ADVANCES IN ELECTRONICS AND ELECTRON PHYSICS
VOLUME 57
CONTRIBUTORS TO
THISVOLUME
R. Stephen Berry P. Braun D.-J. ...
27 downloads
693 Views
24MB Size
Report
This content was uploaded by our users and we assume good faith they have the permission to share this book. If you own the copyright to this book and it is wrongfully on our website, we offer a simple DMCA procedure to remove your content from our site. Start by pressing the button below!
Report copyright / DMCA form
ADVANCES IN ELECTRONICS AND ELECTRON PHYSICS
VOLUME 57
CONTRIBUTORS TO
THISVOLUME
R. Stephen Berry P. Braun D.-J. David Delon C. Hanson Robert J. Kelly Sydney Leach Henry W. Redlien F. Riidenauer F. P. Viehbock
Advances in
Electronics and Electron Physics EDITEDBY CLAJRE MARTON Smithsonian Inst itut ion Washington, D.C.
VOLUME 57
198 1
ACADEMIC PRESS A Subsidiary of Harcourt Brace Jovanovich, Publishers
New York London Toronto Sydney San Francisco
COPYRIGHT @ 198 1, BY ACADEMIC PRESS, 1NC. ALL RIGHTS RESERVED. NO PART OF THIS PUBLICATION MAY BE REPRODUCED OR TRANSMITTED IN ANY FORM OR BY ANY MEANS, ELECTRONIC OR MECHANICAL, INCLUDING PHOTOCOPY, RECORDING, OR ANY INFORMATION STORAGE AND RETRlEVAL SYSTEM, WITHOUT PERMISSION IN WRITING FROM THE PUBLISHER.
ACADEMIC PRESS, INC. I 1 1 Fifth Avenue, New
York, New York 10003
United Kingdom Edition published by ACADEMIC PRESS, INC. ( L O N D O N ) LTD. 24/28 Oval Road, London NWI 7DX
LIBRARY OF CONGRESS CATALOG CARD NUMBER: 49-7504 ISBN 0-12-014657-6 PRINTED IN THE UNITED STATES OF AMERICA
81 82 83 84
9 8 7 6 5 4 3 2 1
CONTENTS CONTRIBUTORS TO VOLUME 57 . . . . . . . . . . . . . . . . . . . . . FOREWORD. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
vii ix
.
Elementary Attachment and Detachment Processes I1 R . STEPHEN BERRY AND SYDNEY LEACH
I . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . .
1
. . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . .
4 125
11. Specific Processes
Fiber Optics in Local Area Network Applications DELONC . HANSON I . System Requirements and Trends . . . . I1. The Optical Communication Medium . . 111. Terminal Device and System Performance . References . . . . . . . . . . . . . . .
. . . .
. . . .
. . . .
. . . .
. . . .
. . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . .
145 162 189 225
Surface Analysis Using Charged-Particle Beams P . BRAUN.F. RUDENAUER. AND F. P. VIEHBOCK I . Introduction . . . . . . . . . . . . . . . . . . I1 . Classification of Methods . . . . . . . . . . . . . 111. Quantitative Elemental Analysis . . . . . . . . . IV . Depth Profiling . . . . . . . . . . . . . . . . . V . Elemental Mapping . . . . . . . . . . . . . . . VI . Three-Dimensional Isometric Elemental Analysis . . VII . Sensitivity and Resolution Limits . . . . . . . . References . . . . . . . . . . . . . . . . . . .
. . . . . . .
. . . . . . .
. . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . .
231 233 242 259 215 292 298 306
Microwave Landing System : The New International Standard HENRYW . REDLIEN AND ROBERT J . KELLY
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . I1. The Operational and Functional Requirement for MLS . . . . . . . .
111. Description of the Microwave Landing System .
. . . . . . . . . . . IV. System Design Considerations . . . . . . . . . . . . . . . . . . . V . Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . V
311 320 327 358 405 406
vi
CONTENTS
Microprocessor Systems D.-J. DAVID I . The Microprocessor Revolution
. . . . . . . . . . . . . . . . . . 411
I1. Components of a Microprocessor System . . . . . . . . . . . . . . 424
111. How to Deal with a Microprocessor-Based Application . . . . . . . . IV . System Development . . . . . . . . . . . . . . . . . . . . . . . V . The Choices in the Designofa Microprocessor System . . . . . . . . VI . Conclusion : A Glimpse into the Future . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . .
448 454 462 469 470
AUTHORINDEX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . SUBJECT INDEX
473 489
CONTRIBUTORS TO VOLUME 57 Numbers in parentheses indicate the pages on which the authors’ contributions begin
R. STEPHEN BERRY,Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois 60637 (1) P. BRAUN,Institut fur Allgemeine Physik, Technische Universitat Wien, Karlsplatz 13, 1040-Vienna, Austria (231)
D.-J. DAVID,University of Paris and ENSAM, Paris Cedex 05, France (41 1) DELON C. HANSON,Hewlett-Packard Company, Optoelectronic Division, Palo Alto, California 94304 (145) ROBERTJ. KELLY,Communications Division, The Bendix Corporation, Towson, Maryland 21204 (31 1) SYDNEY LEACH,Laboratoire de Photophysique Moleculaire du C.N.R.S., Universitt Paris-Sud, 91405 Orsay, France (1) HENRY W. REDLIEN, Communications Division, The Bendix Corporation, Towson, Maryland 21204 (311)
F. RUDENAUER, Institut fur Allgemeine Physik, Technische Universitat Wien, Karlsplatz 13, 1040-Vienna, Austria (23 1)
F. P. VIEHBOCK, Institut fur Allgemeine Physik, Technische Universitat Wien, Karlsplatz 13, 1040-Vienna, Austria (23 1)
vii
This Page Intentionally Left Blank
FOREWORD The five articles that make up this volume survey modern research in two areas of fundamental physics and three areas of engineering. The article by R. Stephen Berry and Sydney Leach completes an extensive review of elementary collision processes and free charged particles at thermal energies in gases. We expect this article to be widely cited. With the extraordinarily rapid growth of fiber optic communications, in-depth reviews of current work such as that by Delon C. Hanson are vital for the development of the field. His article on local area network applications focuses on a particularly important aspect of the subject. One of the strong relations between the principles of electron physics and of materials science is discussed in the article by P. Braun, F. Rudenauer, and F. P. Viehbock in their review of surface analysis, a subject of great interest. Thecontribution by Henry W. Redlien and Robert J. Kelly on microwave landing systems has value not only to those working in the subject, but to a full complement of researchers concerned with ranging and guidance. We are particularly pleased to have this article because it helps us to expand the perspective of the advances. Little need be said about the role of microprocessors in research. D.-J. David’s article deals with information important to anyone working with microprocessors or considering their value to his or her work. As is our custom we present a list of articles to appear in future volumes of Advances in Electronics and Electron Physics. Critical Reviews: Atomic Frequency Standards Electron Scattering and Nuclear Structure Large Molecules in Space The Impact of Integrated Electronics in Medicine Electron Storage Rings Radiation Damage in Semiconductors Visualization of Single Heavy Atoms with the Electron Microscope Light Valve Technology Electrical Structure of the Middle Atmosphere Microwave Superconducting Electronics Diagnosis and Therapy Using Microwaves Computer Microscopy Image Analysis of Biological Tissues Seen in the Light Microscope Low-Energy Atomic Beam Spectroscopy History of Photoemission Power Switching Transistors ix
C. Audouin G. A. Peterson M. and G . Winnewisser J. D. Meindl D. Trines N. D. Wilsey and J. W. Corbett J. S. Wall J. Grinberg L. C. Hale R. Adde M.Gautherie and A. Priou E. M. Glaser E. M. Horl and E. Semerad W. E. Spicer P. L. Hower
X
FOREWORD
Radiation Technology Diffraction of Neutral Atoms and Molecules from Crystalline Surfaces Auger Spectroscopy High Field Effects in Semiconductor Devices Digital Image Processing and Analysis Infrared Detector Arrays Energy Levels in Gallium Arsenide Polarized Electrons in Solid-state Physics The Technical Development of the Shortwave Radio Chemical Trends of Deep Traps in Semiconductors Potential Calculation in Hall Plates Gamma-Ray Internal Conversion CW Beam Annealing Process and Application for Superconducting Alloy Fabrication Polarized Ion Sources Ultrasensitive Detection The Interactions of Measurement Principles, Interfaces and Microcomputers in Intelligent Instruments Fine-Line Pattern Definition and Etching for VLSI Recent Trends in Photomultipliers for Nuclear Physics
L. S. Birks G. Boato and P. Cantini M. Cailler, J. P. Ganachaud, and D. Roptin K. Hess B. R. Hunt D. Long and W. Scott A. G. Milnes H. C. Siegmann, M. Erbudak, M. Landolt, and F. Meier E. Sivowitch P. Vogl G. DeMey 0. Dragoun
J. F. Gibbons H. F. Glavish K. H. Purser W. G. Wolber Roy A. Colclaser J . P. Boutet, J. Nussli, and D. Vallat
Waveguide and Coaxial Probes for Nondestructive Testing of Materials Holography in Electron Microscopy The Measurement of Core Electron Energy Levels Millimeter Radar Recent Advances in the Theory of Surface Electronic Structure Rydberg States Long-Life High-Current-Density Cathodes
Henry Krakauer R. F. Stebbings Robert T. Longo
Supplementary Volumes: Microwave Field-Effect Transistors
J . Frey
Volume 58 : Modeling of Irradiation-Induced Changes in the Electrical Properties of Metal-Oxide Semiconductor Structures
Point Defects in Gap, GaAs, and InP The Collisional Detachment of Negative Ions Implementation for Very Large-Scale Integration Stimulated Cerenkov Radiation Materials Consideration for Advances in Submicron Very Large-Scale Integration
F. E. Gardiol K. J. Hanssen R. N. Lee and C. Anderson Robert D. Hayes
J. N. Churchill, P. E. Hollmstrom, and T. W. Collins U. Kaufmann and J. Schneider R. L. Champion Heiner Ryssel John E. Walsh D. K. Ferry
Our sincere thanks to all of the authors for such splendid and valuable reviews. C. MARTON
ADVANCES IN ELECTRONICS AND ELECTRON PHYSICS
VOLUME 57
This Page Intentionally Left Blank
ADVANCES IN ELECTRONICS AND ELECTRON PHYSICS. VOL. $7
Elementary Attachment and Detachment Processes. I1 R. STEPHEN BERRY Departmeni of Chemistry and The James Franck Institute The University of Chicago Chicago, Illinois
SYDNEY LEACH Laboratoire de Photophysique Moldculaire du C.N.R.S.* Vniversitd Paris-Sud Orsay, France
I. Introduction ..... ....................................... 11. Specific Processes . .......................... A. Dissociative Recombination and Attachment . . . . . . B. Collisional Detachment and Ionization. . . . . . . . . . . . C. Ion-Pair Formation . . . . . .......................................... D . Ion-Ion Neutralization ......................... E. Photoionization ............................................
.......................................... G . Multiphoton Ionization.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . H. Photodetachment . . . . . . . . . . . . . . . .................................. References ..................................................
1
42 60 93
112
I. INTRODUCTION This review continues the task begun in the article by Berry (1980a),which is referred to here as Part I.’ The goal of the review is a description of the elementary collision processes associated with the production and capture of free charged particles in gases at thermal energies, up to a few electron volts, apart from photoionization, which only commences with photons of several volts. We address the scientist who is not a specialist in atomic and molecular colIisions. It is our intent to convey the currently held physical pictures of the most important processes, to give a sense of the orders of magnitude of their rates and cross sections, and to provide an entry into the enormous literature
* Laboratoire associe a I’UniversiteParis-Sud.
’ See Advances in Electronics and Electron Physics, Vol. 51, pp. 137-182 (1980). Copyright 8 1981 by Academic Press, Inc. All rights of reproductionin any form reserved.
ISBN 0-12-014651-6
TABLE I CLASSIFICATION OF ELEMENTARY ATOMIC/MOLECULAR PROCESSES Initial state Process number
Nuclear
Final state
Electronic
Nuclear
Electronic
Special conditions
Name and process Radiationless transition; internal conversion (intersystem crossing if forbidden with respect to change of electron spin) AB +AB* Autoionization, preionization AB or AB* + AB' + e ; autodetachment AB- 4AB e
1
Bound
Bound, excited
Bound, excited
Bound
2
Bound
Bound
Free
3
or Bound, excited Bound or
Bound Bound, excited Bound, excited
Free
Bound
Bound Free
Predissociation ABorAB*+A
4
Bound, excited Bound
Bound
Bound, excited
Inverse autoionization or preionization ; dielectronic recombination AB+ + e -+ AB* ; (radiationless, nondissociative) attachment AB + e + A B Inverse predissociation A + B+AB*orAB
N
5
Free
Bound
6
Free
Bound
or Bound, excited Bound
or Bound, excited Bound
+
Bound Bound, excited Bound Bound
Photon released
+B
Radiative recombination A f B + A B + hv, AB+ radiative attachment AB + e + A B - + hv
+ e + A B + hv,
W
7
Free
Bound
Bound
Free
8
Free, excited
Bound
Bound
Free
9
Free
Bound, excited
Bound
10
Bound
Free
Free, rearranged Free
Bound
11
Free
Bound
Free
Free
12
Free
Bound
Free
Bound, ionic
13
Free
Bound, ionic
Free
Bound
14
Bound
Bound, excited
Free
Bound, ionic
15
Bound
Bound
Bound
Free
Photon absorbed
16
Bound
Bound
Free
Bound
Photon absorbed
17
Bound
Bound
Free
Bound
Associative ionization chemionization, Hornbeck-Molnar process A or A* + B-t AB + e; associative detachment A + B- +AB + e Penning ionization A* + B -t A t B+ + e; Penning detachment A* + B- - t A + B + e Rearrangement ionization, Kuprianov process A* + B C - + A B + + C + e Dissociative recombination AB+ + e+A + B; dissociative attachment AB + e+-A + BColIisional ionization A + B - + A + B+ + e ; collisional detachment A + B-+A + B + e Ion-pair formation A+B-+A++BIon-ion neutralization (occasionally recornbination) A+ + B - - t A + B ( o r A B ) (Dissociative) ion-pair formation AB* + A + + BPhotoionization AB + hv + AB+ + e ; photodetachment AB- + hv -t AB + e Photodissociation AB + hv + A + B or AB + hv+A+ + B Dissociative ionization A B * - t A + B+ + e
4
R. STEPHEN BERRY AND SYDNEY LEACH
in this field. We have also taken this opportunity to point out several unresolved problems, inconsistencies, and discrepancies in the current literature. We do not attempt to be exhaustive in our coverage. As in Part I (Berry, 1980)a), we apologize in advance to our colleagues for omission of material that they may feel we should have included. The organization follows the pattern set in Part I, with minor variations. The processes of interest were given in Table I of Part I ; that table is reproduced here (Table I).Just as the main sections of Part I corresponded approximately to the first 9 categories of this table, the sections of this discussion begin with the 10th category and continue through the 17th. However, we have grouped some closely related processes, notably ion-pair formation (process 12) with dissociative ion-pair production (process 14). Photodissociation is treated only as a competitor for photoionization or photodetachment, on the basis that we are concerned with charged systems, principally. Photodetachment is given its own section, separate from photoionization. Because of the great increase in activity in the subject, we have also given a separate section to multiphoton ionization.
11. SPECIFIC PROCESSES A . Dissociative Recombination and Attachment
1. General Description Dissociative recombination of electrons e
+ AB++A + B
(1)
and dissociative attachment of electrons,
+ AB+A- + B
(2) have so much in common that we treat them together. The close relation of these processes was recognized long ago by Bates (1950b). Note that A or B may be a polyatomic fragment, and that either A or B might be left in an excited state-electronically, or, if the species is molecular, then vibrationally or rotationally-following reaction (1) or (2). The essential physics of both processes is the same: a free electron becomes a bound electron and the reason the electron remains bound is that some or all of the energy released in the attachment process is carried off in the kinetic energy of the dissociating heavy products. Typically, both processes carry the system “downhill” in the following sense. Translational energy of an electron is given up for translational energy of relative motion of heavy particles. For a given amount of translational e
5
ELEMENTARY ATTACHMENT AND DETACHMENT PROCESSES
energy, the density of states and, therefore, the partition function and the entropy are higher if the effective mass is large rather than small. While one can find cases in which dissociative recombination or attachment is endoergic enough to bind fast, hot electrons and generate cold, slowly moving heavy particles, we can expect that when these processes are iso- or exoergic, then they are entropy increasing. Dissociative recombination was reviewed by Bardsley and Biondi (1970) and earlier by Danilov and Ivanov-Kholodnyi (1965).The topic was included in broader reviews by Flannery (1972, 1976) and Bates (1975, 1979). An older review by Biondi (1964) concentrated on the processes relevant to atmospheric recombination. Dissociative attachment was reviewed by FiquetFayard (1974a) and was included both in a review of resonant scattering of electrons (Bardsley and Mandl, 1968) and, peripherally, in the review of the reverse process of associative detachment written by Fehsenfeld (1975). The book edited by Bates (1962) and that by Massey et al. (1974), of course, discuss both processes. Dissociative recombination has been studied extensively for the very simplest systems such as e + H,+ and somewhat for clusters of hydrogen and helium; the process has been pursued in depth by a few laboratories for the heavier rare gas molecule ions: recombination of CH+ + e and H 3 + + e have generated considerable interest for their astrophysical implications: N O + + e has been and continues to be the most popular system for the study of dissociative recombination. A few other systems, often related to these, such as HCO+ + e, have been examined, and recent studies have now e, H 3 0 + e, and been carried out for polyatomic ions such as NH,+ clusters of H,O+.(H,O), .The subsequent discussion is organized along these lines, approximately, following a description of how the process is supposed to occur. Dissociative attachment has been studied almost exclusively with molecules containing halogens or with other highly electronegative “electron catchers” such as 0 atoms or OH groups. There are exceptions; the most notable is H, + e giving HH (Schulz and Asundi, 1965). The physical processes of recombination and attachment are similar in that the electron is drawn to the molecule by a long-range attractive potential, whereupon the energy of attachment must be carried off by the breaking of a chemical bond faster than the electron can regain enough energy to go free again. The essential problem for theorists has been finding out what makes the electron stick long enough to allow a bond to break, and identifying the mechanism of energy transfer between the incoming electron and the other degrees of freedom of the system. The indices available for evaluating the various interpretations have been the temperature dependence of recombination and attachment coefficients-a very difficult and meager index for
+
+
+
6
R. STEPHEN BERRY AND SYDNEY LEACH
testing theory in this particular situation-and, more recently, the dependence of the corresponding cross sections on electron energy (Peart and Dolder, 1973b, 1974a,c; McGowan et al., 1976, 1979; Auerbach et al., 1977; D. Mathur et al., 1978; Mitchell and McGowan, 1978),and the cross sections for production of specific states of the products (Phaneuf et al., 1975; Vogler and Dunn, 1975). Whatever the details of the mechanism at a microscopic level, the most significant gross features of the two processes are these. In dissociative recombination, the cross sections and rate coefficients, in the large, are decreasing functions of electron energy over the range from zero to tens of electron volts. The smallest, simplest molecules, such as H,+, HD’, and D,+, have maximum cross sections between and cm’, for zero-energy electrons (Auerbach et al., 1977); cross sections for larger, more complex molecules are somewhat larger: NH4+ has a recombination cross section of 3 x 10- l 3 at an electron energy of about 0.065 eV (Dubois et al., 1978): that of H,O+ is about 1.5 x 10- 14, based on a thermal rate coefficient of (4.1 f 1.0) x lo-’ cm3/sec at temperatures between 2000 and 2450 K (Hayhurst and Telford, 1974). Clusters such as H5+(Leu et al., 1973b) and H30+.(H,0), (Leu et al., 1973a) have recombination rate coefficients as much as ten times larger than those of the simple H3+ and H 3 0 + ions. An illustration of the behavior of a typical rate coefficient with temperature of the electrons is in Fig. 1. This is a representation of a large number of data assembled by Heppner et al. (1976) for e + H 3 0 + . The cross sections and rate coefficients for dissociative attachment do not have as universal a pattern as their counterparts for dissociative recombination, nor are the parameters for attachment as large. In many cases, the cross sections for attachment of electrons to neutrals are very small for low-energy electrons and rise with electron energy to a maximum somewhere in the range of a few tenths of an electron volt to a few electron volts; moreover, these cross sections frequently exhibit peaks and dips comparable in amplitude with the cross sections themselves. The process e + F, + F + F- is a simple illustration: The rate coefficient for this process appears to have a single sharp peak at or very near the zero ofelectron energy E , and to decrease sharply as E , goes up to about 6 eV (Schneider and Brau, 1978; Tam and Wong, 1978). This coefficient falls as Ep3/’ from just under lo-* to about 6 x lo-’ cm3/sec between about 0.2-0.4 and 6 eV. By contrast, the cross section for formation of 0 - from e + 0, has a sharp onset at E, of 4.4 eV (Schulz, 1962). Carbon monoxide, CO,, SO,, and H,O were also shown by Schulz to have sharp thresholds for the onset of dissociative attachment, with cross sections that rise and then fall with electron energy. Moreover, the cross sections for such processes are comparable to or smaller than gas-kinetic cross sections; the peak of the cross
7
ELEMENTARY ATTACHMENT AND DETACHMENT PROCESSES
I
W v)
‘I
m
z W
I
TEMPERATURE
( O K )
+
+
FIG.I . Rate coefficients measured for the recombination process e HaO++ H H,O. The curves were calculated by Heppner et a/. (1976), with various uncertainties; the solid curve is, in essence, their “base case.” All the points shown represent data considered by Heppner ef a/., with the exception of the two solid circles, which were taken from the recent work of Ogram er a/. (1980). This work was done at high temperatures in a shock tube, and this could account for the high rate at 3000 K.Taken, with permission, from Heppner et al. (1976).
section for e + O2 -+ 0 + 0 - ,just below 7 eV of electron energy, is 1.3 x, lo-’* cm2 (Schulz, 1962), and the peaks for 0-production from CO and CO, are 2.2 x and 4.6 x cm2, respectively. Christophorou and Stockdale (1968) examined cross sections for dissociative attachment, nDA,in some 30 molecules. They found it useful to classify these molecules into three groups according to the energy and magnitude of the peak of cDAas a function of electron energy. For the first group, the peak falls at an energy below the first electronically excited state of the molecule and is 10- l 7 cm2 or more. The second group has peak cross sections between cm2, and the peak occurs above the energy of the first and electronically excited data of the molecule. The third group has cross sections of less than 2 x lo-,’ cm2. The first group includes halogen-containing molecules and one peak of N 2 0 ; the second includes H 2 0 , NO, CD,, one
8
R. STEPHEN BERRY AND SYDNEY LEACH
peak of CO, and N,O and two peaks of H,. The last group includes the lowest peak for H,, one peak of CO,, and the C O molecule. In simplest terms, the reasons for these differences are, first, the difference between the Coulomb attraction of an ion for an electron and the much weaker dipolar or polarization field that a neutral molecule exerts on an electron ; and second, the electron with thermal energy approaching a molecular positive ion always finds bound molecular states available to it, whereas an electron approaching a neutral will, in most cases, have to supply some energy to the molecule to make a bound state available for itself. This second distinction has meant that theorists have been able far more frequently to assign labels to the states responsible for electron capture leading to dissociative attachment than to assign the labels to states responsible for dissociative recombination. 2. Dissociative Recombination: The Rare Gases The demonstration and interpretation of dissociative recombination began with the dilemma of explaining observed ionospheric recombination rates several orders of magnitude greater than those of the mechanisms then considered radiative recombination and ion-ion neutralization. Bates and Massey (1946b) suggested such a dissociative process. High rates of recombination were demonstrated in the laboratory from microwave studies of the decay of plasmas in helium (Biondi and Brown, 1949), whereupon Bates (1950a,b) attributed these rates to the specific process e
+ He:
(3)
42He
Biondi then took up a systematic investigation to establish the mechanism of electron-ion recombination in gases, an investigation that has continued to the present time. The first product of Biondi’s work was the demonstration (1963) that in afterglows following microwave discharges, for a wide range of conditions, electron-ion recombination is a volume process, not a wall process, and that the volume process has kinetics consistent only with the above type of reaction. Notably, he used argon and helium-argon mixtures to show that the recombination of electrons with argon ions occurs via e
+ Ar:
-+Ar
+ Ar*,
Ar* + A r
+ hv
(4)
The mechanism was taken to be the one suggested by Bates, a direct transition from e Ar,+ to a state with a repulsive potential curve dissociating to Ar + Ar*. The presence of excited atoms in rare-gas afterglows was previously established and correlated with the decay of the free electron concentration (Holt et al., 1950; Johnson et al., 1950). Biondi (1963) pointed out in that first paper of his series how important it would be t o measure the
+
ELEMENTARY ATTACHMENT AND DETACHMENT PROCESSES
9
kinetic energy distribution of the emitting atoms, in addition to the temporal dependence of the electron concentration and the temporal, spatial, and spectral distribution of the radiation. [The importance of the spatial distribution of the electron distribution, especially for microwave experiments, was demonstrated by Kasner and Biondi (1965). J The first effort by Biondi and his collaborators (Rogers and Biondi, 1964) to find the high kinetic energies in atoms produced by process (1) was inconclusive. This work, of recombination in helium, was particularly influential in stimulating a series of theoretical and experimental studies that eventually established the special nature of helium; we shall discuss recombination in helium shortly. Connor and Biondi (1965) then investigated recombination in neon, by monitoring the temporal dependence of electron concentration and, by interferometry, the shapes of atomic emission lines in neon afterglows. The allowed singlet-singlet p + s transition at 585.2 nm showed a width appropriate to two neon atoms separating with a relative kinetic energy of 1.25 f 0.07 eV. In fact, the line shapes in the afterglow were interpreted as having narrow central components rising out of the middle of broader lines. The latter parts were attributed to neon atoms that emitted radiation after recombination and dissociation occurred, but before the excited atoms suffered collisions. The narrow central parts were attributed to neon atoms with thermal velocity distributions that had become excited by transfer of electronic energy from a fast excited atom colliding with a slow atom after dissociation. The recombination coefficient at 300 K was found to be about 2 x lo-’ cm3/sec and the cross section for energy exchange, (8 & 2) x cm2 at the velocity of 2.5 x lo5 cm/sec, of the dissociating atoms. Later, Frommhold and Biondi (1969) used the same methods to reinvestigate recombination in neon and to examine the process in argon. They confirmed the basic finding of Connor and Biondi, but pointed out that if the dissociating ions have several possible exit channels, each channel should contribute its own broad component to any Doppler-broadened emission line. All the 22 neon lines and the 5 argon lines studied by Frommhold and Biondi showed broadening indicating dissociative recombination. Some lines, such as the 585.2 nm line of Ne, displayed one dominant broad component, but virtually all of them had at least indications of other components. Frommhold and Biondi were led to suppose that some molecular ions were in an excited state, and that recombination could lead to several possible excited states of the product atoms. Biondi and his group continued to study recombination in the heavier rare gases (Shiu and Biondi, 1977, 1978; Shiu et al., 1977) with emphasis on the dependence of the rate coefficient on electron temperature T, and on the relationship between the electron temperature and which excited states
10
R . STEPHEN BERRY AND SYDNEY LEACH
occur in the product atoms. The trend seems to be that the recombination coefficients a increase slightly with the size of the atoms: (9.1 i- 0.9) x at 300 K for Ar,' + e, (1.6 0.2) x for Kr,' e, and (2.3 i-0.2) x cm3/sec for Xe,' + e. The temperature dependencies of these coefficients are not so systematic: a(Ar) T-o.61, a(Kr) T - 0 . 5 5 and , a(Xe) T - u 3 for 300 < T, < 700 K merging smoothly into T-'.', dependence for higher T . The three substances showed the same behavior regarding the atomic excited states that appeared: When T, was 300 K, the only atomic lines seen were attributable to electrons recombining with the diatomic molecular ions in their ground electronic and vibrational states. When T, was increased to make the mean electron energy of order 0.6-0.7 eV, higher atomic lines were detected, corresponding to electrons recombining with excited ion-molecules. The processes specific to the recombination of hot electrons are presumably much like those that occur in dissociative attachment, involving collisional excitation accompanied by electron capture in the excited state. Hence, these processes are analogous to dielectronic recombination (cf. Berry, 1980a, p. 155; Bates, 1975).In principle, electronic, vibrational, or rotational degrees of freedom of the ion-molecule could be excited by the incoming electron and act as the energy sink to stabilize the newly formed neutral. The evidence suggests that electronic and vibrational excitation may play significant roles in dissociative recombination, but that rotational excitation would only play a role in very cold systems (Bardsley, 1968b). However, the experimental results for neon show significant differences in the behavior of the recombination rate coefficients, when the electrons are heated, roughly as T,- '/', as against T,,'.5 when the electrons and ions are heated in a shock wave (Cunningham and Hobson, 1969). O'Malley (1969) has attributed the rapid falloff in the recombination rate coefficients in the latter case to excitation of vibrations of the ion-molecule. O'Malley's interpretation begins with the supposition that the overlap of the wave function of e Ne, is large for the vibrational-electronic ground state of the ion and the dissociating state responsible for capture, for states of relative translational motion accessible near Re of the ion by collision with thermal electrons. This is generally supposed to be the situation for many diatomics including Ne,', Ar,', Kr,', Xe,', NO', and others. (We shall return to this point.) If the conditions supposed by O'Malley are fulfilled, as in Fig. 2a, then he has the overlap of the initial and final nuclear wave functions-that is, the FranckCondon factor-falling off as u-l/', where u is the vibrational quantum number: but, more important, the factor governing the probability that the molecule dissociates before it autoionizes back to e + ion falls exponentially as 1 - exp(hv/kT,,,). In other words, for the diatomic systems that exhibit very rapid dissociative recombination, the only state of the molecule-ion
+
N
-
+
-
+
ELEMENTARY ATTACHMENT AND DETACHMENT PROCESSES
I
I
I
(el
(d1
11
(f)
FIG.2. Schematic representations of potential curves involved in various cases of dissociative recombination : (a) crossing curves in the most favorable situation for dissociative recombination, yielding A + B in a strongly Fepulsive state from a strongly bound AB' and an electron; (b) another direct case, moderately favorable for dissociative recombination but without a true crossing of the potential curves; (c) an indirect process in which bound, neutral AB is formed in a highly excited state (AB)**, perhaps a Rydberg state, from AB' + e; (AB)** then undergoes a transition to the repulsive state that yields A t B; (d) an indirect process like the preceding, except that the bound Rydberg state (AB)** has a potential that does not cross the curve of AB' + e. In (d), the curves of (AB)** and the repulsive state (AB)* do cross, but they need not, yielding the case shown as (e). In (f), there is a neutral state (AB)* that plays exactly the same role as (AB)* in (b), the difference being that in (f) the state of the neutral has bound vibrational levels, but the transition of interest occurs above the dissociation energy of (AB)** so the excited molecule dissociates as in (b). With the attractive well, some (AB)* molecules could have lifetimes considerably longer than those of (b). Case (a) is the basis of the model of OMalley (1969); (f) was studied by Nielsen and Berry (1971). Note that (f) may also involve a crossing of the two potential curves.
that plays a role is supposedly its ground vibronic state, and the only state of the neutral that enters is the one that crosses through the ionic potential as in Fig. 2a. Now let us return to recombination in helium. The results of Rogers and Biondi (1964) raised questions about the importance of dissociative recombination, just at the time that this mechanism was becoming widely accepted. Shortly before, Hinnov and Hirschberg (1962) had made a strong case that a process He"
+ 2e
-V
He*
+e
(5)
would account much better for their observations: They noted that spectral lines from highly excited states of He became more intense after their discharge was turned off, whereas lines from lower states died away. Then Ferguson et a/. (1965) studied the dependence of several He lines on T, and
12
R. STEPHEN BERRY AND SYDNEY LEACH
summarized the existing data from many sources, concluding that the dissociative recombination coefficient for He,' could be no greater than about 3 x 10- l o cm3/sec. They emphasized the observation of Niles and Robertson (1964) that the emission from the afterglow of a helium discharge is largely from molecular helium very soon after the discharge is cut off. This picture is certainly contrary to the expectations of a system undergoing fast dissociative recombination to excited atoms. The history of the unraveling of this problem has been given in the review by Bates (1979). The set of coupled processes, together called collisional-radiative recombination, including the three-body process (9, its inverse of ionization by electron collision, excitation and deexcitation of atoms by electrons, and radiative processes, appears to account well for what happens in helium except at very low temperatures, and presumably plays an important role in other dense plasmas hot enough that molecules are not present in quantity. First suggested by D'Angelo (1961), Bates and Kingston (1961), and McWhirter (1961), the process was the subject of extensive computations (Bates et al., 1962a,b), followed by many others, culminating in those of Stevefelt et al. (1975). The expression obtained by the last-named group for the collisional-radiative recombination coefficient aCRof electrons in helium is = 1.55 x 10-10T;0.63 aCR(cm3/sec)
+ 6.0 x + 3.8 x
10-9Te-2.18N,0.37
10-9T,-4.5N, (6) The first term, independent of the electron concentration N , , is clearly due purely to radiative processes; the third term, linear in N,,is purely collisional and corresponds to process (5). The middle term is a numerical fit to the complex results of many microscopic processes occurring simultaneously ;in effect, it is the result of the interaction between the collisional and radiative processes. The analysis by Stevefelt et al. seems to give agreement within about a factor of two with experimental data including their own (Boulmer et al., 1973,1974). Other analyses have included the possibilities of molecular contributions, either by dissociative recombination or by the analog of process (l),but with molecular ions instead of atomic (Collins, 1965).Collins referred to the process 2e
+ He,+ +2He + e
(7) as collisional-dissociative recombination. At low pressures, Boulmer et al. (1977) found that Eq. (6) nearly accounted for all their experimental results; they replaced the first term of (6)with u1 = 3.5 x
10-5T;1.9 cm3/sec
ELEMENTARY ATTACHMENT AND DETACHMENT PROCESSES
13
amounting to a small correction, which they attributed to the process He+
+ c + He + 2 H e
(8)
that is, to helium rather than an electron acting as a third body. Typically, the effective recombination coefficient for electrons in helium at pressures of order 25 torr, temperatures between 300 and 500 K,and N , about 10' cm3is about 6 x (Boulmer et al., 1973). It is ironic indeed that the helium plasma, the system that stimulated the entire investigation of dissociative recombination, turns out to be one of the few clear counterexamples. However, it turns out that at cryogenic temperatures, about 10 K, the effective recombination rate coefficient in helium cm3/sec, proportional to T,-10.2 vapor is very large, (4 f 0.6) x (Delpech and Gauthier, 1972) and independent of N , . In agreement with this is the value (3.4 k 1.4) x lo-' at 80 K (Gerard0 and Gusinow, 1971). The reason for the large cross section and behavior more like "traditional" dissociative recombination is that in cold helium plasmas, many of the ions exist as He,+ and He,', not just as He2+.It is the larger ions that are responsible for the large cross sections at low temperatures. Why is helium so different from neon and the other rare gases? Why does dissociative recombination of He,' have a cross section small enough that collisional-radiative recombination is the dominant mechanism for its neutralization? The answer, as best we know, now comes from Mulliken's discussion (1964) of the potential curves of He, and He,'. There are simply no dissociating states of He, whose potential curves stand in relation to the curve of the ground vibronic state of He,' as do the curves of Fig. 2a or b. Only vibrationally excited states of He2+ appear to be available for direct coupling to the dissociating states that produce He He*. The hydrogen molecule also has a paucity of excited states, like helium because of the small number of electrons. In H, one again finds no crossings of repulsive curves with the ground vibronic state of H,', from which H H* can be formed by direct dissociative recombination.
+
+
3. Theories Before turning to the recent experimental work that has dealt largely with very simple systems, we review the state of theoretical discussions of the subject. We shall not attempt to describe the many formalisms and computational procedures; rather, we restrict ourselves to describing the pictures that have emerged. The theoretical treatments range from models intended to be just elaborate enough to rationalize the observations, such as the very early treatment by Bauer and Wu (19561, to full quanta1 calculations of specific kinds and channels of dissociative recombination (Nielsen and Berry, 197 1 ) and formal general theoretical statements (Chen and Mittleman,
14
R. STEPHEN BERRY AND SYDNEY LEACH
1968). For H,’ + e, the most “successful,” i.e., the most recent, theoretical treatments still do not manage to represent the experimental results quantitatively (Bottcher, 1976, for example), but for this system theorists have tried to work with nonempirical treatments and, by and large, the theoretical representation accords reasonably with experiment (Fig. 3). For larger systems, theorists have been more successful by using semiempirical or phenomenological formulations that can be based either on spectroscopic data or ab initio calculations. Probably the most influential formulation has been that of Bardsley (1968a,b). It clarified the vocabulary by comparing previous formulations with Bardsley’s own in common terms; it laid out explicitly the distinctions among several physical processes and their mathematical counterparts; it criticized weaknesses in some of the earlier formulations ; and it showed how to make quantitative estimates from empirical data and thus to estimate the temperature dependence of recombination rate coefficients. More recent theoretical work carried out in a similar spirit includes the application of multichannel quantum defect theory, first by Lee (1977) to N O + + e, and most recently, in a n elegant manner that more properly couples different continua-the electron continuum of e AB’ with the atomic continuum of A + B-by Giusti (1980), with application to CH’ + e. Current dogma divides dissociative recombination into several kinds of processes. These are (1) direct processes in which the transition is made from a state of e + ABf in which AB’ is vibrationally bound to a compound state (AB)* of the neutral that has a repulsive potential leading to A + B, either of which may be excited; (2) indirect processes in which the transition is made first from e AB* to a neutral level (AB)** that is bound both with respect to the electrons and the nuclei, and then from (AB)** to the repulsive state (AB)*, which dissociates; (3) processes-not always distinguished as clearly from the other two in the literature as the physics demands-in which e AB’ makes a transition into a state of the neutral that we shall label (AB)*, whose electronic potential curve supports bound vibrational states, but whose internal energy of nuclear motion is greater than the dissociation energy of the electronic state. The greater part of dissociative recombination appears to go through one or both of the first two processes. However, in hydrogen and perhaps helium, the inverse process of associative ionization seems to contain a significant component from the third mechanism and the dissociative recombination of these species at high temperatures, where vibrationally excited H 2 + is present, probably involves some of the third process as well (Nielsen and Dahler, 1965; Nielsen and Berry, 1971). The direct processes are represented by couplings between curves of the kinds shown in Fig. 2a,b. The indirect processes can occur through processes of the types shown in Fig. 2c,d,e. A fourth type of indirect process through a
+
+
+
ELEMENTARY ATTACHMENT AND DETACHMENT PROCESSES
I5
single intermediate is possible, but is not shown, in which the curve of the e, but the dissociating state (AB)* bound state (AB)** crosses that of AB’ does not cross the curve of (AB)**. Processes of the third kind are illustrated by Fig. 2f; again, the curve of (AB)* could cross that of A B + . Much of the discussion of dissociative recombination by direct processes has the aspect of calling for a deus ex machina in the form of a crossing of the potential curves of (AB)* and (AB)’ in a very specific, rather narrow range of the A-B distance R . Within the conventions of the Franck-Condon picture, electronic transitions occur (1) with no change of internuclear distance, and therefore “vertically” in diagrams of the types of Figs. 2 and 3; and (2) with no change in relative momentum of nuclei, and overwhelmingly at classical turning points, and therefore, “from potential curve to potential curve.” Suppose the free electron approaching AB’ has energy 6 ; this much energy must, within the Franck-Condon picture, go entirely into electronic excitation. Hence, the only internuclear distance at which the transition may occur is R , , as shown in Fig. 4, where the separation between the two potential curves is precisely E. This classical model for the direct mechanism requires that the curves of (AB)* and of (AB)’ have a separation comparable to the kinetic energies of the electrons within the range of R available to the AB+
+
Center-of-moss energy ieV1
FIG.3. Dissociative recombination cross section for Hi + e, with H; in a distribution of vibrational states. Points are measuredby Auerbach et al. (1977); x ’s are from the experiments of Peart and Dolder (1974a). The dashed curve was calculated by Bottcher (1976). Taken, with permission, from Auerbach et al. (1977).
16
R. STEPHEN BERRY AND SYDNEY LEACH
ion-molecules. This means that in a typical afterglow, the separation between the curves of (AB)* and AB' would have to be comparable to the thermal energy of the free electrons in the range of R between the classical turning points of the ground vibrational state $o(R)of AB'. In Fig. 4,the condition is met for electrons having energy 6 at the distance R, and a thermal distribution P(6). The distribution P(R,) of distances at which this thermal distribution could cause capture would be simply the reflection of P ( E )in the difference E,,(R) - EAB+(R).This distribution is not quite yet the probability distribution PDR(R)for dissociative recombination is a function of the distance R. To obtain PDR(R) from P(R,),we must multiply by the probability distribution for finding AB' at distance R ; suppose AB' is in its ground the square of the ground-state vibrational state; this distribution is II+$~(R)(', vibrational wave function for AB'. The construction of P D R ( R ) is shown in Fig. 5, which is based on the curves of Fig. 4 for the states (AB)* and AB'. In the center top is the difference in energy of these two curves, for the region in which the difference is positive and classical dissociative recombination is physically possible. At left is a hypothetical distribution P(E)of electron energies. The curve of P(R,) is constructed by reflection as shown. Below the curve of P(R,) is the probability distribution for the internuclear distance with (AB)* in its ground vibrational state. At the bottom is the product P(R,)[$,,(R)~'; in this case it is only slightly distorted from P(R,), but this is not necessarily always the case.
Et I AB'te
E
I
I
:
I
R-
RCR, R,
+
FIG.4. Closer specification of the potential curves for AB' e ( k = 0 ) and a crossing, repulsive state (AB)+ for dissociative recombination [case (a) of Fig. 21. The internuclear distances indicated by It&), Rotand R, are, respectively, the capture distance for an electron with energy t, the equilibrium distance for AB' and the crossing distance beyond which it is increasingly improbable that A B go into a stable AB' e. The energy of the electron is shown at left from E o , the minimum of the potential curve of AB' ; it is shown again at the center of the diagram starting from the zero-point level of AB' and terminating on the curve of (AB)* ; the point at which this energy separation equals t is precisely the capture distance of R&).
+
+
ELEMENTARY ATTACHMENT AND DETACHMENT PROCESSES
17
If this nearly classical model of direct dissociative recombination gave the full picture, then intersections of the curve of (AB)* with that of AB+ would have to occur at values of R somewhat larger than the left-hand (small R ) classical turning point of $,,(R), and not too far to the right of its right-hand classical turning point. This restricts the crossing region to a ~, p is the reduced mass of the A-B oscillator range of order ( h / p c ~ ) ”where and w is the AB’ vibrational frequency in rad/sec. This range typically is about 0.04 A or less, and the corresponding energy range in which the crossing must occur is of the order of the zero-point energy of AB’. Curves of (AB)*, such as those in Fig. 6, would correspond to states rather ineffective for dissociative recombination ;for the curve labeled (AB):, the electron energy would have to be less than c1 and for the curve labeled (AB)f, the energy of the electron would have to be greater than c 2 for dissociative recombination to occur with a high probability, at least according to the classic model. It is not surprising that H, and He,, with relatively few excited potential curves, seem not to fulfill the required condition. Rather, it is at least a little surprising that
R
FIG.5. Construction from a semiclassical model of the probability distribution P,,(R) of direct dissociative recombination as a function of internuclear distance. The curve P(6) is the exogenous distribution ofelectron energies; the curve of E,,,(R) - E,,+(R) is the separation of the two relevant potentials for the direct recombination; $,(R) is the vibrational wave function of the AB’ molecule. One can apply this model to any of the direct cases of Fig. 2a, b, or f, including the unillustrated case as in Fig. 2f but with a crossing. If the AB+ molecules may have vibrational excitation and if vibrational relaxation is slow compared with recombination, the probability P(R,) should be multiplied by the vibrational distribution ~ p j l $ j ( R ) lofz the AB’ molecules; p j is the probability of thejth vibrational state and I , ~ ~ (isRits ) wave function.
18
R. STEPHEN BERRY AND SYDNEY LEACH
I
FIG.6. Details of the potential curves involved in dissociation recombination. For recombination to be effective in the direct, curve-crossing model, the potential of (AB)* must fall in the range between the dashed curves (AB): and (AB):.
more than one or two diatomic systems can be interpreted successfully in terms of this model. Why, one is forced to ask, d o neon, argon, krypton, and xenon, as well as nitric oxide, oxygen, and nitrogen all seem to conform to a picture based on such a restricted crossing? For polyatomics, there is no problem because of the high density of vibrational levels; the problem lies with diatomics and perhaps triatomics. One part ofthe answer is easily found in the simplification from quantummechanical behavior to classical behavior. As soon as one allows the (AB)* molecule to be described by a translational wave function, the requirement of a curve crossing disappears. The less restrictive condition is only that the curve of the state (AB)* be close enough to that of AB’ for the two translational wave functions to exhibit significant overlap. Second, to meet the conditions of the Franck-Condon approximation, we need only require that the transition from AB’ e to (AB)* be vertical and that the nuclear momentum not change during the transition. This means that the transition need not be “from potential curve to potential curve,” but that if it occurs at an A-B distance R , , the kinetic energy of the nuclei at R , in the upper state (AB*) be the same as that at R , in the lower state. As in the classical model, the energy c of the free electron goes entirely into electronic excitation in this approximation, but the system can make transitions even when the nuclei are moving. This situation is precisely the same as that invoked for Penning ionization, as discussed in Part I (Berry, 1980a). Finding the relative importance of direct and indirect pathways has been a popular way to describe many recent studies of dissociative recombination. The temperature dependence of the recombination rate coefficient has been considered one guide because theoretical arguments have indicated that the rate coefficient for the direct process oftype 1 (Fig. 2a-c) and oftype 3 (Fig. 2f) should vary as Te-1’2at low temperatures (Bardsley, 1968b; Nielsen and
+
ELEMENTARY ATTACHMENT AND DETACHMENT PROCESSES
19
Berry, 1971),but may fall off faster with increasing T at “high” temperatures, and that the rates for indirect processes should fall faster than Te-’”, perhaps as fast as 7‘-3/2.The corresponding behavior of the cross sections would be like Ee- for the low-temperature direct processes and like a higher inverse power of electron energy in other cases. 4. Fitting Experiments and Theories: e
+ Hzi
Experiments with merged electron and ion beams, which give very high energy resolution, have been done to determine the energy dependence of the cross sections for dissociative recombination. These show (Mitchell and McGowan, 1978; McGowan et al., 1979; Mu1 and McGowan, 1979)that the cross sections are smooth, decreasing functions of electron energy, going as Ee- within experimental uncertainty, up to electron energies of about 0.1 eV. Above this energy range, the cross sections fall faster with electron energy and seem to display maxima and minima suggestive of resonances-long-lived intermediate quasibound states-and therefore of indirect processes. Hence, the present state of interpretation would have direct processes playing an important role for many, perhaps all recombination processes at low energies, with indirect processes progressively more important with increasing electron energy. As theoretical work has become more sophisticated, the discussion has begun to turn more toward identifying specific intermediate electronic states and specific product states. For example, in the analysis of e + H2’, the dissociative Rydberg states of(H2)*built on one electron in the antibonding core orbital la, and one in a Rydberg orbital, e.g., the ( laU)(3s) configuration, were suggested by Zhdanov and Chibisov (1978). This proposal was criticized by Derkits et al. (1979) who claimed that Zhdanov and Chibisov overestimated the role of (la,)(nl) repulsive Rydberg states by neglecting their autonionization. Derkits et al. (1979) estimated that such states c;ould only contribute at most about 8 x lo-’’ cm2 to the cross section and then only for electrons with energies well above 3 eV. However, Zhdanov (1980) recalculated the contribution of such states to the limit H(1s) H(n = 4)and compared the results with those of Phaneuf et d.(1975). The excellent agreement implies that repulsive Rydberg states must be included in future calculations of the dissociative recombination of hydrogen. The computed contribution of capture into dissociating regions of bound e. Here, based largely on states, as in Fig. 2f, is a bit larger, at least for Hz the capture of a free s electron, if R is smaller than Re(H2’) or a freed electron if R is larger, Nielsen and Berry (1971) found a cross section having a maximum for E, = 0, and strongly increasing with the vibrational state of H,’.
’
+
+
+
20
R. STEPHEN BERRY AND SYDNEY LEACH
Its magnitude is 2 x lo-'* cm2 for v = 2 when E , is eV, but yields a total cross section of considerably less than 10- l 9 cm2 for an electron energy of 0.1 eV. This picture is based on capture into the (log)(4sa)Rydberg state of (H,), which dissociates to H(1s) H(n = 3). Bottcher's (1976) model has the ion catching the electron in a d wave and going into the (10,)~lC,+ state of (H2)*as the dissociating state, by way of lC,+ intermediate Rydberg states built on one electron in the la, orbital of H,'. The cross sections derived this way are of order cm2 for electrons with about 1 eV of energy, about a factor of 2 higher at this energy than the experimental value of Peart and Dolder (1974a) and considerably higher still than the values of Auerbach et al. (1977) for H,' with vibrational quantum numbers 0, 1, and 2. The experimental and theoretical values are essentially the same for energies of about 0.5 and 2.1 eV and above; below 0.5 eV, Bottcher's theoretical values are too low. Putting this observation together with the results just cited from the group of McGowan, one is led to suspect that a direct low-energy process supplementing the indirect processes called upon by Bottcher would explain this simplest of systems. It is quite unknown whether the direct process would be one of type 1, AB' e + (AB)*-+ A + B, or type 3, AB' e + (AB)* + A + B, or of some more complex form. For example, in H, low-energy recombination might involve transitions through several electronic states, with small amounts of energy being exchanged between electrons and molecular rotation, and larger amounts between electrons and vibrations, in a succession of promotions of the nuclear vibrational state until the molecule reaches a state whose potential is in a favorable relation to a dissociating curve, perhaps but not necessarily that of the (la,)' 'C,' state. The absolute cross sections for e H 2 + and e D 2 + were first determined unambiguously by the inclined beam measurements of Peart and Dolder (1973a,b, 1974a). The cross sections were an order of magnitude less than what had been expected and, in effect, rationalized by Bauer and Wu (1956). The observed cross sections were 17.3 x cm2 at 0.5 eV and and 8.2 x for 6.4 x at 1.01 eV for H2' + e, and 15.3 x D2+ + e at the same energies. These values were confirmed by the measurements of D. Mathur et al: (1978) by an ion-trap method. The results of Auerbach et al. (1977) are also consistent with the others, apart from showing irregular oscillations at electron energies above about 0.1 eV, with amplitudes increasing with E , . Figure 3 shows the results obtained by Auerbach et al. (1977) for H 2 + + e. The oscillations are of order 0.1 eV and their amplitudes contribute roughly 15% of the total cross section. Moreover, the oscillations are dependent on the vibrational state of the H2'ion (McGowan et al., 1976).
+
+
+
+
+
21
ELEMENTARY ATTACHMENT AND DETACHMENT PROCESSES
McGowan and his collaborators attribute the resonance structures to Rydberg states, which we would designate as (H,)** or (H2)* here. One further set of experiments with D 2 + + e may be very important for the interpretation of the mechanism of this recombination. Dunn and coworkers (Phaneuf et al., 1975; Vogler and Dunn, 1975)have followed emission by excited hydrogen atoms to determine the contributions of specific final hydrogenic states to the total cross section for dissociation recombination. About 10% of the total cross section comes from states yielding D(n = 4), over the range 0.6 I E, I 7 eV, from the results of Phaneuf et al. A slightly smaller fraction of the dissociation products are D(n = 2) atoms, according to Vogler and Dunn. It is possible, but seems very unlikely, that fast groundstate atoms could be the principal products. Whether the major excited products are atoms with n = 3 as suggested by Nielsen and Dahler (1965)and used in the model of Nielsen and Berry (1971) remains to be tested. 5. Larger Ions The dissociative recombination cross section of H3+ + e has been measured by Auerbach et al. (1977)for H, in an undertermined assembly of states, and by Peart and Dolder (1974~)using a source of vibrationally cold H 3 + (Peart and Dolder, 1974b). The cross sections are all larger than for H2+ + e, 5 x 10-'6-10-'5 cmz at 1 eV, for example, and slightly larger, perhaps a factor of 2, with the vibrationally deexcited H,+ than with the distribution of Auerbach et al. As with H 2 + + e, the high-energy resolution of Auerbach et al. showed resonance-like structure in the cross section for H,' + e at energies above about 0.2 eV. The process H 3 + e has been treated theoretically only very recently by Kulander and Guest (1979). For electron energies a little above 1 eV, they expect the products to be H(n = 2) H, in its vibrationless ground state. At higher energies, they expect a variety of products; H 2 + + H - should appear above 5.41 eV. At the very lowest energies, they predict the products to be three hydrogen atoms. Now that the vibrational levels are known for H,+ (Carney and Porter, 1980; Oka, 1980), D,' (Carney and Porter, 1980; Shy ef al., 1980),and Rydberg states of H 3 and D, (Herzberg, 1979),we can expect a still more refined theoretical analysis of this recombination process. Cross sections for larger clusters of hydrogen around a proton have not been studied, but thermal rate coefficients have been studied for H,+ e. Leu et al. (1973b) found a value for the rate coefficient of this recombination of 3.6 x cm3/sec at 205 K, by working at pressures up to 0.6 torr in their discharges. Trainor (1978) carried out measurements at higher electric +
+
+
+
22
R. STEPHEN BERRY AND SYDNEY LEACH
fields, and therefore at higher mean electron energies, that were consistent with the results of Leu et al. and indicated that the rate coefficient falls offwith increasing electron energy, as one expects. Diatomic molecules larger than H 2 + and He2+ have been studied, but, apart from NO" + e, not extensively. The recombination of CH+ e plays an important role in certain models of the chemistry of the interstellar medium (Solomon and Klemperer, 1972), and has consequently been studied both theoretically (Bardsley and Junker, 1973; Krauss and Julienne, 1973; Giusti-Suzor and Lefebvre-Brion, 1977; Raseev er al., 1978; Giusti, 1980) and experimentally (Mitchell and McGowan, 1978). The experimental results give a large cross section, (5.1 & 0.5) x cmz for electrons with energies of 0.01 eV, and a rate coefficient of (3.1 f 0.3) x lo-' cm3/sec. This value is large enough-by two orders of magnitude-to be somewhat upsetting to the astrophysical model. Earlier calculated values were lower, of order cm2/sec for the rate coefficient. The large experimental cross section could, however, reflect the presence of vibrationally excited states of the ion: This rationalization could make the laboratory results consistent with the theoretical values and the values used in the astronomical model. e was realized to be a key process for The recombination of NO' removal of electrons in the ionosphere (Biondi, 1964; Danilov and IvanovKholodny, 19 5). The rate coefficient for this process was measured most recently by H iang et al. (1975). It is large, especially for a diatomic, 3 x lo-' cm3/sec at an electron temperature of 500 K. Cross sections were measured by Walls and Dunn (1974) and by Mu1 and McGowan (1979). Theoretical interpretations of the process have been given by Bardsley (1968a,b, 1970), Michels (1975), and Lee (1977). The cross-section measurements appear to agree well for electron energies from below 0.1-1 eV, the region where the two sets overlap: about 2 x cm2 at an energy of about 0.05 eV to about 3 x at an electron energy of 1 eV. They also agree well with the theoretical predictions of Michels. The results of Huang et al. are about 1.7 times the rate coefficients inferred from the cross sections measured by Mu1 and McGowan and by Walls and Dunn. Mu1 and McGowan suggest that the NO' in Huang, Biondi, and Johnsen's experiment could be vibrationally hotter than that in either the Walls-Dunn trapped-ion experiment or the Mul-McGowan merged-beam experiment. Michels' theoretical cross sections do increase with the vibrational quantum number of the N O f . A little commentary is appropriate concerning the states of NO that might be formed in the recombination process. Bardsley invoked two states, the Bf2Aand B2n,after considering several others. Michels derives smaller cross sections using five states; in addition to the B"A and B2n, he considers the 'Zf, the 'll 111 and the states, all of which dissociate to N(2D) + O(3P),and whose potential curves cross that of the X'C' state of NO' in the
+
+
ELEMENTARY ATTACHMENT AND DETACHMENT PROCESSES
23
vicinity of the ground or low vibrational states of the ion. This is an example par excellence of the situation where either Fig. 2a or c could apply. Michels' analysis is based on the former, that is, upon a direct mechanism. However, since all the states he invokes have bound vibrational levels, the situation as Michels supposes it is really a type 3 process, direct but via the part of an attractive potential on the left turning-point side above its dissociation limit-a type 3 process, accomplished by a curve crossing rather than by the proximity of two states as it is portrayed in Fig. 2f. The multichannel quantum-defect treatment of Lee (1977) gives cross sections larger than those of Michels or of the Walls-Dunn and MulMcGowan experiments. When the improved theory of Giusti (1980)is applied to this problem, we may hope to see values from this presumably very powerful formulation that represent the experiments accurately. The same theory can be used, of course, to describe autoionization of NO, a subject discussed at some length in Part I (Berry, 1980a). Like the studies of products from D,, there is one experimental investigation of the products of the dissociative recombination of e + NOt (Kley er al., 1977). Bardsley (1968b) predicts that about half the NO dissociates to give N('D) atoms; Michels has all the N O going to this limit, but with a qualification allowing for a curve crossing that would give some ground-state nitrogen atoms. Kley et al. find that 76 6% of the dissociating N O molecules formed from e + NO" give N('D). This is consistent with the rather crude theories now available and can be used as a test for more elaborate calculations. More important, it provides a basis for a supposed source of excited metastable nitrogen atoms in the upper atmosphere. The studies of recombination of electrons with clusters such as H 3 0 + . (H,O), and NH,+(NH,), were mentioned earlier. A theoretical analysis rationalizing their large cross sections was presented by Bottcher (1978). In his treatment, the vibrational levels of the cluster act as energy acceptors. The number of available vibrational levels is large, so large that there are resonance levels available everywhere to permit indirect recombination. The theory gives a linear dependence of the cross section on the numbers of monomer units in the cluster. Dissociative recombination of clusters was included in a general review of ionic clusters by Smirnov (1977). There is one important problem that arises with such systems and that has been overlooked by almost everyone concerned with such species. The exception is the analysis by Herbst (1978) of the question of what products are formed when a polyatomic molecule dissociates. Herbst uses the statistical model of Light and Pechukas (Pechukas and Light, 1965; Light, 1967), with an orbiting model-a critical radius within which an electron has unit probability of recombining, which may be adequate for polyatomics-and makes specific predictions of (the products. For example, Herbst predicts
R. STEPHEN BERRY AND SYDNEY LEACH
24
+
+
that H,O+ e will give as a primary product H, O H in its ground state. Even a “most extreme case” example gives only 50% of the (H30)*molecules going to HzO + H. Neutralization of CH3+ is expected to give largely CH Hz. However, the product distribution from NH4’ e is probably divided relatively evenly among NH, + H, NH2(XZB,)+ H,, NH2(AzA,) + H, and, NH(X3X-) H, H. The method is too statistical in nature to be valid for H 3 + e. The products from this simplest polyatomic system are H? Both are possible. Kulander and still not known: are they 3H or H, H(n = 2) for Guest (1979) predict 3H for thermal electrons and H, electron energies above 1 eV. It would be worthwhile to consider treating the fragmentation problem by the methods of Quack and Troe (1974) and of Silberstein and Levine (1980).
