326, 398, 329 Koch, W., 264, 268, 269, 271(32), 272 (32), 274(32), 277, 278(42), 279(42), 280, 281(32), 327 Kollath, R., 78(42), 169,283,284(45),327 Kontsevoi, Iu. A., 212(37), 247(37), 248 Kovar, F. R., 105(104), 109(104), 161 Krall, N. A., 79, 169 Krassovsky, V. I., 5, 32, 49 Krause, S., 297(71), 328 Krauss, M., 74, 119, 169 Kuckes, A. F., 156(248), 166 Kushner, R. M., 109(124), 169

L Langmuir, D. B., 295(68), 398 Lamkin, J. C., 78, 169 Lampert, M. A., 103(90), 161 Langevin, P., 104, 154, 161, 166

AUTHOR INDEX

Langstroth, G. F. O., 111(134), 114, 162 Lanigan, M. J., 56(15), 66 Laughlin, C. D., 39, 44 Lawless, W. J., Jr., 45, 6.4 Lawrence, H., 233, 234, 249 Lax, B., 210, 211(36), 248 Lecomte, C., 307(90), 329 Lederhandler, S. R., 208, 209, 248 Ledsham, M., 107(116), 162 Lee, C. A,, 194(21), 2.48 Leffel, C. S., 145(230), 146(230), 147 (230), 166 Lehman, H. S., 172(2), 248 Leiby, C. C., 145(229), 146(229), 147, 150(229), 158(229), 166 Leisegang, S., 307(88), 329 Lenchek, A. M., 40, 44 Lennon, J. J., 129(194), 132(194), 148, 164, 166

Lewis, T. J., 91(69), 95, 152(239), 160, 166

Licklider, J. C. R., 50, 64 Lin, S. C., 102, 161 Lindsay, P. A., 320(110), 329 Lippmann, B. A., 73, 168 Livshits, V. V., 262(25), 327 Lochte-Holtgreven, W., 118, 163 Loeb, L. B., 69, 83(59), 87(59), 168, 160, 186, 249 Logan, R. A., 194(21), 248 Lonergan, W., 59(18), 65 Lowke, J. J., 83(61), 141(61), 160 Lowry, E. S., 50(6), 64 Lukirsky, l'., 262, 263(31), 327 Lynn, N., 108(120), 112, 162 Lyubchenko, V. I., 256(8), 262(8), 386

M McAfee, I<. B., 184, 186, 192, 2.48 McAuslan, J. H. L., 297, 328 McCarroll, R., 107(119), 112(119), 162 McCaulley, J. W., 20(23), 43 McClure, B. T., 144(223), 148(223), 164 McDaniel, E. W., 105(107), 106(107), 109(130), 116(130), 161, 162 McDonough, E., 50(6), 64 McDougall, J., 75(29), 169 McDowell, M. R. C., 104(100), 105(107), 106(107), 109(127), 161, 162

335

McEachran, R. P., 78, 79(37), 169 Machler, W., 154, 166 McIlwain, C. E., 20, 23, 43 McKay, K. G., 186, 187, 188, 192, 194, 195(22), 248 McMullan, D., 295(61), 328 McWhirter, R. W. P., 75(26), 156, 157, 169, 166

Magnuson, G. D., 307(90), 329 Mahl, H., 264, 285, 310, 327, 328, 329 Malamud, H., 75, 78(30), 79(30), 169 Malter, L., 285, 328 Manring, E. R., 9(11), 49 Margenau, H., 81, 104, 160, 161 Marino, L. L., 78, 79(41), 169 Marmet, P., 70(8), 95(8), 97, 135(8), 158 Marmo, F., 270(38), 327 Marovich, E., 9(10), 20(23), 24(32), 42 Martin, I). W., 109(130), 116(130), 162 Maruse, Y., 297(69), 328 Mascrjian, 191, 248 Masscy, H. S. W., 69, 73, 74, 75(28), 76(32), 78, 79, 80(1), 87(65), 97, 107, 110(132), 117, 134, 142(1), 143(28), 151, 155, 158, 169, 162, 163, 164