+
+
+
+
+
+
+
6. Dissociative Attachment: The Simplest Paradigms Most dissociative attachment processes have been interpreted as direct resonance processes: capture of a n electron by a neutral molecule, putting the compound system into a repulsive state or above some dissociation limit of a state with bound vibrational levels, so that the compound state splits into a neutral fragment and a negative fragment. Analogous to dissociative recombination, the rate k,, of this process or its cross section cDAhas been described quantitatively by the crude representation of a product of a cross section (7, for capture of an electron into a resonant state, and a survival probability ps that the electron stays together to preserve the compound negative ion long enough for the nuclei to reach a point of no return, beyond which the electron is truly bound and the molecule separates irrevocably into its fragments (Holstein, 1951; Bardsley et al., 1964; Bardsley, 1968a). The formulation of the rate in this manner was refined to take proper account of the angular momentum of the restrictions on the incoming electron and the capturing molecule (Chen and Peacher, 1967). Chen and Peacher also argue that the kinetic energy of the nuclei at their point of no return must be large relative to the inverse of the survival probability-that is, dissociation must be rather more probable than auto detachment of the electron-or the rate of dissociative attachment may vary significantly with the rotational state of the capturing molecule. The symmetry restrictions arise through the relation between the angular momentum of the incoming electron, the compound state, and the molecules. The most primitive example of dissociative attachment, e H, + H + Hat the lowest possible energies, illustrates this phenomenon. The lowest energy resonance of H, + e is a transient state of H,- with a very short lifetime, of order sec. when the nuclei are separated by about the equilibrium distance for the neutral H,. The incoming electron is captured
+
ELEMENTARY ATTACHMENT AND DETACHMENT PROCESSES
25
into the lowest empty molecular orbital, the la,, which becomes a hydrogenic 1s orbital at the separated-atom limit, but a 2pa orbital in the united atom limit. The latter is the important one for dissociative attachment because the direct resonance model has the incoming electron going from its free state into a transient bound state of the same symmetry type as i t $ initial free $tare. The model supposes that no angular momentum is exchanged between the incoming electron and the nuclei in the capture process. This restricts to p waves the incoming electrons approaching H, to form H + H - via (lo,)’( lo,) 2Zu+state. The p-wave electron encounters a centrifugal barrier which, according to Chen and Peacher, is strongly dependent on the molecular rotational state if the electron is slowly moving. The inference they draw is that for a case in which s-wave electrons can be captured, the simple picture of survival probability suffices, but when electrons must be captured from free states of higher angular momentum, the simple expression of aDA= n,p, should be replaced by a sum of terms, one for each angular momentum state of the molecule. The resonant capture and dissociation process is strongly reminiscent of the picture of chemical reactions of the form A B C + A B + C in which the entire reaction takes place on a single potential surface. For dissociative attachment, the process is usually represented in terms of what appear at first sight to be different potentials, as, for example, those of Fig. 2 or 6. However, these curves can be thought of as sections of a hypersurface drawn for two different placements of the incoming electron. The curves corresponding to e A B or e AB’ have the electron infinitely far away. The curves with the electron attached, e.g., as AB- for dissociative attachment, correspond to the energy of the compound system as a function of R(AB) averaged over the distribution of the electron when it is in its bound or quasi-bound state. Because this limit involves averaging the energy over the position of the electron, it is not exactly the same as the counterpart in the system of three heavy particles, ABC, for which the potential of the exit channel is drawn as E(RAB)when C is very far away. However, the entrance channels are precisely equivalent with e playing the role of A. Moreover, the selection rule restrictions invoked by Chen and Peacher are, in this sense, very much like the role of rotational and nuclear spin constraints invoked by Quack (1977)and Quack and Troe (1975a,b) to describe the state distributions in products of photodissociation and, by implication, of three-body rearrangements. It is interesting to note the parallel between the survival factor p , and the transmission coefficient that appears in mechanistic models of reactive collisions, models such as “absolute rate theory.” The direct resonance model so widely accepted now for dissociative attachment (Bardsley et at., 1964; O’Malley, 1966; Schneider et al., 1979)was not the first explanation for this process. The first explanation, which was
+
+
+
26
R. STEPHEN BERRY AND SYDNEY LEACH
accepted for many years, was given by Bloch and Bradbury (1935). Their picture was the counterpart of the indirect process described previously for dissociative recombination, and shown in Fig. 2f: the potential curves of the neutral and the negative ion (the authors treated only diatomics) were supposed to be identical but displaced on an energy scale. The mechanism of capture was presumed to be the exchange of electronic energy for vibrational energy by the mechanism of breakdown of the Born-Oppenheimer approximation. That is to say that the mathematical representation of Bloch and Bradbury has the e + AB channel coupled to the A - + B channel through the action of the nuclear kinetic energy operator on the electronic wave function. The physical counterpart is a slight tardiness of the electronic wave function in reaching its adiabatic stationary state as the nuclei move, so that the system finds itself in a state that is a mixture of the entry channel and the exit channel, and possibly other states. Bloch and Bradbury illustrated their calculations with the attachment of electrons to oxygen; the contrast between their formulation and the resonance picture was made particularly clear by Herzenberg (1969) when he treated the same molecule. There were three points on which the Bloch-Bradbury model seemed to contradict experiments carried out during the 1960s: the electron-scattering experiments showed several peaks in the electron energy-loss spectrum indicating that vibrational excitation occurs to several final states of 0, when slow electrons scatter inelastically from 0,. This implies, in turn, that the Franck-Condon envelopes and potential curves of the neutral molecule and the compoundstate negative ion molecule do not overlap closely. In fact Herzenberg’s interpretation puts the potentials for 0,- and 0, in about the same relative positions as those of AB’ e and (AB)** in Fig. 2c. Second, Bloch and Bradbury inferred that the electron affinity of O,, which is everywhere the distance from the potential of 0, to that of 0,- in their model, could be no greater than 0.19 eV, but the thermodynamic electron affinity of 0, is now known to be 0.4 eV (Hotop and Lineberger, 1975). Third, the rate of attachment of electrons to 0, goes up as the square of the pressure, not linearly. This implies that the lifetime of a compound state is short and that most compound 0, states lose electrons, rather than become 0 - + 0, contrary to the Bloch-Bradbury picture. It would not be surprising if some examples are found that accomplish dissociative attachment by unambiguous vibronic coupling, but thus far the common and better understood examples seem to be adequately explained by the simpler resonance model. The consistency of the direct resonance model with observations must be taken cautiously, especially in view of the need for both kinds of processes to explain dissociative recombination. One recent suggestion has been made (Tronc et al., 1979) to explain structure in a cross section for e H, + H - + H above 14 eV, in
+
+
ELEMENTARY ATTACHMENT AND DETACHMENT PROCESSES
27
FIG.7. Schematic diagram of the potential curves for H2 (solid curve) and H,- (solid at large R, dissolving at R < R J . The width of the distribution of the diffuse portion of the H2“curve” corresponds to the inverse Iiibtime, or to the imaginary part of the potential if the total potential is represented as a complex function.
which breakdown of the Born-Oppenheimer approximation has been invoked, but calculations of even this simple case have yet to be carried out. This brings us back to the example of hydrogen. The process that occurs at lowest electron energies has a threshold at 3.75 eV and a cross section that rises nearly vertically there to a peak of about 1.7 x cm2, which is rather small, due to the short lifetime of the H,- compound state. The event can be visualized in terms of Fig. 7. To the right of R , , 3 bohr, the state of H, is more stable than that of H, + e ; to the left, where R is less than R , , the state of H,- lies in the continuum of the H, + e system so some process, however slow, couples the quasi-bound electron with the continuum. In a simple Born-Oppenheimer model, the lifetime of the compound electronic state toward autodetachment is a simple function of R ;its inverse, the width, grows from zero at R , to about 3 eV at R = 1 bohr (Bardsley and Mandl, 1968). If the incoming electron has enough energy to raise the molecule to the diffuse energy range of H,- above the Franck-Condon region for H, + e (Fig. 6), then the electron is temporarily trapped and the system stays in its ( 1 0 ~ ) ~ ( 1 0 ’Xuf ~ ) resonant state for a time of order sec. This corresponds to a broad, diffuse peak in the elastic scattering cross section for electrons from H, (Bardsley and Mandl, 1968). If the incoming electron has enough energy to generate the compound state above the dissociation limit of H + H-, 3.75 eV, there is a finite probability that the nuclei can separate to R , or beyond or during the lifetime of the resonance, and dissociative attachment occurs. Under such circumstances, the cross section for dissociative attachment is nonzero at the threshold energy for the process; this is precisely what was found by Schulz and Asundi (1965, 1967). In this case, where the lifetime ofthe complex is very short and the survival factor is small,
28
R. STEPHEN BERRY AND SYDNEY LEACH
the effect of isotopic substitution is the consequence of its effect on the to survival factor. Replacement of H, by D, reduces aDAfrom 1.6 x cm2, nearer to that of H2 cm2, whereas cDA for H D is 1 x 3 x than of D,. If the electron impinging on H, has an energy of about 10 eV, another process may occur. A new resonant channel opens, corresponding to the ( l ~ ~ ) ( l n ”2C,+ ) ~ , state. The potential curves for this state are of course entirely repulsive because of the antibonding nature of the la, orbital. This process was observed by Khvostenko and Dukel’skii (1958)and Schulz (1959) and then studied by Rapp et al. (1964) and interpreted soon thereafter by Bardsley et al. (1966).The cross section is much larger than for the process at about 4 eV; the peak for H2 is 1.3 x cm2. Moreover, the peak in aDAis about 4 eV wide (full width at half height) in contrast with the width of only about half a volt for the low-energy process. Again, the heavier the isotope, the smaller is the likelihood of dissociative attachment. A third “peak” in the cross section for e H, + H H occurs for electron energies between 14 and 15.5 eV (Rapp et al., 1964). In this region, the cross section rises above 2 x lo-,’ cm2 and has a number of small, sharp maxima on the high-energy side of the principal maximum (Tronc et al., 1979). This peak rises just at the threshold energy required to generate H - + H(n = 2) as the dissociation products. Much of the interpretation of these peaks in the cross section for dissociative attachment has been devoted to assigning the angular momentum and spin of the dissociative transient state of the H 2 - . This exercise is much like trying to make assignments of electronic band spectra in the absence of rotational structure; often one can go far by combining calculations and chemical intuition, and with a little luck, make predictions that allow the assignments to be tested. For example, the 14-eV peak with its subsidiary maxima was assigned by Tronc et al. (1979) as due to a transient state ,A, state of H,- built on a lagnun, configuration that correlates with H - + H(n = 3), and that undergoes rotational coupling with a repulsive lagluunu, ,lIs state that dissociates to give H- + H(n = 2). This is a testable suggestion: one could look for the emission of the Lyman-a line from the dissociation products, and even correlate its polarization with the angular distribution of products. High resonant states of H2- and N,- have been identified from differential inelastic electron scattering cross sections by Comer and Read (1971a,b),but the precise states invoked by Tronc et al. have not been seen this way. The theory of the angular distribution of the products of dissociative attachment has been studied by O’Malley and Taylor (1968) and developed further by Klar and Morgner (1979), but as yet there seems to have been no attempt to use the relation between these distributions and
+
+
29
ELEMENTARY ATTACHMENT AND DETACHMENT PROCESSES
other properties of the products-in the case here, the polarization of emitted atomic radiation-to assign quantum numbers to the intermediate state. The angular distributions themselves, however, have been measured and interpreted (Van Brunt and Kieffer, 1970, 1974; Hall et al., 1977; Tronc ef al., 1977; Azria et al., 1979, 1980). A recent and provocative advance in the interpretation of dissociative attachment is the suggestion by Bottcher and Buckley (1979) that the cross [H,-, 'nu]+ H- + H(2p) may be greater than section fore H,(c311,) 10- ' cm2. For hydrogenic plasmas, this result raises the prospect that molecules in the metastable c 3 n Ustate of H, might be as important as molecules in their ground state for capturing thermal electrons, under circumstances in which the metastables are generated. More broadly, the suggestion leads one to question whether electronically excited molecules might be important generally for dissociative attachment in decaying plasmas and plasma sheaths, where electrons are available to generate the excited species. The one other available datum is the comparison of gDRfor O,(a'A,) (Burrow, 1973) with that ofthe ground state of 0, (Henderson et al., 1969); the cross sections for the metastable and the ground state are, at their maxima (4.6 f 1.3) x lo-'' and 1.3 x lo-'' cm2, respectively. Admittedly, the alAg state of 0, has the same configuration as the ground state and might be expected to resemble that state more than the c state of H, resembles the H, ground state. The important hint is merely that attachment cross sections may be considerably larger for excited states than for ground states. It may be useful at this point to remind the reader unfamiliar with the jargon of molecular collision physics about the designations of transient compound states. In many cases, such as the 10-eV peak of uDAfor e H,, the compound system gets its long life because some energy is transferred from the relative motion of the collision partners into a specific, clearly identifiable degree of freedom, leaving the collision partners in a well-defined (but nonstationary) quantum level of the compound system having a welldefined excitation of the target. In our example of e + H,, one electron is promoted from the lo, orbital to the lo, excited orbital, which it then shares with the incoming electron to give H , - ( 1 ~ 7 ~ ) ( 1 0 , ),ng+. ~ When such an internal excitation can be assigned, the resonance is called a Feshbach resonance. In other cases, the collision partners go into a compound state that is not readily identified as having energy from the collision stored in a ,) of e H, at about specific internal excitation. The ( l ~ , ) ~ ( l o , resonance 3 eV that gives rise to dissociative attachment above 3.75 eV is of this type. Such a resonance owes its lifetime to the kinematics of motion in the effective potential, including the centrifugal and polarization contributions to the potential. In fact, in this example, it is generally believed that the centrifugal
'
+
--f
+
+
R. STEPHEN BERRY AND SYDNEY LEACH
30
barrier experienced by an electron in a p-wave about the H, acts as the trap that keeps the electron temporarily bound to the H,. Such a resonance is called a shape resonance. The classical counterpart of a shape resonance is orbiting as it is induced by potential scattering. Thus, both polarization potentials and permanent dipoles can also give rise to resonances in electron scattering that one would call shape resonances. 7. Dissociative Attachment: Halogen and Hydrogen Halide Molecules
The halogens, the hydrogen halides, and larger halogenated molecules play special roles in electron capture because of their large capture cross sections for electrons of low energy. Dissociation of X, e to X- + X is exothermic for all the halogens, as Tam and Wong point out (1978). In the cases of halogens, much effort has gone toward determining thermal rate coefficients for dissociative attachment, particularly because these coefficients are important parameters for the description of halogen lasers. The experimental results are not easy to reconcile, particularly when the electrons have an effective temperature much higher than the halogen molecules. For example, although the rate coefficients for equilibrated e and I, e appear to rise with temperature (Birtwistle and Modinos, Br, 1978; Schneider and Brau, 1978; Trainor and Boness, 1978), their reported magnitudes seem more different than one might expect. Birtwistle and Modinos found rate coefficients of about lo-'' cm3/sec at 250 K and 2 x lo-'' at about 340 K for I, + e. They predict a rapid falloff in the rate coefficient if the molecules are at 300 K but the electron energies rise to more than about 500 K. Truby (1969) finds a rate coefficient at least twice that predicted from Birtwistle and Modinos' data at lower temperatures and, more important, a coefficient that increases with electron energy. The rate e a t about 300 K is not at all well coefficient for thermally equilibrated Br, established: Values have been reported of 0.82 x lo-', cm3/sec (Truby, 1971) and (1.0 f 0.9) x lo-" (Sides et al., 1976), both far less than the value for e I, at the same temperature. Moreover, the rate coefficient fore + Br, (300 K) only reaches 10- cm3/sec when the average electron energy is above about 0.5 eV (Trainor and Boness, 1978). One might expect the halogens to be more similar to one another. The fluorine case has been examined by several groups; the results are in qualitative agreement but certainly differ by factors of 2-4. Schneider and Brau (1978) obtain a rate coefficient of 7-8 x lo-' cm3/sec for e F, with electrons of 1 eV, whereas Chen et a/. (1977) obtain only 2 x lo-' under conditions supposedly about the same. The rate coefficient for e + F, does appear to be somewhat larger than those for the heavier halogens at electron energies of order 1 eV or less. This last observation is itself peculiar in light of the relative cross-section
+
+
+
+
+
+
31
ELEMENTARY ATTACHMENT AND DETACHMENT PROCESSES
measurements made by Tam and Wong (1978). These experiments showed only one peak in oDAnear two electron energy for fluorine and three peaks for the other halogens, in the range of electron energies up to about 8 eV. Three peaks, at zero, 2.51, and 5.76 eV, were reported for C1, just previously (Kurepa and Belic, 1977). From arguments of symmetry, Tam and Wong assign the fluorine peak to a somewhat forbidden capture of an electron into the o,, orbital of a shape resonance, which should occur in the other halogens as well. However, this 2C,,+ resonance would, according to Tam and Wong, be masked by the next resonance, a 'lie core-excited or Feshbach resonance with configuration (o,np)2(n,np)4(n,np)3(a,np)2.This assignment attributes the next two peaks to core excited resonances built on excitation of an electron from the nu or IT,orbital. The puzzlement here is, of course, that it is hard to reconcile the assignments of Tam and Wong with the reported rate for thermal e F, + F- + F, 10-fold larger than those for the heavy halogens. The explanations remain to be found; one suggestion from the discussion of Tam and Wong is that the effects of impurities can be very large in systems containing halogens, considerably larger than is suspected by many investigators. Tam and Wong, by the way, report peaks near zero electron energy for all four halogens; Frost and McDowell(l960) had reported a peak for C1, with a maximum at about 2.5-2.6 eV, which probably corresponds to Tam and Wong's second peak. But, again, the results are puzzling because Tam and Wong say that the peak at zero energy for C1, is much stronger than those at higher energy. However, Frost and McDowell do report peaks at or near zero electron energy for bromine and iodine and find no peaks at higher energies. For iodine, Tam and Wong find the peak just above 2 eV stronger than that at zero ! One can only say that dissociative attachment by halogens is not well understood. The hydrogen halides are somewhat better understood, but the interpretation of some details of their dissociative attachment cross sections are controversial. The process was recognized and accepted at least from the work of Fox (1957);theearly work demonstrated that e HX gives H X-. C1 can also be produced from e HCl Later it was shown that H(Buchel'nikova, 1959). The cross sections for halide formation commence at electron energies of about 0.7 eV for HCl and about 0.2 eV for HBr (Ziesel et al., 1975),essentially at their thermodynamic thresholds. Hydride ions are only produced at somewhat higher electron energies, 6 eV and above (Azria et al., 1973).The process generating C1- has a cross section with one maximum and has generally been attributed to a single 'E+ compound state of HCI- (Fiquet-Fayard, 1974b).Steplike structure appears in the falloff of this cross section at energies above its maximum at about 0.85 eV (Abouaf and Teillet-Billy, 1977). In H F and HBr, the same sort of structure-one peak with steps on the high-energy side-is observed (Abouaf and Teillet-Billy,
+
+
+
+ +
32
R. STEPHEN BERRY AND SYDNEY LEACH
1980a,b).The cross section for formation of H- has two peaks, at about 7.0 and 9.5 eV (Azria et al., 1980), with structure on the high-energy side of the higher energy peak, between 9.5 and 11 eV. These peaks have been identified C1. Taylor er al. with 2X' and 211states of HCI- that dissociate to H(1977) invoked the three states just mentioned and three more states that dissociate to H + C1 + e, in order to rationalize the peaks and steps. FiquetFayard (1974b) supposed in a somewhat ad hoc but intuitively appealing argument that the cross section for dissociative attachment falls to a lower value above each point where the incoming electron has the energy to excite another vibrational state of the HC1 molecule. Nesbet (1977)invoked virtual states for each step, agreeing with Fiquet-Fayard's picture that the steps correspond to successivelyhigher channels of e + HCI (vibrationally excited). The interpretation as vibrational excitation is strongly supported by the study of Azria et al. (1980) of the intensity of zero-energy scattered electrons as a function of the energy of incident electrons. It is clear from this work that at every energy threshold for excitation of a new state of vibrationally excited HC1, one finds some scattered electrons that have given up essentially all their energy, presumably to vibrational excitation, and also a drop in the cross section for dissociative attachment. In short, vibrational excitation and dissociative attachment to H X- are competitive modes of decay of the 'Z' shape resonance of HX- available for very low-energy electrons. At higher energies the resonances are Feshbach resonances derived from configurations with two electrons in Rydberg orbitals around 217 ground states of the HX' ions (Spence and Noguchi, 1975). These states may decay to H + F- in the case of e H F (Abouaf and Teillet-Billy, 1980a), to HC1 with e + HCl (Azria et al., 1980), and presumably to H- + Br and to H- + I with HBr and HI, respectively. Figure 8 shows both the C1- current and the intensity of very low-energy scattered electrons, as functions of the energy of the incident electrons, as measured by Azria et al. It still remains to be seen why the cross sections have step shapes on their high-energy sides; Fiquet-Fayard showed that one assumption would account for them, and both Nesbet and Taylor et al. gave rational bases for this assumption but it still lacks real justification. The absolute cross sections and thermal rate coefficients for these processes show enormous variation from halogen to halogen. The peak cross section fore HCl -P H C1- is just under 0.2 x 10- cm2,at an electron energy of 0.78 eV, as shown in Fig. 8; the peak for HBr is 2.7 x 10- l 6 cm2 and occurs at 0.28 eV; the peak for HI is 2.3 x cm2 and appears at threshold (Christophorou et al., 1968). These cross sections are consistent with the rate coefficients for dissociative attachment of HC1, from 2 x to 1.2 x lo-'' cm3/sec, for flames with temperatures from 1725 to 2475 K
+
+
+
+
+
+
ELEMENTARY ATTACHMENT AND DETACHMENT PROCESSES
33
Electron energy IeV) FIG.8. The spectra of C1- ions (a) and very-low-energy ( 5 8 0 meV) electrons (b) formed by HCI + e +H + CI-. Both the electrons and the ions are those at a 90% scattering angle, and both are restricted to correspond only to C1- ions formed with kinetic energy between 0 and 20 meV. Taken, with permission, from &ria et al. (1980).
(Miller and Gould, 1978) and with a coefficient of approximately 8 x cm3/sec for HBr at 300 K and electrons with 0.6 eV of energy (Trainor and Boness, 1978). However, these data and the cross sections of Buchel'nikova (1959), Azria et af. (1973), and Christophorou et al. (1968) are not consistent with the 1000-fold larger cross sections for HCl implied by the rates of associative detachment found from flowing afterglow studies by Howard et al. (1974) and from flame studies by Burdett and Hayhurst (1977a,b). The discrepancies are smaller for HBr but are nevercheless still well over an order of magnitude. (The various results for HI seem consistent.) In terms of kinetic parameters of an Arrhenius form, with k = A exp( - A E / k q , the discrepancies lie in the preexponential; the activation energies AE are accepted to be equal to the endothermicities of the reactions. Burdett and Hayhurst ascribe the discrepancy to a rapid increase in oDAwith the vibrational state of HCI and HBr. In view of the difference between the findings of Miller and Gould and of Burdett and Hayhurst, it would seem worthwhile to measure oDAfor HCI carrying vibrational excitation, using a beam or swarm experiment. Three orders of magnitude ought not to go unquestioned.
34
R. STEPHEN BERRY A N D SYDNEY LEACH
Alkyl halides and nitrites appear to behave much like the hydrogen halides at low electron energies. One finds dissociative attachment cross sections with peaks in cDAas a function of electron energy corresponding presumably to resonant states (Stockdale et al., 1974). Some production of His observed with e + CH,CN at about 4 eV, but the peaks at lowest electron energies invariably correspond to halide or CN - production. The cross section at its peak is probably about 5 x lo-'' cmz for CH,Br. (Stockdale et al. also find that argon in a high Rydberg state can transfer an electron to CH,I to give CH, + I - with high efficiency.)The behavior of CH,N02 + e is not the same as that of the other methyl compounds; three-body processes play an important role for nitromethane, in contrast to the halomethanes or hydrogen halides.
8. Other Molecules
+
We have commented already on dissociative attachment of e 02.This molecule played an important role in the understanding and interpretation of apparent cross sections, and especially in the importance of the kinetic energy of the ions (Chantry and Schulz, 1967). Until this work, it had seemed that the energy dependence of the cross section for dissociative attachment was inconsistent with the electron affinity of the oxygen atom. Including the effect of the ion kinetic energy reconciled the observations very well. Dissociative attachment to N2 cannot, of course, give rise to N- + N unless the N- is in a metastable state. However, collisional dissociation of N2 by low-energy electrons has been interpreted as going through a transient N(4S) + N-(,P) channel, which in turn gives 2N(4S) + e (Mazeau et al., 1978; Spence and Burrow, 1979). Total cross sections for the process were measured by Spence and Burrow; the peak of 2.5 x 10- cm2 occurs just above the threshold energy of 9.8 eV, leaving electrons with energy of 0.07 eV. At higher electron energies, N - is formed in a higher state, either the 'D or 'S (Hiraoka et al., 1977). The dissociative attachment for triatomic molecules-H2S (Azria et al., 1979),H,O (Compton and Christophorou, 1967), and CO, (Schulz, 1962), for example-have been interpreted with some success by semiclassical statistical theories (Fiquet-Fayard et al., 1972; Goursaud et al., 1976, 1978). This brings the dissociative attachment process to about the same level of understanding as dissociativerecombination of triatomics. Dissociative attachment has also been studied for much larger molecules: SF, (Compton and Cooper, 1973; Astruc et al., 1979) and cyclic anhydrides (Cooper and Compton, 1972, 1973). The latter were shown to produce COz- in a metastable state. The interpretation of the decomposition of such molecules has been given in
'*
ELEMENTARY ATTACHMENT AND DETACHMENT PROCESSES
35
terms of a vibrational predissociation (Klots, 1976a,b)and related to similar processes for neutrals (Quack and Troe, 1974). Electrons attach to acetylene, C2H2,to give dissociative attachment if the electron energy is above 2.3 eV; the product ion in this case is C,H-, and the onset is a sharp function of electron energy. At higher electron energies, one sees H-and C,- ions (ca. 7 eV) and a broad C,- peak between 11 and 15 eV (Azria and Fiquet-Fayard, 1972). B. Collisional Detachment and Ionization
Here we shall look at those processes of the forms A A
+ B + A + B+ + e
+ 0- - + A + B + e
that occur at collision energies of a few electron volts or less, the conditions that may be met in a discharge, arc, or simple plasma. A very recent review of this subject has been given by Lacmann (1980). We shall not discuss ionization processes that rely on direct transfer of momentum from a heavy particle to a bound electron, the kind of ionization that occurs with collisions at energies of tens of kilovolts or more. Such collisions are studied, for example, in beam-foil collisions, but their interpretation is best given in terms of the Born or Bethe-Born approximation, which have been discussed elsewhere (Inokuti, 1971; Inokuti et al., 1978).However, this subject, long studied as it has been, has some important areas that were investigated only relatively recently. An example is the ionization of alkali atoms by fast neutral atoms (Kikiani et al., 1966). 1. Simple Collisional Ionization
Collisional ionization in low-energy collisions is closely related to associative ionization, a process discussed in Part I (Berry, 1980a). If the collision partners A + B are in their ground electronic states or in states that go adiabatically into the compound state AB' + e, then the only apparent difference between collisional ionization and this sort of associative ionization is in the final states of the nuclei: free in the former case, bound in the latter. The same relation holds for collisional detachment and associative detachment; in the former case, A + B- gives e and A + B in a continuum state, and in the latter, e and AB in a bound state. We shall make some comments later about the cases in which one or the other process is dominant or even exclusive.
36
R. STEPHEN BERRY A N D SYDNEY LEACH
Collisional ionization at relatively low energies is especiallyimportant for alkali and alkaline earth atoms, in flames, for example. Although such processes have apparently not been studied extensively by beam collisions, there is information available directly from flame studies. Rate coefficients for these reactions have been reported for all the alkalis with such collision partners as Ar, H,, N,, CO, CO,, and H20(Jensen and Padley, 1966; Hayhurst and Telford, 1972;Kelly and Padley, 1972;Hayhurst and Kittelson, 1974). The kinetics are generally expressed in terms of an Arrhenius form
k
= A exp(EA/kT)
(11)
where, in flames, EA, the activation energy, is approximately the ionization potential; in shocks, the activation energy seems to be the first excitation energy (Johnston and Kornegay, 1963). The crucial quantity to measure for these processes in flames is the preexponential factor A. Kelly and Padley x [T(K)/2000] found, for example, that with Na, A is about 5 x cm3/sec. Generally, the preexponentials are about 5 x lo-' cm3/sec at 2000 K. The corresponding cross sections are about lo-', cm2, ranging from about 0.5 x lo-', for Na + Ar to 3.5 x lo-', for Na + H20,according to Kelly and Padley. These are as much as a 1000-fold greater than the cross sectionsfor gas-kinetic or excitation collisionswith the same species. Bates (1976) criticized Kelly and Padley's method of estimating rates and cross sections for individual species from data taken for the complex mixtures found in flames. In the cases examined by Kelly and Padley, the numerical values of their preexponential factors are fortuitously close to the values estimated by Bates from his more complex expressions for data reduction. However, there are other cases cited by Bates for which the rate coefficients based on an overly simplified model are much too large. No theoretical analysis has yet been put forth to explain these very large preexponential factors, at least not at a microscopic level. 2. Collisional Ionization of Rydberg States and Other Special Cases Collisional ionization of atoms and molecules in high Rydberg states is rather akin to collisional ionization of alkali atoms in that the perturbation of the collision knocks a single, loosely bound electron into a continuum state from a bound orbital or even to an inelastic collision of an atom with a free electron (Fermi, 1936). The process also has much in common with the transfer or capture of an electron from a Rydberg orbital into a bound negative ion level, as was recognized by Stockdale et al. (1974)in their study of dissociativeattachment of methyl halides and other alkyl compounds. The collisional ionization of atoms in Rydberg states has obvious applications to the chemistry of the interstellar medium, where this process is very possibly a
ELEMENTARY ATTACHMENT AND DETACHMENT PROCESSES
37
competitor with radiation and collisional relaxation for the fate of neutrals freshly formed by collisional-radiative recombination. Collisional ionization of atoms and especially of molecules in Rydberg states became especially popular when isotope separation schemes were proposed that were based on Rydberg states (Ambartsumyan et al., 1975, for example).A very natural and intuitively useful way of studying the effects of collisions on molecules in Rydberg states was the determination by Person et al. (1976)of the ratio q of the number of ionizing collisions to the total number of all collisions. This study was done for acetone, methyl bromide, acetaldehyde-both CH,CHO and CD,CDO-and ethylene-d,, with several collision partners including helium, argon, and nitrogen. The values of q are higher for high Rydberg levels than for low levels, of course. In thermal collisions, with Rydberg states of only about 0.04 eV or less from the ionization limit, the values of q for C,H,O, C,D,O, and CH,Br were found to be about 0.9 or more. However, both the acetaldehydes gave less than 10% ions when they were excited to Rydberg levels about 0.07-0.08 eV below the ionization limit. It is puzzling that the fraction of collisions yielding ions from CH,Br was only 0.65 when the Rydberg state or states were only 0.03 eV from the limit, whereas q was almost unity for states 0.04 eV below the limit. The fractional yields of ions from acetone and especially from C2D4 were distinctly lower than those for CH,Br or acetaldehyde, except for the latter at 0.08 eV below the ionization potential. Collisional ionization cross sections of rare gas atoms in Rydberg states were measured for groups of states by Hotop and Niehaus (1968), in the energy range from 0.034 eV below the ionization limit up to only 0.001 eV below that limit. The cross sections were reported to rise from below lo-', cm2 for quantum numbers n c 25, to well over cm2 for quantum numbers of about 40. Cross sections for specific Rydberg states of xenon in collision with SF, were measured more recently by West et al. (1976); these are all about 1.2 x lo-" cm2, for f states with n from 25 to about 40. The comparison has been made of Rydberg state collisions of rare gas atoms with polyatomics and with atoms and diatomic molecules. It appears that the cross sections are larger for collisions with polyatomic neutrals than with diatomics or atoms (Sugiura and Arakawa, 1970; Latimer, 1977). A simple and elegant process that falls between Penning and collisional ionization was demonstrated by Arrathoon et al. (1973)and recently studied in detail by Hultzsch et al. (1979).Consider the collision of He+ with Ba. The energy released by capture of a free electron to form He in its ground state is greater than the sum of the first two ionization potentials of Ba. Hence, the process He' + Ba -+ He + Ba2+ + e can occur in arbitrarily slow collisions. Hultzsch et al. found that He+ + Ba goes through a step in which (Ba+)*is formed by electron transfer, probably of a 5p electron, from Ba to
R. STEPHEN BERRY AND SYDNEY LEACH
38
Hef, and then through an autoionizing transition. The cross sections for both He+ and Na' are decomposable according to the energies of the released electrons. These electrons exhibit sharp energy spectra like photoelectron spectra; Hultzsch et al. were able to measure some cross sections for production of electrons of specific energies, as functions of collision energy. The first prominent electron group, with 8.27 eV of energy, corresponds to a cm2 at a collision process with a peak cross section of about 17 x energy of about zero. Hultzsch et al. interpret this as corresponding to a compound state of (HeBa)' that dips just as low as the energy of the He Ba' * asymptote from which Bat * autoionizes to give the 8.27 eV electrons. The next prominent electron group has an energy of 9.50 eV; its peak cross section of 2.8 x 10- cm2 occurs at a collision energy of 20.5 eV. With He+ on Ca, the system undergoes its autoionization during the lifetime of the (HeCa)' compound state. No estimate was made of the absolute cross Ba. section for this system; it is not as large by any means as that for Hef
+
'
+
3. Collisional and Associative Detachment
Turning now to collisional detachment, A-+ M+A+ M + e
we note the similarity of this process in low-energy collisions to associative detachment, A
+ M +AM + e
(13) which was introduced in Part I (Berry, 1980a) in parallel with associative ionization. The topic was recently reviewed by Fehsenfeld (1975). In the present context we are particularly interested in associative detachment when the colliding species are in their ground states. These processes are the inverses of dissociative attachment and the three-body attachment process M,the colliding that begins with A and M free. To form A M and e from Apair of heavy particles must reach a spatial region and an energy where A M is stable, and the electron must escape before A- and M can separate. The rates for such processes are, in some instances, quite large: about 1.6 x cm3/sec for F- H and 9.6 x lo-'' for C1H, but the nonobservation H, at 300 K of HI e implied a coefficient less than 6 x lo-" for I (Fehsenfeld, 1975).A major reason for such large rate coefficients is the high escape velocity of the electron; Christophorou et a!. (1968) give a total lifesec for HCI-, roughly equally divided between time of about 1.8 x the two decay channels of H C1- and HCl e. The rate coefficients for H + H - +H2 e is about cm3/sec for collision energies up to about 1 eV, and rises possibly almost an order of magnitude over the next decade of energies (Fehsenfeld, 1975), according to
+
+
+
+
+
+
+
+
39
ELEMENTARY ATTACHMENT AND DETACHMENT PROCESSES
calculations from theory. Bieniek and Dalgarno (1979) have elaborated earlier theoretical models to estimate the cross sections for specific vibrational and rotational states of H,. The very important reason for such an elaboration is the possibility that associative detachment of H- + H may be responsible for production of the vibrationally excited hydrogen molecules observed in space (for example, Gautier et al., 1976; Beckwith et al., 1978). Indeed, the cross sections for production of H, with u = 3-6 and J between 7 and 15 are almost as high as 5 x cm2 for collisions at 0.0129 eV in some instances. At an energy 10-fold larger, the cross sections are only about 0.5 x 10- l 6 cm2 at maximum. The total computed cross sections at the two energies are 85.5 x 10- l6 cm2 and 22.0 x 10- l 6 cm2 at the two energies. The computed thermal rate coefficientof 1.89 x cm3/sec is consonant with the experimental value from flowing afterglow studies (Schmeltekopf et al., 1967). While vibrationally excited H, from associative detachment has not been observed in the laboratory, the distribution of vibrational states of HCl from H C1- has been determined very recently (Zwier et al., 1980). From the infrared chemiluminescence of a flowing afterglow, Zwier et al. found that the ratio of HCI (u = 2) to HCI ( u = 1) is 0.60 _+ 0.03; the temperature of 296 K is too low for production of significant amounts of the states with u 2 3. The authors infer by comparison with the displacement reaction C1- + HI that very little HCl (u = 0) is generated by associative detachment. These results are very much in accord with results of Allan and Wong (1981) that the cross section for the reverse process increases 10-fold with each additional vibrational quantum of the HCI. Comer and Schulz (1974), in their study of detachment cross sections from 0 - and S - on a variety of molecular gases, found it useful to distinB, the guish three cases, as follows. In the first class of reactions, with Across section is zero from a collision energy of zero up to an energy equal to the electron affinity of A, above which the products are A B e. In the second class, the cross sections are large for low-energy collisions because AB + e may be formed exothermically. The third class contains those molecules having small but nonzero cross sections at energies below that of the onset of direct collisional detachment. The process 0- 0, falls in the first class; the threshold for this process is 1.465 eV and the cross sections rise from zero at this energy to 10- l 6 cm2 at 5 eV. By contrast, 0 - + CO and 0- H, are in Comer and Schulz’ class 2, with cross sections above 8 x 10- l6 cm2 at zero energy, but dropping to about 10- cm2 at 3-4 eV. The N, molecule with 0 - is examined carefully by these authors; the cross section does rise at collision energies below 2 eV but only from about 0.1 x 10- l6 cm2 to about 0.62 x 10- l 6 at 0.32 eV. The implication is that this system falls in class 3. The O--N, system is compli-
+
+
+ +
+
+
40
R. STEPHEN BERRY AND SYDNEY LEACH
+
cated by the existence of the stable N,O molecule; the potential of NZ(’X) 0- is estimated to cross that of N 2 0 + e over a range of energies ranging from about half a volt above the minimum for the N - 0 stretch for linear N 2 0 to close to that minimum for a bent molecule. In other words, the probability of reaction is very sensitive to the 0 - N z orientation. The results for 0-+ NO at very low energies are controversial; Comer and Schulz find a cross section below 10- l 6 eV for collision energies less than 3 eV, but they cite much higher cross sections reported by others. Hydrocarbons such as C,H2 and CzH4 seem to be in their class 2; CH4 is put in the same class, but the data they give suggest that it may be as appropriately put in class 3. The results of Comer and Schulz are neatly consistent with Risley’s (1977) results for “collisional” detachment of H- on N, . Here, one sees oscillations in the energy spectra of the ejected electron, which Risley interprets as due to Franck-Condon oscillations associated with the formation of a transient N,- molecule. The Nz- then decays into N, + e. The transient N z - is presumably the same as the resonant state seen in a variety of electronscattering experiments,at electron energies between 1 and 4 eV. This process of electron transfer followed by electron loss is almost, but not quite, simple, direct collisional detachment.
4. “Simple” Dissociative Attachment Simple, direct collisional detachment occurs for negative ions colliding with rare-gas atoms. Such processes do have significant cross sections at low collision energies; both the cross sections and rate coefficients have been studied by a number of techniques. Remarkably, there is a very significant unresolved discrepancy regarding the collisional detachment of the halogen atoms; we shall discuss this problem below. Collisional detachment from H- by He at low energies was measured by Bailey e f al. (1957), for H - on 0,by Bailey and Mahadevan (1970), and for H- and D- in beam collisions with He, Ne, Ar, and N, (Champion et al., 1976).The process was modeled theoretically by Lam et al. (1974) who used the formalism of a complex potential to account for passage of the system out of the initial (H- + atom) channel. Collisional detachment of H- by He in the range 0-3 keV was studied theoretically by Herzenberg and Ojha (1979); readers interested in that higher energy range can use this work as a recent entry into the literature. Born-Oppenheimer breakdown dominates the process at low energies. The cross sections for H- and D- on He have flat maxima of approximately 3.4 x cm2 for collision energies of about 15 eV and above (Champion et al., 1976). The detachment cross sections are about half that
41
ELEMENTARY ATTACHMENT AND DETACHMENT PROCESSES
large at 3 eV, and the data are consistent with a threshold at the electron affinity of hydrogen, 0.74 eV. The cross section is slightly larger for D- than for H-, as one would expect from the relative velocities. The detachment cross sections of H- and D- with neon are somewhat smaller than-roughly half of-those with helium (Champion et al., 1976),which may be associated with the small elastic scattering cross section for electrons on neon at low energies. Champion et al. point out the puzzling observation that at each energy, the low-energy detachment cross section for D - on neon is smaller, not larger, than that for H - on neon, despite the longer interaction time for D - . This order holds also for D- and H - on argon, but the cross sections are larger than for neon, more like those with helium. With N,, H- and D- have large cross sections, about 6 x 10- cm2 for collisions of 10-50 eV, and the cross sections of the two isotopes are about the same. Collisional detachment cross sections from 0 - ,OH-, and 0, - have been measured with 0, (Bailey and Mahadevan, 1970) and with rare-gas atoms (Wynn et al., 1970). In the latter case, it was possible to study some cross sections in the very important threshold region-important, because the rates of such processes under thermal conditions depend on the product of the fast-rising cross section and the rapidly falling Boltzmann distribution of relative speeds of the collision partners. Like H - , the cross sections for these cm2 at collision energies of 15 eV or other species are of order 4 x more. The threshold behavior, especially for 0- and He, shows clearly that the cross section ud is directly proportional to the square of the relative energy, and that the detachment process first occurs at the thermodynamic electron affinity of the oxygen atom or the OH radical; the threshold behavior for 0,- has the same dependence, but the threshold seems to be at a collision energy of zero. The collisional detachment cross sections of halide ions with rare gases were studied by Bydin and Dukel’skii (1957) and by Fayeton et al. (1978)at high energies, and at thermal energies by Champion and Doverspike and their collaborators (Champion and Doverspike, 1976a,b; B. T. Smith et al., 1978). The thermal rate coefficients for these processes have been determined by measurements in shock waves (Mandl et al., 1970; Mandl, 1971, 1973, 1976a,b, 1978; Luther et al., 1972; Milstein, 1972; Berry, 1980b). The shock-tube studies are consistent with one another, giving rate coefficients of order 3 x cm3/sec (even for I - ) at temperatures of 5000-5500 K down to about cm3/sec for temperatures near 3500 K. The beam experiments, on the other hand, have yielded cross sections having thresholds at energies roughly double the electron affinities of the halogen atoms, and staying in the range of 10- l 6 cm3 for energies up to 20 eV. The upper limits to the rate coefficients implied by the measurements of B. T. Smith et al. (1978)are, for example, 0.14 x cm3/sec for C1Ar at
’
+
42
R. STEPHEN BERRY AND SYDNEY LEACH
+
4000 K and 1.1 x cm3/sec at 5000 K. For BrAr, the rate coeffiand 0.23 x In cients at the same temperatures are 0.027 x short, the beam measurements yield values far too low to be consistent with the shock-tube studies. Moreover, the low cross sections and the energy thresholds at about twice the electron affinity of the halogens are observed with C1- and Br- on H,, D,, O,, N,, CO, CO,, and CH4 (Doverspike et al., 1980). It is tempting to suppose that the shock-tube systems have additional processes contributing to the detachment rate, possibly X- + e-+ X + 2e or X- M' X M (Berry, 1980b), but there is no positive evidence yet for such a process. On the other hand, it is puzzling that the thresholds for collisional detachment from halide ions are so much higher than for H - , 0 - , or OH-. This remains one of the striking unresolved anomalies of elementary attachment and detachment processes.
+
-+
+
C . Ion-Pair Formation Charge formation and removal processes need not involve free electrons. The negative charge carriers may be heavy particles, particularly if they originate with very electronegative neutrals, such as halogen atoms. The ion-pair formation processes A B A + B- and AB M A+ BM are known to occur and in some circumstances, even dominate the charge formation process. In the latter process, we would usually understand M to mean a heavy particle that produces collisional dissociation of AB to ions. However M may also be a photon or an electron. And the state formed by absorption of the quantum of excitation may be either a state that dissociates directly to A + B-, or a state with a measurable lifetime as an AB* complex; this situation approaches a half-collision parallel to the A B+A+ B- process. Photoproduction of ion pairs is discussed later in the context of photoionization. High-energy collision processes producing ion pairs were the titular topic of a review by Baede (1975).This discussion also summarizes a very large part of the theoretical work on the subject through about 1972. More recently, Los and Kleyn (1978) reviewed the literature on ion-pair formation emphasizing processes involving alkali atoms with halogen atoms and molecules. Berry (1980b) has discussed alkali-halogen and related ion-ion neutralization processes with particular attention to the chemical kinetic phenomena in gases in which these neutralizations are important. The theory of ion-pair production has been essentially a theory of the crossing of potential curves or surfaces. In its simplest form, exemplified by an alkali atom and a halogen atom, the system is somehow produced in an initial state-by excitation of a neutral molecule, by collision of neutral atoms, typically-energetic enough that the atom pair may become an ion
+
+
+
+
+
-+
+
+
-+
+
ELEMENTARY ATTACHMENT AND DETACHMENT PROCESSES
43
pair and dissociate. Figure 9 shows the lowest relevant potential curves of Na I. This system illustrates several of the elementary processes of ion-pair production. If these two neutral atoms collide with kinetic energy greater than Q (the difference of the ionization potential of Na and the electron affinity of I), it is possible, in principle, for an electron to jump from the Na atom to the I atom to form Na’ and I-.
+
1. Collision-Induced Dissociation to Ion Pairs
If a molecule of NaI is struck by one or more argon atoms and is thereby given enough energy to dissociate to atoms in their ground states, no ionpair production can occur. However, it may be that no dissociation occurs either. This would happen if the ionic NaI molecule could not successfully transform itself by electron transfer into two neutral atoms when the distance R between the Na nucleus and the I nucleus is large. The molecule would persist as two ions at all the internuclear distances accessible to it and would stay bound by the attractive Coulomb force at energies as high, perhaps, as I - . However, if the system were to receive the limit of dissociation of Na’
+
Na’(’SltI-(’S)
.-0
t
-
-
Re-1
Re
%+1
R,+2
Re+3 Re+4 R,t5
Internuclear Distance ( A )
FIG.9. The lowest potential curves for the NaI molecule. The region around R = R, is taken from Davidovits and Broadhead (1967); for NaI, Re = 2.71 I A. The region around the crossing distance of 6.9296 is based on an estimated splitting of 0.11 eV at the crossing distance (Grice and Herschbach, 1974). While only one potential curve is drawn from each dissociation limit, there are, of course, several; for &le there are two states with total axial angular momentum R = 1, one with R = 2 (all doubly degenerate), and two with R = 0, all from the limit Na(2S) + l(2P3,2).
44
R . STEPHEN BERRY AND SYDNEY LEACH
energy exceeding the dissociation limit of two ions, then one would expect to see such ion pairs. Experiments with shock-heated alkali halide molecules (Berry et al., 1968; for reviews see Mandl, 1978; Berry, 1980b)and with beams of rare gases colliding with alkali halide molecules (Tully et a!., 1971) give direct evidence for production of alkali-halogen ion pairs by dissociative collisions with heavy particles: MX+A-cMC
+ X- + A
(14)
The thallium halides exhibit similar behavior (Parks et al., 1973a,b, 1977). The process may occur by a succession of collisions, as in the heating behind a shock, or by a single collision with sufficient energy. In these cases, dissociation occurs to ions rather than to atoms because the molecules, which are ionic in their ground electronic states, cannot make the electron transfer that would be required if the electrons behaved entirely adiabatically. Adiabatic behavior would require the dissociating atoms to change from being an ion pair, as they are at distances near the molecular equilibrium point Re, to being an atom pair, as they are at very long distances, if the system is in its electronic ground state, The NaI molecule whose potential curves are shown in Fig. 9 is actually a borderline case; a molecule such as CsCl dissociates overwhelmingly to ions (Sheen et al., 1978) and a molecule with a light alkali, especially Li, dissociates primarily to atoms, following the adiabatic course (Ewing et al., 1971; Berry, 1978, 1980b). The reason, in simple terms, is that the region in which the transition between ionic and atomic charge distributions must occur, namely the region of internuclear separation around R , , where the ionic curve crosses the curve for atoms in their ground states, is at relatively small internuclear distances for Li salts and is a relatively broad region. For salts of Cs and Rb, this transition region occurs at very large internuclear distances and is very narrow indeed. The consequence is that the salts of Cs and Rb could only exhibit adiabatic behavior if the nuclei were moving exceedingly slowly as they pass through the transition region: for the lithium salts, the nuclei may have quite high kinetic energy, even several eV, and the electrons still behave adiabatically. It is important to note that Kr or Xe CsCl yield the alkali-rare gas molecule ion as the principal positive species for the 2-3 eV range from threshold upward (Sheen et al., 1978). Ion-pair production by collision with a third body, M AB M A + + B- has also been studied in flames (Burdett and Hayhurst, 1977a,b, 1979).The rate coefficientsderived this way are in reasonably good agreement with those from shock-tube studies. However, the values one obtains from the Arrhenius parameters inferred by Burdett and Hayhurst correspond to considerably larger variations of the rate coefficients with temperature than
+
+
--+
+
ELEMENTARY ATTACHMENT AND DETACHMENT PROCESSES
+
45
are found in the shock-tube studies. For example, for RbBr M, the flame results give a coefficientof 1.44 x 10- l 7 cm3/sec at 2000 K and 3.83 x 10- l 4 at 3000 K ;the shock-tube results are 1.25 x 10- at 2860 K and 3.6 x 10at 4570 K. The implication is that the effective activation energy is not constant, but depends somewhat on the temperature, presumably the vibrational temperature of the diatomic AB. To achieve ion-pair production by collisional dissociation, the molecule to be dissociated must receive adequate energy. In the processes discussed thus far, this energy comes from the kinetic energy of relative motion of the colliding pair, and, if any is available, from vibrational energy in the diatomic. The experiments of Tully et al. (1971)indicate that the cross sections for such processes may be greater than 10 A2, within about 1 eV above theshold, for a single impact. Hence, direct dissociation to ions by collision is not an unimportant process in gases containing alkali halides, at temperatures in the range lo4 K. Other quantitative information regarding the absolute rates of reactions AB M + A + B- + M comes from the shock-tube experiments of Milstein, Weber, and Berry (Mandl, 1978; Berry, 1980b), and the flame studies of Burdett and Hayhurst (1977b, 1979). The latter give rates for the chlorides, bromides, and iodides of the alkalis and Ga, In, and TI. Their data have been reduced to Arrhenius parameters [ k = A T - 3 . 5exp( - A H / R T ) , in terms of A and AH] (Burdett and Hayhurst, 1979).The rate coefficients for the temperature range of their experiments are typically in the range of cm3/sec for RbCl and cm3/sec for NaCl at 2000 to 2 x about CrCl at 3000. Even if one neglects any decrease in the effective activation energy H with temperature, the rates predicted for 8000 K are of order 10- lo, consistent with the estimates of Tully et al. One might expect rates of these processes to increase faster with temperature than a simple exponential form would predict, because of vibrational excitation of the target molecule. The experiments of Tully et al. (1971) show that the process near threshold is very much more probable if the molecular target contains vibrational energy. The probability of dissociation was unfolded from the dependence of the relative cross section on the vibrational energy of the alkali halide; the result is a steeply rising function, as shown in Fig. 10. From this behavior, we know that vibrational as well as translational energy can contribute to collisional dissociation to ion pairs. If we generalize from this example, we are led to suppose that vibrational energy is the more effective, by a considerable margin. Energy to produce ion pairs by dissociative collisions need not come only from translation or vibration. Bush et a!. (1972) showed that this energy could also be supplied by electronic excitation in a collision partner: helium metastables striking 0, molecules at thermal energies have energy
+
+
46
R. STEPHEN BERRY AND SYDNEY LEACH
Vibration01 Quantum Number
CsBr Internal Energy ( kcol/mole) FIG. 10. The probability of dissociation of CsBr in collision with Ar, as a function d ( n ) vibrational quantum number (with effects of rotation disregarded), and as a function a&,) of internal energy. The dashed curve uHsis the cross section for a hard-sphere endothermic process.
above the 17.3-eV threshold and produce 0' + 0-ion pairs. However, this process is far less likely than the competitive Penning ionization that generates O,+ + e. Electrons can also induce ion-pair formation. The process operates by electronic excitation of the target molecule to a state dissociating to ions, with more energy in the relative motion of the nuclei than the dissociation energy D,*of the excited molecule. The simplest example, H, + e + H f
+ H- + e
(15) was probably observed first by Lozier (1930),but was shown definitively by Khvostenko and Dukel'skii (1958). Its threshold is at 17.3 eV, and the cross section for the process is very small, about cm2 at its maximum. This cross section is displayed in the subsequent discussion of photoionization. The excited state is difficult to identify; in H,, the ionic character passes from one adiabatic excited state to another as the H-H internuclear distance varies (Davidson, 1960; Kolos and Wolneiwicz, 1969; Glover and Weinhold, 1977). Other molecules show the same sort of behavior, especially in the narrow energy band bound between the threshold for ion-pair production A + B- and the threshold for the production of A + B + e. For example, besides H,, CO, NO, and O2 were studied by Locht and Momigny (1971),
+
+
ELEMENTARY ATTACHMENT AND DETACHMENT PROCESSES
47
who were able to interpret structure in the energy dependence of ion-pair production curves in terms of thresholds for specific processes and molecular states. In general, these processes all seem to have small cross sections.
2. Photoproduction of Ion Pairs Intermediate between collisional dissociation to ion pairs and ion-pair production by two-body collisions, A B + A + B-, is photodissociation to ions. This phenomenon occurs frequently as one of two or more competitive decay channels available to a photoexcited molecule. This aspect is discussed later (Section II,E,4,a). One might expect light alkali halides such as LiI to dissociate to ions if they absorb photons of sufficient energy. However, the evidence for ion-pair production by photoabsorption comes primarily from other species more easily studied. Klewer et al. (1977) used two-photon absorption to provide Cs-. The experiments were enough energy for Cs, to dissociate to Cs' carried out with photon energies below the threshold for formation of Cs+ + Cs e. However, formation of Cs2+ is a process competitive with ion-pair formation. In this particular case, ion-pair production is typically two orders of magnitude less probable between the threshold photon energy of 1.95 eV and about 2 eV; above about 2.1 eV, ion-pair production has the higher probability. (The energy absorbed as light is of course twice the energy per photon.) At higher energies, 17-30 eV, photodissociation of O,, NO, and CO to ion pairs has been observed by Oertel et al. (1980; see also Section II,E,4).
+
+
+
+
3. Ion-Pair Production by Charge-Exchange Collisions The simplest two-body processes yielding ion pairs by charge exchange are probably those of hydrogen atoms with rare-gas atoms. Although such processes are too endothermic to be very important in the range of conditions of our primary concern, they nevertheless so basic that some new, definite information about them deserves mention here. Total (i.e., integral cross sections have been measured by Aberle et al. (1980) for collisions of H and D on Ar, Kr, and Xe, to produce H - or D- and the positive rare-gas ion. The cross sections rise slowly from the threshold energies for about 1 eV and then more rapidly. They show large-amplitude variations; that for H + Ar has cm2 at about maxima of about 0.5 x 10- cm2 at about 21 eV, 2 x 20 eV, and 4 x cm2 at about 70 eV. The other combinations have different oscillatory patterns, but their cross sections have maxima of the same order. Aberle et al. interpreted the variations in cross sections with energy as due to interference between the ionic channel and two neutral states, the initial state and one or more Rydberg states whose potential curves lie close to and parallel with that of the ionic state.
48
R . STEPHEN BERRY AND SYDNEY LEACH
At thermal energies, ion-pair production by collision of an electron donor and an electron acceptor is probably of greater general interest than the processes requiring collisions with external sources of energy, such as fast Ar, He* metastables, electrons, or photons. It is useful to distinguish simple electron transfers, as in K + I + K + + I-, from rearrangements, such as N, + CO + NO' + CN-. Again, we refer to Baede (1975) for an extensive review of both theoretical and experimental work on these topics, particularly involving alkali atoms as donors. Experimental studies of these processes began with the simpler systems of alkali atoms colliding with molecules, even in the 1930s and 1940s (Polanyi, 1932; Magee, 1940), but the more elementary atom-atom processes were only studied definitively by the use of colliding beams, beginning in about 1970 with the study of Cs + 0 - Cs' + 0- by Woodward (1970). The cross section for production of Cs' in the energy range 200-1800 eV was found to be about cm2, about an order of magnitude less than that given by the Landau-Zener-Stueckelberg calculations of van den Bos (1970, 1972). The alkali-halogen atom process is simpler still. The energy dependence of the relative cross sections for Li, Na, and K on I to give I - were obtained by Moutinho et al. (1971a, 1974)in the kinetic energy range from threshold to a few eV above threshold. Delvigne and Los succeeded in measuring absolute differential cross sections for Na + I + Na' + I- in the energy range from 13 to 55 eV. Experimental values for the total cross sections for these processes have not been reported, but Los and Kleyn (1978),comparing experimental and theretical results, put them in the range of 5-10% of the geometric cross section based on the internuclear distance of the crossing point of ionic and ground-state atomic potential curves, in the range a few electron volts above threshold. The differential cross section offers a rich subject for study because it shows oscillations due both to the rainbow and Stueckelberg contributions. The rainbow effect arises from the interference of different deflection processes from a single potential that contains both attractive and repulsive parts. The Stueckelberg oscillations are due to interferences between two different potentials inside the crossing radius. The results of Delvigne and Los (1973) were not in good agreement with the theoretical values for large impact parameters, but were quite satisfactory for close collisions. More recent calculations of Li and Na on I, particularly by Faist et al. (1975)and by Faist and Levine (1976)based on close coupling, are more consistent with the experimental results both for differential and total cross sections (Los and Kleyn, 1978).The results support the idea that the Landau-Zener-Stueckelberg picture-the transition probability is dominated by what occurs at a curve crossing, but is modified a bit by what happens elsewhere-is satisfactory for these systems. The Stueckelberg
ELEMENTARY ATTACHMENT AND DETACHMENT PROCESSES
49
semiclassical form, which retains phase information lost in the LandauZener expression, seems to be quite adequate to represent the stringent tests of the total and especially the differential cross sections for K + I, down almost to the threshold energy (Andresen and Kuppermann, 1978; Andresen et al., 1978).We shall see that this is not the case for all A + B = A + + Bprocesses. The flame studies of Burdett and Hayhurst (1977a,b, 1979)provide quantitative values of rates of ion-pair formation. Burdett and Hayhurst measured values of these rates for the alkali, gallium, indium, and thallium salts of C1, Br, and I, at temperatures from 1820 to 2590 K and fit the rates to Arrhenius and parameters. Typically, these rates fall between about cm3/sec. They are not in very close agreement with the values one would naively infer from the shock-tube studies of Milstein, Weber, and Berry (Mandl, 1978; Berry, 1980b) if one assumes that the rates can be computed from the relation (forward rate)/(backward rate) = equilibrium constant. However, the flame results are intended to be the values of the true two-body process, whereas the shock-tube studies give only the effective two-body rate coefficients t h e n the pressure of the third body is effectively constant. By combining Burdett and Hayhurst’s two- and three-body contributions, one obtains results reasonably compatible with the shock-tube results. Collisions of alkali atoms with molecules comprise by far the largest part of the data for ion-pair production processes. The alkali atom-halogen molecule pairs were among the first to be studied by neutral-neutral beam collision processes. The cross sections are of order 100 A’; the processes occurring at lowest energies include both electron transfer and M + X, -+ MX + X. Los and Kleyn (1978) point out how, up to relative velocities of order 3 x lo3 m/sec, K + Br, goes to KBr + Br, but almost entirely to ion-pair formation for the next decade of velocities. The negative ions formed in this process are about 50% Br- at the lower velocities and about 30% Br- at higher velocities (Hubers, 1976; Hubers et d.,1976). The interpretation of the process is summarized by Los and Kleyn, based largely on the interpretations given by the Amsterdam group. The probability of electron transfer from alkali to halogen molecule is large when the initial collision occurs, because the crossing of the ionic M + + X,- and neutral M + X2curves occurs at a small interparticle distance. This in turn is due to the rather small electron affinity of X2 when the X-X distance is near its equilibrium value. However, X2-formed at such a distance is produced at a point high on the inner repulsive part of the potential curve for Xz-,so the two X’s move apart rapidly in the newly born XI- molecule. If the collision occurs in a time longer than the X2- vibration, or at an energy too low to form M + + X,- or M + + X- + X, then MX + X are produced, presumably with MX in a high vibrational state. If the collision happens in a
50
R. STEPHEN BERRY A N D SYDNEY LEACH
time comparable to or somewhat shorter than an X2- vibration, the M + ion leaves before X- can tag along, and the residue appears as X,- or X- + X, depending on the distribution of energy between relative motion of the halogens and the other degrees of freedom. At still higher energies, the process becomes sudden with respect to nuclear motions, and is dominated by the Landau-Zener picture with Franck-Condon factors determining the branching between X,- and X- X fragments. The alkali atom-oxygen molecule system is one of those studied most extensively with regard to ion-pair formation. One of the most recent efforts (Kleyn et al., 1978), which summarizes most of the previous work (see also Baede, 1975) verifies that 0 2 -is the dominant product and that a LandauZener picture suffices to describe the system approximately. A minor product is 0 - ,above the threshold for formation of 0 + 0 - , typically about 9 eV (Moutinho et al., 1971b). The cross sections for 0 2 -production rise from their thresholds of about 1 eV (Cs + 0,) about 5 A2 at 5-10 eV above threshold and then to as much as about 8 A2 at their maxima, in the range of 100 eV. The cross sections should show oscillations with collision duration, according to the analysis of these authors. Ion-pair production in collisions of still more complex species is becoming a subject of quite broad interest. Some simple examples are: the collisions of Li, Na, or K with halomethanes to give alkali positive ions and CH,X- ions (Moutinho er al., 1974); collisions of the same alkalis with SF, to give alkali positives and either SF,- (near threshold) or (SF,- + F) and (SF, + F-) at slightly higher energies (Hubers and Los, 1975);collisions of K and Cs with UF, and WF, to give UF,- and WF,- (Stockdale et al., 1979);and collisions of K and Cs with H,O (Warmack et a/., 1978).These processes all presumably involve a first step of simple electron transfer which, in the last two examples, is followed by dissociation. In the case of SF,-, this dissociation may occur only for collision energies of about 0.5 eV or more, depending on the alkali. Values of0.43 eV (Fehsenfeld,1970)and 0.51 eV (Hubers and Los, 1975)have been reported for K + SF,, for example. Formation of F- occurs only above a second, much higher threshold, 8.2 eV for Na + SF, and 7.30 eV for K SF,, according to Hubers and Los. Like the M AB process (Tully et al., 1971) and the M + I2 process (Aten et al., 1977),the M + SF, process has been examined to determine the sensitivity of the reaction probability both to variation in translational energy and to internal vibrational energy. The M-SF, system shows a complete equipartition of vibrational and translational energy for collisions with very low kinetic energy. However, for SF,- formed above threshold and for SF,- (or F - ) formed more than 2 eV above their thresholds, vibrational energy in the SF, is more effective in enhancing the reaction rate than is energy in translation. This is easily reconciled in terms of “vertical” or rapid transitions from SF, to SF,-.
+
+
+
ELEMENTARY ATTACHMENT AND DETACHMENT PROCESSES
51
The experiments with K or Cs and H 2 0 showed only OH- and, with D20, OD- negative ions. The H 2 0 - molecule is unstable. The ground 'A, state dissociates to H + OH-, whereas higher states dissociate to 0 - + H, and to H- + OH. The results, based on angular distributions of both positive and negative ions, show that electron transfer to form the ground state of H 2 0 - is the only important process for ion-pair formation. The lowest energy of the collisions in these studies was 10 eV; one can be reasonably sure that only H,O- in the 'A, ground state would be produced in collisions at lower energies. The most complex ion-pair formation processes involving alkali atoms are probably those studied by the Oak Ridge group (Compton et al., 1974; Stockdale et al., 1974; Cooper et al., 1975). Collisions of cesium atoms with maleic anhydride
succinic anhydride,
and parabenzoquinone,
yield ion pairs. With maleic anhydride, the principal negative ion from collisionswith energies between 2.5 and about 7 eV is the primary C4H203ion. At higher collision energies, both C2H2C02-and metastable C 0 2 - are as important in the negative ion mass spectrum. No parent negative ion was found from succinic anhydride, but CdH203- and C4H303- (unresolved) were formed at energies of collision from the threshold of 3 eV upward; at 5 eV, C,H,CO,- appeared and dominated the spectrum above about 5.5 eV. The negative ion spectrum of Cs + p-benzoquinone gave a parent ion at energies from 2 eV upward and very small quantities of fragment ions from about 3 eV and beyond. Even species as unstable as anhydrides (which give up C 0 2 under many conditions) can, it appears, become stable negative ions under gentle electron transfer conditions.
52
R. STEPHEN BERRY AND SYDNEY LEACH
4. Charge Exchange with Excited Species Collisions of excited donors with acceptors can provide energy to make otherwise highly improbable ion-pair formation take place. Rare-gas atoms in high Rydberg states react with I, to form 1,- (Gillen et al., 1978), with SF, to form SF,- (Hotop and Niehaus, 1967), and with CH,CN to form CH,CN- (Sugiura and Arakawa, 1970; Stockdale et al., 1974). In these cm2, examples, the cross section for ion-pair formation is about 1.7 x a figure presumably due more to the size of the average orbit of the Rydberg state than to any characteristic of the acceptor. More recently, Dimicoli and Botter (1980, 1981a,b) have carried out further studies of ion-pair formation with argon and xenon atoms in high Rydberg states and with acceptors CCI,, CCl,F, CH31, SF,, and C6F6 from hypersonic nozzle beam sources, so that the acceptors have low internal temperatures. Detection was done by time-of-flight coincidence mass spectrometry. Both CCl, and CC1,F give dissociative attachment, forming C1- and CCl, and CCl,F, respectively. Hence, these are examples of reactive ion-pair formation processes. However, they probably occur in two steps, an elementary electron transfer step to form Ar' + CC1,- or CCl,F, followed by dissociation of the negative ion molecule. With SF,, in slow collision one finds SF,- as the sole product, but at higher energies one obtains SF,- + F, as with alkali atoms as donors. Such processes as these may provide significant channels for the capture of electrons at the boundaries of hot plasmas, in which rare-gas ions are present in high concentration within a hot zone, but electron acceptors are available from cooler regions. With argon (in a high Rydberg level) as a collision partner, the cross sections for ion-pair formation are in the range cm2, one to two orders of magnitude larger than for detachment collisions as with Ar* + CO or CF,. Matsuzawa (1972) and Flannery (1973) have given theoretical descriptions of this process in which the electron in a Rydberg state is considered to be slow moving and nearly free. While the model predicts the correct magnitude of the cross section, it fails to predict the observed rise in cross section with relative velocity exhibited at velocities below about 7 x lo4 cm/sec and quantum numbers n s 28. The theories do not include any allowance for near-resonant behavior that is known from ion-ion neutralization studies (see later) to heighten transition probabilities considerably. A more refined theory will presumably show some kind of maximum for just this reason.
5 . Ion-Pair Formation in Reactive (Rearrangement) Collisions The alkali-oxygen system mentioned previously (Kleyn et al., 1978)is one of the simplest that may bring us to examine truly reactive ion-pair formation. That is, with Na + O,, for example, a rearrangement might, in principle, In fact, such a process was occur of the type Na O2-+NaO+ 0-.
+
+
53
ELEMENTARY ATTACHMENT AND DETACHMENT PROCESSES
observed by Rol and Entemann (1968) and by Neynaber et al. (1969). The cm2 cross section for this particular process is not large, about 4 x according to Neynaber et al., at a collision energy of 7 eV, 1.5 eV above the threshold energy. In this case, the reaction is probably the result of interactions in a compound state NaO,, and not of final-state interactions as CCl, from CCl,-. was the formation of C1Fite and Irving (1972)and Cohen et al. (1973) have looked in some detail at the competitive processes that occur when a metal atom M produces charged species from collision with oxygen. These include associative e , electron transfer M 0, M' + 0,-, ionization M 0, M 0 2 ' and the rearrangement process M + 0, + MO' + 0 - . This work was mentioned in Part I (Berry, 1980a) in connection with associative ionization, which is the dominant process. More recently, Patterson et al. (1978) showed that thorium colliding with ozone gives 0 - and 0,- with Tho,' and T h o + , respectively, as relatively minor products among processes that lead largely to associative ionization and Kuprianov processes; i.e., to the production of free electrons. In the reactions studied by Cohen, Young, and Wexler, the 02-, predominant process gave electron transfer and formation of M' with barium, titanium, and aluminum. Barium and titanium gave about an order of magnitude less MOe + 0 - , and still smaller amounts of pure associative ionization, MO,' -t e. With aluminum, no oxide ions, either A10' or AlO,', were observed, which seems a little surprising in view of the chemical lore that aluminum has a great affinity for oxygen. A still more complicated reaction that generates ion pairs is one of the reactions that takes place between alkali diatomic molecules and halogen molecules. Lin el al. (1974) showed that K, reacted with Br,, I,, IBr, and ICI X-,and (3) KX,- K', with a to give (1) K' + KX + X-,(2) K2X' cm'. This is an order of magtotal reactive cross section of 3-10 x nitude less than the cross section for production of neutrals (Grice, 1975). Rothe el al. (1976), Reck et al. (1977), and Dispert and Lacmann (1977) studied the process in more detail. When the process (1) is energetically allowed, it clearly predominates among the ion-forming channels; when process (1) is not energetically possible but the other two are, the products MX,- and M,X+ are found. In addition, Dispert and Lacmann observed the process K + C1, -+K' + C1,- at energies between 0.5 and 5 eV, and K' C1C1 from 3 eV upward; the latter is about 4 times as likely at its peak (6 eV) as the peak at 3.5 eV of the process giving C1,-. Similar results were found for K -+ Br, . Extensive cross section measurements for K, and Cs, with a number of halides were reported by Wells et al. (1980). The most complex process leading to ion-pair formation from collisions of simple species is the rearrangement reported by Utterback and van Zyl (1978).The process occurs at collision energies above its threshold of 12.1 eV, and therefore falls a bit outside the range we would normally include in this
+
+
+
+
+
+
+
+
+
+
N
+
54
R. STEPHEN BERRY AND SYDNEY LEACH
discussion. However, one can imagine similar processes with lower thresholds that might be quite relevant in flames or plasmas, so we mention the rearrangement ionization reaction here. The remarkable process is N, + CO --t NO+ + CN-. The molecule NO has a relatively low ionization potential and CN has a large electron affinity, so it is not surprising that the process is observed. At high energies, no doubt one gets CN + e, rather than CN-. However, near threshold where the cross section is of order 2 x 10- l 9 cm', one observes CN- in the mass spectrometer detector. In fact, one observes CN- at collision energies up to and a bit beyond a local maximum (- 2 x lo-'' cm') at an energy of 10 eV. D. Ion-Ion Neutralization The inverse of the simplest of the ion-pair formation processes is ion-ion mutual neutralization, A+
+ B- + A + B
(16)
We shall discuss this topic somewhat more briefly than ion-pair formation because its literature is much sparser and because it has been relatively unchanged since its most recent reviews (Moseley et al., 1975;Flannery, 1976; Berry, 1980b). However, we shall use this opportunity to summarize the theoretical picture for both the neutralization process and its inverse. Modern work on ion-ion neutralization begins with the work of Mahan and his collaborators (Carlton and Mahan, 1964; Mahan and Person, 1964a,b; Mahan, 1973), because these were the first studies to extend to pressures low enough to distinguish two-body neutralization from three-body processes. Previously, the studies were restricted to relatively dense gases and were interpreted by models appropriate to those conditions (Langevin, 1903; Thomson, 1924; Loeb, 1960; Natanson, 1960; Mahan and Person, 1964b). Interest in ion-ion recombination in dense gases has been sustained recently by the importance of the rare gas-halide lasers. Consequently, the most elaborate of the earlier theories of three-body neutralization, that of Natanson, has been extended (Mahan and Person, 1964b; Flannery, 1972;Flannery and Yang, 1978a,b; Wadhera and Bardsley, 1978). This theory is based on the notion of a critical radius for the ion pair; if the pair comes closer than this distance, they orbit and are sure to suffer a deactivating collision with a third body. Unfortunately, the work of Mahan and Person seems to have been overlooked in some of the recent literature. This is a precise sorting out of the collisional mechanics of A + + B- + M within the notion that two ions moving in a hyperbolic orbit may be deactivated if one of them suffers a collision with a third body.
55
ELEMENTARY ATTACHMENT AND DETACHMENT PROCESSES
Ion-ion recombination rates can be described by pressure-dependent rate coefficients whose minimum values are, in principle, independent of any carrier gas. In practice, this is not quite true (Carlton and Mahan, 1964), which suggests the formation of some clusters around the ions. However, it seems to be approximately so and the rate coefficients increase linearly with pressure. The limiting low-pressure values are effectively reached when the total pressure is below about 5 or 10 torr with NO' and NO,-, with NO+ and SF,-, and C6H,+ and SF,-. The iodine system, where iodine provides both positive and negative ions of uncertain structure, may have to be carried to slightly lower pressures (Carlton and Mahan, 1964). For all these species, the two-body neutralization rate coefficient at 300 K is between 1 and 2 x lo-' cm3/sec, corresponding to a geometric cross section whose radius is about 200 A, that is, to about lo-" cm2. The rate coefficients for mutual neutralization of alkali positives and halide negatives as measured by kinetic studies behind shock waves are in the range 2-5 x lo-'' cm3/sec for temperatures of 3000 K (Berry, 1980b). The rate coefficients include both the two-body and three-body processes; no pressure dependence was studied in this shock-tube work. The largest value reported for an alkali-halogen pair is 9.3 x lo-' cm3/sec for Na' + C1-, calculated by Olson (1977), who found a value of 1.8 x lo-'' cm3/seg for Kf C1-. The reason for the 100-fold larger value for Na' Cl- is the near-resonant character of mutual neutralization, a point discussed in more detail below. Other atom-atom systems were studied in a flowing afterglow (Church and Smith, 1977),but only upper limits to the rate coefficients could F-, and Kr+ + F-, all in He carrier gas, the be set. For Xe+ + C1-, Xe' Frate coefficients at 300 K were all below 5 x lo-' cm3/sec; for Ar' in He, the upper limit was 1 x lo-' cm3/sec. The values are notably lower than the rate coefficients reported by Mahan and his group, despite the much higher temperatures. The interpretation, as we shall see, lies in the fact that the alkali halide studies all involve electron donors whose parent neutrals have large electron affinities and acceptors whose available levels are sparse and relatively high-lying. Rate coefficients for mutual neutralization of halide ions with alkalis, with Ga, with In, and with T1 have been measured in flames by Burdett and Hayhurst (1977b, 1979).Their values, taken at temperatures between 1900 and 2600 K, are generally considerably lower, sometimes by two orders of magnitude, than the shock-tube values. However, Burdett and Hayhurst distinguished two-body and three-body processes. If one uses the results of Burdett and Hayhurst to distinguish two-body from three-body contributions in the shock-tube data, then thearesults from the flame studies and those from the shock-tube studies appear to be fairly consistent, but then do not fit with Olson's calculated coefficients. Examples of the two-body rate
+
+
+
+
56
R. STEPHEN BERRY AND SYDNEY LEACH
coefficients from Burdett and Hayhurst are: 4.8 x lo-'' cm3/sec for Na', CI-; 1.0 x lo-" cm3/sec for K', Br-; 1.5 x lo-" cm3/sec for Rb', Br-; and 1.5 x cm3/sec for Cs', I-. The three-body contributions, with argon at about 0.1-1 atm and 3000 K, bring the total effective two-body rate coefficients up to 2.5 x lo-", 2.3 x lo-", and 2.5 x 10- l o cm3/sec for the last three of these salts. The combination Na', C1- was not studied in the shock experiments. Species whose ion-ion neutralization has been studied in molecular beams extend from the very simplest H' + H- and He' + H - pairs through some diatomic-triatomic examples such as NO' + NO2- and 02+ + NO2-. These were all reviewed by Moseley et al. (1975), but some more recent work deserves to be singled out. Peart et al. (1976a)improved the resolution of the Hf H- system to show convincing oscillatory structure in the cross section for collisions with center-of-mass energies between 20 and 100 eV. At about 118 eV, the cross section has a very sharp peak at 2.1 x cm2; between about 2 and 1000 eV, its value is between 1 and 2x cm2. At energies below 20 eV, the cross section is a decreasing function of energy; typical of exoergic ion-ion neutralization, its cross section varies as ur;,ttive at very low energies (Aberth et al., 1968). The cross cm2 for section for the He+ H- process is also in the range 1-2 x collision energies between 30 and 10oO eV. The corresponding rate coefficients at the temperatures where these cross sections would be appropriate are of order lo-' cm3/sec. At the lowest energies studied, about 0.2 eV, the cross section for Hf + H - neutralization is about 2.5 x lo-', cm3, corresponding to a rate coefficient again slightly above lo-' cm3/sec. With more complex ions, the cross sections are larger still. For example, 02++ 0,has a cross section for mutual neutralization of about 2 x lo-', cm2 at a relative energy of 0.2 eV, and this is typical of such systems (Moseley et al., 1975). The beam results are in general quite consistent with the bulk gas discharge results of Mahan, Person, and Carlton. The flowing-afterglowstudies have given neutralization coefficientsfor a NO2-, N O + + NO,-, number of molecular species, including NO' CC13+ C1- (Smith and Church, 1976), C1,+ + C1- (Church and Smith, 1977),and NH4+ + C1- (D. Smith et al., 1978a).The rate coefficients for all these processes at 300 K are apparently 4-6 x 10- cm3/sec,indicating both that the detailed nature of the acceptor is not important and, more surprising, that the strength of binding of the last electron to the negative ion is also nearly irrelevant to the rate coefficient or the effective cross section. Even clustered ions such as H,0f-(H20), neutralizing with C1- or N 0 3 - . H N 0 , have about the same cross sections of loTi2 cm2 and rate coefficients of about 5 x lo-* cm3/sec @. Smith et al., 1978a). The flowing-afterglow studies of NO' + NO,- give a value of the rate coefficient of (6.4 & 0.7) x
+
+
+
+
ELEMENTARY ATTACHMENT AND DETACHMENT PROCESSES
57
cm3/sec at 300 K, a large rate on the scale of atomic processes. It was pointed out by Smith and Church (1976) that this is nevertheless almost an order of magnitude lower than the value of 5.1 x lo-' cm3/sec from merged-beam studies (Person et af., 1976), and is significantly smaller than the value of 1.75 x cm3/sec reported for NO' NO2- in a stationary afterglow (Eisner and Hirsh, 1971). It is just consistent with a value based on a (Olson, 1972); Landau-Zener (LZ) curve-crossing model, 1.2 k 0.3 x the crossing, in this case, may be at a close enough internuclear distance to make the LZ model applicable. While the low value seems plausible in light of the many other values for ion-ion neutralization of molecular species, the origin of the discrepancy remains unknown. It would be valuable if flowingafterglow studies were done with some systems involving weakly bound negative ions, such as H- or 0-. Flame studies of molecular positive ions neutralizing with halides (Burdett and Hayhurst, 1976, 1978) also gave rate coefficients of about 3 x lo-' cm3/sec.These investigations were done with both H 3 0 +and N O + and with C1-, Br-, and I-. Again, no measurements were done for negative ions with more weakly bound electrons, ions such as S-, 0 - ,or H-. Information regarding the states involved in ion-ion neutralization comes from the merged-beam experiments of Weiner et al. (1971). While most ion neutralization experiments in beams have been monitored by the amount of total neutral beam formed, or the decrease in charged-particle beam intensity, these experiments followed the light emission from Na' 0 - .The results indicate that the greatest part of the cross section, which is of order 8 x cm2 in the range of 0.5-1.5 eV, is due to electron transfer from the negative ion to the empty 3d level of Na'. This level is the one most nearly resonant with the level of the outermost electron in 0 - ,i.e., with the detachment energy for 0 - + 0 e. A similar phenomenon occurs with Li' + 0 - (B. Blaney, unpublished) and with Na' + I-, where the 3p level of Na is nearly resonant with I - (Gait and Berry, 1977). One other study of product states was that of the light emission from NO+ + NO2- (D. Smith ef al., 1978b). The only observed emission from their flowing afterglow was a set of bands of the 1 system of NO, from the ground vibrational state of NO(A2C') to ground 211 state. The FranckCondon constraints of conservation of nuclear position and momentum would favor the formation of higher electronic states of NO, notably the C211,D2C+,and possibly the B211 in a high vibrational level. The C and D states would be the ones favored by near-resonant conditions for charge exchange. We suspect that the emission observed in the afterglow experiments is the result of collisional relaxation of both electronic and vibrational excitation; Smith et al. noted that this could be occurring at the relatively high pressures (ca. 1 torr) of carrier gas in their afterglow.
+
+
+
58
R. STEPHEN BERRY AND SYDNEY LEACH
It would be valuable to have more information about the products formed in mutual neutralization. We do not know, for example, how energy is partitioned among the degrees of freedom or what dissociation may occur, or even how well the Franck-Condon approximation holds in such processes. What, for example, are the products of neutralization of NH4+ and C1- or H,O+ + C1- ? Clementi's calculations (Clement], 1967; Clementi and Gayles, 1967) indicate NH3 HCl would give NH4Cl, but those analyses did not consider the neutralization reaction with possible subsequent dissociation. The latter reaction was discussed by Burdett and Hayhurst (1976), and the possibilities were considered that H 2 0 H C1 or H,O HCl' is formed, but the real products are unknown. The very large cross sections for ion-ion neutralization were something of a puzzle from the viewpoint of microscopic interpretation, despite their prediction from phenomenological theory (Aberth et a[., 1968). LandauZener theory, based on the supposition that the electron transfer occurs almost exclusively as the nuclei pass through the crossing distance, could account well for processes in which this crossing occurs at distances where atomic orbitals from the two ions overlap significantly, say for R < 30A. However, this model implies that the cross sections for neutralization must become very small if the crossing distance is large (Bates and Lewis, 1955). Until the acceptor states could be identified, this conception was unchallenged. However, the crossing distance for Na(3d) 0 with Na+ + 0 - is 288 A, a distance at which the LZ crossing probability is infinitesimal, in contrast to the measured cross section of almost 10- l 2 cm2.This corresponds to a radius of 50 A, or to a probability of neutralization of about 1 in 33 for collisions within the 288-A radius. While the LZ model and its extensions have continued to be used for many ion neutralization systems (Demkov, 1964; Bandrauk and Child, 1970; Bandrauk, 1972; Janev, 1976; Janev and RaduloviC, 1978), the cross sections obtained this way are sometimes considerably smaller than those observed (Burdett and Hayhurst, 1979, for example). A correct theoretical description presumably could be obtained from the use of the full theory of Delos and Thorson (1972). However, even without this machinery, and without a general theory that can account for the longrange processes quantitatively, we nevertheless have considerable insight into what occurs and into what kind of theory is required. Ion-ion neutralizations with long-range crossings are the worst cases for the LZ model. For one thing, the exponential governing the probability of a curve crossing in LZ theory contains the difference of the slopes of the two potentials in its denominator. When two curves have nearly the same slope, this denominator becomes extremely large and the computed probability, correspondingly unstable. Second, the two curves in these systems are almost degenerate for long ranges of internuclear distance, whereas the LZ model
+
+ +
+
+
59
ELEMENTARY ATTACHMENT AND DETACHMENT PROCESSES
supposes that they cross sharply enough that the two states interact only near the crossing. In mathematical terms, the LZ theory supposes that the stationary phase approximation suffices to give the transition amplitude in a semiclassical action integral representation of the phase of the wave function. The point of stationary phase is, essentially, the crossing point. One might suppose, by contrast, that when two potential curves are nearly parallel the stationary-phase approximation is not adequate and that a significant part of the transition amplitude accumulates over a range of internuclear distances, much of it well away from the crossing distance. This situation is well known in a context only slightly different from ionion neutralization, namely in near-resonant ion-neutral charge transfer. The experimental work (Baker et al., 1962; Fite et a/., 1962)fits very well with the theory (Rapp and Francis, 1962), which accounts for nonresonant, resonant, and near-resonant processes. In the resonant and near-resonant cases, very large contributions to the total transition amplitude come from oscillations of the charge between the two colliding centers. We can expect similar behavior for ion-ion neutralization, especially in systems having long-range crossings. In these instances, the ionic potential curve is nearly parallel to and degenerate with one atomic curve for a long interval. In cases where the only crossings are at shorter distances-cases in which the ionic curve has a low-lying limit for R co,crosses only one or two neutral curves and has these intersections at distances of order 30 A or less, here we expect LZ theory to hold very well. Moreover, the cross sections for such processes are expected to be only slightly larger than geometric; this is just what we saw for the ion-ion neutralization cross sections of most of the alkali-halogen combinations. Sodium iodide is the most extreme exception; this combination has a near-resonant crossing of a neutral curve with its ionic curve. In systems other than the alkali halides, one generally finds that the ionic limit is high enough in energy to cross Rydberg states or other high-lying states, so that a near-resonance is almost always possible. The firmest confirmation of this interpretation comes from a calculation CIby Olson (1977) of the ion-ion neutralization cross sections of Na' and K + + Cl- by the LZ method and by a close-coupling formalism that includes the contributions of the entire collision trajectory to the transition probability. While the curve crossings of these systems are much closer than for Na' + I - with Na(3p) + I, they are large enough, it seems, to show the main point. The cross section for the K-Cl system calculated by the LZ method is about 40% below the close-coupling value. In the direction Na + C1(2P,,z)+ Na' + C1-, the close-coupling cross section is approximately 1.5 x cm2 between 1.5 and 4 eV, and the crossing distance is 9.5 A and the close-coupling cross section is approximately 6 x 10- * cmz between 0.7 and 0.85 eV; the LZ value is several orders of magnitude smaller.
-
+
60
R. STEPHEN BERRY AND SYDNEY LEACH
We conclude, as Weiner et al. suggested (1971),that the LZ picture must be augmented for near-resonant processes. The challenge for theorists now is to formulate a representation, perhaps a reduction of the Delos-Thorson theoretical description, that gives a criterion for when the near-resonant picture and the LZ curve-crossing picture apply, tells us whether these two regions overlap or are separate, and gives us a reliable, convenient algorithm for computing the transition probability in almost all instances.
E . Photoionization We turn now to two processes that involve electron ejection via photon absorption : photoionization of neutral species and photodetachment of electrons from negative ions. These are examples of photoelectric effects, which have been of interest since Hertz’s original discovery in studying the impact of ultraviolet light on solids nearly 100 years ago (Hertz, 1887a,b), and the observation of similar effects in the gas phase (Hughes, 1910).They play an important role in chemical physics, astrophysics, planetary atmospheres, and ionosphere studies, as well as as in various branches of plasma physics and chemistry. Light absorption as an initiator or modifier of electrical discharges was known from the early days of Hertz, and this is now known to be due to photoionization, photodetachment, and, in some cases, to so-called optogalvanic effects in which the atoms and molecules in excited neutral states of atoms and molecules created by light absorption, modify the electrical resistance of the gas, positively or negatively (i.e., changes its propensity to ionization). We point out also that photoionization, photodetachment, and, perhaps, optogalvanic processes are of importance not only in laboratory discharges but also in lightning discharges. Experimental results and theoretical treatments of the followingaspects of photoionization will be discussed : photoionization sources, the physics of the photoionization process; photoelectron ejection (energies, angular distributions, and spin polarization) ;photoionization cross sections and their shape, particularly near thresholds, autoionization features; photoionization efficiencies and their variation with photon energy; dissociative ionization, including the role of autoionization and theoretical and experimental approaches to ion fragmentation; multiphoton ionization (spectroscopy and fragmentation). General results are discussed in these fields and some specific atoms and molecules are treated in depth. Among subjects not discussed are the photoionization of atoms and molecules in external electric and magnetic fields, the photoionization of positive ions (on which relatively little work has been done), and postcollision
ELEMENTARY ATTACHMENT AND DETACHMENT PROCESSES
61
interaction effects, studied recently both in electron scattering experiments and inner-shell photoionization. Recent reviews in some of the areas treated are those of Marr (1967,1976), Eland (1974, 1979), Leach (1974), Samson (1976), Rosenstock (1976), Berkowitz (1979), Johnson (1980a,b), van der Wiel (1980), and Krause (1980), as well as the series of reviews on electron spectroscopy edited by Brundle and Baker (1977, 1978, 1979). Theoretical methods for calculation of photoionization cross sections and photoelectron angular distributions have been expounded in the proceedings of three recent colloquia (Kleinpoppen and McDowell, 1976; Wuilleumier, 1976; Rescigno et al., 1979). Discussion of photodetachment in atoms and molecules is limited to negative ions having positive electron binding energies. Photodetachment cross sections near threshold and dissociative processes are treated. The appropriate review articles are mentioned in that section. 1 . Some General Remarks
a. Photoionization sources. Much of the earlier work on photoionization processes was carried out using line-emission sources of the gas discharge or vacuum spark varieties. Detailed structure in cross-section curves is not easily revealed with such sources. Continuum sources, particularly the highpressure rare-gas continua, the Lyman continuum generated by a highcurrent density discharge through a low-pressure gas, such as in the Garton (1953,1959) source, and the Ballofet-Romand-Vodar (1961) (BRV) vacuum spark source (which has a low inductance, is triggered by an auxiliary sliding spark, and uses refractory high-atomic-weight anode material) have been the principal VUV sources used for quantitative studies. Descriptions and references to these line and continuum sources are given by Samson (1967) and by Zaidel’ and Shreider (1970). Recent developments of the very useful BRV plasma source are described by Damany et al. (1966), Fox and Wheaton (1973), Boursey and Damany (1974), and Lucatorto et al. (1979). In more recent years, the quasi-ideal synchrotron radiation (SR) source has provided more reliable data on photoionization cross sections and other processes induced by photon absorption, The SR sources can provide continuum radiation from the far IR to the X-ray region and, with adapted monochromators, give tunable radiation over this entire range. A comparison of various VUV sources is made in Table 11, taken from Jortner and Leach (1980). It should be noted that one difficulty in the use of continuum sources is to account for scattered light and, especially with synchrotron radiation, eliminating higher spectral-order radiation.
62
R. STEPHEN BERRY A N D SYDNEY LEACH
TABLE 11 COMPARISON BETWEEN SR SOURCES AND VACUUM UV DISCHARGE LAMPS ~
Source Conventional rare-gas continua He continuum (50 torr) Ne continuum (100 torr) Ar continuum (200 torr) Kr continuum (200 torr) Xe continuum Pulsed discharge in rare-gas continua Ar (2000 torr) Kr (2000 torr) Hydrogen discharge Hinterreger lamp Resonance lamps He(1) resonance He(I1) resonance Ne(1) resonance Ne(I1) resonance Plasma sources BRV source
Soft X-ray lines YM5 ZrMr NbMr RhMt MgKu AlKcl CuKu Synchrotron radiation
~
~
~
Useful energy range (eV)
Linewidth (eV)
12-21
-
~~~
~
Pulse length (sec)
Intensity at monochromator exit slit photons/(sec A)
-
lo8
- ID8
12.4- 16.8 8.0-11.8
-
-
6.9-9.9
-
- lo8
6.2-8.4
-
8.0- I 1.8 6.9-9.9
-
-
4-12 21.2 40.8 16.8 26.9 4-250
132.3 151.4 171.4 260.4 1254 1487 8055 10- 1- 1000
--
lo8
lo8
109-1010 109-1010 107
---
10-3
< 10-3
> p(Au = -2) etc.]. The vibrational branching ratios are predicted to oscillate and differ considerably from the FranckCondon values as the photon energy passes through autoionizing resonances (Raoult and Jungen, 1981). The corresponding behavior for the photoelectron asymmetry parameter has been discussed earlier. Autoionization in H, has also been studied by threshold photoelectron spectroscopy at low (Villarejo, 1968; Stockbauer, 1979) and at much higher resolution (Peatman, 1976a,b). Propensity and selection rules have been
-
90
R. STEPHEN BERRY AND SYDNEY LEACH
tested, and the detailed routes examined of several degenerate autoionization processes (i.e., where the superexcited state is quasi-degenerate with the ion state to which it decays). Molecular fluorescence from superexcited states of H,, as well as from states above the dissociation limit at 14.67 eV, has been observed by Roncin et al. (1974) (see also Dieke, 1958) and the states identified. All lines are Q ( J ) , whereas R and P branch lines are absent. This indicates that the emitting levels are 'nu-states. These states, unlike the others known from optical spectra, have no available channels to which decay is much faster than photon emission. Predissociation of superexcited states has also been identified as an important decay channel in H,. The experimental observations of Guyon and his collaborators, using a synchrotron radiation source, are of H atom Lyman-cr, indicating predissociation to H(2p) + H(ls), and H-atom Balmer a, /?,and y lines, corresponding to predissociation to H(n = 3, 4, and 5) H(1s) (Borrell et al., 1977). [The H(2s)/H(2p) ratio has also been measured by Mentall and Guyon (1977), but only for predissociation below the ionization threshold.] Identification ofthe lsa, npo, I&,+ and lsa, npn, 'nustates involved has been made; some of the features are common to the molecular fluorescence excitation spectrum. A particular study has been made of predissociation of npn 'nulevels (n = 3-9) and the predissociation yields deduced for H, rovibronic levels (Guyon et al., 1979). Predissociation was found to be an important decay channel even when in competition with autoionization for the lower npn 'nu+states, whereas the npn 'nu-components have much smaller predissociation yields and decay mainly by a molecular fluorescence transition to the E, F'C,+ state ofH,, thus confirming the observations ofRoncin et al. (1974) mentioned above. Guyon et al. (1979) argue that the 'nu+components predissociate via coupling to 'Xu+ states, perhaps involving accidental predissociation (cf. Glass-Maujean et al., 1978; Glass-Maujean, 1979). Ion-pair formation has been observed by McCulloh and Walker (1974) and, at high resolution, by Chupka et al. (1975). This process is of relatively of the H2+ yield at little importance, having an intensity of about 4 x 714 A. The H - excitation spectra for para-H, are shown in Fig. 24 taken with a resolution of 0.07 A (middle curve) and of 0.035 A (bottom curve). The peaks at 710.2 and 714.3 A correspond to major peaks in the H Balmer-P excitation spectrum. There is no underlying continuum, which indicates that ion-pair formation is entirely by predissociation. The threshold of 17.32 eV ( - 716 A ) lies between the energies of dissociation to H(41) and (51). The features in the H- excitation spectrum can be correlated with Rydberg states converging to H2+ X2Cg+ (u 2 9). Work has also been done on D, and on HD. In the
+
91
ELEMENTARY ATTACHMENT AND DETACHMENT PROCESSES
8t
1
L
7
-
J
,
702
m c .c
3
10-
.
.
.
,
'
'
.
I
.
.
.
,
.
.
.
I
.
704
706
708
710
704
706
708 710 WAVELENGTH
.
.
,
.
.
.
,
.
.
.
,
.
712
714
716
712
714
716
.
(b)
-
.-
-e 4
-
50
-
z Y
-
u
-
o
IA
W
702
PHOTON
(a)
FIG.24. Photoionization efficiency curves for H2+(a) and H - (b,c) from para-H, taken at 78 K. The curves (a) and (b) were taken at wavelength resolution FWHM = 0.07 A, the curve (c) at FWHM = 0.035 A. Same identifications of high-n Rydberg levels converging to H,' X2Z,+, u = 9-11, are indicated. (By permission from Chupka el al., 1975.)
92
R . STEPHEN BERRY AND SYDNEY LEACH
latter case it has been possible to independently observe the channels leading D +. A theoretical discussion has been given by to H + D- and H Durup (1978).[It is perhaps appropriate to mention at this point that ion-pair , and CO has been studied over the photon energy range formation in 0 2NO, 17-30eV using synchrotron radiation (Oertel et al., 1980);see Section II,C,2.] We see that the whole range of decay channels of superexcited states has been observed for the hydrogen molecule. Insufficient information exists for a complete quantitative study of the rates and yields of the various processes over a large spectral range.
+
+
c. Molecular photoionization eficiencies: Larger molecules. In general, it is found that the ionization efficiency for molecules does not reach unity until several electron volts above the ionization threshold. This implies that nonionic channels must have decay rates that are comparable, to within a factor of 100, with autoionization rates over this energy region. There is little detailed work on the competitive processes for molecular species other than hydrogen. When yi reaches unity, autoionization becomes the overwhelming decay process of the superexcited states. In this region, the photoionization crosssection curves show little or no structure as is consistent with the linewidths associated with ultrafast autoionization decay rates ( - 10l6 sec- ') and the high densities of superexcited states at these energies. Illustrative of this behavior is Fig. 25, which shows the absorption and photoionization cross wave number 1.3 1.4
1.2
-n
I'
[lo' cm-l)
I
I
1.5
1.6
1.7
I
I
I
1.8 1.9 2 l
l
600
I
v I I'A1
I
photoionization
-
n 0 1
900
800
.
700 _ I . _ _ . L
w a v e ienyrn
/I\
I
I
600
500
e
51
n 0
\HI
FIG. 25. Absorption cross-section and photoionization cross-section functions for H2in the 900-500 A region; 1 Mb = 10- '*cmz.(Adapted, with permission, from Cook and Metzger, 1964.)
ELEMENTARY ATTACHMENT AND DETACHMENT PROCESSES
93
TABLE 111
DOMAIN OF COMPETITIVE NONIONIC DECAYPROCESSES OF SUPEREXCITED STATES IN SOME MOLECULAR SPECIES
Molecule H2 N2 0 2
co
NO H2 0
co,
NH, CH4 CZH, C2H4 C2H6
C6H6
Adiabatic first ionization potential (eV)
Lower energy limit” for q5i = 1 (eV1
Energy difference AEh (eV)
15.43 15.58 12.07 14.01 9.26 12.62 13.77 10.15 12.62 11.40 10.51 1 1.56 9.26
18.23 20.66 18.09 19.37 17.71 20.66 19.37 17.71 15.49 17.71 16.75 I8 16.53
2.80 4.08 4.02 5.36 8.45 4.04 5.60 7.56 2.87 6.31 6.24 ,.. 6.4 7.27
-
These limits have an accuracy of the order of 0.2-0.5 eV. Difference between third and second columns equals the domain of competitive nonionic decay. a
sections for H, from the work of Cook and Metzger (1964). Photoionization onset is at 804 A, but the corresponding cross section does not attain that of photoabsorption until about 680 A. Table I11 presents for a number of di-, tri-, and polyatomic molecules: column 2 shows the adiabatic first ionization potential (Berkowitz, 1979; Huber and Herzberg, 1979);column 3 gives the photon energy corresponding to ion formation with unit efficiency, estimated mainly from compilations given by Berkowitz (1979); and in column 4, AE, the energy difference between ( 3 ) and (2).AE therefore corresponds to the energy range above the first ionization limit in which superexcited states have nonnegligible probabilities for nonionic decay. It is seen that for this series of molecules, AE has values from -3 to -9 eV, but no systematic trends are obvious. F . Dissociative Ionization 1. Dissociative Ionization in H2
States reached by photoabsorption can give rise not only to stable ionic states by direct or indirect ionization but also to dissociative ionization. In
94
R. STEPHEN BERRY AND SYDNEY LEACH
H,, the dissociative ionization threshold is at 18.076 eV (Fig. 26). At this state that is reached by absorption within the threshold it is the lsog X2Z:,+ Franck-Condon zone (hatched area, Fig. 26).To reach the 2p0, ,Xu+and the still higher 2pn, repulsive states, higher photon energies are required. Dissociative ionization of molecular hydrogen is a particularly important process in interstellar molecule chemistry (Watson, 1975). Experimental studies have been carried out by Browning and Fryar (1973),Fryar and Browning (1973),and Strathdee and Browning (1976)using mass spectrometric detection; Glass-Maujean et al. (1979) studied the emission from excited H atoms formed in the dissociative processes, including dissociative ionization at E > -40 eV where the 2pn, state dissociates to H H + . The H + / H 2 + ratio is a constant 2% over most of the photon range up to 30.5 eV, after which it rises to 5% with the opening up of the 2pa, channel and to 11% at 40.8 eV when the 2pn, channel becomes accessible.
+
Potential mqy (eV)
Photon energy (eW
FIG.26. The ratio HC/H2+ from photodissociative ionization of H, ( 0 )and D+/D2+ from D, between 18 and 30 eV. Curves (a)-(d) are based on calculations using wave functions of varying sophistication for the ground states of H2and H,+ ; (e) shows to scale the potential energy curves for H, and H 2 + necessary to interpret the experimental results. (By permission from Browning and Fryar, 1973.)
ELEMENTARY ATTACHMENT AND DETACHMENT PROCESSES
95
The results of Strathdee and Browning (1976)argue in favor of autoionization effects in the 27 eV region; those of Glass-Maujean et al. (1979) support the contention that above 30 elf, dissociative ionization is a more probable process than (pre)dissociation of neutral superexcited states. Theoretical studies have been carried out by Ford et al. (1975).Agreement with the experimental H + / H 2 + ratios is good up to about 26 eV, beyond which the theory predicts too few H + ions. The “missing” protons could arise from opening up of the Iso, channel or, more probably (Bottcher and Docken, 1974; Hazi, 1974), from absorption into resonance states of H2 formed by adding an electron to the H 2 + 2po, orbital. These resonance processes deserve further experimental and theoretical study. 2. Role of Autoionization in Dissociative Ionization The optical resolution available in recent photoionization mass spectrometric studies has made it possible to study the profiles of autoionization features not only for the parent ion, as was discussed earlier, for example, in the case of H,, but also in the various fragment ion channels of small molecules. The results of systematic studies carried out by Berkowitz and his co-workers on diatomic and triatomic molecules, as well as on neopentane, have been brought together in a paper by Eland et al. (1980),which gives an empirical analysis of the autoionizing resonances observed in the total and partial photoionization cross sections. This analysis is based on the Fano single-resonance formulation extended also to the case of a single resonance interacting with several continua. Although it is clear that in reality there can be many overlapping resonances, as discussed for H, (Jungen, 1980; Jungen and Dill, 1980), nevertheless, in the absence of a full multichannel quantum defect theory treatment, which would require much unavailable data on energy levels, the analysis was carried out, faure de mieux, on a singleresonance basis. The approach can be considered as a simple parameterization in which the observed profile data is expressed in effective Fano q-shape parameter, resonance width r, and the resonance and continuum coupling strengths. The parameterization for the series of species studied gives consistent resonance energies and widths independent of the particular channel. Peak shapes are found to vary systematically with the relative intensity of the resonance and the continuum in the channel examined. Triatomic species of related electronic structure are found to have similar series of low 14) resonances. Further work on this parameterization approach is discussed by Eland (1980). Many results show that thresholds for dissociative photoionization are often associated with autoionization processes rather than direct photoionization. This can be seen, for example, in comparing the ionization cross-
96
R. STEPHEN BERRY AND SYDNEY LEACH
section curve with photoelectron spectra taken at a nonautoionizing photon energy. Such comparisons often show that ionization events, including dissociative processes, can take place in a "Franck-Condon gap." The onset of many dissociative ionization processes occurs at the thermodynamic threshold, which lies within the Franck-Condon gap where the probability of ion formation is extremely low as determined by He1 PES. This is the case for the formation of 0' from N,O (Dibeler e f al., 1967; Berkowitz and Eland, 1977; Nenner et al., 1980); 0 ' from CO, (Dibeler and Walker, 1967; McCulloh, 1973; Eland and Berkowitz, 1977); S+ from COS (Dibeler and Walker, 1968; Eland and Berkowitz, 1979); S' and CS' from CS, (Coppens et al., 1979; Eland and Berkowitz, 1979); SO' from SO, (Dibeler and Liston, 1968; Weiss et al., 1979); C,' from C,N, (Eland, 1979); HCO' from H,CO (Guyon et al., 1976; Vaz Pires et al., 1978); C3H3+from CH3C ECH (Parr (Parr et al., 1978). Some and Elder, 1968); and C3H3+from H,C=C=CH, further examples are given by Murray and Baer (1979). 3. Dissociative Ionization in CO,
The example we will discuss is CO,. The electronic energy levels of the CO,' ion are given in Fig. 20. Figure 27 shows the photoionization efficiency
co; z
0
LW
0'
In In
0
a
0
z
0
l-
a N z 9 w
? la W J
a
I
600 I
20.66 eV
.
I
610
#
I
620
.
I
630
.
'
640
I
650
660
I
I
I
19.99eV
19.37eV
18.78 eV
,
I
670
,
I
680 I
18.22 eV
WAVELENGTH (8) FIG.27. Relative photoion yield curves of C 0 2 + ,O + ,and CO+ in the vicinity of the dissociative ionization thresholds. Each curve is in different arbitrary units. The vertical arrow indicates the C 0 2 + C2Z,+-state threshold energy. (By permission from Eland and Berkowitz, 1977.)
ELEMENTARY ATTACHMENT AND DETACHMENT PROCESSES
97
curves for CO,', CO+, and 0' in the neighborhood of the dissociative ionization thresholds in the 19 eV region taken from the work of Eland and Berkowitz (1977).Each curve is in different arbitrary efficiency units so that their relative intensities are not directly comparable. The He1 PES spectrum of CO, (Fig. 28) (Eland, 1978) shows that this region is not accessible by direct ionization. The threshold for 0' is at 19.07eV (650A) [CO, O'(4S) CO X'X' (u = O)], about 0.32 eV below the e2Z,+-state threshold. The structure in the 0' curve between 19.07 and 19.39 eV indicates clearly that the dissociation processes occur here via superexcited states-the Rydberg levels of the Tanaka, Jursa, LeBlanc series converging to the C2E,+ state of C 0 2 +-which are coupled to dissociative ionization continua corresponding to lower lying CO,' states. The 0' current increases sharply at state threshold. This state has been shown to be completely prethe C'Z,' dissociative (Eland, 1972),thus accounting for the large increase in the partial cross section. However, spin conservation rules are violated here, since the dissociation products O'(4S) CO('Z ') can only form quartet states. At 19.337 eV lies the threshold for forming 0' and the CO molecule in its u = 1 state. Eland (1972), in a study of the kinetic energy distribution of the 0' ion, has concluded that at the e2Z.,' state onset, predissociation to 0' + CO creates about 85% of the CO X'Z,' molecules in the u = 1 state, the remainder in u = 0. The CO' ion is formed at its thermodynamic threshold at 19.446 eV, the process being CO, CO' X2Z,+(u = 0) + O(3P). At this energy the observed CO'/O' ratio from the two dissociative channels is 0.3 at 300 K. Rotationally excited levels of the c2Z,+(u = 0, 0,O) state with J > 40 are above the CO' dissociation limit and predissociation is principally to CO+ + 0. Rather large impact parameters are involved in con--+
+
+
--+
I
20
I
I
I8
I
I
I
16 ionization energy ( e V 1
I
1L
FIG.28. He1 photoelectron spectrum of C 0 2 .(By permission from Eland, 1978.)
98
R. STEPHEN BERRY A N D SYDNEY LEACH
serving angular momentum, which makes it somewhat surprising that the CO+ dissociation channel dominates over the 0' channel. However, this probably reflects the fact that CO+(2C,+) O(3P)correlates with doublet states of C 0 2 +(Leach, 1970) and could thus favor predissociation of c2C,' with respect to the quartet state formed by CO 0'. The structure in the CO+ partial photoionization yield curve indicates that vibrationally excited states open up new channels for CO' production. An experimental difficulty in determining the exact branching ratios for forming parent and fragment ions is the discrimination of ions formed with, or given, different kinetic energies. Most mass spectrometric methods used tend to discriminate against energetic ions so that carefully designed instrumentation is required (Masuoka and Samson, 1980). Measurements of the C 0 2 + / C O + / O + / C +ratios have been made at a number of wavelengths between 304 and 740 A (Berkowitz, 1979).This has been extended down to 90 A with measurements also including doubleionization processes forming C 0 , 2 and C2 (Masuoka and Samson, 1980). Cross-section data can be obtained by two methods: (1) the branching-ratio method in which the mass spectrum is accumulated at a given photon energy and the ratio is determined for the number of ions collected for a particular species to the total number of ions produced; and (2) the ions per photon method in which the wavelength is scanned for a fixed mass, the photon intensity being monitored simultaneously with the ion intensity. The relative cross sections determined by either method are put on an absolute basis by normalization at some calibration point. Double-ionization cross sections are given in Fig. 29. Maximum-peak partial cross sections are as follows: co2+(-37x 10-1Rcm2at-6OOA);CO+(-3.2 x 10-"cm2at -450A); 0 ' (-3.8 x lo-'' cm2, at -310 A); C + (-2.8 x lo-'* cmz at -340 A); C02,+ (-0.35 x lo-'' cm2 at -230 A); and C 2 + (-0.8 x cm2 at 130 8).Cross-section accuracy is estimated to be 10% for C 0 2 +;15% for CO', C + , and 0'; and 50% for C 0 2 2 + and C 2 + .Less-extensive data by other workers are given by Berkowitz (1979)and, for comparison, in the paper by Masuoka and Samson (1980).Recently, the (e, e ion) technique has been used to study ion fragmentation in CO, up to 80 eV (Hitchcock et a/., 1980) with results in good agreement with the photon data. Structure in all the fragmentation curves obtained by the photon and (e, e ion) techniques can be correlated with the multielectron transitions observed in the pseudophotoelectron spectra obtained with the (e,2e) technique by Brion and Tan (1978,1979).The total fragmentation cross section has three principal peaks: (1) -8 x lo-'' cm2 at -420 A ; (2) -9.5 x lo-'' cm2 at -330 A; and (3) 7.8 x 10- cm2 at 230 A (Masuoka and Samson, 1980).The excitation spectrum of vacuum ultraviolet fluorescence from CO, has been measured by
+
+
+
+
-
+
+
-
-
ELEMENTARY ATTACHMENT AND DETACHMENT PROCESSES
0.4,
,
1
1
(a).
- 0.3-Iz
-t
‘CC
0
0
-
0
0
-
.
. 0
-
0
0.2-
w m
$ ‘ *
-
0.
VI
,
g 0.1 E
0
0 0 0 0
u A
U
z o (I:
,
,
,
1
99
:
:
:
I
!
-
0
-
I
’
Lee et al. (1975). The spectrum is similar in shape to the total fragmentation curve determined by Masuoka and Samson ( 1 980). The absolute fluorescence cross sections appear to be about 5-10% of the total fragmentation values. The fluorescence is probably due to excited fragments produced by dissociative photoionization. 4. Theoretical and Experimental Approaches to Ion Fragmentation
Fragmentation of small ions can be treated theoretically in terms of potential energy hypersurfaces and determination of configurational point trajectories. Symmetry and quasi-symmetry properties of initial and final product states can be useful. Unimolecular fragmentation involves interelectronic-state coupling and, in many cases, intramolecular vibrational redistribution. In a recent review (Lorquet et a/., 1980),a discussion is given of nonadiabatic interactions and radiationless transitions in molecular ions. The various topologies of patential energy surfaces presenting nonadiabatic
100
R. STEPHEN BERRY AND SYDNEY LEACH
couplings are exemplified and their kinetic and dynamic implications considered, with applications to a number of small polyatomic ions. A more phenomenological discussion of predissociation processes in molecular ions is given in a review by Momigny (1980) who emphasizes the role of rotational predissociation. Fragmentation of molecular ions has mainly been discussed in terms of the quasi-equilibrium theory (QET) (Rosenstock et al., 1952, 1980; Rosenstock, 1968) or the essentially equivalent RRKM theory (Rice and Ramsperger, 1927; Kassel, 1928; Marcus and Rice, 1951)of mass spectra in which a statistical distribution or redistribution of vibronic energy in excess of a dissociation limit is assumed. A systematic experimental study of the dissociative photoionization of all alkanes from ethane through hexane, as well as n-heptane and n-octane, was carried out by Steiner et al. (1961) in the photon energy range up to 11.9 eV. The results tend to disagree with the statistical theory in the restricted energy region where there is a low density of ion electronic states. Following this valuable and enterprising early work, much has been published in this field, mainly using electron-impact ionization, but more recently, increasingly involving photoionization as well as photodissociation of ground-state molecular ions (Dunbar, 1979). New experimental techniques have been developed (Lifshitz, 1978), in particular coincidence techniques (Baer, 1979). Radiative and nonradiative yields (Leach et al., 1980)and fragmentation yields (Eland, 1979) can be determined by complementary photoion-fluorescence photon and photoion-photoelectron coincidence techniques. The photoion-photoelectron coincidence (PIPECO)techniques are reviewed in detail by Baer (1979). In the latter, the energy-analyzed electron selects the ion internal energy and provides a starting time for ion time-of-flight measurements. This gives much information on ion dynamics, in particular, the kinetic energy released in dissociation and its distribution (KERDs) and the parent ion lifetime with respect to dissociation. In earlier experiments, single wavelength sources, mainly He1 lamps, were used but more recently monochromatized continuum sources, in particular synchrotron radiation, have provided a means of ion-state selection by detection in coincidence with threshold electrons (Fig. 10). We will not enumerate the vast number of experimental results using the large variety of techniques mentioned above. In general (Lifshitz, 1978), the results show that vibrational randomization within a particular electronic state of the ion is complete prior to dissociation, but that internal conversion between electronic states is not always complete, giving rise to the notion of “isolated electronic states,” sometimes involving isomerization. Ion lifetimes have been determined in the lop3-10- sec range. A continuous distribution of lifetimes is observed under photon (and electron) impact ionization. The QET-RRKM theory is found to give reasonable rate constants, whereas the
’’
ELEMENTARY ATTACHMENT AND DETACHMENT PROCESSES
101
phase-space version of QET (Klots, 1964, 1972, 1976a; Pechukas and Light, 1965; Light, 1967), in which emphasis is on product states rather than the activated complex, can be used for energy disposal calculations. However, many questions are still open for particular cases; the general field of molecular ion dissociation dynamics is bound to flourish with the opening up of a variety of new experimental techniques and theoretical approaches. Among the theoretical methods we mention the possible application to the unimolecular decomposition of ions of the phase-space formulation (statistical adiabatic channel model) of Quack and Troe (1974, 1975a,b) and the maximum entropy formulation of the statistical theory of Levine (see, e g , Silberstein and Levine, 1980). G . Multiphoton Ionization 1. Multiphoton Ionization of Atoms
The advent of lasers has made it possible to study multiphoton ionization ( M P I ) processes in atoms and molecules via either real or virtual intermediate states. The ionization probability is a function of the laser frequency, coherence, and polarization, as well as the energy-level structure of the species. A considerable amount of work has been done on the physics of MPI in atoms. This has been reviewed by Lambropoulos (1976), van der Wiel and Granneman (1977), Letokhov (1978), Mainfray and Manus (1978), and Mainfray (1980). On the theoretical level, it is found that time-dependent perturbation theory gives a reasonably good description of MPI (Bebb and Gold, 1965).The ionization probability as a function of laser intensity is given by the lowest-order term in the perturbation series as long as one is far from a real state resonance region. The probability is modified very markedly in the resonance regions. A treatment analogous to that of Fano (1961) for autoionization has been developed for MPI in the resonance region (Beers and Armstrong, 1975; Feneuille and Armstrong, 1975). Laser bandwidth effects on MPI have also been studied in model calculations (Armstrong and Eberly, 1979). High fields (2lo9 W cm-') can induce level shifts and broadening and thus modify the resonance profiles. The variation of the effective order of nonlinearity K in a nominal 4-photon MPI of cesium, is shown in Fig. 30 as a function of resonance detuning AE = E(6F) - E(6S) - 3E(hv) where E(6F) and E(6S) are cesium atom energy levels, E(hv) is the laser photon energy (Morellec et al., 1976). The resonance involved is the 3-photon 6S-6F transition. The fourth power of the intensity law is valid in the off-resonance ( A E 2 10 c m - ' ) region. The corresponding resonance profile in terms of relative number of ions formed is given in Fig. 31 (Mainfray and Manus, 1978).
-30
20 Resonance
0
10
10
-
20
-
detunng B E = EBF E~~ 3 Ep
FIG.30. Variation of the effective order of nonlinearity K as a function of the resonance detuning AE in the four-photon ionization of Cs. (By permission from Morellec el al., 1976.) K = 6 log NJ6 log I . N; (arb1t r a r y u n i t s 1
lo!
10'
10:
102
10
I I
I
10588
10589
ARes. I
4
10590
c
0.3A FIG. 31. Resonance profile due to the 6S+6F three-photon transition in four-photon ionization of Cs. (By permission from Mainfray and Manus, 1978.) I = 4 x 10' W/cmZ.
103
ELEMENTARY ATTACHMENT AND DETACHMENT PROCESSES
Coherence effects become relatively important at high fields (210l2 W cm-2). The characteristic time for off-resonance MPI is -0.1 psec for AE 300 cm- '. For a single-mode laser pulse the coherence time t , is of the order of 10 nsec, whereas for an incoherent laser pulse of bandwidth 10 A, t c 1-10 psec, with the photons now arriving in bunches during the pulse duration, in contrast to the uniform sequential arrival in the single-mode case. The quasi-instantaneous laser intensity is therefore much enhanced in the incoherent laser-pulse case (bunched photons).For example, an enhancement of lo7 in the number of ions was observed in the 11-photon ionization of Xe with a Nd-glass laser pulse when the coherence time was changed from 10 nsec to 10 psec (Lecompte et al., 1975). The off-resonant N-photon ionization rate W is given by the following expression :
-
-
-
where oN is the generalized N-photon ionization cross section, I is the average laser intensity, and fN is the nth-order autocorrelation function. fN = 1 for a single-mode or bandwidth-limited laser pulse, whereas fN = N ! for an incoherent laser pulse whose statistical properties are related to thermal radiation. It follows that off-resonance MPI processes are excellent probes for the statistical properties of laser pulses. It should be noted that oN is a function of the polarization properties of the laser radiation, since selection rules for electric dipole transitions will apply for each stage of the N-photon absorption process. Electric quadrupole transitions have also been observed in a 3-photon MPI process in Na (Lambropoulos et al., 1975). The laser polarization properties were used to study the angular distribution of photoelectrons from the resonant 2-photon MPI process + Na(3p 2P,i2)+ Na+ e - as excited sequentially by two Na(3s 2S1/2) linearly polarized pulsed laser beams (Duncanson et al., 1976; Strand et al., 1978; Leuchs et al., 1979; Hansen et a/., 1980). A theoretical treatment predicted that the photoelectron angular distribution depends on the degree of coherence among the hyperfine levels and on the time interval between the exciting pulse and the ionizing pulse (Strand et al., 1978; Strand, 1979). The experimental results, including the observation of incipient quantum beats (Strand et a/., 1978; Leuchs et a/., 1979; Hansen et al., 1980), confirmed these predictions and also showed that an essentially completely coherent superposition of Na(3p 2P,,2) intermediate hyperfine states is produced. The theory of this process was developed for resonant two-photon ionization of diatomic and linear molecules by Hansen (1979), but no such experiments have been reported at the time of this writing. Laser polarization properties can also be used to produce spin-polarized photoelectrons via MPI. The total cross section for this process gives an MPI
+
104
R . STEPHEN BERRY A N D SYDNEY LEACH
version of the Fano effect (Fano, 1969). However, the angular dependence of spin polarization can be considerable. The coupling between the angular momentum of an excited electron and that of the core, of course, influences the angular distribution of photoelectrons. Moreover, this distribution depends on the value of the Hund’s case coupling of the core (Hansen, 1979). The study by Strand et a!. (1978) included a theoretical prediction of the effects of hyperfine interactions on the angular dependence and the total electron spin polarization produced by two collinear, circularly polarized laser beams via the process Na(’S,,,) -t Na(’P,,,) --* Na+(’S,) e - . It was concluded that laser pulses shorter than 1 nsec arriving almost simultaneously would be necessary to produce completely polarized electrons by resonant two-photon ionization of Na. It is, of course, necessary for the laser bandwidth to be much smaller than t h e j = i,2 separation in the intermediate ’P state, a condition very easily met. Recently, electrons produced by MPI have been observed to undergo free-free transitions as they continue to interact with the laser radiation while in the ion field (Agostini et a/., 1979). It should also be mentioned that multiphoton ionization transitions can be used to obtain coherent emission in the vacuum ultraviolet in Ne 532 A and He 380 (Reintjes et al., 1976, 1977). We mention here the possibility of MPI where the penultimate state is a very highly excited Rydberg state, so that the last stage of ionization would require very little energy. Beiting et a / . (1979) have carried out a two-laser experiment in Na, in which the first laser saturated a D transition, populating the 3p 2P3,2state, while the second excited selected ns or nd Rydberg levels. They observed Na+ ion signals which were consistent with the photoionization of the highly excited atoms by 300 K blackbody radiation. These results illustrate the necessity of avoiding unwanted thermal radiation effects in studying processes involving highly excited atoms and molecules. They also demonstrate the potential of these species as infrared detectors. Finally, for atoms, we stress that MPI studies at high light intensities can be severely perturbed by the existence of even a small fraction of molecular dimers of an atomic gas. This is particularly important in the case of alkali atoms (Held et a/., 1972; Granneman et a/., 1976; Hermann et a/., 1977a,b, 1978; Klewer et a/., 1977).