Mastel, B., 307(90), 329 May, C. J., 106(109), 161 Meacham, L. A., 204, 205, 248 Meckel, €3. B., 307(90), 329 Mecklenburg, W., 324, 326, 329 Megill, L. R., 9(10), 18(17, 18), 33, 34 (511,35, 42, P Meinel, A. B., 14, 43 Merwin-Dagget, M., 51(11), 64 Meyer, N. I., 244, 249 Meyerott, R., 104, 107(113), 161, 169 Michaels, S. E., 204, 205, 248 Misawa, T., 220, 249 Mittleman, M. H., 73(13), 168 Miillenstedt, G., 278, 279(42), 291 (56), 299(76), 308(56), 310, 315(106), 316 (106), 317(106), 319 (log), 320(log), 327, 328, 329

Moffett, It. J., 94, 160 Mohler, F. L., 140, 158(229), 164, 165 Mohr, C. B. O., 107,162 Moiseiwitsch, B. L., 76(32), 78, 108(120), 169, 162

Molnar, J. P., 114(144), 162

336

AUTHOR INDEX

Moore, J. G., 24(28, 29), 43 Moore, W. J., 307(90), 329 Morse, P. M., 73, 74, 169 Motley, R. W., 156(248), 166 Muccini, G. A., 111(135), 116(135), 162 Miiller, H. O., 284(47), 328 Mulcahy, M. J., 129(194), 132(194), 164 Munson, R. J., 109(121), 162 Murley, P. C., 237, 239, 249 Muschlits, E. E., 106(109), 114, 161, 162

N Natason, G. L., 154, 166 Neustadter, S. F., 210, 211(36), 248 Neynaber, R. H., 76, 78(34), 79(41) Nicolet, M., 32(45), 43 Nixon, W. C., 297(70), 328 Normand, C. E., 78(42), 169, 307(91), 308(91), 329 Noyce, R. N., 176, 178(5), 180(5), 181 (51, 248 Nutting, J., 326(116), 329

0 Oatley, C. W., 295(62, 63, 64), 297(64), 328

O’Brien, B. J., 23(27), 39, 42, 43, 44 O’Brien, R. R., 191, 226(49), 227(49), 228, 233(18), 235, 236, 848, 249 Ochs, G. R., 41(57), 44 Odencrants, F. K., 24(29), 43 Olsen, H., 141, 164 O’Malley, T. F., 73(11), 168 Ortenburger, I. B., 38, 43 Oskam, H. J., 115, 140, 148, 162

P Pack, J. L., 83(60, 62), 85, 87(62), 88, 89, 133, 137(210), 160, 164 Packer, D. M., 9(13), 10, 41 Pahl, M., 114, 115, 116(140), 162 Palyukh, B. M., 109(124), 162 Panzer, R., 325(118), 326, 329 Pares, J., 133(200), 164 Parker, J. H., Jr., 91(68), 160 Patapoff, M., 31(43a), 43 Pearce, A. F., 105(101), 161 Pearson, G. L., 194(21), 195(23), 248

Pell, E. M., 205(32), 206, 208, 148 Perri, J. A., 172, 248 Persson, K. B., 144, 150, 166 Pery-Thorne, A., 142(219), 164 Petersen, H. E., 52, 66 Pettit, H. B., 17(16a), 43 Phelps, A. V., 82, 83(62), 85, 87(62),88, 89, 91(50), 92, 94, 95, 103(91), 105 (108), 106(108), 107(91), 114(91, 144), 115, 124(108, 167), 129, 132 (108), 133, 137(210), 139(91), 150 (235), 160, 161, 162, 163, 164 Pliskin, W. A., 172(2), 248 Pohl, J., 264, 327 Powell, C. F., 107(112), 162 Pradal, F., 260(17), 299, 300(77), 313 (103), 314(103), 32?, 328, 329 Prasad, A. N., 124(175), 127(181), 163 PrileZaev, S.,262, 263(31), 327 Prileshayeva, I. N., 262(25), 327 Pritchard, H. O., 135, 164 Pryarnkova, I. A., 262(29), 327 Purdy, C. M., 20(23), 43