+
-
-
a
2. Multiphoton Ionization of Molecules: Spectroscopy; Cross Sections As for any other kind of ionization process, multiphoton ionization of molecules is more complex than for atoms because of the greater number of decay channels. Furthermore, the possibility of dissociation of either ion or
ELEMENTARY ATTACHMENT AND DETACHMENT PROCESSES
105
neutral into (at least some) neutral fragments means that MPI of the fragment(s) can also occur. The effects much studied for atoms-saturation, level shift and broadening, laser-pulse profile-have thus far been little investigated in the case of molecules. Molecular spectroscopy is beginning to benefit considerably from MPI. The one-photon selection rules of traditional absorption spectroscopy are no longer limiting factors; new states can be reached and identified. Assignments of molecular excited states can be determined or verified using polarization properties (McClain, 1974; Berg et al., 1978; Lehmann et al., 1978; McClain and Harris, 1977; Parker and Avouris, 1979; Heath et al., 1980). Photoionization thresholds can also be measured, as is illustrated in Fig. 32 for pyrrole (Williamson et al., 1979). Furthermore, the lifetimes of electronic excited states can also be determined using the MPI technique with a variable delay between pulses from the two lasers used to produce ionization (Parker and El-Sayed, 1979).An example is the H,CO molecule for which a nitrogen and a hydrogen laser were used (Andreyev et al., 1977; Antonov et al., 1977). Spectroscopic studies have been done both using a single wavelength and also a tunable laser. Much more information is obtained when tunable radiation brings the molecule to a resonant intermediate state with a second laser to provide the ionization step. A notable simplificatiofi of the spectrum can be obtained, as has been demonstrated in the case of I , (Williamson and Compton, 1979) in which “competing” 1- or 3-photon resonances can be greatly reduced in importance by this two-laser technique. Further details on, and references to, MPI techniques in molecules are given in the review papers of Johnson (1980a,b). The electronic states revealed by MPI spectroscopy are usually the Rydberg states. This results from the fact that highly excited valence states are relatively strongly coupled to decay channels so that they largely disappear before ionization can occur. However, the valence-excited states of benzene and its derivatives have been studied in detail by MPI (KroghJespersen et al., 1979; Johnson, 1980b). In many cases, Rydberg levels previously masked by valence absorptions in traditional spectroscopy have been revealed via the MPI technique. For example, 3s Rydberg levels, which are parity forbidden in one-photon transitions in molecules having a center of symmetry, have been observed in a number of polyatomic species (Johnson, 1975, 1976; Nieman and Colson, 1978; Turner et al., 1978). As a further example, we present the recent work of Johnson (1980b) on methylbenzenes. Figure 33 shows the one-photon absorption curve of toluene and the MPI spectrum for which there is obviously much more structure and which clearly shows the presence of two Rydberg states in this region. Similar behavior is observed for p-xylene where the Rydberg transition, although
106
R. STEPHEN BERRY AND SYDNEY LEACH
'
"6 "5
ij'...;.11
Lb' ?
I
'
l
IP
4
1 1
l (0
*\ i \
t 0-
I
I
I
I
c
1
I
4480 (500 VUV WAVELENGTH
I >
4520
(A)
2
0
0 4400
4500 LASER WAVELENGTH
4600
(d)
FIG. 32. (a) Single-photon ionization efficiency of pyrrole. Arrows indicate ionization energies of the first band in the photoelectron spectrum of pyrrole. (b) Three-photon ionization signal of pyrrole at a pressure 60 mtorr. The data are not corrected for variation of laser power with wavelength. The background ion signal below threshold energy is due to four-photon ionization. (c) Three-photon ionization signal of pyrrole at its room-temperature vapor pressure of about 8 torr. (By permission from Williamson et al., 1979.)
ELEMENTARY ATTACHMENT AND DETACHMENT PROCESSES
107
I I
I
I
I
I
180
185 190 WAVELENGTH i nm) FIG. 33. Single-photon absorption spectrum (upper curve) and multiphoton ionization spectrum (lower curve) for toluene in the 180-190 nm region. (By permission from Johnson, 1980b.)
parity forbidden, is induced vibronically. Polarization properties were used to assign the Rydberg state symmetry and the 3p, nature of the atomic orbital involved. Multiphoton ionization cross-section calculations are rare for molecules. We mention in particular the case of four-photon ionization of NO, which Cremaschi et al. (1978) have treated using a quantum defect method to calculate the matrix elements. The cross sections obtained enable one to describe the behavior of the system in the short time limit. Rate equations were developed for the long time limit. This kinetic approach to multiphoton processes (Bradley et al., 1972; Zakheim and Johnson, 1980) is often not particularly suitable in practice because of uncertainties in laser intensity, but it can be used to account for most of the spectral feature intensities in NO (Zakheim and Johnson, 1978). The calculated cross sections are in accord with experiment in predicting a greater intensity for a 2 2 ionization (resonance on absorption of second photon) than in a 3 1 ionization process. Order of magnitude values for 2-, 3-, and 4-photon MPI are IO-" cm'sec' and 10-'Oo cm8 sec2. cm4 sec, In much of the work reported, MPI takes place in a static gas cell. Recently, Johnson has introduced the use of supersonic jet (expanded nozzle) beams in MPI (Zakheim and Johnson, 1978).The target molecules are thus cooled to rotational temperatures of the order of 1 K and vibrational temperatures of a few tens of degrees Kelvin (Smalley et al., 1975, 1977). This technique has been applied to the MPI of N O (Zakheim and Johnson, 1978), where the low temperature simplified MPI spectrum aids in analysis, and to aniline (Dietz ef al., 19801, metal carbonyls (Duncan et a/., 1979)and benzene,
+ +
108
R. STEPHEN BERRY A N D SYDNEY LEACH
fluorobenzene and chlorobenzene (Murakami et al., 1980). In this last case, it was concluded that the 4-photon MPI spectrum correctly reflects the two-photon absorption cross sections to the excited S , state. Some work has been done on MPI in liquids, in particular by Vaida et al. (1978)and by Scott et al. (1979).The photon-energy onset of conduction in the liquid phase can, in principle, be used to determine ionization potential stabilization energies with respect to the gas phase.
3. Multiphoton Ionization of Molecules: Dissociative Processes In most of the molecular MPI experiments mentioned above, where the principal aim is spectroscopic in nature, the total ion current is detected. Much more detailed information is available with concurrent mass analysis. Since pulsed lasers are often excitation sources in MPI, mass analysis can be achieved by time-of-flight measurements, although magnetic spectrometers have been used in some cases. With the mass analysis capability comes the possibility of studying dissociative ionization following multiphoton absorption. Fragmentation can ensue by several possible processes: (1) multiphoton transition to a repulsive or predissociative ion state, (2) transition to a stable ion state followed by photon absorption to a dissociative region, and (3) transition to a neutral dissociative or predissociative state that leads to fragments which can undergo ionization via further photon absorption. Mass analysis in MPI was introduced by Klewer et al. (1977) who observed the two-photon ionization of Cs, and also showed the formation of Cs- at photon energies below the Cs2+ threshold. the ion pair Cs' Instruments have been built that give a time-of-flight analysis of the ions or neutrals, a high resolution of the kinetic energy, and the possibility of studying angular distributions (de Vries et al., 1980; van der Wiel, 1980). Angular distributions, as well as polarization ratios of ion current, are of course important in the analysis of the symmetry of intermediate states in MPI. Molecular beams of the effusive kind are also used in MPI. Feldman et al. (1977)studied the MPI (without mass analysis) of a Na, beam as well as of the BaCl product of the Ba HCI reaction, thus demonstrating the utility of MPI as a detection technique in reactive collision experiments. Herrmann et al. (1977a,b, 1978) used a two-laser system and mass analysis to study the MPI of Na,. The isotopically selective formation of Liz+ has been studied by two-photon ionization of Li, beams (B. P. Mathur et al., 1978; Rothe et al., 1978). Two-laser, two-photon ionization of molecular beams, with mass analysis, has been discussed by Letokhov (1977)and results presented on the kinetics of stepwise photoionization and fragmentation of NO,, benzaldehyde, benzophenone, nitrobenzene, and nitrotoluene by Antonov et al.
+
+
ELEMENTARY ATTACHMENT AND DETACHMENT PROCESSES
109
(1978). Polyatomic species were first studied by MPI of a molecular beam with mass analysis by Boesl er al. (1978) whose work on benzene confirms that MPI is a very selective and versatile ionization source for mass spectrometry; in particular it should be stressed that the distinct structure of the intermediate state, reflected in the MPI spectrum, is highly species specific. Indeed, this latter quality has led to consideration of two-photon ionization spectroscopy as a method for teal-time monitoring of atmospheric polluants (Brophy and Rettner, 1979). Ionization of molecular beams, involving the absorption of more than two photons, and with mass analysis, was first carried out by Zandee et al. (1978)on 1,. Extensive studies have been carried out by Zandee and Bernstein (1979a,b) on NO, I,, benzene, and butadiene using a tunable, nitrogenpumped, dye laser. At each resonance corresponding to the m-photon ionization of an n-photon intermediate state, the fragmentation pattern of the ions is measured. The minimum number of photons absorbed per molecule to form a fragment can be deduced if the appearance potential of the fragment is known (which is not always the case). MPI and the ensuing fragmentation remain extremely wavelength selective, even at the highest laser-peak power densities used. The nonresonant contribution to ionization is only a small fraction of the resonance-enhanced ion yields. About of the beam molecules within the focal region are ionized by the laser pulse. Several studies have been carried out on benzene. Using a low-power peak laser, Boesl et a/. (1978)observed formation only of the parent ion in a two-photon ionization process. Rockwood et al. (1979) and Reilly and Kompa (1979), using KrF or ArF lasers, observed fragmentation of benzene, the fragmentation patterns and relative intensities being dependent on the laser-power density. This agrees with the results of Zandee and Bernstein (1979a,b)who found that increasing the laser power favored the formation of smaller fragments. Indeed, it is possible to achieve almost exclusive formation of C + ions, as found also by Cooper et a/. (1980). The fragmentation patterns are also vibronic state dependent as depicted in Fig. 34, which gives a two-dimensional optical-mass spectrum of benzene (Zandee and Bernstein, 1979a,b)for relatively low laser power densities. Zandee and Bernstein’s (1979b)analysis of the results lead them to suggest that the resonance multiphoton dissociative ionization process involves pumping neutral C,H, up its vibronic energy levels until an autoionizing level is reached to yield the fragment ions. Alternatively, the up-pumping to dissociation proceeds via the ionic ladder. In similar molecular beam MPI studies on azulene and naphthalene, but using both single laser and two-laser excitation (Lubman et al., 1980),the data obtained support the suggestion ofZandee and Bernstein that autoionizing states play an important role in the MPI dissociative ionization process, at least in these aromatic systems.
110
R. STEPHEN BERRY AND SYDNEY LEACH
I-
2 Y
a 0:
FIG.34. Two-dimensional optical-mass spectra o f benzene for relatively low laser power intensities. Wavelength spectrum of total ions (top) is broken down into its constituent contributions from each of the Ci fragment ions. (By permission from Zandee and Bernstein, 1979a.b.)
It is clear that dissociative ionization in MPI brings in interesting new theoretical problems to add to those concerning QET-RRKM theory and its validity that we mentioned earlier in the case of one-photon ionization. In a statistical interpretation of the MPI fragmentation in benzene, Silberstein and Levine (1980) argue that differences in fragmentation patterns at different power levels (or also in comparison with electron-impact ion fragmentation studies) do not necessarily reflect dynamical effects. They suggest instead that these differences are due to the phase space available to the different fragments at increasing levels of energy deposition in the molecule. In their view, the initial absorption provides selectivity in MPI, but the subsequent energy uptake and fragmentation will be dominated by the available phase space, unless there are special dynamic constraints such as could exist in molecules having bonds of very different strengths. An example of the latter is to be found in the MPI study ofmetal carbonyls (Duncan et al., 1979).For the case of benzene, Silberstein and Levine (1980)show that on varying the mean energy deposited per parent molecule, a simple statistical theory based on the maximum-entropy formalism was able to predict,
ELEMENTARY ATTACHMENT AND DETACHMENT PROCESSES
111
in reasonable agreement with experiment, the variation of the fragmentation pattern from almost exclusively parent ions at low energies, to fairly large, stable fragment ions at medium energies and small energy-expensive ions at high energies. Fisanick et al. (1980) have obtained experimental results on the multiphoton dissociative ionization of acetaldehyde, which, in general, parallel those mentioned above for the aromatic species, in particular a change of fragmentation pattern with laser power. They used a rate equation approach to explain their results and developed an expression for the individual fragment ion intensities as a function of laser power. All ionization processes were assumed to be direct, i.e., no long-lived predissociating or autoionizing states, with all fragmentation occurring during the laser pulse. Eventual saturation and spatial effects are considered as well as ion loss through dissociation and the further photofragmentation of ions formed. Application to the case of acetaldehyde does account reasonably for the power dependencies found for the parent and fragment ions. 4. Infrared Multiphoton Ionization of Molecules
Besides excitation with visible and ultraviolet lasers, multiphoton ionization of molecules can also be achieved using infrared radiation: BCI, (Akulin e f al., 1975; Karlov et al., 1976), SiF, (Karlov, 1978), H,O and D,O (Chin, 1977; Chin and Faubert, 1978), C H 3 N 0 2(Avouris et a!., 1979), but the exact mechanisms in each case require further investigation. The initiation of CO, laser-induced plasmas has been thought to involve the acceleration and multiplication of preexisting free electrons (Kroll and Watson, 1972; Yablonovitch, 1973),but it is possible that the initiating process is IR-MPI. Further, the production of free electrons by IR-MPI could play an important part in the chemistry of CO, laser-irradiated polyatomic molecules (Avouris et al., 1979). Finally, we mention that previously produced gas-phase ions trapped in ion traps can be dissociated by multiphoton absorption of visible or infrared radiation; most interestingly, the IR intensities used are very much lower than in the usual IR multiphoton dissociation experiments. This work has recently been reviewed by Woodin et al. (1979).Recent work by Coggiola et al. (1980) has investigated the final step in IR multiphoton dissociation of polyatomic ions. They formed highly vibrationally excited CF31+,CF,Br+, and CF,Cl+ ions under collision-free conditions and studied the fragmentaX on absorption of a single lop IR photon. The dissociation tion into CF,' yields peaked sharply at absorption frequencies in the molecular ion, but it is considered that absorption takes place in the vibrational quasi-continuum.
+
112
R. STEPHEN BERRY AND SYDNEY LEACH
H . Photodetachment
1. General Remarks The photoionization processes we have discussed involve ionization thresholds in the UV and vacuum UV regions. An important class of processes is photodetachment, which corresponds to ionization of a negative ion. The outermost electron is weakly bound ( 55 eV) so that photodetachment thresholds are in the IR, visible or near-UV domains. In the present section we will be concerned with photodetachment from negative ions which have positive binding energies (electron affinities); we thus exclude temporary attachment processes that are observed as electron-scattering resonances (Schultz, 1973a,b). Determination of binding energies will not be discussed. Our concern is with processes reviewed in the section on photoionization, cross sections in particular. Furthermore, since theoretical methods of calculating photodetachment cross sections are similar to those used for neutrals, this topic will be little discussed except for a few particular cases. Much of the work in this area stems from activity at the National Bureau of Standards, from the first measurements of the A- + hv -+ A + e - process, on Rb and Cs by Mohler and Boeckner (1929),the extensive pioneering work of Branscomb and his co-workers (Branscomb, 1962)and the development of laser photodetachment studies by Lineberger (1974) and his co-workers. An early, influential, review was a book by Massey in 1936, which has been updated in 1950 and 1976 (1976). Other reviews of interest are those of Berry (1969b), Steiner (1972), Franklin and Harland (1974), Lineberger (1974), Hotop and Lineberger (1975), Lineberger et al. (1976), and Janousek and Brauman (1979). Bibliographies of interest are included in NBS Special Supplement No. 426 (Kieffer, 1976) and its supplements (Gallagher et al., 1978). A review of radiation processes of atomic negative ions, in the context of plasma physics, has been written by Popp (1975). Important driving forces in this field include astrophysics and planetary atmosphere and ionosphere research. In 1939, Wildt suggested that opacity of the sun’s atmosphere in the red and infrared regions could be due to photon absorption by H-. Theoretical calculations of the photodetachment rate supported this idea (Bates and Massey, 1940; Chandrasekhar, 1945; Chandrasekhar and Elbert, 1958). Experimental confirmation in the laboratory was achieved by Branscomb and Smith (1955) and Smith and Burch (1959). The use of lasers has made very high-energy resolution possible in the crossed-beam configuration developed early by Branscomb, but whose resolution was of the order of 100A. Furthermore, PES techniques have also been used on negative ions, using fixed-frequency lasers, in which energy analysis, and sometimes values of the photoelectrons are studied (Celotta et al., 1972, 1974; Hotop et al., 1973a; Siege1 et al., 1972).
ELEMENTARY ATTACHMENT AND DETACHMENT PROCESSES
113
Other techniques have also been used in which high concentrations of negative ions are produced in ion-pair production processes by shock-tube techniques. For example, halogen negative-ion photodetachment has been studied by Berry et al. (1961), as well as the reverse process of radiative attachment (Berry and David, 1964; Muck and Popp, 1968), and the corresponding electron affinities determined with precision (Milstein and Berry, 1971). However, this is a generally more limited technique than that using crossed beams. Another useful technique involves ion storage, in particular ion cyclotron resonance (ICR), which can be used to study photodetachment (Smyth and Brauman, 1972a,b,c; Reed and Brauman, 1974; Janousek and Brauman, 1979). This has been done mainly for molecular negative ions. 2. Photodetachment Cross Sections Near Threshold: Theoretical Remarks Understanding cross-section behavior near threshold is important for photodetachment of negative ions, in particular for determination of accurate threshold energies to give electron affinity values. Furthermore, this behavior provides information on the orbital momentum of the bound detachable electron. Wigner’s (1948) general treatment of the threshold behavior of reactions involving the collision of two particles and having two final products can be applied to this situation. The cross section will be proportional to the product of the squared matrix element between the discrete initial and continuum final states, and the density of states in the continuum. is the photoThe latter is proportional to E’’’ where E = (hv - Ethreshold) electron energy. In determining the behavior of the matrix element with photon energy, it must be recognized that there is an important difference between photoionization and photodetachment. This resides in the nature of the potential field. The radial wave equation contains a 1(1 l)/r2 contribution to the potential. In photoionization, this term falls off much more rapidly than the l/r Coulomb term. The threshold dependence of the photoionization cross section then tends to be a step function. However, in photodetachment, the centrifugalbarrier term dominates over other contributions at long distances, the interaction between photodetached electron and neutral-core final products being short-ranged. This means that Wigner’s result for two neutral products is applicable.There results a variation ofthe photodetachment cross section with energy at threshold, dependent on the angular momentum of the electron in the final free state. Dipole selection rules make it possible to correlate this dependence with the angular momenta of the electron in the initial state (Massey, 1976). With appropriate representation of the continuum wave function, the photodetachment cross section near threshold can be expressed as a power
+
114
R. STEPHEN BERRY A N D SYDNEY LEACH
series in k, the linear momentum of the freed electron, raised to a power that is a function of I, which is essentially the angular momentum component of the continuum state in which the photoejected electron moves under the influence of the residual atom field (Wigner, 1948; Branscomb et al., 1958; Massey, 1976): r ~ ”cc
vk2‘+‘(ao
+ a , k 2 + bk21nk + a2k4 + . . .)
(23)
where the a, and b are constant coefficients whose values depend on the bound-state wave function and on details of the potential (O’Malley, 1965; Hotop et al., 1973b). Since k will be proportional to the square root of the kinetic energy of the photoejected electron, it can be replaced in Eq. (23) by E”’. In general, the electron will be ejected preferentially into the lowest angular momentum state allowed by conservation of angular momentum and parity. For diatomic molecules, the appropriate power law will depend upon the angular momentum, projected along the internuclear axis, associated with the orbital from which the electron is photoejected (Geltman, 1958).It should be noted that Geltman’s theory may not apply very close to threshold since the magnitude of the velocity of the outgoing electron there will be less than or comparable to nuclear velocities, leading to a breakdown of the BornOppenheimer approximation. However, at a few hundred cm- above threshold, this is no longer a problem. A further problem, mentioned later, is that Geltman’s theory takes no account of the cross-section dependence on molecular rotation. Extension of Wigner’s analysis to the case of a species of any molecular symmetry has been achieved by Reed et al. (1 976), using group theory considerations. The limitations of this approach are most evident for systems of low symmetry where there are, of course, few restrictions on the types of allowed transitions. Another shortcoming is that the symmetry rules do not inform us on the relative intensities and post-threshold behavior of allowed transitions. A one-electron formalism has been used very successfully by Reed et al. (1976) to calculate the relative photodetachment cross sections in the threshold region for a number of diatomic and polyatomic negative ions, with results that agree well with experiment in spite of neglect of electrondipole interactions, as in Geltman’s work. Examples will be given later.
’
3. Atomic Negative Ions Photodetachment threshold studies have been made for a number of atomic negative ions (Lineberger et al., 1976). Let us consider the case of photodetachment from Se-, whose electron configuration is . . . 4s2 4p5.
115
ELEMENTARY ATTACHMENT AND DETACHMENT PROCESSES
1
i -*--f 1
14
I
15
16
I
I
17
1 18
I
I
I
19
PHOTON ENERGY ( 1 0 3cm-1) FIG. 35. Se- photodetachment cross section in the energy range (14.000-19,000 cm-': Se-(2P,,,,,,,1 ~ V - + S ~ ( ~ P , . , ,+, , e) - . Fine structure transition thresholds are indicated by vertical arrows. (By permission from Hotop et ol., 1973a.)
+
Detachment of a p electron leads to an outgoing s or d wave, since photon absorption leads to a unit change of the I quantum number. Close to threshold, the d-wave contribution is negligible, so that the cross section at threshold should be proportional to k . Experimentally, several fine-structure transitions are observed by conventional spectroscopy (Berry et al., 1965) and by laser photodetachment spectroscopy (Hotop et al., 1973a), as shown in Fig. 35. The Se- negative ion can exist in the 2P,i2and 2P3/2states, whereas there are three possible final Because of the large 2P,1z-2P312splitting, states in the residual atom, 3P0,L,2. most ions in the beam are in the lowest state, 'P312, which helps in the identification of the various thresholds. It is found that the individual thresholds have shapes predicted by the Wigner threshold law, but only over a restricted photon-energy range (Fig. 36), e.g., as can be seen in the partial photodetachment cross section for Se-(2P,/,) + Se('P,). The relative strengths of the fine-structure transitions measured for Sehave been compared with the results of a number of model calculations (Lineberger et al., 1976). Reasonable agreement is obtained with a model in which the final state is considered as a (Se e - ) complex within the LS
+
116
R. STEPHEN BERRY A N D SYDNEY LEACH
500
I
1
I
1
1
1
I
I
ELECTRON MOMENTUM k [l/a,] FIG. 36. Se-('P3,,)+Se(3P,) + e- partial photodetachment cross section plotted as a function of electron momentum. The straight line represents the Wigner threshold law. (By permission from Hotop et al., 1973a.)
coupling approximation and following the dissociation of the complex into the various fine-structure exit channels (Lineberger and Woodward, 1970; Rau and Fano, 1971). This is in the spirit of the original approach by Wigner (1948)who, in his general discussion of two-particle collision reactions, proposed that the probability of a particular reaction near threshold will depend solely on the propensity to dissociation of the collision complex. The important factor is thus the long-range interaction of the dissociating particles and not the nature of the transition involved. Rau (1976)has pointed out that the behavior of the cross section away from threshold is relatively little influenced by the dynamics of the photodetachment process and that the branching ratios for the individual exit channels are given by an easily evaluated geometrical factor. This approach accounts well for the experimentally observed departures of the branching ratios from the statistical ratios expected at a lower level of approximation. Interesting results are observed in photodetachment to an excited state of the neutral, because of interference effects between ground- and excitedstate channels. Cusps can arise in the ground-state channel cross section as discussed by Wigner ( 1948) and, for photodetachment processes, by Moores and Norcross (1974).Experimental observations in light alkali negative ions, e.g., Na- (Lineberger, 1974) show cross-section shapes corresponding to Wigner cusps near thresholds at opening of 'P channels. For heavier alkali
c
ELEMENTARY ATTACHMENT AND DETACHMENT PROCESSES
117
negative ions, such as Rb- and Cs-, photodetachment in energy regions where the lower np final-state channel opens up is dominated by the doubly excited states of the negative ion, which lie close to this threshold (Patterson et al., 1974; Slater et al., 1978). This gives rise to Fano lineshapes corresponding to window resonances such as is shown in Fig. 37 for Cs- (Slater et al., 1978). The Cs- resonances are consistent with the close-coupling calculations of Moores and Norcross (1974), but the latter d o not take into account the effects of the 'P fine structure. The semiempirical multichannel photodetachment model of Lee (1975) includes the fine structure, and is based on MQDT adapted to the case of an electron interacting with a neutral-atom core. The multichannel wave functions are defined in terms of an R-matrix, whose elements are determined empirically. However, the constraints of the model are such that Lee's theory does not adequately account for the long-range polarization interaction between the electron undergoing photoejection and the neutral core. Furthermore, two-electron correlation becomes more and more important as higher and higher Rydberg levels are involved in the final neutral state. The limiting case is the threshold for photodetachment of two electrons. This is a field of great interest (Lineberger el al., 1976), both from the theoretical and from the experimental
PHOTON E N E R G Y , cm-1 FIG.37. Cs- photodetachment ground-state partial cross section near the 'P threshold: Cs- + hv-+Cs(ZS) + e - . The depth of the minimum near 14,962 c m - ' is limited by the laser linewidth of 3 cm-'. The error bars reflect the uncertainty in the normalization of the 'P partial cross section to the total cross section. (By permission from Slater P I a/., 1978.)
118
R. STEPHEN BERRY AND SYDNEY LEACH
viewpoint, but only preliminary experiments have been reported thus far (Slater et al., 1978). It should also be noted that energetics has been the main concern of photodetachment studies. Relatively little work has been done on photoelectron asymmetry behavior in this case, although there is certainly some theoretical interest (e.g., Moores and Norcross, 1974)and some experimental work has also been done (e.g., Celotta et al., 1974). Before turning to negative molecular ions, we mention a number of other results on atomic negative ions. Following the suggestion of Herzberg (1955) that diffuse interstellar absorption lines at a number of wavelengths in the visible spectral region might be due to autoionizing states of H-, C - , or 0 - , an experimental study of the photodetachment spectrum under high resolution (Herbst et ai., 1974a) shows that these are not viable candidates for the carrier. Multiphoton (two-photon) detachment via a virtual state has been observed and studied in detail for I - by Hall et a/. (1965). Finally, we stress also that our discussion is limited to a few representative ions and that data on photodetachment of other atomic negative ions can be found via the bibliographic review material cited at the beginning of this section, especially the NBS Special Report 426 and its supplements. 4. Diatomic Negative Ions
Photodetachment studies have been made on a large range of diatomic negative ions. The form of the photodetachment threshold law has been predicted for a nonrotating diatomic molecular ion having no permanent dipole moment (Geltman, 1958). This is of little use for most practical cases where the threshold law should depend on molecular rotation and on the permanent electric dipole moment (if any) of the species. Furthermore, from the experimental viewpoint, the negative molecular ions will usually be in a conglomerate of rovibronic states each of which will have its own threshold energy and with various possible behaviors. The O H - / O D - photodetachment cross sections in the 4000-7000 A region are shown in Fig. 38 for the process OH-/OD-(X'C+) hv+ OH/OD(X211i) e - as studied at low resolution ( - 100 A) by Branscomb (1966).The OH-(X'C+) and OH(X211i)potential energy curves are similar in form and parallel to each other [re(OH-) 2 r,(OH)]. The corresponding Franck-Condon transition in the photodetachment process accounts for the existence of a clear-cut threshold. Quasi-identical onsets were found for O H - and OD-. The maximum in the photodetachment function at about 6300 A requires interpretation. High-resolution, laser photodetachment
+
+
ELEMENTARY ATTACHMENT A N D DETACHMENT PROCESSES
h
I2
”EV
11
2
10
0
-
119
9
. -g
8
Y
u
$ $ 0, U -C E c * 0 +
r
a 2
7 6 5 4
3 2 I t -
01
4000
I
4500
1
5-
1
1
5500 6OOO Wavelength (A)
I
6500
hJ 8 7-
7500
FIG.38. Photodetachment cross sections for OH- ( 0 )and OD- (0) using a monochromator with 100-8, resolution (Branscomb, 1966); ( 0 )using bandpass filters (Smith and Branscomb, 1955). (By permission from Branscomb, 1966.)
studies have been made in the threshold region by Hotop et al. (1974) (Fig. 39), and over the whole 3500-7000 8, region by Lee and Smith (1979).There is an unexplained disagreement between the cross-section values of Lee and Smith and those of Branscomb, which are 40% higher. On theoretical grounds, the threshold law for OH-/OD- is expected to have behavior intermediate between the two limiting cases o a Eo (step function) and o a El” (no permanent dipole moment); the true threshold law should also be J dependent, since effects of dipole field rotation will differ with rotation velocity (Hotop et a!., 1974). Further theoretical aspects of rotational effects are discussed by Walker (1973). In his data analysis, Branscomb (1966) assumed a step-function behavior at threshold. This was found not to hold for significantly populated J states in the high-resolution work of Hotop et al. (1974). In the latter, analysis was attempted with both o a E”’ and o a for all J ’ . Best agreement with experiment was found with o a Ell4 (Fig. 39). Another interesting diatomic negative ion is Cz-, which may play an important role in the absorption continua observed in stellar spectroscopy. This ion has the distinction of having a stable, excited electronic state at -2
120
R. STEPHEN BERRY AND SYDNEY LEACH
PHOTON ENERGY
(lo3cm-'1
FIG. 39. OH- photodetachment cross section in the energy range 14,300-15,400 cm-' (700-650 nm): OH-('C+) ~ V + O H ( ~ ~ I e, )- . The dots represent the experimental data. The sharp onset near 14,700 cm-' corresponds to the opening of Q branch channels in the OH 2n3,2 final state. The solid line is a fit to the data using an threshold law and a negative ion temperature of 1200 K. (By permission from Hotop et a]., 1974.)
+
+
eV, i.e., below the photodetachment threshold at -3.5 eV. This also makes C2- the only gas-phase negative molecular ion for which an electronic transition between stable states is known by optical spectroscopy (Herzberg and Lagerqvist, 1968). The photodetachment cross section has been studied near threshold at low resolution (Feldmann, 1970). Lineberger and Patterson (1972) have used a tunable dye laser to study photodetachment in C2- by absorption of two photons, the first of which is used to excite the real 'ELI+ excited state, which is a resonant intermediate state in this process. The structure observed in the apparent photodetachment cross section correlates with levels to be expected from the optical work on the A2X,'-X2Xgf transition of C2-. The absolute oscillator strength of this transition of C,has been measured using shock-tube techniques (Cathro and Mackie, 1973). The 0,-ion, which is of great importance in aeronomy, as well as in plasma physics and also in some biological processes, has been extensively studied by laser PES techniques in efforts to determine the electron binding energy (Celotta et al., 1972). The cross sections for photodetachment have been measured over the photon-energy range 1.93-2.71 eV using a drift-tube
ELEMENTARY ATTACHMENT AND DETACHMENT PROCESSES
121
mass spectrometer and a tunable dye laser (Cosby et al., 1975, 1976). Some structure was suspected in the earlier measurements (1975) but is less evident in the later (1976). In particular, no structure is observed at 2.18 eV, which is the theoretical vertical threshold energy for forming the b'E:,+ final state of 0 2This . result, which is consistent with the threshold dependence predictable for this state, is confirmed by Lee and Smith (1979),whose measurements over the 1.48-3.5 eV photon energy range give cross sections of about 0.9 x lo-'' cm2 at 1.48 eV, about 2.5 x lo-'' cm2 at 3 eV and 3.7 x lo-'* cm2 at 3.5eV. Over the common energy range, these values are in good agreement with earlier measurements, not only of Cosby ef al. (1975,1976) but also those, at lower resolution, of Burch et al. (1958), as well as the fixed-frequency laser-excitation data of Beyer and Vanderhoff (1976). Strong resonances, interpreted as autoionizing features, were first observed in the photodetachment cross section of molecular negative ions near threshold by Zimmerman and Brauman (1977b) in a study of the enolate anion of acetophenone using ICR and laser techniques. A systematic study was carried out by Novick ef al. (1979a) on resonances in the photodetachment cross sections of NaCl-, NaBr-, and NaI- at over 1 eV above the photodetachment threshold. These resonances are interpreted as autodetachment of a 'll state of the NaX- ion embedded in the photodetachment continuum and give rise to a highly vibrationally excited ground state of the neutral NaX molecule. The autoionizing state is estimated to have a lifetime of the order of lo-'' sec on the oversimplified Fano formalism basis of a single discrete state interacting with a single continuum. We give here a partial list of other diatomic negative ions studied by one or other of the experimental techniques mentioned earlier: SH- and SD(Steiner, 1968; Eyler and Atkinson, 1974); SeH- (Smyth and Brauman, I972c); CH- (Feldman, 1970; Kasdan et al., 1975a). and SiH- (Kasdan et a!., 1975b),which also have low-lying bound excited states whose energies were determined, as well as excited states of the neutral, hydrides; NH- (Celotta et al., 1974; Engelking and Lineberger, 1976),for which the PES was used to determine the a'A-X3Z- intercombination energy separation in the neutral NH; NO- (Siege1 et al., 1972); S2- (Celotta et al., 1974); SO- (Feldmann, 1970; Bennett, 1972), for which the energy of the a'A state above the X3Eground state of SO was measured; C1,- (Sullivan et al., 1977; Lee et al., 1979), which undergoes photodissociation rather than photodetachment; C10(Lee et al., 1979), which exhibits both processes; PO- and P H - (Zittel and Lineberger, 1976) for which the a'A-X3E- intercombination energy separation was determined for the neutral hydride; LiCI- (Carlsten et a/., 1976); FeO- (Engelking and Linebttrger, 1977a); F2-,As,- (Feldmann et al., 1977); BeH-, MgH-, CaH-, ZnH-, PH-, ASH- (Rackwitz et al., 1977).
122
R. STEPHEN BERRY AND SYDNEY LEACH
5 . Triatomic and Polyatomic Negative Ions The ICR technique was used by Smyth and Brauman (1972b,c) to study the photodetachment cross-section behavior of NH,-, PH,-, and ASH,for which sharply defined thresholds were observed. The PES spectrum of NH,- was observed by Celotta et al. (1974) and other work on NH,- has been done by Feldmann (1970) and by Reed et al. (1976) who carried out theoretical calculations to compare with the experimental data of Smyth and Brauman (Fig. 40), and on PH,- by Zittel and Lineberger (1976). SO,- was the first triatomic negative ion studied by the PES technique (Celotta et al., 1974).The analysis enabled a determination to be made of the symmetrical valence-mode frequency v of the negative ion. The vibrational structure in the PES is very similar to that calculated by Cederbaum et af. (1977) for the (radiative) electron attachment spectrum. There is as yet no experimental determination of the latter. The NO2- photodetachment cross section has been measured at low resolution by Warneck (1969).The threshold is not well defined in this work. Laser detachment studies were carried out by Herbst et al. (1974b) who determined absolute cross sections and discussed the problem of their energy dependence. The NO, - photodetachment cross section is of importance in understanding the chemistry of the D-region of the ionosphere (Thomas, 1974). The observation of two thresholds in the photodetachment studies of Richardson et al. (1974) and of Herbst er al. (1974b) has led to the suggestion that two NO,- isomers are involved, the ONO-(Czy)species and a higher peroxy NOO- form. Calculations of Pearson et al. (1974)
0.76
0.80
0.84 0.00 0.92
0.96
1.00
104
PHOTON ENERGY ( e V )
FIG.40. Relative experimental ( 0 )and theoretical (-) photodetachment cross sections for NH,- as a function of incident photon energy. (By permission from Reed et a/., 1976.)
ELEMENTARY ATTACHMENT AND DETACHMENT PROCESSES
f 23
support the existence of these two distinct isomers. However, further work on NO2- photodetachment by Huber et al. (1977), using a drift-tube mass spectrometer and a tunable dye laser, has cast some doubt on the existence of the peroxy form of NO2- in these experiments. A peroxy form is indeed known in the case of NO3-, from ion-molecule reaction studies. Photodissociation of NO,- at photon energies less than 2 eV points to this being the peroxy form, since the threshold for normal NO,- should lie at 3.7 t 0.4 eV (Smith el al., 1979b). Photodetachment studies of a number of other molecular negative ions of importance in aeronomy have been carried out using a variety of techniques. For example, photodetachment from CO,-, C 0 3 -.H,O,and 0,ions in a drift tube has been studied by Burt (1972a,b),and 0,by Sinnott and Beaty (1971)and Smith and Lee (1979).Much work on 0, - and 04-has been carried out by Cosby et a!. (1975, 1976, 1978a,b); the results on 0,- indicate that this species has an excited electronic state, which leads to dissociation along the symmetric stretch coordinate. Recent work by Novick et al. (1979b) indicates that the photodissociation cross section is at least one order of magnitude greater than for photodetachment. For 04-,photodissociation is observed, but it is not clear whether or not photodetachment occurs (Cosby et al., 1975, 1976). A detailed study on C 0 3 - has been made by Moseley et al. (1976)using a drift-tube mass spectrometer and various lasers. These authors monitored the destruction of C 0 3 - and the formation of the 0 - ion resulting from the process C 0 3 - + hv -+ C O , + 0-.The results have been extended to shorter wavelengths (3500 A) by Smith et al. (1979a). Structure in the photodissociation cross section of C 0 , - in the photon energy range 1.8-2.7 eV was assigned to transitions from the ground R2B, state to vibrational levels of the first electronic excited state of CO, - which is predissociative. The excited state is thought to have ,A2 electronic symmetry, and to lie at 1.52 eV above W2B2,well below the photodissociation threshold at around 1.8 eV. Frequencies of three vibrational modes of the excited state were determined. CO, - is therefore a case where negative-ion photodissociation dominates over photodetachment in the energy region studied, as confirmed by the work of Novick et al. (1979b), who detected no photoelectrons with laser excitation of CO,-. Very recently, Hiller and Vestal (1980) in a study of CO, - photodissociation have measured cross sections at variance with those of Mosely et al. (1976) and Smith et al. (1979a); they also observed a twophoton dissociation process below 2.2 eV. Work on C 0 3 - (and on 0 2 - ) photodissociation has also been done by Beyer and Vanderhoff (1976) at a number of selected laser excitation wavelengths and using a drift-tube mass spectrometer.
124
R. STEPHEN BERRY AND SYDNEY LEACH
Very recently, photodissociation and photodetachment cross-section measurements for a number of the negative ions discussed above have been made at 2484 a by Hodges et al. (1980) using a rare-gas-halogen excimer laser. The hydride CH, is an important chemical and astrophysical species. The structure of the ground state and the singlet-triplet intercombination energy have long been the subject of controversial determinations. The PES of CH,- was used by Zittel et al. (1976) to make such determinations for the neutral. In particular, a value of 19.5 L 0.7 kcal/rnol was obtained for the g1A,-R3B, splitting, but this is in serious disagreement with a number of values obtained by various techniques and which converge to a value of about 8 k 1 kcal/mol (Lengel and Zare, 1978). Photodetachment has been studied for a considerable number of large polyatomic negative ions. The appropriate references are given by Janousek and Brauman (1979). Most of the work is directed to the determination of electron affinities and on interpreting the effects of chemical substitution in chemically related series. As mentioned earlier, a systematic study comparing theoretical and experimental cross-section behavior near threshold for polyatomic negative ions has been made by Brauman and his co-workers using ICR techniques (Reed et al., 1976; Zimmerman and Brauman, 1977a,b; Janousek and Brauman, 1979). We mention only a few cases. The cyclopentadienide ion C J - (Richardson et a!., 1973; Reed et al., 1976) has a slowly rising cross section over a large photon energy region, well reproduced by calculations (Fig. 41). Jahn-Teller characteristics of the final, neutral
08 m ul
'
'
O
6
0.0 1.8
2.0
2.2
2.4
2.6
2.8
3.0
3.2
PHOTON ENERGY ( e V )
FIG.41. Relative experimental ( 0 )and theoretical (-) photodetachment cross sections for C,H,- plotted as a function of incident photon energy. (By permission from Reed et al., 1976.)
ELEMENTARY ATTACHMENT AND DETACHMENT PROCESSES
125
state (cyclopentadienyl radical C,H, ) have been explored in a PES spectrum of the negative ion by Engelking and Lineberger (1977b). In the case of the pyrrolate ion C4H4N-, Richardson et al. (1975) have shown that there is an orbital reordering when an electron is photodetached, producing a CT radical in spite of the 71 electrons being the most weakly bound. This highlights one of the pitfalls in PES interpretation, i.e., the failure of Koopmans theorem, which postulates no electron reorganization on ionization.
ACKNOWLEDGEMENTS R.S.B. would like to express his thanks to the Laboratoire de Photophysique Moleculaire, Universite de Paris-Sud, Orsay, for hospitality and support during much of the writing of this article. The final preparation of the manuscript was supported in part by a Grant from the National Science Foundation. We would like to thank Drs. Christian Jungen and Helen Lefebvre-Brion for their helpful comments on the manuscript.
REFERENCES Aberle, W., Grosser, J., and Kruger, W. (1980). J . fhys. B 13,2083. Aberth. W., Peterson, J. R., Lorents, D. C., and Cook, C. J. (1968). Phys. Rev. Lett. 20, 979. Abouaf, R., and Teillet-Billy, D. (1977). J . fhys. B 10, 2261. Abouaf, R., and Teillet-Billy, D. (1980a). J . Phys. B 13, L275. Abouaf, R., and Teillet-Billy, D. (1980b). Chem. Phys. Lerr. 73, 106. Agostini, P., Fabre, F., Mainfray, G., Petite, G . ,and Rahman, N. (1979). Phys. Rev. Lett. 42, 1127. Akulin, V. M., Alimpiev, S. S., Karlov, N. V., Karpov, N. A,, Petrov, Yu. N., Prokhorov, A. M., and Shelepin, L. A. (19751. JETP Lett. (Engl. Trunsl.) 22, 45. Allan. M.. and Wong, S. F. (1981). J . Chem. Phys. 74, 1687. Ambartsumyan, R. V., Bekov, G . I., Letokhov, V. S., and Mishin, V. I. (1975). JETP Lett. (Engl. Transl.) 21, 279. Amusia, M. Ya. (1974). Vac. Ultraviolet Radiut. Phys., Proc. Int. Conf:,4th, 1974 p. 205. Amusia, M. Ya., and Cherepkov, N. A. (1975). Case Stud. A t . fhys. 5,41. Amusia, M. Ya., and Ivanov, V. K. (1976). Ph,v.s. Lett. A 59A, 194. Amusia, M. Ya., Cherepkov, N. A., and Chernysheva, L. V. (1972). fhys. Lett. A 40A, 15. Amusia, M. Ya., Ivanov, V. K., Cherepkov, N. A., and Chernysheva, L. V . (1974). SOILPhys.JETP. (Engl. Trunsl.) 39,752. Andresen, B., and Kuppermann, A. (1978). Z. Phys. A 289, 1 I . Andresen, B., Kuppermann, A,, and de Vries, A. C. (1978). Z. Phys. A 289, 1. Andreyev, S. V., Antonov, V. S., Knyazev, I. N.. and Letokhov, V. S. (1977). Chem. Phys. Lett. 45, 166. Antonov, V. S., Knyazev, I. N., Letokhov, V. S., and Morshev, V. G . (1977). Sou. Phy.7.-JETP (Engl. Transl.) 46,697. Antonov, V. S . , Knyazev, I. N., Letokhov, V. S., Matiuk, V. M.. Morshev, V. G., and Potapov, V. K. (1978). Opt. Lett. 3, 37. Armstrong, L., Jr., and Eberly, J. H. (1978). J . Phys. B 12, L291. Arrathoon, R., Littlewood, 1. M., and Webb, C. E. (1973). Phys. Rev. Lerr. 31, 1168. Astruc, J. P., Barbi, R., and Schermann, J. P. (1979). J . Phys. B 12, L377.
126
R. STEPHEN BERRY A N D SYDNEY LEACH
Atabek, O., and Jungen, C. (1976). In “Electron and Photon Interactions with Atoms” (H. Kleinpoppen and M. R. C. McDowell, eds.), p. 613. Plenum, New York. Atabek, O., Dill, D., and Jungen, C. (1974). Phys. Rev. Lett. 33, 123. Aten, J. A., Lanting, G. E. H., and Los, J. (1977). Chem. Phys. 33,333. Auerbach, D., Cacak, R., Caudano, R., Gaily, T. D., Keyser, J., McGowan, J. W., Mitchell, .I. B. A., and Wilk, S. J. (1977). J. Phys. B 10, 3797. Avouris, P., Chan, I. Y., and Loy, M. M. T. (1979). J. Chem. Phys. 70,5315. Azria, R., and Fiquet-Fayard, F. (1972). J. Phys. (Orsay, Fr.) 33,663. Azria, R., Roussier, L., Paineau, R., and Tronc, M. (1973). Rev. Phys. Appl. 9,375. Azria, R., LeCoat, Y.,and Lefevre, G. (1979). J. Phys. B 12, 679. Azria, R., LeCoat, Y., Simon, D., and Tronc, M. (1980). J. Phys. B 13, 1909. Baede, A. P. M. (1975). Adv. Chem. Phys. 30,463. Baer, T. (1979). In “Gas Phase Ion Chemistry” (M. T. Bowers, ed.), Vol. 1, Chapter 5, p. 153. Academic Press, New York. Bahr, J. L., Blake, A. J., Carver, J. H., and Kumar, V. (1969). J. Quant. Spectrosc. Radiat. Transfer 9, 1359. Bahr, J. L., Blake, A. J., Carver, J. H., Gardner, J. L., and Kumar, V. (1972). J. Quant. Spectrosc. Radiat. Transfer 12, 59. Bailey, T. L., and Mahadevan, P. (1970). J. Chem. Phys. 52, 179. Bailey, T. L., May, C. J., and Muschlitz, E. G. (1957). J. Chem. Phys. 26, 1146. Baker, C. E., McGuire, J. M., and Muschlitz, E. E. (1962). J. Chem. Phys. 37,2571. Ballofet, G., Romand, J., and Vodar, B. (1961). C.R. Hebd. Seances Acad. Sci. 252,4139. Bandrauk, A. D. (1972). Mol. Phys. 24,661. Bandrauk, A. D., and Child, M. S. (1970). Mol. Phys. 19, 95. Bardsley, J. N. (1967). Chem. Phys. Lett. 1,229. Bardsley, J. N. (1968a). J . Phys. B 1, 349. Bardsley, J. N. (1968b). J . Phys. B 1, 365. Bardsley, J. N. (1970). Phys. Rev. A 2, 1359. Bardsley, J. N., and Biondi, M. A. (1970). Ado. At. Mol. Phys. 6, I. Bardsley, J. N., and Junker, B. R., (1973). Astrophys. J. (Lett.) 183, L135. Bardsley, J. N., and Mandl, F. (1968). Rep. Prog. Phys. 31,471. Bardsley, J. N., Herzenberg, A., and Mandl, F. (1964). In “Atomic Collision Processes” (M. R. C. McDowell, ed.), p. 415. North-Holland Publ., Amsterdam. Bardsley, J. N., Herzenberg, A., and Mandl, F. (1966). Proc. Phys. Soc., London 89, 305, 321. Bates, D. R. (1950a). Phys. Reo. 77,718. Bates, D. R. (1950b). Phys. Rev. 78,492. Bates, D. R., ed. (1962). “Atomic and Molecular Processes.” Academic Press, New York. Bates, D. R. (1975). Case Stud. At. Phys. 4, 59. Bates, D. R. (1976). Proc. R . Soc. London, Ser. A 348,427. Bates, D. R. (1979). Ado. A t . Mol. Phys. 15,235. Bates, D. R., and Kingston, A. E. (1961). Nature (London) 189,652. Bates, D. R., and Lewis, J. T. (1955). Proc. Phys. Soc., London, Ser. A 68, 173. Bates, D. R., and Massey, H. S. W. (1940). Astrophys. J. 91, 202. Bates, D. R., and Massey, H. S. W. (1946a). Philos. Trans. R. SOC.London, Ser. A 239,269. Bates, D. R., and Massey, H. S. W. (1946b). Proc. R. Soc. London, Ser. A 187,261. Bates, D. R., Kingston, A. E., and McWhirter, R. W. P. (1962a). Proc. R. SOC.London, Ser. A 267, 297. Bates, D. R., Kingston, A. E., and McWhirter, R. W. P. (1962b). Proc. R. SOC.London, Ser. A 270, 155. Bauer, E., and Wu, T. Y. (1956). Can. J. Phys. 34, 1436.
ELEMENTARY ATTACHMENT AND DETACHMENT PROCESSES
127
Baum, G., Lubell, M. S., and Raith, W. (1972). Phys. Rev. A 5, 1073. Bebb, H. B., and Gold, A. (1965). Phys. Rev. 143, I . Beckwith, S., Gatley, I., Matthews, K., and Neugebauer, G . (1978). Astrophys. J. (Lett.) 223,
L41. Beers, B. L., and Armstrong, L. (1975). Phys. Rev. A 12,2447. Beiting, E. J., Hildebrandt, G. F., Kellert, F. G., Foltz, G. W., Smith, K. A,, Dunning, F. B., and Stebbings, R. F. (1979). J . Chem. Phys. 70,3551. Bennett, R. A. (1972). Thesis, University of Colorado, Boulder. Berg, J. O., Parker, D. H., and El-Sayed, M. A. (1978). J . Chem. Phys. 68,5661. Berkowitz, J. (1979). “Photoabsorption, Photoionization and Photoelectron Spectroscopy.” Academic Press, New York. Berkowitz, J., and Eland, J . H. D. (1977). J. Chem. Phys. 67,2740. Berkowitz, J., and Lifshitz, C. (1968). J. Phys. B 1, 438. Berry, R. S. (1963). Proc. Conf. Int. Phenom. Ionis. Gaz, 6th, 1963 Vol. 1, p. 13. Berry, R.S . (1966). J. Chem. Phys. 45, 1228. Berry, R. S. (1969a). Annu. Rev. Phys. Chem. 20,357. Berry, R. S . (1969b). Chem. Rev. 69, 533. Berry, R. S. (1978). I n ‘‘Alkali Halide Vapors” (P. Davidovits and D. L. McFadden, eds.), Chapter 3, p. 77. Academic Press, New York. Berry, R. S. (1980a). Adv. Elecrron. Electron Phys. 51, 137 (referred to as Part I). Berry, R. S. (1980b). J. Chim. Phys. 77,759. Berry, R. S., and David, C. W. (1964). In “Atomic Collision Process” (M. R. C. McDowell, ed.), p. 543. North-Holland Publ., Amsterdam. Berry, R. S., and Nielsen, S. E. (1970). Phys. Rev. A 1,383, 395. Berry, R. S., Reimann, C. W., and Spokes, G. N. (1961). J . Chem. Phys. 35,2237. Berry, R. S., David, C. W., and Maclkie, J. C. (1965). J Chem. Phys. 42,1541. Berry, R. S., Cernoch, T., Coplan, M., and Ewing, J. J. (1968). J. Chem. Phys. 99, 127. Beyer, R. A., and Vanderhoff, J. A, (1976). J . Chem. Phys. 65,2313. Bieneck, R. J., and Dalgarno, A. (1979). Astrophys. J . 228,635. Biondi, M. A. (1963). Phys. Rev. 129, 1181. Biondi, M. A. (1964). Ann. Geophys. 20, 34. Biondi, M. A,, and Brown, S. C. (1949). Phys. Rev. 76, 1697. Birtwistle, D. T., and Modinos, A. (1978). J. Phys. B 11,2949. Bloch, F., and Bradbury, N. E. (1935). Phys. Rev. 48,689. Boesl, U., Neusser, H. J., and Schlag, E. W. (1978). Z. Nuturforsch. A 3321, 1546. Borrell, P., Guyon, P. M., and GIassMaujean, M. (1977). J. Chem. Phys. 66,818. Bottcher, C. (1976). J. Phys. B 9,2899 Bottcher, C. (1978). J. Phys. B 11, 3887. Bottcher, C., and Buckley, B. D. (1979). J . Phys. B 12, L497. Bottcher, C., and Docken, K. K. (1974). J . Phys. B 7, L5. Boulmer, J., Davy, P., Delpech, J.-F., and Gauthier, J.-C. (1973). Phys. Rev. Lett. 30, 179. Boulmer, J., Stevefelt, J., and Delpech, J.-F. (1974). Phys. Rev. Leu. 33, 1248. Boulmer, J., Devos, F., Stevefelt, J., and Delpech, J.-F. (1977). Phys. Rev. A 15, 1502. Boursey, E., and Damany, H. (1974). Appl. Opt. 13,589. Bradley, D. J., Hutchinson, M. H. R., Koetser, H., Morrow, T., New, G. H. C., and Petty, M. S. (1972). Proc. R. Soc. London, Ser. A 328,97. Branscomb, L. M. (1966). Phys. Rev. 148, I I . Branscomb, L. M. (1962). In “Atomic and Molecular Processes” (D. R. Bates, ed.), p. 100. Academic Press, New York. Branscomb, L. M., and Smith, S. J. (1955). Phys. Rev. 98, 1028, 1127.
128
R. STEPHEN BERRY AND SYDNEY LEACH
Branscomb, L. M., Burch, D. S., Smith, S . J., and Geltman, S. (1958). Phys. Rev. 111,504. Brehm, B. (1966). Z . Nuturforsch. A 21A, 196. Briggs, D., ed. (1977). “Handbook of X-Ray and Ultraviolet Photoelectron Spectroscopy.” Heyden, London. Brion, C. E., and Hamnett, A. (1979). Adt. Chem. Phys. Brion, C. E., and Tan, K. H. (1979). J. Electron Spectrosc. Relut. Phenom. 15, 241. Brion, C. E., Tan, K. H., van der Wid, M. J., and van der Leeuw, P. E. (1979). J . Electron Spectrosc. Relut. Phenom. 17, 101. Brion, C. E., and Tan, K. H. (1978). Chem. Phys. 34, 141. Brophy, J. H., and Rettner, C. T. (1979). Opt. Lett. 4, 337. Browning, R., and Fryar, J. (1973). J . Phys. E 6, 364. Brueckner, K. A. (1955a). Phys. Rev. 97,1353. Brueckner, K. A. (1955b). Phys. Rev. 100,36. Brundle, C. R., and Baker, A. D., eds. (1977). “Electron Spectroscopy: Theory, Techniques and Applications,” Vol. 1. Academic Press, New York. Brundle, C. R., and Baker, A. D., eds. (1978). “Electron Spectroscopy: Theory, Techniques, and Applications,” Vol. 2. Academic Press, New York. Brundle, C. R., and Baker, A. D., eds. (1979). ”Electron Spectroscopy: Theory, Techniques and Applications,” Vol. 3. Academic Press, New York. Buchel’nikova, I. S. (1959). Sou. Phys.-JETP (Engl. Trunsl.) 35,783. Buckingham, A. D., Orr, B. J., and Sichet, J. M. (1970). Philos. Truns. R. SOC.London, Ser. A 268, 147. Burch, D. S., Smith, S. J., and Branscomb, L. M. (1958b). Phys. Rev. 112, 171. Burdett, N. A., and Hayhurst, A. N. (1976). J. Chem. SOC.,Furuduy Truns. 1 72,245. Burdett, N. A., and Hayhurst, A. N. (1977a). Chem. Phys. Lett. 48,95. Burdett, N. A., and Hayhurst, A. N. (1977b). Proc. R. SOC.London, Ser. A 355,377. Burdett, N. A., and Hayhurst, A. N. (1978). J. Chem. SOC.,Furuduy Trans. 1 74,63. Burdett, N. A., and Hayhurst, A. N. (1979). Philos. Trans. R. SOC.London 290,299. Burke, P. G., and Seaton, M. J. (1971). Methods Comput. Phys. 10, I . Burke, P. G., and Taylor, K. T. (1979). J . Phys. E 12,2971. Burke, P. G., Hibbert, A., and Robb, W. D. (1971). J. Phys. E S , 37. Burrow, P. D. (1973). J. Chem. Phys. 59,4922. Burt, J. A. ( 1 972a). Ann. Geophys. 28,607. Burt, J . A. (1972b). 1.Chem. Phys. 57,4649. Bush, Y.A., Albritton, D. L., Fehsenfeld, F. C., andSchmeltekopf, A. L. (1972). J . Chem. Phys. 51,4501. Bydin, Iu. F., and Dukel’skii, V. M. (1957). Sou. Phys.-JETP (Engl. Trans/.)4,474. Cairns, R. B., and Samson, J. A. R. (1965). Phys. Rev. A 139, 1403. Cairns, R. B., Harrison, H., and Schoen, R. 1. (1970). J. Chem. Phys. 53,96. Carlson, R. W., Judge, D. L., and Ogawa, M. (1973). J. Geophys. Res. 78,3194. Carlson, T. A. (1967). Phys. Rev. 156, 142. Carlson, T. A. (1971). Chem. Phys. Lett. 9,23. Carlson, T. A., and Anderson, C. P. (1971). Chem. Phys. Lett. 10,561. Carlson, T. A., and Jonas, A. E. (1971). J . Chem. Phys. 55,4913. Carlson, T. A., and McGuire, G. E. (1972). J. Electron Spectrosc. Relut. Phenom. I, 209. Carlson, T. A,, and White, R. M. (1972). Discuss. Furuday SOC.54,285. Carlson, T. A,, Krause, M. O., and Moddeman, W. E. (1971). J . Phys. (Orsuy, Fr), 32-C4,76. Carlson, T. A., McGuire, G. E., Jonas, A. E., Cheng, K. L., Anderson, C. P., Lu, C. C., and Pullen, B. P. (1972). In “Electron Spectroscopy” (D. A. Shirley, ed.), p. 207. NorthHolland Publ.. Amsterdam.
ELEMENTARY ATTACHMENT A N D DETACHMENT PROCESSES
129
Carlsten, J. L., Peterson, J. R., and Lineberger, W. C. (1976). Chem. Phys. Lett. 37,5. Carlton, T. S., and Mahan, B. H. (1964). J. Chem. Phys. 40,3683. Carney, G . D., and Porter, R. N . (1980). Phys. Rev. Lett. 45, 537. Carroll, P. K., Kennedy, E. T., and Sullivan, G. 0. ( 1 978). Opt. Lett. 2, 72. Carroll, P. K . , Kennedy, E. T., and Sullivan, G . 0. (1980). Appl. Opt. 19, 1454. Carter, S . T., and Kelly, H. P. (1975). 1. Phys. B 8, L467. Carter, S. T., and Kelly, H. P. (1976). J. Phys. B 9, 1887. Cathro, W. S., and Mackie, J. C. (1973). J. Chem. Soc., Furuduy Trans. 2 69,237. Caudano, R., Wilk, S. F. J., and McGowan, J. W. (1976). Phys. Electron. At. Collisions, Invited Leer., Rev. Pap., Prog. Rep. Int. Conf., 9th. 1975 p. 389. Cederbaum, L. S., Domke, W., and von Niessen, W. (1977). Mol. Phys. 33, 1399. Celotta, R. J., Bennett, R. A., Hall, J. L., Siegel, M.W., and Levine, J. (1972). fhys. Rev. A 6, 631. Celotta, R. J., Bennett, R. A., and Hall, J. L. (1974). J. Chem. Phys. 60, 1760. Champion, R. L., and Doverspike, L. D. (1976a). Phys. Rev. A 13,609. Champion, R. L., and Doverspike, L. D. (1976b). J . Chem. Phys. 65, 2482. Champion, R. L., Doverspike, L. D., and Lam, S. K. (1976). Phys. Rev. A 13, 617. Chandra, N. (1977). Abstr., Proc. Int. Conf: Phys. Electron. A t . Collisions, IOth, 1977 p. 1210. Chandrasekhar, S. (1945). Astrophys. J . 102, 223. Chandrasekhar, S., and Elbert, D. D. (1958). Asrrophys. J. 128, 633. Chang, E. S. (1978a). J. Phys. B 11, L69. Chang, E. S. (1978b). J . Phys. B 1 1 , L293. Chang, E. S., and Fano, U. (1972). Phys. Rev. A 6, 173. Chang, J.-J., and Kelly, H. P. (1975). Phys. Rev. A 12, 92. Chang, T. N., and Poe, R. T. (1975). Phys. Rev. A 12, 1432. Chantry, P. J., and Schulz, G. J. (1967). Phys. Rev. 156, 134. Chapman, C. J., and Herzenberg, A. (1972). J. fhys. B 5, 790. Chen, H.-L., Center, R. E., Trainor, D. W., and Fyfe, W. 1. (1977). 1.Appl. Phys. 48,2297. Chen, J . C. Y.,and Mittleman, M. H. (1968). Phys. Rev. 174, 185. Chen, J . C. Y., and Peacher, J. L. (1967). Phys. Rev. 163, 103. Cherepkov, N . A. (1976). J . Phys. B 10, L653. Chin, S. L. (1977). fhys. Len. A 61, 311. Chin, S. L., and Faubert, D. (1978). Appl. Ph.vs. Lett. 32,303. Christophorou, L. G., and Stockdale, J. A. D. (1968). J. Chem. Phys. 48, 1956. Christophorou, L. G., Compton, R. N., and Dickson, H. W. (1968). J. Chem. Phys. 48, 1449. Chupka, W. A., and Berkowitz, J. (1969). J. Chem. Phys. 51,4244. Chupka, W . A., Dehmer, P. M.,and Jivery, W. T. ( I 975). J . Chem. Phys. 63,3929. Church, M. J., and Smith, D. (1977). J . Phys. D 11,2199. Clementi, E. (1967). J. Chem. fhys. 47,2323. Clementi, E., and Gayles, J. N. (1967). J. Chem. Phys. 47, 3837. Codling, K., Houlgate, H., West, J. B., and Woodruff, P. R. (1976). J . Phys. B 9 , L83. Coggiola, M. J., Cosby, P. C., and Peterson, J. R. (1980). J . Chem. Phys. 72, 6507. Cohen, H. D., and Fano, U. (1966). Phys. Rev. 150,30. Cohen, R. B., Young, C. E., and Wexler, S. (1973). Chem. Phys. Letr. 19,99. Cole, B. E., Ederer, D. L., Stockbaudr, R., Codling, K., Parr, A. C., West, J. B., Poliakoff, E. D., and Dehmer, J. L. (1980). J . Chem. Phys. 72,6308. Collins, C. B. (1965). Phys. Reu. 140, Al850. Collins, C. B., Hicks, H. S., Wells, W. E., and Burton, R . (1972). Phys. Rev. A 6, 1545. Combet-Famoux, F. (1969). J . Phys. (Orsay, Fr.) 30, 521. Combet-Farnoux, F., and Ben Amar, M.(1980). Phys. Rev. A 21, 1975.
130
R. STEPHEN BERRY A N D SYDNEY LEACH
Comer, J., and Read, F. H. (1971a). J. Phys. E 4,368. Comer, J., and Read, F. H. (1971b). J. Phys. 8 4 , 1055. Comer, J., and Schulz, G. J. (1974). Phys. Rev. A 10,2100. Compton, R. N., and Christophorou, L. G. (1967). Phys. Rev. 154, 110. Compton, R. N., and Cooper, C. D. (1973). J. Chem. Phys. 59,4140. Compton, R. N., Reinhardt, P. W., and Cooper, C. D. (1974). J. Chem. Phys. 60,2953. Connerade, J. P., and Mansfield, M. W. D. (1973). Proc. R. Sac. London, Ser. A 335,87. Connerade, J. P., Mansfield, M. W. D., and Martin, M. A. P. (1976). Proc. R. SOC.London, Ser. A 33,405. Connerade, J. P., Mansfield, M. W. D., Newson, G. H., Tracy, D. H., Aslam Baig, M., and London, Ser. A 290,327. Thimm, K. (1979). Philos. Trans. R. SOC. Connor, T. R., and Biondi, M. A. (1965). Phys. Rev. 14OA, 778. Cook, G. R., and Metzger, P. H. (1964). J. Chem. Phys. 41, 321. Cooper, C. D., and Compton, R. N. (1972). Chem. Phys. Lett. 14,29. Cooper, C. D., and Compton, R. N. (1973). J. Chem. Phys. 59,3550. Cooper, C. D., Naff, W. T., and Compton, R. N. (1975). J. Chem. Phys. 63,2752. Cooper, C. D., Williamson, A. D., Miller, J. C., and Compton, R. N. (1980). J. Chem. Phys. 73, 1527. Cooper, J. W. (1962). Phys. Rev. 128,681. Cooper, J. W., and Zare, R. N. (1968). J. Chem. Phys. 48,942. Coppens, P., Reynaert, J. C., and Drowart, J. (1979). 2. Chem. Soc., Faraday Trans. 2 75,292. Cosby, P. C., Bennett, R. A,, Peterson, J. R., and Moseley, J. T. (1975). J. Chem. Phys. 63, 1612. Cosby, P. C., Ling, J. H., Peterson, J. R., and Moseley, J. T. (1976). J. Chem. Phys. 65, 5267. Cosby, P. C., Moseley, J. T., Peterson, J. R., and Ling, J. H. (1978a). J. Chem. Phys. 69,2771. Cosby, P. C., Smith, G. P., and Moseley, J. T. (1978b). J. Chem. Phys. 69,2779. Cremaschi, P., Johnson, P. M., and Whitten, J. L. (1978). J. Chem. Phys. 69,4341. Cunningham, A. J., and Hobson, R. M. (1969). Phys. Rev. 185,98. Damany, H., Roncin, J. Y.,and Damany-Astoin, N. (1966). Appl. Opt. 5,297. D’Angelo, N. (1961). Phys. Rev. 121, 505. Danilov, A. D., and Ivanov-Kholodny, G. S. (1965). Sou. Phys. (Usp.)(Engl. Transl.) 8,92. Davenport, J. W. (1976). Phys. Rev. Lett. 36,945. Davidovits, P., and Brodhead, D. C. (1967). 1.Chem. Phys. 46,2968. Davidson, E. R. (1960). J. Chem. Phys. 33, 1577. Dehmer, J. L., and Dill, D. (1975). Phys. Rev. Lett. 35, 213. Dehmer, J. L., and Dill, D. (1976a). J. Chem. Phys. 65, 5327. Dehmer, J. L., and Dill, D. (1976b). Phys. Rev. Lett. 37, 1049. Dehmer, J. L., and Dill, D. (1979). In “Electron-Molecule and Photon-Molecule Collisions’’ (T.Rescignor, V. McKoy, and B. Schneider, eds.), p. 225. Plenum, New York. Dehmer, J. L., Chupka, W.A., Berkowitz, J., and Jivery, W. T. (1975). Phys. Rev. A 12, 1966. Dehmer, J. L., Dill, D., and Wallace, S. (1979). Phys. Rev. Lett. 43, 1005. Dehmer, P. M., and Chupka, W. A. (1976). J. Chem. Phys. 65,2243. Dehmer, P. M., Berkowitz, J., and Chupka, W. A. (1973). J . Chem. Phys. 59, 5777. Dehmer, P. M., Berkowitz, J., and Chupka, W. A. (1974). J. Chem. Phys. 60,2676. Delos, J. B., and Thorson, W. R. (1972). Phys. Rev. A 6, 728. Delpech, J. F., and Gauthier, J.-C. (1972). Phys. Rev. A 6, 1932. Delvigne, G. A. L., and Los, J. (1973). Physica (Amsterdam) 67, 166. Demkov, Yu.N. (1964). Sou. Phys.-JETP (Engl. Transl.) 18, 138. Derkits, C., Bardsley, J. N., and Wadhera, J. M. (1979). J. Phys. E 12, L529. de Vries, M. S., van Veen, N. J. A., and de Vries, A. E. (1980). To be published (see ref. 22 in van der Wiel, 1980).
ELEMENTARY ATTACHMENT AND DETACHMENT PROCESSES
131
Dibeler, V. H., and Liston, S. K. (1968). J . Chem. Phys. 49,482. Dibeler, V. H., and Walker, J. A. (1967). J . Opt. Am. Soc. 57, 1007. Dibeler, V. H., and Walker, J. A. (1968). Adv. Muss Specfrom.4, 767. Dibeler, V. H., Walker, J. A., and Liston, S. K. (1967). J . Res. Nut/. Bur. Stand., Sect. A 71,371. Dieke, G. H. (1958). J . Mol. Spectrosc. 2,494. Dietz, T . G., Duncan, M. A., Liverman, M. G., and Smalley, R. E. (1980). Chem. Phys. Lett. 70,246.
Dill, D. (1972). Phys. Rev.A 6, 160. Dill, D. (1973). Phys. Rev.A 7 , 1976. Dill, D. (1976). In “Photoionization and Other Probes of Many Electron Interactions” (F. J. Wuilleumier, ed.), p. 387. Plenum, New York. Dill, D., and Dehmer, J. L. (1974). J. Chem. Phys. 61, 692. Dill, D., and Fano, U. (1972). Phys. Rev. Left.29, 1203. Dill, D., Manson, S. T., and Starace, A. F. (1974). Phys. Rev. Lett. 32,971. Dimicoli, I., and Botter, R. (1980). J. Chim. Phys. 77, 751. Dimicoli, I., and Botter, R. (1981a). J. Chem. Phys. 74, 2346. Dimicoli, I., and Botter, R. (1981b). J. Chem. Phys. 74,2355. Dispert, H., and Lacmann, K. (1977). Chem. Phys. Letr. 47,533. Dorman, F. H., and Morrison, J. D. (1961). 1.Chem. Phys. 35, 575. Doverspike, L. D., Smith, B. T., and Champion, R. L. (1980). Phys. Rev.A 22, 393. Druger, S. D. (1976). J. Chem. Phys. 64,987. Dubau, J. (1978). J. Phys. B 11,4095. Dubau, J., and Wells, J. (1973). J. Phys. B 6, 1452. DuBois, R. D., Jeffries, J. B., and Dunn, G. H. (1978). Phys. Rev.A 17, 1314. Dunbar, R. C. (1979). In “Gas Phase Ion Chemistry” (M. T. Bowers, ed.), Vol. 2, Chapter 14, p. 181. Academic Press, New York. Duncan, M. A., Dietz, T. G., and Smalley, R. E. (1979). Chem. Phys. 49,415. Duncanson, J. A,, Jr., Strand, M., Lindgfird, A., and Berry, R. S. (1976). Phys. Reu. Lett. 37, 987.
Durup, J. (1978). J. Phys. (Orsuy, Fr.) 39,941. Dutta, C. M., Chapman, F. M., Jr., and Hayes, E. F. (1977). J . Chem. Phys. 67, 1904. Duzy, C., and Berry, R. S. (1976). J . Chem. Phys. 64,2421. Ederer, D. L., and Tomboulian, D. H. (1964). Phys. Rev. 133, A1525. Eisner, P. N., and Hirsh, M. N. (1971). Phys. Rev. Lett. 26,874. Eissner, W., and Seaton, M. J. (1 972). J . Phys. B 5, 2 187. Eland, J. H. D. (1972). Inr. J. Muss Spectrom. Ion Phys. 9, 397. Eland, J. H. D. (1974). “Photoelectron Spectroscopy.” Butterworth, London. Eland, J. H. D. (1978). J. Phys. E 11,969. Eland, J. H. D. (1979). In “Electron Spectroscopy: Theory, Techniques and Applications.” (C. R. Brundle and A. D. Baker, eds.), Vol. 3, p. 231. Academic Press, New York. Eland, J. H. D. (1980). J . Chim. Phys. 77,613. Eland, J. H. D., and Berkowitz, J. (1977). J . Chem. Phys. 67,2782 Eland, J. H. D., and Berkowitz, J. (1979). J . Chem. Phys. 70, 5151. Eland, J. H. D., Berkowitz, J., and Monahan, J. E. (1980). J. Chem. Phys. 72,253. Engelking, P. C., and Lineberger, W. C. (1976). J . Chem. Phys. 65,4323. Engelking, P. C., and Lineberger, W. C. (1977a). J. Chem. Phys. 66, 5054. Engelking, P. C., and Lineberger, W. C. (1977b). J. Chem. Phys. 67, 1412. Ewing, J. J., Milstein, R., and Berry, R. S. (1971). J . Chem. Phys. 54, 1752. Eyler, J. R., and Atkinson, G. H. (1974). Chem. Phys. Lett. 28,217. Faist, M. B., and Levine, R. D. (1974). J. Chem. Phys. 64,2953.
132
R. STEPHEN BERRY AND SYDNEY LEACH
Faist, M. B., Johnson, B. R., and Levine, R. D. (1975). Chem. Phys. Lett. 32, I . Fano, U. (1961). Phys. Rev. 124, 1866. Fano, U. (1969). Phys. Rev. 178, 131. Fano, U. (1975). J . Opt. SOC.Am. 65,979. Fano, U., and Cooper, J. W. (1965). Phys. Rev. 137, A 1364. Fano, U., and Dill, D. (1972). Phys. Rev. A 6, 185. Fayeton, J., Dhuicq, D., and Barat, M. (1978). J . Phys. B 11, 1267. Fehsenfeld, F. C. (1970). J. Chem. Phys. 53,2000. Fehsenfeld, F. C. (1975). In “Interactions Between Ions and Molecules” (P. Ausloos, ed.), p. 387. Plenum, New York. Feldmann, D. (1970). Z. Naturforsch. A 25,621. Feldmann, D., Rackwitz, R., Kaiser, H. J., and Heinicke, E. (1977). Z. Naturforsch. A 32% 600. Feldman, D. L., Lengel, R K., and Zare, R. N. (1977). Chem. Phys. Lett. 52,413. Feneuille, S., and Armstrong, L. (1975). J. Phys. Lett. 36, L-235. Ferguson, E. E., Fehsenfeld, F. C., and Schmeltekopf, A. L. (1965). Phys. Rev. 138, A381. Fermi, E. (1936). Ric. Sci., Parte 2 7, 13. Fiquet-Fayard, F. (1974a). Vacuum 24, 533. Fiquet-Fayard, F. (1974b). J . Phys. 87,810. Fiquet-Fayard, F., Sizun, M., and Goursaud, S. (1972). J. Phys. (Paris)33,669. Fisanick, G . J., Eichelberger, T. S., IV,Heath, B. A., and Robin, M. B. (1980). J . Chem. Phys. 72, 5571. Fite, W. L., and Irving, P. (1972). J. Chem. Phys. 56,4227. Fite, W . L., Smith, A. C. H., and Stebbings, R. F. (1962). Proc. R. SOC.London, Ser. A 268,527. Flannery, M. R. (1972). In “Case Studies in Atomic Collision Physics” (E. W. McDaniel and M. R. C. McDowell, eds.), Vol. 2, Chapter 1. North-Holland Publ., Amsterdam. Flannery, M. R. (1973). Ann. Phys. ( N .Y . ) 79,480. Flannery, M. R. (1976). In “Atomic Processes and Applications” (P. G. Burke and B. L. Moiseiwitsch, eds.), p. 408. North-Holland Publ., Amsterdam. Flannery, M. R., and Yang, T. P. (1978a). Appl. Phys. Lett. 32, 327. Flannery, M. R., and Yang, T. P. (1978b). Appl. Phys. Letr. 32, 356. Ford, A. L., Docken, K. K.,and Dalgarno, A. (1975). Astrophys. J. 195,819. Fox, J. N., and Wheaton, J. E. G. (1973). J. Phys. E6,655. Fox, R. E. (1957). J . Chem. Phys. 26, 1281. Franklin, J. L., and Harland, P. W. (1974). Annu. Rev. Phys. Chem. 25,485. Frommhold, L., and Biondi, M. A. (1969). Phys. Rev. 185,244. Frost, D. C., and McDowell, C. A. (1960). Can. J . Chem. 38,407. Fryar, J., and Browning, R. (1973). Planet Space Sci. 21, 709. Gait, P. D., and Berry, R. S. (1977). J . Chem. Phys. 66,2387, 2764. Gallagher, J. W., Beaty, E. C., and Rumble, J. R., Jr. (1978). “Bibliography of Low Energy Electron and Photon Cross Section Data,” Supplement (1975-1977) to NBS Spec. Publ. No. 426. U S . Govt. Printing Office, Washington, D.C. Gardner, J. L., and Samson, J. A. R. (1973). J. Electron Spectrosc. Relat. Phenom. 2,259. Gardner, J. L., and Samson, J. A. R. (1975). J. Electron Spectrosc. Relat. Phenom. 6, 53. Garton, W. R. S. (1953). J . Sci. Instrum. 30, 119. Garton, W. R. S. (1959). J . Sci. Instrum. 36, 11. Gautier, T. N., Fink, U.,Treffers, R. R., and Larson, H. P. (1976). Astrophys. J . (Lett.) 207, L129. Geltman, S. (1956). Phys. Rev. 102, 171. Geltman, S. (1958). Phys. Rev. 112, 176. Gentieu, E. P., and Mentall, J. E. (1976). J. Chem. Phys. 64, 1376.
ELEMENTARY ATTACHMENT AND DETACHMENT PROCESSES
133
Gerardo, J. B., and Gusinow, M. A. (1971). Phys. Reri. A 3,255. Gillen, K. T., Gaily, T. D., and Lorents, D. C. (1974). Chem. Phys. Lett. 57, 192. Giusti, A. (1980). J. Phys. B 13, 3867. Giusti-Suzor, A., and Lefebvre-Brion, H. (1977). Astrophys. J. 214, LIOI. Glass-Maujean, M. (1979). Comments At. Mol. Phys. 7, 83. Glass-Maujean, M., Breton, J., and Guyon, P. M. (1978). Phys. Rra. Lett. 40, 181. Glass-Maujean, M., Kollmann, K., and Ito, K. (1979). J. Phys. B 12, L453. Glover, R. M., and Weinhold, F. (1977). J . Chem. Phys. 66,303. Goursaud, S . , Sizun, M., and Fiquet-Fayard, F. (1976). J. Chem. Phys. 65,5453. Goursaud, S . , Sizun, M., and Fiquet-Fayard, F. (1978). J . Chem. Phys. 68,4310. Granneman, E. H. A., Klewer, M., Nygaard, K. J., and van der Wiel, M. J. (1976). J. Phys. B 9, 865. Grant, I. P., and Starace, A. F. (1975). J. Phys. B 8, 1999. Grice, R . (1975). Adv. Chem. Phys. 30,247. Grice, R., and Herschbach, D. R. (1974). Mol. Phys. 27, 159. Grimm, F. A,, Carlson, T. A,, Dress, W. B., Agron, P., Thomson, J. O., and Davenport, J. W. (1980). J . Chem. Phys. 72,3041. Gustafsson, T., Plummer, E. W., Eastman, D. E., and Gudat, W. (1978). Phys. Reu. A 17, 175. Guyon, P. M., and Nenner, I. (1980). Appl. Opt. 19,4068. Guyon. P. M., Chupka, W. A., and Berkowitz, J. (1976). J. Chem. Phys. 64, 1419. Guyon, P. M., Breton, J., and Glass-Maujean, M. (1979). Chem. Phys. Lett. 68, 314. Hall, J. L., Robinson, E. J., and Branscomb, L. M. (1965). Phys. Reu. Lett. 14, 1013. Hall, R. I., Cadez, I., Schermann, C., and Tronc, M. (1977). Phys. Rev. A 15, 599. Hansen, J. C. (1979). Doctoral Dissertation, University of Chicago, Chicago, Illinois. Hansen, J. C., Duncanson, J. A., Jr., Chien, R.-L., and Berry, R. S. (1980). Phys. Rev. A 21,222. Harland, P., and Thyme, J. C. J. (1969). J. Phys. Chem. 73,4031. Hayhurst, A. N., and Kittleson, D. B. (1974). Proc. R. Soc. London, Ser. A 338, 155, 175. Hayhurst, A. N., and Telford, N. R. (1972). J . Chem. Soc., Furuduy Truns. I 68,237. Hayhurst, A. N., and Telford, N. R. (1974). J. Chem. Soc., Furuduy Truns. I 70, 1999. Hazi, A. U. (1974). Chem. Phys. Lett. 25,259. Heath, B. A., Fisanick, G. J., Robin, M. B., and Eichelberger, T. S., IV (1980). J . Chem. Phys. 72, 5991. Heinzmann, U. (1978). J . Phys. B 11, 399. Heinzmann, U., Kessler, J., and Loraz, J. (1970). Z . Phys. 240, 42. Heinzmann, U., Heuer, H., and Kessler, J. (1975). Phys. Rev. Lett. 34, 441. Heinzmann, U., Heuer, H., and Kessler, J. (1976). Phys. Rev. Lett. 36, 1444. Heinzmann, U., Schonhense, G., and Kessler, J. (1979). Phys. Rec. Lett. 42, 1603. Heinzmann, U., Schafers, F., and Hew, B. A. (1980). Chem. Phys. Lett. 69,284. Held, B., Mainfray, G., Manus, C., and Morellec, J. (1972). Phys. Rev. Lett. 28, 130. Henderson, W. R., Fite, W. L., and Brackmann, R. T. (1969). Phys. Rev. 183, 157. Heppner, R. A,, Walls, F. L.. Armstrong, W. T., and Dunn, G . H. (1976). Phys. Rev. A 13,1000. Herbst, E. (1978). Astrophys. J . 222, 408. Herbst, E., Patterson, T. A., Norcross, D. W., and Lineberger, W. C. (1974a). Astrophys. J. 191, L143. Herbst, E., Patterson, T. A., and Lineberger, W. C. (1974b). J. Chem. Phys. 61, 1300. Herrmann, A., Leutwyler, S., Schumacher, E., and Woste, L. (1977a). Chem. Phys. Lett. 52, 418. Herrmann, A,, Leutwyler, S., Schumacher, E., and Woste, L. (1977b). Helv. Chim. Acta 61, 453. Herrmann, A., Schumacher, E., and Woste, L. (1978). J. Chem. Phys. 68,2327.
134
R. STEPHEN BERRY AND SYDNEY LEACH
Hertz, H. (1887a). Sitzungsber. Berlin. Akad. p. 487. Hertz, H. (1887b). Ann. Phys. (Leipzig) [3] 31, 983. Herzberg, G. (1955). Mem. SOC.R . Sci. Liege [4] 15,291. Herzberg, G. (1979). J. Chem. Phys. 70,4806. Herzberg, G., and Jungen, C. (1972). 1.Mol. Spectrosc.41,425. Herzberg, G., and Lagerqvist, A. (1968). Can. J. Phys. 46,2363. Herzenberg, A. (1969). J. Chem. Phys. 51,4942. Herzenberg, A., and Ojha, P. (1979). Phys. Rev. A 20, 1905. Hiller, J. F., and Vestal, M. L. (1980). J. Chem. Phys. 72,4713. Hinnov, E., and Hirschberg. J. G. (1962). Phys. Rev. 125,795. Hiraoka, H., Nesbet, R. K., and Welsh, L. W., Jr. (1977). Phys. Rev. Lett. 39, 130. Hirota, F. (1976). J . Electron. Spectrosc. Relat. Phenom. 9, 149. Hitchcock, A. P., Brion, C. E., and van der Wiel, M. J. (1980). Chem. Phys. 45,461. Hodges, R. V., Lee, L. C., and Moseley, J. T. (1980). J . Chem. Phys. 72,2998. Holland, D. M. P., Codling, K., West, J. B., and Marr, G. V. (1979). J . Phys. B 12,2465. Holmes, R. M., and Marr, G. V. (1980). J. Phys. B 13,945. Holstein, T. (1951). Phys. Reu. 84, 1073. Holt, R. B., Richardson, J. M., Howland, B., and McClure, B. T. (1950). Phys. Rev. 77,239. Hotop, H., and Lineberger, W. C. (1975). J . Phys. Chem. Ref. Data 4, 539. Hotop, H., and Niehaus, A. (1967). J . Chem. Phys. 47,2506. Hotop, H., and Niehaus, A. (1968). 2.Phys. 215,395. Hotop, H., Bennett, R. A., and Lineberger, W. C. (1973a). J. Chem. Phys. 58, 2373. Hotop, H., Patterson, T. A., and Lineberger, W. C. (1973b). Phys. Rev. A 8,762. Hotop, H., Patterson, T. A., and Lineberger, W. C. (1974). J . Chem. Phys. 60, 1806. Houlgate, R. G., West, J. B., Codling, K., and Marr, G. V. (1974). J. Phys. B 7, L470. Houlgate, R. G., West, J. B., Codling, K., and Marr. G. V. (1976). J . Electron. Spectrosc. Relat. Phenom. 9,205. Howard, C. J., Fehsenfeld, F. C., and McFarland, M. (1974). J. Chem. Phys. 60, 5086. Huang, C.-M., Biondi, M. A., and Johnsen, R. (1975). Phys. Rev. A 11,901. Huang, K. N., Johnson, W. R., and Cheng, K. T. (1979). Phys. Rev. Lett. 43, 1658. Huber, B. A., Cosby, P. C., Peterson, J. R., and Moseley, J. T.(1977). J . Chem. Phys. 66,4520. Huber, K. P., and Herzberg, G. (1979). “Molecular Spectra and Molecular Structure,” Vol. IV. “Constants of Diatomic Molecules.” Van Nostrand-Reinhold, Princeton, New Jersey. Hubers, M. M. (1976). Doctoral Dissertation, Wiskunde de Natuurwetenschappen de Universiteit van Amsterdam. Hubers, M. M., and Los, J. (1975). Chem. Phys. 10,235. Hubers, M. M., Kleyn, A. W., and Los, J. (1976). Chem. Phys. 17, 303. Hughes, A. L. (1910). Proc. Cambridge Philos. SOC.15,483. Hultzscb, W., Kronast, W., Niehaus, A., and Ruf, M. W. (1979). J. Phys. B 12, 1821. Hurst, G. S., OKelly, L. B., and Bortner, T. E. (1961). Phys. Rev. 123, 1715. Inokuti, M. (1971). Rev. Mod. Phys. 43,297. Inokuti, M., Itikawa, Y.,and Turner, J. E. (1978). Revs. Mod. Phys. 50,23. Janev, R. K. (1976). J . Chem. Phys. 64, 1891. Janev, R.K., and RaduloviC, Z. M. (1978). Phys. Rev. A 17, 889. Janousek, B. K., and Brauman, J. I. (1979). In “Gas Phase Ion Chemistry (M. T. Bowers, ed.), Vol. 2, p. 53. Academic Press, New York. Jensen, D. E., and Padley, P. J. (1966). Trans. Faruduy SOC.62,2140. Johnson, P. M. (1975). J. Chem. Phys. 62,4562. Johnson, P. M. (1976). J. Chem. Phys. 64,4143,4638. Johnson, P. M. (1980a). Acc. Chem. Res. 13,20.
ELEMENTARY ATTACHMENT AND DETACHMENT PROCESSES
135
Johnson, P. M. (1980b). Appl. Opr. 19,3920. Johnson, R. A., McClure, B. T., and Holt, R.B. (1950). Phys. Reu. 80,376. Johnson, W. R.,and Cheng, K. T. (1979). Phys. Rev. A 20,978. Johnson, W. R.,and Lin, C. D. (1979). Phys. Reu. A 20,964. Johnston, H. S.,and Kornegay, W.M. (1963). J. Chem. Phys. 38,2242. Jonas, A. E., Schweitzer, G. K., Grimm, F. A,, and Carlson, T. A. (1972). J. Electron. Spectrosc. Relai. Phenom. 1, 29. Jortner, J., and Leach, S . (1980). J. Chim. Phys. 77,7. Jungen, C. (1980). J. Chim. Phys. 77, 27. Jungen, C., and Atabek, 0. (1977). J . Chem. Phys. 66,5584. Jungen, C . , and Dill, D. (1980). J. Chem. Phys. 73,3338. Karlov, N. V. (1978). In “Multiphoton Processes” (J. Eberly and P. Lambropoulos, eds.), p. 57 1. Wiley, New York. Karlov, N. V.,Karpov, N. A., Petrov, Yu. N., Prokhorov, A. M., and Shelepin, L. A. (1976). Sou. Phys.-Dokl. (Engl. Transl.) 21, 32. Kasdan, A., Herbst, E., and Lineberger, W. C. (1975a). Chem. Phys. Left.31,78. Kasdan, A., Herbst, E., and Lineberger, W. C. (1975b). J. Chem. Phys. 62,541. Kasner, W. H.,and Biondi, M. A. (1%5). Phys. Rev. 137, A317. Kasner, W. H., and Biondi, M. A. (1%8). Phys. Rev. 174, 139. Kassel, L. S . (1928). J. Phys. Chem. 33, 225. Kelly, H. P. (1964). Phys. Reo. 136, B896. Kelly, H. P. (1968). Adu. Theor. Phys. 2,75. Kelly, H. P. (1969). Adu. Chem. Phys. 14, 129. Kelly, H. P., and Ron, A. (1972). Phyo. Rev. A 5, 168. Kelly, H. P., and Simons, R. L. (1973). Phys. Rev. Lett. 30,529. Kelly, R.,and Padley, P. J. (1972). Proc. R. SOC.London, Ser. A 327, 345. Kennedy, D. J., and Manson, S. T. (1972). Phys. Rev. A 5,227. Kessler, J. (1976). “Polarized Electrons.” Springer-Verlag, Berlin and New York. Khvostenko, N. I., and Dukel’skii, V. M. (1958). Sou. Phys.-JETP (Engl. Transl.) 6,657. Kibel, M. H., and Nyberg, G. L. (1979). J. Electron Spectrosc. Relai. Phenom. 17, 1. Kibel, M. H., Leng, F. J., and Nyberg, G. L. (1979a). J . Electron Specirosc. Relat. Phenom. 15, 281. Kibel, M. H., Livett, M. K., and Nyberg, G. L. (1979b). J. Electron Specirosc. 15, 275. Kieffer, L. J. (1968). JILA lnf. Cent. Rep. 5. Kieffer, L. J. (1976). “Bibliography of Low Energy Electron and Photon Cross Section Data,” NBS Spec. h b l . No. 426. US Govt. Printing Office, Washington, D.C. Kikiani, B. I., Ogurtsov, G. N., and Flaks, 1. P. (1966). Sou. Phys.-JETP (Engl. Transl.) 22, 264. Klar, H., and Morgner, H. (1979). J . Phys. B 12,2369. Kleinpoppen, H., and McDowell, M, R. C., eds. (1976). “Electron and Photon Interactions with Atoms.” Plenum, New York. Klewer, M., Beerlage, M. J. M., Los, J., and van der Wiel, M. J. (1977). J . Phys. B 10, 2809. Kley, D., Lawrence, G. M., and Stone, E. J. (1977). J. Chem. Phys. 66,4157. Kleyn, A. W., Hubers, M. M., and Los, J. (1978). Chem. Phys. 34, 5 5 . Klots, C. E. (1964). J. Chem. Phys. 41, 117. Klots, C. E. (1972). 2. Naiurforsch. A 270, 5 5 3 . Klots, C. E. (1976a). J . Chem. Phys. 64,4269. Klots, C . E. (1976b). Chem. Phys. Let#.38,61. Kohl, J. L., Lafyatis, G. P., Palenius, ‘H. P., and Parkinson, W. H. (1978). Phys. Rev. 18, 571. Kolos, W., and Wolneiwicz, L. (1969). J . Chem. Phys. 50, 3228.
136
R. STEPHEN BERRY AND SYDNEY LEACH
Koopmans, T. (1934). Physica (Amsterdam) 1, 104. Krause, M. 0. (1971). J . Phys. (Orsay, Fr.) 32, C4, 67. Krause, M. 0.(1980). In “Synchrotron Radiation Research” (S. Doniach and H. Winick, eds.). Chapter 3. Plenum, New York. Krauss, M., and Julienne, P. S. (1973). Asrrophys. 1.Lett. 183, L139. Krogh-Jespersen, K., Rava, R. P., and Goodman, L. (1979). Chem. Phys. 44,295. Kroll, N., and Watson, K. M. (1972). Phys. Rev. A 5, 1883. Kulander, K. C., and Guest, M. F. (1979). J . Phys. B 12, L501. Kurepa, M. V., and BeliC, D. S . (1977). Chem. fhys. Lett. 49, 608. Lacmann, K. (1980). Adv. Chem. fhys. 42,513. Lam, S. K., Delos, J. B., Champion, R. L., and Doverspike, L. D. (1974). fhys. Rev. A 9 , 1828. Lambropoulos, M., Moody, S. E., Smith, S. J., and Lineberger, W. C. (1975). Phys. Rev. Lett. 35, 159. Lambropoulos, P. (1976). Adv. At. Mol. Phys. 12,87. Langevin, P. (1903). Ann. Chim. Phys. 48,433. Langhoff, P. W. (1979). In “Electron-Molecule and Photon-Molecule Collisions” (T. Rescigno, V. McKoy, and B. Schneider, eds.), p. 183. Plenum, New York. Langhoff, P. W., Corcoran, C. T., Sims, J. S., Weinhold, F., and Glover, R. M. (1976). Phys. Rev. A 14, 1042. Langhoff, P. W., Padial, N., Csanak, G., Rescigno, T. N., and McKoy, B. V. (1980). J. Chim. Phys. 17, 589. Latimer, C. J. (1977). J. Phys. B 10, 1889. Leach, S. (1970). J . Chim.Phys., Special issue, Radiationless Transitions in Molecules, p. 74. Leach, S. (1974). In ‘Vacuum Ultraviolet Radiation Physics” (N. Damany, J. Romand, and B. Vodar, eds.) Chap. 7, p. 193. Pergamon Press, Oxford, Leach, S., Devoret, M., and Eland, J. H. D. (1978a). Chem. fhys. 33, 113. Leach, S., Stannard, P. R., and Gelbart, W. M. (1978b). Mol. Phys. 36, 1 119. Leach, S., Dujardin, G., and Taieb, G. (1980). J . Chim. Phys. 77, 705. Lecompte, C., Mainfray, G., Manus, C., and Sanchez, F. (1975). Phys. Rev. A 11, 1009. LeDourneuf, M., Vo Ky Lan, Burke, P. G., and Taylor, K. T. (1975). J. fhys. 88,2640. LeDourneuf, M., Vo Ky Lan, and Hibbert, A. (1976). J. Phys. B 9 , L359. LeDourneuf, M., Vo Ky Lan, and Zeippen, C. J. (1979). J. Phys. B 12,2449. Lee, C. M. (1974). Phys. Rev. A 10, 1598. Lee, C. M. (1975). Phys. Rev. A 11, 1692. Lee, C. M. (1977). Phys. Rev. A 16, 109. Lee, L. C., and Judge, D. L. (1972). J. Chem. Phys. 57,4443. Lee, L. C., and Smith, G. P. (1979). J . Chem. Phys. 70, 1727. Lee, L. C., Carlson, R. W., Judge, D. L., and Ogawa, M. (1975). J . Chem. Phys. 63, 3987. Lee, L. C., Carlson, R. W., and Judge, D. L. (1976). J. fhys. B9, 855. Lee, L. C., Smith, G . P., Moseley, J. T., Cosby, P. C., and Guest, J. A . (1979). . I Chem. . Phys. 70, 3237. Lehmann, K. K., Smolarek, J., and Goodman, L. (1978). J. Chem. Phys. 69, 1569. Lengel, R. K., and Zare, R. N. (1978). J. Am. Chem. SOC.100,7495. Letokhov, V. S . (1977). Comments At. Mol. Phys. 7, 107. Letokhov, V. S. (1978). Comments A:. Mol. Phys. 8, 39. Leu, M. T., Biondi, M. A., and Johnsen, R. (1973a). Phys. Reo. A 7,292. Leu, M. T., Biondi, M. A., and Johnsen, R. (1973b). Phys. Rev. A 8,413. Leuchs, G., Smith, S. J., Khawaja, E., and Walther, H. (1979). Opr. Commun. 31, 313. Lifshitz, C. (1978). Adu. Muss. Spectrom. 7A, 3. Light, J. C. (1967). Discuss. Faruduy Soc. 44, 14.
ELEMENTARY ATTAQHMENT AND DETACHMENT PROCESSES
137
Lin, S. M., Whitehead, J. C., and Grice, R. (1974). Mol. Phys. 27, 741. Lineberger, W. C. (1974). In “Chemical and Biochemical Applications of Lasers” (C. B. Moore, ed.). Vol. I, p. 71. Academic Press, New York. Lineberger, W. C., and Patterson, T. A. (1972). C‘hem. Phys. Lett. 13,40. Lineberger, W. C., and Woodward, B. W. (1970). Phys. Rev. Lett. 25,424. Lineberger, W. C., Hotop, H., and Patterson, T. A. (1976). In “Electron and Photon Interactions with Atoms” (H.Kleinpoppen and M. R. C. McDowell, eds.), p. 125. Plenum, New York. Locht, R., and Momigny, J. (1971). Int. J. Mass Spectrom. Ion Phys. 7, 121. Loeb, L. B. (1960). “Basic Processes of Gaseous Electronics,” Chapter VI. Univ. of California Press, Lorquet, J. C., Dehareng, D., Sannen, C., and Raseev, G. (1980). J. Chim. Phys. 77,719. Los, J., and Kleyn, A. W. (1978). I n “Alkali Halide Vapors” (P. Davidovits and D. L. McFadden, eds.), pp. 275ff. Academic Press, New York. Lowry, J. F., Tomboulian, D. H., and Ederer, D. L. (1965). Phys. Rev. 137, A1054. Lozier, W. W. (1930). Phys. Rev. 36,1417. Lubell, M. S., and Raith, W. (1969). Phys. Rev. Lett. 23,211. Lubman, D. M., Naaman, R., and Zare, R. N. (1980). J. Chem. Phys. 72,3034. Lucatorto, T. B., McIlrath, T. J., and Mehlman, G. (1979). Appl. Opt. 18,2916. Luther, K., Troe, J., and Wagner, H. G. (1972). Ber. Bunsenges. Phys. Chem. 76,53. Lynch, M. J., Gardner, A. B., and Codling, K. (1972). Phys. Lett. A 40,349. Lynch, M. J., Codling, K., and Gardner, A. B. (1973). Phys. Lett. A 43,213. McClain, W. M. (1974). Acc. Chem. Res. 7, 129. McClain, W. M., and Harris, R. A. (1977). In “Excited States” (E. C. Lim, ed.), Vol. 3, p. 1. Academic Press, New York. McCoy, D. G., Morton, J. M., and Marr, G. V. (1978). J. Phys. B 11, L547. McCulloh, K. E. (1973). J. Chem. Phys. 59,4250. McCulloh, K. E., and Walker, J. A. (1974). Chem. Phys. Lett. 25,439. McGowan, J. W., Vroom, D. A., and Comeaux, A. R. (1969). J . Chem. Phys. 51,5626. McGowan, J . W., Caudano, R., and Keyser, J. (1976). Phys. Rev. Lett. 36, 1447. McGowan, J. W., Mul, P. M., D’Angelo, V. S., Mitchell, J. B. A., Defrance, P., and Froelich, H. R. (1979). Phys. Rev. Lett. 42, 373. McGuire, E. J. (1967). Phys. Rev. 161, 51. McWhirter, R. W. P. (1961). Nature (London) 190, 902. Magee, J. L. (1940). J. Chem. Phys. 4 687. Mahajan, C. G., Baker, E. A. M., and Burgess, D. D. (1 979). Opt. Lett. 4,283. Mahan, B. H. (1973). Ado. Chem. Phys. 23, 1. Mahan, B. H., and Person, J. C. (1964a). J. Chem. Phys. 40,392. Mahan, B. H., and Person, J. C. (196db). J . Chem. Phys. 40,2851. Mainfray, G. (1980). Comments At. Mol. Phys. 9, 87. Mainfray, G., and Manus, C. (1978). J. Phys. (Orsuy, Fr.) 39, C1, 1. Mandl, A. (1971). J. Chem. Phys. 54,4129. Mandl, A. (1973). Recent Dev. Shock Tube Res., Proc. Int. Shock Tube Symp., 9th, 1973 p. 227. Mandl, A. (1976a). J. Chem. Phys. 64,903. Mandl, A. (1976b). J. Chem. Phys. 63,2483. Mandl, A. (1978). In “Alkali Halide Vapors” (P. Davidovits and D. L. McFadden, eds.), Chapter 12, p. 389. Academic Prbss, New York. Mandl, A,, Kivel, B., and Evans, E. (1970). J . Chem. Phys. 53,2363. Mansfield, M. W. D. (1973). Astrophys. J. 180, 1011. Manson, S. T. (1976). Adv. Electron. Electron Phys. 41,73.
w.
138
R. STEPHEN BERRY AND SYDNEY LEACH
Manson, S . T. (1977). Adv. Electron. Electron Phys. 44, 1. Manson, S.T., and Cooper, J. W. (1968). Phys. Rev. 165, 126. Marcus, R. A,, and Rice, 0.K. (1951). J. Phys. Colloid Chem. 55, 894. Marr, G. V. (1967). “Photoionization Processes in Gases.’’ Academic Press, New York. Marr, G. V. (1976). In “Electron and Proton Interactions with Atoms” (H. Kleinpoppen and M. R. C. McDowell, eds.), p. 39. Plenum, New York. Marr, G. V. (1978). Daresbury Lab. [Rep.]DL/SRF/R 8,81. Marr, G. V., Morton, J. M., Holmes, R. M., and McCoy, D. G. (1979). 1.Phys. B 12,43. Marr, G. V., Holmes, R. M., and Codling, K.(1980). J. Phys. B 13,283. Massey, H. S.W. (1976). “Negative Ions.” Cambridge Univ. Press, London and New York. Massey, H. S.W., Burhop, E. H. S.,and Gilbody, H. B. (1974). “Electronic and Ionic Impact Phenomena,” Vol. 4. Oxford Univ. Press, London and New York. Masuoka, T., and Samson, J. A. R. (1980). J. Chim. Phys. 77,623. Mathur, B. P., Rothe, E. W., Reck, G. P., and Lightman, A. J. (1978). Chem. Phys. Left. 56, 336. Mathur, D., Khan, S.V., and Hasted, J. B. (1978). J . Phys. B 11,3615. Matsuzawa, M. (1972). J. Phys. SOC.Jpn. 32, 1088. Mazeau, J., Gresteau, F., Hall, R. I., and Huetz, A. (1978). J . Phys. B 11, L557. Meldner, H. W., and Perez, J. D. (1971). Phys. Rev. A 4, 1388. Mentall, J. E., and Guyon, P. M. (1977). J. Chem. Phys. 67,3845. Michels, H. (1975). Final Report, AFWL-TR-73-288. Air Force Weapons Laboratory, Kirkland AFB, New Mexico. Mies, F. (1968). Phys. Rev. 175, 164. Miller, D. L., Dow, J. D., Houlgate, R. G., Marr, G. V.,and West, J. B. (1977). J. Phys. B 10, 3205. Miller, 1. F., and Vestal, M. L. (1980). J. Chem. Phys. 72,4713. Miller, W.J., and Gould, R. K. (1978). J. Chem. Phys. 68,3542. Milstein, R. (1972). Doctoral Dissertation, University of Chicago, Chicago, Illinois. Milstein, R., and Berry, R. S . (1971). J . Chem. Phys. 55,4146. Mitchell, C. J. (1975). J. Phys. B 8 , 25. Mitchell, J. B. A., and McGowan, J. W. (1978). Astrophys. J . (Lett.) 222, 77. Mitchell, P., and Codling, K. (1972). Phys. Lett. A 38A, 31. Mittleman, M. H. (1969). Phys. Rev. 185,394. Mohler, F. L., and Boeckner, C. (1929). J. Res. Nutl. Bur. Stand. 3, 303. Momigny, J. (1980). J. Chim. Phys. 77, 725. Moores, D. L., and Norcross, D. W. (1974). Phys. Rev. A 10, 1646. Morellec, J., Normand, D., and Petite, G. (1976). Phys. Rev. A 14, 300. Moseley, J. T., Olson, R. E., and Peterson, J. R. (1975). Case Stud. At. Phys. 5, 1. Moseley, J. T., Cosby, P. C., and Peterson, J. R. (1976). J. Chem. Phys. 65, 2512. Moutinho, A. M. C., Baede, A. P. M., and Los, J. (1971a). Physicu (Amsterdam) 51,432. Moutinho, A. M. C., Aten, J. A., and Los, J. (1971b). Physica (Amsterdam) 53,471. Moutinho, A. M. C., Aten, J. A., and Los, J. (1974). Chem. Phys. 5,84. Muck, G . ,and Popp, H. P. (1968). Z. Naturforsch. A 23a, 1213. Mul, P. M., and McGowan, J. T. (1979). J. Phys. B 12, 1591. Mulliken, R. S. (1964). Phys. Rev. 136, A962. Murakami, J., Kaya, K., and Ito, M. (1980). J. Chem. Phys. 72,3263. Murray, P. T., and Baer, T. (1979). Int. J. Muss Spectrum. Ion Phys. 30, 165. Natanson, G. L. (1960). Sou. Phys.-Tech. Phys. (Engl. Trunsl.)4, 1263. Nenner, I., Guyon, P. M., Baer, T., and Govers, T. R. (1980). J. Chem. Phys. 72,6587. Nesbet, R. K. (1977). J. Phys. B 10, L739.
ELEMENTARY ATTACHMENT AND DETACHMENT PROCESSES
139
Neynaber, R. H., Myers, B. F., and Trujillo, S. M. (1969). Phys. Rev. 180, 139. Niehaus, A., and Ruf, M. W. (1971). Chem. Phys. Lett. 11,55. Nielsen, S . E., and Berry, R. S. (1971). Phys. Rev. A 4, 865. Nielsen, S. E., and Dahler, J. S. (1965). J. Chem. Phys. 45,4060. Nieman, G. C., and Colson, S. D. (1978). J. Chem. Phys. 68,5656. Niles, F. E., and Robertson, W. W. (1964). J. Chem. Phys. 40,2909. Novick, S . E., Jones, P. L., Mulloney, T. J., and Lineberger, W. C. (1979a). J. Chem. Phys. 70,2210. Novick, S. E., Jones, P. L., Futrell, J. H., and Lineberger, W. C. (1979b). J . Chem. Phys. 70, 2652. Oertel, H., Schenk, H., and Baumgartel, H. (1980). Chem. Phys. 46,251. Ogram, G. L., Chang, J.-S., and Hobson, R. M. (1980). Phys. Rev. A 21,982. Oka, T. (1980). Phys. Rev. Lett. 45,531. Olson, R. E. (1972). J. Chem. Phys. 56,2979. Olson, R. E. (1977). Combust. Flame 30,243. OMalley, T. F. (1965). Phys. Rev. 137, 1668. OMalley, T. F. (1966). Phys. Rev. 150, 14. O’Malley, T. F. (1969). Phys. Rev. 185, 101. O’Malley, T. F., and Taylor, H. S . (1968). Phys. Rev. 176, 207. Parker, D. H., and Avouris, P. (1979). J. Chem. Phys. 71, 1241. Parker, D. H., and El-Sayed, M. A. (1979). Chem. Phys. 42,379. Parks, E. K., Hansen, N. J., and Wexler, S. (1973a). J. Chem. Phys. 58,5489. Parks, E. K., Wagner, A., and Wexler, S. (1973b). J. Chem. Phys. 58, 5502. Parks, E. K., Kuhry, J. G., and Wexler, S. (1977). J. Chem. Phys. 67,3014. Parr, A. C., and Elder, F. A. (1968). J. Chem. Phys. 49, 2659. Parr, A. C.. Jason, A. J., and Stockbaner, R. (1978). Int. J. Mass. Spectrom. Ion Phys. 26, 23. Patterson, T. A,, Hotop, H., Kasdan, A,, Norcross, D. W., and Lineberger, W. C. (1974). Phys. Rev. Lett. 32, 189. Patterson, T. A,, Siegel, M. W., and Fite, W. L. (1978). J. Chem. Phys. 69,2163. Pearson, P. K., Schaefer, H. F., Richardson, J. H., Stephenson, L. M., and Brauman, J. I. (1974). J. Am. Chem. SOC.%, 6778. Peart, B., and Dolder, K. T. (1971). J. Phys. 84, 1496. Peart, B., and Dolder, K. T. (1972a). J. Phys. B 5, 860. Peart, B., and Dolder, K. T. (1972b). J. Phys. B 5, 1554. Peart, B., and Dolder, K. T. (1973a). J. Phys. B 6,2409. Peart, B., and Dolder, K. T. (1973b). J. Phys. B 6, L359. Peart, B., and Dolder, K. T. (1974a). J . Phys. B 7,236. Peart, B., and Dolder. K. T. (1974b). J. Phys. B 7, 1567. Peart, B., and Dolder, K. T. (1974). J , Phys. B 7, 1948. Peart, B., Grey, R., and Dolder, K. T. (1976a). J. Phys. B 9, L369. Peart, B., Grey, R., and Dolder, K. T. (1976b). J . Phys. B 9, L373. Peatman, W. B. (1976a). J. Chem. Phys. 64,4093. Peatman, W. B. (1976b). J . Chem. Phys. 64,4368. Pechukas, P., and Light, J. C. (1965). 1.Chem. Phys. 42,3281. Person, J. C., Watkins, R. L., and Howard, D. L. (1976). J. Phys. B 9, 181 1. Peterson, J. R., Aberth, W. H., Mosele J. T., and Sheridan, J. R. (1971). Phys. Rev. A 3, 1651. Phaneuf, R. A,, Crandall, D. H., and &mn, G. H. (1975). Phys. Reti. A 11, 528. Plummer, E. W., Gustafsson, T., Gudat, W., and Eastman, D. E. (1977). Phys. Rev. A 15,2339. Polanyi, M. (1932). “Atomic Reaction$.” Williams & Norgate, London. Popp, H. P. (1975). Phys. Rep. 16, 169.
140
R. STEPHEN BERRY A N D SYDNEY LEACH
Pradhan, A. K., and Saraph, H. E. (1977). J . Phys. B 10,3365. Quack, M. (1977). Mol. Phys. 34,477. Quack, M., and Troe, J. (1974). Ber. Bwsenges. Phys. Chem. 78,240. Quack, M., and Troe, J. (1975a). Eer. Bunsenges. Phys. Chem. 79, 170. Quack, M., and Troe, J. (1975b). Ber. Bunsenges. Phys. Chem. 79,469. Rackwitz, R., Feldmann, D., Kaiser, H. J., and Heinicke, E. (1977). Z. Naturforsch. A 32a, 594. Raoult, M. (1980). These 3’ cycle, UniversitC Paris-Sud, Orsay. Raoult, M., and Jungen, C. (1981). J . Chem. Phys. 79,3388. Raoult, M., Jungen, C., and Dill, D. (1980). J. Chem. Phys. 77,599. Rapp, D., and Francis, W. E. (1962). J. Chem. Phys. 37,2631. Rapp, D., Sharp, T. E., and Briglia, D. D. (1964). Rep. LMSC6-74-64-45. Lockheed Missiles and Space Co., Palo Alto, California. Raseev, G., Giusti-Suzor, A., and Lefebvre-Brion, H. (1978). J . Phys. E 11,2735. Raseev, G., LeRouzo, H., and Lefebvre-Brion, H. (1980). J. Chem. Phys. 72, 5701. Rau, A. R. P. (1976). In “Electron and Photon Interactions with Atoms” (H. Kleinpoppen and M. R. C. McDowell, eds.), p. 141. Plenum, New York. Rau, A. R. P., and Fano, U. (1971). Phys. Rev. A 4,1751. Reck, G . P., Mathur, B. P., and Rothe, E. W. (1977). J. Chem. Phys. 66,3847. Reed, K. J., and Brauman, J. I. (1974). J. Chem. Phys. 61,4830. Reed, K. J., Zimmerman, A. H., Andersen, H. C., and Brauman, J. I. (1976). J. Chem. Phys. 64, 1368. Reilly, J. P., and Kompa, K. L. (1979). In “Laser Spectroscopy IV” (H. Walther and K. W. Rothe, eds.), p. 631. Springer-Verlag, Berlin and New York. Reintjes, J., Eckhardt, R. C., She, C. Y., Karangelen, N. E., Elton, R. C., and Andrews, R. A. (1976). Phys. Rev. Lett. 37, 1540. Reintjes, J., She, C. Y., Eckhardt, R. C., Karangelen, N. E., Elton, R. C., and Andrews, R. A. (1977). Appl. Phys. Lett. 30,480. Rescigno, T. N., Bender, C. F., McKoy, B. V., and Langhoff, P. W. (1978). J. Phys. E 11,2735. Rescigno, T. N., McKoy, V., and Schneider, B., eds. (1979). “Electron-Molecule and PhotonMolecule Collisions.” Plenum, New York. Rice, 0. K., and Ramsperger, H. C. (1927). J. Am. Chem. SOC.49, 1617. Richardson, J. H., Stephenson, L. M., and Brauman, J. 1. (1973). J . Chem. Phys. 59,5068. Richardson, J. H., Stephenson, L. M., and Brauman, J. I. (1974). Chem, Phys. Lett. 25,318. Richardson, J. H., Stephenson, L. M., and Brauman, J. I. (1975). J. Am. Chem. SOC.97, 1160. Risley, J. S . (1977). Phys. Rev. A 16, 2346. Ritchie, B. (1975). J. Chem. Phys. 63, 1351. Rockwood, S. D., Reilly, J., Hohla, K., and Kompa, K. L. (1979). Opt. Commun. 28, 175. Rogers, W. A., and Biondi, M. A. (1964). Phys. Rev. 134, A1215. Rohr, K. (1978). J. Phys. B 11, 1849. Rol, P. K., and Entemann, E. A. (1968). J . Chem. Phys. 49, 1430. Roncin, J. Y., Damany, H., and Jungen, C. (1974). Vac. Ultraviolet Radial. Phys., Proc. Int. Con$, 41h, 1974 p. 52. Rosenstock, H. M. (1968). Adv. Mass. Spectrom. 4, 523. Rosenstock, H. M. (1976). Int. J. Mass Spectrom. Ion Phys. 20, 139. Rosenstock, H. M., Wallenstein, M. B., Wahrhaftig, A. L., and Eyring, H. (1952). Proc. Natl. Acad. Sci. U S A . 38,667. Rosenstock, H. M., Stockbauer, R., and Parr, A. C. (1980). J . Chem. Phy.7. 77. 745. Rothe, E. W., Mathur, B. P., and Reck, G. P. (1976). J . Chem. Phys. 65,2912. Rothe, E. W., Mathur, B. P., and Reck, G. P. (1978). Chem. Phys. Lett. 53,74.
ELEMENTARY ATTACHMENT AND DETACHMENT PROCESSES
141
Samson, J. A. R.(1966). Ado. At. Mol. Phys. 2, 192. Samson, J. A. R.(1967). “Techniques of Vacuum Ultraviolet Spectroscopy.” Wiley, New York. Samson, J. A. R.(1976). Phys. Lett. 28C, 303. Samson, J. A. R..(1980). In “Handbach der Physik” (W. Mehlhorn, ed.), Vol. 31 (in press). Springer-Verlag, Berlin and New York. Samson, J. A. R.,and Gardner, J. L. (1972). J . Opt. SOC.Am. 62, 856. Samson, J. A. R.,and Gardner, J. L. (1973a). J. Chem. Phys. 58,3771. Samson, J. A. R.,and Gardner, J. L. (1973b). Phys. Rev. Leu. 31, 1327. Samson, J. A. R.,and Haddad, G. N.(1974). Phys. Rev. Lett. 33,875. Samson, J. A. R.,and Petrosky, V. E. (1974). J. Electron Spectrosc. Relat. Phenom. 3,461. Samson, J. A. R.,Gardner, J. L., and Mentall, J. E. (1972). J. Geophys. Res. 77, 5560. Schmeltekopf, A. L., Fehsenfeld, F. C., and Ferguson, E. E. (1967). Astrophys. J. (Lett.) 148, L155.
Schmidt, V.,Sandner, N., Kuntzemuller, H., Dhez, P., Wuilleumier, F., and Kallne, E. (1976). Phys. Rev. A 13, 1748. Schneider, B. I., and Brau, C. A. (1976). Appl. Phys. Lett. 33,569. Schneider, B. I., LeDourneuf, M., and Burke, P. G. (1979). J. Phys. E 12, L365. Schulz, G. J. (1959). Phys. Rev. 113,816. Schulz, G. J. (1961). J . Chem. Phys. 34, 1778. Schulz, G. J. (1 962). Phys. Rev. 128, 178. Schulz, G. J. (1973a). Rev. Mod. Phys. 45,378. Schulz, G. J. (1973b). Rev. Mod. Phys. 45,423. Schulz, G. J., and Asundi, R.K. (1965). Phys. Rev. Lett. 15, 946. Schulz, G. J., and Asundi, R.K. (1967). Phys. Rev. 158,25. Scott, T. W., Twvarowski, A. J., and Albrecht, A. C. (1979). Chem. Phys. Lett. 62,295. Seaton, M. J. (1966). Proc. Phys. Soc., London 88,801. Seaton, M. J. (1 974). J . Phys. E 7, 18 17. Seaton, M. J. (1978). J. Phys. E 11,4067. Sell, J. A., and Kuppermann, A. (1979). J . Chem. Phys. 71,4703. Sharp, T. E. (1971). Ar. Data 2, 119. Shaw, G. B., and Berry, R.S. (1972). J . Chem. Phys. 56,5808. Sheen, S . H., Dimoplon, G., Parks, E. K., and Wexler, S. (1978). J. Chem. Phys. 68,4950. Shiu, Y.-J., and Biondi, M. A. (1977). Phys. Rev. A 16, 1817. Shiu, Y.-J., and Biondi, M. A. (1978). Phys. Reri. A 17, 868. Shiu, Y.J., Biondi, M. A., and Sipler, D. Y. (1977). Phys. Rev. A 15,494. Shy, J. T., Farley, J. W., Lamb, W. E., Jr., and Wing, W. H. (1980). Phys. Rev. Lett. 45, 535. Sichel, J. M. (1970). Mol. Phys. 18, 95. Sides, G. D., Tierman, T. 0.. and Hanrahan, R.J. (1976). J . Chem. Phys. 65, 1966. Siegel, M. W., Celotta, R.J., Hall, J. L.,Levine, J., and Bennett, R.A. (1972). Phys. Rev. A 6, 607.