R Ramsauer, C., 78(42), 169 Randolf, P. L., 124(173), 135, 163 Rathenau, G. W., 326, 329 Rayleigh, Lord, 2, 42 Read, W. T., Jr., 176, 177, 178, 24.8 Recknagel, A,, 256, 258(7, 9), 326, 327 Ree, T., 154(247), 166 Reed; J. W., 91(68), 160 Rees, M. H., 9(10), 20(22), 24, 34(51), 35(51), 39, 42 Reimann, C. W., 121(166), 163 Resler, E. L., 102(85), 161 Richardson, J. M., 144(223), 148(223), 149, 164, 166 Riecke, W. D., 297(71), 328 Risernan, J., 172(2), 248, Rittner, E. S., 220(47), 249 Roach, F. E., 3(5), 9, 17, 18, 20, 23(27), 24(31, 32, 33), 27(33, 37), 34(37), 39, 42, 44 44 Roach, J. R., 27(35), 43 Robinson, L. B., 79(46), 169 Rogers, W. A., 103(92), 109(92), 111(92), 114(92), 146, 149, 150(92), 161, 166

AUTHOR INDEX

Rose, D. J., 103, 161 Rosenberg, D., 308(92), 329 Rosenberg, L., 73, 168 Rothe, E. W., 78, 79(41), 169 Rouze, S. R., 326(115, 116), 329 Ruska, E., 253, 295(67), 310(95), 326, 328, 329 Rutherford, J. A,, 103(93), 111(93), 115 (93), 161 Ryder, E. J., 184(10), 248 Rymaszcwski, E. J., 218(42), 231 (42), 232(42), 249

S Saby, J. S., 198, 200, 201, 24.8 Sah, C. T., 176, 178, 179(5), 180, 181, 248 Sakaki, Y., 297(69), 328 Sandford, B. P., 20, @ Santouil, R., 306(85), 329 Saporoschenko, M., 109(128), 115, 162 Saporte, R., 313(103), 314(103), 329 Sayers, J., 111, 154, 162, 166 Sbitnikova, I. S., 291(55), 328 Scalzi, C. A., 50(6), 64 Schade, W. J., 31(42), 43 Schisslcr, D. O., 116, 162 Schulz, G. J., 70(9), 95, 96, 97(75), 99, 124(172), 125, 127(180, 182), 129 (198), 135(172), 136, 168, 160, 163, 164 Schulze, W., 253(4), 326 Seaton, M., 76(33), 78, 114(33), 169 Sedov, N. N., 278(41), 280(41), 282(41), 291 (41), 327 Seeber, R. R., 52, 64 Seelbach, W. C., 52(13), 66 Seiler, H., 260(18), 283(18), 284(18), 300, 301(18), 527 Seitz, G., 275(40), 277, 327 Seman, M. L., 121(164), 163 Sena, L. A., 109(124), 162 Septier, A,, 258(10, l l ) , 262(10, 24, 27), 267, 314, 319(109), 320(109), 327, 329 Sexton, M. C . , 129(194), 132(194), 144 (225), 148, 164, 166 Shefov, N. N., 5(7), 42 Sheldon, J. W., 109, 162 Shinc, W. W., 79(46), 169

337

Shockley, W., 167(1), 175(1), 176(5), 177, 178(5), 180(5), 181(5), 184(10), 195 (I), 233, 235(1), 248 Shollette, W. P., 114, 168 Shvekin, V. I., 243, 249 Silverman, S. M., 24(28), 43 Si-men, K., 258(13), 327 Simon, R., 260(17), 265(33), 270(33), 299, 300(77), 301(80), 302(80), 313, 314 (103), 327, 528 Singer, D. F., 218(42), 231(42), 232(42), 249 Singer, 8. F., 40(56), 4.4 Smith, A. C. H., 104(94), 112(94, 138), 113(94), 162 Smith, C. A., 12, 13, 43 Smith, K., 78, 79(39), 169 Smith, K. C. A., 295(63, 64, 66), 296(66), 297(64), 328 Smith, 1’. T., 125, 163 Smith, S. J., 72, 118, 119, 120, 121(163, 165), 135(162), 137(163), 168, 163 Snow, W. R., 103(93), 111(93), 115(93), 161 Snyder, R. L., 294, 328 Boa, E.-A., 262(26a), 327 Sparks, J. J., 240, 241, 243(.54), 244, 246 (54), 249 Sparks, M., 184(10), 24.8 Speidel, R., 278(42), 279(42), 306, 307 (871, 327, 32.9 Spitzer, L., 101(84), 102, 161 Spivak, G. V., 256(8), 262(S, 25, 28, 29), 278, 280, 282(41), 291(41), 326, 327 Spokes, G. N., 121(166), 163 Spruch, L., 73(11), 168 Stabler, R. C., 158, 166 Statz, H., 176(8), 184(8), 248 Stebbings, R. F., 78, 79(36), 104(94), 109(125, 126), 110, 112(94, 131, 137, 138), 113, 169, 162 Steigerwald, K. H., 285, 328 Stein, S., 73, 93, 169 Stevenson, D. P., 116, 162 Stewart, A., 107(116), 162 Stueckelberg, E. C. G., 74(17b), 169 Sugiura, M., 38, 44 Suhrmann, R., 265(33), 270(33), 327 Sumner, F. H., 56(15), 66 Button, D. J., 91(68), 160

338

AUTHOR INDEX

T Takeda, S., 83, 89, 160 Tandberg-Hanssen, E., 18(17, 18), 43 Tang, T., 63(20), 66 Tate, J. T., 125, 163 Tauc, J., 192(19), 848 Teig, M., 52(13), 66 Temkin, A,, 78, 79, 169 Temko, X. V., 212(37), 247(37), 248 Theile, R., 292, 328 Thomson, J. J., 154, 165 Thornburn, R., 124(170), 136(208), 163, 164

Thornley, R. F. M., 295(65), 298, 338 Tohmatsu, T., 24(31), 33, 43 Townsend, J. S., 91, 160 Tozer, B. A., 124(170), 127(186, 187), 136, 163, 164 Trillat, J. J., 307(90), 329 Trujillo, S. M., 78, 79(41), 159 Trump, J. G., 284(46), 301(79), 302(79), 328 Turn, R., 63(21), 65 Turner, B. R., 110, 112(131, 138),168 Tyndall, A. M., 107(112), 109(121), 162

U unsold, 101(83), 102(83), 161

V Van Allen, J. A., 23(27), 43 van Chuong, P., 306(84), 328 Van de Graaff, R. J., 284(46), 328 Van Lint, V. A. J., 103(93), 111(93), 115(93), 129(193), 130, 132, 133 (200), 161, 164 Van Rhijn, P. J., 9, 48 Van Roosbroek, W., 199, 202(30), 241 (261, 2@ Varnerin, L. J., Jr., 83, 87, 150, 160, 247, 249

Varney, R. N., 105(104), 109(129), 115, 116, 161, 162 Vilenski, I. M., 101, 161

Vinogradov, D. P., 262(22), 327 Viswanathan, J. C. R., 63(22), 66 von Ardenne, M., 292, 328 von Borries, B., 295(67), 328 Vorobyov, Yu. V., 260(19), , 262(21), 327