Silberstein, J., and Levine, R.D. (1980). Chem. Phys. 74,6. Sinnott, G., and Beaty, E. C. (1971). Proc. Inr. Con$ Electron. At. Collisions, 7th, 1971 Abstracts, p, 176. Slater, J., Read, F. H., Novick, S. E., and Lineberger, W. C. (1978). Phys. Rev. A 17,201. Smalley, R. E., Wharton, L., and Levy, D. H. (1975). J. Chem. Phys. 63,4977. Smalley, R.E., Wharton, L., and Levy, D. H. (1977). Arc. Chem. Res. 10, 139. Smirnov, B. M. (1977). Sou. Phys.-Usp. (Enyl. Transf.)20, 119. Smith, A. L. (1970). Phil. Trans. R. SOC.London. Ser. A 268, 169. Smith, B. T., Edwards, W. R., 111, Doverspike, L. D., and Champion, R.L. (1978). Phys. Rev. A 1% 945.
142
R. STEPHEN BERRY AND SYDNEY LEACH
Smith, D., and Church, M. J. (1976). Int. J. Mass. Spectrom. Ion Phys. 19, 185. Smith, D., Church, M. J., and Miller, T. M. (1978a). J. Chem. Phys. 68, 1224. Smith, D., Adams, N. G., and Church, M. J. (1978b). J . Phys. B 11,4041. Smith, G. P., and Lee, L. C. (1979). J. Chem. Phys. 71,2323. Smith, G . P., Lee, L. C., and Moseley, J. T. (1979a). J. Chem. Phys. 71,4034. Smith, G . P., Lee, L. C., and Cosby, P. C. (1979b). J. Chem. Phys. 71,4464. Smith, L. M., and Branscomb, S. J. (1955). Phys. Rev. 99, 1657A. Smith, S. J., and Burch, D. S. (1959). Phys. Rev. 116, 1125. Smyth, K. C., and Braurnan, J. I. (1972a). J. Chem. Phys. 56, 1132. Smyth, K. C., and Brauman, J. I. (1972b). J. Chem. Phys. 56,4620. Smyth, K. C., and Brauman, J. I. (1972~).J. Chem. Phys. 56, 5993. Solomon, P. M., and Klemperer, W. (1972). Astrophys. J. 178, 389. Spence, D., and Burrow, P. D. (1979). J. Phys. B 12, L179. Spence, D., and Noguchi, T. (1975). J. Chem. Phys. 63,505. Starace, A. F. (1976). In “Photoionization and Other Probes of Many Electron Interactions” (F. J. Wuilleumier, ed.), p. 395. Plenum, New York. Starace, A. F. (1980a). Appl. Opt. 19,4051. Starace, A. F. (1980b). In “Handbuch der Physik” Vol. 31, (W. Mehlhorn, ed.), Vol. 31, p. Springer-Verlag, Berlin and New York (in press). Starace, A. F., and Armstrong, L. A., Jr. (1976). Phys. Rev. A 13, 1850. Starace, A. F., and Shahabi, S. (1980). Phys. Scripra 21,368. Starace, A. F., Rast, R. H., and Manson, S. T. (1977). Phys. Rev. Letr. 38, 1522. Steiner, B. (1968). J. Chem. Phys. 49, 5097. Steiner, B., Giese, C. F., and Inghram, M. G. (1961). J . Chem. Phys. 34, 189. Stevefelt, J., Boulmer, J., and Delpech, J. F. (1975). Phys. Rev. A 12, 1246. Stewart, A. L., and Webb, T. G. (1963). Proc. Phys. Soc., London 82,532. Stockbauer, R. (1979). J . Chem. Phys. 70,2108. Stockdale, J. A. D., Compton, R. N., and Reinhardt, P. W. (1968). Phys. Rev. Lett. 21,664. Stockdale, J. A. D., Compton, R. N., and Schweinler, H. C. (1970). J. Chem. Phys. 53, 1502. Stockdale, J. A. D., Davis, F. J., Compton, R. N., and Klots, C. E. (1974). J. Chem. Phys. 60, 4279. Stockdale, J. A. D., Warmack, R. J., and Compton, R. N. (1979). Chem. Phys. Lett. 63,621. Strand, M. P.(1979). Doctoral Dissertation, University of Chicago, Chicago, Illinois. Strand, M. P., Hansen, J., Chien, R.-L., and Berry, R. S. (1978). Chem. Phys. Lett. 59,205. Strathdee, S . , and Browning, R. (1976). J. Phys. E9, L505. Sugiura, T., and Arakawa, K. (1970). Recent Dev. Mass Spectrosc., Proc. Int. Con$ Mass Spectrosc., 1969 p. 848. Sullivan, S. A., Freiser, 8 . S., and Beauchamp, J. L. (1977). Chem. Phys. Letr. 48,294. Tam, W.-C., and Wong, S. F. (1978). J. Chem. Phys. 68,5626. Tan, K. H., Brion, C. E., van der Leeuw, P. E., and van der Wiel, M. J. (1978). Chem. Phys. 29, 299. Taylor, H. S., Goldstein, E., and Segal, G. A. (1977). J. Phys. B 10,2253. Taylor, K. T., and Burke, P. G. (1976). J. Phys. B 9, L353. Thomas, L. (1974). Radio Sci. 9, 121. Thomson, J. T. (1924). Philos. Mag. [6] 47, 337. Torop, L., Morton, J., and West, J. B. (1976). 1.Phys. B9,2035. Trainor, D. W. (1978). Chem. Phys. Lett. 55, 361. Trainor, D. W., and Boness, M. J. W. (1978). Appl. Phys. Lett. 32, 604. Tronc, M., Fiquet-Fayard, F., Schermann, C., and Hall, R. I. (1977). J . Phys. B 10,305. Tronc, M., Hall, R. I., Schermann, C., and Taylor, H. S. (1979). J. Phys. B 12, L279.
ELEMENTARY ATTACHMENT AND DETACHMENT PROCESSES
143
Truby, F. L. (1969). Phys. Rev. 188,508. Truby, F. L. (1971). Phys. Rev. A 4,613. Tseng, H. K., Pratt, R. H., Yu,S., and Ron, A. (1978). Phys. Rev. A 17, 1061. Tully, F. P., Lee, Y. T., and Berry, R. $. (1971). Chem. Phys. Lett. 9, 80. Tully, J. C., Berry, R. S., and Dalton, B.J. (1968). Phys. Rev. 176,95. Turner, R. E., Vaida, V., Molini, C. A., Berg, J. O., and Parker, D. H. (1978). Chem. Phys. 28, 47. Utterback, N. G., and van Zyl, B. (1978). J. Chem. Phys. 68,2742. Vaida, V., Robin, M. B., and Kuebler, N. A. (1978). Chem. Phys. Letr. 58, 557. Van Brunt, R. J., and Kieffer, L. J. (1970). Phys. Rev. A 2, 1899. Van Brunt, R. J., and Kieffer, L. J. (1974). Phys. Rev. A 10, 1633. van den Bos, J. (1970). J. Chem. Phys. 52,3254. van den Bos, J. (1972). J. Chem. Phys. 57,3586. van der Wiel, M. J. (1980). J . Chim. Phys. 77, 647. van der Wiel, M. J., and Granneman, E.H. (1977). Comments At. Mol. Phys. 7,59. van der Wiel, M. J., Stoll, W., Hamnett, A,, and Brion, C. E. (1976). Chem. Phys. Lett. 37,240. Vaz Pires, M., Galloy, C., and LorqueG J. C. (1978). J. Chem. Phys. 69, 3242. Villarejo, D. (1968). Phys. Rev. 167, 17. Vogler, M., and Dunn, G. H. (1975). Phys. Rev. A 11, 1983. Wadehra, J. M., and Bardsley, J. N. (1978). Appl. Phys. Lett. 32, 76. Walker, T. E. H. (1973). Chem. Phys. Lett. 19,493. Walker, T. E. H., and Waber, J. T. (1973). J . Phys. B 6,1165. Walker, T. E. H., and Waber, J. T. (1974). J. Phys. B 7, 674. Wallace, S., Dill, D., and Dehmer, J. L. (1979). J . Phys. B 12, L417. Walls, F. L., and Dunn, G. H. (1974). J . Geophys. Res. 79, 1911. Wanneberg, B., Gelius, U., and Siegbahn, K. (1974). J. Phys. E7, 149. Warmack, R. J., Stockdale, J. A. D., aqd Compton, R. N. (1978). J . Chem. Phys. 68,916. Warneck, P. (1969). Chem. Phys. Lett. 3, 532. Watson, W. D. (1975). In “Atomic and Molecular Physics and the Interstellar Matter” (R. Balian, P. Encrenaz, and J. Lequeux, eds.), p. 177. North-Holland Publ., Amsterdam. Watson, W. S., and Stewart, D. T. (1974). J. Phys. B7, L466. Weiner, J., Peatman, W. B., and Berry, R. S. (1971). Phys. Rev. A 4, 1825. Weiss, M. J., Hsieh, T.-C., and MeiseIs, G. G. (1979). J. Chem. Phys. 71, 567. Wells, G. J., Reck, G. P., and Rothe, E. W. (1980). J. Chem. Phys. 73, 1280. Wendin, G. (1976). J . Phys. B 10, L297. Wendin, G., and Starace, A. F. (1978). J. Phys. E 11,4119. West, J. B., and Marr, G. V. (1976). Pwc. R. SOC.London, Ser. A 349, 397. West, J. B., Parr, A. C., Cole, B. E., Ederer, D. L., Stockbauer, R., and Dehmer, J. L. (1980). J. Phys. B 13, L105. West, W. P., Foltz, G. W., Dunning, F. B., Latimer, C. S., and Stebbings, R. F. (1976). Phys. Rev. Lett. 36, 854. White, R. M., Carlson, T. A., and Spears, D. P. (1974). J. Electron. Spectrosc. Relat. Phenom. 3, 59. Wight, G. R., van der Wiel, M. J., and Brion, C. E. (1977). J. Phys. B 10, 1863. Wigner, E. P. (1948). Phys. Rev. 73, 1002. Wildt, R. (1939). Astrophys. J. 89, 295. Williamson, A. D., and Compton, R. I$.(1979). Chem. Phys. Lett. 62,295. Williamson, A. D., Compton, R. N., and Eland, J. H.D. (1979). J. Chem. Phys. 70, 590. Woodin, R. L., Bomse, D. S., and Beauchamp, J. L. (1979). In “Chemical and Biochemical Applications of Lasers” (C. B. Moore, ed.), Vol. 4, p. 355. Academic Press, New York.
144
R. STEPHEN BERRY AND SYDNEY LEACH
Woodruff, P. R., and Marr, G. V. (1977). Proc. R. SOC.London, Ser. A 358,87. Woodward, B. W. (1970). Doctoral Dissertation, The University of Colorado, JILA Report 102. Wuilleumier, F. J. (1973). Ado. X-Ray Anal. 16, 63. Wuilleumier, F. J., ed. (1976). “Photnionization and Other Probes of Many-Electron Interactions.” Plenum, New York. Wuilleumier, F. J. (1980). In “Electronic and Atomic Collisions” (N. Oda and K. Takayanagi, eds.), p. 55. North-Holland Publ., Amsterdam. Wuilleumier, F. J., and Krause, M. 0.(1974). Phys. Rev. A 10,242. Wynn, M. J., Martin, J. D., and Bailey, T. L. (1970). J. Chem. Phys. 52, 191. Yablonovitch, E. (1973). Appl. Phys. Lett. 23, 121. Yang, C. N. (1948). Phys. Rev. 74, 764. Young, R. A,, and St. John, G. (1966). Phys. Rev. 152,25. Zaidel’, A. N., and Shreider, E. Ya. (1970). “Vacuum Ultraviolet Spectroscopy.” Ann ArborHumphrey Sci. Publ., Ann Arbor, Michigan. Zakheim, D. S., and Johnson, P. M. (1978). J. Chem. Phys. 68,3644. Zakheim, D. S . , and Johnson, P. M. (1980). Chem. Phys. 46,263. Zandee, L., and Bernstein, R. B. (1979a). J . Chem. Phys. 70,2574. Zandee, L., and Bernstein, R. B. (1979b). J. Chem. Phys. 71, 1359. Zandee, L., Bernstein, R. B., and Lichtin, D. A. (1978). J . Chem. Phys. 69,3427. Zare, R. N., and Herschbach, D. R. (1965). J . Mol. Speccrosc. 15, 462. Zhdanov, V. P. (1980). J. Phys. E 13, L311. Zhdanov, V. P., and Chibisov, M. I. (1978). Sou. Phys.-JETP (Enel. Transl.) 41,38. Ziesel, J. P., Nenner, I., and Schulz, G. J. (1975). J. Chem. Phys. 63, 1943. Zimmerman, A. H., and Brauman, J. I. (1977a). J . Am. Chem. SOC.99,3565. Zimmerman, A. H., and Brauman, J. I. (1977b). J . Chem. Phys. 66,5823. Zittel, P. F., and Lineberger, W. C. (1976). J . Chem. Phys. 65, 1236. Zittel, P. F., Ellison, G. B., O’Neil, S. V., Herbst, E., Lineberger, W. 2 ,and Reinhardt, W. P. (1976). J. Am. Chem. SOC.98,3731. Zwier, T. S., Maricq, M. M., Simpson, C. S. J. M., Bierbaum, V. M., Ellison, G. B., and Leone, S. R. (1980). Phys. Rev. Leu. 44,1050.
ADVANCES IN ELECTRONICS AND ELECTRON PHYSICS. VOL. 57
Fiber Optics in Local Area Network Applications DELON C. HANSON Hewletr-Packard Company Optoelecfronic Division Palo Alto, California
I. System Requirements and Trends A. Introduction . . . . . . . . . . . . . . ............................ B. Transmission-MediumConsiderations . . . . . . . C. Local Area Network Topologies and Trends .............................. D. Standards and Performance Limits of the Transmission Medium . . . . . . . . . . . . . ................
145 149 154 157
.......... C. Connector Design.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184 111. Terminal Device and System Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189 189 A. Optical Source and Transmitter Circuit Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . B. Optical Detector and Receiver Considerations. . . . . . . . 203 213 C. System Design Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225
I. SYSTEM REQUIREMENTS AND TRENDS
A . Introduction In the past few years, major progress has been made in the design of fiber optic data-link components and subsystems. Much of the early effort was applied to the development of long-distance, point-to-point, digital telecommunications (DT) hardware. This has resulted in several major planned installations on routes where Aber optics is now cost competitive. In contrast to the relatively controlled environment and structured communication hierachy of DT systems, local data communication (LDC) links encompass a very diverse set of potential applications. This results from a broad spectrum of data rates, equipment interface requirements, link lengths, and a wide range of packaging and environmental conditions. With this diversity, as actual systems take shape, many of the fundamental issues have shifted from strict technological considerations to such practical issues as the physical size of compohents, availability of power-supply voltages, 145 Copyright Q 1981 hy Academic Press. Inc. All rights of reproduction tn any form reserved. ISBN 0-12-014657-6
146
DELON C . HANSON
compatibility of optical connector options, and the feasibility of nonspecialists assemblying connectors in the field. In addition to individual data-link considerations, local area networks (LANs) are rapidly evolving to meet the interconnect requirements of lower cost digital terminal hardware which is distributed within a local site. Hence, in this article LDC will refer to performance, cost, and technology issues for individual links. This will provide a direct comparison with pointto-point DT links; LAN discussions will relate to the interconnection of links to form a network configuration. The purpose of this article is to bridge the gap between system requirements and technology in order to arrive at a reasonable understanding of the cost-performance trade-offs for fiber optics in LDC and LANs. It may yet be too early to determine the ultimate impact of fiber optics on evolving communication equipment standards; however, trends are becoming apparent.
B. Transmission-Medium Considerations Quite often potential users of fiber optic data links do not have a clear understanding of the relative merits of fiber optic links as compared to other transmission media, e.g., twisted-wire pair or coaxial cable. This situation is particularly true when optocouplers (which contain photon-coupled optical sources and detectors in a single package) are used to provide some degree of the isolation properties which are inherent with optical fiber links. Figure 1 shows a schematic drawing ( 1 ) of the world’s shortest optically coupled link, i.e., an optocoupler built in a dual in-line package having a direct optically coupled path between the source and the detector. The major reasons for using optocouplers in conjunction with metallic links is to suppress common mode voltages which are induced into the cable by the ambient environment and to provide a coupling device between parts of a system which are at different electrical potentials. As Fig. 1 indicates, internal capacitance C&,, induces a parasitic common mode path between the source and the detector and C , , C2 induce parasitic input-output capacitance. Utilizing an integrated detector-amplifier in an optocoupler (discussed in Section III,B,3,a) significantly reduces this common mode capacitance. In addition, if a short fiber stub is used to separate and optically couple the source to the detector in the same package, the input-output capacitance approaches that of a fiber optic link. Optical fiber and wire have inherently different transmission-bandwidth limitation mechanisms. In the case of optical fiber, there is great latitude in controlling the fiber refractive index profile (see Fig. 9) so that multimodepath-propagation delay distortion can be effectively eliminated. The product of the optical fiber 3-dB transmission bandwidth and its effective length [see
FIBER OPTICS IN LOCAL AREA NETWORKS
147
---_L f_ _ _ _ _
Film Shield
Dual In-Line Package
Y
Four-Pin Emitter Lead Frame
I
fv-
GaAsP LED Emitter (Underneath Lead Frame)
Sili det Am Four-Pin Detector Lead Frame
FIG.1. Schematic drawing and cross section of dual in-line optocoupler showing the internal shielding designed to reduce parasitic capacitive coupling ( I ) .
Eq. (7)] can be in the > 1 GHz-km range (2).Since fiber is a dielectric medium having a dielectric constant similar to that of the dielectric between the inner and outer conductors in metallic cable, the propagation delay of the initial propagating wavefront is essentially identical in both optical fiber and coaxial cable. However, for metallic links, skin effect loss increases as the square root of frequency (3).Hence, the step response of a skin-effect-limited cable is non-Gaussian, i.e., it rises slowly for a short time after the incidence of the initial propagating wavefront to a small amplitude, then increases rapidly to a much larger amplitude, and then very slowly to its final value. As a result, the 10-90x response time of a skin-effect-limited cable is about 30 times longer than the 0-50% response time (4). Due to this effect, metallic cable 3-dB bandwidth is inverSely proportional to the square of the link length, rather than being inversely proportional to the effective link length, as in the optical fiber case.
148
DELON C. HANSON
Figure 2 shows a comparison of attenuation versus modulation bandwidth for coaxial cable having various diameters and a relatively low-loss optical fiber cable having the same diameter as the smallest coaxial cable. Skin-effect loss governs the slope of the coaxial cable attenuation curves. As noted in Section II,B,l, the typical outer diameter D of LDC fiber optic cable is 2.5 mm. This is equivalent to the diameter of the RG-l79B/U cable, but there is an order of magnitude difference in attenuation even for a moderate bandwidth of 10 MHz. The coaxial cable diameter must be increased to 23 mm (RG-219/U) to achieve an equivalent lO-dB/km attenuation at 10-MHz modulation bandwidth.
149
FIBER OPTICS IN LOCAL AREA NETWORKS
WIRE
FIBER OPTIC
BANDWIDTH-LENGTH I
l
l
1
I
l
l
l
l
ISOLATION ( EM1 )
DURABILITY
FIG.3. Summary of relative merits of wire versus fiber optic cable (5).
As a result, even though optocouplers may be used with metallic cable to reduce effects of ground loops, common-mode coupling, and voltage differences between nodes, the inherent pulse distortion (or reduced bandwidth) caused by skin-effect loss in metallic cables and their susceptibility to electromagnetic noise pickup and emission are not reduced. Since it becomes more costly to compensate for both of these effects with increasing data rate, optical fiber transmission becomes increasingly more attractive with the trend toward higher speed and distributed data transmission. Figure 3 shows a summary of the relative merits of wire versus fiber optic cable (5).The rating system is a subjective assessment of the importance of the various performance factors. Cost is particularly subjective and is variable with application since there are many contributions beyond the raw cable cost which enter in. These contributions may include: special cable shielding, duct installation cost (which may be $10-20/m), and the complex terminal electronics required to compensate for cable pulse distortion and temperature variation if performance is pushed to the limit. As a result, in many cases, fiber optics is cost effective today and will become even more attractive as the data rate and link length of distributed systems increase.
C. Local Area Network Topologies and Trends
Local area networks (LANs) refer to communication capability within a building or between adjacent 'buildings on a common site. The LAN is designed to interconnect a broad spectrum of data nodes, e.g., computers,
150
DELON C. HANSON
terminals, mass storage devices, plotters, printers, and gateways to other networks within a restricted area which is typically less than 2 km in diameter. Until now, LANs have primarily used proprietary interfaces with protocols designed to solve a specific problem, or have interconnected only a local cluster of nodes via a standard interface, e.g., IEEE 488 (see Fig. 5). With the rapid expansion of lower cost digital hardware, many more nodes will exist in a local area and will require interconnection for efficient operation. The 1980s will witness a major thrust toward LAN standardization with the IEEE Computer Society spearheading this effort. Individual companies are beginning to specify multiple-user, distributed data communication equipment (6) and may create de fucto standards in the interim. Fiber optic network components must either be compatible with or compete against this movement. The objective of LAN standardization (7), is to separate the required end-to-end protocols into a prescribed communication hierarchy and to specify the interface between the respective levels. The International Standards Organization (ISO) levels of primary importance to LANs are shown in Table I. In order to successfully complete a message transfer between network nodes, there must be compatibility up through level 4. The primary emphasis of this article is on fiber optic physical hardware at level 1. The separation of the protocol levels is particularly important for incorporating a new technology, e.g., fiber optics, since if the level definitions are properly thought out, they avoid the need for changes at all levels prior to implementation. The number of LANs which have been developed or proposed is as large as the number of organizations who have considered the problem. A recent summary (8) includes more than 70 alternatives which use a spectrum of TABLE I
I S 0 DATACOMMUNICATION HIERARCHY Level designation
Level functions
4
Network transport protocol Network control protocol Link control protocol Physical (electrical, mechanical and functional description along with procedures for establishing, maintaining and disconnecting the link)
3 2 1
FIBER OPTICS IN LOCAL AREA NETWORKS
151
network topologies, transmission media, and communication protocols. These topologies can be summarized by four basic generic types, as shown in Fig.4 and summarized in Table 11. For the fully connected network, shown in Fig. 4a, any two nodes which must communicate have a dedjcated channel between them. In the case where all N nodes communicate, (N)x (N - 1)/2 duplex links must exist. Each link may operate over a different medium, at different data rates and with different control protocols. Respective nodes are addressed through polling. Since each link has permanently dedicated hardware and there is no reallocation of transmission paths, considerable total communication capability and flexibility is wasted. It is difficult to expand the network since N extra duplex links are required for each new fully connected node. The perceived reliability of this network is high since breaking a link only affects one communication path. If alternate routing is incorporated, this topology offers the highest reliability. The star topology, shown in Fig. 4b, has low connectivity, since it requires only N duplex links. Nodes are interconnected through a central control
Loop Control Node
4 (C)
(d)
FIG.4. Four generic network topc/logiesfor local data communication: (a) fully connected; (b) star; (c) ring/loop; (d) bus.
TABLE I1 LOCAL AREA NETWORK P
~
R ANDSFEATIJRFS
Parameters
Network topology
Number of network links
Network protocol
Features
Link data rate
% O ( N - 1)
Polling
Node rate
Star
N
Polling
Node rate
Ring or loop (active repeaters) Distributed data bus
N
Multiplexing or contention Contention
> N.(node rate)
Fully connected
1
>(node rate)
Ease of expanding or tapping
Perceived network Ease of reliability synchronization
Difficult (many extra lines) Moderate
High
-
High
Moderate (shut down network) Easy (with coax)
Low
Easy (nodes independent) Easy
High
Difficult
FIBER OPTICS IN M C A L AREA NETWORKS
153
node. The performance features of this topology are similar to the fully connected case, but it has no redundancy and has potentially low reliability due to dependence on the central node. This network is preferred for local cluster communication. The ring or loop, in Fig. 4c, has minimum connectivity, since it requires only N simplex links. In an active repeatered ring, each node is connected to two other nodes with a desigpated direction of data flow. The distinction between a ring and loop is that a loop has a single control node (shown dashed), whereas a ring distributes the control among the various nodes. Extensive analysis and implementation of rings has been reported (9, 10). They have many desirable features for widely distributed network nodes. Rings and loops utilize various forms of time division multiplexing (TDM) in which particular time slots of an information field (which is passing around the loop) are either allocated to each node permanently or messages are inserted into time slots on a dynamic contention basis. Since all nodes are interconnected by a common data path, TDM requires that the link data rate be more than N times the node rate, in order to include the framing and error control required to operate the network. With active repeaters at each node, it is relatively straightforward to extend a ring network. However, the need to shut down the ring while adding a node is a distinct disadvantage. Due to the fact that all information flows through each node, the perceived network reliability is low since a “down” node or broken cable may shut down the entire network. Methods (11) of building in redundancy or of achieving a “soft”failure procedure are of major importance. The ring has a major advantage for high data rate TDM systems because network throughput is not limited by propagation delay between the network’s most remote nodes, since the protocol is not based on dynamic optical contention on the network between nodes competing for control. The distributed bus network, shown in Fig. 4d, is the topology traditionally thought of when wire or coaxial LANs are used, since low-perturbation electrical taps onto the network are relatively straightforward. Ethernet (12)is a well-documented version of this topology using CATV-type coaxial cable and taps. The network protocol incorporates dynamic contention by the individual nodes to gain control of the network. Certain rules of behavior (13), e.g., “listen before talking” (by sensing the carrier) and “listen while talking” (by comparing injected data with network data) are incorporated to increase network utilization efficiency. From a coaxial hardware standpoint, it is relatively simple to “tap on” additional nodes without disturbing the network. The perceived network reliability is high due to the totally passive transmission medium. Extensive work has been done to mathematically model (13) and measure (14) the multiple-access Ethernet. Operating at 2.94 Mb/sec with 120 nodes distrib-
154
DELON C. HANSON
uted over a 600-m coaxial cable, the Xerox results (14) demonstrated up to 90% network utilization efficiencyeven under high offered load conditions. In contrast to the baseband Ethernet coaxial contention network, broadband coaxial networks are also being developed using CATV coaxial hardware (15).This approach utilizes distributed control and packet network protocols, derived from public packet networks (CCITT X.28), to combine voice, video, and data transmission on a single coaxial cable network. From a bandwidth standpoint, thousands of low-speed terminals can be supported simultaneously or can be intermixed with other communication requirements. This article is primarily concerned with the physical link design trade-offs at level 1 (Table I) to provide a perspective for fiber optic network development. McQuillan (16) has stated that networks have traditionally been designed backwards, i.e., starting from technology and working toward user needs. The higher level protocols (to allow equipment manufactured by different vendors to communicate) have come last and require one to two orders of magnitude more man-years of work to resolve than the hardware itself. Why then consider fiber optics for LANs when the transmission capability of coaxial cable has barely been exploited for even moderate bandwidth LANs? The answer to this question is dependent on the application. Even though it is possible, in principle, to solve any problem caused by transmission distortion, induced or radiated noise, common-mode or system differential voltages when using a metallic cable, the cost of the terminal hardware and required special engineering may outweigh the cost of an equivalent fiber optic alternative which provides an assured solution. The challenge for the system designer is to determine the preferred solution, based on true costs, ahead of time so that the installation does not require a rework cycle at even greater cost. D. Standards and Performance Limits of’ the Transmission Medium Figure 5 shows a comparison of projected data rate versus distance limits of various level 1 communications standards (17).The lower portion of this figure shows four widely used wire-based standards. Of these, RS-232, RS-422, and RS-423 are serial data links, whereas IEEE 488 incorporates eight parallel data lines and eight control lines in a byte serial data bus protocol. The oldest and most widely used standard (RS-232) couples the communication level specifications and has low performance, but is very cost effective when it satisfies the transmission requirements.
FIBER OPTICS IN LOCAL AREA NETWORKS LIN ME
LOCAL DATA COMMUNICATIONS
1
2nd GENERATION
155
DIGITAL TELECOMMUN -
1' LEVEL 1 DATA TRANSMISSION OPTIONS
0.1
1.0
10
LINK
100
1K
10K
lOOK
LENGTH ( m )
FIG.5. Level 1 data transmission standards and trends with respect to data rate versus link length.
Transmission performance is improved by one or two orders of magnitude by using integrated electronic interface circuits, as in the case of RS-422 and RS-423 standards. The order of magnitude performance improvement of RS-422 over RS-423 is the result of using balanced drive and detection circuits to compensate for skin-effect-induced pulse distortion in the cable. The IEEE-488 (or HP-IB) standard was originally developed for interconnecting clustered instrumentation systems but has been considerably expanded in application over the past 10 years. The maximum data rate is 1 Mbaud (MBd) over each of B data lines. Due to reflections and impedance mismatches, the allowed link length is 2 m per node or a maximum of 20 m. This data bus has recently been extended to provide a 1-km separation between instrument clusters by serializing the 16 data and control lines and utilizing a 1-km full duplex fiber optic link (18). In the region above 1 MBd per channel, the main-frame parallel data bus is typically less than 1 m long and is used to transmit very high-speed data along the back plane of a cohputer. Above 20 MBd, parasitics, impedance mismatching, and cross-talk become increasingly more serious even with
156
DELON C . HANSON
this short link length. Fiber optics provides an excellent solution for these problems but introduces an additional, potentially serious, fixed propagation delay due to the required optoelectronic transducer devices at each end of the fiber links. Digital telecommunications (DT) transmission relates to the region greater than 1 MBd- 1 km. The designation baud (one symbol per second) is often used to distinguish between the transmission rate of information (in bits/second) and the transmission rate of pulse transitions (in baud). For the designer of transmission media and terminal hardware, the baud has more meaning because it directly relates to the response time of the physical link. Thus, a transmission medium can be specified independent of how the information is coded on the line. For comparison, Table I11 shows a summary of United States-based, T-carrier digital telecommunications options which fit into this region. The repeater spacings for the various conventional transmission technology options are shown plotted in Fig. 5. Since central offices are typically spaced 4-10 km apart, it is clear that repeaters are required for the wire/coaxialbased links. It is expected that DT fiber optic links will “prove in” at greater than 20 Mb/sec due to the fact that fiber costs are dropping relative to copper and intermediate repeaters can be eliminated (19). In the local data communications (LDC) region, applications are very diverse and the established communication hierarchy of DT does not currently exist. Data rates are often limited by higher level computer software protocols rather than the transmission medium itself (19). First-generation LDC links encompass data rates from 100 Bd to 10 MBd and link lengths from 1 to 2000 m. This region includes the existing wire-medium standards described earlier and has a segment not covered by existing wire standards. With the ground swell of activity (6) among major LSI microprocessor TABLE I11 UNITED STATESDIGITAL TELECOMMUNICATIONS T-CARRIER SUMMARY
System
Data rate (Mbisec)
Voice channels
TI
1.5
24
T2
6.3
96
T3 T4
44.7 214
672 4032
Transmission-medium technology
Repeater spacing (km)
“Screened” twisted wire Digital radio (2 GHz) “Lo-cap” twisted wire Digital radio (2-6 GHz) Digital radio (6- 1 1 GHz) Air dielectric coax Digital radio (18 GHz)
1.7 221 4.5 221 2-21 1.6 4.8
FIBER OPTICS IN LOCAL AREA NETWORKS
I57
companies to dominate the coaxial-based, LAN standards in this region ( 20 MBd-km. Second-generation link requirements extend to > 100 MBd-km. The upper two curves in Figure 21 are fiber types intended for firstgeneration links utilizing relatively high NA (0.29) for A = 0.02. The stepindex case shows a calculated pulse dispersion of 50 nsec/km. In practice, the dispersion is less due to the more rapid attenuation of higher-order modes in the cable. The plot for NA = 0.29, a = 8, is the fiber type proposed by Hanson et al. (47) for use in moderate-bandwidth LDC applications. This 0.d. and is listed for comparison fiber has a 100-pm-core/l40-ym-cladding in Table VI. With an LED linewidth of 40 nm centered at Lo = 820 nm, the composite pulse dispersion is 17.5 nsec/km for this fiber. This corresponds to a 20-MHz-km fiber bandwidth-distance product. The two intermediate curves are fiber parameters intended for use with second-generation LDC systems having data rates < 100 MBd. The NA has been reduced from 0.29 to 0.25 and u from 8 to 3 in order to achieve greater than 100 MBd-km performance with a 40-nm spectral linewidth LED at 820 nm. Note that there is not a significant pulse dispersion advantage in using a LD source with this fiber at this wavelength. As will be noted later in
192
DELON C. HANSON
100 1
LASER-4
80+60--
+LED-
10
STEP INDEX ( 01 = 00)
40--
-E
( A = 0.02, NA = 0.29)
E 20--
. 24
(y
Y
--
=8
I U
a
0
0
.o
2
-
E 100
x
+
u
z w
bl
Y
2 I
X
Lal b
1000
*
e c e I(A= 0.01, N A
o*2 0.1
t :
0.1
n
= 0.21)
I
II
1.o
10
SOURCE SPECTRAL LINE WIDTH
1
(nm)
FIG.21. Pulse spreading versus source spectral linewidth for various fiber profile parameters I,.
a, NAs, and operating wavelengths
FIBER OPTICS IN LOCAL AREA NETWORKS
193
this section, this reduction in NA and c( introduces more than 2.5-dB additional coupling loss in order to achieve the improved bandwidth. 2. LED Response Time If 100-MBd-km system performance is desired, there is not much point to specifying an LED wavelength which minimizes transmission pulse distortion unless the LED optical power can be modulated fast enough to avoid its being the bandwidth-limiting factor for the link. Figure 22 shows an equivalent circuit for LEDs used in fiber optic applications; R, is the source series resistance, c d the diffusion or recombination capacitance, C,the space charge junction capacitance, and id = Io[exp(vd/nkT)-']
(23)
where vd is the junction voltage and n w 2 for heavily doped GaAs devices. In an ideal LED, the rise time would be governed solely by the spontaneous recombination time of the carriers. In practical LEDs, however, the junction and stray capacitance delay the arrival time of carriers and thus both factors contribute to the overall response time. As a result, both materiallimited and circuit-limited design contributions enter in. The LED effective response time 7 is given by 'l= (cs
+ cd)/gd
(24)
where g d = aid/&),= qZo/nkT [from Eq. (23)]. The relationship between the optical output power from an LED with constant current drive and the modulation frequency (63) is given by
P(d =po/p
+ (04 3 112 2
(25)
where Po is the optical power at zero modulation frequency. To increase the modulation rate, 7 can be reduced by increasing the active-layer doping
FIG.22, LED equivalent circuit.
194
DELON C. HANSON
lo3
N
X
-
E X
P
102
I
5
n
z
d m
DOPING DENSITY ( G e ) , c ~ n - ~ FIG.23. DH Burrus-type LED bandwidth and effective carrier lifetime versus active-layer doping density (63).
level or by decreasing the thickness of the active layer at lower doping levels, as discussed by Lee and Dentai (63)and shown in Fig. 23. Unfortunately, for system designers interested in 100-MBd performance, reducing T results in a proportional reduction (6.3)in output power Po, as shown in Fig. 24. Thus, in addition to the more than 2.5-dB coupling-loss penalty described in the previous section (due to increasing the fiber bandwidth from 20 to 100 MHz-km), reducing the LED response time from 15 to 5 nsec for operation at 100 MBd reduces the optical output power by an additional 4.8 dB. 3. LED Design and Fiber-Coupling Eficiency
The objective of LED device design is to maximize the conversion of LED drive current into optical power coupled into steady-state fiber modes. The starting point for this is the LED internal quantum conversion efficiency. Another objective is to create an exit radiation pattern which couples effectively into the acceptance cone of fibers of interest. Device design also has significant implications on junction temperature, heat-sinking capability, and the ability to easily package the device with a well-designed optical port.
195
FIBER OPTICS IN LOCAL AREA NETWORKS
-- 400
30
- __ -E
3
w
3
, \
DIAMETER = 50pm
\
--200 --loo
0 0 d I-1 * a l o5: :
I
a
2.-
‘\t.
0
1-
- -50
!
1
1
I
--20
I
of band-
The source comparison summary in Table VIII lists three basic LED types, i.e., surface emitters (64),etched well (Burrus) surface emitters (65) and edge or stripe emitters (66). The considerations described in Sections III,A,l and III,A,2 apply to eqch of these LED types, independent of device configuration. Devices of each type, designed for operation in the 800-850 nm range, are shown in Figs. 25,26, and 27, respectively. The spherical lens in Fig. 25 could, in general, be aspherical or cylindrical in shape. These structures can be described as an “epitaxial layer cake.” It is evident from these figures that this is an apt description. Multiple layers of dissimilar semiconductors having different thicknesses and doping levels are needed for efficient operation in order to define the operating wavelength, confine injected electrons and holes in an active layer, and confine the optical power generated by the recombination of these carriers. The active region is confined to a small physical area (preferably smaller than the fiber-core area) by the contact area restriction and the lateral resistance of the epitaxial layers. Junctions between dissimibr semiconductors with different energy gaps are called heterojunctions. With respect to Figs. 25 and 27, the relatively
196
DELON C. HANSON
SPHERE LENS Zn DIFFUSED LAYER
1
I
FIG.25. Surface-emitting GaAlAs LED (641.
highly doped aluminum layers, e.g., Alo.3and Alo.4 for 30 or 40% aluminum concentration, provide optical confinement since the added aluminum content reduces the refractive index and traps the optical radiation, just as in the case of an optical fiber illustrated in Fig. 9. This heterostructure also provides carrier confinement because of the energy barriers which are formed as a result of the relative energy gaps. Chin et al. (67) have theoretically and experimentally compared the performance of single-heterostructure (SH) and double-heterostructure (DH) LEDs for use in optical data links. When interfacing with high numerical aperture (NA = 0.36) fibers desired for LDC applications, they concluded that the D H LEDs launch at least eight times more optical power into a fiber than a similarly designed SH LED. This is due to the fact that for SH LEDs the active layer must be a compromise between the need for current confinement and the resultant undesired increase in nonradiative recombination at the contact. The active layer in a SH device (67)must be doped 100times more heavily than a DH device, with a resultant factor of two reduction in efficiency. D H LEDs of interest for fiber optic applications have internal quantum efficiency > 50% (63). Both types of surface emitters have emission patterns which are essentially Lambertian [Z(O) = I, cos O ] with about 120" beamwidth at the halfpower points. On the contrary, the edge-emitting DH structure, shown in Fig. 27, uses partial internal reflection of the spontaneous radiation to funnel
197
FIBER OPTICS Xh’ LOCAL AREA NETWORKS
LIGHT
ETCHED “WELL”
GLASS FIBER
METAL TAB
EPOXY RESIN n-TYPE GaAs
PRIMARY LIGHT EMITTING AREA FIG.26. Burrus-type surface-emitting GaAlAs LED (65).
CONTACT-
FIG.27. High-radiance edge-emitting GaAlAs LED (66).
198
DELON C. HANSON
the emitted optical power into a beam exiting from the junction edge. As a result of the very thin active layer, e.g., 0.05 pm, which is required for efficient edge emitter operation and of a junction width of 50-80 pm, the radiation pattern is very asymmetrical, i.e., about 30" half-power angle in the vertical plane and 120" in the horizontial plane (68). The number of steady-state optical modes N which a fiber can trap was developed in Section II,A,l,a and is given by
For a perfectly aligned LED-fiber interface to an LED junction area which is smaller than the fiber-core area nu2,the power coupling efficiency qc into an optical fiber (69) is proportional to N and is given by
A plot of the dependence of coupling efficiency on the index profile parameter c( for various NA values is shown in Fig. 28. It is noted that there is 3-dB penalty in coupling efficiency for a graded index (a = 2) fiber relative to the step index (a = co)in each case. In addition, for a graded index fiber, optimal direct butt coupling between an LED source and fiber requires that the source diameter be approximately one-half the core diameter (69). A great deal of controversy exists about the relative merits of surface emitters and edge emitters for use in fiber optic systems. Based on idealized assumptions, Marcuse (70) has shown that an edge-emitting LED with an internal guiding region and the same intrinsic radiance and active layer thickness, e.g., 2.5 pm, as a surface emitter should be capable of coupling 3.5 times more power into a fiber. Botez and Ettenberg (71)and Gloge (72) state that for NA < 0.2, edge emitters have a factor of four coupling efficiency advantage over surface emitters. In addition, Botez and Ettenberg conclude that edge emitters are superior to surface-emitting LEDs for optical data rates > 20 Mb/sec and fibers with NA < 0.3. Although the collimation of the exit radiation pattern improves coupling efficiency, it creates the challenge of growing very thin, e.g., 0.05-pm, active layers. Also, there is some difficulty in packaging edge-emitting LEDs because of the need to heat sink the device effectively and yet mount it near the heat-sink edge for efficient optical fiber butt coupling to the emitting junction. The emitting junction has the advantage, however, of being located near the heat-sink surface (68). The above arguments are based on direct fiber butt coupling to the collimated beam of an edge-emitting junction in order that the fiber can
FIBER OPTICS IN LOCAL AREA NETWORKS
199
16.
14-
FIG.28. Minimum direct-sourcefiber-coupling loss versus profile parameter a and NA.
extend directly up to the junction region. The coupling efficiency advantage for butt coupling into low-NA fibers is, of course, due to the narrow, e.g., 30",emission beam in the vertical junction plane. Surface emitters on the other hand are much less affected by reabsorption and interfacial recombination (65). In the case of the etched well (Burrus)
200
DELON C . HANSON
emitter, the contact on the junction side of the heat sink may have a relatively high reflection coefficient.This allows photons emitted toward the contact to be reflected back and coupled into the fiber. This advantage also brings the disadvantage of handling a very thin, e.g., 15-pm, junction membrane during the final device process and dieattach to the heatsink. It is generally conceded that etched well emitters have the advantage of radiating about 3 times more optical power into air. The problem is that the 60" half-power emission angle of surface-emitting LEDs greatly exceeds the fiber acceptance angle (Om,, = 17.50' for NA = 0.3, Fig. 9). Considerable progress has been made recently in matching the half-power emission angle of surface emitters to the acceptance angle of fibers through the use of relatively high-index microlenses which are mounted directly on or near the emitting surface (73, 74). It is claimed (73) that improvements in coupling efficiency of up to 30 times over butt coupling can be achieved by this method. This exceeds the claimed advantage for edge emitters. Usually, engineers trained in electronics and communication systems do not have a good feel for the limiting performance factors of optical lenses. In summary, the best that can be achieved for incoherent sources, regardless of how complex the lens system may be, is that radiance be conserved (75) by the lens in translating from one surface to another. This means that the product of source diameter d and emission angle 8, can at best be transformed by the lens into the product of fiber-core diameter 2a and fiber acceptance angle Om,, without loss of optical power. A lens cannot increase the power coupled from a larger area incoherent source into a smaller area fiber. Thus, a microlens which theoretically could couple all the optical power from a surface emitter (8, = 60') into a telecommunications fiber (2a = 50 pm, NA = 0.21, Om, = 12.1') would require that the source diameter be less than 10 pm. For an LDC fiber having core diameter 2a = 100 pm, NA = 0.30, Om,, = 17.50", the source must have d < 29 pm in order to avoid exceeding the optical pattern transforming capability of even a perfect lens. These are not totally impractical junction dimensions, but they place a severe burden on the quality of the semiconductor junction material and contact since they must reliably sustain current densities in the range lo5 A/cm2. Speer and Hawkins (74) have taken the approach of magnifying the emitting junction to achieve a prescribed exit NA through the use of a microlens. This relaxes the lateral position sensitivity caused by dimensional tolerances in the optical connector and allows the possibility that larger fibers may be coupled to the optical port with increased coupling efficiency. However, this also results in a corresponding reduction in coupling efficiency
FIBER OPTICS IN LOCAL AREA NETWORKS
20 1
for smaller fibers. The small physical size of this optical component is a significant factor for achieving practical fiber-optic link hardware. Yamaoka and Masayuki (76)have taken an alternate approach to achieve improved coupling by forming a spherical lens on the end of the coupling fiber. While this does improve coupling efficiency, it requires more skill during fabrication and final assembly than using microspheres, and is not likely to be used extensively. 4. Transmitter Circuit and Package Design
With reference to Fig. 22, the circuit required to drive an LED effectively for LDC applications is relatively simple when compared to receiver circuit considerations which are discussed in Section II1,B. The primary functions of the transmitter circuit are the following: Providing the desired current level with adequate compensation to minimize optical power variation due to changes in temperature and supply voltage. Reducing the overall response time t of the LED by providing a current spike at the leading and trailing edges of the drive pulse and providing a small hold-on bias current to reduce the diffusion time constant. Possible incorporation of special circuitry to transform the time dependence of the input data stream so as to produce a data-independent average optical power level which will lead to zero dc component in the electrical spectrum at the receiver. At data rates under 10 MBd, discretely packaged devices may satisfy the above functions without serious parasitic problems by utilizing separate resistor and capacitor components mounted on a printed circuit board. However, if board space is critical, it is much more space efficient to integrate these functions onto a single custom integrated circuit, thereby achieving better parameter control as a bonus. For high-volume applications, cost may also favor transmitter circuit integration. In the range 10-100 MBd it is even more desirable to develop custom integrated circuits, since it beaomes important to reduce circuit parasitics and control the LED switching time. Above 100 MBd, laser sources are recommended although they bring with them the additional associated complexity of optical detection and feedback in order to control the drive current over temperature and with aging. A complete transmitter module containing a custom integrated circuit which incorporates all of the ~ b o v efeatures has been developed (47), as shown in Fig. 29. The integrated circuit functional diagram is shown in Fig.
202
DELON C. HANSON
30. The current drive for the LED is supplied by three current sources: I , is normally OFF, I , is normally ON, I , is a low-level hold-on current used to reduce the LED switching time. With this arrangement, the LED can be driven in either of two modes: (1) Mode select high. The LED drive current and output optical power are direct replicas of the TTL level electrical input signal, as shown in Fig. 30. (2) Mode select low. The drive current and output optical power have the time dependence shown on the middle plot in Fig. 30. This optical power waveform has a midlevel from which equal area positive and negative pulses occur at the positive and negative input data transitions, respectively. Refresh pulses having the same pulse area are generated with the same polarity as a previous data pulse if the input waveform remains in a particular state for more than = 3 p e c . If a refresh pulse occurs simultaneously with a data pulse, the data pulse overrides (as shown in Fig. 30) so that pulse jitter does not occur. This waveform has the purpose of producing zero dc and negligible low-frequency components in the electrical spectrum at the receiver so that the receiver can be effectively ac-coupled while still functioning from zero to the maximum specified data rate (47).This results from operating on the differential pulses defined at the edges of the input pulse waveform.
I
I
I
i5cm
DIELECTRIC STANDOFF
CAPACITOR
SOURCE OR DETECTOR>,
cm
L 4.34cm _ 1 FIG.29. Hewlett-Packard fiber optic module (47).
203
FIBER OPTICS IN LOCAL AREA NETWORKS
With Mode Select
’ c
OUT MODE SELECT LOW
OUT MODE SELECT
HIGH
U
n n n
U
s
n
n
-
FIG.30. Transmitter equivalent circuit and related electrical and optical waveforms ( 5 ) .
The hybrid package shown in Fig. 29 incorporates butt coupling between the optical fiber and surface or etched-well (Burrus) emitters. The optical interface from the hybrid module to the optical connector uses a precision ferrule which is an integral part of the module. The precisely positioned fiber stub is sealed in the hybrid package feedthrough port. This terminal device is a good physical example of a particular case for the general model shown in Fig. 6. B. Optical Detector and Receiver Considerations
The optical detector in a fiber optic link serves the vital function of converting the received optical power into the electrical current for the receiver preamplifer input. As such, it has several key requirements: High responsivity R (A/W) at the optical wavelengths of interest, e.g., R > 0.5 A/W; low leakage and dark current, e.g., < 1 nA; fast response time, e.g., < 3 nsec; low-voltage operation, e.g., < 5 V ; low cost; small size; and small variation with temperature.
204
DELON C . HANSON
1. Optical Detector Design
As noted in Section I,E,2, the requirement for low-voltage operation in LDC practically eliminates avalanche photodiodes (APDs) from serious consideration for all but the most stringent applications which can afford the extra physical size and cost of dc-to-dc converters and temperature stabilization circuitry. Similar practical considerations argue against using the lower fiber attenuation which is achievable in the region 1.0-1.6 pm (as shown in Fig. 8), because of the less mature technological development status and higher cost of both sources and detectors in this longer-wavelength region. This conclusion also results from the fact that the tandem insertion loss contributions of connectors, couplers and switches in distributed networks may far exceed the link-length-dependent insertion loss in most LANs. Thus, the wavelength range 800-900 nm is of primary interest for present- and next-generation LDC applications. Silicon p-i-n and p-n junction detectors provide efficient, mature, and low-cost solutions to the optical detection problem in this range. Figure 31 shows a cross-sectional drawing of p-n and p-i-n junction detectors. For the p-i-n detector, the lightly doped n region is depleted of carriers by a relatively high electric field. The electron-hole pairs formed by photorecombination are swept across the reverse-biased junction. For efficient operation, the depletion width must be sufficiently thick relative to the recombination length (l/cto)so that a large fraction of the incident optical power is absorbed and thus creates electron-hole pairs. The photodiode responsivity R (A/W) is defined by
R = ip/Po = [q(l
- r)/hv](l - edaoL)
(27)
where i, is the detected photocurrent; Po, incident optical power; q, electron charge; 1 - r, surface transmission coefficient; hv, photon energy; cia, absorption coefficient (cm- ) : L, width of depletion layer. R is a function of
'
FIG.31. Cross section of (a) p-n and (b) p-i-n photodiode detectors.
FIBER OPTICS IN LOCAL AREA NETWORKS
205
optical wavelength since the photon energy must exceed the junction energy gap in order for photorecombination to occur, and thus Q, decreases with increasing wavelength. This wavelength dependence of R is shown for a p-i-n photodetector in Fig. 32, as developed by Melchior (77). It is evident that at A0 = 850 nm, it is necessary to have L > 10 pm in order for R > 0.5 A/W. As wavelength is increased, a correspondingly greater depletion-layer width is required for a given responsivity. The speed of response of a photodiode is primarily determined by the drift velocity in the depletion region, if the photodiode is sufficiently reversebiased. When the depletion-layer electric field in silicon is above 2 x lo4 V/cm, the carrier velocity is saturated at u > 5 x lo6 cm/sec. As a result, the top scale in Fig. 32 indicates that the carrier transit time is well under 1 nsec. A significant potential advantage of p-n junction photodetectors for LDC is that they can be integrated directly with the associated amplifier and digital output circuits on a single silicon chip. In the region less than 20 MBd, where dc-coupled amplifiers can be used effectively, this represents a significant cost advantage. It may also be a significant EM1 advantage since
CARRIER TRANSIT TIME ( n s e c )
D E P L E T I O N L A Y E R W I D T H (pm) FIG.32. Absorption efficiency versus depletion layer width or carrier transit time for silicon p-i-n photodiode near the absorption band edge (771.
206
DELON C. HANSON
+j&-; tis(t)
FIG.33. Photodiode equivalent circuit.
long bonding leads between the detector and preamplifier are eliminated and thus the package does not require electromagnetic shielding. There are several significant limitations, however, for p-n junction photodetectors: To be compatible with the process for the associated silicon integrated circuits, the epitaxial thickness is typically less than 7.5 pm. Since this places an upper limit on the depletion width L, Fig. 32 shows that this results in a substantial, e.g., 3-dB, reduction in optical conversion efficiency. Since the junction capacitance is inversely proportional to depletion width L, the p-n diode junction capacitance is proportionally larger than for a p-i-n detector. This ultimately limits the upper frequency of operation. The equivalent circuit of a photodetector is shown in Fig. 33. The fact that the detected current i, is represented by a high-impedance current source is significant for preamplifier circuit design. 2. Receiver Preamplijier Design Comparison Before the detected signal from the photodetector can reestablish the input data-pulse sequence, it must be amplified by many orders of magnitude and threshold detected to distinguish the signal from noise. The total noise at the preamplifer input includes the noise associated with the signal and the photodetector. Pulse distortion associated with the originating signal or the transmission medium has the potential of creating intersymbol interference and thus increasing the probability that a signal pulse will be incorrectly identified by the threshold detector. Thermal and shot-noise sources associated with the receiver can be treated through the use of Gaussian statistics (20).If this same assumption is made for other noise sources and if intersymbol interference is neglected [it is later included in Eq. (29)], then the probability of error (P,) can bt: directly related to the signal-to-noise ratio Q.For a two-level signal, P, is very closely approximated (78) by
FIBER OPTICS IN LOCAL AREA NETWORKS 10-5,
I
207
1
SIGNAL-TO-NOISE R A T I O , Q FIG.34. Probability of error versus signal-to-noise ratio for two-level digital signals (78).
Equation (28) is shown plotted in Fig. 34. Note that P, = for Q = 6 and that P, is a very rapidly decreasing function of Q,i.e., increasing Q by 6:( reduces P by an order of magnitude. This is in sharp contrast with analog transmission systems which require signal-to-noise ratios of 40 dB and thus severely strain the capability of fiber optic subsystems (19). There have been many reviews of receiver circuit designs for accomplishing these objectives, in particular by Personick et al. (19,7840).The primary emphasis of the reviews has been on digital telecommunications (DT) applications. A typical DT receiver/regenerator (19) is shown in Fig. 35. At the minimum optical input signal level, the avalanche photodiode (APD) back bias is automatically adjusted for an avalanche gain of about 50 and the following variable gain amplifier provides about 66 dB of gain in order to achieve a 1-V output signal level. At the maximum optical input signal, the APD gain is reduced to less than 10 (a 7-dB reduction) so that, along with a 33-dB automatic reduction in gain of the variable gain amplifier, a 40-dB dynamic range is achieved with a constant output signal level. a. Preamplijer design alternatives. The preamplifier design for a DT receiver, shown in Fig. 35, and for LDC receivers, described later in Section III,B is the primary factor for acheving a prescribed receiver SNR. Figure 36 shows the two primary candidate designs for fiber optic preamplifier circuits
208
DELON C . HANSON
TIMING RECOVERY
t LOW NOISE PREAMPLIFIER
t
VARIABLE GAIN AMP1 IF IER
OPTICAL SIGNAL
VARIABLE H V
FIG.35. Typical receiver/regenerator block diagram for telecommunicationsapplications (18).
which interface between the photodetector and the postamplifier. The highimpedance (HZ) approach has been utilized extensively in early D T applications, whereas the transimpedance (TZ) design has been used extensively in LDC applications. b. Preamplifier modeling. For modeling, the photodiode equivalent circuit in Fig. 33 has been simplified to a single current source i,(t) in parallel with capacitance C, . In both cases the preamplifier is characterized by the input parameters R , and C, and noise sources in@) and en@).The preamplifier
I
I lbl
FIG.36. Comparison of equivalent circuits for (a) transimpedance (TZ) and (b) highimpedance (HZ)receiver preamplifiers (f8).
FIBER OPTICS IN LOCAL AREA NETWORKS
209
gain stage is assumed to be noiseless. In the TZ case, it is represented by open-loop frequency dependence A , ( o ) and by constant A in the HZ case. The noise contribution from TZ feedback resistor R, is represented by if@), while the noise contribution from the large value, parallel bias resistor R , for the HZ preamplifier is represented by ib(t).The noise of the additional amplification stage A at the output of the TZ preamplifier is accounted for e,,(t). The transfer function Iffi&) at the output of the HZ preamp is needed to compensate for the integration characteristic of the HZ input. The output filter in the TZ case is much less critical since the much lower input impedance does not cause integration of the input signal. The required average optical input signal power Pavefor a specified SNR Q is given by where q is the electronic charge; R , photodetector responsivity (A/W) ; Tb, baud period; 2, dimensionless noise parameter (80) for the receiver. Equation (29) is a particularly useful relationship for the system designer since it explicitly contains all of the parameters needed to specify a digital receiver’s performance. The receiver’s noise performance is included in the parameter Z which was described originally by Personick (80) as Z”’. In order to compare HZ and TZ preamplifiers directly, Z can be represented in a common form:
where R , = R , for TZ; R , = R , for HZ; SI is the single-sided current spectral density (AZ/Hz);SE, single-sided voltage spectral density (V2/Hz); S,, = SE S,, for TZ, SE. = S , for HZ; R , = R , for TZ, R , = R , for HZ; R , = [ l / R , 1 / R b ] - ’ ;k, Boltzmann’s constant; T, absolute temperature; C, = C, C,; I,, I , , parameters relating the input and equalized output pulse shapes (80). For bipolar preamplifiers, SI = 2qIb,,, and S, = 2kT/g,. It is clear from Eq. (30)that to minimize the noise contribution it is necessary to minimize C, and maximize the resistance parameters. The 2 parameter is very similar for TZ and HZ amplifiers if R , = R,, respectively. However, the reason HZ amplifiers are so named is that, typically, an FET input device i s used and R, must be made very large to minimize noise. As a result, the input admittance is dominated by C, and thus signal integration results. The equalizer H,,&) plays a vital role for the HZ amplifier since it is necessary to restore the pulse shape of the integrated input signal. If a simple differentiator is used for this purpose, the low-frequency signal components
+ + +
210
DELON C. HANSON
are heavily attenuated. The problem is that to minimize the noise contribution, the amplification must occur before equalization. As a result, high-level, low-frequency signal components occur ahead of the equalizer. The dynamic range of the HZ preamplifier is limited because the input voltage continues to build up on CTif the signal stays in one state for multiple baud periods. In addition, to utilize the noise advantage of the HZ preamplifier it may be necessary to individually adjust the equalization circuitry and compensate it over temperature. The TZ preamplifier has found widespread acceptance because of its wide bandwidth capability, wider dynamic range, and ease of integration on silicon. When the amplifier gain is very large, the TZ amplifier is a current to voltage converter (hence the name) as defined by the feedback resistor R , . In practice, the amplifier gain is finite and thus there is a limit to how large R, can be. As a result, from Eq. (30), there is a lower limit on the noise contribution of R , . Even with this limitation, practical system dynamic range requirements of 20-40 dB, along with reasonable freedom from input signal pulse distortion, is achieved. 3. LDC Receiver Design Alternatives
The TZ preamplifier, which is primarily used in LDC applications for the reasons sited in Section III,B,2 is incorporated into one of the three following basic receiver circuits, depending on the operating frequency range and required receiver dynamic response time. Performance trade-offs for each circuit design will be summarized in the following sections with emphasis on functional performance differences, ease of integration, and overall complexity. a. dc-Coupled receivers. The dc-coupled receiver is shown in Fig. 31. It is the simplest to realize in integrated form. The dc current I,, can be set to
-
RF
FIG.37. Generalized block diagram of dc-coupled receiver.
FIBER OPTICS IN LOCAL AREA NETWORKS
21 1
balance the nominal level of the detected signal current. Particularly when a p-n photodetector is incorporated as part of the same silicon chip, it can be packaged on a simple header without the use of any external hybrid components. Because of dc coupling and the absence of energy storage elements, it responds rapidly to changes in pulse amplitude, which makes it suitable for passive distributed data bus networks in which dynamic contention occurs between signals received from different nodes in the network. A major disadvantage of this design is the pulse distortion which occurs as a result of using a fixed-threshold detection level for all input signal levels. Since the signals have nonzero rise and fall times, this causes substantial pulse distortion and ultimately limits the maximum data rate and allowed dynamic range. Since dc levels are coupled through this circuit, the design is relatively sensitive to component mismatch. As a rule, the integrated dccoupled receiver for fiber optic applications is limited to less than 20 MBd due to these difficulties. b. ac-Coupled receivers. This design approach, shown in Fig. 38, uses series-coupling capacitors to eliminate the component mismatch problem. In addition, pulse distortion is minimized since the detection threshold is maintained in the middle of the waveform over the entire signal amplitude range, if the average signal duty factor is 50%. If a TZ preamp is utilized, a relatively wide dynamic range results. If the AGC, shown dotted in Fig. 38, is not incorporated and the coupling capacitors are small, a relatively fast response time occurs. As noted above, this circuit is limited to use with 50% duty factor signals, e.g., with Manchester encoding. As a consequence, even with large interstage coupling capacitors it does not accommodate asynchronous operation without transmitter encoding. Particularly with integrated circuit design, the requirement to use relatively large, off-chip, interstage capacitors increases
I T
r-+-k&- 1
@@+qp&-p I
- -1 -
4
RF FIG.38. Generalized block diagram of ac-coupled receiver.