Voshall, R. E., 88, 89, 160

W Wainfan, N., 270(37), 327 Walker, W. C., 270(37), 327 Wannier, G., 103(89), 161 Warner, R. M., Jr., 233, 234, 249 Warren, R. W., 91(68), 160 Watanabe, K., 270(38), 3%' Watson, K. M., 73(13), 168 Weber, O., 118, 123(154), 163 Webster, W. M., 220(46), 849 Wegmann, L., 311(101), 312(101), 329 Wehner, G., 308(92), 329 Weimar, U.,115, 162 Weissler, G. L., 141(215), 164, 270(37), 32r Wells, 0. C.,295(64), 297(64), 328 Wentworth, R. C., 40(56), 44 Westermann, E., 310(96), 329 Wharmby, J. S., 129(196), 164 Williams, C., 104(100), 161 Wu, T., 143, 164

Y Yadav, H. N., 109(127), 162 Yao, I. G., 3(4), 19, 20, 48 Yarin, V. I., 5(7), 48; Yeung, T. H. Y., 152, 166 Yonts, 0. C.,307, 308(91), 329 Young, R. A., 31(43), 43

Z Zener, C., 184, 2.@ Ziegler, B., 109, 162 Zierdt, C. H., Jr., 173, 174, 221, 848 Zumwalt, D., 133(200), 164 Zworykin, V. K., 294, 388

Subject Index Acceleration hypothesis, local, 36, 39-42 Afterglow electron density time variation, 130-140 equations governing particle behavior during, 138-140 microwave, 90-91 Aging, accelerated, of transistors, 178-175 Airglow, 1-2 stations, IGY, 8 Atoms, excited, with kinetic energy of dissociation, 145-146 Attachment dissociative, 124-128 IZ molecule, 126-127 0 2 molecule, 124-125 ozone, 125 of electrons, 116-137 radiative, by O2 molecules, 123-124 three-body , 128-134 OZmolecule, 129-132 Avalanche breakdown, 184-196

by trapping, 177-178 Cathode lens electron optics, 254-262 system with aperture, 258-260 system without aperture, 255-258 resolution limit, 256-257, 260 Cathode sputtering, 307-309 Charge control method of component analysis, 241 ff transfer accidcntal resonance, 112-113 critical distance, 112-113 cross sections, 102-116 He-02, 111 nonresonant, 110-112 probability, 102-103 resonant, 107-110 Circle of least confusion, 256-257 Collisions elastic, of electrons with atoms and molecules, 75-91 Balmer lines of H2, continuum radiation low-energy atomic, 67-165 associated with, 141 elastic and inelastic, 75-116 Bartz secondary emission microscope, Computer fixed-plus-variable structure, 62-64 286, 287 organization, 45-65 Bas ion-induced electron microscope, Conductivity 314-3 15 Bayh secondary emission microscope, 285 complex, of electron gas, 81-82 Bethge, Eggert and Herbold photomicrowave, 82-83 emission microscope, 272 modulation, 201-202, 243-244 Contamination Block addressing system, 56-57 in high voltage scanning microscope, 298 Breakdown in ion-induced emission microscope, double emitter, 229 internal field emission, 192-194 306-307 Contrast in emission microscopy, 252-253 reverse, p-n junction diode, 184-196 Cross section Brightness, 2-4 charge transfer, 102-1 16 momentum transfer, 71, 103 Cambridge scanning secondary electron photodetachment of electrons microscope, 295, 297 Capacitance, layer, junction transistor, from H- ions, 119-120 232-235 from 0- and 0 2 - ions, 120-121 total scattering, 70-71 Capture, radiative, of electrons, 74 Carrier very low energy momentum transfer, generation by trapping, 177-178 85-91 minority helium, 85-86 drift field, 213-216 neon, 87 excess, 199, 208 nitrogen, 87, 88 lifetime, 206 ff noble gases, 87-89 polar molecules, 88-90 transport, 199 Current multiplication in p-n junction, 186 ff density in thermionic emission microrecombination Shockley-Read theory, 176-177 scope, 32&323 339

340

SUBJECT INDEX

excess reverse, 176 ff gain, common emitter, 235-237 hysteresis in p-n junction diode, 171 reverse, from space generation of minority carriers, 179 total, due to electron diffusion and drift, 201 Damping hypothesis, 36, 38-39 Decker secondary emission microscope, 286-288 Detachment collisional, 128-134 of electrons, 116-137 Diffusion, ambipolar, 201-203 Diode, p-n junction, 169-216 forward characteristic, 196-204 reverse breakdown, 184-196 reverse current, 175-184 transient characteristic, 204-21 6 unstable reverse characteristics, 170-175 Drum transfers, 57-58 Duker-Illenberg ion induced emission microscope, 315 Einstein photoeffect relation, 263 Electron affinities, 135-137 ambipolar diffusion coefficient, 103 attachment t o complex molecules, 134-135 t o SFe, 134-135 thermal, 129 density decay following microwave discharge, 132-133 detachment, I1 6-137 emission ion induced, 301-305 microscopy, 251-329 energy distribution in thermionic emission microscope, 32&323 equation of motion i n electric and magnetic fields, 255 -hydrogen atom scattering, 75-80 ion extracted, energy distribution, 298301 low energy atomic collisions involving, 67-165 elastic scattering by hydrogen atoms, 73 mobility, 81, 83-85 secondary emission dependence on target material, 284

energy distribution, 283 influence of angle of incidence, 284285 swarm experiments, 80 ff Emissions, nightglow, 5 Etching, ionic, 307-309 Excitation by electrons accelerated by an electric field, 33-35 mechanisms, nightglow, 29-42 rotational, of molecules by an electron, 73-74 vibrational in nitrogen, 96-99 in oxygen, 99-101 Fermi distribution of electrons inside an emitter, 320 Fert-Simon ion induced electron microscope, 313-314 Field emission, secondary, 285 “Frequency,” collision, 72 Hole distribution, 207 Huguenin photoemission microscope, 266-268 Hydrogen discharge lamp, 270-272 emission in the nightglow, 29 Hydroxyl bands, 12-13 excitation mechanisms, 32 nightglow, 13-14 vibrational levels, 12 Image quality in ion induced emission microscope, 298-310 Impurity atom distribution equation, 227 Injection efficiency, emitter, 237-239 Inversion layer effect on forward characteristics, 200 n-type, on transistors, 221-225 semiconductor, 180-181 Ion (a) -atom charge transfer, 106-113 collisions at low energies, 102-116 conversion reactions, 113-116 potential scattering, 104-106 bombardment surface cleaning, 276277 -electron scattering, 101-102

SUBJECT INDEX

low energy, atomic collisions involving, 67-165 mobility, 102-103 for rcsonant charge transfer, 107-108 thermal, 105-106 studies in gas plasma afterglow, 113114 Ionization rate for holes and electrons, 189 Isophote maps, 17-18 Knoll scanning secondary eIectron microscope, 292-294 Koch photoemission microscope, 268-272 Lifetime minority carrier, 206 ff of semiconductor components, 170-171 LIFO stack, 59-62 Mahl ion induced emission microscope, 310 Malter effect, 285 Man-machine systems, 50-51 Memory content-addressed, 52-54 one-level, 55-59 Metaprograms, 46-49 input-output control systems, 47-48 supervisor, 47 translators, assemblers, compilers, 48 Metioskop, 31 1-313 Microfields, magnetic, imaging of, 291 Microscopy electron emission, 251-329 mirror, 252 reflection, 252 replica, 252 ion induced emission, 298-320 applications, 315-320 cathode sputtering, 307-309 contamination in, 30G307 contrast dependence on ion beam orientation, 305-306 depth of focus, 309-310 image quality, 298-310 photoemission, 262-283 applications, 280-283 instruments, 264-274 resolution limit, 262-264 scanning electron with secondary electrons, 291-298 limitations, 295-297