212
DELON C . HANSON
T RF
DATA
T
--
A FIG.39. Generalized block diagram of dc-feedback receiver.
the packaging difficulty. This integrated circuit design approach has been taken by Biard (81). c. dc Feedback receivers. A generalized block diagram of a dc feedback (DCFB) receiver is shown in Fig. 39. This is a hybrid of the first two design approaches since it is basically a dc-coupled design in which effective ac coupling is achieved through DCFB, which supresses the dc response and compensates for component drift. With this design, the difficult to package interstage coupling capacitors are replaced by two capacitors which are connected to ground for DCFB and AGC signal averaging, respectively (82). The DCFB signal is obtained from the average value of the three-level middle waveform in Fig. 30 or from a 50% duty factor, two-level signal. The AGC signal is derived from the peak value of the amplified signal. The DCFB resistor provides an additional source of noise relative to the ac-coupled receiver for a TZ preamplifier. This circuit is primarily intended for point-to-point applications in which constant-amplitude signals are received, since the acquisition time is very large due to the DCFB loop. A schematic of a fully integrated example of this receiver (82)is shown in Fig. 40. Because of the two sets of threshold detectors, this circuit recovers either the two-level or three-level signals shown in Fig. 30. In addition, a link monitor output signal is provided to indicate link continuity. This continuity signal occurs even in the absence of data for the three-level waveform in Fig. 30. The link monitor is a useful function for many applications where system status is required.
213
FIBER OPTICS IN LOCAL AREA NETWORKS BIAS
GAIN CONTROL ? PREAMP STAGE
DIFFERENTIAL AMPLIFIER STAGE
LOGIC HIGH
ALC AMP
LlNK MONITOR
MONITOR OUTPUT
FIG.40. Schematic drawings of Hewlett-Packard integrated dc feedback receiver circuit (5).
C . System Design Considerations
Having summarized the design considerations for the individual components of a fiber optic link, it is appropriate to discuss how the individual device specifications interrelate so that when they are interconnected a viable link with adequate performance margin results. From a SNR or bit error rate (BER) standpoint, the key consideration is the sensitivity specification of the receiver relative to the available received optical signal power. 1. Link-Reliability Margin
Figure 41 shows schematically the distribution of received optical power. There may be a reduction (movement toward the left) as time increases, due to LED or connector degradation. For high production yield, the receiver optical power specification limit for a given BER must be well above the actual receiver sensitivity distribution, when temperature and supply voltage margins are accounted for. As a result of these distributions and the absolute minimum-maximum specification limits which are assigned to individual devices, it is very likely that the total link will function satisfactorily even if one component is outside of its specification limits. Thus, there is some controversy about how to
214
DELON C . HANSON OPTICAL SIGNAL POWER AVAILABLE A T RECEIVER PORT __c
A~RANSMITTER TYPICAL
TYPICAL RECEIVER DISTRIBUTION RECEIVER SENSITIVITY SPECIFICATION
FIG.41. Sketch of possible reduction of receiver optical signal power with time versus receiver specification and sensitivity distribution.
establish device specification margins in order to achieve realistic system reliability projections. The reliability R of a device is the probability that it will perform its intended function for a specified period of time under specified conditions. Assuming it is in a constant failure rate region R can be expressed by R
=
exp(-r/MTBF)
(311
where t is the designated mission time, MTBF is the mean time between failures, and R is the probability of survival for time t . The failure rate F is the number of failures relative to stated conditions in a given total number of operating hours. The MTBF is related to F by the inverse relationship, MTBF
=
1/F
(32)
Generally, users are concerned with the reliability of a fiber optic component for a given mission time t. If the component has an MTBF = 100,000 hr and the mission time is 5 yr with 70% utilization, then t = 5 yr x (8760 hr/yr) x 0.7 = 30,660 hr. As a consequence, the component reliability R = exp(-30,660/100,000) = 0.74, even though the MTBF is more than three times longer than the mission time. Note that if the mission time equals the MTBF, R = 0.37. Thus, 63% of the components will have failed by the end of the mission. A data link network consists of several components in tandem such that
FIBER OPTICS IN LOCAL AREA NETWORKS
215
catastrophic failure of any one component will cause network failure, Thus, the system MTBF, is given by MTBF, =
[ ']' i =I
MTBF,
(33)
where MTBF, is the mean time between individual component catastrophic failures. Except for catastrophic failures, individual devices may drift out of their data sheet specification limits and the link will continue to function satisfactorily. With reference to Table I, the optical output power of GaAsP LEDs degrades slowly and continuously with time but tends not to instantly fail because of dark-line defects. On the other hand, GaAlAs LEDs tend to maintain nearly constant optical output power but may experience a rapid degradation mechanism. Clearly, the link optical power margins should be set differently in these two cases. As discussed in relation to the generic network topologies shown in Fig. 4, fiber optic local area networks (LANs) are configured using either point-topoint (PP) links with active repeaters or passive data bus (PDB) hardware. The PP case includes simplex and duplex links, which are configured into either fully connected, star or ring/loop networks having active nodes. The PDB case includes linear and cluster interconnections in which dynamic optical contention occurs on the network in order to gain control before transmitting a block of data. System considerations for these two cases will be summarized in the following sections. 2. Distributed Point-to-Point Local Area Networks Figures 42 and 43 show point-to-point (PP) links with active repeaters configured in simplex loop and full duplex linear configurations. In both
I'
4
HYI'ASSEI)
PORT
FIG.42. Loop data bus using point-to-point links and optical bypassing of disabled node.
216
DELON C . HANSON
I.
OPTICAL BYPASS
SWITCH
FIG.43. Dual-direction linear network using point-to-point links and optical bypassing of disabled nodes.
cases, local bypass switching (discussed later) is shown to prevent an inactive repeater from disabling the network. a. Sysrem power budget. Figure 44 shows a typical example of a system optical power budget. It accounts for an operating temperature range of 0-70°C, a worst-case BER = at the highest specified data rate of 10 MBd. For this particular example, the total worst-case-system optical power budget is 18 dB. This is the difference between the transmitter output power at worst-case temperature and the required receiver input optical signal 10-9BER AT 10 Mbaud
O°C-70°C v1 v1
I
0
20
Z 0
16
a
* e Z
1
12
8
TOTAL INSERTION LOSS
4 I
E
a
0 100
300
500
700
900
1100 1300
P - C A B L E LENGTH ( m ) FIG.44. Typical point-to-point link optical power budget showing total insertion loss versus cable length and associated power margin in triangular region.
FIBER OPTICS IN LOCAL AREA NETWORKS
217
power for the specified BER and for worst-case conditions. The total link insertion loss for worst-case temperature is offset upward by the connector loss. The optical power budget margin is represented by the triangular region. In particular, at 1 km a worst-case margin of 3.5 dB exists. The typical power margin at 1 km is over 10.0 dB. For a first-generation L D C link operating at 10 MBd, the optical budget is the primary link design consideration. As the data rate is increased to 100 MBd, the link pulse distortion limits, shown in Fig. 21, must also be accounted for to ensure satisfactory system operation. If the assumption is made that from a system reliability standpoint, it is only necessary to allow for a single inactive node, the optical power budget of the network must only accommodate the attenuation of two cable lengths (one on each side of the “down” mode) and the bypass switch loss. An additional cable and switch insertion-loss contribution must be added for each additional inactive node allowed in tandem. Thus, the major advantage of P P active repeater networks is that localized, well-defined optical power budgets can be specified on the network independent of the number of tandem nodes. The received power level is relatively constant (except for the instant when an inactive repeater is bypassed), since it only originates from one source. b. Optical bypass switch design. Several design approaches have been proposed for node bypass switches. These include solid-state optoelectronic designs which require no moving parts, as well as optomechanical designs. The practicality and ultimate performance specifications of either approach remains to be proven, but several comparisons can be made. The optoelectronic switches use liquid-cystal (83), magneto-optic, or acousto-optic materials and applied voltage to shift a divergent optical beam, which is leaving one fiber, between at least two other fibers with reasonable efficiency.Since there are no moving parts, switching can occur in the submillisecond range and the components have small physical size. For the liquid-crystal switch, key concerns are the lack of adequate isolation between channels, the relatively high minimum insertion loss, restricted temperature range, and relatively high switching voltages. A variety of optomechanical bypass switches have been proposed. These include rotating spherical mirrors which reflect an optical beam between selected channels (84), moving optical-fiber pigtail switches (85), and rigid single-motion fiber switch assemblies (86). The latter approach (86),which is potentially attractive for LAN applications, is shown in Fig. 45. Using 100-pm core/140-pm-o.d. fibers, this design has achieved greater than 50-dB isolation between channels with less than 2-dB insertion loss. Switching speed is in the 10 msec range. Prototypes have been operated 25,000 cycles before failure.
218
DELON C. HANSON DATA OUT
t
, T O REPEATER
SPACER FIBER
0,
ym
I
& ’
FROM REPEATER (a)
(b)
FIG.45. Schematic drawing of prototype optical fiber bypass switch (86): (a) top view; (b) side view.
c. Loop network implementation. Casto (87)has described Harris Corporation’s decision to implement a fiber optic loop LAN using PP links. A second redundant loop was included to provide a reliability backup. The network, designed to distribute high-resolution satellite image data between 35 nodes in a meteorological center, operates at 50 Mb/sec. TDM time slots are allocated dynamically, based on traffic requirements. Twisted wire cable was eliminated due to bandwidth and ground loop problems. CATV coax provided the necessary bandwidth performance and ground loop immunity for this application but had insufficient EM1 and radiation protection. Okuda et al. (88) summarized Toshiba’s Ring Century Bus, which uses PP links for separate data and control rings. Projected data rate using TDM is 100 Mbfsec with up to 300-m separation between nodes. Hence, P P links allow the implementation of real-world distributed loop networks with performance exceeding that achievable with conventional coaxial-based network hardware. The development of practical automatic bypass switching and “soft failure” network redundancy schemes will considerably enhance the acceptance of this network technology. 3. Distributed Data Bus As discussed in relation to the generic network topologies in Section I,C, the distributed data bus in Fig. 4d is the topology usually chosen when coaxial cable is the transmission medium. The perceived advantages of this network were outlined previously in Section 1,C. They are primarily the totally passive nature of the transmission medium and the ability to easily install low-perturbation taps on the transmission line without disrupting the operating network.
FIBER OPTICS IN LOCAL AREA NETWORKS
219
For a fiber-optic-based network, the configuration in Fig. 4d is the most difficult to implement since an optical equivalent of essentially zero perturbation, bidirectional electrical taps does not exist to couple the optical data signals efficiently into and out of the main network fiber. In addition, it is necessary to sever the main network fiber (i.e., shut down the network) in order to introduce the coupler. a. Passive optical fiber couplers. Considerable research has been undertaken to develop optical fiber couplers and power splitters because of the key role these devices will play in distributed data bus networks. Coupler designs include micro-optic Selfoc lenses with mirrors (89), bifurcation of quartz rods (90),offsetting of fibers in a plastic waveguide housing (91)and biconically tapered multimode fibers (92-94). For LANs, the most practical design approach appears to be the biconically tapered, multimode coupler sketched in elementary form in Fig. 46. The same technology is used both for two fiber couplers [in which the reported directivity is > 55 dB and excess loss < 0.5 dB (92,93)]and for 4-100 fiber star couplers (94-96). Because the couplers are fabricated from the same type of fiber which is used in the network itself, minimal discontinuities occur from inserting the coupler into the network. The operation of biconically tapered couplers is based on the principle that by reducing the modal volume of the fiber core through tapering, the higher-order optical modes are forced to the outer tapered cladding surface which has an air interface. In the expanding tapered region of the fused coupler, the source fiber optical modes tend to become equally distributed among the exit optical fibers. Through scattering, these modes become trapped in the cores of the exit fibers. For most efficient and uniform performance, care must be given to achieve the proper degree of twisting and tapering and to avoid bubbles and discontinuities during the fusion process. Lightstone(94) has discussed the fact that in order to avoid the irreversible loss of optical modes from the biconical taper into air, a fiber having core
DIRECTIVITY
= -10 log
(z)
FIG.46. Schematic drawing of two-fiber biconically tapered multimode coupler.
220
DELON C. HANSON
radius a with a given NA must have its tapered-core diameter aT limited so that aT/a > NA/(n: - 1)1/2
(34)
For an F fiber-channel coupler, the coupling fraction C,, from the source fiber to an auxiliary output is limited by the area ratio (aT/a)2through the relationship
(35)
CFA < (1/F){1 - [(NA)’/(n: - I)])
The intrinsic nonuniformity of the optical power coupling to the exit end of the source fiber C,, (due to lower order modes which propagate directly through the coupler), relative to the other auxiliary fibers is given by (94) CFS
=1
- (F - 1)CFA
(36)
Thus, for NA = 0.3 and n, = 1.458, the taper must satisfy (aT/a)> 0.28. Table IX shows the limiting coupler asymmetry for various numbers of fiber channels F. It is clear from Table IX that as the number of fiber channels increases, the imbalance in optical power between the output end of the source fiber and the other auxiliary fibers becomes quite drastic, e.g., 5.4 dB for F = 32. Since this imbalance adds directly to the required receiver dynamic range, the designer is challenged to circumvent this phenomenon, e.g., through local mode mixing. b. Passivejber optic loop and linear data buses. The fiber optic implementation of the LAN shown in Fig. 4d is more readily achieved in the loop configuration sketched in Fig. 4c and shown in more detail in Fig. 47. When the network is closed into a loop, transmitter To and receiver R , are located at the same loop control node. The loop active repeater nodes, discussed in Sec. III,C,2, are thus replaced by passive, optical fiber couplers which provide efficient coupling into and out of the main network fiber, and their associated terminal devices. TABLE IX TRANSMISSIVE STARCOUPLING PARAMETERS Number of fiber channels 4
8 16 32
Auxilary fiber coupling fraction (CF1
Source fiber Coupling fraction (CFsl
0.230 0.115
0.195
1.30 2.32
0.13 0.10
3.51 5.45
0.058
0.029
0.31
Ratio 10 b g , , ( c F , / o (dB)
FIBER OPTICS IN LOCAL AREA NETWORKS
22 1
FIG.47. Passive loop data bus insertion-loss components (see text for explanation of symbols).
The worst-case optical power budget between the nodes in Fig. 47 must be examined with several cases in mind since the same terminal device specifications apply at any location. Hudson and Thiel(97) and Barnowski (98)have analyzed this network for fiber bundles. Single-fiber systems are considered here since they are more practical for LANs. Depending on the choice of parameters, the highest attenuation loss between nodes could be: u0.N- 1 u0.N
= P(N- i)RIPoT, = PNRIPoT,
u1.N- 1 ul,N
=
P(N-1 ) R I P i - r
= PNR/PIT
where transmitter and receiver power parameters Pi are identified in Fig. 47. The relationships for these optical power ratios are (for N > 3):
+ LN + Lc + ( N - 2)Lu (37) = Lc, + LcT - L, + ( N - 2)L" (38) = 2LN + 2Lc + LT + ( N - 2)Lu (39) = Lc, + LN + Lc + ( N - 2)Lu (40) where Lu = LN + 2Lc + LT, network unit attenuation per added node and a0,N-I
=
L,,
a1,N-l
UO,N a1.N
associated cable; LCT,transmitter coupling loss; LCR,receiver tap loss; L,, coupler transmission loss; Lc, connector loss; LN,fiber transmission loss. In the node coupler configuration in Fig. 47, the receiver coupler precedes the transmitter coupler in the direction of optical power transmission. Because of the relatively high isolation this configuration provides between the local transmitter and receiver (due to the opposite coupler fiber orientation into the network), it is possible to "listen while talking" without serious receiver dynamic range problems. This is a key feature of the coaxial Ethernet data bus network described in Section 1,C. A disadvantage of this configuration is that the dual coupler, redrawn in Fig. 48a, is substantially more
222
DELON C . HANSON
FIG.48. Two-fiber node coupler alternatives for passive loop data bus: (a) dual coupler; (b) single coupler.
difficult to fabricate than the coupler configuration shown in Fig. 48b. Although easy to fabricate in the latter case, the local transmitter is directly coupled to the local receiver, thus increasing the required receiver dynamic range. Electronic switching may be used to disable the local receiver when its transmitter is “talking” but this overrides the “listen while talking” feature for the network. Selection of parameters for LAN performance evaluation depends on the technology used for the passive couplers. If biconically tapered couplers of the type shown in Fig. 46 are used, the typical excess loss equals -10 log(B1) = 0.8 dB or p1 = 0.83. In order to minimize the receiver dynamic range requirement, it is desirable that all of the attenuation coefficients in Eqs. (37)-(40) be equal. In addition, it is desirable to minimize the network unit attenuation L, in order to increase the number of allowed tandem nodes. Assuming that aO,Ncan be adjusted (as a special case if necessary), this implies that in designing network coupler parameters the boundary condition should be imposed that LcR
+ L, + Lc = LcR +
LCT
- LT
(41)
If the network is designed to accommodate 300 m of lO-dB/km cable between nodes, then L, = 3.0 dB. It is reasonable to assign a second-generation connector loss Lc = 1.0 dB. Thus, Eq. (41) reduces to Bi(1
-
Copt)= 2.581COpt
(42)
so that Copt= 0.29
or
- 10 logl0(C,,,) = 5.4 dB
In summary, the network parameters are:
(43)
223
FIBER OPTICS IN LOCAL AREA NETWORKS
Thus, for N > 3, Eqs. (37)-(40) reduce to
+ ( N - 2)7.3] dB M O ~ N= [10.3 + (N - 2)7.3] dB
a O , N - l= a l , N - l = a I , N= [10.2
(44) (45)
It is interesting to observe that at each node there is nearly an equal balance between the connector and coupler transmission loss, i.e., LT = 2Lc. Adding an individual node introduces 2Lc + LT = 4.3-dB loss plus the associated cable attenuation. With this parameter optimization, it is noted from Eqs. (44) and (45) that the worst-case insertion loss between all nodes is essentially equal. In addition to characterizing the maximum insertion loss between nodes, it is also necessary to establish the minimum insertion loss in order to determine the required receiver dynamic range. With reference to Fig. 47, the minimum insertion loss occurs at the end nodes when there is zero cable attenuation LN and is given by a,
=
ag, 1
= aN- 1,N = Lc
+ L,,
= Lc
+ Lc-
(46)
For the parameters selected above, i.e., Lc = l.OdB,
L,,
=
LCT= 6.2dB,
then amin= 7.2dB.
c. Transmissive star data bus. Figure 49 shows a schematic drawing of a transmissive star data bus configured with F = 3 fiber channels. The parameter designation is the same as in Fig. 47. From a functional standpoint, the network can be configured with dual channel cables between the individual T/R modules and the star coupler at the central node. Because all links are effectively in parallel, the optical power budget is very simple, i.e.,
aij = PjR/PIT= 4Lc
+ 2LN + bS,
FIG.49. Passive transmissive star data bus for F = 3 fiber channels with L, L, = 3.0 dB, and L, = 1.0 dB; hsis coupler transmission loss.
(47)
=
1.0 dB,
224
DELON C. HANSON
where L , = 10 log,,(F) + LE,F is the number of optical star channels, and L, is the excess loss per channel. Assuming the same parameter values as previously, i.e.,
L, = 1.0 dB,
L, = 3.0 dB,
LE = 1.0dB,
Equation (47) is plotted in Fig. 50 versus the number of nodes N (or star channels F). Also plotted is the maximum and minimum insertion loss between nodes for the loop data bus. It is useful to note that a 32-channel transmissive star data bus having a 300-m radial arm length has no more node-to-node insertion loss than a loop data bus with 4 hops of 300-m length between nodes. Also, a loop bus with 8 hops requires over 50dB of worst-case optical power budget. This is a major challenge for terminal device design and severely restricts the general implementation of the passive loop fiber optic data bus networks. lo(1
m
m
80
0
-1
z
LOOP OR LINEAR DATA BUS
0ILL Y
-
in
z
60
Y
n
0
z
I
0
7 40 Y
a 0
z Y v1
d
u c
20
in
LL
0
3 0 8
I I
I
16
24
I
NUMBER OF N O D E S , N
FIG.50. Worst-case node-to-node insertion loss for loop and transmissive star passive data buses versus number of nodes. Star coupler parameters: Lc = 1.0 dB, L, = 3.0 dB, and L, = 1.0 dB. Loop data bus parameters: Lc = 1.0 dB, L, = 3.0 dB, LT = 2.3 dB, L,, = L C T = 6.2 dB.
FIBER OPTICS IN LOCAL AREA NETWORKS
225
ACKNOWLEDGMENT The author would like to acknowledge his interaction with many individuals in the HewlettPackard Company who have contributed to his understanding of design trade-offs for fiber optics in local-area network applications. A partial list includes : Tom Hornak, Bob Burmeister, George Kaposhilin, Bill Brown, Eric Hanson, and Ron Hiskes of the Hewlett-Packard Corporate Research Laboratory, who have been instrumental in exploring technology and design alternatives; Roland Haitz, Lee Rhodes, Joe Tajnai, Bob Weissman, and Steve Garvey of the Optoelectronic Division, who have contributed extensively to discussions and projects directed toward the development of commercial products for fiber optic data link and network applications. He would also like to express appreciation for the diligent efforts of Terry Lincoln in typing the manuscript and Betty Downs in drawing the figures.
REFERENCES 1. Gage, S., Evans, D., Hodapp, M., and Sorensen, H. (1977). “Optoelectronics Applications
Manual,” McGraw-Hill, New York, p. 3.5. 2. Blankenship, M. G. et al. (1979). Optical Fiber Communication Digest, Washington,D . C.,
p. PD3. 3. Winningstad, C. N. (1961). Nanosecond pulse measurements, West Coast Electronics Conference, (WESC0N)-San Francisco, p. 231. 4. Thomas, R. J. (1968). Choosing coaxial cable for fast pulse response, Microwaves, No. 11, p. 56. 5. Applications Engineering Staff of Hewlett-Packard Optoelectronics Division (1981), “Optoelectronics/Fiber-Optics Applications Manual,” 2nd Edition, McGraw-Hill, New York, p. 10.1. 6. Xerox, DEC and Intel plan Ethernet as de facto communications standard, Electronics Business 6, No. 8, p. 30 (Aug. 1980). 7. Cotton, 1. W.,and Folts, H.C. (1977). “International standards for data communications: A status report,” Proc. Fifth Data Communications Symposium, 1977, p. 4. 8. Metcalf, R. M., and Shoch, J. F. (1980). Conference on Local Computer Networks, Los Angeles, California, McGraw-Hill, New York. 9. Pierce, J. R. (1972). How far can data loops go? IEEE Trans. Commun. COM-20, No. 3,527. 10. Hayes, J. F., and Sherman, D. N. (1971). Traffic analysis of a ring switched data transmission system, Bell. Syst. Tech. J. 50, No. 9, p. 2947. 11. Saltzer, J. H., and Pogram, K. T. (1979). A star-shaped ring network with high maintainability, Proc. Local Area Commun. Networks Symp., p. 179. I2. Metcalf, R. M., and Boggs, D. R. (1976). Ethernet: distributed packet switching for local computer networks, Commun. ACM 19, No. 7,395. 13. Tobagi, F. A., and Hunt, V. B. (1979). Performance analysis of carrier sense, multiple access with collision detection, Proc. Local Area Commun. Networks Symp., p. 217. 14. Shoch, J. F., and Hupp, J. A. (1979). Performance of an ethernet local network: a preliminary report, Proc. Local Area Commun. Networks Symp., p. 113. IS. Dineson, M. A., and Picazo, J. J. (1980). Broadband technology magnifies local networking capability, Data Communications, p. 61. 16. McQuillan, J. M. (1979). Local network technology and the lessons of history, Proc. Local Area Commun. Networks Symp., p. 191. 17. Hanson, D. C. (Feb., 1981). Impact of terminal device design on fiber optic local area networks, Digest of Compcon, Spring. 1981, Sun Francisco, California.
226
DELON C. HANSON
f8.Grady, R. B., and Hanson, D. C. (1979). High-speed fiber optic link provides reliable realtime HP-IB extension and a ready-to-use fiber optic link for data communications, HewlettPackard Journal 30, No. 12,3. 19. Personick, S. D., Rhodes, N. L., Hanson, D. C., and Chan, K. H. (1980). Contrasting fiber optic component design requirements in telecommunications, analog and local data communications applications, Proc. IEEE 68, No. 10, 1254. 20. Staff of Bell Telephone Laboratories, “Transmission Systems for Communication,” Western Electric Co. (1970). 21. Anderson, R. J. (1979). Local data networks-traditional concepts and methods, Proc. Local Area Commun. Networks Symp., p. 127. 22. Gloge, D., et al. (1980). High-speed digital lightwave communication using LEDs and PIN photodiodes at 1.3 pm, Bell Syst. Tech. J . 59, No. 8 , 1365. 23. Kao, K. C., and Hockhan, G. A. (1966). Dielectric-fiber surface waveguides for optical frequencies, Proc. IEEE 113, p. 1151. 24. Miya, T., et al. (1979). Ultimate low-loss single mode fiber at 1.55 pm. Electron. Lett. I 5 , p . 106. 25. Beales, K. J., and Day, C. R. (Feb., 1980). A review of glass fibers for optical communications, Phys. Chem. Glasses 21, No. 1,5. 26. Pinnow, D. A., et al. (1973). Fundamental optical attenuation limits in liquid and glassy state with application to optical fiber waveguides, Appl. Phys. Lett. 22, p. 527. 27. Gloge, D. (1979). The optical fiber as a transmission medium, Progress in Physics42, p. 1778. 28. Gloge, D., and Marcatili, E. A. J. (1973). Multimode theory of graded-core fibers, Bell Syst. Tech. J . 52, No. 9, 1563. 29. Marcatili, E. A. J. (1975). Theory and design of fibers for transmissions, Optical Fiber Transmission Proc., Williamsburg, Virginia, p. TuC4. 30. Payne, D. N., and Gambling, W. A. (1975). Zero material dispersion in optical fibers, Electron. Lett. 11, p. 176. 31. Olshansky, R. (1975). Mode coupling effects in graded index optical fibers, Appl. Opt. 14, p. 935. 32. Marcuse, D. (1973). Loss and impulse response of a parabolic index fiber with random bends, Bell Syst. Tech. J . , 52, p. 245. 33. Gloge, D. (1975). Optical fiber packaging and its influence on fiber straightness and loss, BeN Syst. Tech. J . 54, p. 1423. 34. Hanson, Eric (I981 ). Origin of temperature dependence of microbending attenuation in fiber optic cable, Fiber Integr. Opt. 3, Nos. 2-3. 35. Olshansky, R. (1975). Distortion losses in cabled optical fibers, Appl. Opt. 14, p. 20. 36. Olshansky, R., and Keck, D. (1976). Pulse broadening in graded index optical fibers, Appl. Opt. 15, p. 483. 37. Gardner, W. B. (1975). Microbending loss in optical fibers, Bell Syst. Tech. J. 54, p. 457. 38. Griffith, A. A. (1920). The phenomena of rupture and flow in solids, Philos. Trans. R. SOC. London, Ser. A 221, p. 163. 39. Weibull, W. (1939). A statistical theory of the strength of materials. Proc. R. Swed. Inst. Eng. Res., No. 151 (unpublished). 40. Love, R. E. (March, 1976). The strength of optical waveguide fibers, Proc. SOC.Photo-Opt. Instrum. Eng. 11,Reston, Virginia. 41. Justice, B. (1977). Strengthconsiderations of optical waveguides, Fiber Integr. Opt. I,p. 115. 42. Kalish, D., and Tariyal, B. K. (Dec., 1978). Static and dynamic fatique of fused silica opticalfibers, J. Am. Ceram. SOC.61, Nos. 11-12, 521. 43. Hiskes, R. (1979). Improved fatigue resistance in high strength optical fibers, Digest of Topical Meeting on Optical Fiber Trans. III, Washington, D.C., p. WF6.
FIBER OPTICS IN LOCAL AREA NETWORKS
227
44. Charles, R. J. (1958). Static fatigue of glass 11. J. Appl. Phys. 29, p. 1554. 45. Kapron, F. P., Keck, D. B., and Maurer, R. D. (1970). Radiation losses in glass optical waveguides, Appl. Phys. Lett. 17,423. 46. Blyler, L. L., and Hart, A. C., (1977). Polymer claddings for optical fiber waveguides, 35th ANTEC Prepr.. SOC.Plastic Eng., p. 383. 47. Hanson, D. C., et al. (July, 1978). Integrated transducer modules, connectors and cable for industrial fiber optic data links, IEEE Trans. Commun. COM-26, No. 7, 1068. 48. Hanson, D. C. (October, 1979). Getting a fix on fiber optic tradeoffs, Instrum. Control Syst. 52, No. 10, p. 41. 49. Morrow, A. J., et al. (1979). Design and fabrication of optical fiber for data processing applications, Digest of Optical Fiber Commun. ConJ. Washington, D.C., p. WF2. 50. Schwartz, M. I., Gloge, D., and Kempf, R. A. (1979). Optical cable design, in “Optical Fiber Telecommunications” (Miller, S. E., and Chynoweth, A. G., eds.), p. 435. Academic Press,
New York. 51. Ishihara, K., et al. (Sept., 1979). Determination of optimum structure in coated optical fiber and cable unit, Opt. Commuv. Con$ Proc.. Amsterdam, p. 7.3-1. 52. Hawk, R. M., and Thiel, F. L. (1975). Low loss splicing and connection of optical waveguide cables, SPIE Guided Optical Communications, 63, p. 109. 53. Young, M. (March, 1973). Geometrical theory of multimode optical fiber-to-fiber connector, Opt. Commun. 7, No. 3, 253. 54. Miyazaki, K., et al. (January, 1975). Theoretical and experimental considerations of optical fiber connector, Digest of Opt. Fiber Trans. Conj:, Williamsburg, Virginia, WA4. 55. Bowen, T. (1978). Low cost connectors for single optical fibers, Proc. of 28th Elect. Comp. ConJ -Anaheim, p. 140. 56. Nawata, K. (1980). Multimode and single-mode fiber connectors technology, IEEE. J. Quantum Electron. QE-16, No. 6,618. 57. Archer. J. D. (1978). Single fibre optical connections, New Electronics 11, No. 2, 58. 58. North, J. C., and Stewart, J. H. (Sept., 1979). A rod lens connector for optical fibers, Opr. Commun. Conf.-Amsterdam, p. 9.4-1. 59. Runge, P. K., Curtis, L., and Young, W. C. (1977). Precision transfer molded single fiber optic connector and encapsulated connectorized devices, Tech. Dig. Opt. Fiber Trans. Conj:.p. WA4. 60. Hodge, M. H. (1978). A low loss single fiber connector alignment guide, Proc. of’ Fiber Opt. and Commun. (FOCI-Chicago, p. 11 1. 61. Holzman, M. A. (1978). Interconnection of multimode optical waveguides, Proc. SOC. Photo-Opt. Instrum. Eng. 150, Laser and Fiber Opt. Commun., San Diego, p. 152. 62. Li, T. (1978). Optical fiber communication-The state of the art, IEEE Trans. Commun. COM-26, NO. 7,946 63. Lee, T. P. and Dentai, A. G. (1978). Power and modulation bandwidth of GaAs-AIGaAs high radiance LEDs for optical communication systems, IEEE J . Quantum Electron. QE-14, p. 150. 64. Shirahata, K., et al. (1978). High radiance AlGaAs LED for fiber-optic communications, Proc. of Fiber Opt. and Commun. (F0C)-Chicago, p. 92. 65. Burrus, C. A,, and Miller, B. I. (1971). Small-area DH AlGaAs electroluminescent diode sources for optical fiber transmission lines, Opt. Commun. 4, No. 4, 307. 66. Ettenberg, M., Kressel, H., and Wittke, J. P. (1976). Very high radiance, edge-emitting LEDs, IEEE J. Quantum Electron, QE-12, p. 360. 67. Chin, A. K., Berkstresser, G. W, and Keramides, V. G. (1979). Comparison of single heterostructure and double heterostructure GaAs-GaAIAs LEDs for optical data links, Bell Syst. Tech. J . 58, No. 7, 1579.
228
DELON C. HANSON
68. Kressel, H., el al. (1980). Laser diodes and LEDs for-fiber optical communication, Top. Appl. Phys. 39, p. 43. 69. Marcuse, D., Gloge, D., and Marcatili, E. A. J. (1979). Guiding properties of fibers, in “Optical Fiber Telecommunications” (Miller, S. E., and Chynoweth, A. G., eds.), p. 68. Academic Press, New York. 70. Marcus, D. (1977). LED fundamentals: comparison of front- and edge-emitting diodes, IEEE J. Quantum Electron. QE-13, p. 819. 71. Botez, D., and Ettenberg, M. (1979). Comparison of surface and edge-emitting LEDs for use in fiber-optical communications, IEEE Trans. Electron Devices ED-26, p. 1230. 72, Gloge, D. (1977). LED design for fiber system, Electron. Lett. 13, No. 4, 399. 73. Carter, A. C., Goodfellow, R. C., and Davis, R. (1980). 1.3-1.6 pm GaInAsP LEDs and their application to long haul, high data rate fiber optic systems, Digest of Int. ConJ on Communications, Seattle, Washington, p. 28. I . 74. Speer, R., and Hawkins, B. M. (1980). Planar DH GaAlAs LED packaged for fiber optics, Proc. of Elect. Comp. Con$, Sun Francisco. 75. Hudson, M. C. (1974). Calculation of the maximum optical coupling efficiency into multimode optical waveguides, Appl. Opt. 13, No. 5, 1029. 76. Yamaoka, T., and Masayuki, A. (1978). GaAlAs LEDs for fiber optical communications systems, Fujitsu Sci. Tech. J. 14, No. 1, p. 133. 77. Melchior, H. (1973). Semiconductor detectors for optical communications, Comp. Laser Eng. Abstract, IEEE J. Quantum Elecrron. QE-9, p. 659. 78. Smith, R. G., and Personick, S.D. (1980). Receiver design for optical fiber communication systems, Top. Appl. Phys. 89, p. 135. 79. Personick, S . D. (1977). Receiver design for optical fiber systems, Proc. IEEE 65, No. 12, 1670. 80. Personick, S . D. (1973). Receiver design for digital fiber optic communications systems, Bell Syst. Tech. J. 52, No. 6, 843. 81. Elmer, B. R., and Biard, J. R. (1978). “Fiber Optics Receiver Integrated Circuit Development,” AFAL-TR-78-185, Final Report, p. 5. 82. Brown, W. W., et al. (1978). System and circuit considerations for integrated industrial fiber optic data links, lEEE Trans. Commun. COM-26, No. 7,976. 83. Soref, R. A. (Aug., 1978). Multimode switching components for multi-terminal links, Proc. Soc. Photo-Opt. Instrum. Eng., 150, Laser and Fiber Opt. Commun. San Diego, p. 142. 84. Spillman, Jr., W. B. (1979). Mechanical one-to-many fiber optic switch, Appl. Opt. 18, No. 12,2068. 85. Yamamoto, H., and Ogiwara, H. (1978). Moving optical fiber switch experiment, Appl. Opt. 17, No. 22, 3675. 86. Rawson, E. G . , and Bailey, M. D. (1980). A fiber optical relay for bypassing computer network repeaters, Opt. Eng. 19, No. 4, 628. 87. Casto, T. L. (1980). Dynamic bandwidth allocation of a fiber optic data bus, Proc. of Electro Program, p. 2812. 88. Okuda, N., Kunikyo, T., and Kaji, T. (1978). Ring century bus-An experimental high speed channel for computer communications, Proc. of 4th ICCC, Kyoto, p. 161. 89. Kobayashi, K. et al. (1977). Micro-optics devices for branching, coupling, multiplexing and demultiplexing, Proc. ConJ on Int. Optics, Opt. Comm., Tokyo, p.367. 90. Milton, A. F., and Lee, A. B. (1976). Optical access couplers and a comparison of multiterminal fiber communication systems, Appl. Opt. 15, p. 244. 91. Auracher, F., and Witte, H. H. (1977). New planar optical coupler for a data bus system with multimode fibers, Appl. Opt. 15, p. 2195.
FIBER OPTICS IN LOCAL AREA NETWORKS
229
92. Ozeki, T., and Kawasaki, B. S. (1976). Optical directional coupler using tapered sections in multimode fibers, Appl. Phys. Leii. 28, p. 528. 93. Kawasaki, B. S., and Hill, K. 0. (1977). Low-loss access couplers for multimode optical fiber distribution networks, Appl. Opt. 16, p. 1794. 94. Lightstone, A. W.(1980). Characteristics of multiport biconical duplex and star couplers for military and commercial applications, Proc. of Fiber Opt. and Commun. (FOO-Sun Francisco, p. 261. 95. Rawson, E. G., and Nafarrate, A. B. (1978). Star couplers using fused biconically tapered multimode fibers Electron. Lett. 14, p. 274. 96. Rawson, E. G. (1979). Optical fibers for local computer networks, Digest of Opt. Fiber Corn. Topical M f g . , Washington, D.C., p. 60. 97. Hudson, M. C., and Thiel, F. L. (1974). The star coupler: A unique interconnection component for multimode optical waveguide communications systems. Appl. Opt. 13, p. 2540. 98. Barnowski, M. K. (1975). Data distribution using fiber optics, Appl. Opi. 14, No. 1 I , 2571.
This Page Intentionally Left Blank
ADVANCES IN ELECTRONICS AND ELECTRON PHYSICS, VOL. 51
Surface Analysis Using Charged-Particle Beams P. BRAUN, F. RUDENAUER,*
AND
F. P. VIEHBOCK
Institut f u r Allgemeine Physik Technische Universitat Wien Vienna, Austria
I. introduction . . . . . . . . . . . . . . . . . . . . . . , . . .
.. . . . , , .. ... .. , .. .. ... . , .
11. Classification of Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . , . . . . . . , . ,
A. Analysis of Electrons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B. Analysis of Ions.. C. Short Comparison of Selecte 111. Quantitative Elemental Analysis A. Quantitation of AES . . . . . , . . . . , . , . . . . . . . . . . . . . . , . . . . . . . . . . . . . . . . . . . . , , B. Quantitation of SIMS C. Quantitation ofISS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D. Quantitation of RBS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1V. Depth Profiling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. Nondestructive Methods . . . . . . . . . . . . . . . . . . . . . . . , . . . . . , . . . . . . . . . . . . . . . . B. Destructive Methods. . . . . . . . . . . . . . . . . . . . . V. Elemental Mapping.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. Auger Mapping . . . ... B. SIMS Mapping ...................................................... C. Elemental Mapping Using Other Ion Method VI. Three-Dimensional Isometric Elemental Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. Terminology Used in Multidimensional Digital Imaging . . . . . . . . . . . . . . . . . . . B. Practical Examples of Three-Dimensional SIMS Analysis . . . . . . . . . . . . . . . . . VII. Sensitivity and Resolution Limits . . . . . . . . . . . . . . . . . . . . A. Sensitivity and Resolution in AES . . . . . . . . . . . . . . . . B. Resolution and Sensitivity Limits in SIMS . . . . . . . . , . . . . . . . . . . . . . . . . . . . . . . ...
23 I 233 233 237 24 1 242 242 245 255 258 259 259 26 1 275 275 219 290 292 29 3 296 298 298 300 306
I. INTRODUCTION Surface analysis, i.e., the investigation of the compositional, structural, and electronic properties of the solid-vacuum interface is a relatively new field of investigation. Neverthekss, many of the surface analytical techniques have found wide application in such diverging areas as microelectronics, corrosion research, biology, geology, and cosmology. Also, the relative merits and capabilities of these techniques have been discussed in many * Also affiliated with 6sterreichiscbes Forschungszentrum Seibersdorf 1082-Wien, Lenaugasse 10, Austria. 23 I Copyright 01981 by Academic Press, Inc. All rights of reproduction in any form rewrved. ISBN 0-12-014657-6
232
P. BRAUN, F. RUDENAUER, AND F. P. VIEHBOCK
excellent review papers so that, at first glance, a further review appears to be somewhat inappropriate. We have therefore intentionally limited the scope of this article to a selection of techniques and to a few important subjects which either have received increased attention or which have been newly developed during the last few years. As far as the selection of techniques is concerned, we will describe only surface analytical methods in which charged-particle beams are used for signal stimulation (primary beams) and also constitute the informationcarrying signal radiation itself (secondary beam) ; AES, ISS, RBS, SIMS, among others, belong to this category. One of the most important capabilities of a surface analytical technique is quantitative elemental analysis, i.e., the determination of fractional atomic concentrations of the elements present in the sample surface ; generally, the element-specific signal supplied directly by the detection arrangement is not proportional to the element concentration. Mathematical algorithms have to be developed to transform relative signal intensities to elemental concentration values. A survey of these algorithms is presented. However, it will become clear that practical quantitation is still performed on an empirical basis (using experimentally determined elemental sensitivity factors) ; quantitation algorithms based on physical models of the particular signal stimulation and emission process, in almost any case, only allow analysis with considerably reduced accuracy. The reduced accuracy, however, is somewhat balanced by the less stringent requirements on a priori knowledge on the analytical sample. A second subject which is treated in some depth in this article is elemental imaging; i.e., the determination of the spatial distribution of elements in a solid sample. Conventional imaging techniques which have been extensively used in the past have the disadvantage that they primarily determine the two-dimensional distribution of an element-specific signal strength rather than the distribution of true elemental concentrations across the solid surface. With the increased use of digital computers controlling both, data acquisition and data evaluation in surface analytical instruments, imageprocessing techniques, applying elemental quantitation routines in each pixel of the uncorrected image are receiving increased attention. In a recent development, the techniques of computerized image analysis have been extended to perform complete three-dimensional elemental characterization of the surface near volume of a solid sample. This review therefore begins in Section I1 with a description of the fundamentals of selected particle-beam techniques (divided into electron methods and ion methods), continues with a survey of quantitation methods (Section III), and finally (Section IV-VI) deals with different analytical modes (point analysis, depth profiling, and image and volume analysis). In the concluding
SURFACE ANALYSIS USING CHARGED-PARTICLE BEAMS
233
section (Section VII), the analytical limitations of the two most frequently applied techniques, AES and SIMS, are discussed. It appears, that surface analytical techniques eventually will be able to perform three-dimensional quantitative analysis of solids with spatial resolution of 10 nm (and much lower than that in the depth-profiling mode) for the major elements of a sample.
11. CLASSIFICATION OF METHODS Analytical methods using charged particles are based on electron and ion interactions with surfaces. A . Analysis of Electrons
In Fig. 1 an overview of the most important methods discussed in this section is given. Methods using electrons as probe and secondaries are Auger electron spectrometry (Harris, 1968; Chang, 1971; Taylor, 1971; Palmberg, 1970; Weber, 1970; Connell and Gupta, 1971), electron energy-loss spectrometry (Raether, 1965; Boersch et al., 1962), threshold spectrometries, ionization loss spectrometry (Gerlach et al., 1970; Gerlach, 1971), and ion neutralization spectrometry (Hagstrum, 19721. 1. Auger Electron Spectrometry ( A E S )
The technique is based on the Auger effect whereby an incoming electron with sufficient energy ionizes an atom by removing a core electron. The relaxation to the ground state follows several possible paths. One possibility is the emission of a photon with characteristic energy, but here the interesting case is the emission of a kinetic electron, the Auger electron. The difficulty in this technique is to measure the small number of Auger electrons in the secondary electron distribution. Energy analysis of these electrons yields elemental identification of surface atoms with an information depth depending on the Auger electron energy. The primary electrons will penetrate the material analyzed to a significant depth. However, Auger electrons generated deeper in the substrate will also undergo ineleastic collisions and contribute to the secondary electron distribution (Feibelman, 1973; Brundle, 1974). Only Auger electrons from atoms at the very surface will not change their kinetic energy and are detected in the spectrum. The detection depth will depend slightly on the material analyzed, but will in general follow the square root of kinetic energy for energies > 80 eV. In practical application, the information depth is roughly 0.5-2 nm. The contribution of the various layers decreases exponentially and hence the signal depends mostly on the
234
P. BRAUN, F. RUDENAUER,AND F. P. VIEHBOCK
A*
(C)
(d 1
FIG.1. Overview ofelectron methods discussed in Section II,A. (a) AES; (b) ELS; (c) ILS; (d) INS.
surface layer; AES thus became a very popular technique for surface analysis. Using electronic differentiation, about 0.1% of a monolayer can be detected. A second reason for the popularity of AES is that it is a simple way of obtaining atomic and chemical information from the energy spectrum. On the other hand, quantitative analysis needs improved operation of the system by careful calibration as well as sufficient knowledge about the influencing parameters like current density, ionization cross section, Auger transition probability, analyzer transmission, contribution of backscattered electrons, and surface topography. High-energy resolution is necessary if chemical information and type of bonding of surface atoms is demanded. Surface atoms involved in a chemical bonding change their electron binding energy corresponding to the charge transfer caused by the electronegativity of the
SURFACE ANALYSIS USING CHARGED-PARTICLE BEAMS
235
atoms. For a certain Auger transition, the kinetic electron energy is determined by the sum of the shifts of the energy levels involved. The strongest change both in energetic position and peak shape will take place if the valence band is involved in the Auger transition (Fahlman et al., 1966).
2. Electron Energy-Loss Spectrometrv ( E L 8 In ELS the inelastic electrons are collected either in the vicinity of a diffracted beam or by a wide angular aperture. With the use of ELS, surface electronic transitions and surface vibrations of clean and gas-covered surfaces have been investigated. ELS provides information about the spectrum of empty electron states near the surface in combination with valence- and corelevel spectroscopies. Localized vibrations of adsorbates contain collective and structural information about the degree of dissociation, binding energies, and lateral interactions. These studies may therefore contribute significantly to catalytic researeh. The information depth of ELS is not simply determined by the electron mean free path but by the wavelength of the charge density fluctuation near the surface. Sensitivities of lo-’ and l o p 2 monolayers have been reported for electronic and vibrational excitations, respectively. The electrons in the conduction band of a metal closely approximate a degenerate gas or plasma of free electrons in a positive potential. Excitations of the plasma can arise in electron density oscillations of discrete energy values, which depend on the free-electron density and dielectric properties of the metal (Ferrel, 1956; Pines, 1963). The experiment can be carried out in an electron spectrometer if sufficient energy resolution is provided. The information and results obtained by this method are closely related to those of optical methods, but ELS is in many cases an simpler method and gives more direct information. Another advantage of this method arises from the fact that theories are more easily applicable. ELS has been demonstrated not only for vibrational spectra of adsorbed gases, but also for loss spectra arising from electronic transitions (Froitzheim, 1977). For single electronic transitions and collective electronic transitions (plasmon excitation), a resolution of about 0.5 eV is sufficient, whereas for vibrational spectra of adsorbates a resolution of a few milli-electron volts is necessary. 3. Threshold Spectrometries In threshold spectrometries the excitation or ionization of an atom in the inner shells corresponds to an interband transition between a core level and the unoccupied states of the valence band. Excitation can only occur if the excitation energy is sufficient to raise an electron from deep-lying levels into
236
P. BRAUN, F. RUDENAUER,AND F. P. VIEHBOCK
the unoccupied states above E F ;then the number of electrons per energy interval, given by N(E), is the density of states. As in free atoms, excitation is not necessarily accompanied by the loss of an electron. The loss of an electron will occur only if it has enough energy to pass the work function barrier. a. Observation of secondaryparticles. Secondary particles emitted during deexcitation, e.g., Auger electrons or characteristic X rays, leads to Auger electron appearance potential spectroscopy (AEAPS) and soft X-ray appearance potential spectroscopy (SXAPS). sec, accomA core-hole state decays after a time of the order of panied by the emission of Auger electrons or X rays. In general, the decay is not a single-electron transition, but a transition cascade including CosterKronig transitions, creating various kinetic secondary electrons. A series of secondaries is emitted and leaves the atom multiple-charged (Plesonton and Snell, 1957). The measuring principle is simple: by detecting the target current, which is the difference between the primary and secondary currents, AEAPS results as the most sensitive threshold spectrometry (Kirschner and Staib, 1975). b. Analysis of the exciting beam. The observation of the exciting beam and its variation near threshold leads to disappearance potential spectrometry (DAPS). The results of the former group depend on the deexcitation mechanism, whereas the latter does not by analogy to the FranckHertz experiment. When the primary energy is sufficient to produce a new excitation, those electrons which created a core hole lose energy and disappear from the measured reflected beam (Kirschner and Staib, 1973). The reflection coefficient decreases at excitation thresholds and is a measure of the excitation probability. All secondary decay processes are neglected by this method, because the excitation is observed directly. Electronic differentiation improves the rather poor signal-to-noise ratio. The experimental setup is simple: the energy of the electron gun is varied over the energy range of interest and the pass energy of the analyzer is varied simultaneously to measure the quasi-elastic part of the electron energy spectrum (Kirschner, 19771. 4. Ionization Loss Spectrometry (ILS)
Ionization loss spectrometry is related to threshold spectrometries insofar as characteristic losses are observed, but in ILS the energy spectrum is analyzed. The applicability of ILS to elemental analysis is evident. The core-level excitation process is the same as in threshold spectrometries; a sensitivity to chemical effects can be expected by modification of the density of states or by shifts of the core levels. ILS resembles DAPS in that it samples the excitation itself, independent of the following decay processes. Again,
SURFACE ANALYSIS USING CHARGED-PARTICLE BEAMS
237
Auger- or X-ray yields are unimportant in this method, but the mean free path for primary and secondary electrons depends on their different energy compared with DAPS. The main advantage of ILS for elemental analysis lies in the simplicity of the spectra. As in threshold spectrometries, in ILS the number of lines is relatively small, the lines are sharp, and overlap is rare (Kirschner, 1977).
5 . Zon Neutralization Spectrometry (INS) Secondary electrons for surface analysis can also be generated by bombarding ions. INS is a method that uses ion-electron interaction whereby slow primary ions at the surface are neutralized by a resonance process or an Auger transition. The potential of this method is, of course, not elemental analysis but investigation of adsorption and desorption phenomena on solid surfaces. The results are comparable with UV-photoelectron spectroscopy studies, especially if single-electron processes are involved (Hagstrum, 1972).
B. Analysis of Ions I . Zon Scattering Spectrometry (ZSS) Elastic binary collisions of low-energy (< 10 keV) primary ions with target atoms provide information on the elemental composition of the sample surface via the energy spectrum of backscattered primary ions. Figure 2 PRIMARY ION
SCATTERED ION
SAMPLE
000000 000000 FIG.2. Experimental geometry of ISS (schematic); formula for energy of scattered ions for scattering angle of 90" is shown. [From Honig and Harrington (1973).]
238
P. BRAUN, F. RUDENAUER,AND F. P. VIEHBOCK
shows a schematic of the scattering geometry. An incoming ions of mass number M1 and energy EO is elastically scattered by a surface atom mass number of M , through a laboratory scattering angle 8. The scattered primary ion retains an energy E l , given by (Smith, 1967), E1/Eo = ((1
+ M2)-1/M1)Z[cos8 + (M2/M1)' sin2 01
(1)
Energy analysis of primary ions backscattered through an angle 8 can therefore, in principle at least, provide unambiguous information on the mass number M , of elements present at the sample surface. In many practical ISS arrangements (Goff, 1973), a scattering angle 0 = 90" is chosen; the range of detectable elements in these cases is limited to those with M , > M , . The backscattered ion current Is=+can be written as (Honig and Harrington, 1973; Baun, 1978),
where Zp is the primary current, k is a constant G ( E o ) ,a factor taking into account the geometric arrangement of atoms at the sample surface [masking effect (Werner, 1977a)], c the differential scattering cross section, Pn(vl)is the velocity-dependent neutralization probability for the emerging scattered particle, and N o is the number of target atoms with mass number M , per square centimeter of surface. Scattering cross-section data have been calculated on the basis of a screened Coulomb potential and, for a given primary ion, typically vary within one order of magnitude through the period system, the lighter elements being the less sensitive ones. The factor 1- Pn(ul)depends on the primary ion/target combination and has been measured for a limited number of systems only (Verbeek and Eckstein, 1980). Quantitative determination of elemental concentrations by means of ISS does not yet have a firm theoretical basis; practical applications, therefore, frequently resort to an empirical sensitivity factor approach (see Section 111,C). The advantages of ISS are its surface sensitivity (the origin at the ions scattered into the elastic peak is limited to the topmost monolayer of the sample), and its capability of practically nondestructive analysis, particularly when light primary ions (H', He+) are used. With suitable instrumental additions the method can be applied for depth profiling and low-resolution lateral imaging (Minnesota, Mining and Manufacturing Co., 1979). 2. Rutherford Backscattering Spectroscopy (RBS) Similar to ISS, in RBS the elemental composition of a sample is also deduced from the energy losses of an incoming primary ion beam in a single
SURFACE ANALYSIS USING CHARGED-PARTICLE BEAMS
239
collision with a target atom. In RBS, however, light ions ( H + , He+) are used almost exclusively, together with much higher incident ion energies (several 100 keV to several MeV). As a consequence, not only the topmost atomic layer but also subsurface layers are accessible to analysis. Figure 3 schematically shows the scattering geometry used in RBS. A primary ion with energy E l is incident at the target surface; due to its high energy it penetrates into the solid to a depth x where it suffers a single wideangle collision with a target atom. The scattered ion is deflected back to the surface where it emerges with an energy E , . The incoming and outgoing ion-path sections are straight lines; here the ion loses energy in collisions with electrons and plasmons but is not deflected. The differential electronic energy loss dE per unit path length s can be written in the form of a power law,
d E / d s = -AYE'
(3)
where E is the ion energy and v an exponent depending on the energy range ( - 1 < v < 1/2) (Behrisch and Scherzer, 1973); A , is a constant, depending on v. When, therefore, the ion has penetrated into the solid to a depth x below the surface (see Fig. ll), it has slowed down to an energy E; (Behrisch and Scherzer, 1973),
E;
=
[Ei-' -(1
- v)A,(x/cosM)]~'('-')
(4)
The energy loss which this ion now suffers in a collision with a target atom
\ FIG.3. Experimental geometry of RBS (schematic); for further explanation see text., [From Behrisch and Scherzer (1973).]
240
P. BRAUN, F. RUDENAUER, AND F. P. VIEHBOCK
of mass number M 2 in a depth x is characterized by the “nuclear energy-loss factor” k ,
M, cose M, (5) M , M, M , M2 where E ; is the ion energy immediately after the collision. The outgoing ion again suffers electronic energy loss [analogous to Eq. (4)]so that the final ion energy E , can be calculated from Eqs. (4) and ( 5 ) as
+
+
+
Obviously, measurement of the scattered-ion energy yields information on the mass number M , of the target atom (via k ) as well as on the depth x where the collision has taken place. RBS can therefore provide compositional as well as depth-profiling information in a practically nondestructive analysis mode. Note, however, that a simultaneous determination of these two parameters is not always unambiguous since a light surface element may appear at the same energy E , as a heavy element in a greater depth x. Figure 4 shows a typical application of RBS for the analysis of a multilayer thin-film sample. The thickness of the individual layers can be calculated from the width of the elemental scattering peaks. Note that the stoichiometry of the SiO, film can be obtained from the step in the Si continuum.
-
, a]4
ENERGY OF BACKSCATTEREO 4He (keV) 5yO 500 I 1000 lop0 1500 2000 II 15pO I I I T I I NI on
69000-
rz
=I
0
40,000-
2 ; , 0 0
-
Surfoce
*ev
u
AU
LT--l
EXPANDED SCALE FIG. 44. Examples for depth profiling with RBS; thickness of Au layer ca. 600 A. [From Ziegler (1975).]
SURFACE ANALYSIS USING CHARGED-PARTICLE BEAMS
24 1
Quantitative determination of the composition of the oxide film can be performed by integration of the peak areas for Si and 0 (see Section 111,D).
3. Secondary Ion Mass Spectrometry (SIMS) Bombardment of a solid with an energetic ion beam (1-20 keV) gives rise to the development of collision cascades between knock-on target particles (Sigmund, 1969), transfering energy and momentum from the bombarding ion to target atoms. Some “branches” of the collision cascade return to the surface where they may cause ejection of surface particles when the transferred energy exceeds the surface binding energy of the solid. A generally small fraction of the ejected atomic and molecular particles are (positively or negatively) ionized ; mass analysis of this ionized fraction yields information on the elemental and (with limitations) molecular composition of the surface. The range of the primary ion in a solid is of the order of 10 nm, the developing collision cascade having approximately the same dimensions ; a secondary ion may therefore be emitted in lateral distances of the order of 5 nm from the impact point of the primary ion. By far the largest contribution to the secondary ion-emission originates from the momentary topmost atomic layer of the solid, the contribution of deeper layers being not quite certain (“information depth” generally is less than three atomic monolayers). Continued primary beam bombardment causes erosion of the sample and the macroscopic surface recedes; continued analysis of this receding surface is the basis of the depth-profiling capability of SIMS. The lateral distribution of elements may be determined using one of three different experimental techniques (see Section V,B, l), and a combination of lateral “imaging” with continued surface erosion permits three-dimensional isometric compositional analysis of a solid (see Section V1,B). Further advantages of SIMS are the extreme sensitivity for trace element detection (ppb to ppm); the capability of analyzing all elements in the periodic system including hydrogen (down to the 10-ppma level) and the ability of in situ determination of isotopic abundances. The quantitation of SIMS, i.e., the determination of relative or absolute elemental concentrations from the SIMS spectrum has not yet been put on a satisfactory theoretical basis; phenomenological methods have, however, been developed, range permitting semiquantitative analysis with accuracy in the 10 rel. (see Section 111,B). C . Short Comparison of Selected Particle-Beam Methods
Table I gives order of magnitude information on the essential analytical features of the surface analytical particle-beam methods described in the
242
P. BRAUN, F. RUDENAUER, AND F. P. VIEHROCK TABLE 1 GENERAL ANALYTICAL FEATURES OF PARTICLE BEAMTECHNIQUES Technique ~
a
Feature
AES
ISS
RBS
SIMS
Elemental range Elemental resolution Yield variation Limit of detection (atomic fraction) Lateral resolution Depth resolution (atomic layers) Atomic location Chemical information
2 Li AZ= I 10
2 Li
2 Li
>ti
10
100 10- 4- 10-
10-3-10-~
0.1-0.5 pm 2-20
No Some
10- 3- 10- *
'
1000 90h
F
1.5'
358*J
45'
5Oj
6 x 20%"'
F zz l.SL"
EST, external standard; WC, working curve; RSF, relative sensitivity factors; IIN, internal indicators (MISR); SAD, standard addition; CAR, CARISMA; SLTE, simplified LTE; 1 P, 1 parameter LTE; NS, standard, free LTE; SNLTE, sputter-normalized LTE. PweRtkeses -ate d t m m t e evafuationmethods. M , , M , are matrix ion species. N is the number of elements present in the sample. S is the internal standard element. 1 Estimated average accuracy of analyses 20% with careful measurement Smith and Christie (1978). Werner (1980b). Leta and Morrison (1980a). Rudat and Morrison (1979). Limited experience. Smith and Christie (1977). " Morgan and Werner (1978a). " Drummer and Morrison (1980).
-
'
258
P. BRAUN, F. RUDENAUER, AND F. P. VIEHBOCK
ratio of elemental area densities No(A)/No(B)may be substituted by the ratio of the squares of the atomic radii a. (Baun, 1978),
The concentration (relative surface coverage) B(A) of element A is then calculated from the standard formula (see Section III,B,l,c),
where the I(X) are the measured elastic peak currents of the elements X present in the sample. The general limitations to the application of a simple sensitivity factor formula such as Eq. (34) are discussed in Section III,B,l. In particular, the definition of similarity of calibration sample and unknown may be complicated in ISS by effects such as crystal structure, multiple scattering, selective sputtering, etc. (Honig and Harrington, 1973 ; Baun, 1978).
D. Quantitation of RBS The probability R for a high-energy primary ion to be backscattered into the solid-angle interval dsZ and energy internal dE, is given by Behrisch and Scherzer (1973) as d2N/N,
=
n,do(E;) dxfcos
= R(E1, E z , CI,
p, ~ p dE, ) dR
(36)
(see also Fig. 4), where dn is the Rutherford differential cross section do
=
ZlZ2e2 cos e - (1 - [ ( M , / M , ) ~ i n e ] ’ ) ~ / ~ 4E;’ sin4B{1 - [(M1/MZ)sin B]2)1/2
~
(37)
d2N is the number of ions scattered into the interval (dE,,dR), N , is the number of primary ions incident onto the target during the registration time of a spectrum, and nT is the number of target atoms per cubic centimeter. For a given primary ion and fixed scattering angle, the cross section is therefore a function of mass number M , and atomic number of the target atom only. Using Eqs. (4)-(6) from Section II,B,2, Eq. (36) can be written in the form d 2 N ( X )d& dR
= N,n(X)f(Zz,
M , , a, 0, E l )
N,n(X)f(X) (38) Here, d2N(X)is the number of ions scattered from target atoms of element X into the interval (dE2,dR), n(X) is the number of X atoms per cubic centimeter =
SURFACE ANALYSIS USING CHARGED-PARTICLE BEAMS
259
of the target, and f is a function depending on the indicated variables (for fixed primary energy and geometry, f is a property of the target element only). Integrating d 2 N ( X )with respect to dE, in effect means determination of the peak area A ( X )corresponding to scattering from a particular element X (e.g., the Ni peak in Fig. 4): A ( X ) = d N ( X )d o = N,n(X)
s
f ( X )dE, = N , n ( X ) f ( X )
(39)
where, again, f(x) = I f ( X ) dE2 is a function of element X . Obviously, one can define elemental sensitivity factors S ( X ) (see Section III,B), S(X) = 4 X ) / n ( X )= N , f ( X )
(40)
which, in principle at least, can be analytically calculated from the formulas given in this section and Section II,B,2. For a particular experimental arrangement, it is better to determine relative sensitivity factors SR(X)with respect to a reference element R from measurements on calibration samples (e.g., thin films of pure elements and known thickness),
The absolute number n(X) of X atoms per cubic centimeter of sample then can be calculated with the familiar formula
A set of sensitivity factors determined from pure elements is valid, in principle, for a particular primary energy and mean target atomic number only. Taking the appropriate experimental precautions, a quantitative determination of absolute elemental volume concentration can be performed with accuracies of a few rel. %.
IV. DEPTH PROFILING A . Nondestructive Methods
1. Methods Using Electron Spectroscopy An obvious possibility is to tqke advantage of the dependence of the mean free path of electrons on the primary energy (see Section 111,A). In AES the simplest way is to use different Auger electron transitions for the same
260
P. BRAUN, F. RUDENAUER, AND F. P. VIEHBOCK
element if different transitions are available. In this way information about the depth distribution of elements in a substrate can be found. The Auger signal I , for a given transition depends on (Section 111,A): I,
N
1;
cA(z)
exp( - z / l , cos a) dz
(43)
cA(z) is the concentration of element A with depth z, I , is the mean free path of the electrons of the Auger transition considered, and a is the angle between surface normal and analyzer entrance slit. Because of Eq. (43), depth distribution can also be obtained by variation of angle a. We therefore define an effective escape depth according to Fig. 8 (Hofmann, 1980):
leff = L A cos a
(44)
This method can be used directly if the solid angle of acceptance of the analyzer is small enough to select the angle a. This is the case for analyzers that do not have a symmetric axis, which includes source, entrance, and exit, e.g., spherical analyzer. In the case of a great acceptance angle, e.g., a cylindrical mirror analyzer (CMA), the following relation for the take-off angle can be given (Zeller, 1980): cos a = C O S ~ ~coscp ,
+ sinrp, sinrp cos 9
(45)
wherecp, is the analyzer entrance angle (for the CMAqA equals 42.3"),rp the sample normal, and 9 the azimuthal angle (see Fig. 9 for explanation). Using a CMA, the depth resolution is rather complicated but can be simplified by selecting the azimuthal angle 9. This can be done by using a drum device (Hofmann, 1980). In this CMA a diaphragm decreases the azimuthal angle from 2n to about 6" and is rotatable by a feed through.
FIG.8. Definition of effective electron escape depth.
SURFACE ANALYSIS USING CHARGED-PARTICLE BEAMS
26 1
FIG.9. Variation of take-off angle for a CMA.
Moving 9 from 0" to 180" the take-off angle a ranges forq =qAfrom 0" to 84.6".The effective escape depth then becomes
Aetr = A,
for a = 0";
AeR
=
0.1AA
for a = 84.6"
Changing the take-off angle from surface normal to about 5" off the surface plane, the information depth changes by a factor of 10.
2. Depth Profiling Using RBS The method of depth profiling with RBS has been briefly described in Section II,B,2. With limitations, RBS is suitable for quasi-nondestructive determination of depth profiles in surface layers of thicknesses not greater than about 10 pm and for elements present in concentrations of the order of 100 ppm or above. The interaction of light ions in the 100-keV range is intrinsically accompanied by radiation damage in the sample lattice. When the degree of damage is tolerable with respect to the postanalysis use of the sample (e.g., for analysis with a different method or, in the case of microelectronic devices, to the postanalysis functioning of the device), RBS analysis may be considered nondestructive. A theoretical and practical survey of the method has been given in the literature, e.g., by Ziegler (1975). B. Destructive Methods
Depth profiling can be done in an destructive way by removing surface layers by ion bombardment simultaneously with many analytical techniques (Wehner, 1975), or by methods using tapered sectioning (Werner, 1980a). 1. Sputtering of Composite Materials
The ejection of material from solid surfaces under energetic ion bombardment is well known as sputtering. Although sputtering of elements has
262
P. BRAUN, F. RUDENAUER, AND F. P. VIEHBOCK
been extensively investigated, sputtering of composite materials has been studied more extensively only recently. One of the reasons is that within the last 10 years sputtering has become a widely used method for depth profiling in combination with different surface analytical techniques such as AES, I S , XPS, and SIMS (Wehner, 1975). It has been found that sputtering of composite materials will often change the very surface composition of the sample that is analyzed by this method (Andersen, 1974; Oechsner, 1976). Whenever a multicomponent system is ion bombarded, selective sputtering generally occurs. Due to different partial sputtering yields of the individual components, an altered surface layer will build up. If steady-state conditions are reached, the target will be sputtered stoichiometrically, simply from conservation of matter. However, in general the surface will have a composition other than the bulk. Also, total sputtering yields of multicomponent systems have been found to be different from a superposition of the yields of the components (Betz et al., 1977b; Dahlgren and McClanahan, 1972; Ogar et al., 1969; Szymonski et al., 1978; Poate et al., 1976). Considering the sputtering process of composite materials, one has to distinguish between solid solutions or compounds and multiphase systems. For the first group, steady-state conditions will be reached quickly after removing a layer comparable to the penetration depth of the primary ions. For the second group, grains of different phases are present at the surface and it is obvious that selective sputtering will occur, if the individual phases have different sputter rates. Steady-state conditions will be reached after removing a layer with a thickness of several grain diameters (Henrich and Fan, 1974), which will generally be in the pm range. Surface roughness will develop and due to “back and forth” sputtering between the phases, the very surface composition of a phase will be also determined by the surface topography and the other phases present (Wehner and Hajicek, 1971). Cone formation and accumulation of “difficult-to-sputter” species result in a very complicated sputtering behavior, which depends on the evolution of the topography with time and also on impurity concentrations. Although sputtering of elements is quite well understood and different theoretical approaches (Sigmund, 1981 ; Betz et al., 1971 ; Ishitani and Shimizu, 1974) have yielded satisfactory agreement between experiment and theory, no comprehensive theory of alloy or compound sputtering has yet been established. Semiquantitative calculations by various authors (Haff, 1977; Haff and Switkowski, 1976; Kelly, 1978)predict surface enrichment of the heavier component. Andersen and Sigmund (1974) have extended their theory of random collision cascades to the problem of energy sharing among the components of a multicomponent system. They predict for systems with a large mass ratio of the constituents, that the energy
SURFACE ANALYSIS USING CHARGED-PARTICLE BEAMS
263
spectrum of the heavier component goes considerably faster to zero than for the light constituent, as compared to the components. This should also result in a higher ejection probability for the lighter constituent and therefore produce surface enrichment of the heavier component. However, these predictions are complicated by the surface binding energies. Two components having nearly the same mass may have very different surface binding energies and hence very different sputter yields, although recoil energy and slowing down densities are the same. The second complication appears as soon as an altered surface layer develops, due to different partial sputtering yields, and the condition of homogeneity for applying the theory is no longer fulfilled. a. Selective sputtering. Surface enrichment of one component due to selective sputtering has been shown for different binary and ternary alloy systems (Betz, 1980; Opitz e i al., 1980). To observe changes in the surface composition of alloys under ion bombardment it is necessary to start from a “clean” surface with a composition equal to the bulk composition. Different methods can be used to create such a surface for solid solutions (Braun and Farber, 1975): Fracturing the samples in the ultra-high-vacuum (UHV) system prior to analysis. If the fracture is transgranular, e.g., through the grains, the surface created should have a composition equal to the bulk. For an intergranular fracture, segregation to the grain boundaries can give rise to a surface different in composition to the bulk. Scribing the samples with a stainless steel or diamond tip in UHV also results in a surface with a composition equal to the bulk by a nonthermal melting process in a microscopic region (Meyer, 1977). Provided the same composition is found for these quite different methods to create a new surface, it can be assumed that it is also equal to the bulk composition. However, a different surface composition can be found for heterogeneous alloy systems, e.g., Ag-Cu (Farber et al., 1976). Using AES for determining the surface composition, the ratio of the Auger signals of the alloy components from a sputtered surface can be compared with the Auger signal ratio of scribed and fractured samples to determine changes in surface composition due to ion bombardment. This procedure is more advantageous than the use of pure standards for two reasons. First, different surface topography of the standards and the sputtered alloys can give rise to different results and, second, the contribution of backscattered primary electrons can be different for the standards and the alloys (Joshi et al., 1975). When sputtered and scribed or fractured alloys are compared, however, we find that the matrix will be the same except for the altered layer thickness. Under steady-state conditions one can derive the following relation between the component sputtering yields S(A), S(B),and the Auger intensi-
264
P. BRAUN, F. RUDENAUER,AND F. P. VIEHBOCK
ties Z, ZB for the bulk and rA , 4 for the surface composition after sputtering (Shimizu and Saeki, 1977): S(A)/S(B) =
(zA/zB)/(TA/rB)
(46)
This equation for the equilibrium case remains also valid when diffusion processes are assumed to take place, possibly enhanced due to sputter damage (Ho, 1978). Therefore, the ratio of the component sputtering yields can be seen directly as the difference between the sputtered surface and the scribed or fractured bulk composition ratios. For example, analysis of the Ag-Au system using AES is shown in Fig. 10 ;S(Ag)/S(Au) was found to be 1.8 according to Eq. (46). To study the sputter behavior of composite materials, a first approximation is needed to compare the component sputtering yields in the alloy with the sputtering yields of the pure elements. According to Sigmund’s theory (Sigmund, 1981) the sputtering yield of the elements is given as: S(E) = 0.042LSn(E)/U0
(47)
where S,(E) is the nuclear stopping power, E the energy of the incoming ion, U, the surface binding energy taken as the heat of sublimation, and L a function of M , / M , . The expression S(E)U, is a quantity proportional to the recoil energy density deposited at the surface from the collision cascade created by the impinging ion. This function is plotted in Fig. 11 for 2-keV Ar ions and different target materials (dashed line). It has been shown that Sigmund’s L function is high by at least a factor of 2 for large mass ratios (Sigmund, 1977; Andersen and Bay, 1973), which is probably caused by a lack of surface corrections in the theory. Using the experimentally derived
FIG.10. Measured surface concentration ratio of Ag (351-355 eV) and Au (2024 eV) versus ratio of bulk concentrations for Ag-Au alloy; [from Betz (1980)l:0 , fractured; A, scribed; 0, sputtered.
SURFACE ANALYSIS USING CHARGED-PARTICLE BEAMS
lo-
A Al
;"w
Ag
Cr
N
Au
265
U
Pt
FIG.11. Recoil energy density SU,,for 2-keV Ar ions on different target materials according to the sputtering theory of Sigmund (1981) (dashed line) and with values for L ( M , / M , ) according to Andersen and Bay (1973) (solid line).
L function from Andersen and Bay (1973), the fully drawn line in Fig. 11 is found for S(E)U,. As can be seen, the recoil energy density increases strongly only for light target materials and is constant for target atomic weights above 100, indicating that differences in the individual sputtering yields for the heavier elements are only determined by the surface binding energies. b. Consequences of selective sputtering. The observations for all binary, one-phase systems analyzed thus far, show that the sputtering yields of the components are more or less preserved in the alloys, and enrichment occurs for the component that has the lower yield as a pure element. In addition, the results for the ternary systems Ag-Au-Cu (Betz et al., 1980)and Fe-Cr-Ni (Opitz et al., 1980) exhibit the same behavior as the corresponding binary systems. Contrary to these observations, it has been proposed from RBS measurements (Liau et al., 1977) that, as a rule, enrichment of the heavier component occurs under ion bombardment. For Ag-Au enrichment in Au, Cu-Pd in Pd, Cu-Pt in Pt, and Ni-Pt in Pt, it is observed that the enrichment component is the heavier one as well as the component with the lower yield of the pure constituents. For Cu-Au, with a large mass ratio of 3: 1, no Au enrichment exists at 1 and 2 keV and only a minor enrichment exists for higher ion energies, in agreement with equal sputtering yields for Au and Cu. For Cu-Ni and Pd-Ni the lighter component Ni is enriched; and this is also true for Au-Pd wherein the lighter component is Pd. For Ag-Pd, with a mass ratio of 1, strong Pd enrichment is also observed in accordance with the much smaller yield of Pd compared to Ag. On the other hand, for metallic compound phases AI-Au,, A1,-Au, AI-Cu, and intermetallic silicides Si-Ni, Si-Pt, and Si-Pt, enrichment of
266
P. BRAUN, F. RUDENAUER,AND F. P. VIEHBOCK
the heavier component was found using RBS (Liau et al., 1977; Chu et al., 1976), although the sputtering-yield ratios of the pure components would indicate in all these cases enrichment of the lighter component. A study of Al-Au, Al-Fe, A1-Ni, and Al-Cr compounds (Opitz, 1979) under 2-keV argon ion bombardment shows depletion in Al, which is always the lighter and low-sputtering-yield component. Partly for these alloys the mass ratio is exceptionally large. It is however interesting to note that enrichment of the heavier component is only found if the recoil energy densities of the pure components are quite different, as can be seen from Fig. 11. For all the alloys with surface enrichment in agreement with the yields of the pure elements, the recoil energy density is either the same, because both components have the same mass, e.g., as for Cu-Ni and Ag-Pd, or their atomic weights are large enough so that the recoil energy density no longer varies with mass. If, on the other hand, the recoil energy densities of the pure components are quite different, enrichment of the heavier component, which is also the one with the higher recoil energy density, exists. All these experimental results are in agreement with the following assumption: For composite materials with components of nearly the same recoil energy density UoS, surface enrichment and component sputtering yields are only determined by the surface binding energies of the alloy constituents, which seem to be in qualitative agreement with those of the pure components. Therefore, the ratio of the component sputtering yields agrees qualitatively with that of the pure elements, and enrichment of the low-yield constituent is observed. This indicates that the recoil energy densities are preserved in the alloy. For alloys with quite different recoil energy densities of the constituents, collision cascade effects generally play the dominant role, and enrichment of the heavier component, as predicted by theoretical models (Haff, 1977; Haff and Switkowski, 1976; Kelly, 1978; Andersen and Sigmund, 1974) is observed.
2. Limits of Depth Profiling Using the Sputtering Method A universally applicable method for removing thin layers from a solid is bombardment by energetic ions of energies between a few hundred to a few thousand electron volts. Simultaneous detection of sputtered ions by SIMS makes this method very powerful for depth analysis, although any surface analysis method may be used for depth profiling in combination with sputtering (e.g., AES). The vital result of any depth-profile measurement is the concentration cA of element A as a function of depth z from the surface. The measured
SURFACE ANALYSIS USING CHARGED-PARTICLE BEAMS
267
distribution should be transformed to the actual depth profile if cA is a function of the measured signal (Auger electron current or secondary ion current; see Section 111) and z is a function of the sputtering time. The constant sputtering rate with time is only a rough assumption in depth profiling where the sputtering time is taken as a measure for the removed layers. However, the sputtering yields of the various elements are all within one order of magnitude; therefore, a rough proportionality between sputtering time and depth is given. More accuracy is necessary for the sputter yields, not only of the pure elements but also of composite materials which are present in the specimen. The sample consists of a two- or multiphase system, with no solid solubility of one constituent in the other. It was then found that the sputter rate remains close to that of the Eow-yield constituent (Braun, 1979), if at least 30 at.% of this component are present in the alloy; for lower amounts, the total sputtering yield increases to that of the high-yield component. For a nonmixable two-phase system, the number of atoms NAand N , , sputtered by an ion dose It from the two phases, should be NA =
SAAAIt
(48)
NB = SBABIt
(49)
where SA, SBare the sputtering yields of the pure elements, and A,, A B are the fractional surface areas of each component. For steady-state conditions, NJNB = = S A A A / S B A B if cA, cBare the bulk concentrations of the two elements. Therefore, one obtains for the total sputtering yield st
*
~/(cA/SA
+ cB/SB>
(50)
The sputtering yields for the nonmixable systems Ag-Cu (Betz, 1980) and Ag-Ni and Ag-Co (Dahlgreq and McClanahan, 1972) are shown in Fig. 12. The disagreement between the calculated and the measured yield values, and the constant sputtering yield over a wide concentration range, indicates that the low rates were caused by coating the Ag phase with the low-yield phase (Cu, Ni, Co) after changes in surface topography, due to the different erosion rates of the crystallites. Wehner and Hajicek (1971) observed similar reductions in the sputter yield due to coating the high-sputter yield material with a low-yield one. They explain the yield reduction on basis of cone formation and back and forth sputtering between the cones. Furthermore, for Ag-Cu thin films it was found that after ion bombardment is stopped, the surface becomes enriched in Ag within a few minutes. This effect was explained by surface diffusion of Ag covering the Cu crystallites by approximately one monolayer of Ag (Betz et al., 1977a).This indicates the presence
268
P. BRAUN, F. RUDENAUER, AND F. P. VIEHBOCK
8 C
._ \
g 6 c
0
L
2
0
20
LO
M)
80
100
at% Ag
FIG. 12. Sputtering yields (2-keV A r t ) for Ag-Cu alloy films on glass (0) and on Ta,O, ( 0 )substrates, and for (1.5-keV Kr') Ag-Ni (m) and Ag-Co ( 0 )alloys. [From Dahlgren and McClanahan (1972).] The dashed lines are the yield curves according to Eq. (50).
of two controversial processes for nonmixable systems : Topography changes and contamination of the high-yield phase (Ag) with low-yield atoms resulting in low-sputter rate, and after sputtering the surface becomes covered with one overlayer (Ag) due to surface diffusion. For a solid solution of two components with nearly equal mass, the recoil energy density SV, (Section IV,B,l) in the alloy is the same as in either pure constituent because different, but equal, mass atoms are not distinguished in the development of the collision cascade. Different sputtering yields of the components and selective sputtering effects in the alloy can therefore only arise due to different surface binding energies of the components. For Cu-Ni and also for Au-Cu and Ag-Au, a linear increase of the sputtering yield with the concentration from the value of the low-yield component to the value of the high-yield component is observed (Betz, 1980); Fig. 13 shows this behavior for Au-Cu alloys. I ._: 5 \
5
5 L3-
I
SURFACE ANALYSIS USING CHARGED-PARTICLE BEAMS
269
3. Methods Using Tapered Sectioning Tapered areas of samples can be established by mechanical angle lapping or by sputter-crater etching and profiling with the probing beam by a line scan over the cross section. Obviously, the preparation method uses destructive processes, but the depth information obtained is nondestructive. Inherent to the preparation method are variations of the sample composition as a result of mechanical lapping or sputtering. By lapping composite materials, one has to distinguish between single- and multiphase alloys or compounds. In the latter, a smearing of constituents with tensile strength lower than the other ones can take place in the surface layers. Generally, sputtering also will vary the surface composition of composite materials, by selective sputtering, and leads to a new equilibrium surface concentration; this is treated in detail in Section IV,B,l. By mechanically preparing a tapered section at an typically of 0.1" and using a probing beam of diameter I pm, a depth angle /?, resolution of about 2 nm should be obtainable. After a surface is sputtered for a short period of time, a crater will develop with a nearly Gaussian profile (Hofmann, 1976): z(u) = zo exp( - u 2 / 2 0 2 )
(51)
Az(u)/Au = tan /? = uz(u)/02
(52)
Figure 14 illustrates the crater profile. In the deepest part of the crater the slope will be tan /? = for typical values of crater radius o = 1 mm and of depth z,, = 200 nm, corresponding to an angle /? = 20".If the electron beam (AES) is scanned from the bottom of the crater to the edge, the depth analyzed changes gradually. The important difference to the conventional
4 FIG.14. Development of 8 sputtering crater with a Gaussian profile.
270
P. BRAUN, F. RUDENAUER,AND F. P. VIEHBOCK
angle-lapping method often used in electron microprobe analysis is that the angle can be made much smaller in crater sputtering. The advantages of tapered sectioning over conventional sputter depth profiling (see Section IV,B,2) are that the depth profile can be obtained after sputtering with no limitation in data recording over the depth of interest and that lateral inhomogeneities of elements in depth distribution can be studied quickly in more detail.
4. Considerations in Auger Depth Projiling When an element has to be depth profiled in a homogeneous matrix, the sputtering yield yIoIis generally constant in that the depth scale is proportional to sputtering time. When, e.g., an element has to be profiled through a multilayer system, variations in sputtering yield may cause distortions in the measured profile. Recently, optical methods have been developed allowing in situ measurement of sputtering speed with a depth resolution down to the nanometer range (Kempf, 1979). The quality of a depth profile measurement may be assessed by two parameters: depth resolution Az and dynamic range R D . These parameters may be defined with respect to a step function (100-0%) concentration change: Az is the depth which has to be sputtered before the elemental signal at the interface changes from 95 to 5% of its maximum level; and R D is the ratio of maximum to minimum signal when sputtering through the interface into a region originally containing no X atoms. The true depth profile may be smeared and distorted in the measurement due to several instrumental and physical factors: ion beam homogeneity ; material transport from crater rim to crater center ; sputter redeposition of material on surrounding electrodes ; mass interference in low-resolution SIMS instruments or line interference in AES ; statistical nature of layer removal; atomic mixing in collision cascade; finite information depth of sputtered ions in SIMS and of characteristic electrons in AES; surface roughness and topography ; distortion of profiles by field-induced migration caused by ion beam charging of insulators. If the sputter rate dz/dt varies within the area analyzed, but is constant with time, this leads to a constant relative depth resolution Az/z(Werner, 1974). In AES a further limitation to depth resolution is set up by the statistical
SURFACE ANALYSIS USING CHARGED-PARTICLE BEAMS
27 1
nature of sputtering [factor (5)]. A quantitative estimate can be obtained from the successive-sputtering model proposed by Benninghoven ( 1970). The basic assumptions of this model are that sputtering takes place only in the actual surface layer and that the sputtering yield is the same for all layers independent of any different layer composition. As result, the relation between depth and relative depth resolution is given by
Az/z
=
2(d/~)”~
(53)
with the monolayer thickness d. For example, with a value d = 0.4 nm, the relative depth resolution Az/z at a 4-nm sputtered depth is 63%, at 40 nm it is 20%, and at 400 nm, 6%. Evidence of the validity of this relation could be shown in the work of Hofmann (1976) and Evans (1972). For example, an Auger depth profile of a multilayer interference coating of a selective solar absorber for 2-keV Ar+ ion sputtering is given in Fig. 15. The Auger signal versus time is in most cases sufficient for comparing of data but not if the absolute depth distribution is desired. In Fig. 15 the layers consist of A1203,MOO,, AI2O, on Mo with their individual sputtering yields, which differ strongly. The ratio S(Mo03)/S(A120,) for 10-keV
10
2
sputtering time FIG. 15. Auger depth profile of AlZ0,-MoO,A1,0, with 2-keV Ar’ ions.
coating on Mo substrate; sputtered
272
P. BRAUN, F. RUDENAUER, AND F. P. VIEHBOCK
Kr’ ion bombardment (Kelly and Lam, 1973) equals about 6. The absolute depth distribution will then show the A1,0, layers to be 6 times as thin as given in Fig. 15. For the time-to-depth transformation, the sputter rates of composite materials and compounds are important. Data from different authors for the same element and energy can vary greatly and a careful data selection should be done in any case study (Wehner, 1975; Betz, 1980). 5. Practical Examples for SIMS Depth Projling In SIMS depth profiling, the sample to be analyzed is bombarded with a primary beam current Z,(t), constant in time. The secondary ion current Zx(t)of a selected element X is recorded as a function of time. The time scale t can be transformed into a depth scale z through apriori knowledge or in situ measurement of the sputtering speed so that the desired depth profile of an element cx(z) can be obtained, CX(4 =
klx(t)
(54)
where k is a constant and cx(z) is the elemental concentration of element X as a function of depth (Werner, 1978). Experimentally obtained values for the relative depth resolution Az/z are of the order of 0.4% remaining constant at great sputtering depths (Werner, 1974,1977b). The effects distorting a true profile have already been listed in Section IV,B,4. Dynamic ranges in excess of lo4: 1 (measured in the tail of implantation profiles) have been obtained in well-adjusted instruments (Werner, 1974). Concerning the fidelity of the shape of a measured profile, the distorting effects (1)-(3) in Section IV,B,4 can be minimized through experimental refinements (see Fig. 16). Here the profile of a “B” implant in Si is severely smeared because an unfocused primary beam is used; rastering a focused beam only slightly increases the dynamic range due to remaining crater-edge effects. Rastering plus electronic gating the central crater section brings about a dramatic increase in dynamic range [better than with rastering and mechanical gating by extracting lens and diaphragm (Magee et al., 1977)l; finally, four orders of magnitude in the dynamic range can be obtained by combined use of rastering a focused beam, electronic gating, and mechanical aperture (extraction lens). The residual signal level may then affect only the traced instrumental effect (3) or any of the physical limitations (4)-(9) (see p. 270). The statistical nature of sputtering sets a limit to depth resolution mainly in extremely shallow gradients (Az = 5-10 atomic layers); atomic mixing may cause an asymmetric profile broadening at the interior side (McHugh, 1975). Serious modifications of profiles in insulators may be expected for ions with high mobility when using positive primary ions. In
273
SURFACE ANALYSIS USING CHARGED-PARTICLE BEAMS
static beam
\
rasteronly
\-r
raster +lens
Si
I
5 keV4'Ar+
raster +. electronic gate
raster electronic gate
+ +
lens
0
0.5
1.0
1.5
depth ( p m )
FIG. 16. Optimization of dynamic range in SIMS depth profiling; see test. [From Magee et al. (1977).]
these cases (e.g., Na, K in glass matrices), the use of negative primary ions and means for external charge suppression are achievable (Werner and Morgan, 1976; Gossink et al., 1978). Mass interference of isobaric molecules can be avoided in high-resolution instruments when the required resolution does not exceed MjAM = 15,000 (Magee, 1979). A different type of profile distortion may be caused by variations in the degree of ionization of the sputtered particles with depth (e.g., sputtering through an interface between different matrices). Efficient means to correct for this effect have not yet been developed; fortunately, in depth profiling of ion implants (one of the most important fields requiring high-sensitivity,
274
P. BRAUN, F. RUDENAUER,AND F. P. VIEHBOCK I5KeV PROTON IMPLANT INTOSILICON
t
o
y
-
r
B AND
-
ldsO
0.1
0.2
0.3
0.4
P DOUBLE DIFFUSION
p
0.5
0.5
0.6
1.0
1.5
2.0
DEPTH ( p m )
(b)
FIG.17. (a) Depth profiles of H - and 30SiH- using Cs+ bombardment; no background subtraction. (b) Simultaneous profiling of B and P diffusion layer to determine junction depth. Both figures from Magee (1979).
TABLE 111 DEPTH-PROFILING DETECTION LIMITS' IMPLANTS I N Si USINGAES AND POSITIVE (0,') OR NEGATIVE (CS') SIMSb
FOR [ON
SlMS Element
AES
0 2+
cs
1019
10i7
1OI6
1017
3 x 10'6
H C 0
+
1017
B
1019 1019
1014-1015
As
loi9
P
I O ~ ~ - I O *3~
1019
S Se Te Au In atoms/cm3. After Werner (1978b).
1017
1oi5
3 x 1015 2 x 10'6 3 x 10'6
1OI6 1015
SURFACE ANALYSIS USING CHARGED-PARTICLE BEAMS
275
high-resolution profiles), yield variations may be neglected in virtually all practical cases. When all of these artifact effects are properly dealt with, SIMS is the most sensitive and precise method for depth-profiling elements throughout the periodic system (hydrogen included). Examples of measured ion implant profiles (Perkin-Elmer, 1979) are shown in Fig. 17. A compilation of practically obtained detection limits in depth profiling is given in Table 111.
V. ELEMENTAL MAPPING The development of surface analytical instrumentation with spatial resolution capabilities makes possible two-dimensional and, by utilization of the sputtering method for removal of the surface layer, even three-dimensional (steric) elemental analysis of surfaces and the surface near volume of a solid sample. The primary information obtained by these instruments is always the two-dimensional distribution of an element-characteristic signal (e.g., Auger electron or secondary ion signal). These two-dimensional distributions have generally been termed Auger or secondary ion “maps,” or, less accurately, “elemental maps” of the particular element to which the instrument has been tuned. In many cases these “micrographs,” as they should correctly be called, give valuable information concerning the distribution of an element across the sample surface. Extreme care should be taken, however, when considering micrographs as directly representative of the local distribution of elemental concentrations. Ideally, the signal intensity across such micrographs should be directly proportional to the local elemental concentration (“concentration contrast”). In general, however, the physical processes involved in the stimulation, emission, and detection of the electron and ion signals from a solid surface lead to a nonlinear relationship between local element concentration and local signal intensity, thus introducing artifacts into the contrast distribution of electron and ion micrographs. Analog and digital methods have been devised, capable of removing, in many cases, “artifact contrast” from electron and ion micrographs, thereby transforming “micrographs” into “concentration maps” of the respective element. A . Auger Mapping
For a comprehensive, surface analysis determination of the surface composition of a point, line, or area with high, uniform sensitivity, high spatial resolution, designed for practical problem solving is important. A scanning Auger microprobe provides an almost nondestructive elemental analysis of
276
P. BRAUN, F. RUDENAUER, AND F. P. VIEHBOCK
a specimen surface with atom-layer-depth resolution and lateral resolution in the submicron range. It employs a scanning electron beam (energy, 1-30 keV) as a probe for AES analysis. The diameter of the impinging electron beam can be preselected (see Section VILA) and determines the minimum size of the area analyzed. 1. Instrumentation
An Auger image, or “elemental map,” shows the spatial distribution of a single element over the surface analyzed. It is obtained by setting the spectrometer to a specific Auger peak and scanning the electron beam over the selected area of the sample. The electron beam can be stepped point by point in unit beam diameter steps as done in commercial instruments (Perkin-Elmer, 1979; MacDonald and Waldrop, 1971). The Auger peak intensity above the adjacent background level for each spatial point is measured and stored in a memory. Images are composed of up to 250 lines with 250 points per line and have a number of gray levels discernable in the picture, determined by the signal-to-noise ratio (Browning and Prutton, 1979).If the electron gun is coaxial in the CMA a minimization of misleading effects due to topographic distortions is given. Topography effects can be also minimized by dividing each data-point signal N ( E J by the background signal N(E,). Figure 18 shows an example of computer-generated Auger maps and line scans of a sulfide inclusion in iron (Perkin-Elmer, 1979). One line scan gives a quantitative indication of the elemental distribution across the sample. Selection of horizontal or vertical line location and number of elements per line depend on the analytical problem and uses routine programs in computerized system control.
2. Quantitation of Auger Maps By elemental mapping, the relative concentrations of the various constituents in a sample can be determined with high lateral resolution. Use of quantitation routines for the Auger signal of each data point lead to lateral distribution of the elements over the selected sample area. Generally, the local signal and elemental concentration will not be proportional. The topography of the surface especially determines the local dependency of the Auger electron yield. For different elements the influence of surface topography will partly level off and a first-order approximation can be given. The contribution of backscattered electrons to the Auger signal also depends on topography and can be minimized only if they are not significant or essentially different for the elements of interest (El Gomati et al., 1979).
SURFACE ANALYSIS USING CHARGED-PARTICLE BEAMS
277
I.tm FIG.18. Computer-generated Auget maps of S, Fe, and Mn (left) and line scans (right) of a sulfide inclusion in iron. [After Perkin Elmer (1979).]
278
P. BRAUN, F. RUDENAUER, AND F. P. VIEHBOCK
FIG.19. SEM image of a steel fracture surface (top) and Fe Auger images before (center) and after (bottom) topographical correction. [After Perkin-Elmer (1980).]
279
SURFACE ANALYSIS USING CHARGED-PARTICLE BEAMS
Application of topographical correction routines using background subtraction results in a correct picture of elemental distribution. Figure 19 shows a scanning electron micrograph (SEM) of a steel fracture surface and Auger images of iron before and after application of this topographical correction routine (Perkin-Elmer, 1980). Additional effects in elemental mapping are vibrations of the sample against the focused electron beam and magnetic stray fields, which should be Minimized also. B. SIMS Mapping 1. Instrumentation
Three basic types of SIMS instrumentation are available for obtaining information on the lateral distribution of elements on a solid surface (see Fig. 20): a. The ion microscope (direct imaging instrument). Here, the sample is bombarded by a large primary ion beam (of the order of 500-pm diam.); secondary ions are emitted from the bombarded area with a local current density distribution related to the local concentrations of the different elements present in the bombarded area. The sample plane is “imaged” in a rigid ion optical sense onto the surface of an ion/electron converter. The optical system performing this imaging consists of an extraction and
U
\I/
(a)
(b)
(C)
FIG.20. Three basic modes of SIM$ Imaging (schematic). The direct-imaging scanning ion microprobe (b) combines the secondary ion extraction system of the direct-imaging ion microscope (c) with the mass filter and detecoon systems of the scanning ion microprobe (a). [From McHugh et a/. (1977).]
280
P. BRAUN, F. RUDENAUER,AND F. P. VIMBOCK
immersion lens, a transfer lens system, a (single or double focusing) mass analyzer system, and a projection lens system (Castaing and Slodzian, 1962; Rouberol et al., 1968; Gourgout, 1967). The essential action of the mass spectrometer is to separate out an individual mass-analyzed elemental image from the global image produced by the immersion lens. The magnified elemental ion image at the converter surface is transferred into an electron image with the same current distribution; this electron image may be visually observed or photographed from a scintillator screen. Total lateral magnification is of the order of !OO. Different versions of the ion microscope have been built. The original instrument, designed by Castaing and Slodzian (1962) used a single focusing magnet for mass analysis; owing to the large energy spread of secondary ions, mass resolution was therefore limited to about M / A M = 250. A second-generation instrument, produced by CAMECA S.A. of France, used a double-magnetic prism/electrostatic mirror system to limit the energy bandpass of secondary ions, thereby reducing peak tailing and increasing mass resolution. With the same instrument high-resolution mass spectra (MIAM 5 5000) were obtained using an optional electrostatic sector (Morrison and Slodzian, 1975). Lateral resolution in the imaging mode was of the order of 1 pm or better. The third-generation instrument of CAMECA (the IMS-3F) incorporates a truly double-focusing stigmatic mass spectrometer allowing high mass resolution (MIAM I7500) to be obtained in both the imaging and the mass spectrometric mode; in the latter mode, mass resolution may be increased to about 12,000 (Gourgout, 1977). The primary beam can be focused to small diameters (2 pm) and can be scanned to obtain a flat-bottomed crater; this feature is useful in depth profiling (see Section IV,B,4). b. The scanning ion microprobe. Here the lateral resolution is obtained by scanning a microfocus primary ion beam (of the order 2-pm diam.) across the sample surface. The secondary ions emitted from the sample are collected by an electrostatic extraction optics and mass analyzed by a mass spectrometer. The mass-analyzed secondary ions are usually registered by a high-gain multiplier detector. The detector current may be used to modulate the beam intensity of an oscilloscope, which is scanned in synchronism with the primary ion beam. Thus, an image of the secondary ion current density distribution at the sample surface is produced at the oscilloscope screen, the lateral resolution corresponding to the diameter of the scanning primary ion beam. Since in this type of instrument the mass analyzer does not have to transport image information it can be designed for high transmission (Slodzian, 1979) and high mass resolution (Williams and Evans, 1975); also, nonfocusing types of mass analyzers, such as the quadrupole mass filter, can be used, thus considerably reducing the cost of the total instrument
SURFACE ANALYSIS USING CHARGED-PARTICLE BEAMS
28 1
(Wittmaak, 1978; Riidenauer et al., 1978). The original version of the IMMA scanning ion microprobe of ARL (Liebl, 1967) was the predecessor of various types of commercial (Banner and Stimpson, 1974; Tamura et al., 1970; Wittmaak, 1978) and laboratory instruments (Riidenauer and Steiger, 1974; Riidenauer et af., 1978). c. The image-dissecting ion microprobe. This type of instrument combines features of the ion microscope and the scanning ion microprobe (McHugh et al., 1977). As in the ion microscope a large primary beam and an emission lens system is used which produces a global (non-mass-analyzed) image of the secondary ion current density distribution at the bombarded sample surface. This global image is raster-scanned across an aperture; thus, only ions corresponding to a small surface area are allowed to pass into a mass spectrometer, which, as in the scanning ion microprobe, does not have image-conserving properties and can be designed for high transmission and abundance sensitivity. An elemental image can be obtained by modulating the beam intensity of an oscilloscope, scanned in synchronism with the global image, with the output signal of the mass spectrometer detector. 2. Quantitation of SIMS Maps a. Contrast mechanisms, “Contrast” in secondary ion micrographs, i.e., spatial variations in signal intansity, may be due to several sample- and instrument-related phenomena. On flat surfaces the most prominent contrast effects are the following: ( i ) Concentration contrast; the secondary ion signal only depends on local elemental concentration. When, in addition, this dependence is linear, the ion micrograph directly reflects the distribution of the respective element across the surface. (ii) Matrix contrast; i.e., local variations in absolute and relative ion yields due to local variation in matrix composition or locally variable reactive gas adsorption. (iii) Crystallographic contrqst ; i.e., variations in secondary ion yield due to locally variable orientation of microcrystallites with respect to the sample surface (Prager, 1975; Scilla and Morrison, 1977).
On rough or nonplanar surfaces additional artifacts may be introduced by the following : (iu) Topographic contrast; i.e., local variations in primary beam incidence angle (Kobayashi et al., 1977) and secondary ion collection efficiency due to topographic microstructure (shading effect).
282
P. BRAUN, F. RUDENAUER, AND F. P. VIEHBOCK
(u) Chromatic contrast; i.e., element-dependent ion collection efficiency due to element-dependent ion emission energies (Steiger and Rudenauer, 1979). In the presence of a strong ion extraction field the electrostatic potential distribution near microstructures at a sample surface acts to some degree as an energy preselector for the secondary ions; generally, the signal extraction from deep crevices or from behind sharp ridges is easier for slow ions than for fast ions.
In addition to these sample-related effects [(g-(u)], the ion detector itself may cause distortions of the contrast in secondary ion images : (ui) Detector contrast appears to be particularly important in ion microscopes due to the various steps involved in image recording with instruments of this type. Fasset et al. (1977) have taken into account nonhomogeneous detector response and detector nonlinearity due to blackening of photographic film when the ion micrograph is recorded by direct film exposure in the ion microscope and digitized in a scanning microdensitometer. Analog and digital methods have been devised to remove one or more of these “artifact” contrast effects [(i)-(ui)]from an ion micrograph and obtain “corrected maps” more representative of the actual elemental distribution than the original ion micrographs. b. Analog processing of ion micrographs. Kobayashi et al. (1 977) have developed a fast on-line hardware current-division method capable of removing predominantly topographic contrast from ion micrographs produced by a scanning ion microprobe. The experimental arrangement is shown in Fig. 21. The essential feature is a “total ion monitor” situated between the electrostatic and magnetic sectors of the double-focusing TOTAL ION MONITOR
Etec1ron Multiplier I
+
FIG.21. Scanning ion microprobewith total ion monitoring (schematic). [From Kobayashi et af. (1977).]
SURFACE ANALYSIS USING CHARGED-PARTICLE BEAMS
283
secondary ion mass analyzer. Part of the energy-analyzed secondary ion beam impinges on an ion/electron converter plate; the ion-induced secondary electrons are accelerated to a scintillatorfphotomultiplier combination, thus producing a reference current It', which is modulated as the primary ion beam is scanned across the sample; I,' is proportional to the locally emitted total secondary ion current. The central portion of the energy-analyzed secondary ion beam, correspanding to the energy bandpass of the instrument, is passed to the magnetic sector of the spectrometer through a diaphragm in the converter plate. When it is assumed that topographic features alone are causing the modulation in the total emitted secondary ion current, the mass-analyzed element-specific ion current I + , which is detected at the final multiplier detector, can be expected to carry the same local modulation as the reference current Zt+. In the arrangement of Kobayashi et al., the mass-analyzed current I + is referenced to the total ion monitor current I,+ in a fast analog reference circuit. Therefore, topographic contrast will be removed in the I+/Z,' signal. The remaining signal modulation can thus be interpreted as being due to either concentration contrast or a superposition of the artifact contrast effects (other than topographic) described in V,B,2,a. Figure 22 illustrates the effect of on-line total ion referencing on line-scan signals from a fracture surface of steel. Obviously, the modulation in the Fe+ signal and the total ion monitor signal are similar so that only a small modulation remains in the referenced signal ZFe+/It+,leaving open only the possibility for a considerably smaller local variation in Fe concentration than the uncorrected ion signal IFe+ appears to indicate. A similar reduction of topographic contrast has been demonstrated by applying the same technique to correct full secondary ion micrographs ("ion images") (Kobayashi
I
I
0
1
I
100 200 300 ANALYZED DISTANCE ( p n )
I, 400
FIG.22. Line scans across steel fracture surface showing effect of total ion monitor correction; I , + , total ion monitor current; IF,+, Fe current. [From Kobayashi et al. (1977).]
284
P. BRAUN, F.
RUDENAUER, AND F.
P. VIEHBOCK
et al., 1977). Since fast electronic circuitry is used for analog division, the time required to record a fully referenced or unreferenced ion micrograph (characteristically, 2 10 msec) only depends on amplifier response speed (generally limited by the I+ signal) ; moreover, both maps are simultaneously available (see Fig. 21) immediately after completion of a scanning frame. c. Digital processing of ion micrographs. Quantitative correction of a set of corresponding locally registered ion micrographs is equivalent to performing a complete quantitative elemental point analysis in each image point of a “scene” (as defined in Section V1,A). Often, it is desired that the quantitation be carried out not only at selected characteristic points or features of the ion micrographs, but that the calculated concentration values be arranged in a “concentration map” of sufficient spatial detail. In this case the huge number of analytical points contained in a scene and the computation time required for calculating absolute concentration values in a single image point (see Section V,B,2,c,v) practically necessitates the extensive use of digital computers for instrument control as well as for data recording and evaluation. Digital image handling and image-processing techniques therefore will have to be widely applied. (i) Global sensitiuityfuctors. Buger et al. (1977) and Schilling and Biiger (1978) were the first to utilize the advantages of digitally recorded spaceresolved secondary ion intensity data for display and quantitation of secondary ion micrographs. Their experimental setup consisted of an ARL IMMA controlled by a PDP-11 computer. The computer, among other functions, controlled the scanning of the primary ion beam (digital two-dimensional step scan) and the secondary ion counting electronics. The ion intensity data were punched on paper tape, which was further evaluated on a larger computing facility in an off-line mode. The quantitation was carried out in each pixel of the input scene (see Section VI,A) and relied essentially on a set of pixel-independent “correction factors” ai applied to the elemental ion currents Zi(x, y ) in each pixel (x, y). The correction factors ai essentially were reciprocal relative sensitivity factors and were defined as
Here, fi,fR and t i ,tR are the secondary ion currents (count rates) and relative atomic concentrations, respectively, of element i and a reference element R, averaged across the full images. The t i were obtained by applying a twointernal-standard global LTE-correction routine to the spatially averaged secondary ion currents ii.The image correction then proceeds as a pixelwise image application of the RSF method. The computer was also employed to manipulate and record micrographs and corrected elemental maps.
SURFACE ANALYSIS USING CHARGED-PARTICLE BEAMS
285
Hard copy-image data were obtained in the form of y-modulated twodimensional images or selected elemental line scans outputted on a digital plotter. Figure 23 shows “quantitative line scans” (note that scale is calibrated in atomic percent) obtained by plotting the results of the correction routine for different elements across a selected line of the image. The sample in this case was modular cast iron ;a single carbon precipitate of 30-pm diam. may be identified in the center of the line scan. Since the correction factors mi are pixel independent, this method obviously cannot account for local variations in the matrix contrast, which can be expected when phases of widely different composition are present in the scanned sample area. Note, however, that topographic contrast will be removed (although, in the particular case of Fig. 23 the sample was polished flat), and that the concentrations (averaged across the field of view) will be correctly returned with an acauracy characteristic of LTE correction.
FIG.23. Line scans across polished&eel surface, quantitated by local application of global sensitivity factors. [From Biiger er a/. (1977).]
286
P. BRAUN, F. RUDENAUER, AND F. P. VIEHBOCK
(ii) Internal indicators (MZSR). Internal indicators, or MISR, quantitation requires the ion micrographs of the elements to be quantified, plus micrographs of two matrix ion species as input data. Additional a priori information required is the knowledge of the MISR curves (RSF versus internal indicator or MISR, respectively) for all elements of interest (see Section III,B,l,d). The first step in a MISR-image quantitation is the calculation of a “ratio map” (ratio of matrix ion species intensities in each pixel); for the second step, local concentration values are calculated by referring to the RSF versus MISR curves for the respective elements. For ease of computation the RSF curves are stored in lookup table format containing RSFs for the unknown elements at suitable intervals of the MISR. Between these points RSFs are linearly interpolated. Drummer and Morrison (198 I) applied this technique to obtain elemental concentration maps of minor elements in low-alloy steel samples and demonstrated an analytical accuracy of the order of 30% relative error, which is of the same order as the sampling error which can be expected in the particular microsampling situation. Note that the applicability of a certain set of MISR curves in a particular analytical point is ensured only when the local sample matrix is similar to the matrix in which the particular MISR curves have been determined. This is additional a priori information which may not always be available in an unknown sample. The application of the same set of MISR curves in all different phases (inclusions etc.) of a multiphase sample might considerably reduce analytical accuracy. ( i i i ) Local LTE correction. Quantitative elemental point analysis by means of simplified two- or one-parameter LTE (Andersen and Hinthorne, 1973; Simons et al., 1976; Riidenauer et al., 1969; Morgan and Werner, 1978c) requires as input data the monoatomic elemental ion currents of all elements present in the analytical sample point, as well as absolute atomic concentration values for one or more internal standard elements (see Section III,B,3). Extending this to LTE analysis of a two-dimensional sample area, the following input data are needed (see Fig. 24) :
(a) Registered ion micrographs of all elements present in the imaged sample area (“input scene”). These should be already available in digitized form, i.e., a digitized ion current (ion count) value per element in each of the N ( x ) , N ( y ) pixels and should be corrected for detector distortion. (b) Absolute concentration values for one or more internal standard elements in each pixel; these values may be thought of being arranged in two-dimensional “internal standard maps.” These maps should already be registered with respect to the ion micrographs.
SURFACE ANALYSIS USING CHARGED-PARTICLE BEAMS
ion micrographs
..........
I L T E correction
287
IMi ( N ( x ) , N(y))
1 .....
internal standard map( 6)
SMj IN(x), N(y))
concentration maps
CMj (N(x), N(y)) FIG.24. Local LTE correction of ion micrographs. [From Steiger and Riidenauer (1979).]
Now, in each of the N ( x ) , N ( y ) pixels, corresponding ion currents and concentration values from the set of input micrographs and internal standard maps are sent through a LTE correction routine, yielding absolute concentration values for all elements for which ion micrographs are available. Thus, computed elemental “concentration maps” are obtained showing the “true” two-dimensional distribution of elements across the imaged sample area. Obviously, correction of secondary ion micrographs generally requires “local standards” on a microscale as compared to the “global standards” used in conventional LTE analysis of flat, compositionally homogeneous samples. There, internal standard concentrations may be derived from a bulk analysis of the sample by other standardized analytical techniques. Such an approach may be taken in image correction only if it can be assumed that the element selected as global internal standard is homogeneously distributed within the imaged sample area so that contrast in the ion micrograph of that standard element is “artifact contrast” in the sense discussed above. In all the other cases, local standards have to be defined in each pixel.
288
P. BRAUN, F. RUDENAUER, AND F. P. VIEHBOCK
New techniques have to be devised for this purpose, e.g., application of multiple space-resolved analytical techniques on the same sample (electron microprobe, Auger microprobe, etc.), or the use of ion-implanted local or global standards. Riidenauer et al. (1979), Riidenauer and Steiger (1977), and Steiger and Riidenauer (1979) have used two- and one-parameter LTE algorithms with internal concentration normalization (Cci = 1 ; see Section III,B,2) to correct elemental line scans and full ion micrographs, taken from fractured glass surfaces. In these samples it could be ascertained by optical techniques that the elemental oxygen of the glass matrix was homogeneously distributed and therefore was a suitable “global” internal standard element. Results of the one-parameter, one internal standard correction procedure are shown in Fig. 25. Note the following important facts : (a) Contrast distributions of corresponding ion micrographs and concentration maps are often grossly different so that interpretation of a single ion micrograph in terms of quantitative element distribution may lead to entirely wrong conclusions. (b) Since the ratio of two local elemental ion currents depends exponentially on the “temperature” parameter T, the strong contrast in the T-map indicates a strong nonproportionality of local elemental ion currents across the analytical area and, therefore, the presence of other than only topographic contrary effects ;a global sensitivity-factoralgorithm would therefore give inaccurate results on this particular sample. In the computer-generated images of Fig. 25 the local brightness is proportional to the registered number of ion counts/pixel (ion micrographs) or to absolute atomic concentration, respectively (concentration maps). The images were generated on a bistable storage oscilloscope from image data stored on a magnetic disk by suitably quantizing the pixel intensities and point-density modulation of the oscilloscope screen. The image-processing software package also allows for continuous “zooming” and “roaming” of a selected subimage, image interpolation to a finer image raster (for smoother display appearance), display of isointensity lines (ion count or concentration), contrast modification by arbitrary selection of quantitation levels, etc. (Steiger and Riidenauer, 1979). (iu) Sputter normalized L TE (SNLTE).Drummer and Morrison (1981) used the simplified LTE algorithm described in Section III,B,2 for pointwise correction of ion micrographs. This method requires in each image point, the apriori knowledge of the concentration of at least one internal standard element and the a posteriori measurement of the total amount of sample atoms sputtered during one frame (exposure) time (local data). The local
290
P. BRAUN, F. RUDENAUER,AND F. P. VIEHBOCK
internal standard was generated by implanting fluorine (as BF3) in a maskgenerated pattern into the sample (NBS-SRM-664, low-alloy steel). At the low doses used ( w
(57b)
where w is the Auger peak width. The shot-noise current is given by (Spangenberg, 1948): fN =
(58)
(2eIBB)”’
where B is the instrument bandwidth. From Eqs. (56)-(58) follows l,/IN = ( ~ / W ) ( I ~ T A E E ~ / O . ~ for ~ B )AE ’ ~ ~> w
The maximum &/INof about lo4 can be reached under typical operating conditions by choosing AE equal to w . Normally, I,/& will be lowered by a factor of 10, especially by a mixmatch of AE and w. The bandwidth B is related to the time constant for recording (depending on the electronic circuitry) by B
- I/T
(60)
The recording time is determined by the stability of the surface analyzed, which depends strongly on the vacuum conditions. Figure 28 shows the relation between the time needed for build-up of a monolayer of contamination versus the pressure in the test chamber. By this fact the time T limits the
TEST CHAMBER PRESSURE (rnbar)
FIG.28. Relation between pressureand time needed for buildup of one monolayer of oxygen on a clean surface.
300
P. BRAUN, F. RUDENAUER, AND F. P. VIEHBOCK
04'*
1
10-10
I
10-9 beam current
1
10-8
I
10-7
1-6
(A1
FIG.29. Dependence of electron beam diameter on the beam current for a lanthanum hexaboride cathode. [From Perkin-Elmer ( 1980).]
signal-to-noise ratio. To compensate for a higher signal-to-noise ratio a higher primary beam current is necessary; but for a certain primary electron current density, 9 = 41,,/nd2 (61) depending on the stability of the target material under the electron beam (Braun et al., 1977), a decrease in spatial resolution will be the result. Figure 29 demonstrates the dependence of the beam diameter from the beam current for a commercial instrument (Perkin-Elmer, 1980). For any surface analyzed the parameters mentioned should be well tuned. A prerequisite are the vacuum conditions which determine the recording time. The primary beam current determines the spot size and therefore the spatial resolution. Both recording time and beam current are responsible for the signal-to-noise ratio, which defines the elemental detection limit. B. Resolution and Sensitivity Limits in SIMS 1. La feral Resolution
As has been pointed out in Section V,B,l, information on the lateral distribution of elements can be obtained by three types of instrumentation : the scanning ion microprobe, the ion microscope, and the image-dissecting ion microscope. The lateral resolution in a mass-separated image produced by any of these techniques is subject to three types of limits : a. Intrinsic resolution limit. This limit is imposed by the fact that the point of impact of a primary ion, owing to the formation of collision cascades near the sample surface, is not identical with the point of emission of the
SURFACE ANALYSIS USING CHARGED-PARTICLE BEAMS
30 1
secondary ion. A value of the order of 150 will be representative for the diameter of the cascades and, therefore, the intrinsic resolution limit (Benninghoven et al., 1981). b. Useful resolution limit. This limit is imposed by the fact that owing to the destructive nature of the SIMS technique, a certain number of atoms of the target material have to leave the surface before enough secondary ions have been accumulated on the detector so that the local secondary ion emission of element i can be determined with a precision p (rel. %). These sputtered atoms naturally occupy a finite volume V of the solid (Castaing and Slodzian, 1962)
v = 104/upZa+(X)c(~)~, (cm3)
(62)
where n is the total number of target atoms/cm3, a+(X) is the degree of ionization, c(X) is the fractional atomic concentration of element X, and I; is the total transmission of the secondary ion mass analyzer (defined as number of ions X being detected per total number of emitted ions X). This limiting volume may have different dimensions in all three coordinate directions. When, however, in three-dimensional analysis it is desired to have equal lateral resolution in all coordinate axes, the “useful resolution” follows from Eq. (62) as 6, =
P I 3 =
104i3(p2na+(X)c(X)1;)-”3(cm)
(63)
c. Ion optical resolution limit. This limit is set up by the imperfections of ion optical lenses and depends on the mode of image formation. For scanning ion microprobes the ion optical limit is imposed by the finite primary beam spot size which can be focused onto the target by the primary ion gun. Figure 30 shows a graph of spot diameters achievable when the conversion angle of the primary beam at the target is limited to the value given at the abscissa. Four sets of lines representing different contributions to spot size (Benninghoven el al., 1981) are shown in the figure: the brightness limit (I/b), determined by the brightness p of the ion gun only; the spherical aberration limit (ds),determined by the spherical aberration of the last primary focusing lens; the chromatic aberration limit (dch),determined by both the energy spread of the primary ion beam and the chromatic aberration of the last primary lens; dzffraction limit (dJ, set up by the wave properties of a particle beam.
It can be seen from Fig. 30 that spherical aberration is dominating at spot sizes of 1 pm and above; begow 1 pm chromatic aberration is the limiting factor for duoplasmatron sources (Benninghoven et al., 198l), whereas for surface ionization sources chramatic aberration becomes dominating only below 100 A. The graph also shows that for a minimum required probe current of lo-’’ A, the minimum obtainable spot size is of the order of
302
P. BRAUN, F. RUDENAUER, AND F. P. VIEHFIOCK
FIG.30. Dependence of spot diameter on angle of convergence at target for microfocus ion beam; focal length of last focusing lens is 2 cm. Chromatic aberration limits shown for ion sources with different energy spread SV/V (duoplasmatron, SVjV = 5 x l W 4 ; surface ionization source, SV/V = 2 x lO-’-EHD source, SV/V = 1.5 x
0.1 pm when duoplasmatron sources are used (Liebl, 1978) (source brightness fi I100 A/cm2.sr) and of the order of 200 A with a cesium surface ionization source (p I1000 A/cm* * sr). A major improvement in spot sizes and focusable ion currents appears to be possible with field ionization or electrohydrodynamic ion sources (Levi-Setti and Fox, 1980; Krohn and Ringo, 1976; Seliger, 1972). In ion microscopes and image-dissecting ion microscopes, the spatial resolution is determined by the properties of the emission lens only. This lens accelerates the secondary ions from the target and forms a virtual image of the illuminated surface area (Slodzian, 1964); the following focusing and dispersing lenses mainly magnify the aberrations of this lens, together with the image, introducing only a small additional aberration. The resolution
SURFACE ANALYSIS USING CHARGED-PARTICLE BEAMS
303
limit minimum set up by the combined aperture and chromatic aberration of the emission lens is given by
hmi, = Z/Fo (cm) (64) where 1 (in electron volts) is the maximum lateral energy of the secondary ion beam, and F, (in electron volts) the electrostatic field strength in the acceleration gap. In practical instruments, F, is of the order of lo4 V/cm and 5 of the order of 1 V, so that lateral resolution limits of the order of 1 pm are obtained. Further reduction of the lateral ion energy (by suitable aperturing in the lens crossover) improves lateral resolution at the cost of transmitted intensity. 2. Sensit iv itv Limits The factors influencing the sensitivity of a SIMS instrument with respect to the capability of trace-element detection can be understood by rearranging Eq. (62)
cmi,(x) = 104/npza+(xiT~v
(65)
essentially connecting the minimum detectable fractional concentration cmin of an element to the sample volume V consumed during an analysis. The larger this volume, the lower is the detection limit of a certain element (at a given precision of measurement); a’(X) cannot be calculated from first principles (see also Section 111,B,2); the instrument transmission can be theoretically calculated, requiring the knowledge of ion optical, geometric, and target parameters (e.g., energy distribution of selected element). Theoretical transmission figures, however, are hardly ever achieved due to unavoidable misalignments and the dependence of energy distributions on the different experimental parameters. Nevertheless, the capabilities of an individual instrument with respect to trace-element detection, depth profiling, and local microspot analysis can be assessed when the practical sensitivities Sp(X) of this individual instrument are known for an element X. Sp(X) is a global measure of secondary ion emission and instrument transmission (see also Section III,B,l) SP(X) = Po