341

secondary emission, 283-298 improved image quality using apcrture, 288 nonconducting specimen surfaces, 289-29 1 resolution, 288-289 using imaging lenses, 285-291 thcrmionic emission, 320-326 current density, 320-323 electron energy distribution, 3203 23 instruments, 323-326 Mollenstedt-Duker emission microscope, 310-311 Momentum-transfer cross section, 103 frequency, 81 Multiprogramming, 49-52 batch, 50 real-time, 51 Neutralization, mutual, 151-153 Nightglow, 1-44 cellular patterns, 15-18 excitation mechanisms, 29-42 heights, Van Rhijn formula for, 9-11 instrumentation, 6-9 observatories, 9 radiation covariance, 21-22 spectroscopic description, 4-6 Noise pulses of junction current a t breakdown, 194-196 Objectives, immersion, 254 Oxygen 5577 line, 14-22 altitude distribution, 19-21 association energy as source, 31 aurora and trapped electrons, 35-42 diurnal variation, 15 ff statistical distribution of intensities, 18-1 9 molecule nightglow, 29 6300 line, 22-28 activity in the tropics, 27-28 arcs, midlatitude, during time of magnetic activity, 23-27 Page address registers, 56 “Penning” ionizing reaction, 114 Photochemical reactions, 30-33 Photoelectrons from silver, energy -_distribution, 262-263

342

SUBJECT INDEX

Photoemission factors influencing, 274-280 surface layers, 274-277 increase by added thin layers, 277-280 Photometer, Fritz Peak birefringent, 7 Polymer layer formation by radiation, 275 Potential equilibrium junction, 235 punch-through, 226-229 Punch-through potential, 226-229 Push down store, 59 Rate coefficient, three-body, 72 Ray equation, paraxial, 258 ltayleigh, unit of brightness, 2-4 Recombination coefficient, electron energy dependence, 150-151 dielectronic, 142 dissociative, 142-151 helium, 146-148 electron stabilized, 155-158 neon and argon, 144-145, 148 N2-Ne mixture, 149-150 neutral particle stabilized, 153-155 of positive ions with electrons and negative ions, 137-158 radiative, 140-142 three-body, 75, 153-158 two-body, 140-153 Reflection electron microscopy, 252 Register stacks, last-in first-out, 59-62 Replica electron microscopy, 252 Resolution limit cathode lens, 256-257, 260 photoemission microscope, 262-283 secondary emission microscope, 288289 Resolving power, diffraction limit, 261262 Retarding potential difference scheme, 95-96 Richardson-Dushman thermionic emission equation, 321 Richtstrahlwert, 295 Saturation current p-n junction, 175, 178 surface barrier, 182 Scattering elastic of very low energy electrons, 80-91

electron -hydrogen atom, 75-80 -ion, 101-102 inelastic electron involving rotation excitation of molecules, 92-94 involving vibrational molecule excitation, 94-101 Semiconductor device evaluation, 167-250 Sensitivity, photoemissive, 264, 265 Sodium D in nightglow, 28-29 Spectrograph, ICY, speed, 7 Stored-charge characteristic, junction transistor, 240-247 Surface channel formation on junction transistors, 229-230 cleaning by ion bombardment, 276-277 contamination of junction transistors, 219 ff leakage, 180 ff protection of silicon diodes, 172 ThFI, wedge-shaped, layer to increase emission, 278-279 Time constant junction transistor collector, 243 ff saturation, 246-247 “Townsend avalanche,” 186-187 Transistor, junction, 216-247 base-region minority distribution, 241242 collector time constant, 243 ff drift field, 237-238 large-signal switching, 240-241 layer capacitance, 232-235 small signal parameters, 231-239 stability, 218-225 steady-state characteristics, 225-23 1 surface contamination, 219 ff “Transparency thickness” of electron microscope specimen, 251 Transport efficiency, base region, 237-239 Trapped electron method, 95-96 Tubes, geomagnetic, 36 ff Velocity, surface recombination, 220-221 Volt-ampere property of p-n junction, 175 Zener breakdown, 184-196 Zenith distance, 10 Zworykin, Hillier and Snyder scanning electron microscope, 294-295